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My dear Friends, I am told that the phenomenon with the prism — at the end of yesterday's lecture — has after all proved difficult for some of you to understand. Do not be troubled if this is so; you will understand it better by and by. We shall have to go into the phenomena of light and colour rather more fully. They are the real piece de resistance, even in relation to the rest of Physics, and will therefore provide a good foundation. You will realize that the main idea of the present course is for me to tell you some of the things which you will not find in the text-books, things not included in the normal lines of the scientific study and only able to be dealt with in the way we do here. In the concluding lectures we shall consider how these reflections can also be made use of in school teaching. What I was trying to explain is in its essence a special kind of interplay of light and dark — i.e. the unimpaired brightness and on the other hand the dimming or clouding of the light. I was trying to show how through the diverse ways in which light and dark work together — induced especially by the passage of a cylinder of light through a prism — the phenomena of colour, in all their polar relation to one-another, are brought about. Now in the first place I really must ask you to swallow the bitter pill (I mean, those of you who found things difficult to understand). Your difficulty lies in the fact that you are always hankering after a phoronomical treatment of light and colour. The strange education we are made to undergo instils this mental habit. Thinking of outer Nature, people will restrict themselves to thoughts of a more or less phoronomical character. They will restrict their thoughts to what is arithmetical, spatially formal, and kinematical. Called on to try and think in terms of qualities as you are here, you may well be saying to yourselves: Here we get stuck! You must attribute it to the unnatural direction pursued by Science in modern time. Moreover — I speak especially to Waldorf-School and other teachers — you will yourselves to some extent still have to take the same direction with your pupils. It will not be possible, all at once, to bring the really healthy ideas into a modern school. We must find ways of transition. For the phenomena of light and colour, let us now begin again, but from the other end. I take my start from a much disputed saying of Goethe's. In the 1780's a number of statements as to the way colours arise in and about the light came to his notice. Among other things, he learned of the prismatic phenomena we were beginning to study yesterday. It was commonly held by physicists, so Goethe learned, that when you let colourless light go through a prism the colourless light is analyzed and split up. For in some such way the phenomena were interpreted. If we let a cylinder of colourless light impinge on the screen, it shows a colourless picture. Putting a prism in the way of the cylinder of light, the physicists went on to say, we get the sequence of colours: red, orange, yellow, green, blue — light blue and dark blue, — violet. Goethe heard of it in this way: the physicists explain it thus, so he was told — The colourless light already contains the seven colours within itself — a rather difficult thing to imagine, no doubt, but that is what they said. And when we make the light go through the prism, the prism really does no more than to fan out and separate what is already there in the light, — the seven colours, into which it is thus analyzed. Goethe wanted to get to the bottom of it. He began borrowing and collecting instruments, — much as we have been doing in the last few days. He wanted to find out for himself. Buettner, Privy Councillor in Jena, was kind enough to send him some scientific instruments to Weimar. Goethe stacked them away, hoping for a convenient time to begin his investigations. Presently, Councillor Buettner grew impatient and wanted his instruments back. Goethe had not yet begun; — it often happens, one does not get down to a thing right away. Now Goethe had to pack the instruments to send them back again. Meanwhile he took a quick look through the prism, saying to himself as he did so: If then the light is analyzed by the prism, I shall see it so on yonder wall. He really expected to see the light in seven colours. But the only place where he could see any colour at all was at some edge or border-line — a stain on the wall for instance, where the stain, the dark and clouded part, met the lighter surface. Looking at such a place through the prism he saw colours; where there was uniform white he saw nothing of the kind. Goethe was roused. He felt the theory did not make sense. He was no longer minded to send the instruments back, but kept them and went on with his researches. It soon emerged that the phenomenon was not at all as commonly described. If we let light pass through the space of the room, we get a white circle on the screen. Here we have cut it out very neatly; you see a pretty fair circle. Put a prism in the way of the body of light that is going through there, — the cylinder of light is diverted, (Figure IIc), but what appears in the first place is not the series of seven colours at all, only a reddish colour at the lower edge, passing over into yellow, and at the upper edge a blue passing over into greenish shades. In the middle it stays white. Goethe now said to himself: It is not that the light is split up or that anything is separated out of the light as such. In point of fact, I am projecting a picture, — simply an image of this circular aperture. The aperture has edges, and where the colours occur the reason is not that they are drawn out of the light, as though the light had been split up into them. It is because this picture which I am projecting — the picture as such — has edges. Here too the fact is that where light adjoins dark, colours appear at the edges. It is none other than that. For there is darkness outside this circular patch of light, while it is relatively light within it. The colours therefore, to begin with, make their appearance purely and simply as phenomena at the border between light and dark. This is the original, the primary phenomenon. We are no longer seeing the original phenomenon when by reducing the circle in size we get a continuous sequence of colours. The latter phenomenon only arises when we take so small a circle that the colours extend inward from the edges to the middle. They then overlap in the middle and form what we call a continuous spectrum, while with the larger circle the colours formed at the edges stay as they are. This is the primal phenomenon. Colours arise at the borders, where light and dark flow together. This, my dear Friends, is precisely the point: not to bring in theories to tamper with the facts, but to confine ourselves to a clean straightforward study of the given facts. However, as you have seen, in these phenomena not only colours arise; there is also the lateral displacement of the entire cone of light. To study this displacement further — diagrammatically to begin with — we can also proceed as follows. Suppose you put two prisms together so as to make them into a single whole. The lower one is placed like the one I drew yesterday, the upper one the opposite way up (Figure IIIa). If I now made a cylinder of light pass through this double prism, I should of course get something very like what we had yesterday. The light would be diverted — upward in the one case, downward in the other. Hence if I had such a double prism I should get a figure of light still more drawn out than before. But it would prove to be rather indistinct and dark. I should explain this as follows. Catching the picture by a screen placed here, I should get an image of the circle of light as if there were two pushed together, one from either end. But I could now move the screen farther in. Again I should get an image. That is to say, there would be a space — all this is remaining purely within the given facts — a space within which I should always find it possible to get an image. You see then how the double prism treats the light. Moreover I shall always find a red edge outside, — in this case, above and below — and a violet colour in the middle. Where I should otherwise merely get the image extending from red to violet, I now get the outer edges red, with violet in the middle and the other colours in between. By means of such a double prism I should make it possible for such a figure to arise, — and I should get a similar figure if I moved the screen farther away. Within a certain distance either way, such a picture will be able to arise — coloured at the edges, coloured in the middle too, and with transitional colours. Now we might arrange it so that when moving the screen to and fro there would be a very wide space within which such pictures could be formed. But as you probably divine, the only way of doing this would be to keep on changing the shape of the prism. If for example, taking a prism with a larger angle, I got the picture at a given place, if I then made the angle smaller I should get it elsewhere. Now I can do the whole thing differently by using a prism with curved instead of plane surfaces from the very outset. The phenomenon, difficult to study with the prism, will be much simplified. We therefore have this possibility. We let the cylinder of light go through the space and then put in its way a lens, — which in effect is none other than a double prism with its faces curved. The picture I now get is, to begin with, considerably reduced in size. What then has taken place? The whole cylinder of light has been contracted. Look first at the original cross-section: by interposing the lens I get it narrowed and drawn together. Here then we have a fresh interaction between what is material — the material of the lens, which is a body of glass — and the light that goes through space. The lens so works upon the light as to contract it. To draw it diagrammatically (Figure IIIa, above), here is a cylinder of light. I let the light go through the lens. If I confronted the light with an ordinary plate of glass or water, the cylinder of light would just go through and a simple picture of it on the screen would be the outcome. Not so if instead of the simple plate, made of glass or water, I have a lens. Following what has actually happened with my drawing, I must say: the picture has grown smaller. The cylinder of light is contracted. Now there is also another possibility. We could set up a double prism, not as in the former instance but in cross-section as I am now drawing it (Figure IIIb), — the prisms meeting at the angle. I should again get the phenomenon described before, only in this instance the circle would be considerably enlarged. Once again, while moving the screen to and fro within a certain range, I should still get the picture — more or less indistinct. Moreover in this case (Figure IIIb, above and on the right) I should get violet and bluish colours both at the upper and at the lower edge, and red in the middle, — the opposite of what it was before. There would again be the intermediate colours. Once more I can replace the double prism by a lens, — a lens of this cross-section (Figure IIIb). The other was thick in the middle and thin at the edges; this one is thin in the middle and thick at the edge. Using this lens, I get a picture considerably bigger than the cross-section of the cylinder of light would be without it. I get an enlarged picture, again with colours graded from the edge towards the centre. Following the phenomena in this case I must say: the cylinder of light has been widened, — very considerably thrust apart. Again: the simple fact. What do we see from these phenomena? Evidently there is an active relation between the material — though it appears transparent in all these lenses and prisms — and what comes to manifestation through the light. We see a kind of interaction between them. Taking our start from what we should get with a lens of this type (thick at the edge and thin in the middle), the entire cylinder of light will have been thrust apart, — will have been widened. We see too how this widening can have come about, — obviously through the fact that the material through which the light has gone is thinner here and thicker here. Here at the edge, the light has to make its way through more matter than in the middle, where it has less matter to go through. And now, what happens to the light? As we said, it is widened out — thrust apart — in the direction of these two arrows. How can it have been thrust apart? It can only be through the fact that it has less matter to go through in the middle and more at the edges. Think of it now. In the middle the light has less matter to go through; it therefore passes through more easily and retains more of its force after having gone through. Here therefore — where it goes through less matter — the force of it is greater than where it goes through more. It is the stronger force in the middle, due to the light's having less matter to go through, which presses the cylinder of light apart. If I may so express myself, you can read it in the facts that this is how it is. I want you to be very clear at this point it is simply a question of true method in our thinking. In our attempts to follow up the phenomena of light by means of lines and diagrams we ought to realize that with every line we draw we ourselves are adding something which has nothing to do with the light as such. The lines I have been drawing are but the limits of the cylinder of light. The cylinder of light is brought about by the aperture. What I draw has nothing to do with the light; I am only reproducing what is brought about by the light's going through the slit. And if I say, “the light moves in this direction”, that again has nothing to do with the light as such; for if I moved the source of light upward, the light that falls on the slit would move in this way and I should have to draw the arrow in this direction. This again would not concern the light as such. People have formed such a habit of drawing lines into the light, and from this habit they have gradually come to talk of “light-rays”. In fact we never have to do with light-rays; here for example, what we have to do with is a cone of light, due to the aperture through which we caused the light to pass. In this instance the cone of light is broadened out, and it is evident: the broadening must somehow be connected with the shorter path the light has to go through in the middle of the lens than at the edge. Due to the shorter path in the middle, the light retains more force; due to the longer path at the edge, more force is taken from it. The stronger light in the middle presses upon the weaker light at the edge and so the cone of light is broadened. You simply read it in the facts. Truth is that where we simply have to do with images or pictures, the physicists speak of all manner of other things, — light-rays and so on. The “light-rays” have become the very basis of materialistic thinking in this domain. To illustrate the point more vividly, we will consider another phenomenon. Suppose I have a vessel here (Figure IIId), filled with liquid — water, for example. On the floor of the vessel there is an object — say, a florin. Here is the eye. I can now make the following experiment. Omitting the water to begin with, I can look down at the object and see it in this direction. What is the fact? An object is lying on the bottom of the vessel (Figure IIIc). I look and see it in a certain direction. Such is the simple fact, but if I now begin explaining: there is a ray of light proceeding from the object to the eye, affecting the eye, and so on, — then, my dear Friends, I am already fancying all kinds of things that are not given. Now let me fill the vessel with water or some other liquid up to here. A strange thing happens. I draw a line from the eye towards the object in the direction in which I saw it before. Looking in this direction, I might expect to see the same as before, but I do not. A peculiar thing happens. I see the object lifted to some extent. I see it, and with it the whole floor of the vessel lifted upward. We may go into it another time, as to how this effect can be determined, by which I mean measured. I now only refer to the main principle. To what can this effect be due? How shall I answer this question, purely from the facts? Having previously seen the thing in this direction, I expect to find it there again. Yet when I look, I do not see it there but in this other direction. When there was no water in the vessel I could look straight to the bottom, between which and my eye there was only air. Now my sighting line impinges on the water. The water does not let my force of sight go through as easily as the air does; it offers stronger resistance, to which must give way. From the surface of the water onward I must give way to the stronger resistance, and, that I have to do so, comes to expression in that I do not see right down as before but it all looks lifted upward. It is as though it were more difficult for me to see through the water than through the air; the resistance of the water is harder for me to overcome. Hence I must shorten the force and so I myself draw the object upward. In meeting the stronger resistance I draw in the force and shorten it. If I could fill the vessel with a gas thinner than air (Figure IIIe), the object would be correspondingly lowered, since I should then encounter less resistance, — so I should push it downward. Instead of simply noting this fact, the physicists will say: There is a ray of light, sent from the object to the surface of the water. The ray is there refracted. Owing to the transition from a denser medium to a more tenuous, the ray is refracted away from the normal at the point of incidence; so then it reaches the eye in this direction. And now the physicists go on to say a very curious thing. The eye, they say, having received information by this ray of light, produces it on and outward in the same straight line and so projects the object thither. What is the meaning of this? In the conventional Physics they will invent all manner of concepts but fail to reckon with what is evidently there, — with the resistance which the sighting force of the eye encounters in the denser medium it has to penetrate. They want to leave all this out and to ascribe everything to the light alone, just as they say of the prism experiment: Oh, it is not the prism at all; the seven colours are there in the light all the time. The prism only provides the occasion for them to line up like so many soldiers. The seven naughty boys were there in the light already; now they are only made to line up and stand apart. The prism isn't responsible. Yet as we say, the colours are really caused by what arises in the prism. This wedge of dimness is the cause. The colours are not due to the light as such. Here now you see it again. We must be clear that we ourselves are being active. We, actively, are looking with our eye, — with our line of sight. Finding increased resistance in the water, we are obliged to shorten the line of sight. What say the physicists on the other hand? They speak of rays of light being sent out and refracted and so on. And now the beauty of it, my dear Friends! The light, they say, reaches the eye by a bent and broken path, and then the eye projects the picture outward . So after all they end by attributing this activity to the eye: “The eye projects ...” Only they then present us with a merely phoronomical conception, remote from the given realities. They put a merely fancied activity in place of what is evidently given: the resistance of the denser water to the sighting force of the eye. It is at such points that you see most distinctly how abstract everything is made in our conventional Physics. All things are turned into mere phoronomic systems; what they will not do is to go into the qualities. Thus in the first place they divest the eye of any kind of activity of its own; only from outer objects rays of light are supposed to proceed and thence to reach the eye. Yet in the last resort the eye is said to project outward into space the stimulus which it receives. Surely we ought to begin with the activity of the eye from the very outset. We must be clear that the eye is an active organism. We will today begin our study of the nature of the human eye. Here is a model of it (Figure IIIf). The human eye, as you know, is in form like a kind of sphere, slightly compressed from front to back. Such is the eye-ball, seated in the bony cavity or orbit, and with a number of skins enveloping the inner portion. To draw it in cross-section (Figure IIIf). it will be like this. (When looking at your neighbour's eye you look into the pupil. I am now drawing it from the side and in cross-section.) This then would be a right-hand eye. If we removed the eye from the skull, making an anatomical preparation, the first thing we should encounter would be connective tissue and fatty tissue. Then we should reach the first integument of the eye properly speaking — the so-called sclerotic and the transparent portion of it, the cornea. This outermost integument (I have here drawn it) is sinewy, — of bony or cartilaginous consistency. Towards the front it gets transparent, so that the light can penetrate into the eye. A second layer enveloping the inner space of the eye is then the so-called choroid, containing blood-vessels. Thirdly we get the inner-most layer, the retina so-called, which is continued into the optic nerve as you go farther in into the skull. Herewith we have enumerated the three integuments of the eye, And now behind the cornea, shown here, — embedded in the ciliary muscle — is a kind of lens. The lens is carried by a muscle known as the ciliary muscle. In front is the transparent cornea, between which and the lens is the so-called aqueous humour. Thus when the light gets into the eye it first passes through the transparent cornea, then through the aqueous humour and then through this lens which is inherently movable by means of muscles. From the lens onward the light then reaches what is commonly known as the vitreous body or vitreous humour, filling the entire space of the eye. The light therefore goes through the transparent cornea, through the aqueous humour, the lens itself and the vitreous humour and from thence reaches the retina, which is in fact a ramification of the optic nerve that then goes on into the brain, This, therefore, (Figure IIIf), — envisaging only what is most important to begin with — would be a diagrammatic picture of the essential parts of the eye, embedded as it is in its cavity within the bony skull. Now the eye reveals very remarkable features. Examining the contents of this fluid that is between the lens and the cornea through which the light first has to pass, we find it very like any ordinary liquid taken from the outer world. At this place in the human body therefore — in the liquid or aqueous humour of the eye, between the lens and the outer cornea, — a man in his bodily nature is quite of a piece with the outer world. The lens too is to a high degree “objective” and unalive. Not so when we go on to the vitreous body, filling the interior of the eye and bordering on the retina. Of this we can no longer say that it is like any external body or external fluid. In the vitreous humour there is decided vitality, — there is life. Truth is, the farther back we go into the eye, the more life do we find. In the aqueous humour we have a quite external and objective kind of fluid. The lens too is still external. Inside the vitreous body on the other hand we find inherent vitality. This difference, between what is contained in this more outward portion of the eye and what is there in the more contained parts, also reveals itself in another circumstance. Tracing the comparative development of the eye from the lower animals upward, we find that the external fluid or aqueous humour and the lens grow not from within outward but by the forming of new cells from the surrounding and more peripheral cells. I must conceive the forming of the lens rather in this way. The tissue of the lens, also the aqueous humour in the anterior part of the eye, are formed from neighbouring organs, not from within outward; whilst from within the vitreous body grows out to meet them. This is the noteworthy thing. In fact the nature of the outer light is here at work, bringing about that transformation whereby the aqueous humour and the lens originate. To this the living being then reacts from within, thrusting outward a more living, a more vital organ, namely the vitreous body. Notably in the eye, formations whose development is stimulated from without, and others stimulated from within, meet one-another in a very striking way. This is the first peculiarity of the eye, and there is also another, scarcely less remarkable. The expanse of the retina which you see here is really the expanded optic nerve. Now the peculiar thing is that at the very point of entry of the optic nerve the eye is insensitive; there it is blind. Tomorrow I shall try to show you an experiment confirming this. The optic nerve thence spreads out, and in an area which for the right-hand eye is a little to the right of the point of entry the retina is most sensitive of all. We may begin by saying that it is surely the nerve which senses the light. Yet it is insensitive to light precisely at its point of entry. If it is really the nerve that senses the light we should expect it to do so more intensely at the point of entry, but it does not. Please try to bear this in mind. That this whole structure and arrangement of the eye is full of wisdom — wisdom, if I may so put it, from the side of Nature — this you may also tell from the following fact. During the day when you look at the objects around you — in so far as you have healthy eyes — they will appear to you more or less sharp and clear, or at least so that their sharpness of outline is fully adequate for orientation. But in the morning when you first awaken you sometimes see the outlines of surrounding objects very indistinctly, as if enveloped with a little halo. The rim of a circle for example will be indistinct and nebular when you have just awakened in the morning. What is it due to? It is due to there being two different kinds of things in our eye, namely the vitreous body and the lens. In origin, as we have seen, they are quite different. The lens is formed more from without, the vitreous body more from within. While the lens is rather unalive, the vitreous body is full of vitality. Now in the moment of awakening they are not yet adapted to one-another. The vitreous body still tries to picture the objects to us in the way it can; the lens in the way it can. We have to wait till they are well adapted to each other. You see again how deeply mobile everything organic is. The whole working of it depends on this. First the activity is differentiated into that of the lens and the vitreous body respectively. From what is thus differentiated the activity is thereupon composed and integrated; so then the one has to adapt itself to the other. From all these things we shall try gradually to discover how the many-coloured world emerges for us from the relation of the eye to the outer world. Now there is one more experiment I wish to shew today, and from it we may partly take our start tomorrow in studying the relation of the eye to the external world. Here is a disc, mounted on a wheel and painted with the colours which we saw before — those of the rainbow: violet, indigo, blue, green, yellow, orange and red. First look at it and see the seven colours. We will now bring it into rotation. I can turn fairly quickly and you still see the seven colours as such — only rotating. But when I turn quickly enough you can no longer see the colours. You are no doubt seeing a uniform grey. So we must ask: Why do the seven colours appear to us in grey, all of one shade? This we will try to answer tomorrow. Today we will adduce what modern Physics has to say about it, — what is already said in Goethe's time. According to modern Physics, here are the colours of the rainbow: red, orange, yellow, green, blue, indigo, violet. We bring the disc into rotation. The single impression of light has not time enough to make itself felt as such in our eye. Scarcely have I seen the red at a particular place, the quick rotation brings the orange there and then the yellow, and so on. The red itself is there again before I have time to rid myself of the impressions of the other colours. So then I get them all at once. The violet arrives before the impression of the red has vanished. For the eye, the seven colours are thus put together again, which must once more give white. Such was the scientific doctrine even in Goethe's time, and so he was instructed. Bring a coloured top into quick enough rotation: the seven colours, which in the prism experiment very obediently lined up and stood apart, will re-unite in the eye itself. But Goethe saw no white. All that you ever get is grey, said Goethe. The modern text-books do indeed admit this; they too have ascertained that all you get is grey. However, to make it white after all, they advise you to put a black circle in the middle of the disc, so that the grey may appear white by contrast. A pretty way of doing things! Some people load the dice of “Fortune”, the physicists do so with “Nature” — so they correct her to their liking. You will discover that this is being done with quite a number of the fundamental facts. I am trying to proceed in such a way as to create a good foundation. Once we have done this, it will enable us to go forward also in the other realms of Physics, and of Science generally.

The Light Course

Lecture III

https://rsarchive.org/Lectures/GA320/English/GSF1977/19191225p01.html

Stuttgart

25 Dec 1919

GA320-3

My dear Friends, I will begin by placing before you what we may call the “Ur-phenomenon” — primary phenomenon — of the Theory of Colour. By and by, you will find it confirmed and reinforced in the phenomena you can observe through the whole range of so-called optics or Theory of Colour. Of course the phenomena get complicated; the simple Ur-phenomenon is not always easy to recognize at once. But if you take the trouble you will find it everywhere. The simple phenomenon — expressed in Goethe's way, to begin with — is as follows: When I look through darkness at something lighter, the light object will appear modified by the darkness in the direction of the light colours, i.e. in the direction of the red and yellowish tones. If for example I look at anything luminous and, as we should call it, white — at any whitish-shining light through a thick enough plate which is in some way dim or cloudy, then what would seem to me more or less white if I were looking at directly, will appear yellowish or yellow-red (Figure IVa). This is the one pole. Conversely, if you have here a simple black surface and look at it directly, you will see it black, but if you interpose a trough of water through which you send a stream of light so that the liquid is illumined, you will be looking at the dark through something light. Blue or violet (bluish-red) tones of colour will appear (Figure IVb). The other pole is thus revealed. This therefore is the Ur-phenomenon: Light through dark — yellow; dark through light — blue. This simple phenomenon can be seen on every hand if we once accustom ourselves to think more realistically and not so abstractly as in modern science. Please now recall from this point of view the experiment which we have done. We sent a cylinder of light through a prism and so obtained a real scale of colours, from violet to red; we caught it on a screen. I made a drawing of the phenomenon (see Figure IIc and Figure IVc). You will remember; if this is the prism and this the cylinder of light, the light in some way goes through the prism and is diverted upward. Moreover, as we said before, it is not only diverted. It would be simply diverted if a transparent body with parallel faces were interposed. But we are putting a prism into the path of the light — that is, a body with convergent faces. In passing through the prism, the light gets darkened. The moment we send the light through the prism we therefore have to do with two things: first the simple light as it streams on, and then the dimness interposed in the path of the light. Moreover this dimness, as we said, puts itself into the path of the light in such a way that while the light is mainly diverted upward, the dimming that arises, raying upward as it does, shines also in the same direction into which the light itself is diverted. That is to say, darkness rays into the diverted light. Darkness is living, as it were, in the diverted light, and by this means the bluish and violet shades are here produced. But the darkness rays downward too, so, while the cylinder of light is diverted upward, the darkness here rays downward and works contrary to the diverted light but is no match for it. Here therefore we may say: the original bright light, diverted as it is, overwhelms and outdoes the darkness. We get the yellowish or yellow-red colours. If we now take a sufficiently thin cylinder of light, we can also look in the direction of it through the prism. Instead of looking from outside on to a screen and seeing the picture projected there, we put our eye in the place of this picture, and, looking through the prism, we then see the aperture, through which the cylinder of light is produced, displaced (Figure IVc). Once again therefore adhering strictly to the facts, we have the following phenomenon: Looking along here, I see what would be coming directly towards me if the prism were not there, displaced in a downward direction by the prism. At the same time I see it coloured. What then do you see in this case? Watch what you see, state it simply and then connect it with the fundamental fact we have just now been ascertaining. Then, what you actually see will emerge in all detail. Only you must hold to what is really seen. For if you are looking thus into the bright cylinder of light — which, once again, is coming now towards you — you see something light, namely the cylinder of light itself, but you are seeing it through dark. (That there is something darkened here, is clearly proved by the fact that blue arises in this region). Through something darkened — through the blue colour, in effect — you look at something light, namely at the cylinder-of-light coming towards you. Through what is dark you look at what is light; here therefore you should be seeing yellow or yellowish-red — in a word, yellow and red, — as in fact you do. Likewise the red colour below is proof that here is a region irradiated with light. For as I said just now, the light here over-whelms the dark. Thus as you look in this direction, however bright the cylinder of light itself may be, you still see it through an irradiation of light, in relation to which it is dark. Below, therefore, you are looking at dark through light and you will see blue or bluish-red. You need but express the primal phenomenon, — it tells you what you actually see. Your eye is here encountered by what you would be seeing in the other instance. Here for example is the blue and you are looking through it; therefore the light appears reddish. At the bottom edge you have a region that is lighted up. However light the cylinder of light may be, you see it through a space that is lit up. Thus you are seeing something darker through an illumined space and so you see it blue. It is the polarity that matters. For the phenomenon we studied first — that on the screen — you may use the name “objective” colours if you wish to speak in learned terms. This other one — the one you see in looking through the prism — will then be called the “subjective” spectrum. The “subjective” spectrum appears as an inversion of the “objective”. Concerning all these phenomena there has been much intellectual speculation, my dear Friends, in modern time. The phenomena have not merely been observed and stated purely as phenomena, as we have been endeavouring to do. There has been ever so much speculation about them; indeed, beginning with the famous Newton, Science has gone to the utter-most extremes in speculation. Newton, having first seen and been impressed by this colour-spectrum, began to speculate as to the nature of light. Here is the prism, said Newton; we let the white light in. The colours are already there in the white light; the prism conjures them forth and now they line up in formation. I have then dismembered the white light into its constituents. Newton now imagined that to every colour corresponds a kind of substance, so that seven colours altogether are contained as specific substances in the light. Passing the light through the prism is to Newton like a kind of chemical analysis, whereby the light is separated into seven distinct substances. He even tried to imagine which of the substances emit relatively larger corpuscles — tiny spheres or pellets — and which smaller. According to this conception the Sun sends us its light, we let it into the room through a circular opening and it goes through in a cylinder of light. This light however consists of ever so many corpuscles — tiny little bodies. Striking the surface of the prism they are diverted from their original course. Eventually they bombard the screen. There then these tiny cannon-balls impinge. The smaller ones fly farther up, the larger ones remain farther down. The smallest are the violet, the largest are the red. So then the large are separated from the small. This idea that there is a substance or that there are a number of substances flying through space was seriously shaken before long by other physicists — Huyghens, Young and others, — until at last the physicists said to themselves: The theory of little corpuscular cannon-balls starting from somewhere, projected through a refracting medium or not as the case may be, arriving at the screen and there producing a picture, or again finding their way into the eye and giving rise in us to the phenomenon of red, etc., — this will not do after all. They were eventually driven to this conclusion by an experiment of Fresnel's, towards which some preliminary work had however been done before, by the Jesuit Grimaldi among others. Fresnel's experiment shook the corpuscular theory very considerably. His experiments are indeed most interesting, and we must try to get a clear idea of what is really happening when experiments are set up in the way he did. I beg you now, pay very careful attention to the pure facts; we want to study such a phenomenon quite exactly. Suppose I have two mirrors and a source of light — a flame for instance, shedding its light from here (Figure IVd). If I then put up a screen — say, here — I shall get pictures by means of the one mirror and also pictures by means of the other mirror. Such is the distribution you are to assume; I draw it in cross-section. Here are two looking-glasses — plane mirrors, set at a very small angle to one another, — here is a source of light, I will call it L , and here a screen. The light is reflected and falls on to the screen; so then I can illumine the screen with the reflected light. For if I let the light strike here, with the help of this mirror I can illumine this part of the screen, making it lighter here than in the surrounding region. Now I have here a second mirror, by which the light is reflected a little differently. Part of the cone of light, as reflected from here below (from the second mirror) on to the screen, still falls into the upper part. The inclination of the two mirrors is such that the screen is lighted up both by reflection from the upper mirror and by reflection from the lower. It will then be as though the screen were being illumined from two different places. Now suppose a physicist, witnessing this experiment, were thinking in Newton's way. He would argue: There is the source of light. It bombards the first mirror, hurling its little cannon-balls in this direction. After recoiling from the mirror they reach the screen and light it up. Meanwhile, the others are recoiling from the lower mirror, for many of them go in that direction also. It will be very much lighter on the screen when there are two mirrors than when there is only one. Therefore if I remove the second mirror the screen will surely be less illumined by reflected light than when the two mirrors are there. So would our physicist argue, although admittedly one rather devastating thought might occur to him, for surely while these little bodies are going on their way after reflection, the others are on their downward journey (see the figure). Why then the latter should not hit the former and drive them from their course, is difficult to see. Nay, altogether, in the textbooks you will find the prettiest accounts of what is happening according to the wave-theory, but while these things are calculated very neatly, one cannot but reflect that no one ever figures out, when one wave rushes criss-cross through the other, how can this simply pass unnoticed? Now let us try to grasp what happens in reality in this experiment. Suppose that this is the one stream of light. It is thrown by reflection across here, but now the other stream of light arrives here and encounters it, — the phenomenon is undeniable. The two disturb each other. The one wants to rush on; the other gets in the way and, in consequence, extinguishes the light coming from the other side. In rushing through it extinguishes the light. Here therefore on the screen we do not get a lighting-up but in reality darkness is reflected across here. So we here get an element of darkness (Figure IVe). But now all this is not at rest, — it is in constant movement. What has here been disturbed, goes on. Here, so to speak, a hole has arisen in the light. The light rushed through; a hole was made, appearing dark. And as an outcome of this “hole”, the next body-of-light will go through all the more easily and alongside the darkness you will have a patch of light so much the lighter. The next thing to happen, one step further on, is that once more a little cylinder of light from above impinges on a light place, again extinguishes the latter, and so evokes another element of darkness. And as the darkness in its turn has thus moved on another step, here once again the light is able to get through more easily. We get the pattern of a lattice, moving on from step to step. Turn by turn, the light from above can get through and extinguishes the other, producing darkness, once again, and this moves on from step to step. Here then we must obtain an alternation of light and dark, because the upper light goes through the lower and in so doing makes a lattice work. This is what I was asking you most thoroughly to think of; you should be able to follow in your thought, how such a lattice arises. You will have alternating patches of light and dark, inasmuch as light here rushes into light. When one light rushes into another the light is cancelled — turned to darkness. The fact that such a lattice arises is to be explained by the particular arrangement we have made with these two mirrors. The velocity of light — nay, altogether what arises here by way of differences in velocity of light, — is not of great significance. What I am trying to make clear is what here arises within the light itself by means of this apparatus, so that a lattice-work is reflected — light, dark, light, dark, and so on. Now yonder physicist — Fresnel himself, in fact — argued as follows: If light is a streaming of tiny corpuscular bodies, it goes without saying that the more bodies are being hurled in a particular direction, the lighter it must grow there, — or else one would have to assume that the one corpuscle eats up the other! The simple theory of corpuscular emanation will not explain this phenomenon of alternating light and dark. We have just seen how it is really to be explained. But it did not occur to the physicists to take the pure phenomenon as such, which is what one should do. Instead, and by analogy with certain other phenomena, they set to work to explain it in a materialistic way. Bombarding little balls of matter would no longer do. Therefore they said: Let us assume, not that the light is in itself a stream of fine substances, but that it is a movement in a very fine substantial medium — the “ether”. It is a movement in the ether. And, to begin with, they imagined that light is propagated through the ether in the same way as sound is through air (Euler for instance thought of it thus). If I call forth a sound, the sound is propagated through the air in such a way that if this is the place where the sound is evoked, the air in the immediate neighbourhood is, to begin with, compressed. Compressed air arises here. Now the compressed air presses in its turn on the adjoining air. It expands, momentarily producing in this neighbourhood a layer of attenuated air. Through these successions of compression and expansion, known as waves, we imagine sound to spread. To begin with, they assumed that waves of this kind are also kindled in the ether. However, there were phenomena at variance with this idea; so then they said to themselves: Light is indeed an undulatory movement, but the waves are of a different kind from those of sound. In sound there is compression here, then comes attenuation, and all this moves on. Such waves are “longitudinal”. For light, this notion will not do. In light, the particles of ether must be moving at right angles to the direction in which the light is being propagated. When, therefore, what we call a “ray of light” is rushing through the air — with a velocity, you will recall, of 300,000 kilometres a second — the tiny particles will always be vibrating at right angles to the direction in which the light is rushing. When this vibration gets into our eye, we perceive it. Apply this to Fresnel's experiment: we get the following idea. The movement of the light is, once again, a vibration at right angles to the direction in which the light is propagated. This ray, going towards the lower one of the two mirrors, is vibrating, say, in this way and impinges here. As I said before, the fact that wave-movements in many directions will be going criss-cross through each other, is disregarded. According to the physicists who think along these lines, they will in no way disturb each other. Here however, at the screen in this experiment, they do; or again, they reinforce each other. In effect, what will happen here? When the train of waves arrives here, it may well be that the one infinitesimal particle with its perpendicular vibrations happens to be vibrating downward at the very moment when the other is vibrating upward. Then they will cancel each other out and darkness will arise at this place. Or if the two are vibrating upward at the same moment, light will arise. Thus they explain, by the vibrations of infinitesimal particles, what we were explaining just now by the light itself. I was saying that we here get alternations of light patches and dark. The so-called wave-theory of light explains them on the assumption that light is a wave-movement in the other [ether?]. If the infinitesimal particles are vibrating so as to reinforce each other, a lighter patch will arise; if contrary to one another, we get a darker patch. You must realize what a great difference there is between taking the phenomena purely as they are — setting them forth, following them with our understanding, remaining amid the phenomena themselves — and on the other hand adding to them our own inventions. This movement of the ether is after all a pure invention. Having once invented such a notion we can of course make calculations about it, but that affords no proof that it is really there. All that is purely kinematical or phoronomical in these conceptions are merely thought by us, and so is all the arithmetic. You see from this example: our fundamental way of thought requires us so to explain the phenomena that they themselves be the eventual explanation; they must contain their own explanation. Please set great store by this. Mere spun-out theories and theorizings are to be rejected. You can explain what you like by adding things out of the blue, of which man has no knowledge. Of course the waves might conceivably be there, and it might be that the one swings upward when the other downward so that they cancel each other out. But they have all been invented ! What is there however without question is this lattice, — this we see fully reflected. It is to the light itself that we must look, if we desire a genuine and not a spurious, explanation. Now I was saying just now: when the one light goes through the other, or enters into any kind of relation to it, it may well have a dimming or even extinguishing effect upon the other, just as the effect of the prism is to dim the light. This is again brought out in the following experiment, which we shall actually be doing, I will now make a drawing of it. We may have what I shewed you yesterday — a spectrum extending from violet to red — engendered directly by the Sun. But we can also generate the spectrum in another way. Instead of letting the Sun shine through an opening in the wall, we make a solid body glow with heat, — incandescent (Figure IVf). When we have by and by got it white-hot, it will also give us such a spectrum. It does not matter if we get the spectrum from the Sun or from an incandescent body. Now we can also generate a spectrum in a somewhat different way (Figure IVg). Suppose this is a prism and this a sodium flame — a flame in which the metal sodium is volatilizing. The sodium is turned to gas; it burns and volatilizes. We make a spectrum of the sodium as it volatilizes. Then a peculiar thing happens. Making a spectrum, not from the Sun or from a glowing solid body but from a glowing gas, we find one place in the spectrum strongly developed. For sodium light it is in the yellow. Here will be red, orange, yellow, you will remember. It is the yellow that is most strongly developed in the spectrum of sodium. The rest of the spectrum is stunted — hardly there at all. All this — from violet to yellow and then again from yellow to red — is stunted. We seem to get a very narrow bright yellow strip, or as is generally said, a yellow line. Mark well, the yellow line also arises inasmuch as it is part of an entire spectrum, only the rest of the spectrum in this case is stunted, atrophied as it were. From diverse bodies we can make spectra of this kind appearing not as a proper spectrum but in the form of bright, luminous lines. From this you see that vice-versa, if we do not know what is in a flame and we make a spectrum of it, we can conclude, if we get this yellow spectrum for example, that there is sodium in the flame. So we can recognize which of the metals is there. But the remarkable thing comes about when we combine the two experiments. We generate this cylinder of light and the spectrum of it, while at the same time we interpose the sodium flame, so that the glowing sodium somehow unites with the cylinder of light (Figure IVh). What happens then is very like what I was shewing you in Fresnel's experiment. In the resulting spectrum you might expect the yellow to appear extra strong, since it is there to begin with and now the yellow of the sodium flame is added to it. But this is not what happens. On the contrary, the yellow of the sodium flame extinguishes the other yellow and you get a dark place here. Precisely where you would expect a lighter part you get a darker. Why is it so? It simply depends on the intensity of force that is brought to bear. If the sodium light arising here were selfless enough to let the kindred yellow light arising here it would have to extinguish itself in so doing. This it does not do; it puts itself in the way at the very place where the yellow should be coming through. It is simply there, and though it is yellow itself, the effect of it is not to intensify but to extinguish. As a real active force, it puts itself in the way, even as an indifferent obstacle might do; it gets in the way. This yellow part of the spectrum is extinguished and a black strip is brought about instead. From this again you see, we need only bear in mind what is actually there. The flowing light itself gives us the explanation. These are the things which I would have you note. A physicist explaining things in Newton's way would naturally argue: If I here have a piece of white — say, a luminous strip — and I look at it through the prism, it appears to me in such a way that I get a spectrum: red, orange, yellow, green, blue, dark blue, violet (Figure IVi). Goethe said: Well, at a pinch, that might do. If Nature really is like that — if she has made the light composite — we might well assume that with the help of the prism this light gets analyzed into its several parts. Good and well; but now the very same people who say the light consists of these seven colours — so that the seven colours are parts or constituents of the light — these same people allege that darkness is just nothing, — is the mere absence of light. Yet if I leave a strip black in the midst of white — if I have simple white paper with a black strip in the middle and look at this through a prism, — then too I find I get a rainbow, only the colours are now in a different order (Figure IVk), — mauve in the middle, and on the one side merging into greenish-blue. I get a band of colours in a different order. On the analysis-theory I ought now to say: then the black too is analyzable and I should thus be admitting that darkness is more than the mere absence of light. The darkness too would have to be analyzable and would consist of seven colours. This, that he saw the black band too in seven colours, only in a different order, — this was what put Goethe off. And this again shews us how needful it is simply to take the phenomena as we find them.

The Light Course

Lecture IV

https://rsarchive.org/Lectures/GA320/English/GSF1977/19191226p01.html

Stuttgart

26 Dec 1919

GA320-4

My dear Friends, Today I will begin by shewing, as well as may be with our limited resources, the experiment of which we spoke last time. You will remember: when an incandescent solid body spreads its light and we let this light go through a prism, we get a “spectrum”, a luminous picture, very like what we should get from the Sun, (compare Figure IVf), towards the end of Lecture IV). Now we can also obtain a luminous picture with the light that spreads from a glowing gas; however this picture only shews one or more single lines of light or little bands of light at different places, according to the substance used, (Figure IVg). The rest of the spectrum is stunted, so to speak. By very careful experiment, it is true, we should perceive that everything luminous gives a complete spectrum — expending all the way from red to violet, to say no more. Suppose for example we make a spectrum with glowing sodium gas: in the midst of a very feeble spectrum there is at one place a far more intense yellow line, making the rest seem even darker by contrast. Sodium is therefore often spoken of as giving only this yellow line. And now we come to the remarkable fact, which, although not unknown before, was brought to light above all in 1859 by the famous experiment of Kirchhoff and Bunsen. If we arrange things so that the source of light generating the continuous spectrum and the one generating, say, the sodium line, can take effect as it were simultaneously, the sodium line will be found to act like an untransparent body. It gets in the way of the quality of light which would be appearing at this place (i.e. in the yellow) of the spectrum. It blots it out, so that we get a black line here in place of yellow, (Figure IVh). Simply to state the fact, this then is what we have to say: For the yellow of the spectrum, another yellow (the strength of which must be at least equal to the strength of light that is just being developed at this place of the spectrum) acts like an opaque body. As you will presently see, the elements we are compiling will pave the way to an understanding also of this phenomenon. In the first place however we must get hold of the pure facts. We will now shew you, as well as we are able, that this dark line does really appear in the spectrum when we interpose the glowing sodium. We have not been able to arrange the experiment so as to project the spectrum on to a screen. Instead we will observe the spectrum by looking straight into it with our eyes. For it is possible to see the spectrum in this way too; it then appears displaced downward instead of upward, moreover the colours are reversed. We have already discussed, why it is that the colours appear in this way when we simply look through the prism. By means of this apparatus, we here generate the cylinder of light; we let it go through here, and, looking into it, we see it thus refracted. (The experiment was shewn to everyone in turn). To use the short remaining time — we shall now have to consider the relation of colours to what we call “bodies”. As a transition to this problem looking for the relations between the colours and what we commonly call “bodies” — I will however also shew the following experiment. You now see the complete spectrum projected on to the screen. Into the path of the cylinder of light I place a trough in which there is a little iodine dissolved in carbon disulphide. Note how the spectrum is changed. When I put into the path of the cylinder of light the solution of iodine in carbon disulphide, this light is extinguished. You see the spectrum clearly divided into two portions; the middle part is blotted out. You only see the violet on the one side, the reddish-yellow on the other. In that I cause the light to go through this solution — iodine in carbon disulphide — you see the complete spectrum divided into two portions; you only see the two poles on either hand. It has grown late and I shall now only have time for a for a few matters of principle. Concerning the relation of the colours to the bodies we see around us (all of which are somehow coloured in the last resort), the point will be explained how it comes about that they appear coloured at all. How comes it in effect that the material bodies have this relation to the light? How do they, simply by dint of their material existence so to speak, develop such relation to the light that one body looks red, another blue, and so on. It is no doubt simplest to say: When colourless sunlight — according to the physicists, a gathering of all the colours — falls on a body that looks red, this is due to the body's swallowing all the other colours and only throwing back the red. With like simplicity we can explain why another body appears blue. It swallows the remaining colours and throws back the blue alone. We on the other hand have to eschew these speculative explanations and to approach the fact in question — namely the way we see what we call “coloured bodies” — by means of the pure facts. Fact upon fact in proper sequence will then at last enable us in time to “catch” — as it were, to close in upon — this very complex phenomenon. The following will lead us on the way. Even in the 17th Century, we may remember, when alchemy was still pursued to some extent, they spoke of so-called “phosphores” or light-bearers. This is what they meant: — A Bologna cobbler, to take one example, was doing some alchemical experiments with a kind of Heavy Spar (Barytes). He made of it what was then called “Bologna stone”. When he exposed this to the light, a strange phenomenon occurred. After exposure the stone went on shining for a time, emitting a certain coloured light. The Bologna stone had acquired a relation to the light, which it expressed by being luminous still after exposure — after the light had been removed. Stones of this kind were then investigated in many ways and were called “phosphores”, If you come across the word “phosphor” or “phosphorus” in the literature of that time, you need not take it to mean what is called “Phosphorus” today; it refers to phosphorescent bodies of this kind — bearers of light, i.e. phos-phores. However, even this phenomenon of after-luminescence — phosphor escence — is not the simplest. Another phenomenon is really the simple one. If you take ordinary paraffin oil and look through it towards a light, the oil appears slightly yellow. If on the other hand you place yourself so as to let the light pass through the oil while you look at it from behind, the oil will seem to be shining with a bluish light — only so long, however, as the light impinges on it. The same experiment can be made with a variety of other bodies. It is most interesting if you make a solution of plant green — chlorophyll (Figure Va). Look towards the light through the solution and it appears green. But if you take your stand to some extent behind it — if this (Figure Va) is the solution and this the light going through it, while you look from behind to where the light goes through — the chlorophyll shines back with a red or reddish light, just as the paraffin shone blue. There are many bodies with this property. They shine in a different way when, so to speak, they of themselves send the light back — when they have somehow come into relation to the light, changing it through their own nature — than when the light goes through them as through a transparent body. Look at the chlorophyll from behind: we see — so to speak — what the light has been doing in the chlorophyll; we see the mutual relation between the light and the chlorophyll. When in this way a body shines with one kind of light while illumined by another kind of light, we call the phenomenon Fluorescence. And, we may say: what in effect is Phosphorescence? It is a Fluorescence that lasts longer. For it is Fluorescence when the chlorophyll, for instance, shines with a reddish light so long as it is exposed to light. When there is Phosphorescence on the other hand, as with the Bologna stone, we can take the light away and the thing still goes on shining for a time. It thus retains the property of shining with a coloured light, — a property the chlorophyll does not retain. So you have two stages. The one is Fluorescence: we make a body coloured so long as we illumine it. The second is Phosphorescence: we cause a body to remain coloured still for a certain time after illumination. And now there is a third stage: the body, as an outcome of whatever it is that the light does with it, appears with a lasting colour. We have this sequence: Fluorescence, Phosphorescence, Colouredness-of-bodies. Thus we have placed the phenomena, in a manner of speaking, side by side. What we must try to do is to approach the phenomena rightly with our thinking, our forming of ideas. There is another fundamental idea which you will need to get hold of today, for we shall afterwards want to relate it to all these other things. Please, once again, only think quite exactly of what I shall bring forward. Think as precisely as you can. I will remind you again (as once before in these lectures) of the formula for a velocity, say \(v\). A velocity is expressed, as you know, in dividing \(s\), the distance which the mobile object passes through, by the time \(t\). This therefore is the formula: Now the opinion prevails that what is actually given in real Nature in such a case is the distance \(s\) the body passes through, and the time \(t\) it takes to do it. We are supposed to be dividing the real distance \(s\) by the real time \(t\), to get the velocity \(v\), which as a rule is not regarded as being quite so real but more as a kind of function, an outcome of the division sum. Thus the prevailing opinion. And yet in Nature it is not so. Of the three magnitudes — velocity, space and time, — velocity is the only one that has reality. What is really there in the world outside us is the velocity; the \(s\) and \(t\) we only get by splitting up the given totality, the \(v\), into two abstract entities. We only arrive at these on the basis of the velocity, which is really there. This then, to some extent, is our procedure. We see a so-called “body” flowing through space with a certain velocity. That it has this velocity, is the one real thing about it. But now we set to work and think. We no longer envisage the quick totality, the quickly moving body; instead, we think in terms of two abstractions. We dismember, what is really one, into two abstractions. Because there is a velocity, there is a distance moved through. This distance we envisage in the first place, and in the second place we envisage the time it takes to do it. From the velocity, the one thing actually there, we by our thinking process have sundered space and time; yet the space in question is not there at all save as an outcome of the velocity, nor for that matter is the time. The space and time, compared to this real thing which we denote as \(v\), are no realities at all, they are abstractions which we ourselves derive from the velocity. We shall not come to terms with outer reality, my dear Friends, till we are thoroughly clear on this point. We in our process of conception have first created this duality of space and time. The real thing we have outside us is the velocity and that alone; as to the “space” and “time”, we ourselves have first created them by virtue of the two abstractions into which — if you like to put it so — the velocity can fall apart for us. From the velocity, in effect, we can separate ourselves, while from the space and time we cannot; they are within our perceiving, — in our perceiving activity. With space and time we are one. Much is implied in what I am now saying. With space and time we are one. Think of it well. We are not one with the velocity that is there outside us, but we are one with space and time. Nor should we, without more ado, ascribe to external bodies what we ourselves are one with; we should only use it to gain a proper idea of these external bodies. All we should say is that through space and time, with which we ourselves are very intimately united, we learn to know and understand the real velocity. We should not say “The body moves through such and such a distance”; we ought only to say: “The body has a velocity”. Nor should we say, “The body takes so much time to do it,” but once again only this: “The body has a velocity”. By means of space and time we only measure the velocity. The space and time are our own instruments. They are bound to us, — that is the essential thing. Here once again you see the sharp dividing line between what is generally called “subjective” — here, space and time — and the “objective” thing — here, the velocity. It will be good, my dear Friends, if you will bring this home to yourselves very clearly; the truth will then dawn upon you more and more: \(v\) is not merely the quotient of \(s\) and \(t\). Numerically, it is true, \(v\) is expressed by the quotient of \(s\) and \(t\). What I express by this number \(v\) is however a reality in its own right — a reality of which the essence is, to have velocity. What I have here shewn you with regard to space and time — namely that they are inseparable from us and we ought not in thought to separate ourselves from them — is also true of another thing. But, my dear Friends (if I may say this in passing), people are still too much obsessed with the old Konigsberg habit, by which I mean, the Kantian idea. The “Konigsberg” habit must be got rid of, or else it might be thought that I myself have here been talking “Konigsberg”, as if to say “Space and Time are within us.” But that is not what I am saying. I say that in perceiving the reality outside us the — velocity — we make use of space and time for our perception. In effect, space and time are at once in us and outside us. The point is that we unite with space and time, while we do not unite with the velocity. The latter whizzes past us. This is quite different from the Kantian idea. Now once again: what I have said of space and time is also true of something else. Even as we are united by space and time with the objective reality, while we first have to look for the velocity, so in like manner, we are in one and the same element with the so-called bodies whenever we behold them by means of light. We ought not to ascribe objectivity to light any more than to space and time. We swim in space and time just as the bodies swim in it with their velocities. So too we swim in the light, just as the bodies swim in the light. Light is an element common to us and the things outside us — the so-called bodies. You may imagine therefore: Say you have gradually filled the dark room with light, the space becomes filled with something — call it \(x\), if you will — something in which you are and in which the things outside you are. It is a common element in which both you, and that which is outside you, swim. But we have still to ask: How do we manage to swim in light? We obviously cannot swim in it with what we ordinarily call our body. We do however swirl in it with our etheric body. You will never understand what light is without going into these realities. We with our etheric body swim in the light (or, if you will, you may say, in the light-ether; the word does not matter in this connection). Once again therefore: With our etheric body we are swimming in the light. Now in the course of these lectures we have seen how colours arise — and that in many ways — in and about the light itself. In the most manifold ways, colours arise in and about the light; so also they arise, or they subsist, in the so-called bodies. We see the ghostly, spectral colours so to speak, — those that arise and vanish within the light itself. For if I only cast a spectrum here it is indeed like seeing spectres; it hovers, fleeting, in space. Such colours therefore we behold, in and about the light. In the light, I said just now, we swim with our etheric body. How then do we relate ourselves to the fleeting colours? We are in them with our astral body; it is none other than this. We are united with the colours with our astral body. You have no alternative, my dear Friends but to realise that when and wheresoever you see colours, with your astrality you are united with them. If you would reach any genuine knowledge you have no alternative, but must say to yourselves: The light remains invisible to us; we swim in it. Here it is as with space and time; we ought not to call them objective, for we ourselves are swimming in them. So too we should regard the light as an element common to us and to the things outside us; whilst in the colours we have to recognize something that can only make its appearance inasmuch as we through our astral body come into relation to what the light is doing there. Assume now that in this space \(ABCD\) you have in some way brought about a phenomenon of colour — say, a spectrum. I mean now, a phenomenon that takes its course purely within the light. You must refer it to an astral relation to the light. But you may also have the phenomenon of colour in the form of a coloured surface. This therefore — from \(A\) to \(C,\) say — may be appearing to you as a coloured body, a red body for example. We say, then, \(AC\) is red. You look towards the surface of the body, and, to begin with, you will imagine rather crudely. Beneath the surface it is red, through and through. This time, you see, the case is different. Here too you have an astral relation; but from the astral relation you enter into with the colour in this instance you are separated by the bodily surface. Be sure you understand this rightly! In the one instance you see colours in the light — spectral colours. There you have astral relations of a direct kind; nothing is interposed between you and the colours. When on the other hand you see the colours of bodily objects, something is interposed between you and your astral body, and through this something you none the less entertain astral relations to what we call “bodily colours”. Please take these things to heart and think them through. For they are basic concepts — very important ones — which we shall need to elaborate. Only on these lines shall we achieve the necessary fundamental concepts for a truer Physics. One more thing I would say in conclusion. What I am trying to present in these lectures is not what you can get from the first text-book you may purchase. Nor is it what you can get by reading Goethe's Theory of Colour . It is intended to be, what you will find in neither of the two, and what will help you make the spiritual link between them. We are not credulous believers in the Physics of today, nor need we be of Goethe. It was in 1832 that Goethe died. What we are seeking is not a Goetheanism of the year 1832 but one of 1919, — further evolved and developed. What I have said just now for instance — this of the astral relation — please think it through as thoroughly as you are able.

The Light Course

Lecture V

https://rsarchive.org/Lectures/GA320/English/GSF1977/19191227p01.html

Stuttgart

27 Dec 1919

GA320-5

My dear Friends, In our last lecture we were going into certain matters of principle which I will now try to explain more fully. For if we start from the experiences we can gain in the realm of light, it will also help us observe and understand other natural phenomena which we shall presently be studying. I will therefore begin today with these more theoretical reflections and put off the experimental part until tomorrow. We must determine still more exactly the method of our procedure. It is the task of Science to discern and truly to set forth the facts in the phenomena of Nature. Problems of method which this task involves can best be illustrated in the realm of Light. Men began studying the phenomena of light in rather recent times, historically speaking. Nay, the whole way of thinking about the phenomena of Physics, presented in the schools today, reaches hardly any farther back than the 16th century. The way men thought of such phenomena before the 16th century was radically different. Today at school we get so saturated with the present way of thought that if you have been through this kind of schooling it is extremely difficult for you to find your way back to the pure facts. You must first cultivate the habit of feeling the pure facts as such; please do not take my words in a too trivial meaning. You have to learn to sense the facts, and this takes time and trouble. I will now take my start from a particular instance wherein we may compare the way of thought prevailing in the schools today with that which can be gained by following the facts straightforwardly. Suppose this were a plate of glass, seen in cross-section (Figure VIa). Through it you look at a luminous object. As I am drawing it diagrammatically, let me represent the latter simply by a light circle. Cast your mind back to what you learned in your school days. What did they teach you of the phenomenon you see when you observe the luminous object, — with your eye, say, here — looking through the glass? You were no doubt told that rays of light proceed from the luminous object. (We are imagining the eye to be looking in this particular direction, — see the Figure). Rays, you were told, proceed from the shining object. In the direction of the “ray” I am now drawing, the light was said to penetrate from a more tenuous into a denser medium. Simply by looking through the glass and comparing what you see with what you saw before the plate of glass was there, you do indeed perceive the thing displaced. It appears at a different place than without the glass. Now this is said to be due to the light being “refracted”. This is how they are wont to put it: — When the light passes from a more tenuous into a denser medium, to find the direction in which the light will be refracted, you must draw the so-called “normal at the point of incidence”. If the light went on its way without being hindered by a denser medium, it would go on in this direction. But, they now say, the light is “refracted” — in this case, towards the normal, i.e. towards the perpendicular to the glass surface at the point of incidence. Now it goes out again, — out of the glass. (All this is said, you will remember, in tracing how the “ray of light” is seen through the denser medium.) Here then again, at the point of exit from the glass, you will have to erect the normal. If the light went straight on it would go thus : but at this second surface it is again refracted — this time, away from the normal — refracted just enough to make it go on parallel to its original direction. And now the eye, looking as it is from here, is said to produce the final direction of the ray of light and thus to project the luminous object so much the higher up. This then is what we are asked to assume, if we be looking through such a plate of glass. Here, to begin with, the light impinges on the plate, then it is twice refracted — once towards the normal, a second time away from the normal. Then, inasmuch as the eye has the inner faculty to do so (.... or is it to the soul, or to some demon that you ascribe this faculty ....) the light is somehow projected out into space. It is projected moreover to a position different from where it would appear if we were not seeing it through a refracting medium; — so they describe the process. The following should be observed to begin with, in this connection. Say we are looking at anything at all through the same denser medium, and we now try to discriminate, however delicately, between the darker and lighter portions of what we see. Not only the lighter parts, the darker too will appear shifted upward. The entire complex we are looking at is found to be displaced. Please take this well into account. Here is a darker part bordering on a lighter. The dark is shifted upward, and since one end of it is lighter we see this shifted too. Placing before us any such complex, consisting of a darker and a lighter part, we must admit the lighter part is displaced simply as the upper boundary of the darker. Instead, they speak in such a way as to abstract the one light patch from all the rest that is there. Mostly they speak as though the light patch alone were suffering displacement. Surely this is wrong. For even if I fix my gaze on this one patch of light, it is not true that it alone is shifted upward. The part below it, which I am treating as if it were just nothing when I describe it thus, is shifted upward too. In point of fact, what is displaced in these optical phenomena can never be thus abstractly confined. If therefore I repeat Newton's experiment — I let into the room a cone of light which then gets diverted by the prism — it simply is not true that the cone of light is diverted all alone. Whatever the cone of light is bordering on — above it and below — is diverted too. I really ought never to speak of rays of light or anything of that kind, but only of luminous pictures or spaces-of-light being diverted. In a particular instance I may perhaps want to refer to some isolated light, but even then I still ought not to speak of it in such a way as to build my whole theory of the phenomenon upon it. I still ought to speak in such a way as to refer at the same time to all that borders on the light. Only if we think in this way can we begin to feel what is really going on when the phenomena of colour comes into being before our eyes. Otherwise our very habit of thought begets the impression that in some way the colours spring from the light alone. For from the very outset we have it settled in our mind that the one and only reality we are dealing with is the light. Yet, what we have before us in reality is never simply light as such; it is always something light, bordered on one side or other by darkness. And if the lighter part — the space it occupies — is shifted, the darker part is shifted too. But now, what is this “dark”? You must take the dark seriously, — take it as something real. (The errors that have crept into modern Physics since about the 16th century were only able to creep in because these things were not observed spiritually at the same time. Only the semblance, as appearing to the outer senses, was taken note of; then, to explain this outer semblance, all kinds of theoretical inventions were added to it). You certainly will not deny that when you look at light the light is sometimes more and sometimes less intense. There can be stronger light and less strong. The point is now to understand: How is this light, which may be stronger or weaker related to darkness? The ordinary physicist of today thinks there is stronger light and less strong; he will admit every degree of intensity of light, but he will only admit one darkness — darkness which is simply there when there is no light. There is, as it were, only one way of being black. Yet as untrue as it would be to say that there is only one kind of lightness, just as untrue is it to say that there is only one kind of darkness. It is as one-sided as it would be to declare: “I know four men. One of them owns £25, another £50; he therefore owns more than the other. The third of them is £25 in debt, the fourth is £50 in debt. Yet why should I take note of any difference in their case? It is precisely the same; both are in debt. I will by all means distinguish between more and less property, but not between different degrees of debt. Debt is debt and that is all there is to it.” You see the fallacy at once in this example, for you know very well that the effect of being £25 in debt is less than that of being £50 in debt. But in the case of darkness this is how people think: Of light there are different degrees; darkness is simply darkness. It is this failure to progress to a qualitative way of thinking, which very largely prevents our discovering the bridge between the soul-and-spirit on the one hand, and the bodily realm on the other. When a space is filled with light it is always filled with light of a certain intensity; so likewise, when a space is filled with darkness, it is filled with darkness of a certain intensity. We must proceed from the notion of a merely abstract space to the kind of space that is not abstract but is in some specific way positively filled with light or negatively filled with darkness. Thus we may be confronting a space that is filled with light and we shall call it “qualitatively positive”. Or we may be confronting a space that is filled with darkness and we shall judge it “qualitatively negative” with respect to the realm of light. Moreover both to the one and to the other we shall be able to ascribe a certain degree of intensity, a certain strength. Now we may ask: How does the positive filling of space differ for our perception from the negative? As to the positive, we need only remember what it is like when we awaken from sleep and are surrounded by light, — how we unite our subjective experience with the light that floods and surges all around us. We need only compare this sensation with what we feel when surrounded by darkness, and we shall find — I beg you to take note of this very precisely — we shall find that for pure feeling and sensation there is an essential difference between being given up to a light-filled space and to a darkness-filled space. We must approach these things with the help of some comparison. Truly, we may compare the feeling we have, when given up to a light-filled space, with a kind of in-drawing of the light. It is as though our soul, our inner being, were to be sucking the light in. We feel a kind of enrichment when in a light-filled space. We draw the light into ourselves. How is it then with darkness? We have precisely the opposite feeling. We feel the darkness sucking at us. It sucks us out, we have to give away, — we have to give something of ourselves to the darkness. Thus we may say: the effect of light upon us is to communicate, to give; whilst the effect of darkness is to withdraw, to suck at us and take away. So too must we distinguish between the lighter and the darker colours. The light ones have a quality of coming towards us and imparting something to us; the dark colours on the other hand have a quality of drawing on us, sucking at us, making us give of ourselves. So at long last we are led to say: Something in our outer world communicates itself to us when we are under the influence of light; something is taken from us, we are somehow sucked out, when under the influence of darkness. There is indeed another occasion in our life, when — as I said once before during these lectures — we are somehow sucked-out as to our consciousness; namely when we fall asleep. Consciousness ceases. It is a very similar phenomenon, like a cessation of consciousness, when from the lighter colours we draw near the darker ones, the blue and violet. And if you will recall what I said a few days ago about the relation of our life of soul to mass , — how we are put to sleep by mass, how it sucks-out our consciousness, — you will feel something very like this in the absorption of our consciousness by darkness. So then you will discern the deep inner kinship between the condition space is in when filled with darkness and on the other hand the filling of space which we call matter, which is expressed in “mass”. Thus we shall have to seek the transition from the phenomena of light to the phenomena of material existence. We have indeed paved the way, in that we first looked for the fleeting phenomena of light — phosphorescence and fluorescence — and then the firm and fast phenomena of light, the enduring colours. We cannot treat all these things separately; rather let us begin by setting out the whole complex of these facts together. Now we shall also need to recognize the following, When we are in a light-filled space we do in a way unite with this light-filled space. Something in us swings out into the light-filled space and unites with it. But we need only reflect a little on the facts and we shall recognize an immense difference between the way we thus unite with the light-flooded spaces of our immediate environment and on the other hand the way we become united with the warmth-conditions of our environment, — for with these too, as human beings, we do somehow unite. We do indeed share very much in the condition of our environment as regards warmth; and as we do so, here once again we feel a kind of polarity prevailing, namely the polarity of warm and cold. Yet we must needs perceive an essential difference between the way we feel ourselves within the warmth-condition of our environment and the way we feel ourselves within the light-condition of our environment. Physics, since the 16th century, has quite lost hold of this difference. The open-mindedness to distinguish how we join with our environment in the experience of light upon the one hand and warmth upon the other has been completely lost; nay, the deliberate tendency has been, somehow to blur and wipe away such differences as these. Suppose however that you face the difference, quite obviously given in point of fact, between the way we experience and share in the conditions of our environment as regards warmth and light respectively. Then in the last resort you will be bound to recognize that the distinction is: we share in the warmth -conditions of our environment with our physical body and in the light -conditions, as we said just now, with our etheric body. This in effect — this proneness to confuse what we become aware of through our ether-body and what we become aware of through our physical body — has been the bane of Physics since the 16th century. In course of time all things have thus been blurred. Our scientists have lost the faculty of stating facts straightforwardly and directly. This has been so especially since Newton's influence came to be dominant, as it still is to a great extent today. There have indeed been individuals who have attempted from time to time to draw attention to the straightforward facts simply as they present themselves. Goethe of course was doing it all through, and Kirchhoff among others tried to do it in more theoretic ways. On the whole however, scientists have lost the faculty of focusing attention purely and simply on the given facts. The fact for instance that material bodies in the neighbourhood of other material bodies will under given conditions fall towards them, has been conceived entirely in Newton's sense, being attributed from the very outset to a force proceeding from the one and affecting the other body — a “force of gravity”. Yet ponder how you will, you will never be able to include among the given facts what is understood by the term “force of gravity”. If a stone falls to the Earth the fact is simply that it draws nearer to the Earth. We see it now at one place, now at another, now at a third and so on. If you then say “The Earth attracts the stone” you in your thoughts are adding something to the given fact; you are no longer purely and simply stating the phenomenon. People have grown ever more unaccustomed to state the phenomena purely, yet upon this all depends. For if we do not state the phenomena purely and simply, but proceed at once to thought-out explanations, we can find manifold explanations of one and the same phenomenon. Suppose for example you have two heavenly bodies. You may then say: These two heavenly bodies attract one another, — send some mysterious force out into space and so attract each other (Figure VIb). But you need not say this. You can also say: “Here is the one body, here is the other, and here (Figure VIc) are a lot of other, tiny bodies — particles of ether, it may be — all around and in between the two heavenly bodies. The tiny particles are bombarding the two big ones — bombarding here, there and on all sides; — the ones between, as they fly hither and thither, bombard them too. Now the total area of attack will be bigger outside than in between. In the resultant therefore, there will be less bombardment inside than outside; hence the two bodies will approach each other. They are, in fact, driven towards each other by the difference between the number of impacts they receive in the space between them and outside them.” There have in fact been people who have explained the force of gravity simply by saying: It is a force acting at a distance and attracts the bodies towards each other. Others have said that that is nonsense; according to them it is unthinkable for any force to act at a distance. They then invite us to assume that space is filled with “ether”, and to assume this bombardment too. The masses then are, so to speak, for ever being sprayed towards each other. To add to these explanations there are no doubt many others. It is a classical example of how they fail to look at the real phenomenon but at once add their thought-out explanations. Now what is at the bottom of it all? This tendency to add to the phenomena in thought — to add all manner of unknown agencies and fancied energies, presumed to be doing this or that — saves one the need of doing something else. Needless to say, the impacts in the theory of Figure VIc have been gratuitously added, just as the forces acting at a distance have been in the other theory. These adventitious theories, however, relieve one of the need of making one fundamental assumption, from which the people of today seem to be very much averse. For in effect, if these are two independent heavenly bodies and they approach each other, or show that it is in their nature to approach each other, we cannot but look for some underlying reason why they do so; there must be some inner reason. Now it is simpler to add in thought some unknown forces than to admit that there is also another way, namely no longer to think of the heavenly bodies as independent of each other. If for example I put my hand to my forehead, I shall not dream of saying that my forehead “attracts” my hand, but I shall say: It is an inner deed done by the underlying soul-and-spirit. My hand is not independent of my forehead; they are not really separate entities. I shall regard the phenomenon rightly only by recognising myself as a single whole. I should have no reality in mind if I were to say: There is a head, there are two arms and hands, there is a trunk, there are two legs. There would be nothing complete in that; I only have something complete in mind if I describe the whole human body as a single entity, — if I describe the different items so that they belong together. My task is not merely to describe what I see; I have to ponder the reality of what I see. The mere fact that I see a thing does not make it real. Often I have made the following remark, — for I have had to indicate these things in other lectures too. Take a crystal cube of rock-salt. It is in some respect a totality. (Everything will be so in some respect). The crystal cube can exist by virtue of what it is within the compass of its six faces. But if you look at a rose, cut from the shrub it grew on, this rose is no totality. It cannot, like the cube of rock-salt, exist by virtue of all that is contained within it. The rose can only have existence by being of the rose-bush. The cut rose therefore, though you can see it just as you can see the cube of rock-salt, is a real abstraction; you may not call it a reality by itself. The implications of this, my dear Friends, are far-reaching. Namely, for every phenomenon, we must examine to what extent it is a reality in itself, or a mere section of some larger whole. If you consider Sun and Moon, or Sun and Earth, each by itself, you may of course invent and add to them a force of gravity, just as you might invent a force of gravity by means of which my forehead would attract my right hand. But in considering Sun and Earth and Moon thus separately, the things you have in mind are not totalities; they are but parts and members of the whole planetary system. This then is the essential thing; observe to what extent a thing is whole, or but a section of a whole. How many errors arise by considering to be a whole what is in fact only a partial phenomenon within a larger whole! By thus considering only the partial phenomena and then inventing energies to add to these, our scientists have saved themselves the need of contemplating the inherent life of the planetary system. The tendency has been, first to regard as wholes those things in Nature which are only parts, and by mere theories then to construe the effects which arise in fact between them. This therefore, to sum up, is the essential point: For all that meets us in Nature we have to ask: What is the whole to which this thing belongs? Or is it in itself a whole? Even then, in the last resort, we shall find that things are wholes only in certain respects. Even the crystal cube of rock-salt is a totality only in some respect; it too cannot exist save at certain temperatures and under other requisite conditions. Given some other temperature, it could no longer be. Our need is therefore to give up looking at Nature in the fragmentary way which is so prevalent in our time. Indeed it was only by looking at Nature in this fragmentary way that Science since the 16th century conceived this strange idea of universal, inorganic, lifeless Nature. There is indeed no such thing, just as in this sense there is no such thing as your bony system without your blood. Just as your bony system could only come into being by, as it were, crystallizing out of your living organism as a whole, so too this so-called inorganic Nature cannot exist without the whole of Nature — soul and Spirit-Nature — that underlies it. Lifeless Nature is the bony system, abstracted from Nature as a whole. It is impossible to study it alone, as they began doing ever since the 16th century and as is done in Newtonian Physics to this day. It was the trend of Newtonian Physics to make as neat as possible an extract of this so-called inorganic Nature, treating it then as something self-contained. This “inorganic Nature” only exists however in the machines which we ourselves piece together from the parts of Nature. And here we come to something radically different. What we are wont to call “inorganic” in Nature herself, is placed in the totality of Nature in quite another way. The only really inorganic things are our machines, and even these are only so insofar as they are pieced together from sundry forces of Nature by ourselves. Only the “put-togetherness” of them is inorganic. Whatever else we may call inorganic only exists by abstraction. From this abstraction however present-day Physics has arisen. This Physics is an outcome of abstraction; it thinks that what it has abstracted is the real thing, and on this assumption sets out to explain whatever comes within its purview As against this, the only thing we can legitimately do is to form our ideas and concepts in direct connection with what is given to us from the outer world — the details of the sense-world. Now there is one realm of phenomena for which a very convenient fact is indeed given. If you strike a bell and have some light and very mobile device in the immediate neighbourhood, you will be able to demonstrate that the particles of the sounding bell are vibrating. Or with a pipe playing a note, you will be able to show that the air inside it is vibrating. For the phenomena of sound and tone therefore, you have the demonstrable movement of the particles of air or of the bell; so you will ascertain that there is a connection between the vibrations executed by a body or by the air and our perceptions of tone or sound. For this field of phenomena it is quite patent: vibrations are going on around us when we hear sounds. We can say to ourselves that unless the air in our environment is vibrating we shall not hear any sounds. There is a genuine connection — and we shall speak of it again tomorrow — between the sounds and the vibrations of the air. Now if we want to proceed very abstractly we may argue: “We perceive sound through our organs of hearing. The vibrations of the air beat on our organ of hearing, and when they do so we perceive the sound. Now the eye too is a sense-organ and through it we perceive the colours; so we may say: here something similar must be at work. Some kind of vibration must be beating on the eye. But we soon see it cannot be the air. So then it is the ether.” By a pure play of analogies one is thus led to the idea: When the air beats upon our ear and we have the sensation of a sound, there is an inner connection between the vibrating air and our sensation; so in like manner, when the hypothetical ether with its vibrations beats upon our eye, a sensation of light is produced by means of this vibrating ether. And as to how the ether should be vibrating: this they endeavour to ascertain by means of such phenomena as we have seen in our experiments during these lectures. Thus they think out an universal ether and try to calculate what they suppose must be going on in this ethereal ocean. Their calculations relate to an unknown entity which cannot of course be perceived but can at most be assumed theoretically. Even the very trifling experiments we have been able to make will have revealed the extreme complication of what is going on in the world of light. Till the more recent developments set in, our physicists assumed that behind — or, should we rather say, within — all thus that lives and finds expression in light and colour there is the vibrating ether, a tenuous elastic substance. And since the laws of impact and recoil of elastic bodies are not so difficult to get to know, they could compute what these vibrating little cobolds must be up to in the ether. They only had to regard them as little elastic bodies, — imagining the ether as an inherently elastic substance. So they could even devise explanations of the phenomena we have been showing, — e.g. the forming of the spectrum. The explanation is that the different kinds of ether-vibrations are dispersed by the prism; these different kinds of vibrations then appear to us as different colours. By calculation one may even explain from the elasticity of the ether the extinction of the sodium line for example, which we perceived in our experiment the day before yesterday. In more recent times however, other phenomena have been discovered. Thus we can make a spectrum, in which we either create or extinguish the sodium line (i.e., in the latter case, we generate the black sodium line). If then in addition we bring an electro-magnet to bear upon the cylinder of light in a certain way, the electro-magnet affects the phenomenon of light. The sodium line is extinguished in its old place and for example two other lines arise, purely by the effect of the electricity with which magnetic effects are always somehow associated. Here, then, what is described as “electric forces” proves to be not without effect upon those processes which we behold as phenomena of light and behind which one had supposed the mere elastic ether to be working. Such discoveries of the effect of electricity on the phenomena of light now led to the assumption that there must be some kinship between the phenomena of light and those of magnetism and electricity. Thus in more recent times the old theories were rather shaken. Before these mutual effects had been perceived, one could lean back and rest content. Now one was forced to admit that the two realms must have to do with each other. As a result, very many physicists now include what radiates in the form of light among the electro-magnetic effects. They think it is really electro-magnetic rays passing through space. Now think a moment what has happened. The scientists had been assuming that they knew what underlies the phenomena of light and colour: namely, undulations in the elastic ether. Now that they learned of the interaction between light and electricity, they feel obliged to regard, what is vibrating there, as electricity raying through space. Mark well what has taken place. First it is light and colour which they desire to explain, and they attribute them to the vibrating ether. Ether-vibrations are moving through space. They think they know what light is in reality, — it is vibrations in the elastic ether. Then comes the moment when they have to say: What we regarded as vibrations of the elastic ether are really vibrations of electro-magnetic force. They know still better now, what light is, than they did before. It is electro-magnetic streams of force. Only they do not know what these are! Such is the pretty round they have been. First a hypothesis is set up: something belonging to the sense-world is explained by an unknown super-sensible, the vibrating ether. Then by and by they are driven to refer this super-sensible once more to something of the sense-world, yet at the same time to confess that they do not know what the latter is. It is a highly interesting journey that has here been made; from the hypothetical search for an unknown to the explanation of this unknown by yet another unknown. The physicist Kirchhoff was rather shattered and more or less admitted: It will be not at all easy for Physics if these more recent phenomena really oblige us no longer to believe in the undulating ether. And when Helmholtz got to know of the phenomenon, he said: Very well, we shall have to regard light as a kind of electro-magnetic radiation. It only means that we shall now have to explain these radiations themselves as vibrations in the elastic ether. In the last resort we shall get back to these, he said. The essence of the matter is that a genuine phenomenon of undulation — namely the vibrating of the air when we perceive sounds — was transferred by pure analogy into a realm where in point of fact the whole assumption is hypothetical. I had to go into these matters of principle today, to give the necessary background. In quick succession we will now go through the most important aspects of those phenomena which we still want to consider. In our remaining hours I propose to discuss the phenomena of sound, and those of warmth, and of electro-magnetics; also whatever explanations may emerge from these for our main theme — the phenomena of optics.

The Light Course

Lecture VI

https://rsarchive.org/Lectures/GA320/English/GSF1977/19191229p01.html

Stuttgart

29 Dec 1919

GA320-6

My dear Friends, We will begin today with an experiment bearing upon our studies of the theory of colour. As I have said before, all I can give you in this Course can only be improvised and aphoristic. Hence too I cannot keep to the conventional categories of the Physics textbooks, — in saying which I do not mean to imply that it would be better if I did. In the last resort I wish to lead you to a certain kind of insight into Science, and you must look on all that I bring forward in the meantime as a kind of preparation. We are not advancing in the usual straight line. We try to gather up the diverse phenomena we need, forming a circle as it were, — then to move forward from the circumference towards the centre. You have seen that wherever colours arise there is a working-together of light and darkness. What we now have to do is to observe as many phenomena as we can before we try to theorize. We want to form a true conception of what underlies this interplay of light and darkness. Today I will begin by shewing you the phenomenon of coloured shadows, as they are called. Here are two candles (Figure VIIa), — candles as sources of light — and an upright rod which will throw shadows on this screen. You see two shadows, without perceptible colour. You only need to take a good look at what is here before you, you will be bound to say: the shadow you are seeing on the right is the one thrown by the left-hand source of light. It is produced, in that the light from this source is hidden by the rod. Likewise the shadow on the left arises where the light from the right-hand source is covered. Relatively dark spaces are created, — that is all. Where the shadow is, is simply a dark space. Moreover, looking at the surface of the screen apart from the two bands of shadow, you will agree it is illumined by both sources of light. Now I will colour the one (the left-hand) light. I make the light go through a plate of coloured glass, so that this one of the lights is now coloured — that is, darkened to some extent. As a result, you will see that the shadow of the rod, due to this left-hand source of light — the one which I am darkening to red — this shadow on the right becomes green. It becomes green just as a purely white background does when you look sharply for example at a small red surface for a time, then turn your eye away and look straight at the white. You then see green where you formerly saw red, though there is nothing there. You yourself, as it were, see the green colour on to the white surface. In such a case, you are seeing the green surface as an after-image in time of the red which you were seeing just before, when you exposed your eye to the red surface that was actually there. And so in this case: when I darken the source of light to red, you see the shadow green. What was mere darkness before, you now see green. And now I darken the same source of light to green, — the shadow becomes red. And when I darken it to blue, an orange shadow is produced. If I should darken it to violet, it would give yellow. And now consider please the following phenomenon; it is most important, therefore I mention it once more. Say in a room you have a red cushion with a white crochet cover, through the rhombic-patterned apertures of which the red of the cushion shines through. You look at the red rhombic pattern and then look away to the white. On the white ground you see the same lattice-work in green. Of course it isn't there, but your own eye is active and makes an after-effect, which, as you focus on the white, generates the green, “subjective” images, as one is wont to call them. Goethe was familiar with this phenomenon, and also knew that of the coloured shadows. I darken this source of light and get green, said Goethe to himself, and he went on to describe it somewhat as follows: When I darken this source of light, the white screen as a whole shines red. I am not really seeing the white screen; what I see is a reddish-shining colour. In fact I see the screen more or less red. And as an outcome — as with the cushion mentioned just now — I with my own eye generate the contrasting colour. There is no real green here. I only see the green incidentally, because the screen as a whole now has a reddish colour. However, this idea of Goethe's is mistaken, as you may readily convince yourselves. Take a little tube and look through it, so that you only see the shadow; you will still see it green. You no longer see what is around it, you only see the green which is objectively there at the place you look at. You can convince yourself by this experiment that the green really is objective. It remains green, hence the phenomenon cannot be one of mere contrast but is objective. We cannot now provide for everyone to see it, but as the proverb says, durch zweier Zeugen Mund wird alle Wahrheit kund — two witnesses will always tell the truth. I will produce the phenomenon and you must now look through on to the green strip. It stays green, does it not? So with the other colour: if I engendered red by means of green, it would stay red. Goethe in this instance was mistaken, and as the error is incorporated in his Theory of Colour it must of course be rectified. 1 After some careful experiments on a later occasion, Dr. Steiner admitted that there is an error here. (See the Translator's Note on this passage.) He also recommended chemical and photographic researches to show the real nature of coloured shadows. Now to begin with, my dear Friends, along with all the other phenomena which we have studied, I want you to take note of the pure fact we have just demonstrated. In the one case we get a grey, a bit of darkness, a mere shadow. In the other case we permeate the shadow, so to speak, with colour. The light and darkness then work together in a different way. We note that by darkening the light with red the objective phenomenon of the green is called forth. Now side by side with this, I also drew your attention to what appears, as is generally said, “subjectively”. We have then, in the one case, what would be called an “objective” phenomenon, the green that stays there on the screen; though not a permanently fixed colour, it stays as long as we create the requisite conditions. Whilst in the other case we have something, as it were, subjectively conditioned by our eye alone. Goethe calls the green colour that appears to me when I have been exposing my eye for a time to red, the colour or coloured after-image that is evoked or “required” ( gefordert ), — called forth by reaction. Now there is one thing we must insist on in this connection. The “subjective, objective” distinction, between the colour that is temporarily fixed here and the colour that seems only to be called forth as an after-image by the eye, has no foundation in any real fact. When I am seeing red through my eyes, as at this moment, you know there is all the physical apparatus we were describing a few days ago; the vitreous body, the lens, the aqueous humour between the lens and the cornea, — a highly differentiated physical apparatus. This physical apparatus, mingling light and darkness as it does in the most varied ways with one another, is in no other relation to the objectively existent ether than all the apparatus we have here set up — the screen, the rod and so on. The only difference is that in the ^one case the whole apparatus is my eye; I see an objective phenomenon through my own eye. It is the same objective phenomenon which I see here, only that this one stays. By dint of looking at the red, my eye will subsequently react with the “required” colour — to use Goethe's term, — the eye, according to its own conditions, being gradually restored to its neutral state. But the real process by means of which I see the green when I see it thus, as we are wont to say, “subjectively” — through the eye alone, — is in no way different from what it is when I fix the colour “objectively” as in this experiment. Therefore I said in an earlier lecture: You, your subjective being, do not live in such a way that the ether is there vibrating outside of you and the effect of it then finds expression in your experience of colour. No, you yourself are swimming in the ether — you are one with it. It is but an incidental difference, whether you become at one with the ether through this apparatus out here or through a process that goes on in your own eye. There is no real nor essential difference between the green image engendered spatially by the red darkening of the light, and the green afterimage, appearing afterwards only in point of time. Looked at objectively there is no tangible difference, save that the process is spatial in the one case and temporal in the other. That is the one essential difference. A sensible and thoughtful contemplation of these things will lead you no longer to look for the contrast, “subjective and objective” as we generally call it, in the false direction in which modern Science generally tries to see it. You will then see it for what it really is. In the one case we have rigged-up an apparatus to engender colour while our eye stays neutral — neutral as to the way the colours are here produced — and is thus able to enter into and unite with what is here. In the other case the eye itself is the physical apparatus. What difference does it make, whether the necessary apparatus is out there, or in your frontal cavity? We are not outside the things, then first projecting the phenomena we see out into space. We with our being are in the things; moreover we are in them even more fully when we go on from certain kinds of physical phenomena to others. No open-minded person, examining the phenomena of colour in all their aspects, can in the long run fail to admit that we are in them — not, it is true, with our ordinary body, but certainly with our etheric body and thereby also with the astral part of our being. And now let us descend from Light to Warmth. Warmth too we perceive as a condition of our environment which gains significance for us whenever we are exposed to it. We shall soon see, however, that as between the perception of light and the perception of warmth there is a very significant difference. You can localize the perception of light clearly and accurately in the physical apparatus of the eye, the objective significance of which I have been stressing. But if you ask yourself in all seriousness, “How shall I now compare the relation I am in to light with the relation I am in to warmth?”, you will have to answer, “While my relation to the light is in a way localized — localized by my eye at a particular place in my body, — this is not so for warmth. For warmth the whole of me is, so to speak, the sense-organ. For warmth, the whole of me is what my eye is for the light”. We cannot therefore speak of the perception of warmth in the same localized sense as of the perception of light. Moreover, precisely in realizing this we may also become aware of something more. What are we really perceiving when we come into relation to the warmth-condition of our surroundings? We must admit, we have a very distinct perception of the fact that we are swimming in the warmth-element of our environment. And yet, what is it of us that is swimming? Please answer for yourselves the question: What is it that is swimming when you are swimming in the warmth of your environment? Take then the following experiment. Fill a bucket with water just warm enough for you to feel it lukewarm. Put both your hands in — not for long, only to test it. Then put your left hand in water as hot as you can bear and your right hand in water as cold as you can bear. Then put both hands quickly back again into the lukewarm water. You will find the lukewarm water seeming very warm to your right hand and very cold to your left. Your left hand, having become hot, perceives as cold what your right hand, having become cold, perceives as warmth. Before, you felt the same lukewarmness on either side. What is it then? It is your own warmth that is swimming there. Your own warmth makes you feel the difference between itself and your environment. What is it therefore, once again, — what is it of you that is swimming in the warmth-element of your environment? It is your own state-of-warmth, brought about by your own organic process. Far from this being an unconscious thing, your consciousness indwells it. Inside your skin you are living in this warmth, and according to the state of this your own warmth you converse — communicate and come to terms — with the element of warmth in your environment, wherein your own bodily warmth is swimming. It is your warmth-organism which really swims in the warmth of your environment. — If you think these things through, you will come nearer the real processes of Nature — far nearer than by what is given you in modern Physics, abstracted as it is from all reality. Now let us go still farther down. We experience our own state-of-warmth by swimming with it in our environment-of-warmth. When we are warmer than our environment we feel the latter as if it were drawing, sucking at us; when we are colder we feel as though it were imparting something to us. But this grows different again when we consider how we are living in yet another element. Once more then: we have the faculty of living in what really underlies the light; we swim in the element of light. Then, in the way we have been explaining, we swim in the element of warmth. But we are also able to swim in the element of air, which of course we always have within us. We human beings, after all, are to a very small extent solid bodies. More than 90% of us is just a column of water, and — what matters most in this connection — the water in us is a kind of intermediary between the airy and the solid state. Now we can also experience ourselves quite consciously in the airy element, just as we can in the element of warmth. Our consciousness descends effectively into the airy element. Even as it enters into the element of light and into the element of warmth, so too it enters into the element of air. Here again, it can “converse”, it can communicate and come to terms with what is taking place in our environment of air. It is precisely this “conversation” which finds expression in the phenomena of sound or tone . You see from this: we must distinguish between different levels in our consciousness. One level of our consciousness is the one we live with in the element of light, inasmuch as we ourselves partake in this element. Quite another level of our consciousness is the one we live with in the element of warmth, inasmuch as we ourselves, once more, are partaking in it. And yet another level of our consciousness is the one we live with in the element of air, inasmuch as we ourselves partake also in this. Our consciousness is indeed able to dive down into the gaseous or airy element. Then are we living in the airy element of our environment and are thus able to perceive the phenomena of sound and of musical tone. Even as we ourselves with our own consciousness have to partake in the phenomena of light so that we swim in the light-phenomena of our environment; and as we have to partake in the element of warmth so that we swim also in this; so too must we partake in the element of air. We must ourselves have something of the airy element within us in a differentiated form so that we may be able to perceive — when, say, a pipe, a drum or a violin is resounding — the differentiated airy element outside us. In this respect, my dear Friends, our bodily nature is indeed of the greatest interest even to outward appearance. There is our breathing process: we breathe-in the air and breathe it out again. When we breathe-out the air we push our diaphragm upward. This involves a relief of tension, a relaxation, for the whole of our organic system beneath the diaphragm. In that we raise the diaphragm as we breathe-out and thus relieve the organic system beneath the diaphragm, the cerebrospinal fluid in which the brain is swimming is driven downward. Here now the cerebrospinal fluid is none other than a somewhat condensed modification, so to speak, of the air, for it is really the out-breathed air which brings about the process. When I breathe-in again, the cerebrospinal fluid is driven upward. I, through my breathing, am forever living in this rhythmic, downward-and-upward, upward-and-downward undulation of the cerebrospinal fluid, which is quite clearly an image of my whole breathing process. In that my bodily organism partakes in these oscillations of the breathing process, there is an inner differentiation, enabling me to perceive and experience the airy element in consciousness. Indeed by virtue of this process, of which admittedly I have been giving only a rather crude description, I am forever living in a rhythm-of-life which both in origin and in its further course consists in an inner differentiation of the air. In that you breathe and bring about — not of course so crudely but in a manifold and differentiated way — this upward and downward oscillation of the rhythmic forces, there is produced within you what may itself be described as an organism of vibrations, highly complicated, forever coming into being and passing away again. It is this inner organism of vibrations which in our ear we bring to bear upon what sounds towards us from without when, for example, the string of a musical instrument gives out a note. We make the one impinge upon the other. And just as when you plunge your hand into the lukewarm water you perceive the state-of-warmth of your own hand by the difference between the warmth of your hand and the warmth of the water, so too do you perceive the tone or sound by the impact and interaction of your own inner, wondrously constructed musical instrument with the sound or tone that comes to manifestation in the air outside you. The ear is in a way the bridge, by which your own inner “lyre of Apollo” finds its relation, in ever-balancing and compensating interplay, with the differentiated airy movement that comes to you from without. Such, in reality is hearing. The real process of hearing — hearing of the differentiated sound or tone — is, as you see, very far removed from the abstraction commonly presented. Something, they say, is going on in the space outside, this then affects my ear, and the effect upon my ear is perceived in some way as an effect on my subjective being. For the “subjective being” is at long last referred to — described in some kind of demonology — or rather, not described at all. We shall not get any further if we do not try to think out clearly, what is the underlying notion in this customary presentation. You simply cannot think these notions through to their conclusion, for what this school of Physics never does is to go simply into the given facts. Thus in effect we have three stages in man's relation to the outer world — I will describe them as the stage of Light, the stage of Warmth, and that of Tone or Sound. There is however a remarkable fact in this connection. Look open-mindedly at your relation to the element of light — your swimming in the element of light — and you will have to admit: It is only with your etheric body that you can live in what is there going on in the outer world. Not so when you are living in the element of warmth. You really live in the warmth-element of your environment with your whole bodily nature. Having thus contemplated how you live in light and warmth, look farther down — think how you live in the element of tone and sound — and you will recognize: Here you yourself are functioning as an airy body. You, as a living organism of air, live in the manifoldly formed and differentiated outer air. It is no longer the ether; it is external physical matter, namely air. Our living in the warmth-element is then a very significant border-line. Our life in the element of warmth is for our consciousness a kind of midway level — a niveau . You recognize it very clearly in the simple fact that for pure feeling and sensation you are scarcely able to distinguish outer warmth from inner warmth. Your life in the light-element however lies above this level:— For light, you ascend as it were into a higher, into an etheric sphere, therein to live with your consciousness. On the other hand you go beneath this level, beneath this niveau , when in perceiving tone or sound you as a man-of-air converse and come to terms with the surrounding air. While upon this niveau itself (in the perceiving of warmth) you come to terms with the outer world in a comparatively simple way. Now bring together what I have just been shewing with what I told you before out of Anatomy and Physiology. Then you will have to conceive the eye as the physical apparatus, to begin with. Indeed the farther outward you go, the more physical do you find the eye to be; the farther in you go, the more is it permeated with vitality. We therefore have in us a localized organ — the eye — with which to lift ourselves above a certain level or niveau . Upon this actual niveau we live as it were on equal terms with our environment; with our own warmth we meet the warmth of our environment and perceive the difference, whatever it may be. Here we have no such specialized organ as the eye; the whole of us, we ourselves in some way, become the sense-organ. And we dive down beneath this level or niveau when functioning as airy man, — when we converse and come to terms with the differentiated outer air. Here once again the “conversation” becomes localized — localized namely in this “lyre of Apollo”, in this rhythmic play of our whole organism, of which the rhythmic play of our spinal fluid is but the image and the outcome. Here then again we have something localized — only beneath the niveau this time, whilst in the eye it is above this midway level. The Psychology of our time is, as you see, in an even sorrier position than the Physiology and Physics, and we can scarcely blame our physicists if they speak so unrealistically of what is there in the outer world, since they get so little help from the psychologists. The latter, truth to tell, have been only too well disciplined by the Churches, which have claimed all the knowledge of the soul and Spirit for their own domain. Very obediently the psychologists restrict their study to the external apparatus, calling this external apparatus “Man”. They speak no doubt of soul and mind, or even Spirit, but in mere words, mere sounding phrases, until Psychology becomes at last a mere collection of words. For in their books they never tell us what we are to understand by soul and mind and Spirit, — how we should conceive them. So then the physicists come to imagine that the light is there at work quite outside us; this light affects the human eye. The eye somehow responds; at any rate it receives an impression. This then becomes subjective inner experience. Now comes the veriest tangle of confused ideas. The physicists allege it to be much the same as to the other sense-organs. They follow what they learn from the psychologists. In text-books of Psychology you will generally find a chapter on the Science of the Senses, as though such a thing as “sense” or “sense-organ” in general existed. But if you put it to the test: study the eye, — it is completely different from the ear. The one indeed lies above and the other beneath the “ niveau ” which we explained just now. In their whole form and structure, eye and ear prove to be totally diverse organs. This surely is significant and should be borne in mind. Today now we will go thus far; please think it over in the meantime. Taking our start from this, we will tomorrow speak of the science of sound and tone, whence you will then be able to go on into the other realms of Physics. There is however one more thing I want to demonstrate today. It is among the great achievements of modern Physics; it is in truth a very great achievement. You know that if you merely rub a surface with your finger — exerting pressure, using some force as you do so, — the surface will get warm. By this exertion you have generated warmth. So too by calling forth out-and-out mechanical processes in the objective world external to yourself, you can engender warmth. Now as a basis for tomorrow's lecture, we have rigged up this apparatus. If you were now to look and read the thermometer inside, you would find it a little over 16° C. The vessel contains water. Immersed in the body of water is a kind of drum or flywheel which we now bring into quick rotation, thus doing mechanical work, whirling the portions of the water all about, stirring it thoroughly. After a time we shall look at the thermometer again and you will see that it has risen. By dint of purely mechanical work the water will have gained in warmth. That is to say, warmth is produced by mechanical work. It was especially Julius Robert Mayer who drew attention to this fact, which was then worked out more arithmetically. Mayer himself derived from it the so-called “mechanical equivalent of warmth” (or of heat). Had they gone on in the same spirit in which he began, they would have said no more than that a certain number, a certain figure expresses the relation which can be measured when warmth is produced by dint of mechanical work or vice-versa. But they exploited the discovery in metaphysical fashion. Namely they argued: If then there is this constant ratio between the mechanical work expended and the warmth produced, the warmth or heat is simply the work transformed. Transformed, if you please! — where in reality all that they had before them was the numerical expression of the relation between the two.

The Light Course

Lecture VII

https://rsarchive.org/Lectures/GA320/English/GSF1977/19191230p01.html

Stuttgart

30 Dec 1919

GA320-7

My dear Friends, The way of speaking about sound and tone which you will find in the customary description of modern Physics may be said to date back to the 15th century at the earliest. By such examples you will most readily confirm what I so often speak of more generally in Spiritual Science. Namely, before that turning-point in time, man's whole way of thinking was very different from what it then became. The way we speak of the phenomena of sound and tone in the scholastic system of modern Physics came about only gradually. What first caught their attention was the velocity with which sound is propagated. To a first approximation it is not difficult to find what may be interpreted as the speed of propagation of sound. If a gun is fired at some distance from you, you see the flash of light in the distance and hear the report some time later, just as you hear the thunder after you see the lightning. If you neglect that there is such a thing as a velocity of light, you may then call the time that elapses between your perception of the impression of light and your perception of the sound, the time the sound has taken to go the corresponding distance. So you can calculate how quickly the sound advances in air — how far it goes, say, in a second — and you get something like a “velocity of propagation of sound”. This was one of the earliest things to which men became attentive in this domain. They also became attentive to the so-called phenomena of resonance — sympathetic vibration. Leonardo da Vinci was among the first. If for example you twang a violin-string or the like, and another string attuned to it — or even quite a different object that happens to be so attuned — is there in the same room, the other will begin vibrating too. The Jesuits especially took up the study of these things. In the 17th century much was done for the science of sound or tone by the Jesuit Mersenne, who made important researches on what is called the ‘pitch’ of a musical note. A note contains three elements. It has first a certain intensity; secondly a certain pitch; thirdly a certain quality or colouring of sound. The problem is to ascertain what corresponds to the pitch, — to ascertain this from the point of view which, as I said, has gradually been adopted in modern time, — adopted most of all, perhaps, in this branch of Science. I have already drawn your attention to the fact which can indeed easily be ascertained. Whenever we perceive a sound or a musical note, there is always some oscillatory phenomenon that underlies it — or, shall we rather say, accompanies, runs parallel to it. The usual experiments can easily be reproduced, to demonstrate this oscillatory character of air or other bodies. Here is a tuning-fork with a point attached, which as it moves can make a mark in the layer of soot, deposited on this glass plate. We need not actually do all these experiments, but if we did strike the tuning-fork to begin with, the picture on the glass plate would reveal that this tuning-fork is executing regular movements. These forms of movement are naturally conveyed to the air and we may therefore say that when we hear any sounding body the air between it and us is in movement. Indeed we bring the air itself directly into movement in the instruments called pipes. Now scientists have gradually discovered what kind of movement it is. It takes place in ‘longitudinal’ waves, as they are called. This too can be directly demonstrated. We kindle a note in this metallic tube, which we connect with another tube full of air, so that the movements of the metallic tube are communicated to this air. If we then put a very light and mobile dust into the tube that is filled with air, the mobility of the tiny spheres of dust enables us to recognize that the sound is propagated just in this way; first there arises a condensation, a densifying of the air; this will beat back again however as soon as the body oscillates the other way. So there arises a thinning-out, a dilution of the air. Then at the next forward beat of the metal the original condensation goes forward; so then dilutions and condensations alternate. We can thus prove by direct experiment that we are dealing with dilutions and condensations of the air. We really need not do all these experiments; they are at hand, if I may say so. What you can get from the text-books is not what I am here to shew. It is significant indeed, how much was done for these branches of Physics, especially at the beginning of modern time, either by the Jesuits themselves, or else was set on foot by them through all their social connections. Now from this side there was always the strong tendency, above all things, not to enter spiritually into the processes of Nature, — not to penetrate to the spiritual in Nature. The spiritual should be reserved for the religious life. Among the Jesuits it was always looked upon as dangerous to apply to the phenomena of Nature spiritual forms of thought such as we have grown accustomed to through Goethe. They wanted to study Nature in purely materialistic ways, — not to approach Nature with the Spirit. In some respects therefore, the Jesuits were among the first to cultivate the materialistic ideas which are so prevalent today. Historically it is of course well-known, but people fail to reflect that this whole way of thinking, applied to Physics nowadays, is fundamentally a product of the said tendency, characteristically Roman-Catholic as indeed it is. One of the main things we now have to discover is what happens when we perceive notes of different pitch. How do the external phenomena of vibration, which accompany the note, differ with respect to notes of different pitch? The answer can be shewn by such experiments as we are now about to demonstrate. You see this disc with its rows of holes. We can rotate it rapidly. Herr Stockmeyer will be so kind as to direct a stream of air on to the moving disc. (He did.) You can at once distinguish the different pitch of the two notes. How then did it arise? Nearer the centre of the disc are fewer holes, — 40 in fact. When Herr Stockmeyer blew the stream of air on to here, every time it came upon a hole it went through, then in the intervening space it could not get through, then again it could, and so on. Again and again, by the quick motion of the disc, the next hole came where the last had been, and there arose as many beats as there were holes arriving at the place where the stream of air was going. Thus on the inner circle we got 40 beats, but on the outer we got 80 in the same period of time. The beats bring about the wave, the oscillations or vibrations. Thus in the same period of time we have 80 beats, 80 air-waves in the one case and 40 in the other. The note that arises when we have 80 oscillations is twice as high as the note that arises when we have 40. Sundry experiments of this kind shew how the pitch of the note is connected with the number of vibrations arising in the medium in which the sound is propagated. Please take together what I have just been saying and what was said once before; it will then lead you to the following reflection. A single oscillation of condensation and attenuation gives, as regards the distance it has gone through, what we call the wave-length. If n such waves arise in a second and the length of each wave is s , the whole wave-movement must be advancing n times s in a second. The path, the distance therefore, through which the whole wave-movement advances in a second, is n times s . Now please recall what I said in an earlier lecture. I said that we must carefully distinguish all that is “phoronomical” on the one hand, and on the other hand all that which we do not merely think out in our own inner life of thought but which consists of outer realities. In effect, I said, outward realities can never be merely spatial, or arithmetical (able to be numbered and calculated), nor can they be mere displacements. Velocities on the other hand are outward realities, — they always are. And of course this remains so when we come to sound or tone. Neither the s nor the n can be experienced as an external reality, for the s is merely spatial while the n is a mere number. What is real is inherent in the velocity. The velocity contains the real being, the real entity which we are here describing as ‘sound’ or ‘tone’. If I now divide the velocity into two abstractions, in these abstractions I have no realities; I only have what is abstracted, separated out and divided from it. Such are the wave-lengths — the spatial magnitudes — and also the number n. If on the other hand I want to look at the reality of the sound — at what is real in the world outside myself, — then I must concentrate upon the inner faculty of the sound to have velocity. This then will lead me to a qualitative study of the sound, whereas the way of studying it which we have grown accustomed to in modern Physics is merely quantitative. In the theory of sound, in acoustics especially, we see how modern Physics is always prone to insert what can be stated and recorded in these extraneous, quantitative, spatial and temporal, kinematical and arithmetical forms, in place of the qualitative reality which finds expression simply and solely in a certain faculty of speed, or of velocity. Today however, people no longer even notice how they sail off into materialistic channels even in the theory of sound. It is so evident, they may well argue, that the sound as such is not there outside us; outside us are only the oscillations. Could anything be clearer? — so they may well contend. There are the waves of condensation and attenuation. Then, when my ear is in the act of “hearing”, what is really there outside me are these condensations and attenuations; that unknown something within me (which the physicist of course need not go into, — it is not his department) therefore transforms the waves into subjective experiences, — transforms the vibrations of the vibrating bodies into the quality that is the ‘sound’ or ‘tone’. In all manner of variations you will find ever the same proposition. Outside us are the vibrations; in us are the effects of the vibrations — effects that are merely subjective. In course of time it has become part of their very flesh and bone, till such results emerge as you find quoted from Robert Hamerling for instance in my Riddles of Philosophy . Having absorbed and accepted the teachings of Physics, Hamerling says at the very outset: What we experience as the report of a gun, is, in the world outside us, no more nor less than a certain violent disturbance of the air. And from this premise Hamerling continues: Whoever does not believe that the sensory impression he experiences is only there in himself while in the world outside him is simply vibrating air or vibrating ether, — let him put down the book which Hamerling is writing; such books are not for him. Robert Hamerling even goes on to say: Whoever thinks that the picture which he obtains of a horse corresponds to an outward reality, understands nothing at all and had better close the book. Such things, dear Friends, for once deserve to be followed to their logical conclusion. What would become of it if I treated you, who are now sitting here, according to this way of thinking (I do not say method, but way-of-thinking) which physicists have grown accustomed to apply to the phenomena of sound and light? This surely would be the outcome: You, all of you, now sitting here before me, — I only have you here before me through my own impressions, which (if this way of thought be true) are altogether subjective, since my sensations of light and sound are so. None of you are there outside me in the way I see you. Only the oscillations in the air, between you and me, lead me to the oscillations that are there in you, and I am led to the conclusion that all your inner being and life of soul — which, within you and for yourselves, is surely not to be denied — is not there at all. For me, this inner soul of everyone of you who are here seated is only the effect on my own psyche, while for the rest, all that is really there, seated on these benches, are so many heaps of vibrations. If you deny to light and sound the inner life and being which you experience in a seemingly subjective way, it is precisely as it would be if, having you here before me, I looked on all that is before me as merely part of my subjective life, and thus denied to you the experience of inner life and being. What I have now been saying is indeed so obvious, so trite, that physicists and physiologists will naturally not presume that they could ever fall into such obvious mistakes. And yet they do. The whole distinction that is usually made of the subjective impression (or whatsoever is alleged to be subjective) from the objective process, amounts to this and nothing else. It is of course open to the physicist to be quite candid and to say: I, as physicist, am not proposing to investigate the sound or tone at all; I do not enter into what is qualitative. All I am out to investigate are the external, spatial processes (he will not have to call them “objective processes” for that again would beg the question). All I am out to investigate are the outwardly spatial processes, which of course also go on into my own body. These are the subject-matter of my researches. These I abstract from the totality; what is qualitative is no concern of mine. A man who speaks like this is at least candid and straightforward, only he must not then go on to say that the one is “objective” and the other “subjective”, or that the one is the “effect” of the other. What you experience in your soul, — when I experience it with you it is not the effect upon me of the vibrations of your brain. To see through a thing like that is of untold significance; nothing could be of greater importance for the requirements of the new age, not only in science but in the life of humanity at large. We ought not to be too reluctant to go into deeper questions when dealing with these matters. How easily it can be argued that the uniquely oscillatory character of sound or tone is evident if only from the fact that if I twang a violin-string a second string in the same room, attuned to the same note, will resound too, this being due to the fact that the intervening medium propagates the accompanying oscillations. Yet we do not understand what is happening in such a case unless we bring it into connection with a more widespread phenomenon. I mean the following for instance, — it has in fact been observed. You have a pendulum clock; you wind it up and start it. In the same room there is another pendulum clock; it must, admittedly, be of a certain type. This you do not wind up. In favourable circumstances you may observe that the second clock starts of its own accord. We will call this the “mutual sympathy” of phenomena; it can be investigated in a very wide domain. The last phenomenon of this type, still connected to some extent with the outer world, could be examined far more than it generally is, for it is very frequent. Times without number you may have this experience. You are at table with another person and he says something you yourself have just been thinking. You were thinking it but did not say it; he now utters it. It is the sympathetic going-together of events (or complexes of events) in some way attuned to one-another, which is here making itself felt in a highly spiritual realm. We need to recognize the whole range of continuity from the simple resonance of a violin-string which one may still interpret crudely and unspiritually within the sequence of outer material events, to these parallel phenomena which appear so much more spiritual — as when we experience one-another's thoughts. Now we shall never gain insight into these things unless we have the will to see and understand how man himself is placed into the midst even of so-called physical Nature. A few days ago we were demonstrating and to some extent analyzing the human eye. Today we will do the same with the human ear. As we go inward in the eye, you will remember we come to the vitreous body, which, as we said, still has considerable vitality. Then there is the fluid between the lens and the cornea. As we go inward, we were saying, the eye gets ever more alive and vital, whereas the outer part is increasingly like a piece of physical apparatus. Now we can of course equally well describe the human ear, and in a purely external sense we may aver: Just as the light affects the eye and the optic nerve receives the stimulus, so do the oscillations of sound affect the ear. They go on into the external auditory canal and beat upon the drum which forms the inner end of this canal. Behind the drum are the minute bones or ossicles, called hammer, anvil and stirrup from their appearance. That which arises (speaking in terms of Physics) in the outer world and finds expression in waves of alternate compression and expansion in the air, is transmitted through this peculiar system of ossicles to the inner ear. There is the so-called cochlea, filled with a kind of fluid, and here the auditory nerve has its ending. Before the cochlea we come to the three semicircular canals, — their planes at right angles to each other according to the three dimensions of space. Thus we can imagine the sound penetrating here in the form of air-waves and transmitted by the ossicles until it comes into this fluid. There then it reaches the nerve and so affects the sentient brain. So we should have the eye as one sense-organ, the ear — another. We put them neatly side by side, and — for a further abstraction — we may even elaborate a general physiology of the senses and of sensation. But it will not seem so simple if you recall what I said recently of the whole rhythm of the ascending and descending cerebrospinal fluid and how it interacts with what is taking place more externally in the outer air. Remember too what I was saying: a thing may look complete and self-contained when outwardly regarded, but we must not therefore take it to be a finished reality, for it need not be so at all. The rose I cut off from the shrub is no reality. It cannot be by itself. It can only come to existence by virtue of its connection with the whole rose-bush. If I think of it as a mere rose by itself, it is in truth an abstraction. I must go on to the totality — to the whole rose-bush at the very least. So too for hearing: the ear alone is no reality, though it is nearly always represented as such in this connection. What is transmitted inward through the ear must first interact in a certain way with the inner rhythm, manifested in the rise and fall of the cerebrospinal fluid. But we have still not reached the end. All this that takes its course in rhythm — and, as it were, includes the brain within its span — is also fundamental, in the real human being, to what appears in quite another part of our body, namely in the larynx and adjoining organs when we are speaking. There is the act of speaking, — its instruments quite obviously inserted into the breathing process, to which the rhythmic rise and fall of the cerebrospinal fluid is also due. In the whole rhythm which arises in you when you breathe, you can therefore insert on the one hand your active speaking and on the other hand your hearing. Then you will have a totality; it only comes to manifestation in a more intelligent or perceptive way in your hearing and in a more volitional way in your speaking. Once more, you only have a totality when you take together the more volitional element pulsating through the larynx and the more sensitive or intelligent that goes through the ear. To separate the ear on the one hand, the larynx on the other, is an abstraction; you have no real totality so long as you separate these two. The two belong together; this is a matter of fact and you need to see it. The physiological physicist or physical physiologist who studies the larynx and the ear apart from one-another proceeds as you would do if you cut up a human being so as to bring him to life instead of seeing things in living interaction. If we have recognized the facts, this is what we shall see:— Consider what is left of the eye if I first take away the vitreous body and also the whole or at least part of what is here spread out — the retina (Figure IIIf). If I were able to remove all this, what would be left would be the ciliary muscle, the lens and the external liquid — the aqueous humour. What kind of organ would that represent? It would be an organ, my dear Friends, which I could never compare with the ear if I were thinking realistically, but only with the larynx. It is not a metamorphosis of the ear; it is a metamorphosis of the larynx. Only to touch upon the coarsest aspect: just as the muscles of the larynx take hold of the vocal chords, widening or narrowing the aperture between them, so do the ciliary muscles with the lens. The lens is inherently mobile and they take hold of it. So far I should have separated-out what is larynx-like, so to speak, for the ethereal, even as the larynx is for the air. And if I now reinsert first the retina, then the vitreous body, and then for certain animals the pecten, which man only has etherically, or the falciform process, (blood-bearing organs, continued into the eye in certain lower animals), — this part alone I shall be able truly to relate to the ear. Such things as the expanding portions of the pecten, these I may rightly compare to what expands in the ear, — in the labyrinth and so on. Thus, at one level in the human body I have the eye. In its more inward parts it is a metamorphosed ear, enveloped from without by a metamorphosed larynx. If we take larynx and ear together as a single whole, we have a metamorphosed eye upon another level. What I have now been pointing out will lead us presently along a most important path. We can have no real knowledge of these things if we relate them falsely to begin with by simply placing eye and ear side by side, whereas in truth the ear can only be compared to the part of the eye behind the lens — the inner and more vital part — while that which reaches farther forward and is more muscular in character must be related to the larynx. This of course makes the theory of metamorphosis more difficult. It is no use looking for metamorphoses in crude, external ways. You must be able to see into the inner dynamic qualities, for these are real. If it be so however, my dear Friends, we shall no longer be able to conceive as parallel, without more ado, all that goes on in the phenomena of tone and sound on the one hand and on the other hand the phenomena of light. Having begun with the mistaken premise that eye and ear are equally sense-organs, we shall be no less mistaken in our approach to the related phenomena. My seeing in effect is fundamentally different from my hearing. When I am seeing, the same thing happens in my eye as when I hear and speak at the same time. Here, in a higher realm, an activity which can only be compared to the activity of speech accompanies the receptive activity as such — the perceiving, receiving activity of the eye. You will get nowhere in these realms unless you apprehend what is real. For if you once become aware that in the eye two things are welded together which are assigned to seemingly distinct organs of the body in sound or hearing, then you will realize that in seeing, in the eye, we have a kind of monologue, — as when you converse and come to an understanding with yourself. The eye always proceeds as you would do if you were listening intently and every time, to understand what you were hearing, you first repeated it aloud. Such is the eye's activity, — it is as though you were listening to someone and at the same time repeating what you heard, word for word. The other person says, “he writes”, but this does not suffice you. You first repeat aloud, “he writes”, — then and then only is the thing complete. So it is with the eye and the phenomena of light. What comes into our consciousness as an outcome of this whole complex — namely through the fact that we have the more vital, inner part of the eye to begin with — only becomes the full experience of sight, in that we reproduce it in the portion of the eye that corresponds to the larynx and that lies farther forward. Etherically we are talking to ourselves when we are seeing. The eye is engaged in a monologue, and it is wrong to compare the outcome of this monologue — in which the human being's own activity is already contained — with hearing alone, for this is but a single factor of the dual process. I do believe, dear Friends, that if you work it through for yourselves this will give you much indeed. For it will shew you among other things how far astray materialistic Physics goes and how unreal it becomes in its study of the World, in that it starts by comparing what is not directly comparable — the eye and ear in this instance. It is this purely outward way of study — failing to look and see what are totalities and what are not — which leads away from any spiritual view of Nature. Think for example of what Goethe does at the conclusion of his Theory of Colour , where in the chapter on the “Ethical-Aesthetical Effects of Colour” he evolves the spiritual logically from what is physical. You will never do this if you take your start from the colour-theory of modern Physics. Now I admit that sound or tone may cause misgivings. Is it not evident that in the outer world mere oscillations are going on when you hear sound? (In some such words it will be stated.) However, ask yourselves another question and then decide whether the very putting of it does not give the answer. Might it not be as follows? Suppose you had a globe or bell-jar, full of air, provided with an aperture and stopcock. Open the stopcock, — nothing will happen if the air inside has the same density as outside. But if there is a vacuum inside, plenty will happen. Air from outside will whistle in and fill the empty space. Will you then say that the air which the globe now contains came into being simply by virtue of what was going on inside the globe? No. You will say: This air has come in from outside, but the empty space — purely to describe the phenomenon as you see it — has somehow sucked it in. So also when we turn this disc and blow against the holes, we create the conditions for a kind of suction to arise, — this is a true way to describe it. The tone, the sound that will appear when as I work the siren I cause the air to oscillate, — this tone is already in existence, only it is outside of space. It is not yet in space. The conditions for it to enter space are not given until I make them, even as the conditions for the outer air to get into the globe are not given until I make them. The outer air-waves can only be compared to the vacuum inside the globe, and what then grows audible can only be compared to what penetrates from the surrounding space into the vacuum inside when the conditions have been created for this to happen. In essence the air-waves have no more to do with the sound than that, where these waves are, a process of suction is produced to draw the sound from its non-spatial realm into the spatial. Of course the kind of sound, the particular tone that is drawn in, is modified by the kind of air-waves, but so too would it modify what happens in the evacuated globe if I made special-shaped channels in the aperture by which the air is to be drawn in. The air would then expand into the inner space along certain lines, of which an image was there. So have the processes of sound or tone their external image in the observed processes of oscillation. You see from this, dear Friends, the fundamentals of a true Physical Science, which we aspire to, are not so easy to conceive. It is by no means enough to entertain a few mathematical notions about wave-movements or oscillations. We must make greater demands on the qualitative element in human thinking. If such demands are unfulfilled, we only get once more the picture of the World which is so worshipped in the Physics of today, and which is to reality as is a tissue-paper effigy to a living man.

The Light Course

Lecture VIII

https://rsarchive.org/Lectures/GA320/English/GSF1977/19191231p01.html

Stuttgart

31 Dec 1919

GA320-8

My dear Friends, I am sorry these explanations have had to be so improvised and brief, so that they scarcely go beyond mere aphorisms. It is inevitable. All I can do during these days is to give you a few points of view, with the intention of continuing when I am here again, so that in time these explanations may be rounded off, to give you something more complete. Tomorrow I will give a few concluding aspects, also enabling us to throw some light on the educational use of scientific knowledge. Now to prepare for tomorrow, I must today draw your attention to the development of electrical discoveries, beginning no doubt with things that are well-known to you from your school days. This will enable us, in tomorrow's lecture, to gain a more comprehensive view of Physics as a whole. You know the elementary phenomena of electricity. A rod of glass, or it may be of resin, is made to develop a certain force by rubbing it with some material. The rod becomes, as we say, electrified; it will attract small bodies such as bits of paper. You know too what emerged from a more detailed observation of these phenomena. The forces proceeding from the glass rod, and from the rod of resin or sealing-wax, prove to be diverse. We can rub either rod, so that it gets electrified and will attract bits of paper. If the electrical permeation, brought about with the use of the glass rod, is of one kind, with the resinous rod it proves to be opposite in kind. Using the qualitative descriptions which these phenomena suggest, one speaks of vitreous and resinous electricities respectively; speaking more generally one calls them “positive” and “negative”. The vitreous is then the positive, the resinous the negative. Now the peculiar thing is that positive electricity always induces and brings negative toward itself in some way. You know the phenomenon from the so-called Leyden Jar. This is a vessel with an electrifiable coating on the outside. Then comes an insulating layer (the substance of the vessel). Inside, there is another coating, connected with a metal rod, ending perhaps in a metallic knob (Figure IXa). If you electrify a metal rod and impart the electricity to the one coating, so that this coating will then evince the characteristic phenomena, say, of positive electricity, the other coating thereby becomes electrified negatively. Then, as you know, you can connect the one coating, imbued with positive, and the other, imbued with negative electricity, so as to bring about a connection of the electrical forces, positive and negative, with one another. You have to make connection so that the one electricity can be conducted out here, where it confronts the other. They confront each other with a certain tension, which they seek to balance out. A spark leaps across from the one to the other. We see how the electrical forces, when thus confronting one another, are in a certain tension, striving to resolve it. No doubt you have often witnessed the experiment. Here is the Leyden Jar, — but we shall also need a two-pronged conductor to discharge it with. I will now charge it. The charge is not yet strong enough. You see the leaves repelling one another just a little. If we charged this sufficiently, the positive electricity would so induce the negative that if we brought them near enough together with a metallic discharger we should cause a spark to fly across the gap. Now you are also aware that this kind of electrification is called frictional electricity, since the force, whatever it may be, is brought about by friction. And — here again, I am presumably still recalling what you already know — it was only at the turn of the 18th and 19th centuries that they discovered, in addition to this “frictional electricity”, what is called “contact electricity”, thus opening up to modern Physics a domain which has become notably fruitful in the materialistic evolution of this science. I need only remind you of the main principles. Galvani observed the leg of a frog which was in touch with metal plates and began twitching. He had discovered something of very great significance. He had found two things at once, truth to tell, — two things that should really be distinguished from one-another and are not yet quite properly distinguished, unhappily for Science, to this day. Galvani had discovered what Volta, a little later, was able to describe simply as “contact electricity”, namely the fact that when diverse metals are in contact, and their contact is also mediated by the proper liquids, an interaction arises — an interaction which can find expression in the form of an electric current from the one metal to the other. We have then the electric current, taking place to all appearances purely within the inorganic realm. But we have something else as well, if once again we turn attention to the discovery made by Galvani. We have what may in some sense be described as “physiological electricity”. It is a force of tension which is really always there between muscle and nerve and which can be awakened when electric currents are passed through them. So that in fact, that which Galvani had observed contained two things. One of them can be reproduced by purely inorganic methods, making electric currents by means of different metals with the help of liquids. The other thing which he observed is there in every organism and appears prominently in the electric fishes and certain other creatures. It is a state of tension between muscle and nerve, which, when it finds release, becomes to all appearances very like flowing electricity and its effects. It was then these discoveries which led upon the one hand to the great triumphs in materialistic science, and on the other hand provided the foundations for the immense and epoch-making technical developments which followed. Now the fact is, the 19th century was chiefly filled with the idea that we must somehow find a single, abstract, unitary principle at the foundation of all the so-called “forces of Nature”. It was in this direction, as I said before that they interpreted what Julius Robert Mayer, the brilliant Heilbronn doctor had discovered. You will remember how we demonstrated it the other day. By mechanical force we turned a flywheel; this was attached to an apparatus whereby a mass of water was brought into inner mechanical activity. The water thereby became warmer, as we were able to shew. The effect produced — the development of warmth — may truly be attributed to the mechanical work that was done. All this was so developed and interpreted in course of time that they applied it to the most manifold phenomena of Nature, — nor was it difficult to do so within certain limits. One could release chemical forces and see how warmth arose in the process. Again, reversing the experiment which we have just described, warmth could be used in such a way as to evoke mechanical work, — as in the steam-engine and in a multitude of variations. It was especially this so-called transformation of Nature's forces on which they riveted attention. They were encouraged to do this by what began in Julius Robert Mayer's work and then developed ever further. For it proves possible to calculate, down to the actual figures, how much warmth is needed to produce a given, measurable amount of work; and vice-versa, how much mechanical work is needed to produce a given, measurable amount of warmth or heat. So doing, they imagined — though to begin with surely there is no cause to think of it in this way — that the mechanical work, which we expended for example in making these vanes rotate in the water, has actually been transformed into the warmth. Again, they assumed that when warmth is applied in the steam-engine, this warmth is actually transformed into the mechanical work that emerges. The meditations of physicists during the 19th century kept taking this direction: they were always looking for the kinship between the diverse forces of Nature so-called, — trying to discover kinships which were to prove at last that some abstract, everywhere equal principle is at the bottom of them all, diverse and manifold as they appear. These tendencies were crowned to some extent when near the end of the century Heinrich Hertz, a physicist of some genius, discovered the so-called electric waves — here once again it was waves! It certainly seemed to justify the idea that the electricity that spreads through space is in some way akin to the light that spreads through space, — the latter too being already conceived at that time as a wave-movement in the ether. That “electricity” — notably in the form of current electricity — cannot be grasped so simply with the help of primitive mechanical ideas, but makes it necessary to give our Physics a somewhat wider and more qualitative aspect, — this might already have been gathered from the existence of induction currents as they are called. Only to indicate it roughly: the flow of an electric current along a wire will cause a current to arise in a neighbouring wire, by the mere proximity of the one wire to the other. Electricity is thus able to take effect across space, — so we may somehow express it. Now Hertz made this very interesting discovery:— he found that the electrical influences or agencies do in fact spread out in space in a way quite akin to the spreading of waves, or to what could be imagined as such. He found for instance that if you generate an electric spark, much in the way we should be doing here, developing the necessary tension, you can produce the following result. Suppose we had a spark jumping across this gap. Then at some other point in space we could put two such “inductors”, as we may call them, opposite and at a suitable distance from one-another, and a spark would jump across here too. This, after all, is a phenomenon not unlike what you would have if here for instance — Figure IXb — were a source of light and here a mirror. A cylinder of light is reflected, this is then gathered up again by a second mirror, and an image arises here. We may then say, the light spreads out in space and takes effect at a distance. In like manner. Hertz could now say that electricity spreads out and the effect of it is perceptible at a distance. Thus in his own conception and that of other scientists he had achieved pretty fair proof that with electricity something like a wave-movement is spreading out through space, — analogous to the way one generally imagines wave-movements to spread out. Even as light spreads out through space and takes effect at a distance, unfolding as it were, becoming manifest where it encounters other bodies, so too can the electric waves spread out, becoming manifest — taking effect once more — at a distance. You know how wireless telegraphy is based on this. The favourite idea of 19th century physicists was once again fulfilled to some extent. For sound and light, they were imagining wave-trains, sequences of waves. Also for warmth as it spreads outward into space, they had begun to imagine wave-movements, since the phenomena of warmth are in fact similar in some respects. Now they could think the same of electricity; the waves had only to be imagined long by comparison. It seemed like incontrovertible proof that the way of thinking of 19th century Physics had been right. Nevertheless, Hertz's experiments proved to be more like a closing chapter of the old. What happens in any sphere of life, can only properly be judged within that sphere. We have been undergoing social revolutions. They seem like great and shattering events in social life since we are looking rather intently in their direction. Look then at what has happened in Physics during the 1890's and the first fifteen years, say, of our century; you must admit that a revolution has here been going on, far greater in its domain than the external revolution in the social realm. It is no more nor less than that in Physics the old concepts are undergoing complete dissolution; only the physicists are still reluctant to admit it. Hertz's discoveries were still the twilight of the old, tending as they did to establish the old wave-theories even more firmly. What afterwards ensued, and was to some extent already on the way in his time, was to be revolutionary. I refer now to those experiments where an electric current, which you can generate of course and lead to where you want it, is conducted through a glass tube from which the air has to a certain extent been pumped out, evacuated. The electric current, therefore, is made to pass through air of very high dilution. High tension is engendered in the tubes which you here see. In effect, the terminals from which the electricity will discharge into the tube are put far apart — as far as the length of the tube will allow. There is a pointed terminal at either end, one where the positive electricity will discharge (i.e. the positive pole) at the one end, so too the negative at the other. Between these points the electricity discharges; the coloured line which you are seeing is the path taken by the electricity. Thus we may say: What otherwise goes through the wires, appears in the form in which you see it here when it goes through the highly attenuated air. It becomes even more intense when the vacuum is higher. Look how a kind of movement is taking place from the one side and the other, — how the phenomenon gets modified. The electricity which otherwise flows through the wire: along a portion of its path we have been able, as it were, so to treat it that in its interplay with other factors it does at last reveal, to some extent, its inner essence. It shews itself, such as it is; it can no longer hide in the wire! Observe the green light on the glass; that is fluorescent light. I am sorry I cannot go into these phenomena in greater detail, but I should not get where I want to in this course if I did not go through them thus quickly. You see what is there going through the tube, — you see it in a highly dispersed condition in the highly attenuated air inside the tube. Now the phenomena which thus appeared in tubes containing highly attenuated air or gas, called for more detailed study, in which many scientists engaged, — and among these was Crookes. Further experiments had to be made on the phenomena in these evacuated tubes, to get to know their conditions and reactions. Certain experiments, due among others to Crookes, bore witness to a very interesting fact. Now that they had at last exposed it — if I may so express myself — the inner character of electricity, which here revealed itself, proved to be very different from what they thought of light for instance being propagated in the form of wave-movements through the ether. What here revealed itself was clearly not propagated in that way. Whatever it is that is shooting through these tubes is in fact endowed with remarkable properties, strangely reminiscent of the properties of downright matter. Suppose you have a magnet or electromagnet. (I must again presume your knowledge of these things; I cannot go into them all from the beginning.) You can attract material objects with the magnet. Now the body of light that is going through this tube — this modified form, therefore, of electricity — has the same property. It too can be attracted by the electromagnet. Thus it behaves, in relation to a magnet, just as matter would behave. The magnetic field will modify what is here shooting through the tube. Experiments of this kind led Crookes and others to the idea that what is there in the tube is not to be described as a wave-movement, propagated after the manner of the old wave-theories. Instead, they now imagined material particles to be shooting through the space inside the tube; these, as material particles, are then attracted by the magnetic force. Crookes therefore called that which is shot across there from pole to pole, (or howsoever we may describe it; something is there, demanding our consideration),— Crookes called it “radiant matter”. As a result of the extreme attenuation, he imagined, the matter that is left inside the tube has reached a state no longer merely gaseous but beyond the gaseous condition. He thinks of it as radiant matter — matter, the several particles of which are raying through space like the minutest specks of dust or spray, the single particles of which, when charged electrically, will shoot through space in this way. These particles themselves are then attracted by the electromagnetic force. Such was his line of thought: the very fact that they can thus be attracted shews that we have before us a last attenuated remnant of real matter, not a mere movement like the old-fashioned ether-movements. It was the radiations (or what appeared as such) from the negative electric pole, known as the cathode, which lent themselves especially to these experiments. They called them “cathode rays”. Herewith the first breach had, so to speak, been made in the old physical conceptions. The process in these Hittorf tubes (Hittorf had been the first to make them, then came Geissler) was evidently due to something of a material kind — though in a very finely-divided condition — shooting through space. Not that they thereby knew what it was; in any case they did not pretend to know what so-called “matter” is. But the phenomena indicated that this was something somehow identifiable with matter, — of a material nature. Crookes therefore was convinced that this was a kind of material spray, showering through space. The old wave-theory was shaken. However, fresh experiments now came to light, which in their turn seemed inconsistent with Crookes's theory. Lenard in 1893 succeeded in diverting the so-called rays that issue from this pole and carrying them outward. He inserted a thin wall of aluminium and led the rays out through this. The question arose: can material particles go through a material wall without more ado? So then the question had to be raised all over again: Is it really material particles showering through space, — or is it something quite different after all? In course of time the physicists began to realize that it was neither the one nor the other: neither of the old conceptions — that of ether-waves, or that of matter — would suffice us here. The Hittorf tubes were enabling them, as it were, to pursue the electricity itself along its hidden paths. They had naturally hoped to find waves, but they found none. So they consoled themselves with the idea that it was matter shooting through space. This too now proved untenable. At last they came to the conclusion which was in fact emerging from many and varied experiments, only a few characteristic examples of which I have been able to pick out. In effect, they said: It isn't waves, nor is it simply a fine spray of matter. It is flowing electricity itself; electricity as such is on the move. Electricity itself is flowing along here, but in its movement and in relation to other things — say, to a magnet — it shews some properties like those of matter. Shoot a material cannonball through the air and let it pass a magnet, — it will naturally be diverted So too is electricity. This is in favour of its being of a material nature. On the other hand, in going through a plate of aluminium without more ado, it shews that it isn't just matter. Matter would surely make a hole in going through other matter. So then they said: This is a stream of electricity as such. And now this flowing electricity shewed very strange phenomena. A clear direction was indeed laid out for further study, but in pursuing this direction they had the strangest experiences. Presently they found that streams were also going out from the other pole, — coming to meet the cathode rays. The other pole is called the anode; from it they now obtained the rays known as “canal rays”. In such a tube, they now imagined there to be two different kinds of ray, going in opposite directions. One of the most interesting things was discovered in the 1890's by Roentgen ... From the cathode rays he produced a modified form of rays, now known as Roentgen rays or X -rays. They have the effect of electrifying certain bodies, and also shew characteristic reactions with magnetic and electric forces. Other discoveries followed. You know the Roentgen rays have the property of going through bodies without producing a perceptible disturbance; they go through flesh and bone in different ways and have thus proved of great importance to Anatomy and Physiology. Now a phenomenon arose, making it necessary to think still further. The cathode rays or their modifications, when they impinge on glass or other bodies, call forth a kind of fluorescence; the materials become luminous under their influence. Evidently, said the scientists, the rays must here be undergoing further modification. So they were dealing already with many different kinds of rays. Those that first issued directly from the negative pole, proved to be modifiable by a number of other factors. They now looked round for bodies that should call forth such modifications in a very high degree — bodies that should especially transform the rays into some other form, e.g. into fluorescent rays. In pursuit of these researches it was presently discovered that there are bodies — uranium salts for example — which do not have to be irradiated at all, but under certain conditions will emit rays in their turn, quite of their own accord. It is their own inherent property to emit such rays. Prominent among these bodies were the kind that contain radium, as it is called. Very strange properties these bodies have. They ray-out certain lines of force — so to describe it — which can be dealt with in a remarkable way. Say that we have a radium-containing body here, in a little vessel made of lead; we can examine the radiation with a magnet. We then find one part of the radiation separating off, being deflected pretty strongly in this direction by the magnet, so that it takes this form (Figure IXc). Another part stays unmoved, going straight on in this direction, while yet another is deflected in the opposite direction. The radiation, then, contains three elements. They no longer had names enough for all the different kinds! They therefore called the rays that will here be deflected towards the right, ß -rays; those that go straight on, γ -rays; and those are deflected in the opposite direction, α -rays. Bringing a magnet near to the radiating body, studying these deflections and making certain computations, from the deflection one may now deduce the velocity of the radiation. The interesting fact emerges that the ß -rays have a velocity, say about nine-tenths the velocity of light, while the velocity of the α -rays is about one-tenth the velocity of light. We have therefore these explosions of force, if we may so describe them, which can be separated-out and analyzed and then reveal very striking differences of velocity. Now I remind you how at the outset of these lectures we endeavoured in a purely spiritual way to understand the formula, v = s/t . We said that the real thing in space is the velocity; it is velocity which justifies us in saying that a thing is real. Here now you see what is exploding as it were, forth from the radiating body, characterized above all by the varying intensity and interplay of the velocities which it contains. Think what it signifies: in the same cylinder of force which is here raying forth, there is one element that wants to move nine times as fast as the other. One shooting force, tending to remain behind, makes itself felt as against the other that tends to go nine times as quickly. Now please pay heed a little to what the anthroposophists alone, we must suppose, have hitherto the right not to regard as sheer madness! Often and often, when speaking of the greatest activities in the Universe which we can comprehend, we had to speak of differences in velocity as the most essential thing. What is it brings about the most important things that play into the life of present time? It is the different velocities with which the normal, the Luciferic and the Ahrimanic spiritual activities work into one-another. It is that differences of velocity are there in the great spiritual streams to which the web and woof of the world is subjected. The scientific pathway which has opened out in the most recent times is compelling even Physics — though, to begin with, unconsciously — to go into differences of velocity in a way very similar to the way Spiritual Science had to do for the great all-embracing agencies of Cosmic Evolution. Now we have not yet exhausted all that rays forth from this radium-body. The effects shew that there is also a raying-forth of the material itself. But the material thus emanated proves to be radium no longer. It presently reveals itself to be helium for instance — an altogether different substance. Thus we no longer have the conservation, — we have the metamorphosis of matter. The phenomena to which I have been introducing you, all of them take their course in what may be described as the electrical domain. Moreover, all of them have one property in common. Their relation to ourselves is fundamentally different from that of the phenomena of sound or light for example, or even the phenomena of warmth. In light and sound and warmth we ourselves are swimming, so to speak, as was described in former lectures. The same cannot be said so simply of our relation to the electrical phenomena. We do not perceive electricity as a specific quality in the way we perceive light, for instance. Even when electricity is at last obliged to reveal itself, we perceive it by means of a phenomenon of light. This led to people's saying, what they have kept repeating: “There is no sense-organ for electricity in man.” The light has built for itself in man the eye — a sense-organ with which to see it. So has the sound, the ear. For warmth too, a kind of warmth-organ is built into man. For electricity, they say, there is nothing analogous. We perceive electricity indirectly. We do, no doubt; but that is all that can be said of it till you go forward to the more penetrating form of Science which we are here at least inaugurating. In effect, when we expose ourselves to light, we swim in the element of light in such a way that we ourselves partake in it with our conscious life, or at least partially so. So do we in the case of warmth and in that of sound or tone. The same cannot be said of electricity. But now I ask you to remember what I have very often explained: as human beings we are in fact dual beings. That is however to put it crudely, for we are really threefold beings: beings of Thought, of Feeling and of Will. Moreover, as I have shewn again and again, it is only in our Thinking that we are really awake, whilst in our feelings we are dreaming and in our processes of will we are asleep — asleep even in the midst of waking life. We do not experience our processes of will directly. Where the essential Will is living, we are fast asleep. And now remember too, what has been pointed out during these lectures. Wherever in the formulae of Physics we write m for mass , we are in fact going beyond mere arithmetic — mere movement, space and time. We are including what is no longer purely geometrical or kinematical, and as I pointed out, this also corresponds to the transition of our consciousness into the state of sleep. We must be fully clear that this is so. Consider then this memberment of the human being; consider it with fully open mind, and you will then admit: Our experience of light, sound and warmth belongs — to a high degree at least, if not entirely — to the field which we comprise and comprehend with our sensory and thinking life. Above all is this true of the phenomena of light. An open-minded study of the human being shews that all these things are akin to our conscious faculties of soul. On the other hand, the moment we go on to the essential qualities of mass and matter , we are approaching what is akin to those forces which develop in us when we are sleeping. And we are going in precisely the same direction when we descend from the realm of light and sound and warmth into the realm of the electrical phenomena. We have no direct experience of the phenomena of our own Will; all we are able to experience in consciousness is our thoughts about them. Likewise we have no direct experience of the electrical phenomena of Nature. We only experience what they deliver, what they send upward, to speak, into the realms of light and sound and warmth etc. For we are here crossing the same boundary as to the outer world, which we are crossing in ourselves when we descend from our thinking and idea-forming, conscious life into our life of Will. All that is light, and sound, and warmth, is then akin to our conscious life, while all that goes on in the realms of electricity and magnetism is akin — intimately akin — to our unconscious life of Will. Moreover the occurrence of physiological electricity in certain lower animals is but the symptom — becoming manifest somewhere in Nature — of a quite universal phenomenon which remains elsewhere unnoticed. Namely, wherever Will is working through the metabolism, there is working something very similar to the external phenomena of electricity and magnetism. When in the many complicated ways — which we have only gone through in the barest outline in today's lecture — when in these complicated ways we go down into the realm of electrical phenomena, we are in fact descending into the very same realm into which we must descend whenever we come up against the simple element of mass. What are we doing then when we study electricity and magnetism? We are then studying matter , in all reality. It is into matter itself that you are descending when you study electricity and magnetism. And what an English philosopher has recently been saying is quite true — very true indeed. Formerly, he says, we tried to imagine in all kinds of ways, how electricity is based on matter. Now on the contrary we must assume, what we believe to be matter, to be in fact no more than flowing electricity. We used to think of matter as composed of atoms; now we must think of the electrons , moving through space and having properties like those we formerly attributed to matter. In fact our scientists have taken the first step — they only do not yet admit it — towards the overcoming of matter. Moreover they have taken the first step towards the recognition of the fact that when in Nature we pass on from the phenomena of light, sound and warmth of those of electricity, we are descending — in the realm of Nature — into phenomena which are related to the former ones as is the Will in us to the life of Thought. This is the gist and conclusion of our studies for today, which I would fain impress upon your minds. After all, my main purpose in these lectures is to tell you what you will not find in the text-books. The text-book knowledge I may none the less bring forward, is only given as a foundation for the other.

The Light Course

Lecture IX

https://rsarchive.org/Lectures/GA320/English/GSF1977/19200102p01.html

Stuttgart

2 Jan 1920

GA320-9

My dear Friends, I will now bring these few improvised hours of scientific study to a provisional conclusion. I want to give you a few guiding lines which may help you in developing such thoughts about Nature for yourselves, taking your start from characteristic facts which you can always make visible by experiment. In Science today — and this applies above all to the teacher — it is most important to develop a right way of thinking upon the facts and phenomena presented to us by Nature. You will remember what I was trying to shew yesterday in this connection. I shewed how since the 1890's physical science has so developed that materialism is being lifted right out of its bearings, so to speak, even by Physics itself. This is the point to remember above all in this connection. The period when Science thought that it had golden proofs of the universality of waves and undulations was followed, as we say, by a new time. It was no longer possible to hold fast to the old wave-theories. The last three decades have in fact been revolutionary. One can imagine nothing more revolutionary in any realm than this most recent period has been in Physics. Impelled by the very facts that have not emerged, Physics has suffered no less a loss than the concept of matter itself in its old form. Out of the old ways of thinking, as we have seen, the phenomena of light had been brought into a very near relation to those of electricity and magnetism. Now the phenomena produced by the passage of electricity through tubes in which the air or gas was highly rarefied, led scientists to see in the raying light itself something like radiating electricity. I do not say that they were right, but this idea arose. It came about in this way:— The electric current until then had always been hidden as it were in wires, and one had little more to go on than Ohm's Law. Now one was able, so to speak, to get a glimpse of the electricity itself, for here it leaves the wire, jumps to the distant pole, and is no longer able as it were to conceal its content in the matter through which it passes. The phenomena proved complicated. As we say yesterday, manifold types of radiation emerged. The first to be discovered were the so-called cathode rays, issuing from the negative pole of the Hittorf tube and making their way through the partial vacuum. In that they can be deflected by magnetic forces, they prove akin to what we should ordinarily feel to be material. Yet they are also evidently akin to what we see where radiations are at work. This kinship comes out most vividly when we catch the rays (or whatsoever it is that is issuing from the negative electric pole) upon a screen or other object, as we should do with light. Light throws a shadow. So do these radiations. Yet in this very experiment we are again establishing the near relation of these rays to the ordinary element of matter. For you can imagine that a bombardment is taking place from here (as we say yesterday, this is how Crookes thinks of the cathode rays). The “bombs” do not get through the screen which you put in the way; the space behind the screen is protected. This can be shewn by Crookes's experiment, interposing a screen in the way of the cathode rays. We will here generate the electric current; we pass it through this tube in which the air is rarefied. It has its cathode or negative pole here, its anode or positive pole here. Sending the electricity through the tube, we are now getting the so-called cathode rays. We catch them on a screen shaped like a St. Andrew's cross. We let the cathode rays impinge on it, and on the other side you will see something like a shadow of the St. Andrew's cross, from which you may gather that the cross stops the rays. Observe it clearly, please. Inside the tube is the St. Andrew's cross. The cathode rays go along here; here they are stopped by the cross; the shadow of the cross becomes visible upon the wall of the vessel behind it. I will now bring the shadow which is thus made visible into the field of a magnet. I beg you to observe it now. You will find the shadow influenced by the magnetic field. You see then, just as I might attract a simple bit of iron with a magnet, so too, what here emerges like a kind of shadow behaves like external matter. It behaves materially. Here then we have a type of rays which Crookes regards as “radiant matter” — as a form of matter neither solid, liquid or gaseous but even more attenuated, — revealing also that electricity itself, the current of electricity, behaves like simple matter. We have, as it were, been trying to look at the current of flowing electricity as such, and what we see seems very like the kind of effects we are accustomed to see in matter. I will now shew you, what was not possible yesterday, the rays that issue from the other pole and that are called “canal rays”. You can distinguish the rays from the cathode, going in this direction, shimmering in a violet shade of colour, and the canal rays coming to meet them, giving a greenish light. The velocity of the canal rays is much smaller. Finally I will shew you the kind of rays produced by this apparatus: they are revealed in that the glass becomes fluorescent when we send the current through. This is the kind of rays usually made visible by letting them fall upon a screen of barium platinocyanide. They have the property of making the glass intensely fluorescent. Please observe the glass. You see it shining with a very strong, greenish-yellow, fluorescent light. The rays that shew themselves in this way are the Roentgen rays or X-rays, mentioned yesterday. We observe this kind too, therefore. Now I was telling you how in the further study of these things it appeared that certain entities, regarded as material substances, emit sheaves of rays — rays of three kinds, to begin with. We distinguished them as \(\alpha\)-, \(\beta\)-, and \(\gamma\)-rays (cf. the Figure IXc). They shew distinct properties. Moreover, yet another thing emerges from these materials, known as radium etc. It is the chemical element itself which as it were gives itself up completely. In sending out its radiation, it is transmuted. It changes into helium, for example; so it becomes something quite different from what it was before. We have to do no longer with stable and enduring matter but with a complete metamorphosis of phenomena. Taking my start from these facts, I now want to unfold a point of view which may become for you an essential way, not only into these phenomena but into those of Nature generally. The Physics of the 19th century chiefly suffered from the fact that the inner activity, with which man sought to follow up the phenomena of Nature, was not sufficiently mobile in the human being himself. Above all, it was not able really to enter the facts of the outer world. In the realm of light, colours could be seen arising, but man had not enough inner activity to receive the world of colour into his forming of ideas, into his very thinking. Unable any longer to think the colours, scientists replaced the colours, which they could not think, by what they could, — namely by what was purely geometrical and kinematical — calculable waves in an unknown ether. This “ether” however, as you must see, proved a tricky fellow. Whenever you are on the point of catching it, it evades you. It will not answer the roll-call. In these experiments for instance, revealing all these different kinds of rays, the flowing electricity has become manifest to some extent, as a form of phenomenon in the outer world, — but the “ether” refuses to turn up. In fact it was not given to the 19th-century thinking to penetrate into the phenomena. But this is just what Physics will require from now on. We have to enter the phenomena themselves with human thinking. Now to this end certain ways will have to be opened up — most of all for the realm of Physics. You see, the objective powers of the World, if I may put it so, — those that come to the human being rather than from him — have been obliging human thought to become rather more mobile (albeit, in a certain sense, from the wrong angle). What men regarded as most certain and secure, that they could most rely on, was that they could explain the phenomena so beautifully by means of arithmetic and geometry — by the arrangement of lines, surfaces and bodily forms in space. But the phenomena in these Hittorf tubes are compelling us to go more into the facts. Mere calculations begin to fail us here, if we still try to apply them in the same abstract way as in the old wave-theory. Let me say something of the direction from which it first began, that we were somehow compelled to bring more movement into our geometrical and arithmetical thinking. Geometry, you know, was a very ancient science. The regularities and laws in line and triangle and quadrilateral etc., — the way of thinking all these forms in pure Geometry — was a thing handed down from ancient time. This way of thinking was now applied to the external phenomena presented by Nature. Meanwhile however, for the thinkers of the 19th century, the Geometry itself began to grow uncertain. It happened in this way. Put yourselves back into your school days: you will remember how you were taught (and our good friends, the Waldorf teachers, will teach it too, needless to say; they cannot but do so), — you were undoubtedly taught that the three angles of a triangle (Figure Xa) together make a straight angle — an angle of 180°. Of course you know this. Now then we have to give our pupils some kind of proof, some demonstration of the fact. We do it by drawing a parallel to the base of the triangle through the vertex. We then say: the angle \(\alpha\), which we have here, shews itself here again as \(\alpha'\). \(\alpha\) and \(\alpha'\) are alternate angles and therefore equal. I can transfer this angle over here, then. Likewise this angle \(\beta\), over here; again it remains the same. The angle \(\gamma\) stays where it is. If then I have \(\gamma = \gamma'\), \(\alpha = \alpha'\) and \(\beta=\beta'\), while \(\alpha'+\beta;' + \gamma'\) taken together give an angle of 180° as they obviously do, \(\alpha + \beta + \gamma\) will do the same. Thus I can prove it so that you actually see it. A clearer or more graphic proof can scarcely be imagined. However, what we are taking for granted is that this upper line A'B' is truly parallel to the lower line \(AB\), — for this alone enables me to carry out the proof. Now in the whole of Euclid's Geometry there is no way of proving that two lines are really parallel, i.e. that they only meet at an infinite distance, or do not meet at all. They only look parallel so long as I hold fast to a space that is merely conceived in thought. I have no guarantee that it is so in any real space. I need only assume that the two lines meet, in reality, short of an infinite distance; then my whole proof, that the three angles together make 180°, breaks down. For I should then discover: whilst in the space which I myself construct in thought — the space of ordinary Geometry — the three angles of a triangle add up to 180° exactly, it is no longer so when I envisage another and perhaps more real space. The sum of the angles will no longer be 180°, but may be larger. That is to say, besides the ordinary geometry handed down to us from Euclid other geometries are possible, for which the sum of the three angles of a triangle is by no means 180°. Nineteenth century thinking went a long way in this direction, especially since Lobachevsky, and from this starting-point the question could not but arise: Are then the processes of the real world — the world we see and examine with our senses — ever to be taken hold of in a fully valid way with geometrical ideas derived from a space of our own conceiving? We must admit: the space which we conceive in thought is only thought. Nice as it is to cherish the idea that what takes place outside us partly accords with what we figure-out about it, there is no guarantee that it really is so. There is no guarantee that what is going on in the outer world does really work in such a way that we can fully grasp it with the Euclidean Geometry which we ourselves think out. Might it not be — the facts alone can tell — might it not be that the processes outside are governed by quite another geometry, and it is only we who by our own way of thinking first translate this into Euclidean geometry and all the formulae thereof? In a word, if we only go by the resources of Natural Science as it is today, we have at first no means whatever of deciding, how our own geometrical or kinematical ideas are related to what appears to us in outer Nature. We calculate Nature's phenomena in the realm of Physics — we calculate and draw them in geometrical figures. Yet, are we only drawing on the surface after all, or are we penetrating to what is real in Nature when we do so? What is there to tell? If people once begin to reflect deeply enough in modern Science — above all in Physics — they will then see that they are getting no further. They will only emerge from the blind alley if they first take the trouble to find out what is the origin of all our phoronomical — arithmetical, geometrical and kinematical — ideas. What is the origin of these, up to and including our ideas of movement purely as movement, but not including the forces? Whence do we get these ideas? We may commonly believe that we get them on the same basis as the ideas we gain when we go into the outer facts of Nature and work upon them with our reason. We see with our eyes and hear with our ears. All that our senses thus perceive, — we work upon it with our intellect in a more primitive way to begin with, without calculating, or drawing it geometrically, or analyzing the forms of movement. We have quite other categories of thought to go on when our intellect is thus at work on the phenomena seen by the senses. But if we now go further and begin applying to what goes on in the outer world the ideas of “scientific” arithmetic and algebra, geometry and kinematics, then we are doing far more — and something radically different. For we have certainly not gained these ideas from the outer world. We are applying ideas which we have spun out of our own inner life. Where then do these ideas come from? That is the cardinal question. Where do they come from? The truth is, these ideas come not from our intelligence — not from the intelligence which we apply when working up the ideas derived from sense-perception. They come in fact from the intelligent part of our Will. We make them with our Will-system — with the volitional part of our soul. The difference is indeed immense between all the other ideas in which we live as intelligent beings and on the other hand the geometrical, arithmetical and kinematical ideas. The former we derive from our experience with the outer world; these on the other hand — the geometrical, the arithmetical ideas — rise up from the unconscious part of us, from the Will-part which has its outer organ in the metabolism. Our geometrical ideas above all spring from this realm; they come from the unconscious in the human being. And if you now apply these geometrical ideas (I will say “geometrical” henceforth to represent the arithmetical and algebraic too) to the phenomena of light or sound, then in your process of knowledge you are connecting, what arises from within you, with what you are perceiving from without. In doing so you remain utterly unconscious of the origin of the geometry you use. You unite it with the external phenomena, but you are quite unconscious of its source. So doing, you develop theories such as the wave-theory of light, or Newton's corpuscular theory, — it matters not which one it is. You develop theories by uniting what springs from the unconscious part of your being with what presents itself to you in conscious day-waking life. Yet the two things do not directly belong to one-another. They belong as little, my dear Friends, as the idea-forming faculty which you unfold when half-asleep belongs directly to the outer things which in your dreaming, half-asleep condition you perceive. In anthroposophical lectures I have often given instances of how the dream is wont to symbolize. An undergraduate dreams that at the door of the lecture-theatre he gets involved in a quarrel. The quarrel grows in violence; at last they challenge one-another to a duel. He goes on dreaming: the duel is arranged, they go out into the forest, he sees himself firing the shot, — and at the moment he wakes up. A chair has fallen over. This was the impact which projected itself forward into the dream. The idea-forming faculty has indeed somehow linked up with the outer phenomenon, but in a merely symbolizing way, — in no way consistent with the real object. So too, what in your geometrical and phoronomical thinking you fetch up from the subconscious part of your being, when you connect it with the phenomena of light. What you then do has no other value for reality than what finds expression in the dream when symbolizing an objective fact such as the fall and impact of the chair. All this elaboration of the outer world — optical, acoustic and even thermal to some extent (the phenomena of warmth) — by means of geometrical, arithmetical and kinematical thought-forms, is in point of fact a dreaming about Nature. Cool and sober as it may seem, it is a dream — a dreaming while awake. Moreover, until we recognize it for what it is, we shall not know where we are in our Natural Science, so that our Science gives us reality. What people fondly believe to be the most exact of Sciences, is modern mankind's dream of Nature. But it is different when we go down from the phenomena of light and sound, via the phenomena of warmth, into the realm we are coming into with these rays and radiations, belonging as they do to the science of electricity. For we then come into connection with what in outer Nature is truly equivalent to the Will in Man. The realm of Will in Man is equivalent to this whole realm of action of the cathode rays, canal rays, Roentgen rays. \(\alpha\)-, \(\beta\)- and \(\gamma\)-rays and so on. It is from this very realm — which, once again, is in the human being the realm of Will, — it is from this that there arises what we possess in our mathematics, in our geometry, in our ideas of movement. These therefore are the realms, in Nature and in Man, which we may truly think of as akin to one-another. However, human thinking has in our time not yet gone far enough, really to think its way into these realms. Man of today can dream quite nicely, thinking out wave-theories and the like, but he is not yet able to enter with real mathematical perception into that realm of phenomena which is akin to the realm of human Will, in which geometry and arithmetic originate. For this, our arithmetical, algebraical and geometrical thinking must in themselves become more saturated with reality. It is along these lines that physical science should now seek to go. Nowadays, if you converse with physicists who were brought up in the golden age of the old wave-theory, you will find many of them feeling a little uncanny about these new phenomena, in regard to which ordinary methods of calculation seem to break down in so many places. In recent times the physicists have had recourse to a new device. Plain-sailing arithmetical and geometrical methods proving inadequate, they now introduce a kind of statistical method. Taking their start more from the outer empirical data, they have developed numerical relations also empirical in kind. They then use the calculus of probabilities. Along these lines it is permissible to say: By all means let us calculate some law of Nature; it will hold good throughout a certain series, but then there comes a point where it no longer works. There are indeed many things like this in modern Physics, — very significant moments where they lose hold of the thought, yet in the very act of losing it get more into reality. Conceivably for instance, starting from certain rigid ideas about the nature of a gas or air under the influence of warmth and in relation to its surroundings, a scientist of the past might have proved with mathematical certainty that air could not be liquefied. Yet air was liquefied, for at a certain point it emerged that the ideas which did indeed embrace the prevailing laws of a whole series of facts, ceased to hold good at the end of this series. Many examples might be cited. Reality today — especially in Physics — often compels the human being to admit this to himself: “You with your thinking, with your forming of ideas, no longer fully penetrate into reality; you must begin again from another angle.” We must indeed; and to do this, my dear Friends, we must become aware of the kinship between all that comes from the human Will — whence come geometry and kinematics — and on the other hand what meets us outwardly in this domain that is somehow separated from us and only makes its presence known to us in the phenomena of the other pole. For in effect, all that goes on in these vacuum tubes makes itself known to us in phenomena of light, etc. Whatever is the electricity itself, flowing through there, is imperceptible in the last resort. Hence people say: If only we had a sixth sense — a sense for electricity — we should perceive it too, directly. That is of course wide of the mark. For it is only when you rise to Intuition, which has its ground in the Will, it is only then that you come into that region — even of the outer world — where electricity lives and moves. Moreover when you do so you perceive that in these latter phenomena you are in a way confronted by the very opposite than in the phenomena of sound or tone for instance. In sound or in musical tone, the very way man is placed into this world of sound and tone — as I explained in a former lecture — means that he enters into the sound or tone with his soul and only with his soul. What he then enters into with his body, is no more than what sucks-in the real essence of the sound or tone. I explained this some days ago; you will recall the analogy of the bell-jar from which the air has been pumped out. In sound or tone I am within what is most spiritual, while what the physicist observes (who of course cannot observe the spiritual nor the soul) is but the outer, so-called material concomitant, the movement of the wave. Not so in the phenomena of the realm we are now considering, my dear Friends. For as I enter into these, I have outside me not only the objective, so-called material element, but also what in the case of sound and tone is living in me — in the soul and spirit. The essence of the sound or tone is of course there in the outer world as well, but so am I. With these phenomena on the other hand, what in the case of sound could only be perceived in soul, is there in the same sphere in which — for sound — I should have no more than the material waves. I must now perceive physically, what in the case of sound or tone I can only perceive in the soul. Thus in respect of the relation of man to the external world the perceptions of sound, and the perceptions of electrical phenomena for instance, are at the very opposite poles. When you perceive a sound you are dividing yourself as it were into a human duality. You swim in the elements of wave and undulation, the real existence of which can of course be demonstrated by quite external methods. Yet as you do so you become aware; herein is something far more than the mere material element. You are obliged to kindle your own inner life — your life of soul — to apprehend the tone itself. With your ordinary body — I draw it diagrammatically (the oval in Figure Xb) — you become aware of the undulations. You draw your ether— and astral body together, so that they occupy only a portion of your space. You then enjoy, what you are to experience of the sound or tone as such, in the thus inwarded and concentrated etheric-astral part of your being. It is quite different when you as human being meet the phenomena of this other domain, my dear Friends. In the first place there is no wave or undulation or anything like that for you to dive into; but you now feel impelled to expand what in the other case you concentrated (Figure Xc). In all directions, you drive your ether— and astral body out beyond your normal surface; you make them bigger, and in so doing you perceive these electrical phenomena. Without including the soul and spirit of the human being, it will be quite impossible to gain a true or realistic conception of the phenomena of Physics. Ever-increasingly we shall be obliged to think in this way. The phenomena of sound and tone and light are akin to the conscious element of Thought and Ideation in ourselves, while those of electricity and magnetism are akin to the sub-conscious element of Will. Warmth is between the two. Even as Feeling is intermediate between Thought and Will, so is the outer warmth in Nature intermediate between light and sound on the one hand, electricity and magnetism on the other. Increasingly therefore, this must become the inner structure of our understanding of the phenomena of Nature. It can indeed become so if we follow up all that is latent in Goethe's Theory of Colour. We shall be studying the element of light and tone on the one hand, and of the very opposite of these — electricity and magnetism — on the other. As in the spiritual realm we differentiate between the Luciferic, that is akin to the quality of light, and the Ahrimanic, akin to electricity and magnetism, so also must we understand the structure of the phenomena of Nature. Between the two lies what we meet with in the phenomena of Warmth. I have thus indicated a kind of pathway for this scientific realm, — a guiding line with which I wished provisionally to sum up the little that could be given in these few improvised hours. It had to be arranged so quickly that we have scarcely got beyond the good intentions we set before us. All I could give were a few hints and indications; I hope we shall soon be able to pursue them further. Yet, little as it is, I think what has been given may be of help to you — and notably to the Waldorf School teachers among you when imparting scientific notions to the children. You will of course not go about it in a fanatical way, for in such matters it is most essential to give the realities a chance to unfold. We must not get our children into difficulties. But this at least we can do: we can refrain from bringing into our teaching too many untenable ideas — ideas derived from the belief that the dream-picture which has been made of Nature represents actual reality. If you yourselves are imbued with the kind of scientific spirit with which these lectures — if we may take them as a fair example — have been pervaded, it will assuredly be of service to you in the whole way you speak with the children about natural phenomena. Methodically too, you may derive some benefit. I am sorry it was necessary to go through the phenomena at such breakneck speed. Yet even so, you will have seen that there is a way of uniting what we see outwardly in our experiments with a true method of evoking thoughts and ideas, so that the human being does not merely stare at the phenomena but really thinks about them. If you arrange your lessons so as to get the children to think in connection with the experiments — discussing the experiments with them intelligently — you will develop a method, notably in the Science lessons, whereby these lessons will be very fruitful for the children who are entrusted to you. Thus by the practical example of this course, I think I may have contributed to what was said in the educational lectures at the inception of the Waldorf School. I believe therefore that in arranging these scientific courses we shall also have done something for the good progress of our Waldorf School, which ought really to prosper after the good and very praiseworthy start which it has made. The School was meant as a beginning in a real work for the evolution of our humanity — a work that has its fount in new resources of the Spirit. This is the feeling we must have. So much is crumbling, of all that has developed hitherto in human evolution. Other and new developments must come in place of what is breaking down. This realization in our hearts and minds will give the consciousness we need for the Waldorf School. In Physics especially it becomes evident, how many of the prevailing ideas are in decay. More than one thinks, this is connected with the whole misery of our time. When people think sociologically, you quickly see where their thinking goes astray. Admittedly, here too most people fail to see it, but you can at least take notice of it; you know that sociological ways of thought will find their way into the social order of mankind. On the other hand, people fail to realize how deeply the ideas of Physics penetrate into the life of mankind. They do not know what havoc has in fact been wrought by the conceptions of modern Physics, terrible as these conceptions often are. In public lectures I have often quoted Hermann Grimm. Admittedly, he saw the scientific ideas of his time rather as one who looked upon them from outside. Yet he spoke not untruly when he said, future generations would find it difficult to understand that there was once a world so crazy as to explain the evolution of the Earth and Solar System by the theory of Kant and Laplace. To understand such scientific madness would not be easy for a future age, thought Hermann Grimm. Yet in our modern conceptions of inorganic Nature there are many features like the theory of Kant and Laplace. And you must realize how much is yet to do for the human beings of our time to get free of the ways of Kant and Konigsberg and all their kindred. How much will be to do in this respect, before they can advance to healthy, penetrating ways of thought! Strange things one witnesses indeed from time to time, shewing how what is wrong on one side joins up with what is wrong on another. What of a thing like this? Some days ago — as one would say, by chance — I was presented with a reprint of a lecture by a German University professor. (He prides himself in this very lecture that there is in him something of Kant and Konigsberg!) It was a lecture in a Baltic University, on the relation of Physics and Technics, held on the 1st of May 1918, — please mark the date! This learned physicist of our time in peroration voices his ideal, saying in effect: The War has clearly shewn that we have not yet made the bond between Militarism and the scientific laboratory work of our Universities nearly close enough. For human progress to go on in the proper way, a far closer link must in future be forged between the military authorities and what is being done at our Universities. Questions of mobilization in future must include all that Science can contribute, to make the mobilization still more effective. At the beginning of the War we suffered greatly because the link was not yet close enough — the link which we must have in future, leading directly from the scientific places of research into the General Staffs of our armies. Mankind, my dear Friends, must learn anew, and that in many fields. Once human beings make up their minds to learn anew in such a realm as Physics, they will be better prepared to learn anew in other fields as well. Those physicists who go on thinking in the old way, will never be so very far removed from the delightful coalition between the scientific laboratories and the General Staffs. How many things will have to alter! So may the Waldorf School be and remain a place where the new things which mankind needs can spring to life. In the expression of this hope, I will conclude our studies for the moment.

The Light Course

Lecture X

https://rsarchive.org/Lectures/GA320/English/GSF1977/19200103p01.html

Stuttgart

3 Jan 1920

GA320-10

My dear friends, The present course of lectures will constitute a kind of continuation of the one given when I was last here. I will begin with those chapters of physics which are of especial importance for laying a satisfactory foundation for a scientific world view, namely the observations of heat relations in the world. Today I will try to lay out for you a kind of introduction to show the extent to which we can create a body of meaningful views of a physical sort within a general world view. This will show further how a foundation may be secured for a pedagogical impulse applicable to the teaching of science. Today we will therefore go as far as we can towards outlining a general introduction. The theory of heat, so-called, has taken a form during the 19th century which has given a great deal of support to a materialistic view of the world. It has done so because in heat relationships it is very easy to turn one's glance away from the real nature of heat, from its being, and to direct it to the mechanical phenomena arising from heat. Heat is first known through sensations of cold, warmth, lukewarm, etc. But man soon learns that there appears to be something vague about these sensations, something subjective. A simple experiment which can be made by anyone shows this fact. Imagine you have a vessel filled with water of a definite temperature, \(t\); on the right of it you have another vessel filled with water of a temperature \(t-t_1\), that is of a temperature distinctly lower than the temperature in the first vessel. In addition, you have a vessel filled with water at a temperature \(t+t_1\). When now, you hold your fingers in the two outer vessels you will note by your sensations the heat conditions in these vessels. You can then plunge your fingers which have been in the outer vessels into the central vessel and you will see that to the finger which has been in the cold water the water in the central vessel will feel warm, while to the finger which has been in the warm water, the water in the central vessel will feel cold. The same temperature therefore is experienced differently according to the temperature to which one has previously been exposed. Everyone knows that when he goes into a cellar, it may feel different in winter from the way it feels in summer. Even though the thermometer stands at the same point circumstances may be such that the cellar feels warm in the winter and cool in the summer. Indeed, the subjective experience of heat is not uniform and it is necessary to set an objective standard by which to measure the heat condition of any object or location. Now, I need not here go into the elementary phenomena or take up the elementary instruments for measuring heat. It must be assumed that you are acquainted with them. I will simply say that when the temperature condition is measured with a thermometer, there is a feeling that since we measure the degree above or below zero, we are getting an objective temperature measurement. In our thinking we consider that there is a fundamental difference between this objective determination in which we have no part and the subjective determination, where our own organization enters into the experience. For all that the 19th century has striven to attain it may be said that this view on the matter was, from a certain point of view, fruitful and justified by its results. Now, however, we are in a time when people must pay attention to certain other things if they are to advance their way of thinking and their way of life. From science itself must come certain questions simply overlooked in such conclusions as those I have given. One question is this: Is there a difference, a real objective difference, between the determination of temperature by my organism and by a thermometer, or do I deceive myself for the sake of getting useful practical results when I bring such a difference into my ideas and concepts? This whole course will be designed to show why today such questions must be asked. From the principal questions it will be my object to proceed to those important considerations which have been overlooked owing to exclusive attention to the practical life. How they have been lost for us on account of the attention to technology you will see. I would like to impress you with the fact that we have completely lost our feeling for the real being of heat under the influence of certain ideas to be described presently. And, along with this loss, has gone the possibility of bringing this being of heat into relation with the human organism itself, a relation which must be all means be established in certain aspects of our life. To indicate to you in a merely preliminary way the bearing of these things on the human organism, I may call your attention to the fact that in many cases we are obliged today to measure the temperature of this organism, as for instance, when it is in a feverish condition. This will show you that the relation of the unknown being of heat to the human organism has considerable importance. Those extreme conditions as met with in chemical and technical processes will be dealt with subsequently. A proper attitude toward the relation of the unknown being of heat to the human organism has considerable importance. Those extreme conditions as met with in chemical and technical processes will be dealt with subsequently. A proper attitude toward the relation of the heat-being to the human organism cannot, however, be attained on the basis of a mechanical view of heat. The reason is, that in so doing, one neglects the fact that the various organs are quite different in their sensitiveness to this heat-being, that the heart, the liver, the lungs differ greatly in their capacity to react to the being of heat . Through the purely physical view of heat no foundation is laid for the real study of certain symptoms of disease, since the varying capacity to react to heat of the several organs of the body escapes attention. Today we are in no position to apply to the organic world the physical views built up in the course of the 19th century on the nature of heat. This is obvious to anyone who has an eye to see the harm done by modern physical research, so-called, in dealing with what might be designated the higher branches of knowledge of the living being. Certain questions must be asked, questions that call above everything for clear, lucid ideas. In the so-called “exact science,” nothing has done more harm than the introduction of confused ideas. What then does it really mean when I say, if I put my fingers in the right and left hand vessels and then into a vessel with a liquid of an intermediate temperature, I get different sensations? Is there really something in the conceptual realm that is different from the so-called objective determination with the thermometer? Consider now, suppose you put thermometers in these two vessels in place of your fingers. You will then get different readings depending on whether you observe the thermometer in the one vessel or the other. If then you place the two thermometers instead of your fingers into the middle vessel, the mercury will act differently on the two. In the one it will rise; in the other it will fall. You see the thermometer does not behave differently from your sensations. For the setting up of a view of the phenomenon, there is no distinction between the two thermometers and the sensation from your finger. In both cases exactly the same thing occurs, namely a difference is shown from the immediately preceding conditions. And the thing our sensation depends on is that we do not within ourselves have any zero or reference point. If we had such a reference point then we would establish not merely the immediate sensation but would have apparatus to relate the temperature subjectively perceived, to such a reference point. We would then attach to the phenomenon just as we do with the thermometers something which really is not inherent in it, namely the variation from the reference point. You see, for the construction of our concept of the process there is no difference. It is such questions as these that must be raised today if we are to clarify our ideas, or all the present ideas on these things are really confused. Do not imagine for a moment that this is of no consequence. Our whole life process is bound up with this fact that we have in us no temperature reference point. If we could establish such a reference point within ourselves, it would necessitate an entirely different state of consciousness, a different soul life. It is precisely because the reference point is hidden for us that we lead the kind of life we do. You see, many things in life, in human life and in the animal organism, too, depend on the fact that we do not perceive certain processes. Think what you would have to do if you were obliged to experience subjectively everything that goes on in your organism. Suppose you had to be aware of all the details of the digestive process. A great deal pertaining to our condition of life rests on this fact that we do not bring into our consciousness certain things that take place in our organism. Among these things is that we do not carry within us a temperature reference point — we are not thermometers. A subjective-objective distinction such as is usually made is not therefore adequate for a comprehensive grasp of the physical. It is this which has been the uncertain point in human thinking since the time of ancient Greeks. It had to be so, but it cannot remain so in the future. For the old Grecian philosophers, Zeno in particular, had already orientated human thinking about certain processes in a manner strikingly opposed to outer reality. I must call your attention to these things even at the risk of seeming pedantic. Let me recall to you the problem of Achilles and the tortoise, a problem I have often spoken about. Let us assume we have the distance traveled by Achilles in a certain time \(a\). This represents the rate at which he can travel. And here we have the tortoise \(s\), who has a start on Achilles. Let us take the moment when Achilles gets to the point marked \(1\). The tortoise is ahead of him. Since the problem stated that Achilles has to cover every point covered by the tortoise, the tortoise will always be a little ahead and Achilles can never catch up. But, the way people would consider it is this. You would say, yes, I understand the problem all right, but Achilles would soon catch the tortoise. The whole thing is absurd. But if we reason that Achilles must cover the same path as the tortoise and the tortoise is ahead, he will never catch the tortoise. Although people would say this is absurd, nevertheless the conclusion is absolutely necessary and nothing can be urged against it. It is not foolish to come to this conclusion but on the other hand, it is remarkably clever considering only the logic of the matter. It is a necessary conclusion and cannot be avoided. Now what does all this depend on? It depends on this: that as long as you think, you cannot think otherwise than the premise requires. As a matter of fact, you do not depend on thinking strictly, but instead you look at the reality and you realize that it is obvious that Achilles will soon catch the tortoise. And in doing this you uproot thinking by means of reality and abandon the pure thought process. There is no point in admitting the premises and then saying, “Anyone who thinks this way is stupid.” Through thinking alone we can get nothing out of the proposition but that Achilles will never catch the tortoise. And why not? Because when we apply our thinking absolutely to reality, then our conclusions are not in accord with the facts. They cannot be. When we turn our rationalistic thought on reality it does not help us at all that we establish so-called truths which turn out not to be true. For we must conclude if Achilles follows the tortoise that he passes through each point that the tortoise passes through. Ideally this is so; in reality he does nothing of the kind. His stride is greater than that of the tortoise. He does not pass through each point of the path of the tortoise. We must, therefore, consider what Achilles really does, and not simply limit ourselves to mere thinking. Then we come to a different result. People do not bother their heads about these things but in reality they are extraordinarily important. Today especially, in our present scientific development, they are extremely important. For only when we understand that much of our thinking misses the phenomena of nature if we go from observation to so-called explanation, only in this case will we get the proper attitude toward these things. The observable, however, is something which only needs to be described. That I can do the following for instance, calls simply for a description: here I have a ball which will pass through this opening. We will now warm the ball slightly. Now you see it does not go through. It will only go through when it has cooled sufficiently. As soon as I cool it by pouring this cold water on it, the ball goes through again. This is the observation, and it is this observation that I need only describe. Let us suppose, however, that I begin to theorize. I will do so in a sketchy way with the object merely of introducing the matter. Here is the ball; it consists of a certain number of small parts — molecules, atoms, if you like. This is not observation, but something added to observation in theory. At this moment, I have left the observed and in doing so I assume an extremely tragic role. Only those who are in a position to have insight into these things can realize this tragedy. For you see, if you investigate whether Achilles can catch the tortoise, you may indeed begin by thinking “Achilles must pass over every point covered by the tortoise and can never catch it.” This may be strictly demonstrated. Then you can make an experiment. You place the tortoise ahead and Achilles or some other who does not run even so fast as Achilles, in the rear. And at any time you can show that observation furnishes the opposite of what you conclude from reasoning. The tortoise is soon caught. When, however, you theorize about the sphere, as to how its atoms and molecules are arranged, and when you abandon the possibility of observation, you cannot in such a case look into the matter and investigate it — you can only theorize. And in this realm you will do no better than you did when you applied your thinking to the course of Achilles. That is to say, you carry the whole incompleteness of your logic into your thinking about something which cannot be made the object of observation. This is the tragedy. We build explanation upon explanation while at the same time we abandon observation, and think we have explained things simply because we have erected hypotheses and theories. And the consequence of this course of forced reliance on our mere thinking is that this same thinking fails us the moment we are able to observe. It no longer agrees with the observation. You will remember I already pointed out this distinction in the previous course when I indicated the boundary between kinematics and mechanics. Kinematics describes mere motion phenomena or phenomena as expressed by equations, but it is restricted to verifying the data of observation. The moment we pass over from kinematics to mechanics where force and mass concepts are brought in, at this moment, we cannot rely on thinking alone, but we begin simply to read off what is given from observation of the phenomena. With unaided thought we are not able to deal adequately even with the simplest physical process where mass plays a role. All the 19th century theories, abandoned now to a greater or lesser extent, are of such a nature that in order to verify them it would be necessary to make experiments with atoms and molecules. The fact that they have been shown to have a practical application in limited fields makes no difference. The principle applies to the small as well as to the large. You remember how I have often in my lectures called attention to something which enters into our considerations now wearing a scientific aspect. I have often said: From what the physicists have theorized about heat relations and from related things they get certain notions about the sun. They describe what they call the “physical conditions” on the sun and make certain claims that the facts support the description. Now I have often told you, the physicists would be tremendously surprised if they could really take a trip to the sun and could see that none of their theorizing based on terrestrial conditions agreed with the realities as found on the sun. These things have a very practical value at the present, a value for the development of science in our time. Just recently news has gone forth to the world that after infinite pains the findings of certain English investigators in regard to the bending of starlight in cosmic space have been confirmed and could now be presented before a learned society in Berlin. It was rightly stated there “the investigations of Einstein and others on the theory of relativity have received a certain amount of confirmation. But final confirmation could be secured only when sufficient progress had been made to make spectrum analysis showing the behavior of the light at the time of an eclipse of the sun. Then it would be possible to see what the instruments available at present failed to determine.” This was the information given at the last meeting of the Berlin Physical Society. It is remarkably interesting. Naturally the next step is to seek a way really to investigate the light of the sun by spectrum analysis. The method is to be by means of instruments not available today. Then certain things already deduced from modern scientific ideas may simply be confirmed. As you know it is thus with many things which have come along from time to time and been later clarified by physical experiments. But, people will learn to recognize the fact that it is simply impossible for men to carry over to conditions on the sun or to the cosmic spaces what may be calculated from those heat phenomena available to observation in the terrestrial sphere . It will be understood that the sun's corona and similar phenomena have antecedents not included in the observations made under terrestrial conditions. Just as our speculations lead us astray when we abandon observation and theorize our way through a world of atoms and molecules, so we fall into error when we go out into the macrocosm and carry over to the sun what we have determined from observations under earth conditions. Such a method has led to the belief that the sun is a kind of glowing gas ball, but the sun is not a glowing ball of gas by any means. Consider a moment, you have matter here on the earth. All matter on the earth has a certain degree of intensity in its action. This may be measured in one way or another, be density or the like, in any way you wish, it has a definite intensity of action. This may become zero. In other words, we may have empty space. But the end is not yet. That empty space is not the ultimate condition I may illustrate to you by the following: Assume to yourselves that you had a boy and that you said, “He is a rattle-brained fellow. I have made over a small property to him but he has begun to squander it. He cannot have less than zero. He may finally have nothing, but I comfort myself with the thought that he cannot go any further once he gets to zero!” But you may now have a disillusionment. The fellow begins to get into debt. Then he does not stop at zero; the thing gets worse than zero. It has a very real meaning. As his father, you really have less if he gets into debt than if he stopped when he had nothing. The same sort of thing, now, applies to the condition on the sun. It is not usually considered as empty space but the greatest possible rarefaction is thought of and a rarefied glowing gas is postulated. But what we must do is to go to a condition of emptiness and then go beyond this. It is in a condition of negative material intensity. In the spot where the sun is will be found a hole in space. There is less there than empty space. Therefore all the effects to be observed in the sun must be considered as attractive forces not as pressures of the like. The sun's corona, for instance, must not be thought of as it is considered by the modern physicist. It must be considered in such a way that we have the consciousness not of forces radiating outward as appearances would indicate, but of attractive force from the hole in space, from the negation of matter. Here our logic fails us. Our thinking is not valid here, for the receptive organ or the sense organ through which we perceive it is our entire body. Our whole body corresponds in this sensation to the eye in the case of light. There is no isolated organ, we respond with our whole body to the heat conditions. The fact that we may use our finger to perceive a heat condition, for instance, does not militate against this fact. The finger corresponds to a portion of the eye. While the eye therefore is an isolated organ and functions as such to objectify the world of light as color, this is not the case for heat. We are heat organs in our entirety. On this account, however, the external condition that gives rise to heat does not come to us in so isolated a form as does the condition which gives rise to light. Our eye is objectified within our organism. We cannot perceive heat in an analogous manner to light because we are one with the heat. Imagine that you could not see colors with your eye but only different degrees of brightness, and that the colors as such remained entirely subjective, were only feelings. You would never see colors; you would speak of light and dark, but the colors would evoke in you no response and it is thus with the perception of heat. Those differences which you perceive in the case of light on account of the fact that your eye is an isolated organ, such differences you do not perceive at all in the case of heat. They live in you . Thus when you speak of blue and red, these colors are considered as objective. When the analogous phenomenon is met in the case of heat, that which corresponds to the blue and the red is within you. It is you yourself. Therefore you do not define it. This requires us to adopt an entirely different method for the observation of the objective being of heat from the method we use of the objective being of light . Nothing had so great a misleading effect on the observers of the 19th century as this general tendency to unify things schematically. You find everywhere in physiologies a “sense physiology.” Just as though there were such a thing! As though there were something of which it could be said, in general, “it holds for the ear as for the eye, or even for the sense of feeling or for the sense of heat. It is an absurdity to speak of a sense physiology and to say that a sense perception is this or that. It is possible only to speak of the perception of the eye by itself, or the perception of the ear by itself and likewise of our entire organism as heat sense organ, etc. They are very different things. Only meaningless abstractions result from a general consideration of the senses. But you find everywhere the tendency towards such a generalizing of these things. Conclusions result that would be humorous were they not so harmful to our whole life. If someone says — Here is a boy, another boy has given him a thrashing. Also then it is asserted — Yesterday he was whipped by his teacher; his teacher gave him a thrashing. In both cases there is a thrashing given; there is no difference. Am I to conclude from this that the bad boy who dealt out today's whipping and the teacher who administered yesterday's are moved by the same inner motives? That would be an absurdity; it would be impossible. But now, the following experiment is carried out: it is known that when light rays are allowed to fall on a concave mirror, under proper conditions they become parallel. When these are picked up by another concave mirror distant form the first they are concentrated and focused so that an intensified light appears at the focus. The same experiment is made with so-called heat rays. Again it may be demonstrated that these too can be focused — a thermometer will show it — and there is a point of high heat intensity produced. Here we have the same process as in the case of the light; therefore heat and light are fundamentally the same sort of thing. The thrashing of yesterday and the one of today are the same sort of thing. If a person came to such a conclusion in practical life, he would be considered a fool. In science, however, as it is pursued today, he is no fool, but a highly respected individual. It is on account of things like this that we should strive for clear and lucid concepts, and without these we will not progress. Without them physics cannot contribute to a general world view. In the realm of physics especially it is necessary to attain to these obvious ideas. You know quite well from what was made clear to you, at least to a certain extent, in my last course, that in the case of the phenomena of light, Goethe brought some degree of order into the physics of that particular class of facts, but no recognition has been given to him. In the field of heat the difficulties that confront us are especially great. This is because in the time since Goethe the whole physical consideration of heat has been plunged into a chaos of theoretical considerations. In the 19th century the mechanical theory of heat as it is called has resulted in error upon error. It has applied concepts verifiable only by observation to a realm not accessible to observation. Everyone who believes himself able to think, but who in reality may not be able to do so, can propose theories. Such a one is the following: a gas enclosed in a vessel consists of particles. These particles are not at rest but in a state of continuous motion. Since these particles are in continuous motion and are small and conceived of as separated by relatively great distance, they do not collide with each other often but only occasionally. When they do so they rebound. Their motion is changed by this mutual bombardment. Now when one sums up all the various slight impacts there comes about a pressure on the wall of the vessel and through this pressure one can measure how great the temperature is. It is then asserted, “the gas particles in the vessel are in a certain state of motion, bombarding each other. The whole mass is in rapid motion, the particles bombarding each other and striking the wall. This gives rise to heat.” They may move faster and faster, strike the wall harder. Then it may be asked, what is heat? It is motion of these small particles. It is quite certain that under the influence of the facts such ideas have been fruitful, but only superficially. The entire method of thinking rests on one foundation. A great deal of pride is taken in this so-called “mechanical theory of heat,” for it seems to explain many things. For instance, it explains how when I rub my finger over a surface the effort I put forth, the pressure or work, is transformed into heat. I can turn heat back into work, in the steam engine for instance, where I secure motion by means of heat. A very convenient working concept has been built up along these lines. It is said that when we observe these things objectively going on in space, they are mechanical processes. The locomotive and the cars all move forward etc. When now, through some sort of work, I produce heat, what has really happened is that the outer observable motion has been transformed into motion of the ultimate particles. This is a convenient theory. It can be said that everything in the world is dependent on motion and we have merely transformation of observable motion into motion not observable. This latter we perceive as heat. But heat is in reality nothing but the impact and collision of the little gas particles striking each other and the walls of the vessel. The change into heat is as though the people in this whole audience suddenly began to move and collided with each other and with the walls etc. This is the Clausius theory of what goes on in a gas-filled space. This is the theory that has resulted from applying the method of the Achilles proposition to something not accessible to observation. It is not noticed that the same impossible grounds are taken as in the reasoning about Achilles and the tortoise. It is simply not as it is thought to be. Within a gas-filled space things are quite otherwise than we imagine them to be when we carry over the observable into the realm of the unobservable. My purpose today is to present this idea to you in an introductory way. From this consideration you can see that the fundamental method of thinking originated during the 19th century, begins to fail. For a large part of the method rests on the principle of calculating from observed facts by means of the differential concept. When the observed conditions in a gas-filled space are set down as differentials in accordance with the idea that we are dealing with the movements of ultimate particles, then the belief follows that by integrating something real is evolved. What must be understood is this: when we go from ordinary reckoning methods to differential equations, it is not possible to integrate forthwith without losing all contact with reality. This false notion of the relation of the integral to the differential has led the physics of the 19th century into wrong ideas of reality. It must be made clear that in certain instances one can set up differentials but what is obtained as a differential cannot be thought of as integrable without leading us into the realm of the ideal as opposed to the real. The understanding of this is of great importance in our relation to nature. For you see, when I carry out a certain transformation period, I say that work is performed, heat produced and from this heat, work can again be secured by reversal of this process. But the processes of the organic cannot be reversed immediately. I will subsequently show the extent to which this reversal applies to the inorganic in the realm of heat in particular. There are also great inorganic processes that are not reversible, such as the plant processes. We cannot imagine a reversal of the process that goes on in the plant from the formation of roots, through the flower and fruit formation. The process takes its course from the seed to the setting of the fruit. It cannot be turned backwards like an inorganic process. This fact does not enter into our calculations. Even when we remain in the inorganic, there are certain macrocosmic processes for which our reckoning is not valid. Suppose you were able to set down a formula for the growth of a plant. It would be very complicated, but assume that you have such a formula. Certain terms in it could never be made negative because to do so would be to disagree with reality. In the face of the great phenomena of the world I cannot reverse reality. This does not apply, however, to reckoning. If I have today an eclipse of the moon I can simply calculate how in time past in the period of Thales, for instance, there was an eclipse of the moon. That is, in calculation only I can reverse the process, but in reality the process is not reversible. We cannot pass from the present state of the earth to former states — to an eclipse of the moon at the time of Thales, for instance, simply by reversing the process in calculation. A calculation may be made forward or backward, but usually reality does not agree with the calculation. The latter passes over reality. It must be defined to what extent our concepts and calculations are only conceptual in their content. In spite of the fact that they are reversible, there are no reversible processes in reality. This is important since we will see that the whole theory of heat is built on questions of the following sort: to what extent within nature are heat processes reversible and to what extent are they irreversible?

The Warmth Course

Lecture I

https://rsarchive.org/Lectures/GA321/English/MP1980/19200301p01.html

Stuttgart

1 Mar 1920

GA321-1

My dear friends, Yesterday I touched upon the fact that bodies under the influence of heat expand. Today we will first consider how bodies, the solid bodies as we call them, expand when acted upon by the being of warmth. In order to impress these things upon our minds so that we can use them properly in pedagogy — and at this stage the matter is quite simple and elementary — we have set up this apparatus with an iron bar. We will heat the iron bar and make its expansion visible by noting the movements of this lever-arm over a scale. When I press here with my finger, the pointer moves upwards. (see drawing.) Figure 1a You can see when we heat the rod, the pointer does move upwards which indicates for you the act that the rod expands. The pointer moves upwards at once. Also you notice that with continued heating the pointer moves more and more, showing that the expansion increases with the temperature. If instead of this rod I had another consisting of a different metal, and if we measured precisely the amount of the expansion, it would be found other than it is here. We would find that different substances expanded various amounts. Thus we would be able to establish at once that the expansion, the degree of elongation, depended on the substance. At this point we will leave out of account the fact that we are dealing with a cylinder and assume that we have a body of a certain length without breadth or thickness and turn our attention to the expansion in one direction only. To make the matter clear we may consider it as follows: here is a rod, considered simply \(L_o\) the length of the rod at the original temperature, the starting temperature. The length attained by the rod when it is heated to a temperature \(y\), we will indicate by \(L\). Now I said that the rod expanded to various degrees depending upon the substance of which it is composed. We can express the amount of expansion to the original length of the rod. Let us denote this relative expansion by \(\alpha\). Then we know the length of the rod after expansion. For the length \(L\) after expansion may be considered as made up of the original length \(L_o\) and the small addition to this length contributed by the expansion. This must be added on. Since I have denoted by \(\alpha\) the fraction giving the ratio of the expansion and the original length, I get the expansion for a given substance by multiplying \(L_o\) by \(\alpha\). Also since the expansion is greater the higher the temperature, I have to multiply by the temperature \(t\). Thus I can say the length of the rod after expansion is \(L_o + L_o \alpha t\), which may be written \(L_o (1 + \alpha t)\). Stated in words: if I wish to determine the length of a rod expanded by heat, I must multiply the original length by a factor consisting of \(1\) plus the temperature times the relative expansion of the substance under consideration. Physicists have called \(\alpha\) the expansion coefficient of the substance considered. Now I have considered here a rod. Rods without breadth and thickness do not exist in reality. In reality bodies have three dimensions. If we proceed from the longitudinal expansion to the expansion of an assumed surface, the formula may be changed as follows: let us assume now that we are to observe the expansion of a surface instead of simply an expansion in one dimension. There is a surface. This surface extends in two directions, and after warming both will have increased in extent. We have therefore not only the longitudinal expansion to \(L\) but also an increase in the breadth to \(b\) to consider. Taking first the original length, \(L_o\), we have as before the expansion in this direction to \(L\) or $$L = L_o (1 + \alpha t)$$ Considering now the breadth \(b_o\) which expands to \(b\), I must write down: $$b=b_o(1+ \alpha t)$$ (It is obvious that the same rule will hold here as in the case of the length.) Now you know that the area of the surface is obtained by multiplying the length by the breadth. The original area I get by multiplying \(b_o\) and \(L_o\), and after expansion by multiplying \(L_o (1 + \alpha t)\) and \(b_o (1 + \alpha t)\) $$Lb=[L_o (1 + \alpha t)][b_o(1 + \alpha t)]$$ or $$Lb = L_o b_o (1 + \alpha t)^2$$ or $$Lb = L_o b_o (1 + 2 \alpha t + \alpha^2 t^2)$$ This gives the formula for the expansion of the surface. If now, you imagine thickness added to the surface, this thickness must be treated in the same manner and I can then write: $$Lbd = L_ob_od_o(1 + 3 \alpha t + 3 \alpha^2 t^2 + \alpha^3 t^3)$$ When you look at this formula I will ask you please to note the following: in the first two terms of you see \(t\) raised no higher than the first power; in the third term you see the second, and in the fourth term it is raised to the third power. Note especially these last two terms of the formula for expansion. Observe that when we deal with the expansion of a three-dimensional body we obtain a formula containing the third power of the temperature. It is extremely important to keep in mind this fact that we come here upon the third power of the temperature. Now I must always remember that we are here in the Waldorf School and everything must be presented in its relation to pedagogy. Therefore I will call your attention to the fact that the same introduction I have made here is presented very differently if you study it in the ordinary textbooks of physics. I will not well you how it is presented in the average textbook of physics. It would be said: \(\alpha\) is a ratio. It is a fraction. The expansion is relatively very small as compared to the original length of the rod. When I have a fraction whose denominator is greater than its numerator, then when I square or cube it, I get a much smaller fraction. For if I square a third, I get a ninth and when I cube a third I get a twenty-seventh. That is, the third power is a very, very small fraction. \(\alpha\) is a fraction whose denominator is usually very large. Therefore say most physics books: if I square \(\alpha\) to get \(\alpha^2\) or cube it to get \(\alpha^3\) with which I multiply \(t^3\) these are very small fractions and can simply be dropped out. The average physics text says: we simply drop these last terms of the expansion formula and write \(l \cdot b \cdot d\) — this is the volume and I will write is as \(V\) — the volume of an expanded body heated to a certain temperature is: $$V=V_o(1 + 3 \alpha t)$$ In this fashion is expressed the formula for the expansion of a solid body. It is simply considered that since the fraction \(\alpha\) squared and cubed give such small quantities, these can be dropped out. You recognize this as the treatment in the physics texts. Now my friends, in doing this, the most important thing for a really informative theory of heat is stricken out. This will appear as we progress further. Expansion under the influence of heat is shown not only by solids but by fluids as well. Here we have a fluid colored so that you can see it. We will warm this colored fluid (See Figure 1b). Now you notice that after a short time the colored fluid rises and from that we can conclude that fluids expand just like solids. Since the colored fluid rises, therefore fluids expand when warmed. Figure 1b Now we can in the same way investigate the expansion of a gaseous body. For this purpose we have here a vessel filled simply with air. (See Figure 2). We shut off the air in the vessel and warm it. Notice that here is a tube communicating with the vessel and containing a liquid whose level is the same in both arms of the tube. When we simply warm the air in the vessel, which air constitutes a gaseous body, you will see what happens. We will warm it by immersing the vessel in water heated to a temperature of 40°. (Note: temperatures in the lectures are given in degrees Celsius.) You will see, the mercury at once rises. Why does it rise? Because the gaseous body in the vessel expands. The air streams into the tube, presses on the mercury and the pressure forces the mercury column up into the tube. From this you see that the gaseous body has expanded. We may conclude that solid, liquid and gaseous bodies all expand under the influence of the being of heat, as yet unknown to us. Figure 2 Now, however, a very important matter approaches us when we proceed from the study of the expansion of solids through the expansion of liquids to the expansion of a gas. I have already stated that \(\alpha\), the relation of the expansion to the original length of the rod, differed for different substances. If by means of further experiments that cannot be performed here, we investigate \(\alpha\) for various fluids, again we will find different values for various fluid substances. When however, we investigate \(\alpha\) for gaseous bodies then a peculiar thing shows itself, namely that \(\alpha\) is not different for various gases but that this expansion coefficient as it is called, is the same and has a constant value of about \(1/273\). This fact is of tremendous importance. From it we see that as we advance from solid bodies to gases, genuinely new relations with heat appear . It appears that different gases are related to heat simply according to their property of being gases and not according to variations in the nature of the matter composing them. The condition of being a gas is, so to speak, a property which may be shared in common by all bodies. We see indeed, that for all gases known to us on earth, the property of being a gas gathers together into a unity this property of expanding. Keep in mind now that the facts of expansion under the influence of heat oblige us to say that as we proceed from solid bodies to gases, the different expansion values found in the case of solids are transformed into a kind of unity, or single power of expansion for gases . Thus if I may express myself cautiously, the solid condition may be said to be associated with an individualization of material condition . Modern physics pays scant attention to this circumstance. No attention is paid to it because the most important things are obscured by the fact of striking out certain values which cannot be adequately handled. The history of the development of physics must be called in to a certain extent in order to gain insight into the things involved in a deeper insight into these matters. All the ideas current in the modern physics texts and ruling the methods by which the facts of physics are handled are really not old. They began for the most part in the 17th century and took their fundamental character from the new impulse given by a certain scientific spirit in Europe through Academia del Cimento in Florence. This was founded in 1667 and many experiments in quite different fields were carried out there, especially however, experiments dealing with heat, acoustics and tone. How recent our ordinary ideas are may be realized when we look up some of the special apparatus of the Academia del Cimento. It was there for instance, that the ground work for our modern thermometry was laid. It was at this academy that there was observed for the first time how the mercury behaves in a glass tube ending at the bottom in a closed cylinder, when the mercury filling the tube is warmed. Here, in the Academia del Cimento, it was first noticed that there is an apparent contradiction between the experiments where the expansion of liquids may be observed and another experiment. The generalization had been attained that liquids expand. But when the experiment was carried out with quicksilver it was noticed that it first fell when the tube was heated and after that began to rise. This was first explained in the 17th century, and quite simply, by saying: When heat is applied, the outer glass is heated at the start and expands. The space occupied by the quicksilver becomes greater. It sinks at first, and begins to rise only when the heat has penetrated into the mercury itself. Ideas of this sort have been current since the 17th century. At the same time, however, people were backward in a grasp of the real ideas necessary to understand physics, since this period, the Renaissance, found Europe little inclined to trouble itself with scientific concepts. It was the time set aside for the spread of Christianity. This in a certain sense, hindered the process of definite physical phenomena. For during the Renaissance, which carried with it an acquaintance with the ideas of ancient Greece, men were in somewhat the following situation. On the one hand encouraged by all and every kind of support, there arose institutions like the Academia del Cimento, where it was possible to experiment. The course of natural phenomena could be observed directly. On the other hand, people had become unaccustomed to construct concepts about things. They had lost the habit of really following things in thought. The old Grecian ideas were now taken up again, but they were no longer understood. Thus the concepts of fire or heat or as much of them as could be understood were assumed to be the same as were held by the ancient Greeks. And at this time was formed that great chasm between thought and what can be derived from the observation of experiments. This chasm has widened more and more since the 17th century. The art of experiment reached its full flower in the 19th century, but a development of clear, definite ideas did not parallel this flowering of the experimental art. And today, lacking the clear, definite ideas, we often stand perplexed before phenomena revealed in the course of time by unthinking experimentation. When the way has been found not only to experiment and to observe the outer results of the experiments but really to enter into the inner nature of the phenomena, then only can these results be made fruitful for human spiritual development. Note now, when we penetrate into the inner being of natural phenomena then it becomes a matter of great importance that entirely different expansion relations enter in when we proceed from solids to gases. But until the whole body of our physical concepts is extended we will not really be able to evaluate such things as we have today drawn plainly from the facts themselves. To the facts, already brought out, another one of extraordinary importance must be added. You know that a general rule can be stated as we have already stated it, namely if bodies are warmed they expand. If they are cooled again they contract. So that in general the law may be stated: “Through heating, bodies expand; through cooling they contract.” But you will recollect from your elementary physics that there are exceptions to this rule, and one exception that is of cardinal importance is the one in regard to water. When water is made to expand and contract, then a remarkable fact is come upon. If we have water at 80° say, and we cool it, it first contracts. That goes without saying, as it were. But when the water is cooled further it does not contract but expands again. Thus the ice that is formed from water — and we will speak further of this — since it is more expanded and therefore less dense than water, floats on the surface of the water. This is a striking phenomenon, that ice can float on the surface of the water! It comes about through the fact that water behaves irregularly and does not follow the general law of expansion and contraction. If this were not so, if we did not have this exception, the whole arrangement of nature would be peculiarly affected. If you observe a basin filled with water or a pond, you will see that even in the very cold winter weather, there is a coating of ice on the surface only and that this protects the underlying water from further cooling. Always there is an ice coating and underneath there is protected water. The irregularity that appears here is, to use a homely expression, of tremendous importance in the household of nature. Now the manner of forming a physical concept that we can depend on in this case must be strictly according to the principles laid down in the last course. We must avoid the path that leads to an Achilles-and-the-turtle conclusion. We must not forget the manifested facts and must experiment with the facts in mind, that is, we must remain in the field where the accessible facts are such as to enable us to determine something. Therefore, let us hold strictly to what is given and from this seek an explanation for the phenomena. We will especially hold fast to such things, given to observation, as expansion and irregularity in expansion like that of water (noting that it is associated with a fluid.) Such factual matters should be kept in mind and we must remain in the world of actualities. This is real Goetheanism. Let us now consider this thing, which is not a theory but a demonstrable fact of the outer world. When matter passes into the gaseous condition there enters in a unification of properties for all the substances on the earth and with the passage to the solid condition there takes place an individualizing, a differentiation. Now if we ask ourselves how it can come about that with the passage from the solid to the gaseous through the liquid state a unification takes place, we have a great deal of difficulty in answering on the basis of our available concepts. We must first, if we are to be able to remain in the realm of the demonstrable, put certain fundamental questions. We must first ask: Whence comes the possibility for expansion in bodies, followed finally by change into the gaseous state with its accompanying unification of properties? You have only to look in a general way at all that is to be known about the physical processes on the earth in order to come to the following conclusion: Unless the action of the sun were present, we could not have all these phenomena taking place through heat. You must give attention to the enormous meaning that the being of the sun has for the phenomena of earth. And when you consider this which is simply a matter of fact, you are obliged to say: this unification of properties that takes place in the passage from the solid through the fluid and into the gaseous state, could not happen if the earth were left to itself. Only when we go beyond the merely earthly relations can we find a firm standpoint for our consideration of these things. When we admit this, however, we have made a very far reaching admission. For by putting the way of thinking of the Academia del Cimento and all that went with it in place of the above mentioned point of view, the old concepts still possible in Greece were robbed of all their super-earthly characteristics. And you will soon see, that purely from the facts, without any historical help, we are going to come back to these concepts. It will perhaps be easier to win way into your understanding if I make a short historical sketch at this time. I have already said that the real meaning of those ideas and concepts of physical phenomena that were still prevalent in ancient Greece have been lost. Experimentation was started and without the inner thought process still gone through in ancient Greece, ideas and concepts were taken up parrot-fashion, as it were. Then all that the Greeks included in these physical concepts was forgotten. The Greeks had not simply said, “Solid, liquid, gaseous,” but what they expressed may be translated into our language as follows: Whatever was solid was called in ancient Greek earth ; Whatever was fluid was called in ancient Greece water ; Whatever was gaseous was called in ancient Greece air . It is quite erroneous to think that we carry our own meaning of the words earth, air and water over into old writings where Grecian influence was dominant, and assume that the corresponding words have the same meaning there. When in old writings, we come across the word water we must translate it by our word fluid ; the word earth by our words solid bodies . Only in this way can we correctly translate old writings. But a profound meaning lies in this. The use of the word earth to indicate solid bodies implied especially that this solid condition falls under the laws ruling on the planet earth. (As stated above, we will come upon these things in following lectures from the fact themselves; they are presented today in this historical sketch simply to further your understanding of the matter.) Solids were designated as earth because it was desired to convey this idea: When a body is solid it is under the influence of the earthly laws in every respect. On the other hand, when a body was spoken of as water , then it was not merely under the earthly laws but influenced by the entire planetary system. The forces active in fluid bodies, in water, spring not merely from the earth, but from the planetary system. The forces of Mercury, Mars, etc. are active in all that is fluid. But they act in such a way that they are oriented according to the relation of the planets and show a kind of resultant in the fluid. The feeling was, thus, that only solid bodies, designated as earth, were under the earthly system of laws; and that when a body melted it was influenced from outside the earth. And when a gaseous body was called air , the feeling was that such a body was under the unifying influence of the sun, (these things are simply presented historically at this point,) this body was lifted out of the earthly and the planetary and stood under the unifying influence of the sun. Earthly air being were looked upon in this way, that their configuration, their inner arrangement and substance were principally the field for unifying forces of the sun. You see, ancient physics had a cosmic character. It was willing to take account of the forces actually present in fact. For the Moon, Mercury, Mars, etc. are facts. But people lost the sources of this view of things and were at first not able to develop a need for new sources. Thus they could only conceive that since solid bodies in their expansion and in their whole configuration fell under the laws of the earth, that liquid and gaseous bodies must do likewise. You might say that it would never occur to a physicist to deny that the sun warmed the air, etc. He does not, indeed do this, but since he proceeds from concepts such as I characterized yesterday, which delineate the action of the sun according to ideas springing from observations on the earth, he therefore explains the sun in terrestrial terms instead of explaining the terrestrial in solar terms. The essential thing is that the consciousness of certain things was completely lost in the period extending from the 15th to the 17th centuries. The consciousness that our earth is a member of the whole solar system and that consequently every single thing on the earth had to do with the whole solar system was lost. Also there was lost the feeling that the solidity of bodies arose, as it were, because the earthly emancipated itself from the cosmic, that it tore itself free to attain independent action while the gaseous, for example, the air, remained in its behavior under the unifying influence of the sun as it affected the earth as a whole. It is this which has led to the necessity of explaining things terrestrially which formerly received a cosmic explanation. Since man no longer sought for planetary forces acting when a solid body changes to a fluid, as when ice becomes fluid — changes to water — since the forces were no longer sought in the planetary system, they had to be placed within the body itself. It was necessary to rationalize and to theorize over the way in which the atoms and molecules were arranged in such a body. And to these unfortunate molecules and atoms had to be ascribed the ability from within to bring about the change from solid to liquid, from liquid to gas. Formerly such a change was considered as acting through the spatially given phenomena from the cosmic regions beyond the earth. It is in this way we must understand the transition of the concepts of physics as shown especially in the crass materialism of the Academia del Cimento which flowered in the ten year period between 1657 and 1667. You must picture to yourselves that this crass materialism arose through the gradual loss of ideas embodying the connection between the earthly and the cosmos beyond the earth. Today the necessity faces us again to realize this connection. It will not be possible, my friends, to escape from materialism unless we cease being Philistines just in this field of physics. The narrow-mindedness comes about just because we go from the concrete to the abstract, for no one loves abstractions more than the Philistine. He wishes to explain everything by a few formulae, a few abstract ideas. But physics cannot hope to advance if she continues to spin theories as has been the fashion ever since the materialism of the Academia del Cimento. We will only progress in such a field as that of the understanding of heat if we seek again to establish the connection between the terrestrial and the cosmic through wider and more comprehensive ideas than modern materialistic physics can furnish us. ˂˂ Previous Table of Contents Next ˃˃ You can see when we heat the rod, the pointer does move upwards which indicates for you the act that the rod expands. The pointer moves upwards at once. Also you notice that with continued heating the pointer moves more and more, showing that the expansion increases with the temperature. If instead of this rod I had another consisting of a different metal, and if we measured precisely the amount of the expansion, it would be found other than it is here. We would find that different substances expanded various amounts. Thus we would be able to establish at once that the expansion, the degree of elongation, depended on the substance. At this point we will leave out of account the fact that we are dealing with a cylinder and assume that we have a body of a certain length without breadth or thickness and turn our attention to the expansion in one direction only. To make the matter clear we may consider it as follows: here is a rod, considered simply \(L_o\) the length of the rod at the original temperature, the starting temperature. The length attained by the rod when it is heated to a temperature \(y\), we will indicate by \(L\). Now I said that the rod expanded to various degrees depending upon the substance of which it is composed. We can express the amount of expansion to the original length of the rod. Let us denote this relative expansion by \(\alpha\). Then we know the length of the rod after expansion. For the length \(L\) after expansion may be considered as made up of the original length \(L_o\) and the small addition to this length contributed by the expansion. This must be added on. Since I have denoted by \(\alpha\) the fraction giving the ratio of the expansion and the original length, I get the expansion for a given substance by multiplying \(L_o\) by \(\alpha\). Also since the expansion is greater the higher the temperature, I have to multiply by the temperature \(t\). Thus I can say the length of the rod after expansion is \(L_o + L_o \alpha t\), which may be written \(L_o (1 + \alpha t)\). Stated in words: if I wish to determine the length of a rod expanded by heat, I must multiply the original length by a factor consisting of \(1\) plus the temperature times the relative expansion of the substance under consideration. Physicists have called \(\alpha\) the expansion coefficient of the substance considered. Now I have considered here a rod. Rods without breadth and thickness do not exist in reality. In reality bodies have three dimensions. If we proceed from the longitudinal expansion to the expansion of an assumed surface, the formula may be changed as follows: let us assume now that we are to observe the expansion of a surface instead of simply an expansion in one dimension. There is a surface. This surface extends in two directions, and after warming both will have increased in extent. We have therefore not only the longitudinal expansion to \(L\) but also an increase in the breadth to \(b\) to consider. Taking first the original length, \(L_o\), we have as before the expansion in this direction to \(L\) or Considering now the breadth \(b_o\) which expands to \(b\), I must write down: $$b=b_o(1+ \alpha t)$$ (It is obvious that the same rule will hold here as in the case of the length.) Now you know that the area of the surface is obtained by multiplying the length by the breadth. The original area I get by multiplying \(b_o\) and \(L_o\), and after expansion by multiplying \(L_o (1 + \alpha t)\) and \(b_o (1 + \alpha t)\) $$Lb=[L_o (1 + \alpha t)][b_o(1 + \alpha t)]$$ or $$Lb = L_o b_o (1 + \alpha t)^2$$ or $$Lb = L_o b_o (1 + 2 \alpha t + \alpha^2 t^2)$$ This gives the formula for the expansion of the surface. If now, you imagine thickness added to the surface, this thickness must be treated in the same manner and I can then write: $$Lbd = L_ob_od_o(1 + 3 \alpha t + 3 \alpha^2 t^2 + \alpha^3 t^3)$$ When you look at this formula I will ask you please to note the following: in the first two terms of you see \(t\) raised no higher than the first power; in the third term you see the second, and in the fourth term it is raised to the third power. Note especially these last two terms of the formula for expansion. Observe that when we deal with the expansion of a three-dimensional body we obtain a formula containing the third power of the temperature. It is extremely important to keep in mind this fact that we come here upon the third power of the temperature. Now I must always remember that we are here in the Waldorf School and everything must be presented in its relation to pedagogy. Therefore I will call your attention to the fact that the same introduction I have made here is presented very differently if you study it in the ordinary textbooks of physics. I will not well you how it is presented in the average textbook of physics. It would be said: \(\alpha\) is a ratio. It is a fraction. The expansion is relatively very small as compared to the original length of the rod. When I have a fraction whose denominator is greater than its numerator, then when I square or cube it, I get a much smaller fraction. For if I square a third, I get a ninth and when I cube a third I get a twenty-seventh. That is, the third power is a very, very small fraction. \(\alpha\) is a fraction whose denominator is usually very large. Therefore say most physics books: if I square \(\alpha\) to get \(\alpha^2\) or cube it to get \(\alpha^3\) with which I multiply \(t^3\) these are very small fractions and can simply be dropped out. The average physics text says: we simply drop these last terms of the expansion formula and write \(l \cdot b \cdot d\) — this is the volume and I will write is as \(V\) — the volume of an expanded body heated to a certain temperature is: $$V=V_o(1 + 3 \alpha t)$$ In this fashion is expressed the formula for the expansion of a solid body. It is simply considered that since the fraction \(\alpha\) squared and cubed give such small quantities, these can be dropped out. You recognize this as the treatment in the physics texts. Now my friends, in doing this, the most important thing for a really informative theory of heat is stricken out. This will appear as we progress further. Expansion under the influence of heat is shown not only by solids but by fluids as well. Here we have a fluid colored so that you can see it. We will warm this colored fluid (See Figure 1b). Now you notice that after a short time the colored fluid rises and from that we can conclude that fluids expand just like solids. Since the colored fluid rises, therefore fluids expand when warmed. Figure 1b Now we can in the same way investigate the expansion of a gaseous body. For this purpose we have here a vessel filled simply with air. (See Figure 2). We shut off the air in the vessel and warm it. Notice that here is a tube communicating with the vessel and containing a liquid whose level is the same in both arms of the tube. When we simply warm the air in the vessel, which air constitutes a gaseous body, you will see what happens. We will warm it by immersing the vessel in water heated to a temperature of 40°. (Note: temperatures in the lectures are given in degrees Celsius.) You will see, the mercury at once rises. Why does it rise? Because the gaseous body in the vessel expands. The air streams into the tube, presses on the mercury and the pressure forces the mercury column up into the tube. From this you see that the gaseous body has expanded. We may conclude that solid, liquid and gaseous bodies all expand under the influence of the being of heat, as yet unknown to us. Figure 2 Now, however, a very important matter approaches us when we proceed from the study of the expansion of solids through the expansion of liquids to the expansion of a gas. I have already stated that \(\alpha\), the relation of the expansion to the original length of the rod, differed for different substances. If by means of further experiments that cannot be performed here, we investigate \(\alpha\) for various fluids, again we will find different values for various fluid substances. When however, we investigate \(\alpha\) for gaseous bodies then a peculiar thing shows itself, namely that \(\alpha\) is not different for various gases but that this expansion coefficient as it is called, is the same and has a constant value of about \(1/273\). This fact is of tremendous importance. From it we see that as we advance from solid bodies to gases, genuinely new relations with heat appear . It appears that different gases are related to heat simply according to their property of being gases and not according to variations in the nature of the matter composing them. The condition of being a gas is, so to speak, a property which may be shared in common by all bodies. We see indeed, that for all gases known to us on earth, the property of being a gas gathers together into a unity this property of expanding. Keep in mind now that the facts of expansion under the influence of heat oblige us to say that as we proceed from solid bodies to gases, the different expansion values found in the case of solids are transformed into a kind of unity, or single power of expansion for gases . Thus if I may express myself cautiously, the solid condition may be said to be associated with an individualization of material condition . Modern physics pays scant attention to this circumstance. No attention is paid to it because the most important things are obscured by the fact of striking out certain values which cannot be adequately handled. The history of the development of physics must be called in to a certain extent in order to gain insight into the things involved in a deeper insight into these matters. All the ideas current in the modern physics texts and ruling the methods by which the facts of physics are handled are really not old. They began for the most part in the 17th century and took their fundamental character from the new impulse given by a certain scientific spirit in Europe through Academia del Cimento in Florence. This was founded in 1667 and many experiments in quite different fields were carried out there, especially however, experiments dealing with heat, acoustics and tone. How recent our ordinary ideas are may be realized when we look up some of the special apparatus of the Academia del Cimento. It was there for instance, that the ground work for our modern thermometry was laid. It was at this academy that there was observed for the first time how the mercury behaves in a glass tube ending at the bottom in a closed cylinder, when the mercury filling the tube is warmed. Here, in the Academia del Cimento, it was first noticed that there is an apparent contradiction between the experiments where the expansion of liquids may be observed and another experiment. The generalization had been attained that liquids expand. But when the experiment was carried out with quicksilver it was noticed that it first fell when the tube was heated and after that began to rise. This was first explained in the 17th century, and quite simply, by saying: When heat is applied, the outer glass is heated at the start and expands. The space occupied by the quicksilver becomes greater. It sinks at first, and begins to rise only when the heat has penetrated into the mercury itself. Ideas of this sort have been current since the 17th century. At the same time, however, people were backward in a grasp of the real ideas necessary to understand physics, since this period, the Renaissance, found Europe little inclined to trouble itself with scientific concepts. It was the time set aside for the spread of Christianity. This in a certain sense, hindered the process of definite physical phenomena. For during the Renaissance, which carried with it an acquaintance with the ideas of ancient Greece, men were in somewhat the following situation. On the one hand encouraged by all and every kind of support, there arose institutions like the Academia del Cimento, where it was possible to experiment. The course of natural phenomena could be observed directly. On the other hand, people had become unaccustomed to construct concepts about things. They had lost the habit of really following things in thought. The old Grecian ideas were now taken up again, but they were no longer understood. Thus the concepts of fire or heat or as much of them as could be understood were assumed to be the same as were held by the ancient Greeks. And at this time was formed that great chasm between thought and what can be derived from the observation of experiments. This chasm has widened more and more since the 17th century. The art of experiment reached its full flower in the 19th century, but a development of clear, definite ideas did not parallel this flowering of the experimental art. And today, lacking the clear, definite ideas, we often stand perplexed before phenomena revealed in the course of time by unthinking experimentation. When the way has been found not only to experiment and to observe the outer results of the experiments but really to enter into the inner nature of the phenomena, then only can these results be made fruitful for human spiritual development. Note now, when we penetrate into the inner being of natural phenomena then it becomes a matter of great importance that entirely different expansion relations enter in when we proceed from solids to gases. But until the whole body of our physical concepts is extended we will not really be able to evaluate such things as we have today drawn plainly from the facts themselves. To the facts, already brought out, another one of extraordinary importance must be added. You know that a general rule can be stated as we have already stated it, namely if bodies are warmed they expand. If they are cooled again they contract. So that in general the law may be stated: “Through heating, bodies expand; through cooling they contract.” But you will recollect from your elementary physics that there are exceptions to this rule, and one exception that is of cardinal importance is the one in regard to water. When water is made to expand and contract, then a remarkable fact is come upon. If we have water at 80° say, and we cool it, it first contracts. That goes without saying, as it were. But when the water is cooled further it does not contract but expands again. Thus the ice that is formed from water — and we will speak further of this — since it is more expanded and therefore less dense than water, floats on the surface of the water. This is a striking phenomenon, that ice can float on the surface of the water! It comes about through the fact that water behaves irregularly and does not follow the general law of expansion and contraction. If this were not so, if we did not have this exception, the whole arrangement of nature would be peculiarly affected. If you observe a basin filled with water or a pond, you will see that even in the very cold winter weather, there is a coating of ice on the surface only and that this protects the underlying water from further cooling. Always there is an ice coating and underneath there is protected water. The irregularity that appears here is, to use a homely expression, of tremendous importance in the household of nature. Now the manner of forming a physical concept that we can depend on in this case must be strictly according to the principles laid down in the last course. We must avoid the path that leads to an Achilles-and-the-turtle conclusion. We must not forget the manifested facts and must experiment with the facts in mind, that is, we must remain in the field where the accessible facts are such as to enable us to determine something. Therefore, let us hold strictly to what is given and from this seek an explanation for the phenomena. We will especially hold fast to such things, given to observation, as expansion and irregularity in expansion like that of water (noting that it is associated with a fluid.) Such factual matters should be kept in mind and we must remain in the world of actualities. This is real Goetheanism. Let us now consider this thing, which is not a theory but a demonstrable fact of the outer world. When matter passes into the gaseous condition there enters in a unification of properties for all the substances on the earth and with the passage to the solid condition there takes place an individualizing, a differentiation. Now if we ask ourselves how it can come about that with the passage from the solid to the gaseous through the liquid state a unification takes place, we have a great deal of difficulty in answering on the basis of our available concepts. We must first, if we are to be able to remain in the realm of the demonstrable, put certain fundamental questions. We must first ask: Whence comes the possibility for expansion in bodies, followed finally by change into the gaseous state with its accompanying unification of properties? You have only to look in a general way at all that is to be known about the physical processes on the earth in order to come to the following conclusion: Unless the action of the sun were present, we could not have all these phenomena taking place through heat. You must give attention to the enormous meaning that the being of the sun has for the phenomena of earth. And when you consider this which is simply a matter of fact, you are obliged to say: this unification of properties that takes place in the passage from the solid through the fluid and into the gaseous state, could not happen if the earth were left to itself. Only when we go beyond the merely earthly relations can we find a firm standpoint for our consideration of these things. When we admit this, however, we have made a very far reaching admission. For by putting the way of thinking of the Academia del Cimento and all that went with it in place of the above mentioned point of view, the old concepts still possible in Greece were robbed of all their super-earthly characteristics. And you will soon see, that purely from the facts, without any historical help, we are going to come back to these concepts. It will perhaps be easier to win way into your understanding if I make a short historical sketch at this time. I have already said that the real meaning of those ideas and concepts of physical phenomena that were still prevalent in ancient Greece have been lost. Experimentation was started and without the inner thought process still gone through in ancient Greece, ideas and concepts were taken up parrot-fashion, as it were. Then all that the Greeks included in these physical concepts was forgotten. The Greeks had not simply said, “Solid, liquid, gaseous,” but what they expressed may be translated into our language as follows: Whatever was solid was called in ancient Greek earth ; Whatever was fluid was called in ancient Greece water ; Whatever was gaseous was called in ancient Greece air . It is quite erroneous to think that we carry our own meaning of the words earth, air and water over into old writings where Grecian influence was dominant, and assume that the corresponding words have the same meaning there. When in old writings, we come across the word water we must translate it by our word fluid ; the word earth by our words solid bodies . Only in this way can we correctly translate old writings. But a profound meaning lies in this. The use of the word earth to indicate solid bodies implied especially that this solid condition falls under the laws ruling on the planet earth. (As stated above, we will come upon these things in following lectures from the fact themselves; they are presented today in this historical sketch simply to further your understanding of the matter.) Solids were designated as earth because it was desired to convey this idea: When a body is solid it is under the influence of the earthly laws in every respect. On the other hand, when a body was spoken of as water , then it was not merely under the earthly laws but influenced by the entire planetary system. The forces active in fluid bodies, in water, spring not merely from the earth, but from the planetary system. The forces of Mercury, Mars, etc. are active in all that is fluid. But they act in such a way that they are oriented according to the relation of the planets and show a kind of resultant in the fluid. The feeling was, thus, that only solid bodies, designated as earth, were under the earthly system of laws; and that when a body melted it was influenced from outside the earth. And when a gaseous body was called air , the feeling was that such a body was under the unifying influence of the sun, (these things are simply presented historically at this point,) this body was lifted out of the earthly and the planetary and stood under the unifying influence of the sun. Earthly air being were looked upon in this way, that their configuration, their inner arrangement and substance were principally the field for unifying forces of the sun. You see, ancient physics had a cosmic character. It was willing to take account of the forces actually present in fact. For the Moon, Mercury, Mars, etc. are facts. But people lost the sources of this view of things and were at first not able to develop a need for new sources. Thus they could only conceive that since solid bodies in their expansion and in their whole configuration fell under the laws of the earth, that liquid and gaseous bodies must do likewise. You might say that it would never occur to a physicist to deny that the sun warmed the air, etc. He does not, indeed do this, but since he proceeds from concepts such as I characterized yesterday, which delineate the action of the sun according to ideas springing from observations on the earth, he therefore explains the sun in terrestrial terms instead of explaining the terrestrial in solar terms. The essential thing is that the consciousness of certain things was completely lost in the period extending from the 15th to the 17th centuries. The consciousness that our earth is a member of the whole solar system and that consequently every single thing on the earth had to do with the whole solar system was lost. Also there was lost the feeling that the solidity of bodies arose, as it were, because the earthly emancipated itself from the cosmic, that it tore itself free to attain independent action while the gaseous, for example, the air, remained in its behavior under the unifying influence of the sun as it affected the earth as a whole. It is this which has led to the necessity of explaining things terrestrially which formerly received a cosmic explanation. Since man no longer sought for planetary forces acting when a solid body changes to a fluid, as when ice becomes fluid — changes to water — since the forces were no longer sought in the planetary system, they had to be placed within the body itself. It was necessary to rationalize and to theorize over the way in which the atoms and molecules were arranged in such a body. And to these unfortunate molecules and atoms had to be ascribed the ability from within to bring about the change from solid to liquid, from liquid to gas. Formerly such a change was considered as acting through the spatially given phenomena from the cosmic regions beyond the earth. It is in this way we must understand the transition of the concepts of physics as shown especially in the crass materialism of the Academia del Cimento which flowered in the ten year period between 1657 and 1667. You must picture to yourselves that this crass materialism arose through the gradual loss of ideas embodying the connection between the earthly and the cosmos beyond the earth. Today the necessity faces us again to realize this connection. It will not be possible, my friends, to escape from materialism unless we cease being Philistines just in this field of physics. The narrow-mindedness comes about just because we go from the concrete to the abstract, for no one loves abstractions more than the Philistine. He wishes to explain everything by a few formulae, a few abstract ideas. But physics cannot hope to advance if she continues to spin theories as has been the fashion ever since the materialism of the Academia del Cimento. We will only progress in such a field as that of the understanding of heat if we seek again to establish the connection between the terrestrial and the cosmic through wider and more comprehensive ideas than modern materialistic physics can furnish us. ˂˂ Previous Table of Contents Next ˃˃ (It is obvious that the same rule will hold here as in the case of the length.) Now you know that the area of the surface is obtained by multiplying the length by the breadth. The original area I get by multiplying \(b_o\) and \(L_o\), and after expansion by multiplying \(L_o (1 + \alpha t)\) and \(b_o (1 + \alpha t)\) This gives the formula for the expansion of the surface. If now, you imagine thickness added to the surface, this thickness must be treated in the same manner and I can then write: When you look at this formula I will ask you please to note the following: in the first two terms of you see \(t\) raised no higher than the first power; in the third term you see the second, and in the fourth term it is raised to the third power. Note especially these last two terms of the formula for expansion. Observe that when we deal with the expansion of a three-dimensional body we obtain a formula containing the third power of the temperature. It is extremely important to keep in mind this fact that we come here upon the third power of the temperature. Now I must always remember that we are here in the Waldorf School and everything must be presented in its relation to pedagogy. Therefore I will call your attention to the fact that the same introduction I have made here is presented very differently if you study it in the ordinary textbooks of physics. I will not well you how it is presented in the average textbook of physics. It would be said: \(\alpha\) is a ratio. It is a fraction. The expansion is relatively very small as compared to the original length of the rod. When I have a fraction whose denominator is greater than its numerator, then when I square or cube it, I get a much smaller fraction. For if I square a third, I get a ninth and when I cube a third I get a twenty-seventh. That is, the third power is a very, very small fraction. \(\alpha\) is a fraction whose denominator is usually very large. Therefore say most physics books: if I square \(\alpha\) to get \(\alpha^2\) or cube it to get \(\alpha^3\) with which I multiply \(t^3\) these are very small fractions and can simply be dropped out. The average physics text says: we simply drop these last terms of the expansion formula and write \(l \cdot b \cdot d\) — this is the volume and I will write is as \(V\) — the volume of an expanded body heated to a certain temperature is: In this fashion is expressed the formula for the expansion of a solid body. It is simply considered that since the fraction \(\alpha\) squared and cubed give such small quantities, these can be dropped out. You recognize this as the treatment in the physics texts. Now my friends, in doing this, the most important thing for a really informative theory of heat is stricken out. This will appear as we progress further. Expansion under the influence of heat is shown not only by solids but by fluids as well. Here we have a fluid colored so that you can see it. We will warm this colored fluid (See Figure 1b). Now you notice that after a short time the colored fluid rises and from that we can conclude that fluids expand just like solids. Since the colored fluid rises, therefore fluids expand when warmed. Figure 1b Now we can in the same way investigate the expansion of a gaseous body. For this purpose we have here a vessel filled simply with air. (See Figure 2). We shut off the air in the vessel and warm it. Notice that here is a tube communicating with the vessel and containing a liquid whose level is the same in both arms of the tube. When we simply warm the air in the vessel, which air constitutes a gaseous body, you will see what happens. We will warm it by immersing the vessel in water heated to a temperature of 40°. (Note: temperatures in the lectures are given in degrees Celsius.) You will see, the mercury at once rises. Why does it rise? Because the gaseous body in the vessel expands. The air streams into the tube, presses on the mercury and the pressure forces the mercury column up into the tube. From this you see that the gaseous body has expanded. We may conclude that solid, liquid and gaseous bodies all expand under the influence of the being of heat, as yet unknown to us. Figure 2 Now, however, a very important matter approaches us when we proceed from the study of the expansion of solids through the expansion of liquids to the expansion of a gas. I have already stated that \(\alpha\), the relation of the expansion to the original length of the rod, differed for different substances. If by means of further experiments that cannot be performed here, we investigate \(\alpha\) for various fluids, again we will find different values for various fluid substances. When however, we investigate \(\alpha\) for gaseous bodies then a peculiar thing shows itself, namely that \(\alpha\) is not different for various gases but that this expansion coefficient as it is called, is the same and has a constant value of about \(1/273\). This fact is of tremendous importance. From it we see that as we advance from solid bodies to gases, genuinely new relations with heat appear . It appears that different gases are related to heat simply according to their property of being gases and not according to variations in the nature of the matter composing them. The condition of being a gas is, so to speak, a property which may be shared in common by all bodies. We see indeed, that for all gases known to us on earth, the property of being a gas gathers together into a unity this property of expanding. Keep in mind now that the facts of expansion under the influence of heat oblige us to say that as we proceed from solid bodies to gases, the different expansion values found in the case of solids are transformed into a kind of unity, or single power of expansion for gases . Thus if I may express myself cautiously, the solid condition may be said to be associated with an individualization of material condition . Modern physics pays scant attention to this circumstance. No attention is paid to it because the most important things are obscured by the fact of striking out certain values which cannot be adequately handled. The history of the development of physics must be called in to a certain extent in order to gain insight into the things involved in a deeper insight into these matters. All the ideas current in the modern physics texts and ruling the methods by which the facts of physics are handled are really not old. They began for the most part in the 17th century and took their fundamental character from the new impulse given by a certain scientific spirit in Europe through Academia del Cimento in Florence. This was founded in 1667 and many experiments in quite different fields were carried out there, especially however, experiments dealing with heat, acoustics and tone. How recent our ordinary ideas are may be realized when we look up some of the special apparatus of the Academia del Cimento. It was there for instance, that the ground work for our modern thermometry was laid. It was at this academy that there was observed for the first time how the mercury behaves in a glass tube ending at the bottom in a closed cylinder, when the mercury filling the tube is warmed. Here, in the Academia del Cimento, it was first noticed that there is an apparent contradiction between the experiments where the expansion of liquids may be observed and another experiment. The generalization had been attained that liquids expand. But when the experiment was carried out with quicksilver it was noticed that it first fell when the tube was heated and after that began to rise. This was first explained in the 17th century, and quite simply, by saying: When heat is applied, the outer glass is heated at the start and expands. The space occupied by the quicksilver becomes greater. It sinks at first, and begins to rise only when the heat has penetrated into the mercury itself. Ideas of this sort have been current since the 17th century. At the same time, however, people were backward in a grasp of the real ideas necessary to understand physics, since this period, the Renaissance, found Europe little inclined to trouble itself with scientific concepts. It was the time set aside for the spread of Christianity. This in a certain sense, hindered the process of definite physical phenomena. For during the Renaissance, which carried with it an acquaintance with the ideas of ancient Greece, men were in somewhat the following situation. On the one hand encouraged by all and every kind of support, there arose institutions like the Academia del Cimento, where it was possible to experiment. The course of natural phenomena could be observed directly. On the other hand, people had become unaccustomed to construct concepts about things. They had lost the habit of really following things in thought. The old Grecian ideas were now taken up again, but they were no longer understood. Thus the concepts of fire or heat or as much of them as could be understood were assumed to be the same as were held by the ancient Greeks. And at this time was formed that great chasm between thought and what can be derived from the observation of experiments. This chasm has widened more and more since the 17th century. The art of experiment reached its full flower in the 19th century, but a development of clear, definite ideas did not parallel this flowering of the experimental art. And today, lacking the clear, definite ideas, we often stand perplexed before phenomena revealed in the course of time by unthinking experimentation. When the way has been found not only to experiment and to observe the outer results of the experiments but really to enter into the inner nature of the phenomena, then only can these results be made fruitful for human spiritual development. Note now, when we penetrate into the inner being of natural phenomena then it becomes a matter of great importance that entirely different expansion relations enter in when we proceed from solids to gases. But until the whole body of our physical concepts is extended we will not really be able to evaluate such things as we have today drawn plainly from the facts themselves. To the facts, already brought out, another one of extraordinary importance must be added. You know that a general rule can be stated as we have already stated it, namely if bodies are warmed they expand. If they are cooled again they contract. So that in general the law may be stated: “Through heating, bodies expand; through cooling they contract.” But you will recollect from your elementary physics that there are exceptions to this rule, and one exception that is of cardinal importance is the one in regard to water. When water is made to expand and contract, then a remarkable fact is come upon. If we have water at 80° say, and we cool it, it first contracts. That goes without saying, as it were. But when the water is cooled further it does not contract but expands again. Thus the ice that is formed from water — and we will speak further of this — since it is more expanded and therefore less dense than water, floats on the surface of the water. This is a striking phenomenon, that ice can float on the surface of the water! It comes about through the fact that water behaves irregularly and does not follow the general law of expansion and contraction. If this were not so, if we did not have this exception, the whole arrangement of nature would be peculiarly affected. If you observe a basin filled with water or a pond, you will see that even in the very cold winter weather, there is a coating of ice on the surface only and that this protects the underlying water from further cooling. Always there is an ice coating and underneath there is protected water. The irregularity that appears here is, to use a homely expression, of tremendous importance in the household of nature. Now the manner of forming a physical concept that we can depend on in this case must be strictly according to the principles laid down in the last course. We must avoid the path that leads to an Achilles-and-the-turtle conclusion. We must not forget the manifested facts and must experiment with the facts in mind, that is, we must remain in the field where the accessible facts are such as to enable us to determine something. Therefore, let us hold strictly to what is given and from this seek an explanation for the phenomena. We will especially hold fast to such things, given to observation, as expansion and irregularity in expansion like that of water (noting that it is associated with a fluid.) Such factual matters should be kept in mind and we must remain in the world of actualities. This is real Goetheanism. Let us now consider this thing, which is not a theory but a demonstrable fact of the outer world. When matter passes into the gaseous condition there enters in a unification of properties for all the substances on the earth and with the passage to the solid condition there takes place an individualizing, a differentiation. Now if we ask ourselves how it can come about that with the passage from the solid to the gaseous through the liquid state a unification takes place, we have a great deal of difficulty in answering on the basis of our available concepts. We must first, if we are to be able to remain in the realm of the demonstrable, put certain fundamental questions. We must first ask: Whence comes the possibility for expansion in bodies, followed finally by change into the gaseous state with its accompanying unification of properties? You have only to look in a general way at all that is to be known about the physical processes on the earth in order to come to the following conclusion: Unless the action of the sun were present, we could not have all these phenomena taking place through heat. You must give attention to the enormous meaning that the being of the sun has for the phenomena of earth. And when you consider this which is simply a matter of fact, you are obliged to say: this unification of properties that takes place in the passage from the solid through the fluid and into the gaseous state, could not happen if the earth were left to itself. Only when we go beyond the merely earthly relations can we find a firm standpoint for our consideration of these things. When we admit this, however, we have made a very far reaching admission. For by putting the way of thinking of the Academia del Cimento and all that went with it in place of the above mentioned point of view, the old concepts still possible in Greece were robbed of all their super-earthly characteristics. And you will soon see, that purely from the facts, without any historical help, we are going to come back to these concepts. It will perhaps be easier to win way into your understanding if I make a short historical sketch at this time. I have already said that the real meaning of those ideas and concepts of physical phenomena that were still prevalent in ancient Greece have been lost. Experimentation was started and without the inner thought process still gone through in ancient Greece, ideas and concepts were taken up parrot-fashion, as it were. Then all that the Greeks included in these physical concepts was forgotten. The Greeks had not simply said, “Solid, liquid, gaseous,” but what they expressed may be translated into our language as follows: Whatever was solid was called in ancient Greek earth ; Whatever was fluid was called in ancient Greece water ; Whatever was gaseous was called in ancient Greece air . It is quite erroneous to think that we carry our own meaning of the words earth, air and water over into old writings where Grecian influence was dominant, and assume that the corresponding words have the same meaning there. When in old writings, we come across the word water we must translate it by our word fluid ; the word earth by our words solid bodies . Only in this way can we correctly translate old writings. But a profound meaning lies in this. The use of the word earth to indicate solid bodies implied especially that this solid condition falls under the laws ruling on the planet earth. (As stated above, we will come upon these things in following lectures from the fact themselves; they are presented today in this historical sketch simply to further your understanding of the matter.) Solids were designated as earth because it was desired to convey this idea: When a body is solid it is under the influence of the earthly laws in every respect. On the other hand, when a body was spoken of as water , then it was not merely under the earthly laws but influenced by the entire planetary system. The forces active in fluid bodies, in water, spring not merely from the earth, but from the planetary system. The forces of Mercury, Mars, etc. are active in all that is fluid. But they act in such a way that they are oriented according to the relation of the planets and show a kind of resultant in the fluid. The feeling was, thus, that only solid bodies, designated as earth, were under the earthly system of laws; and that when a body melted it was influenced from outside the earth. And when a gaseous body was called air , the feeling was that such a body was under the unifying influence of the sun, (these things are simply presented historically at this point,) this body was lifted out of the earthly and the planetary and stood under the unifying influence of the sun. Earthly air being were looked upon in this way, that their configuration, their inner arrangement and substance were principally the field for unifying forces of the sun. You see, ancient physics had a cosmic character. It was willing to take account of the forces actually present in fact. For the Moon, Mercury, Mars, etc. are facts. But people lost the sources of this view of things and were at first not able to develop a need for new sources. Thus they could only conceive that since solid bodies in their expansion and in their whole configuration fell under the laws of the earth, that liquid and gaseous bodies must do likewise. You might say that it would never occur to a physicist to deny that the sun warmed the air, etc. He does not, indeed do this, but since he proceeds from concepts such as I characterized yesterday, which delineate the action of the sun according to ideas springing from observations on the earth, he therefore explains the sun in terrestrial terms instead of explaining the terrestrial in solar terms. The essential thing is that the consciousness of certain things was completely lost in the period extending from the 15th to the 17th centuries. The consciousness that our earth is a member of the whole solar system and that consequently every single thing on the earth had to do with the whole solar system was lost. Also there was lost the feeling that the solidity of bodies arose, as it were, because the earthly emancipated itself from the cosmic, that it tore itself free to attain independent action while the gaseous, for example, the air, remained in its behavior under the unifying influence of the sun as it affected the earth as a whole. It is this which has led to the necessity of explaining things terrestrially which formerly received a cosmic explanation. Since man no longer sought for planetary forces acting when a solid body changes to a fluid, as when ice becomes fluid — changes to water — since the forces were no longer sought in the planetary system, they had to be placed within the body itself. It was necessary to rationalize and to theorize over the way in which the atoms and molecules were arranged in such a body. And to these unfortunate molecules and atoms had to be ascribed the ability from within to bring about the change from solid to liquid, from liquid to gas. Formerly such a change was considered as acting through the spatially given phenomena from the cosmic regions beyond the earth. It is in this way we must understand the transition of the concepts of physics as shown especially in the crass materialism of the Academia del Cimento which flowered in the ten year period between 1657 and 1667. You must picture to yourselves that this crass materialism arose through the gradual loss of ideas embodying the connection between the earthly and the cosmos beyond the earth. Today the necessity faces us again to realize this connection. It will not be possible, my friends, to escape from materialism unless we cease being Philistines just in this field of physics. The narrow-mindedness comes about just because we go from the concrete to the abstract, for no one loves abstractions more than the Philistine. He wishes to explain everything by a few formulae, a few abstract ideas. But physics cannot hope to advance if she continues to spin theories as has been the fashion ever since the materialism of the Academia del Cimento. We will only progress in such a field as that of the understanding of heat if we seek again to establish the connection between the terrestrial and the cosmic through wider and more comprehensive ideas than modern materialistic physics can furnish us. ˂˂ Previous Table of Contents Next ˃˃ Now we can in the same way investigate the expansion of a gaseous body. For this purpose we have here a vessel filled simply with air. (See Figure 2). We shut off the air in the vessel and warm it. Notice that here is a tube communicating with the vessel and containing a liquid whose level is the same in both arms of the tube. When we simply warm the air in the vessel, which air constitutes a gaseous body, you will see what happens. We will warm it by immersing the vessel in water heated to a temperature of 40°. (Note: temperatures in the lectures are given in degrees Celsius.) You will see, the mercury at once rises. Why does it rise? Because the gaseous body in the vessel expands. The air streams into the tube, presses on the mercury and the pressure forces the mercury column up into the tube. From this you see that the gaseous body has expanded. We may conclude that solid, liquid and gaseous bodies all expand under the influence of the being of heat, as yet unknown to us. Now, however, a very important matter approaches us when we proceed from the study of the expansion of solids through the expansion of liquids to the expansion of a gas. I have already stated that \(\alpha\), the relation of the expansion to the original length of the rod, differed for different substances. If by means of further experiments that cannot be performed here, we investigate \(\alpha\) for various fluids, again we will find different values for various fluid substances. When however, we investigate \(\alpha\) for gaseous bodies then a peculiar thing shows itself, namely that \(\alpha\) is not different for various gases but that this expansion coefficient as it is called, is the same and has a constant value of about \(1/273\). This fact is of tremendous importance. From it we see that as we advance from solid bodies to gases, genuinely new relations with heat appear . It appears that different gases are related to heat simply according to their property of being gases and not according to variations in the nature of the matter composing them. The condition of being a gas is, so to speak, a property which may be shared in common by all bodies. We see indeed, that for all gases known to us on earth, the property of being a gas gathers together into a unity this property of expanding. Keep in mind now that the facts of expansion under the influence of heat oblige us to say that as we proceed from solid bodies to gases, the different expansion values found in the case of solids are transformed into a kind of unity, or single power of expansion for gases . Thus if I may express myself cautiously, the solid condition may be said to be associated with an individualization of material condition . Modern physics pays scant attention to this circumstance. No attention is paid to it because the most important things are obscured by the fact of striking out certain values which cannot be adequately handled. The history of the development of physics must be called in to a certain extent in order to gain insight into the things involved in a deeper insight into these matters. All the ideas current in the modern physics texts and ruling the methods by which the facts of physics are handled are really not old. They began for the most part in the 17th century and took their fundamental character from the new impulse given by a certain scientific spirit in Europe through Academia del Cimento in Florence. This was founded in 1667 and many experiments in quite different fields were carried out there, especially however, experiments dealing with heat, acoustics and tone. How recent our ordinary ideas are may be realized when we look up some of the special apparatus of the Academia del Cimento. It was there for instance, that the ground work for our modern thermometry was laid. It was at this academy that there was observed for the first time how the mercury behaves in a glass tube ending at the bottom in a closed cylinder, when the mercury filling the tube is warmed. Here, in the Academia del Cimento, it was first noticed that there is an apparent contradiction between the experiments where the expansion of liquids may be observed and another experiment. The generalization had been attained that liquids expand. But when the experiment was carried out with quicksilver it was noticed that it first fell when the tube was heated and after that began to rise. This was first explained in the 17th century, and quite simply, by saying: When heat is applied, the outer glass is heated at the start and expands. The space occupied by the quicksilver becomes greater. It sinks at first, and begins to rise only when the heat has penetrated into the mercury itself. Ideas of this sort have been current since the 17th century. At the same time, however, people were backward in a grasp of the real ideas necessary to understand physics, since this period, the Renaissance, found Europe little inclined to trouble itself with scientific concepts. It was the time set aside for the spread of Christianity. This in a certain sense, hindered the process of definite physical phenomena. For during the Renaissance, which carried with it an acquaintance with the ideas of ancient Greece, men were in somewhat the following situation. On the one hand encouraged by all and every kind of support, there arose institutions like the Academia del Cimento, where it was possible to experiment. The course of natural phenomena could be observed directly. On the other hand, people had become unaccustomed to construct concepts about things. They had lost the habit of really following things in thought. The old Grecian ideas were now taken up again, but they were no longer understood. Thus the concepts of fire or heat or as much of them as could be understood were assumed to be the same as were held by the ancient Greeks. And at this time was formed that great chasm between thought and what can be derived from the observation of experiments. This chasm has widened more and more since the 17th century. The art of experiment reached its full flower in the 19th century, but a development of clear, definite ideas did not parallel this flowering of the experimental art. And today, lacking the clear, definite ideas, we often stand perplexed before phenomena revealed in the course of time by unthinking experimentation. When the way has been found not only to experiment and to observe the outer results of the experiments but really to enter into the inner nature of the phenomena, then only can these results be made fruitful for human spiritual development. Note now, when we penetrate into the inner being of natural phenomena then it becomes a matter of great importance that entirely different expansion relations enter in when we proceed from solids to gases. But until the whole body of our physical concepts is extended we will not really be able to evaluate such things as we have today drawn plainly from the facts themselves. To the facts, already brought out, another one of extraordinary importance must be added. You know that a general rule can be stated as we have already stated it, namely if bodies are warmed they expand. If they are cooled again they contract. So that in general the law may be stated: “Through heating, bodies expand; through cooling they contract.” But you will recollect from your elementary physics that there are exceptions to this rule, and one exception that is of cardinal importance is the one in regard to water. When water is made to expand and contract, then a remarkable fact is come upon. If we have water at 80° say, and we cool it, it first contracts. That goes without saying, as it were. But when the water is cooled further it does not contract but expands again. Thus the ice that is formed from water — and we will speak further of this — since it is more expanded and therefore less dense than water, floats on the surface of the water. This is a striking phenomenon, that ice can float on the surface of the water! It comes about through the fact that water behaves irregularly and does not follow the general law of expansion and contraction. If this were not so, if we did not have this exception, the whole arrangement of nature would be peculiarly affected. If you observe a basin filled with water or a pond, you will see that even in the very cold winter weather, there is a coating of ice on the surface only and that this protects the underlying water from further cooling. Always there is an ice coating and underneath there is protected water. The irregularity that appears here is, to use a homely expression, of tremendous importance in the household of nature. Now the manner of forming a physical concept that we can depend on in this case must be strictly according to the principles laid down in the last course. We must avoid the path that leads to an Achilles-and-the-turtle conclusion. We must not forget the manifested facts and must experiment with the facts in mind, that is, we must remain in the field where the accessible facts are such as to enable us to determine something. Therefore, let us hold strictly to what is given and from this seek an explanation for the phenomena. We will especially hold fast to such things, given to observation, as expansion and irregularity in expansion like that of water (noting that it is associated with a fluid.) Such factual matters should be kept in mind and we must remain in the world of actualities. This is real Goetheanism. Let us now consider this thing, which is not a theory but a demonstrable fact of the outer world. When matter passes into the gaseous condition there enters in a unification of properties for all the substances on the earth and with the passage to the solid condition there takes place an individualizing, a differentiation. Now if we ask ourselves how it can come about that with the passage from the solid to the gaseous through the liquid state a unification takes place, we have a great deal of difficulty in answering on the basis of our available concepts. We must first, if we are to be able to remain in the realm of the demonstrable, put certain fundamental questions. We must first ask: Whence comes the possibility for expansion in bodies, followed finally by change into the gaseous state with its accompanying unification of properties? You have only to look in a general way at all that is to be known about the physical processes on the earth in order to come to the following conclusion: Unless the action of the sun were present, we could not have all these phenomena taking place through heat. You must give attention to the enormous meaning that the being of the sun has for the phenomena of earth. And when you consider this which is simply a matter of fact, you are obliged to say: this unification of properties that takes place in the passage from the solid through the fluid and into the gaseous state, could not happen if the earth were left to itself. Only when we go beyond the merely earthly relations can we find a firm standpoint for our consideration of these things. When we admit this, however, we have made a very far reaching admission. For by putting the way of thinking of the Academia del Cimento and all that went with it in place of the above mentioned point of view, the old concepts still possible in Greece were robbed of all their super-earthly characteristics. And you will soon see, that purely from the facts, without any historical help, we are going to come back to these concepts. It will perhaps be easier to win way into your understanding if I make a short historical sketch at this time. I have already said that the real meaning of those ideas and concepts of physical phenomena that were still prevalent in ancient Greece have been lost. Experimentation was started and without the inner thought process still gone through in ancient Greece, ideas and concepts were taken up parrot-fashion, as it were. Then all that the Greeks included in these physical concepts was forgotten. The Greeks had not simply said, “Solid, liquid, gaseous,” but what they expressed may be translated into our language as follows: Whatever was solid was called in ancient Greek earth ; Whatever was fluid was called in ancient Greece water ; Whatever was gaseous was called in ancient Greece air . It is quite erroneous to think that we carry our own meaning of the words earth, air and water over into old writings where Grecian influence was dominant, and assume that the corresponding words have the same meaning there. When in old writings, we come across the word water we must translate it by our word fluid ; the word earth by our words solid bodies . Only in this way can we correctly translate old writings. But a profound meaning lies in this. The use of the word earth to indicate solid bodies implied especially that this solid condition falls under the laws ruling on the planet earth. (As stated above, we will come upon these things in following lectures from the fact themselves; they are presented today in this historical sketch simply to further your understanding of the matter.) Solids were designated as earth because it was desired to convey this idea: When a body is solid it is under the influence of the earthly laws in every respect. On the other hand, when a body was spoken of as water , then it was not merely under the earthly laws but influenced by the entire planetary system. The forces active in fluid bodies, in water, spring not merely from the earth, but from the planetary system. The forces of Mercury, Mars, etc. are active in all that is fluid. But they act in such a way that they are oriented according to the relation of the planets and show a kind of resultant in the fluid. The feeling was, thus, that only solid bodies, designated as earth, were under the earthly system of laws; and that when a body melted it was influenced from outside the earth. And when a gaseous body was called air , the feeling was that such a body was under the unifying influence of the sun, (these things are simply presented historically at this point,) this body was lifted out of the earthly and the planetary and stood under the unifying influence of the sun. Earthly air being were looked upon in this way, that their configuration, their inner arrangement and substance were principally the field for unifying forces of the sun. You see, ancient physics had a cosmic character. It was willing to take account of the forces actually present in fact. For the Moon, Mercury, Mars, etc. are facts. But people lost the sources of this view of things and were at first not able to develop a need for new sources. Thus they could only conceive that since solid bodies in their expansion and in their whole configuration fell under the laws of the earth, that liquid and gaseous bodies must do likewise. You might say that it would never occur to a physicist to deny that the sun warmed the air, etc. He does not, indeed do this, but since he proceeds from concepts such as I characterized yesterday, which delineate the action of the sun according to ideas springing from observations on the earth, he therefore explains the sun in terrestrial terms instead of explaining the terrestrial in solar terms. The essential thing is that the consciousness of certain things was completely lost in the period extending from the 15th to the 17th centuries. The consciousness that our earth is a member of the whole solar system and that consequently every single thing on the earth had to do with the whole solar system was lost. Also there was lost the feeling that the solidity of bodies arose, as it were, because the earthly emancipated itself from the cosmic, that it tore itself free to attain independent action while the gaseous, for example, the air, remained in its behavior under the unifying influence of the sun as it affected the earth as a whole. It is this which has led to the necessity of explaining things terrestrially which formerly received a cosmic explanation. Since man no longer sought for planetary forces acting when a solid body changes to a fluid, as when ice becomes fluid — changes to water — since the forces were no longer sought in the planetary system, they had to be placed within the body itself. It was necessary to rationalize and to theorize over the way in which the atoms and molecules were arranged in such a body. And to these unfortunate molecules and atoms had to be ascribed the ability from within to bring about the change from solid to liquid, from liquid to gas. Formerly such a change was considered as acting through the spatially given phenomena from the cosmic regions beyond the earth. It is in this way we must understand the transition of the concepts of physics as shown especially in the crass materialism of the Academia del Cimento which flowered in the ten year period between 1657 and 1667. You must picture to yourselves that this crass materialism arose through the gradual loss of ideas embodying the connection between the earthly and the cosmos beyond the earth. Today the necessity faces us again to realize this connection. It will not be possible, my friends, to escape from materialism unless we cease being Philistines just in this field of physics. The narrow-mindedness comes about just because we go from the concrete to the abstract, for no one loves abstractions more than the Philistine. He wishes to explain everything by a few formulae, a few abstract ideas. But physics cannot hope to advance if she continues to spin theories as has been the fashion ever since the materialism of the Academia del Cimento. We will only progress in such a field as that of the understanding of heat if we seek again to establish the connection between the terrestrial and the cosmic through wider and more comprehensive ideas than modern materialistic physics can furnish us.

The Warmth Course

Lecture II

https://rsarchive.org/Lectures/GA321/English/MP1980/19200302a01.html

Stuttgart

2 Mar 1920

GA321-2

My dear friends, Today in order to press toward the goal of the first of these lectures, we will consider some of the relations between the being of heat and the so-called state of aggregation. By this state of aggregation I mean what I referred to yesterday as called in the ancient view of the physical world, earth, water, air. You are acquainted with the fact that earth, water, and air, or as they are called today, solid, fluid, and gaseous bodies may be transformed one into another. In this process however, a peculiar phenomenon shows itself so far as heat relations are concerned. I will first describe the phenomenon and then we will demonstrate it in a simple fashion. If we select any solid body and heat it, it will become warmer and warmer and finally come to a point where it will go over from the solid to the fluid condition. By means of a thermometer we can determine that as the body absorbs heat, its temperature rises. At the moment when the body begins to melt, to become fluid, the thermometer ceases rising. It remains stationary until the entire body has become fluid, and only begins to rise again when all of the solid is melted. Thus we can say: during the process of melting, the thermometer shows no increase in temperature. It must not be concluded from this however, that no heat is being absorbed. For if we discontinue heating, the process of melting will stop. (I will speak more of this subsequently.) Heat must be added in order to bring about melting, but the heat does not show itself in the form of an increase in temperature on the thermometer. The instrument begins to show an increase in temperature only when the melting has entirely finished, and the liquid formed from the solid begins to take up the heat. Let us consider this phenomenon carefully. For you see, this phenomenon shows discontinuity to exist in the process of temperature rise. We will collect a number of such facts and these can lead us to a comprehensive view of heat unless we go over to some reasoned-out theory. We have prepared here this solid body, sodium thiosulphate, which solid we will melt. You see here a temperature of about 25° C. Now we will proceed to heat this body and I will request someone to come up and watch the temperature to verify the fact that while the body is melting the temperature does not rise.(Note: The thermometer went to 48° C. which is the melting point of sodium thiosulphate, and remained there until the substance had melted.) Now the thermometer rises rapidly, since the melting is complete, although it remained stationary during the entire process of melting. Suppose we illustrate this occurrence in a simple way, as follows: The temperature rise we will consider as a line sloping upward in this fashion (Fig. 1). Assume we have raised the temperature to the melting point as it is called. So far as the thermometer shows, the temperature again rises. It can be shown that through this further temperature rise, with its corresponding addition of heat, the liquid in question expands. Now if we heat such a melted body further, the temperature rises again from the point at which melting took place (dotted line.) It rises as long as the body remains fluid. We can then come upon another point at which the liquid begins to boil. Again we have the same phenomenon as before. The thermometer shows no further temperature rise until the entire liquid is vaporized. At the moment when the fluid has vaporized, we would find by holding the thermometer in the vapor that it again shows a temperature rise (dot-dash line.) You can see here that during vaporizing the instrument does not rise. There I find a second place where the thermometer remains stationary. (Note: the thermometer remained at 100° C. in a vessel of boiling water.) Now I will ask you to add to the fact I have brought before you, another which you will know well from ordinary experience. If you consider solids, which form our starting point, you know that they hold their shape of themselves, whatever form is given them they maintain. If I place a solid here before you it remains as it is. If you select a fluid, that is, a body that has by the application of heat been made to go through the melting point, you know that I cannot handle it piece by piece, but it is necessary to place it in a vessel, and it takes the form of the vessel, forming a horizontal upper surface. (Fig. 3) If I select a gas — a body that has been vaporized by passing through the boiling point, I cannot keep it in an open vessel such as I use for the liquid, it will be lost. Such a gas or vapor I can hold only in a vessel closed in on all sides, otherwise the gas spreads out in all directions. (Fig. 4) This holds, at least for superficial observation, and we will consider the matter first in this way. And now I would ask you to make the following consideration of these things with me. We make this consideration in order to bring facts together so that we can reach a general conception of the nature of heat. Now have we determined the rise in temperature? We have determined it by means of the expansion of quicksilver. The expansion has taken place in space. And since at our ordinary temperature quicksilver is a liquid, we must keep clear in our minds that it is confined in a vessel, and the three dimensional expansion is summed up so that we get an expansion in that direction. By reducing the expansion of quicksilver in three dimensions to a single dimension, we have made this expansion measure the temperature rise. Let us proceed from this observation which we have laid out as a fundamental and consider the following: Assume a line (Fig. 5) Naturally, a line can only exist in thought. And suppose on this line there lie a number of points \(a\), \(b\), \(c\), \(d\), etc. If you wish to reach these points you can remain in the line. If, for instance, you are at this point \(a\) you can reach c by passing along the line. You can pass back again and again reach the point a. In brief, if I desire to reach the points \(a\), \(b\), \(c\), \(d\), I can do so and remain entirely in the line. The matter is otherwise when we consider the point \(e\) or the point \(f\). You cannot remain in the line if you wish to reach point \(e\) or \(f\). You must go outside to reach these points. You have to move along the line and then out of it to get to these points. Now assume you have a surface, let us say the surface of the blackboard, and again I locate on the surface of this board a number of points; \(a\), \(b\), \(c\), \(d\). (Fig. 6) In order to reach these points you may remain always in the surface of the blackboard. If you are at this point \(x\) you may trace your way to each of these points over a path that does not leave the blackboard. You cannot, however, if you wish to remain in the surface of the board, reach this point which is at a distance in front of the board. In this case you must leave the surface. This consideration leads to a view of the dimensionality of space from which one can say: To reach points in one dimension, movement in this single direction suffices, for those in two dimensions movement in two dimensions gives access to them. It is however, not possible to reach points outside a single dimension without leaving this dimension and likewise one cannot pass through points in three dimensions by moving about in a single plane. What is involved when I consider the points e and f in relation to the single dimension represented by points \(a\), \(b\), \(c\) and \(d\) ? Imagine a being who was able to observe only one dimension and who had no idea of a second or third dimension. Such a being would move in his one dimension just as you do in three dimensional space. If such a being carried the point \(a\) to the position \(b\) and the point then slipped off to e, at that moment the content of the point would simply vanish from the single dimension of the being. It would no longer exist for this being from the moment it left the single dimension of which he is aware. Likewise the points outside a surface would not exist for a being aware only of two dimensions. When a point dropped out of the plane, such a being would have no way of following it; the point would disappear form his space realm. What kind of a geometry would a unidimensional being have? He would have a one-dimensional geometry. He would be able to speak only of distance and the like, of the laws relating to such things as they applied in a single dimension. A two-dimensional being would be able to speak of the laws of plane figures and would have a two-dimensional geometry. We men have at the outset a three-dimensional geometry. A being with a unidimensional geometry would have no possibility of understanding what a point does when it leaves the single dimension. A being with a two-dimensional geometry would be unable to follow the motion of a point that left a surface and moved out in front of it as we supposed was the case when the point left a surface and moved out in front of it as we supposed was the case when the point left the surface of the blackboard. We men — I state again — have a three-dimensional geometry. Now I may just as well do what I am obliged to do on account of the reducing of the three-dimensional expansion of the quicksilver to a single dimension. I may draw two lines in two directions so as to form a system of axes, thus giving as in Fig. 7 an axis of abscissae and an axis of ordinates. At right angles to the plane of these two, suppose we have a third line which we will call a space line. 1 Referring again to the temperature rise diagram – tr . Just as soon as I come either to the melting point or the boiling point, at that moment I am not in a position to proceed with the line (Fig. 8). Theoretically or hypothetically there is no possibility of continuing the line. Let us assume that we can say, the rise of temperature is represented by this line. We can proceed along it and still have a point of connection with our ordinary world. But we do not as a matter of fact have such a point of connection. For when I draw this temperature curve and come to the melting or boiling point, I can only continue the curve from the same point (\(x\), \(x\) in Fig. 8). I had reached when the body had begun to melt or vaporize. You can see from this, that in regard to the melting or boiling point, I am in a position not different from that of the one-dimensional being when a point moves out of his first dimension into the second dimension, or of the two-dimensional being when a point disappears for him into the third dimension. When the point comes back again and starts from the same place, or as in Fig. 5 when the point moves out to one side and returns, then it is necessary to continue the line on in its one dimension. Considered simply as an observed phenomenon, when the temperature rise disappears at the melting and boiling point, it is as though my temperatures curve were broken, and I had to proceed after a time from the same point. But what is happening to the heat during this interruption falls outside the realm in which I draw my curve. Formally speaking, I may say that I can draw this on the space line. There is, at first considered — note I say at first — an analogy present between the disappearance of the point a from the first and into the second dimension and what happens to the temperature as shown by the thermometer when the instrument stands still at the melting point and the boiling point. Now we have to bring another phenomenon in connection with this. Please note that in this linking together of phenomena we make progress, not in elaborating some kind of theory, but in bringing together phenomena so that they naturally illuminate each other. This is the distinction between the physics of Goethe that simply places phenomena side by side so that they throw light on each other, and modern physics which tends to go over into theories, and to add thought-out elaborations to the facts. For atoms and molecules are nothing else but fancies added to the facts. Let us now consider another phenomenon along with this disappearance of the temperature recorded by the thermometer during the process of melting. This other phenomenon meets us when we look at yesterday's formula. This formula was written: $$V=V_o(1 + 3 \alpha t + 3 \alpha^2 t^2 + \alpha^3 t^3)$$ You remember that I said yesterday you should pay especial attention to the last two terms. It is especially important for us at this time to consider \(t^3\), the third power of the temperature. Imagine for a moment ordinary space. In this ordinary space you speak in mathematical terms of length, breadth, and thickness. These are actually the three dimensions of space. Now when we warm a rod, as we did yesterday, we can observe the expansion of this rod. We can also note the temperature of this rod. There is one thing we cannot bring about. We cannot bring it about that the rod while it is expanding, does not give off heat to its surroundings, that it does not stream out or radiate heat. This we cannot prevent. It is impossible for us to think — note the word — of a propagation of heat in one dimension. We can indeed think of a space extension in one dimension as one does in geometry in the case of a line. But we cannot under any circumstances imagine heat propagated along a line . When we consider this matter we cannot say that the propagation of heat is to be thought of as represented in space in reality by the line that I have drawn here. (Fig. 1) This curve does not express for me the whole process involved in the heat. Something else is active besides what I can deduce from the curve. And the activity of this something changes the entire nature and being of what is shown by this curve, which I am using as a symbol which may be considered equally well as a purely arithmetical or geometrical fact. We have, thus, a peculiar situation. When we try to grasp the heat condition, in so far as the temperature shows this condition, by means of an ordinary geometrical line, we find it cannot be done. Now this has another bearing. Imagine for a moment that I have a line. This line has a certain length: \(l\) (Fig. 9) I square this line, and then I can represent this \(l^2\) by a square surface. Assume that I obtain \(l^3\) then I can represent the third power by a cube, a solid body. But suppose I obtain the fourth power, \(l^4\). How can I represent that? I can pass over from the line to the surface, from the surface to the solid, but what can I do by following this same method if I wish to represent the fourth power? I cannot do anything if I remain in our three-dimensional space. The mathematical consideration shows this. But we have seen that the heat condition in so far as it is revealed by temperature is not expressible in space terms. There is something else in it. If there were not, we could conceive of the heat condition passing along a rod as confined entirely to the rod. This, however, is impossible. The consequence of this is that when I really wish to work in this realm, I ought not to look upon the powers of \(t\) in the same manner as the powers of a quantity measured in space. I cannot think about the powers of \(t\) in the same way as those of \(l\) or of any other mere space quantity. When, for instance, and I will consider this tomorrow hypothetically, when I have the first power and find it not expressible as a line, then the second power \(t^2\) cannot be expressed as a surface and certainly the third power \(t^3\) cannot be expressed as a solid. In purely mathematical space, it is only after I have obtained the third power that I get outside of ordinary space, but in this other case I am quite outside of ordinary space in the case of the second power and the third as well. Therefore, you must realize that you have to conceive of \(t\) as different entirely in its nature from space quantities. You must consider \(t\) as something already squared, as a second power and the squared \(t\) you must think of as of the third power, the cubed \(t\) as of the fourth power. This takes us out of ordinary space. Consider now how this gives our formula a very special aspect. For the last member, which is in this super-space, forces me to go out of ordinary space. In such a case when I confine myself to reckoning I must go beyond three dimensional space for the last member of the formula. There is such a possibility in purely mathematical formulae. When you observe a triangle and determine that it has three angles, you are dealing, at the start, with a conceived triangle. Since merely thinking about it is not enough to satisfy your senses, you draw it, but the drawing adds nothing to your idea. You have given, the sum of the angles is 180, or a right-angled triangle — the square of the hypotenuse equals the sum of the squares of the other two sides. These things are handled as I now handle the power of \(t\). Let us now go back and see what we have established as fact. This is the way it is done in geometry. It is always true that when I observe an actual triangle in bridge construction or elsewhere, the abstract idea verifies itself. What I have thought of in the abstract \(t\) has at first a similarity with melting and vaporizing. (We will gradually get nearer to the essence of the reality.) Melting and vaporizing I could not express in terms of the three dimensions of space. The only way I could force them into the curve was to stop and then continue again. In order to prove the hypothesis that I made for you, it was necessary, in the case of the third power, the cube of the temperature, to go outside of three-dimensional space. You see, I am showing you how we must, as it were, break a path if we wish to place together those phenomena which simply by being put side by side illustrate the being of heat and enable us to attain to an understanding similar to that reached in the preceding course of lectures on light. The physicist Crookes approached this subject from entirely different hypotheses. It is significant that his considerations led him to a result similar to the one we have arrived at tentatively and whose validity we will establish in the next lectures. He also concluded the temperature changes had essentially to do with a kind of fourth dimension in space. It is important at this time to give attention to these things because the relativists, with Einstein at their head, feel obliged when they go outside of three-dimensional space, to consider time as the fourth dimension. Thus, in the Einstein formulae, everywhere one finds time as the fourth dimension. Crookes, on the other hand, considered the gain or loss of heat as the fourth dimension. So much for this side-light on historical development. To these phenomena I would ask you now to add what I have formerly emphasized. I have said: An ordinary solid may be handled and it will keep its form, (Fig. 2). That is, it has a determinate boundary. A fluid must be poured into a vessel, (Fig. 3). It always forms a flat upper surface and for the rest takes the shape of the vessel. This is not so for a gas or vaporous body which extends itself in every direction. In order to hold it, I must put it into a vessel closed on all sides, (Fig. 4). This completely closed vessel gives it its form. Thus, in the case of a gas, I have a form only when I shut it in a vessel closed on all sides. The solid body possesses a form simply by virtue of the fact that it is a solid body. It has a form of itself, as it were. Considering the fluid as an intermediate condition, we will note that the solid and gaseous bodies may be described as opposites. The solid body provides for itself that which I must add to the gaseous body, namely the completely surrounding boundary. Now, however, a peculiar thing occurs in the case of a gas. When you put a gas into a smaller volume (Fig. 10), using the same amount of gas but contracting the walls all around, you must use pressure. You have to exert pressure. This means nothing else but that you have to overcome the pressure of the gas. You do it by exerting pressure on the walls which give form to the gas. We may state the matter thus: that a gas which has the tendency to spread out in all directions is held together by the resistance of the bounding walls. This resistance is there of itself in the case of the solid body. So that, without any theorizing, but simply keeping in mind the quite obvious facts, I can define a polaric contrast between a gas and a solid body in the following way: That which I must add to the gas from the outside is present of itself in the solid. But now, if you cool the gas, you can pass back again to the boiling point and get a liquid from the vapor, and if you cool further to the melting point, you can get the solid from the liquid. That is to say, you are able by processes connected with the heat state to bring about a condition such that you no longer have to build the form from the outside, but the creation of form takes place of itself from within. Since I have done nothing but bring about a change in the heat condition, it is self-evident that form is related in some way to changes in the heat state. In a solid, something is present which is not present in a gas. If we hold a wall up against a solid, the solid does not of itself exert pressure against the wall unless we ourselves bring this about. When, however, we enclose a gas in a vessel, the gas presses against the solid wall. You see, we come upon the concept of pressure and have to bring this creation of pressure into relation with the heat condition. We have to say to ourselves: it is necessary to find the exact relation between the form of solid bodies, the diffusing tendency of gases and the opposition of the boundary walls that oppose this diffusion. When we know this relation we can hope really to press forward into the relation between heat and corporeality.

The Warmth Course

Lecture III

https://rsarchive.org/Lectures/GA321/English/MP1980/19200303p01.html

Stuttgart

3 Mar 1920

GA321-3

My dear friends, You will perhaps have noticed that in our considerations here, we are striving for a certain particular goal. We are trying to place together a series of phenomena taken from the realm of heat in such a manner that the real nature of warmth may be obvious to us from these phenomena. We have become acquainted in a general way with certain relations that meet us from within the realm of heat, and we have in particular observed the relation of this realm of the expansionability of bodies. We have followed this with an attempt to picture to ourselves mentally the nature of form in solid bodies, fluids and gaseous bodies. I have also spoken of the relation of heat to the changes produced in bodies in going from the solid to the fluid and from the fluid to the gaseous or vaporous condition. Now I wish to bring before you certain relations which come up when we have to do with gases or vapors. We already know that these are so connected with heat that by means of this we bring about the gaseous condition, and again, by appropriate change of temperature that we can obtain a liquid from a gas. Now you know that when we have a solid body, we cannot by any means interpenetrate this solid with another. The observation of such simple elementary relations is of enormous importance if we really wish to force our way through to the nature of heat. The experiment I will carry out here will show that water vapor produced here in this vessel passes through into this second vessel. And now having filled the second vessel with water vapor, we will produce in the first vessel another vapor whose formation you can follow by reason of the fact that it is colored. (The experiment was carried out.) You see that in spite of our having filled the vessel with water vapor, the other vapor goes into the space filled with the water vapor. That is, a gas does not prevent another gas from penetrating the space it occupies. We may make this clear to ourselves by saying that gaseous or vaporous bodies may to a certain extent interpenetrate each other. I will now show you another phenomenon which will illustrate one more relation of heat to certain facts. We have here in the left hand tube, air which is in equilibrium with the outer air with which we are always surrounded. I must remind you that this outer air surrounding us is always under a certain pressure, the usual atmospheric pressure, and it exerts this pressure on us. Thus, we can say that air inside the left hand tube is under the same pressure as the outer air itself, which fact is shown by the similar level of mercury in the right and left hand tubes. You can see that on both right and left hand sides the mercury column is at the same height, and that since here on the right the tube is open to the atmosphere the air in the closed tube is at atmospheric pressure. We will now alter the conditions by bringing pressure on the air in the left hand tube, (\(2\) × \(p\)) . By doing this we have added to the usual atmospheric pressure, the pressure due to the higher mercury column. That is, we have simply added the weight of the mercury from here to here. (Fig. 1b from \(a\) to \(b\)). By thus increasing the pressure exerted on this air by the pressure corresponding to the weight of the mercury column, the volume of the air in the left hand tube is, as you can see, made smaller. We can therefore say when we increase the pressure on the gas its volume decreases. We must extend this and consider it a general phenomenon that the space occupied by a gas and the pressure exerted on it have an inverse ratio to each other. The greater the pressure the smaller the volume, and the greater the volume the smaller must be the pressure acting on the gas. We can express this in the form of an equation where the volume \(V_1\) divided by the volume \(V_2\) equals the pressure \(P_2\) divided by the pressure \(P_1\). From which it follows: This expresses a relatively general law (we have to say relative and will see why later.) This may be stated as follows: volume and pressure of gases are so related that the volume-pressure product is a constant at constant temperature. As we have said, such phenomena as these must be placed side by side if we are to approach the nature of heat. And now, since our considerations are to be thought of as a basis for pedagogy we must consider the matter from two aspects. On the one hand, we must build up a knowledge of the method of thinking of modern physics and on the other, we must become acquainted with what must happen if we are to throw aside certain obstacles that modern physics places in the path to a real understanding of the nature of heat. Please picture vividly to ourselves that when we consider the nature of heat we are necessarily dealing at the same time with volume increases, that is with changes in space and with alterations of pressure. In other words, mechanical facts meet us in our consideration of heat. I have to speak repeatedly in detail of these things although it is not customary to do this. Space changes, pressure changes. Mechanical facts meet us. Now for physics, these facts that meet us when we consider heat are purely and simply mechanical facts. These mechanical occurrences are, as it were, the milieu in which heat is observed. The being of heat is left, so to speak, in the realm of the unknown and attention is focused on the mechanical phenomena which play themselves out under its influence. Since the perception of heat is alleged to be purely a subjective thing, the expansion of mercury, say, accompanying change of heat condition and of sensation of heat, is considered as something belonging in the realm of the mechanical. The dependence of gas pressure, for instance, on the temperature, which we will consider further, is thought of as essentially mechanical and the being of heat is left out of consideration. We saw yesterday that there is a good reason for this. For we saw that when we attempt to calculate heat, difficulties arise in the usual calculations and that we cannot, for example, handle the third power of the temperature in the same way as the third power of an ordinary quantity in space. And since modern physics has not appreciated the importance of the higher powers of the temperature, it has simply stricken them out of the expansion formulae I mentioned to you in former lectures. Now you need only consider the following. You need consider only that in the sphere of outer nature heat always appears in external mechanical phenomena, primarily in space phenomena. Space phenomena are there to begin with and in them the heat appears. This it is, my dear friends, that constrains us to think of heat as we do of lines in space and that leads us to proceed from the first power of extension in space to the second power of the extension. When we observe the first power of the extension, the line, and we wish to go over to the second power, we have to go out of the line. That is, we must add a second dimension to the first. The standard of measurement of the second power has to be thought of as entirely different from that of the first power. We have to proceed in an entirely similar fashion when we consider a temperature condition. The first power is, so to speak, present in the expansion. Change of temperature and expansion are so related that they may be expressed by rectilinear coordination (Fig. 2). I am obliged, when I wish to make the graph representing change in expansion with change in temperature, to add the axis of abscissae to the axis of ordinates. But this makes it necessary to consider what is appearing as temperature not as a first power but as a second power, and the second power as a third. When we deal with the third power of the temperature, we can no longer stay in our ordinary space. A simple consideration, dealing it is true with rather subtle distinctions, will show you that in dealing with the heat manifesting itself as the third power, we cannot limit ourselves to the three directions of space. It will show you how, the moment we deal with the third power, we are obliged, so far as heat effects are concerned, to go out of space. In order to explain the phenomena, modern physics sets itself the problem of doing so and remaining within the three dimensional space. You see, here we have an important point where physical science has to cross a kind of Rubicon to a higher view of the world. And one is obliged to emphasize the fact that since so little attempt is made to attain clarity at this point, a corresponding lack enters into the comprehensive world view. Imagine to yourselves that physicists would so present these matters to their students as to show that one must leave ordinary space in which mechanical phenomena play when heat phenomena are to be observed. In such a case, these teachers of physics would call forth in their students, who are intelligent people since they find themselves able to study the subject, the idea that a person cannot really know it without leaving the three dimensional space. Then it would be much easier to place a higher world-view before people. For people in general, even if they were not students of physics, would say, “We cannot form a judgment on the matter, but those who have studied know that the human being must rise through the physics of space to other relations than the purely spatial relations.” Therefore so much depends on our getting into this science such ideas as those put forth in our considerations here. Then what is investigated would have an effect on a spiritually founded world view among people in general quite different from what it has now. The physicist announces that he explains all phenomena by means of purely mechanical facts. This causes people to say, “Well, there are only mechanical facts in space. Life must be a mechanical thing, soul phenomena must be mechanical and spiritual things must be mechanical.” “Exact sciences” will not admit the possibility of a spiritual foundation for the world. And “exact science” works as an especially powerful authority because they are not familiar with it. What people know, they pass their own judgment on and do not permit it to exercise such an authority. What they do not know they accept on authority. If more were done to popularize the so-called “rigidly exact science,” the authority of some of those who sit entrenched in possession of this exact science would practically disappear. During the course of the 19th century there was added to the facts that we have already observed, another one of which I have spoken briefly. This is that mechanical phenomena not only appear in connection with the phenomena of heat, but that heat can be transformed into mechanical phenomena. This process you see in the ordinary steam locomotive where heat is applied and forward motion results. Also mechanical processes, friction and the like, can be transformed back again into heat since the mechanical processes, as it is said, bring about the appearance of heat. Thus mechanical processes and heat processes may be mutually transformed into each other. We will sketch the matter today in a preliminary fashion and go into the details pertaining to this realm in subsequent lectures. Further, it has been found that not only heat but electrical and chemical processes may be changed into mechanical processes And from this has been developed what has been called during the 19th century the “mechanical theory of heat.” This mechanical theory of heat has as its principal postulate that heat and mechanical effects are mutually convertible one into the other. Now suppose we consider this idea somewhat closely. I am unable to avoid for you the consideration of these elementary things of the realm of physics. If we pass by the elementary things in our basic consideration, we will have to give up attaining any clarity in this realm of heat. We must therefore ask the questions: what does it really mean then when I say: Heat as it is applied in the steam engine shows itself as motion, as mechanical work? What does it mean when I draw from this idea: through heat, mechanical work is produced in the external world? Let us distinguish clearly between what we can establish as fact and the ideas which we add to these facts. We can establish the fact that a process subsequently is revealed as mechanical work, or shows itself as a mechanical process. Then the conclusion is drawn that the heat process, the heat as such, has been changed into a mechanical thing, into work. Well now, my dear friends, if I come into this room and find the temperature such that I am comfortable, I may think to myself, perhaps unconsciously without saying it in words: In this room it is comfortable. I sit down at the desk and write something. Then following the same course of reasoning as has given rise to the mechanical theory of heat, I would say: I came into the room, the heat condition worked on me and what I wrote down is a consequence of this heat condition. Speaking in a certain sense I might say that if I had found the place cold like a cellar, I would have hurried out and would not have done this work of writing. If now I add to the above the conclusion that the heat conducted to me has been changed into the work I did, then obviously something has been left out of my thinking. I have left out all that which can only take place through myself. If I am to comprehend the whole reality I must insert into my judgment of it this which I have left out. The question now arises: When the corresponding conclusion is drawn in the realm of heat, by assuming that the motion of the locomotive is simply the transformed heat from the boiler, have I not fallen into the error noted above? That is, have I not committed the same fallacy as when I speak of a transformation of heat into an effect which can only take place because I myself am part of the picture? It may appear to be trivial to direct attention to such a thing as this, but it is just these trivialities that have been completely forgotten in the entire mechanical theory of heat. What is more, enormously important things depend on this. Two things are bound together here. First, when we pass over from the mechanical realm into the realm where heat is active we really have to leave three dimensional space, and then we have to consider that when external nature is observed, we simply do not have that which is interpolated in the case, where heat is changed over into my writing. When heat is changed into my writing, I can note from observation of my external bodily nature that something has been interpolated in the process. Suppose however, that I simply consider the fact that I must leave three dimensional space in order to relate the transformation of heat into mechanical effects. Then I can say, perhaps the most important factor involved in this change plays its part outside of three dimensional space. In the example that concerned myself which I gave you, the manner in which I entered into the process took place outside of three dimensions. And when I speak of simple transformation of heat into work I am guilty of the same superficiality as when I consider transformation of heat into a piece of written work and leave myself out. This, however, leads to a very weighty consequence. For it requires me to consider in external nature even lifeless inorganic nature, a being not manifested in three dimensional space. This being, as it were, rules behind the three dimensions. Now this is very fundamental in relation to our studies of heat itself. Since we have outlined the fundamentals of our conception of the realm of heat, we may look back again on something we have already indicated, namely on man's own relation to heat. We may compare the perception of heat to perception in other realms. I have already called attention to the fact that, for instance, when we perceive light, we note this perception of light to be bound up with a special organ. This organ is simply inserted into our body and we cannot, therefore, speak of being related to color and light with our whole organism, but our relation to it concerns a part of us only. Likewise with acoustical or sound phenomena, we are related to them with a portion of our organism, namely the organ of hearing. To the being of heat we are related through our entire organism. This fact, however, conditions our relation to the being of heat. We are related to it with our entire organism. And when we look more closely, when we try, as it were, to express these facts in terms of human consciousness, we are obliged to say, “We are really ourselves this heat being. In so far as we are men moving around in space, we are ourselves this heat being.” Imagine the temperature were to be raised a couple of hundred degrees; at that moment we could no longer be identical with it, and the same thing applies if you imagine it lowered several hundred degrees. Thus the heat condition belongs to that in which we continually live, but do not take up into our consciousness. We experience it as independent beings, but we do not experience it consciously. Only when some variation from the normal condition occurs, does it take conscious form. Now with this fact a more inclusive one may be connected. It is this. You may say to yourselves when you contact a warm object and perceive the heat condition by means of your organism, that you can do it with the tip of your tongue, with the tip of your finger, you can do it with other parts of your organism: with the lobes of your ears, let us say. In fact, you can perceive the heat condition with your entire organism. But there is something else you can perceive with your entire organism. You can perceive anything exerting pressure. And here again, you are not limited strictly as you are in the case of the eye and color perception to a certain member of your entire organism. If would be very convenient if our heads, at least, were an exception to this rule of pressure perception; we would not then be made so uncomfortable from a rap on the head. We can say there is an inner kinship between the nature of our relationship to the outer world perceived as heat and perceived as pressure. We have today spoken of pressure volume relations. We come back now to our own organism and find an inner kinship between our relation to heat and to pressure. Such a fact must be considered as a groundwork for what will follow. But there is something else that must be taken into account as a preliminary to further observations. You know that in the most popular text books of physiology, a good deal of emphasis is laid on the fact that we have certain organs within our bodies by means of which we perceive the usual sense qualities. We have the eye for color, the ear for sound, the organ of taste for certain chemical processes, etc. We have spread over our entire organism, as it were, the undifferentiated heat organ, and the undifferentiated pressure organ. Now, usually, attention is drawn to the fact that there are certain other things of which we are aware but for which we have no organs. Magnetism and electricity are known to us only through their effects and stand, as it were, outside of us, not immediately perceived. It is said sometimes that if we imagine our eyes were electrically sensitive instead of light sensitive, then when we turned them towards a telegraph wire we would perceive the streaming electricity in it. Electricity would be known not merely by its effects, but like light and color, would be immediately perceived. We cannot do this. We must therefore say: electricity is an example of something for whose immediate perception we have no organ. There are aspects of nature, thus, for which we have organs and aspects of nature for which we do not have organs. So it is said. The question is whether perhaps a more unbiased observer would not come to a different conclusion from those whose view is expressed above. You all know, my dear friends, that what we call our ordinary passive concepts through which we apprehend the world, are closely bound up with the impressions received through the eye, the ear and somewhat less so with taste and smell impressions. If you will simply consider language, you may draw from it the summation of your conceptual life, and you will become aware that the words themselves used to represent our ideas are residues of our sense impressions. Even when we speak the very abstract word Sein (being), the derivation is from Ich habe gesehen , (I have seen.) What I have seen I can speak of as possessing “being.” In “being” there is included “what has been seen.” Now without becoming completely materialistic (and we will see later why it is not necessary to become so), it may be said that our conceptual world is really a kind of residue of seeing and hearing and to a lesser extent of smelling and tasting. (Those last two enter less into our higher sense impressions.) Through the intimate connection between our consciousness and our sense impressions, this consciousness is enabled to take up the passive concept world. But within the soul nature, from another side, comes the will, and you remember how I have often told you in these anthroposophical lectures that man is really asleep so far as his will is concerned. He is, properly considered, awake only in the passive conceptual realm. What you will, you apprehend, only through these ideas or concepts. You have the idea. I will raise this glass. Now, in so far as your mental act contains ideas, it is a residue of sense impressions. You place before yourself in thought something which belongs entirely in the realm of the seen, and when you think of it, you have an image of something seen. Such an immediately derived image you cannot create from a will process proper, from what happens when you stretch out your arm and actually grasp the glass with your hand and raise it. That act is entirely outside of your consciousness. You are not aware of what happens between your consciousness and the delicate processes in your arm. Our unconsciousness of it is as complete as our unconsciousness between falling asleep and waking up. But something really is there and takes place, and can its existence be denied simply because it does not enter our consciousness? Those processes must be intimately bound up with us as human beings, because after all, it is we who raise the glass. Thus we are led in considering our human nature from that which is immediately alive in consciousness to will processes taking place, as it were, outside of consciousness. (Fig. 3) Imagine to yourselves that everything above this line is in the realm of consciousness. What is underneath is in the realm of will and is outside of consciousness. Starting from this point we proceed to the outer phenomena of nature and find our eye intimately connected with color phenomena, something which we can consciously apprehend; we find our ear intimately connected with sound, as something we can consciously apprehend. Tasting and smelling are, however, apprehended in a more dreamlike way. We have here something which is in the realm of consciousness and yet is intimately bound up with the outer world. If now, we go to magnetic and electrical phenomena, the entity which is active in these is withdrawn from us in contrast with those phenomena of nature which have immediate connection with us through certain organs. This entity escapes us. Therefore, say the physicists and physiologists: we have no organ for it; it is cut off from us. It lies outside us. (Fig. 3 above) We have realms that we approach when we draw near the outer world — the realms of light and heat. How do electrical phenomena escape us? We can trace no connection between them and any of our organs. Within us we have the results of our working over of light and sound phenomena as residues in the form of ideas. When, however, we plunge down (Fig. 3 below), our own being disappears from us into will. I will now tell you something a bit paradoxical, but think it over until tomorrow. Imagine we were not living men, but living rainbows, and that our consciousness dwelt in the green portion of the spectrum. On the one side we would trail off into unconsciousness in the yellow and red and this would escape us inwardly like our will. If we were rainbows, we would not perceive green, because that we are in our beings, we do not perceive immediately; we live it. We would touch the border of the real inner when we tried, as it were, to pass from the green to the yellow. We would say: I, as a rainbow, approach my red portion, but cannot take it up as a real inner experience; I approach my blue-violet, but it escapes me. If we were thinking rainbows, we would thus live in the green and have on the one side a blue-violet pole and on the other side a yellow-red pole. Similarly, we now as men are placed with our consciousness between what escapes us as external natural phenomena in the form of electricity and as inner phenomena in the form of will.

The Warmth Course

Lecture IV

https://rsarchive.org/Lectures/GA321/English/MP1980/19200304a01.html

Stuttgart

4 Mar 1920

GA321-4

My dear friends, I would have liked to carry out for you today some experiments to round out the series of facts that lead us to our goal. It is not possible to do so, however, and I must accordingly arrange my lecture somewhat differently from the way I intended. The reason for this is partly that the apparatus is not in working order and partly because we lack alcohol today, just as we lacked ice yesterday. We will therefore take up in more detail the things that were begun yesterday. I will ask you to consider all these facts that were placed before you for the purpose of obtaining a survey of the relationships of various bodies to the being of heat. You will realize that certain typical phenomena meet us. We can say: These phenomena carry the impress of certain relations involving the being of heat, at first unknown to us. Heat and pressure exerted on a body or the state of aggregation that a body assumes according to its temperature, also the extent of space occupied, the volume, are examples. We are able on the one side, to see how a solid body melts, and can establish the fact that during the melting of the solid, no rise in temperature is measurable by the thermometer or any other temperature-measuring instrument. The temperature increase stands still, as it were, during the melting. On the other hand, we can see the change from a liquid to a gas, and there again we find the disappearance of the temperature increase and its reappearance when the whole body has passed into the gaseous condition. These facts make up a series that you can demonstrate for yourselves, and that you can follow with your eyes, your senses and with instruments. Yesterday, also, we called attention to certain inner experiences of the human being himself which he has under the influence of warmth and also under the influence of other sense qualities such as light and tone. But we saw that magnetism and electricity were not really sense impressions, at least not immediate sense impressions, because as ordinary physics says, there is no sense organ for these entities. We say, indeed, that so far as electrical and magnetic properties are concerned we come to know them through determining their effects, the attraction of bodies for instance, and the many other effects of electrical processes. But we have no immediate sense perception of electricity and magnetism as we have for tone and light. We then noted particularly, and this must be emphasized, that our own passive concepts, by which we represent the world, are really a kind of distillation of the higher sense impressions. Wherever you make an examination you will find these higher concepts and will be able to convince yourselves that they are the distilled essence of the sense impressions. I illustrated this yesterday in the case of the concept of being. You can get echoes of tone in the picture of the conceptual realm, and you can everywhere see showing through how these concepts have borrowed from light . But there is one kind of concept where you cannot do this, as you will soon see. You cannot do it in the realm of the mathematical concepts. In so far as they are purely mathematical, there is no trace of the tonal or the visible. Now we must deceive ourselves here. Man is thinking of tone when he speaks of the wave number of sound vibrations. Naturally I do not refer to this sort of thing. I mean all that is obtained from pure mathematics. Such things, for instance, as the content of the proposition of Pythagoras, that the sum of the angles of a triangle is 180°, or that the whole is greater than the part, etc. The basis of our mathematical concepts does not relate itself to the seen or the heard, but it relates itself in the last analysis to our will impulse . Strange as it may seem to you at first, you will always find this fact when you look at these things from the psychological point of view, as it were. The human being who draws a triangle (the drawn triangle is only an externalization) is attaining in concept to an unfolding of the will around the three angles . There is an unfolding of action around three angles as shown by the motion of the hand or by walking, by turning of the body. The thing that you have within you as a will-concept, that in reality you carry into the pure mathematical concept. That is the essential distinction between mathematical concepts and other concepts. This is the distinction about which Kant and other philosophers waged such controversy. You can distinguish the inner determination of mathematical concepts. This distinction arises from the fact that mathematical concepts are so rigidly bound up with our own selves, that we carry our will nature into them. Only what subsists in the sphere of the will is brought into mathematical operations. This is what makes them seem so certain to us. What is not felt to be so intimately bound up with us, but is simply felt through an organ placed in a certain part of our make-up, that appears uncertain and empirical. This is the real distinction. Now, I wish to call your attention to a certain fact. When we dip down into the sphere of will, whence came, in a vague and glimmering way, the abstractions which make up the sum of our pure arithmetical and geometrical concepts, we enter the unknown region where the will rules, a region as completely unknown to us in the inner sense, as electricity and magnetism are in the outer sense. Yesterday I endeavored to illustrate this by asking you to imagine yourselves living, thinking rainbows with your consciousness in the green, in consequence of which you did not perceive the green but perceived the colors on each side of it, fading into the unknown. I compared the red to the dipping down inwardly into the unknown sphere of the will and the blue-violet to the outward extension into the spheres of electricity and magnetism and the like . Now I am inserting at this point in our course this psychological-physiological point of view, as it might be called, because it is very essential for the future that people should be led back again to the relation of the human being to physical observations. Unless this relationship is established, the confusion that reigns at present cannot be eliminated. We will see this as we follow further the phenomena of heat. But it is not so easy to establish this relationship in the thinking of today. The reason is just this, that modern man cannot easily bridge the gap between what he perceives as outer space phenomena in the world, or better, as outer sense phenomena and what he experiences within. In these modern times there is such a pronounced dualism between all which we experience as knowledge of the outer world and what we experience inwardly, that it is extraordinarily difficult to bridge this gap, But the gap must be bridged if physics is to advance. To this end we must use the intuitive faculties rather than the rational when we relate something external to what goes on within man himself. Thus we can begin to grasp how we must orient ourselves, in observing phenomena so difficult as those arising from heat. Let me call your attention to the following: Suppose you learn a poem by heart. You will, as you learn it, first find it necessary to become acquainted with the ideas that underlie the poem. At first you will always have the tendency, when you recite the poem, to let those ideas unroll in your mind. But you know that the more frequently you recite the poem, especially when there is a lapse of time between the recitations, the less intensely you are obliged to think of the ideas. There may come a time when it is not necessary to think at all, but simply to reel off the recitation mechanically. We never actually reach this point; do not wish to, in fact, but we approach the condition asymptotically as it were. Our feelings as human beings prevent us from reaching this stage of purely mechanical repetition, but it is thinkable that we would get to the point where we needed to think not at all, but when we spoke the first line the rest of the poem would follow without any thinking about it. You recognize the similarity between such a condition and the approach of the hyperbola to its asymptotes. But this leads us to the conception that when we speak a poem we are dealing with two different activities working simultaneously in our organism. We are dealing with a mechanical reeling-off of certain processes, and along with this go the processes included in our soul concepts. On the one hand, we have what we can properly speak of as playing itself out mechanically in space, and on the other hand, we have a soul process which is entirely non-spatial in nature. When now, you fasten your attention simply on that which reels itself off mechanically, and you do this in thought, for instance, if you imagine you recited a poem in an unknown language, then you have simply the mechanical process. The instant you accompany this mechanical process with thinking, then you have an inner soul activity that cannot be brought out into space. You cannot express in space the thinking with which a man accompanies the recitation, as you can the mechanical processes of actual speaking, of the pronouncing of words. Let me give you an analogy. When we follow the heating of a solid body up to the time it arrives at its melting point, the temperature becomes higher. We can see this on the thermometer. When the body begins to melt, the thermometer stands still until the melting is complete. There is an analogy between what we can follow with the thermometer, the outer physical process, and what we can follow physically in the spoken word. And there is an analogy also between what escapes us, and lies in the concepts of the reciter and what happens to the heat while the melting goes on . Here you see, we have an example where we can, by analogy, at least bridge the gap between an outer observation and something in the human being. In other realms than that of speech we do not have such ready examples to bridge the gap. This is because in speech there is, on the one hand, the possibility imaginable, at least, that a person could mechanically speak out something learned by heart. Or on the other hand, that the person would not speak at all but simply think about it and thus remove it entirely from the realm of space. In other spheres we do not have the opportunity to make this cleavage and see precisely how one activity passes over into another. Especially is this difficult when we wish to follow the nature of heat. In this case we have to set out to investigate physiologically and psychologically how heat behaves when we have taken it up into ourselves. Yesterday, by way of illustration, I said to you: “I go into a room that is comfortably warmed, I sit down and write.” I cannot so directly find the inter-relationships between what I experience or feel when I go into the warm room. What goes on within me parallels the outer warmth, when I write my thoughts down. But I cannot determine the relationship so readily as I can between speaking something and thinking about it. Thus it is difficult to find the something within that corresponds to the outer sensation of warmth. It is a question of gradually approaching the concepts that will lead us further in this direction and in this connection I want to call your attention to something you know from your anthroposophy. You know, when we make the attempt to extend our thinking by meditation, to increase its inner intensity, and so to work with our thoughts that we come again and again into the condition where we know we are using soul-forces without the help of the body, we notice a certain thing. We notice that in order to do this, our entire inner soul life has to change. With ordinary abstract thoughts man cannot enter the higher region of human soul life. There thoughts become picture-like and they have to be translated out of the imaginative element in order to get them into abstract form, if they are to be brought into the outer world which is not grasped by the imaginative element. But you need to understand a method of looking at these things, such as is presented, for instance, in my Occult Science . In this book the endeavor is to be as true to the facts as possible, and it is this which has so disturbed the people who are only able to think abstractly. For the attempt must be made to get things over into picture form, as I have done to some extent in the description of the Saturn and Sun states. There you will find purely picture concepts mixed in with the others. It is very hard for people to go over into the pictures, because these things cannot be put into the abstract form. The reason for this is that when we think abstractly, when we move within the narrow confines of concepts, in which people today are so much at home, and especially so in the realm of natural science, when we do this we are using ideas completely dependent on our bodies. We cannot, for instance, do without our bodies when we set out to think through the things set forth as laws in the physics books. There we must think in such a way that we use our bodies as instruments. When we rise to the sphere of the imagination, then the abstract ideas must be completely altered, because our inner soul life no longer uses the physical body. Now you can take what I might call a comprehensive view of the realm of imaginative thought. This realm of imaginative thought has in us nothing to do with what is tied up in our outer corporeality. We rise to a region where we live as beings of soul and spirit without dependence on our corporeality. In other words, the instant we enter the realm of the imaginative, we leave space. We are then no longer in space. Note now, this has an extremely important bearing. I have in the previous course, made a very definite differentiation between mere kinematics and what enters into our consideration as mechanical, such as mass, for instance. As long as I consider only kinematics, I need only think of things. I can write them down on a blackboard or a sheet of paper and complete the survey of motion and space so far as my thinking takes me. But in that case I must remain within what can be surveyed in terms of time and space. Why is this? This is so for a very definite reason. You must make the following clear to yourselves: All human beings, as they exist on earth, are as you yourselves, within time and space. They are bounded by a definite space and are related as space objects to other space objects. Therefore, when you speak of space, you are not able, considering the matter in an unprejudiced way, to take seriously the Kantian ideas. For if space were inside of us, then we could not ourselves be within space. We only think space is inside of us. We can free ourselves of this fancy, of this notion, if we consider the fact that this being-within space has a very real meaning for us. If space were inside of us, it would have no meaning for a person whether he were born in Moscow or Vienna. But where we are born has a very real significance. As a terrestrial-empirical person, I am quite completely a product of space facts. That is, as a human being, I belong to relations that form themselves in space. Likewise, with time, you would all be different persons if you had been born 20 years earlier. That is to say, your life does not have time inside of it, but time has your life within it. Thus as experiencing persons, you stand within time and space. And when we talk of time and space, or when we make a picture of will impulses, as I have explained we do in geometry, this is because we ourselves live inside of spatial and temporal relations, and are therefore quite definitely conditioned by them, and so are able, a priori, to speak of them as we do in mathematics. When you go over to the concept of mass, this is not so. The matter must then be put otherwise. In respect to mass, you are dealing with something quite special. You cannot say that you cut out a portion of time or space, but rather that you live in the general space mass and make it into your own mass. This mass then, is within you. It cannot be gainsaid that this mass with all its activities, all of its potentialities, is active inside of you; at this moment it falls into a different category from time and space so far as its relations to you are concerned. It is precisely because you yourself take part, as it were, with your inner being in the properties of the mass, because you take it up into your being, that it does not allow itself to be brought into consciousness like time and space. In the realm where the world gives us our own substance, we thus enter an unknown region. This is related to the fact that our will is, for instance, closely connected with the phenomena of mass inside us. But we are unconscious of these phenomena; we are asleep to them. And we are related to the will activity and accompany mass phenomena within us in no other way than we are to the world in general between going to sleep and waking up. We are not conscious of either one. Both these things are hidden from human consciousness, and in this respect, there is no immediate distinction between them. Thus we gradually bring these things nearer to the human being. It is this that the physicists shy away from, the bringing of such things near to man. But in no other way can we obtain real concepts except by developing relationship between the human being and the world, a relationship that does not exist at the start, as in the case of time and space. We speak of time and space, let us say, out of our rational faculties, whence comes the remoteness of the mathematical and kinematical sciences. Of the things experienced merely through the senses, in an external fashion, things related to mass, we can at first speak only in an empirical fashion. But we can analyze the relation between the activity of a portion of mass within us and outer mass activity. As soon as we do this we can begin to deal with mass in the same way that we deal with the obvious relation between ourselves and time or ourselves and space. That is, we must grow inwardly into such relation with the world in our physical concepts, as we have for the mathematical or kinematical concepts. It is a peculiar thing that, as we loosen ourselves from our own bodies in which all those things take place to which we are asleep, as we raise ourselves to imaginative concepts, we really take a step nearer the world. We approach always nearer to that which otherwise reigns in us unconsciously. There is no other way to enter into the objectivity of the facts than to push forward with our own developed inner soul forces. At the same time that we detach ourselves from our own materiality, we approach more and more closely to what is going on in the outside world. However, it is not so easy to obtain even the most elementary experiences in this region, since a person must so transform himself that he pays attention to things that are not noticed at all under ordinary circumstances. But now, I will tell you something that will probably greatly astonish you. Let us suppose you have advanced further on the path of imaginative thinking. Suppose you have really begun to think imaginatively. You will then experience something that will astonish you. It will be much easier than it formerly was for you to recite in a merely mechanical way a poem that you have learned by heart. It will not be more difficult for you, but less so. If you examine your soul organism without prejudice and with care, you will at once find that you are more prone to recite a poem mechanically without thinking about it, if you have undergone an occult training than if you have not undergone such a training. You do not dislike this going over into the mechanical so strongly as you did before the occult development. It is such things as this that are not usually stated but are meant when it is said over and over again: The experiences you have in occult training are really opposed to the concepts that are ordinarily had before you enter occult training and thus it is, when the more advanced stage is reached, that one comes to look more lightly on the ideas of ordinary life. And therefore, anyone who advances in occultism is exposed to the danger of afterwards becoming a greater mechanist than before. An orderly occult training guards against this, but the tendency to become materialistic is quite marked in the very people who have undergone occult development. I will, by example, tell you why. You see, in ordinary life, it is really, as the theorists say it is, the brain thinks. But ordinarily, a man does not actually experience this fact. It is quite possible in this ordinary life to carry out such a dialogue as I did in my childhood with a youthful friend who as a crass materialist and became more and more so. He would say, “When I think my brain does the thinking.” I would say to that: “ Yes, but when you are with me you always say, I will do this, I think. Why do you not say, my brain will do this, my brain thinks? You are always speaking an untruth.” The reason is that for the theoretical materialist, quite naturally, there does not exist the possibility of observing the processes in the brain. He cannot observe these physical processes. Therefore, materialism remains for him merely a theory. The moment a person advances somewhat from imaginative to inspirational ideas, he becomes able really to observe the parallel processes in the brain. Then what goes on in the material part of the brain becomes really visible. Aside from the fact that it is extremely seductive, the things a person can observe in his own activity appear to him more and more wonderful to a high degree. For this activity of the brain is observable as something more wonderful than all that the theoretical materialists can describe about it. Therefore, the temperature comes to grow materialistic for the very reason that the activity of the human brain has become observable. Only one is, as has been said, protected from this. But as I have explained to you these steps in occult development, I have at the same time showed you how this development creates the possibility of a deeper penetration into material processes. This is the extraordinary thing. He who functions in the spirit simply as an abstract thing, will be relatively powerless in the face of nature. He grows into contact with other natural phenomena as he has already grown into contact with time and space. We must now set up on the one side, all the things we have just tried to place before our minds, and on the other side, those things that have met us from the realm of heat. What has come to us from the realm of heat? Well, we followed the rise of temperature as we warmed a solid body to melting point. We showed how the temperature rise disappeared for a time, and then re-appeared until the body began to boil, to evaporate. When we extended our observations, another thing appeared. We could see that the gas produced passed over in all directions on its surroundings. (Fig. 1a), seeking to distribute itself in all directions, and could only be made to take on form if its own pressure were opposed by an equal and opposite pressure brought to bear from the outside. These things have been brought out by experiment and will be further cleared up by other experiments. The moment the temperature is lowered to the point where the body can solidify, it can give itself a form (Fig. 1b). When we experience temperature rise and fall, we experience what corresponds externally to form. We are experiencing the dissolution of form and the re-establishment of it. The gas shows us the dissolution, the solid pictures for us the establishment of form. We experience the transition between these two, also, and we experience it in an extremely interesting fashion. For, imagine to yourselves the solid and the gas and the liquid, the fluid body standing between. This liquid need not be enclosed by a vessel surrounding it completely, but only on the bottom and sides. On the upper side, the liquid forms its own surface perpendicular to the line between itself and the center of the earth. Thus we can say that we have here a transition form between the gas and the solid (Fig. 1c). In a gas we never have such a surface. In a liquid such as water, we have one surface formed. In the case of a solid, we have that all around the body which occurs in the liquid only on the upper surfaces. Now this is an extremely interesting and significant relation. For it directs our attention to the fact that a solid body has over its entire surface something corresponding to the upper surface of a liquid, but that it determines the establishment of the surface on a body of water. It is at right angles to the line joining it to the center of the earth. The whole earth conditions the establishment of the surface. We can therefore say: In the case of water, each point within it has the same relation to the entire earth that the points in a solid have to something within the solid. The solid therefore includes something which in the case of water resides in the relation of the latter to the earth. The gas diffuses. The relation to the earth does not take part at all. It is out of the picture. Gases have no surface at all. You will see from this that we are obliged to go back to an old conception. I called your attention in a previous lecture to the fact that the old Greek physicists called solid bodies Earth . They did this, not account of some superficial reason such as has been ascribed to them by people today, but they did it because they were conscious of the fact that the solid, of itself, takes care of that which is the case of water is taken care of by the earth as a whole. The solid takes into itself the role of the earthly. It is entirely justified to put the matter in this way: The earthly resides within a solid. In water it does not reside within, but the whole earth takes up the role of forming a surface on the liquid. Thus you see, when we proceed from solid bodies to water, we are obliged to extend our considerations not only to what actually lies before us but in order to get an intelligent idea of the nature of water, we must extend them to include the water of the whole earth and to think of this as a unity in relation with the central point of the earth. To observe a “fragment” of water as a physical entity is absurd, just as much so as to consider a cut-off garment of my little finger as an organism. It would die at once. It only has meaning as an organism if it is considered in its relation to the whole organism. The meaning that the solid has in itself , can only be attached to water if we consider it in relation to the whole earth. And so it is with all liquids on earth. And again, when we pass on from the fluid to the gaseous, we come to understand that the gaseous removes itself from the influence of the earth. It does not form surfaces. It partakes of everything which is not terrestrial. In other words, we must not merely look on the earth for the activities of a gas, we must bring in the environment of the earth to help us out, we must go out into space and seek there the forces involved. When we wish to learn the laws of the gaseous state, we become involved in nothing less than astronomical considerations. Thus you see how these things are related to the whole terrestrial scheme when we examine the phenomena that we have up to this time simply gathered together. And when we come to such a point as the melting or boiling point, then there enter in things that must now appear to us as very significant. For, if we consider the melting point we pass from the terrestrial condition of the solid body where it determines its own form and relations, to something which includes the whole earth. The earth takes the sold captive when the latter goes over into the fluid state. From its own kingdom, the solid body enters the terrestrial kingdom as a whole when we reach the melting point. It ceases to have individuality. And when we carry the fluid body over into the gaseous condition, then we come to the point where the connection with the earth as shown by the formation of a liquid surface is loosened. The instant we go from a liquid to a gas, the body loosens itself from the earth, as it were, and enters the realm of the extra-terrestrial. When we consider a gas, the forces active in it are to be thought of as having escaped from the earth. Therefore, when we study these phenomena we cannot avoid passing from the ordinary physical-terrestrial into the cosmic. For we no longer are in contact with reality if our attention is not turned to what is actually working in the things themselves. But now another phenomena meets us. Consider such a thing as the one you know very well and to which I have called your attention, namely that water behaves so remarkably, in that ice floats on water, or, stated otherwise, is less dense than water. When it goes over into the fluid condition its temperature rises, and it contracts and becomes denser. Only by virtue of this fact can ice float on the surface of the water. Here we have between zero and four degrees, water showing an exception to the general rule that we find when temperature increases, namely that bodies become less and less dense as they are warmed up. This range of four degrees, where water expands as the temperature is lowered, is very instructive. What do we learn from this range? We learn that the water sets up an opposition. As ice it is a solid body with a kind of individuality, but opposes the transition to an entirely different sphere. It is very necessary to consider such things. For then we begin to get an understanding as to why, under certain conditions, the temperature as determined by a thermometer disappears, say at the melting or boiling points. It disappears just as our bodily reality disappears when we rise to the realm of imagination. We will go into the matter a little more deeply, and it will not appear so paradoxical when we try to clear up further the following: What happens then, when a heat condition obliges us to raise the temperature to the third power, or in this case to go into the fourth dimension, thus passing out of space altogether? Let us at this time, put this proposition before our souls and tomorrow we ill speak further about it. Just as it is possible for our bodily activity to pass over into the spiritual when we enter the imaginative realm, so we can find a path leading from the external and visible in the realm of heat tot he phenomena that are pointed to by our thermometer when the temperature rise we are measuring with it disappears before our eyes. What process goes on behind this disappearance? That is the question which we are asking ourselves today. Tomorrow we will speak of it further.

The Warmth Course

Lecture V

https://rsarchive.org/Lectures/GA321/English/MP1980/19200305p01.html

Stuttgart

5 Mar 1920

GA321-5

My dear friends, We will today first examine a phenomenon that comes in the region where heat, pressure and the expansion of bodies are related. You will see that by a simultaneous examination of the things we experience in this field the way will open to an understanding of what heat really is. First we will turn our attention to what is revealed here in these three tubes. In the first one on the right, we have mercury in a barometer tube and on top of it is some water. Water placed in such a manner in this space evaporates. The water is in a vacuum, as we call it, in empty space, and it can be stated that the water evaporated. The small amount of water in the tube gives off vapor. We can determine that it evaporates by testing for the presence of water vapor in the space above the mercury. When you compare the height of the mercury column in this tube with the height here where the mercury is under the normal atmospheric pressure, and where there is no water vapor over the mercury, you will see that the level is lower in the tube containing water (Fig. 1a, 1b). Naturally, the mercury can lower only if there is a pressure on top of the column. For in the barometer tube, there is no pressure on the top of the column. There is only empty space and the mercury column balances the atmospheric pressure and is equal to if. Here it is forced down. When we measure we find the value of this difference in height. And the amount of the depression is brought about by the pressure of the water vapor, by the vapor tension as it is called. That is, the mercury volume is forced down here. We see therefore, that vapor always presses on the confining walls. Moreover, a definite pressure corresponds to a definite temperature. We can demonstrate this by warming the upper part of the tube. You can see that when the temperature is raised, the mercury column sinks, due to the increased pressure of the vapor. Thus we see that the vapor increases its pressure on the wall more and more the higher its temperature. You can observe the mercury fall and see how the vapor tension increases with the temperature. The volume occupied by the vapor is correspondingly increased. In the second tube we have alcohol over the column of mercury (Fig. 1c). Again you can see the liquid alcohol occupying definite volume. It evaporates and consequently the column is less in height than the barometric column on the left. If I measure, I find that it is shorter than the column which is under the pressure of the water vapor. We must wait until the water vapor returns to the same temperature as it was before being heated. Then we will find the vapor tension dependent on the substance we are using. The tension is greater in the case of alcohol than in the case of water. Here again, I can make the same experiment with heat. You will see that the pressure becomes considerably greater when we raise the temperature. When we cool the vapor to the same point at which it was at first, the mercury column rises, since with smaller vapor tension there is less pressure. In the third tube we have ether under the same conditions as in the other tubes. It also evaporated (Fig. 1d). You observe the column here is very low. From this you can see that ether evaporating under the same conditions as water shows a widely different pressure. Not only is the pressure exerted by a vapor dependent on the temperature, but on the material as well. Here you see the effect of increased temperature, but on the material as well. Here you see the effect of increased temperature, shown by lowering of the column (tube warmed slightly) due to the rise in vapor pressure. We can again in this case, verify the phenomena and thus round out our survey and lead to the result we wish to attain. Now there is an occurrence that I wish especially to call to your attention. You know from the foregoing observation and also from elementary physics that solids may be changed to liquids and liquids to solids if we raise the temperature above the melting point and lower it below the melting point. Now, when a fluid body is solidified by being brought under the melting point, it remains a solid body. The noteworthy fact, however, is that if we impose on this solid body a sufficiently great pressure, it will melt at a temperature below its melting point under ordinary pressure. Thus it can become liquid at a lower temperature than the one at which it solidified. You know that water changed to ice at 0°C. and it must be a solid at all temperatures under 0°C. We will now carry out an experiment on this ice which will show you that we can make it a liquid without raising the temperature. Ordinarily, we would have to raise the temperature to do this. In this case we will not raise the temperature but simply exert a strong pressure on the ice. This we can do by hanging a weight over the ice by means of a thin wire. The ice melts under the wire, and the wire cuts its way through the ice. Now, you would expect this block of ice to fall apart into two pieces since it is being cut through the middle. It we could make it work faster you would see the results of this experiment. (Note: the cutting of the block proceeded so slowly that the result described in the following did not occur until several hours after the end of the lecture.) If you will now step up here and examine the block of ice, you will find there is no reason to fear that the two halves will crash down when the wire has cut its way through. For the solid ice grows together at once above the cut; so that the wire goes through the block, the weight falls off and the block remains whole. This shows that fluidity is brought about under the pressure of the wire, but as soon as the fluid is released from the spot where the pressure is exerted, it solidifies and the block of ice becomes whole again. At the temperature of ice, the state of fluidity only establishes itself under increased pressure. Thus a solid can be melted at a temperature under its melting point, but the pressure must be maintained if it is to stay melted. As soon as the pressure is released it reverts to the solid state. This is what you would see if you could wait here an hour or so. A third thing I wish to present to you and which will furnish support for our observations is the following: To illustrate it we can take any bodies making an alloy, that is, mixing without forming a chemical compound; the principle holds for all of them. In this tube we have bismuth that melts at 269°C. and here we have tin, melting at 232°C. Thus we have three bodies all of which have melting points over 200°C. Now we will first melt these three, bringing them into the fluid condition in order to form an alloy. They will mix without combining chemically. (Note: the three metals were melted and poured together.) Now, you would naturally reason as follows: Since each of these metals has a melting point above 200°C. it would remain solid in boiling water, for water has a melting point of 0°C. and a boiling point of 100°C. Therefore these three metals could not melt in boiling water. Let us however carry out the experiment of bringing the allow, the mixture of the three, into water, just at the boiling point of 100°C. In this way we can see how it acts. We hold the thermometer here in the fluid metallic mixture and read a temperature of 94°C. This shows that although no single metal was fluid at this temperature, the alloy is fluid. We can state the fact thus: when metals are mixed, the fact is brought out that the melting point of the mixture is lower than the melting point of any of its constituents. Thus you can see how bodies mutually influence each other. From this particular fact we can derive an important principle for our view of the nature of heat phenomena. Here we have the still fluid alloy in boiling water that is at 100°C., and now we let the water cool, observing the temperature meanwhile. The alloy finally solidifies. By measuring the temperature of the water at this point, we have the melting point of the alloy and can show that this melting point is lower than the melting point of any of the single metals. We have now added this phenomenon to the others to extend the foundations of our view. Let us continue by tying in the things we considered yesterday in regard to the distinction between the solid, the fluid and the gaseous or vapor states. You know that solid bodies such as most metals and other mineral bodies, occur not in an indefinite form, but in very definite shapes that we call crystals. We can say: Under ordinary circumstances as they exist on the earth, solids occur in very definite shapes or crystal forms. This naturally leads us to turn our attention to these forms, and to try to puzzle out how these crystals originate. What forces lie at the foundation of crystal formation? In order to gain some insight into these matters, it will be necessary for us to consider the forces on and around the earth in their entirety as they are related to solids. You know that when we hold a solid in our hand and let go of it, it falls to the earth. In physics this is usually explained as follows: The earth attracts solid bodies, exerts a force on them; under the influence of this force — the gravitational force — the body falls to the earth. When we have a fluid and cool it so that it solidifies, if forms definite crystals. The question is now, that is the relation between the force acting on all solids — gravitation — to these forces tending to produce crystal form which must be present and active to a certain extent? You might easily think that gravity as such, through whose agency a body falls to the earth (we may at this stage speak of the force of gravity) you might think that this gravitational force had nothing to do with the building of crystal form. For gravity affects all crystals. No matter what form an object may have, it is subject to gravity. We find when we have a number of solids in a row and take way the support, that they all fall to earth in parallel lines. This fall may be represented in somewhat the following way: (Fig. 3). We can say, whatever form a solid may have, it falls along a line perpendicular to the surface of the earth. When now, we draw the perpendicular to these parallel lines of fall, we obtain a surface parallel to the earth's surface (line a-b, Fig. 3). By drawing all possible perpendiculars, to the lines of fall, we will obtain a complete surface parallel to the earth's surface. This is at first an imagined surface. We may now ask the question, where in reality is this surface? It is actually present in fluid bodies. A liquid which I place in a vessel shows as a real liquid surface that which I have assumed here as produced by drawing perpendiculars to the line of fall (see c, d, e, f, in Fig. 3). What is really involved here and what does it mean? What we are speaking of is a thing of tremendous import. For, imagine to yourselves the following: Suppose someone were trying to explain the liquid surface and stated it this way. Every minute portion of the liquid has the tendency to fall to the earth. Since the other portions hinder this, the liquid surface is formed. The forces are really there, and the presence of the liquid causes the surface to form. Picture to ourselves the real condition of the bodies you are going to let fall, and nature herself will show you what you have said in this explanation, (Fig. 4). You must include the liquid surface in your thinking. I have said formerly: the liquid surface is to be thought of in its relation to solids at right angles to their line of fall. When you think this through to the end, you come upon the noteworthy thing that what you have to bring into the solid as something thought out, this is represented in a material way before you by liquid bodies. These incorporate, as it were, what is materially present in the liquid. We may say: bodies of lower degrees of aggregation, solids in their relation to the earth, show a picture of that which is really present in the liquid, in a material way, and which in the case of water present in the liquid, in a material way, and which in the case of water prevents the surface particles from falling into the liquid. This is pictured, as it were, in considering the solid in its relation to the whole earth. Think what this enables us to do When I draw the line of fall and the surface formed under the pressure of a system of falling bodies, then I have a picture of the gravitational activity. This is a direct representation of matter in the liquid state. We can proceed further. When we leave water at any temperature sufficiently long it dries up. Water is always evaporating. The conditions under which it forms a liquid surface are only relative. It must be confined all around except on the liquid surface. It evaporates continuously, more rapidly in a vacuum. If we draw lines showing the direction in which the water is tending, their direction must indicate the movement of the water particles when it actually evaporates. When I actually draw these lines, however, I get nothing more or less than a representation of a gas that is enclosed all around and is striving to escape in every direction (Fig. 5). On the surface of water there is a certain tendency which, when I picture it for explanatory purposes, represents a gas set free and distributing itself in all directions. So again, we can state the proposition: that which we observe in water as a force is actually represented in a material way in a gas. There is a curious fact brought out here. If we look at fluids correctly from a certain point of view, we discover in them a picture of the gaseous state of aggregation. When we picture solids properly, we discover in them a representation of the fluid state of aggregation. In every step as we go down there is a representation of the preceding step . Let us illustrate by going from below up. We can say, in the solids we have a representation of the fluid state, in the fluid a representation of the gaseous, in the gaseous a representation of heat . It is this that we have especially to deal with tomorrow. I will say only this today, that we have sought to find the bridge for thought from gases to heat. It will become clearer tomorrow. Now when we have followed further this path of thinking: In solids the picture of the fluid state; In fluids the picture of the gaseous state; In gases the picture of the heat state; Then we will have, indeed, taken a great step ahead. We have advanced to the point where we have a picture in the gaseous state which is accessible to human observation, of heat manifestations and even of the real nature of heat itself. The possibility then exists for us that by rightly seeking the representations of heat in the gaseous state, we can explain its nature even though we are obliged to admit that it is an unknown entity to us at the outset. But we must do this in a proper manner . When the various phenomena that we have described so far are handled as physics usually handles them, we get nowhere. But when we hold correctly in our minds those things that are revealed to us by bodies under the influence of heat and pressure, then we will see how we, actually in fact, come to stand before that which the gases can reveal to us — the real being of heat. In cooling, where we deal with the liquid and solid states, the being of heat penetrates further. We have then to recognize in these states the nature of this entity, although we can do it best in the gaseous condition where it is more evident. We must see whether in the fluid and solid states, heat suffers a special change, and thus work out the distinction between the manifestation in the gas where it shows itself in pictures form and its manifestation in fluids and solids.

The Warmth Course

Lecture VI

https://rsarchive.org/Lectures/GA321/English/MP1980/19200306p01.html

Stuttgart

6 Mar 1920

GA321-6

My dear friends, You will recall how yesterday we had here a block of ice which we would have expected to fall apart in two pieces when we cut it with a wire from which a weight was hanging. Although you only saw the beginning of the experiment, you were able to convince yourselves that such was not the case, because as soon as the pressure of the wire liquefied the ice below, it immediately froze together again above the wire. That is to say a liquefaction took place only in consequence of the pressure. Therefore, since we preserved the ice as ice, the heat entity acted in such a way that the block closed itself up at once. I am using the expression advisedly. Now this surprised you considerably at first, did it not? But it surprised you only because you are not accustomed to the matter of fact observation necessary if you are really to follow physical phenomena In another case you are making the same experiment all the time and do not wonder at it at all. For when you take up your pencil and pass it through the air, you are continually cutting the air and it is immediately closing up behind. You are then doing nothing else than what we did yesterday with the block of ice, but you are doing it in another sphere, in another realm. We can learn quite a little from this observation, for we see that when we simply pass the pencil through the air (the conditions under which we do this will not be taken up) that the properties of the air itself bring about the closing up of the material behind the pencil. In the case of the ice we cannot avoid the thought that the heat entity enters into the process in such a way that it contributes the same thing as is contributed by the nature of the air itself when the pencil passes through. You have here only a further extension of what I said to you yesterday. When you picture the air to yourselves and imagine it cut and closing up at once, the matter composing the air is responsible for all that you can perceive. When you are dealing with a solid body, such as ice, then the heat is active in the same manner as the material air itself is in the other case. That is, you met here with a real picture of what goes on in heat. And again you have established that when we observe the gaseous or vapor condition — air is vaporous, gaseous in reality — we have represented in a material way in the phenomena of gases a picture of what takes place in the heat entity. And if we observe heat phenomena in a solid body we have fundamentally nothing other than the solid existing alongside of something taking place in the realm of the heat being. We see, as it were, before our eyes, the phenomena within the realm of heat which we see also playing through gas. From this we can conclude or rather simply state, since it is only the obvious that we are presenting, we can state the following: If we wish to approach the being of heat in its reality we must seek as well as we can to force our way into the realm of the gaseous, into the gaseous bodies. And in what goes on in gases we will see simply pictures of the phenomena within the heat realm. Thus nature conjures up before our eyes, as it were, pictures of processes in the heat being by a manifestation of certain phenomena in gases. Notice now, we are being led very far from the modern method of observation as practiced in natural science generally, not merely physics. Let us ask ourselves where the modern method really leads us ultimately. I have here a work by Eduard von Hartmann, in which he treats a special field from his point of view, namely the field of modern physics. Here is a man who has built up for himself entirely out of the spirit of the times a broad horizon, and who we may say, is therefore in a position to say something as a philosopher about physics. Now it is interesting to see how such a man, speaking entirely in the modern spirit, deals with physics. He begins the very first chapter as follows: “Physics is the study of transformations and movements of energy and of its separation into factors and their resummation.” Having said this, he must naturally add a further statement. He says further: “Physics is the study of the movements and transformations of energy (force) and of its resolution into factors and its summations. The validity of this definition is not dependent on how we consider energy. It does not rest on our considering it as something final, ultimate, nor on our looking upon it as really a product of some more widely embracing factors. Nor is it dependent on whether we hold this or that view of the constitution of matter. It only states all observations and perceptions of energy to rest on the fact that it can change place and form and be analyzed within these categories.” ( View of the World According to Modern Physics by Edw. V. Hartmann, Leipzig, 1902, Hermann Haake, page 3) Now what does it mean when one speaks in such a fashion? It means that an attempt is made so to define what is before one physically that there is no necessity to enter into its real nature. A certain concept of energy is formed and it is said: all that meets us from without, physically, is only a transformation of this energy concept. That is to say, everything essential is thrown out of one's concepts, and one is thought to be quite secure, because it is not realized that this is precisely the most insecure sort of a definition. But this sort of thing has found its way to a most unfortunate extent into our physical concepts. So completely has it entered in, my friends, that it is today almost impossible for us to make experiments that will reveal reality to us. All our laboratories, which we depend upon to do physical research, are completely given over to working out the theoretical views of modern physics. We cannot easily use what we have in the way of tools to reveal the essential physical nature of things. The cure for this situation is that first a certain number of people should become acquainted with the effect on methods of entering into the real physical nature of things. This group then will have to find the experimental method, the appropriate laboratory set-up to make possible a gradual entrance into reality. We need, in fact today, not merely to overhaul our view of the world in its conceptual aspect, but we need research institutes working to our manner of thinking. We cannot proceed as rapidly as we should in getting people to consider anthroposophy unless we are able to take them out of the rut in which modern thinking runs. Just as the physicists can point to factories to show plainly, very plainly, that what he says is true, so we must show people by experiments that what we say about things is correct. Naturally however, we must penetrate to real physical thinking before we can do this. And to think in real physical terms it is necessary that we bring ourselves into the state of mind indicated in these lectures, especially yesterday's lecture. Is it not true that the modern physicist observes what happens, and when he observes it, he at once bends every effort to strike out from the perceived phenomena all that he cannot reduce to calculation. Let us now make this experiment in order to place before our minds today something that we will build on in the course of subsequent lectures. We set up this paddle which can be turned in a liquid and arrange it so that the paddle rotated by means of this apparatus will transmit mechanical world. As a result of the fact that this mechanical work is transmitted to the water in which the paddle is immersed, we will have a marked rise in temperature. There is thus brought before us in the most elementary experimental way what is called the transformation of mechanical energy into warmth or thermal energy. We have now a temperature of 16° and after a short time we will note the temperature again. (Later the rise in temperature was determined.) Let us now return for a moment to what has already been said. We have tried to grasp the destiny, so to speak, of physical corporeality, by carrying the corporeality through the melting and boiling points. That is, by making solid bodies fluid and fluid bodies gaseous. I will now speak of these things in the simplest terms possible. We have seen that the fundamental property of solid bodies is the possession of form. The solids do not show form-building forces as these latter act in liquids before evaporation has had time to take place. Solids have a form of themselves. Liquids must be enclosed in a vessel, and in order to form a liquid surface, as they do everywhere, they require the forces of the entire earth. We have indeed, brought this before our souls. This requires us to make the following statement: When we consider the liquids of the whole earth in their totality, we are obliged to consider them as related to the body of the earth in its totality. Only the solids emancipate themselves from this relation to the earth, they take on an individuality, assume their own form. If now we bring to bear the method by which ordinary physics represents things on what is called gravity, on what causes the formation of the liquid surface, then we must do it in the following way. We must, if we are to stick to the observable, in some way introduce into individualized solid bodies the thing that is essential in this horizontal liquid surface. In some way or other, we must conceive of that which is active in the liquid surface, and which is thought of under the heading of gravity as within solids which, therefore, in a certain way individualize gravity. Thus we see that solids take gravity up within themselves. On the other hand we see that at the moment of evaporation the formation of liquid surface ceases. Gas does not form a surface. If we wish to give form to a gas, to limit the space occupied by it, we must do so by placing it in a vessel closed on all sides. In passing from the liquid to the gas we find that the surface formation ceases. We see dissipated this last remainder of the earth-induced tendency to surface formation as shown by the liquid. And we see also that all gases are grouped together in a unity, as illustrated by the fact that they all have the same co-efficient of expansion; gases as a whole represent material emancipated from the earth. Now place these thoughts vividly before yourselves: you find yourselves on the earth as a carbonaceous organism, you are among the phenomena produced by the solids of the earth. The phenomena produced by the solids are ruled by gravity which, as stated, manifests itself everywhere. As earth men you have solids around you that have in some way taken up gravity for their form-building. But consider the phenomena manifested by the solids in the case I spoke of yesterday where you added in thought a liquid surface to the system — in this phenomenon you have a kind of continuum, something you can think of as a sort of invisible fluid spread out everywhere. Thus solids of the earth, in so far as they are free to move, manifest as a whole what may be considered as a fluid state. They constitute something similar to what is manifested in a material fluid. We can therefore say: since we are placed on the earth we are aware of this, calling it gravity. Working on the liquid it forms a surface. Imagine now, that we were as human beings able to live on a fluid cosmic body, being so organized that we could exist on such a body. We would then live in the surface of this liquid, and we would have the same relation to the gaseous, striving outward in all directions that we now have to the fluid. This means nothing more or less than that we should be unaware of gravity. To speak of gravity would cease to have a meaning. Gravity rules only solid planetary bodies and is only known to those beings who live on such bodies . Beings who could live on a fluid planet would know nothing of gravity. It would not be possible to speak of such a thing. And beings who lived on a gaseous planetary body would regard as normal something which would be the opposite of gravity, a striving in all directions away from the center. If I may express myself somewhat paradoxically I might say: Beings dwelling on a gaseous planet instead of seeing bodies falling toward the planet would see them always flying off. We must think in really physical terms and not merely in mathematical terms, which stand outside of reality if we are to find the path here. Then we can state the matter thus: Gravity begins when we find ourselves on a solid planet. In passing from the solid to the gaseous planet, we go through a kind of null-point, and come to an opposite condition to that on the solid planet, to a manifestation of forces in space which may be considered negative in respect to gravity. You see therefore that as we pass through the material states, we actually come to a null-point in spatiality, to a sphere where the spatiality is zero. For this reason we have to consider gravity as something quite relative. But when we conduct heat to a gas (the experiment has been shown to you) this heat which always raises the diffusing tendency in the gas shows you again the picture I am trying to bring before you. Does not that which is active in the gas really lie on the far side of this null-point on this side of which gravity is active? Is it not possible for us to think the matter through further, still remaining in close contact with the actual phenomena when we say that going from a solid to a gaseous planet we pass through a null-point? Below we have gravity; above, this gravity changing into its opposite, in a negative gravity. Indeed we find this, we do not have to imagine it. The being of heat does just what a negative gravity would do. Certainly, we have not completely attained our goal but we have reached a point where we can comprehend the being of heat in a relative fashion to such an extent that the matter may be stated so: The being of heat manifests exactly like the negation of gravity, like negative gravity . Therefore, when one deals with physical formulae involving gravity and sets a negative sign in front of the symbol representing gravity, it is necessary to think of the magnitude in question not as a gravity quantity nor as a line of action of gravity, but as a heat quantity, a line of action of heat. Do you not see that in this way we can suffuse mathematics with vitality? The formulae as they are given may be looked upon as representing a gravitational system, a mechanical system. If we set negative signs in front of “g” then we are obliged to consider as heat what formerly represented gravity. And we realize from this that we must grasp these things concretely if we are to arrive at real results. We see that in passing from the solid to the fluid we go through a condition in which form is dissolved. The form loses itself. When I dissolve a crystal or melt it, it loses the form that it previously had. It goes over into that form which is imposed upon it by virtue of the fact that it comes under the general influence of the earth. The earth gives it a liquid surface and I must put this liquid into a vessel if I am to preserve it. Now let us consider another general phenomenon which we will approach more concretely later. If a liquid is divided into sufficiently small particles there comes about the formation of drops, which take on the spherical shape. Fluids have the possibility, when they are finely enough subdivided, of emancipating themselves from the general gravitational field and of manifesting in this special case that which otherwise comes to light in solids as crystalline shape. Only, in the case of fluids, the peculiarity is that they all take on the form of the sphere. If now, I consider this spherical form, I may regard it as the synthesis of all polyhedral shapes, of all crystal forms. When I pass from the fluid to the gas, I have the diffusion, the dissolution of the spherical form, but in this case, outwardly directed. And now we come to a rather difficult idea. Imagine to yourselves that you are observing some simple form, say a tetrahedron, and you wished to turn it inside out as you might do a glove. You will then realize that in going through this process of turning inside out it is necessary to pass through the sphere. Moreover, all the form relations become negative and a negative body appears. As the tetrahedron is put through this transformation, you must imagine to yourselves that the entire space outside the tetrahedron is filled, within it is gaseous. With this outside space filled you must imagine in a tetrahedral hole. There it is empty. You must then make the quantities related to the tetrahedron negative. Then you have formed the negative, the opened-up tetrahedron, in place of the one filled with matter. But the intermediate condition between the positive and the negative tetrahedron is the sphere. The polyhydric body goes over into its negative only by passing through the spherical as a null-point. Now let us follow this completely in the case of actual bodies. You have the solid body with definite form. It goes through the fluid form, that is the sphere, and becomes a gas. If we wish to look rightly on the gas we must look upon it as a form, but as a negative form. We reach a type of form here which we can comprehend only by passing through the zero point into the negative. That is to say, when we go over to the gaseous, the picture of the phenomena of heat, we do not enter into the region of the formless. We enter only into a region more difficult to comprehend than the one in which we live ordinarily where form is positive and not negative. But we see just here that any body in which the fluid state is in question is in an intermediate position. It is in the state between the formed and that which we call the “formless,” or that of negative form. Do we have any example where we can actually follow this? Aside from what is in our immediate environment, an example which we observe but do not really enter into vitality? We can do it when we consider the phenomenon of the melting of a solid or the evaporation of a liquid. But can we in any way enter vitally into this? Yes, we can and as a matter of fact we do so continually. We experience this process by virtue of our status as earth men, and because the earth, or at least the part of it on which we live, is a solid upon which are other solids involving many phenomena which we observe. In addition there is embedded in the earthly and belonging to it, the fluid state. The gaseous also belongs to it. Now there comes about a great distinction between what I will call Wärmenacht and Wärmetag . (I use these terms in order to lead us nearer to an understanding of the problem.) What is Wärmenach ? Wärmenacht and Wärmetag are simply what happens to our earth under the influence of the heat being of the cosmos. And what does happen? Let us take up these phenomena of the earth so that we can grasp what can be easily understood by our thinking. Under the influence of the Wärmenach, that is during the time when the earth is not exposed to the sun, while the earth is left to herself and is emancipated from the influence of the cosmic sun being, she strives for form as the droplet takes on form when it can withdraw itself from the general force of gravitation. We have therefore, when we consider the general striving of the earth for form, the characteristic of the Wärmenach as compared to ordinary night. It is quite justifiable for me to say in this connection that the earth strives toward the drop form. Many other tendencies are operative during the Wärmenach, such as a tendency toward crystallization. And what we experience every night is a continuous emergence of forces tending toward crystallization. During the day under the influence of the being of the sun, a continual dissolving of this tendency toward crystallization is present, a continual will to overcome form. And we may speak of the “dawn” and “twilight” of this heat condition. By dawn we mean that after the earth has sought to crystallize during the Wärmenach , this crystallization process dissolves again and the earth goes through the sphere state in her atmosphere and seeks to scatter herself again. Following the Wärmetag comes a twilight condition where the earth again starts seeking to form a sphere and crystallize during the night. We have thus to think of the earth as caught up in a cosmic process consisting in a drawing together in the Wärmenach when the motion of the earth turns it away from the sun, a tendency to become a crystal. At the proper time this is checked when the earth is led through the dawn condition, through the sphere. Then the earth seeks to dissipate her forces through the cosmos until the twilight condition reestablishes the opposite forces. In the case of the earth we do not have to do with something fixed in the cosmos, but with something that vibrates between two conditions, Wärmetag and Wärmenach. You se e it is with such things as this that our research institute should deal. To our ordinary thermometer, hygrometers, etc., we should add other instruments through which we could show that certain processes of the earth, especially of the fluid and gaseous portions, take place at night otherwise than during the day . You can see further that we have here a rational leading to a physical view by which we can finally demonstrate with appropriate instruments the delicate differences in all the processes in liquids and gases during the day and during the night. In the future we must be able to make a given experiment during the day and at a corresponding hour of the night and have measuring instruments that will show us the difference in the way the process goes by day and by night. For by day those forces tending toward crystallization in the earth do not play through the process, but by night, they do. Forces arise that come from the cosmos in the night. And these cosmic forces that seek to crystallize the earth necessarily have their effect on the process. Here is opened a way of experimentation which will show the relation of the earth to the cosmos. You can realize that the research institute that must in the future be established according to our anthroposophically oriented views of the world will have weighty problems. They must reckon with the things which today are taken into account only rarely. Naturally we do take them into account today, with light phenomena at least in certain cases when we have to darken the room artificially, etc. But in other phenomena that take place within a certain null sphere, we do not. Then, when we have made these facts obvious and have demonstrated them, we will replace by them all kinds of theoretical forces in atoms and molecules. The whole matter as it is understood now rests on the belief that we can investigate everything during the day. In this new sort of investigation, we will, for instance, first find in crystallization differences depending on whether we carry out the same experiment during the day or during the night . This is the sort of thing our attention must be turned to especially. And on such a path will we first come to true physics. For today, physical facts really stand in a chaotic relation to each other. We speak for instance of mechanical energy, of acoustical energy. But it is not to be understood that when we think about these things in the correct way mechanical energy can only operate where there are solids. The fluid realm lies between the purely mechanical and the acoustical energies. Indeed, when we leave the region in which we observe most readily the acoustical energy, the gaseous region, then we come to the region of the next state of aggregation, as it is called, to heat. This lies above the gaseous, just as the fluid lies above the solid. We may tabulate these things as follows: X Heat Gaseous-acoustical Fluid Solid mechanical We find the mechanical as a characteristic of the solid state. In the gaseous we find acoustical energy as the characteristic. Just as we have left out the fluid here, so we must leave out the heat realm and above we find something that I will at this time indicate by X. Thus we have to look beyond the heat region for something. Between this X and our acoustic phenomena playing themselves out in the air would lie the being of heat, just as the fluid condition lies between the gaseous and the solid states. We are trying, you see, to grasp the nature of heat in all the ways we can, to approach it by all possible paths. And when you say to yourselves: the fluid condition lies between the gaseous and X, you must in a similar way seek to pass from the heat condition to the X condition. You must find something which lies on the far side of the heat region just as for instance the tone world as it is expressed in the air lies on this side of the heat region. By this means you see how to attempt to build such real concepts of the physical as will lead you out of the mere abstract. Geometry really comprehends space forms but can never comprehend the mechanical except as motion. The concepts we are forming attempt really to include the physical. They immerse themselves in the nature of the physical and toward such concepts must we strive. Therefore I would think these are properly the sort of thing that should belong to what lies at the foundation of the “Free Waldorf School.” The attempt should be made to extend the experimental in the manner indicated here today. What is very much neglected in our physical processes, time and the passage of time, will thus be drawn into physical experiments.

The Warmth Course

Lecture VII

https://rsarchive.org/Lectures/GA321/English/MP1980/19200307p01.html

Stuttgart

7 Mar 1920

GA321-7

My dear friends, Yesterday we carried out an experiment which brought to your attention the fact that mechanical work exerted by friction of a rotating paddle in a mass of water has changed into heat. You were shown that the water in which the paddle turned became warmer. Today we will do just the opposite. We showed yesterday that we must in some ways seek an explanation for the coming of heat into existence upon the expenditure of work. Now let us follow the reverse process. We will first of all heat this air (see Figures at end of Chapter) using a flame, raise the pressure of the vapor, and thus bring about a mechanical effect by means of heat, in a way similar to that by which all steam engines are moved. Heat is turned into work through pressure change. By letting the pressure come through from one side we raise the bell up and by letting the vapor cool, the pressure is lessened, the bell goes down again and we have performed mechanical work, consistive in this up and down movement. We can see the condensation water which reappears when we cool, and runs into this flask. After we have let the entire process take place, after the heat that we have produced here has transformed itself into work, let us determine whether this heat has been entirely transformed into the up and down movement of the bell or whether some of it has been lost. The heat not changed into work must appear as such in the water. In case of a complete transformation the condensation water would not show any rise in temperature. If there is a rise in temperature which we can determine by noting whether the thermometer shows a temperature above the ordinary, then this temperature rise comes from the heat we have supplied. In this case, we could not say that the heat has been completely changed over into work; there would be portion remaining over. Thus we can ascertain whether the whole of the heat has gone over into work or whether some of it appears as heat in the condensate. The water is 20° and we can see whether the condensate is 20° or shows a higher temperature indicating a loss of heat to this condensate. Now we condense the vapor; the condensate water drops in the flask. A machine can be run in this way. If the experiment succeeds fully, you may determine for yourselves that the condensate shows a considerable increase in temperature. In this way we can demonstrate, when we carry out the reverse of yesterday's experiment, that it is not possible to get back as mechanical work in the form of up and down movement of the bell all the heat left over. The heat used in producing work does not change completely, but a portion always remains. We wish first to grasp this phenomenon. Now let us consider how ordinary physics and those who use ordinary physical principles handle these things. We have at the beginning to deal with the fact that we in fact do change heat into work and work into heat just as it is said we do. As previously stated an extension of this idea has been made. It is supposed that every form of so-called energy — heat energy, mechanical energy, and the experiment may be made with other forms — that all such energies are mutually changeable the one into the other. We will for the moment neglect the quantitative aspect of the transformation and consider only the fact. Now, the modern physicist says: It is therefore impossible for energy to arise anywhere except from energy of another sort already present. If I have a closed system of energy, let us say of a certain form, and another energy appears, then this must be considered as transformation of the energy already present in the closed system. In a closed system, energy can never appear except as a transformation product. Eduard von Hartmann, who, as I have said, expressed current physical views in the form of philosophical concepts, states the so-called first law of the mechanical theory of heat as follows: “A perpetuum mobile of the first kind is impossible.” Now we come to the second series of phenomena illustrated for us by today's experiment. This is that in an energy system apparently closed, we have one form of energy changing over to another form. In this transformation however, it is apparent that a certain law underlies the process and this law is related to the quality of the energy. In this case of heat energy, the relation is such that it cannot go over completely to mechanical energy, but there is always a certain amount unchanged. Thus it is impossible in a closed system to transform completely all the heat energy into its mechanical equivalent. If this were possible the reverse transformation of mechanical energy completely into heat energy would also be possible. We would then have in a closed energy system one type of energy transformed into another. This law is stated, again by Eduard von Hartmann, as follows: A closed energy system in which for instance, the entire amount of heat could be changed into work, or where work could be completely changed into heat, when a cycle of complete transformation could exist, this would be a perpetuum mobile of the second type. But, says he, a perpetuum mobile of the second type is impossible. Fundamentally, these two are the principle laws of the mechanical theory of heat as this theory is understood by thinkers in the realm of physics in the 19th century and the early part of the 20th century. “A perpetuum mobile of the first type is an impossibility.” This concept is intimately connected with the history of physics in the 19th century. The first person to call attention to this change of heat into other forms of energy or vice-versa was Julius Robert Mayer. He had observed, as a physician, that the venous blood showed a different behavior in the tropics and in the colder regions, and from this concluded that there was a different sort of physiological work involved in the human organism in the two cases. Using principally these experiences, he later presented a somewhat confused theory which as he worked it out meant little more than this, that it was possible to transform one type of energy into another. The matter was then taken up by various people, Helmholtz among others, and further developed. In the case of Helmholtz a characteristic form of physical-mechanical thinking was taken as the starting point for these things. If we consider the most important treatise by which Helmholtz sought to support the mechanical theory of heat in the forties of the 19th century, we see that such ideas as expressed by Hartmann are really postulated as their foundation. A perpetuum mobile of the first type is impossible. Since it is impossible the various forms of energy must be transformations of each other. No form of energy can arise from nothing. The axiom from which we proceed — “a perpetuum mobile of the first type is impossible” — can be changed into another: the sum of the energy in the universe is constant. Energy never is created, never disappears, it is only transformed. The sum of the energy in the universe is constant. These two principles fundamentally, then, mean precisely the same thing. “There is no perpetuum mobile of the first type.” “The sum of all the energy in the cosmos is constant.” Now applying the method of thinking that we have used before in all our observations, let us throw a little light on this whole point of view. Note now, when we make an experiment with the object of transforming heat into what we call work, that some of the heat is lost so far as the transformation is concerned. Heat reappears as such and only a portion of it can be turned into the other energy form, the mechanical form. What we learn from this experiment we may apply to the cosmos. This is what the 19th century investigators did. They reasoned somewhat as follows: “In the world about us work is present and heat is present. Processes are continually going on by which heat is transformed into work. We see that heat must be present if we would produce work. Only recollect how great a part of our technical achievements rest on the fact that we produce work by the use of heat. But it always comes out that we cannot completely transform heat into work, a portion remains as heat. And since this is so, these remainders not capable of yielding work, accumulate. These non-transformable residues accumulate. And the universe approaches a condition in which all mechanical work will have been turned into heat.” It has even been said that the universe in which we live is approaching what has been learnedly called its “warmth-death.” We will speak in coming lectures of the so-called entropy concept. For the present our interest lies in the fact that certain ideas have been drawn from experiment bearing on the fate of the universe in which we find ourselves. Eduard von Hartmann has presented the matter very neatly. He says: physical observation shows that the world-process in the midst of which we live, exhibits two sorts of phenomena. In the end, however, all mechanical work can be produced, and the universe will have to come to an end. Thus says Eduard von Hartmann; physical phenomena shows that the world process is running down. This is the way he expresses himself about the conditions within which we live. We live in a universe whose processes preserve us, but which has a tendency to become more and more sluggish and finally to lapse into a state of complete inaction. I am merely repeating Eduard von Hartmann's own words. Now we must make clear to ourselves the following point. Is there ever really the possibility of calling forth a series of processes in a closed system? Note well what I am saying. If I consider the totality of my experimental implements, I certainly am not myself in a vacuum, in empty space. And even when I believe myself to be standing in empty space, I am still not entirely certain but that this empty space is empty only because I am unable to perceive what is really in it. Do I therefore ever really carry out my experiments in a closed system? Is it not so that what I carry out in the simplest experiment has to be thought of as dovetailed into the world process immediately around me? Can I conceive of the matter otherwise than in this fashion, that when I do all these things it is as though I took a small needle and pricked myself here? When I prick myself here I experience pain which prevents me from having an idea that I would otherwise have had. It is quite certain indeed, that I cannot consider merely the prick of the needle and the reaction of the skin and muscles as the whole of the process. In such a case I would not be placing the whole process before my eyes. The process is not entirely contained in these factors. Imagine for a moment that I am so clumsy as to pick up a needle, prick myself and experience the pain. I will pull the needle away. What appears thus as an effect is very definitely not comprehended when I hold in mind only what goes on in the skin. The drawing back of the needle is in reality nothing other than a continuation of what I apprehend when I hold before my mind the first part of the process. If I wish to describe the whole process, I must take into account that I have not stuck the needle into my clothes, but into my organism. This organism must be considered as a regulating whole, calling forth the consequences of the needle prick. Is it legitimate for me to speak of an experiment such as we have before our eyes in the following way: “I have produced heat, and caused mechanical work. The heat not transformed remains over in the condensation water as heat.” It is not in this way that I stand in relation to the whole thing. The production or retention of heat, the passage of it into the condensation water are related to the reaction of the whole great system as the reaction of my whole organism is to the small activity of being pricked with the needle. What must be taken into account especially is: That it is never valid for me to consider an experimental procedure as a closed system . I must keep in mind that this whole experimental procedure falls under the influence of energies that work out of this environment. Consider along with this another fact. Suppose you have to begin with a vessel containing a liquid with its liquid surface which implies an action of forces at right angles to this surface. Suppose now that through cooling, this liquid goes over into a solid state. It is impossible for you to think of the matter otherwise than that the forces in the liquid are short through by another set of forces. For the liquid forces are such as to make it imperative that I hold this liquid, say water, in a vessel. The only form assumed by the water on its own account is the upper surface. When by solidification a definite form arises it is absolutely necessary to assume that forces are added to those formerly present. More observation convinces us of it. And it is quite absurd to think that the forces creating the form are present in some way or other in the water itself. For if they were there they would create the form in the water. They are thus added to the system, but must have come into it from the outside. If we simply take the phenomenon as it is presented to us we are obliged to say: when a form appears, it represents as a matter of fact a new creation. If we simply consider what we can determine from observation we have to think of the form as a new creation. It is simply a matter of observation that we bring about the solid state from the fluid. We see that the form arises as a new creation. And this form disappears when we change the solid back into a liquid. One simply rests on that which is given as an observable fact. What follows now from this whole process when one makes it over into a concept? It follows that the solid seeks to make itself an independent unit, that it tends to build a closed system, that it enters into a struggle with its surroundings in order to become a closed system. I might put the matter in this way, that here in the solidification of a liquid we can actually lay our hands on nature's attempt to attain a perpetuum mobile. But the perpetuum mobile does not arise because the system is not left to itself but is worked upon by its whole environment. The view may therefore be advanced: in space as given us, there is always present the tendency for a perpetuum mobile to arise. But a counter tendency appears at once. We can therefore say that wherever the tendency arises to form a perpetuum mobile, the opposite tendency arises in the environment to prevent this. If you will orient your thinking in this way you will see that you have altered the abstract method of modern 19th century physics through and through. The latter starts from the proposition: a perpetuum mobile is impossible, therefore etc. etc. If one stands by the facts the matter has to be stated thus: a perpetuum mobile is always striving to arise. Only the constitution of the cosmos prevents it. And the form of the solid, what is it? It is the impress of the struggle. This structure that forms itself in the solid is the impress of the struggle between the substance as individuality which strives to form a perpetuum mobile and the hindrance to its formation by the great whole in which the perpetuum mobile seeks to arise. The form of a body is the result of opposition to this striving to form a perpetuum mobile. It might be better understood in some quarters if, instead of perpetuum mobile, I spoke of a self-contained unit, carrying its own forces within itself and its own form-creating power. Thus we arrive at a point where we have to reverse completely the entire point of view, the manner of thinking of 19th century physics. Physics itself, insofar as it rests on experiment, which deals with facts, we do not have to modify. The physical way of thinking works with concepts that are not valid and it cannot realize that nature strives universally for that which it holds as impossible. For this manner of thinking it is quite easy to consider the perpetuum mobile as impossible, but it is not impossible because of the abstract reasons advanced by the physicists. It is impossible because the instant the perpetuum mobile strives to establish itself in any given body, at that instant the environment becomes jealous, if I may borrow an expression from the realm of morals, and does not let the perpetuum mobile arise. It is impossible because of facts and not because of logic. You can appreciate how twisted a theory is that departs from reality in its very foundation postulate. If the facts are adhered to, it is not possible to get around what I presented to you yesterday in a preliminary sketchy way. We will elaborate this sketchy presentation in the next few days. I said to you: we have, to begin with, the realm of solids. Solids are the bodies which manifest in definite forms. We have, touching on the realm of the solids as it were, the realm of fluids. Form is dissolved, disappears, when solids become liquids. In the gaseous bodies we have a striving in all directions, a complete formlessness — negative form. Now how does this negative form manifest itself? If we look in an unbiased manner on gaseous or aeriform bodies we can see in these that which may be considered as corresponding to the entity elsewhere manifested as form. Yesterday I called your attention to the realm of acoustics, the tone world. In the gas, as you know, the manifestation of tone arises through condensations and rarefactions. But when we change the temperature we also have to do with condensation and rarefaction in the body of the gas as a whole. Thus if we pass over the liquid state and seek to find in the gas what corresponds to form in the solid, we must look for it in condensation and rarefaction. In the solid we have a definite form; in the gas, condensation and rarefaction. And now we pass to the realm next adjacent to the gaseous. Just as the fluid realm borders on the solid, and just as we know how the solid pictures the fluid, the fluid gives the foreshadowing of the gaseous, so the gas pictures the realm which we must conceive as lying next to the gaseous, i.e. the realm of heat. The realm lying next above heat, we will have to postulate for the time being and call it the X region. If now, I seek to advance further, at first merely through analogy, I must look in this X region for something corresponding to but beyond condensation and rarefaction (this will be verified in our subsequent considerations.) I must look for something else there in the X region, passing over heat, just as we passed over the fluid state below. If you begin with a definitely formed body, then imagine it to become gaseous and by this process to have simply changed its original form into another manifesting as rarefaction and condensation and if then you think of the condensation and rarefaction as heightened in degree, what is the result? As long as condensation and rarefaction are present, obvious matter is still there. But now, if you rarefy further and further you finally pass entirely out of the realm of the material. And this extension we have spoken of must, if we are to be consistent, be made thus: a material-becoming — a spiritual-becoming. When you pass over the heat realm into the X realm you enter a region where you are obliged to speak of the condition in a certain way. Holding in mind this passage from solid to fluid and the condensation and rarefaction in gases you pass to a region of materiality and non-materiality. You cannot do other than enter the region of materiality and non-materiality. Stated otherwise: when we pass through the heat realm we actually enter a realm which is in a sense a consistent extension of what we have observed in the realms beneath it. Solids oppose heat — it cannot come to complete expression in them. Fluids are more susceptible to its action. In gases there is a thorough-going manifestation of heat — it plays through them without hindrance. They are in their material behavior a complete picture of heat. I can state it thus: the gas is in its material behavior essentially similar to the heat entity. The degree of similarity between matter and heat becomes greater and greater as I pass from solids through fluids to gases. Or, liquefaction and evaporation of matter means a becoming similar of this matter to heat. Passage through the heat realm, however, where matter becomes, so to speak, identical with heat leads to a condition where matter ceases to be. Heat thus stands between two strongly contrasted regions, essentially different from each other, the spiritual world and the material world. Between these two stands the realm of heat . This transition zone is really somewhat difficult for us. We have on the one hand to climb to a region where things appear more and more spiritualized, and on the other side to descend into what appears more and more material. Infinite extension upwards appears on the one hand and infinite extension downward on the other. (Indicated by arrows.) But now we use another analogy that I am bringing before you today because through a general view of individual natural facts a sound science may be developed. It will perhaps be useful to array these facts before our souls. (See below.) If you observe the usual spectrum you have red, orange, yellow, green, blue, indigo and violet. Infra red——————————roygrbiv——————————Ultra Violet You have the colors following each other in a series of approximately seven nuances. But you know that the spectrum does not break off at either end. If we follow it further below the red we come to a region where there is more and more heat, and finally we arrive at a region where there is no light, but only heat, the infra red region. On the other side of the violet, also, we no longer have light. We come to the ultra violet where chemical action is manifested, or in other words effects that manifest themselves in matter. But you know also that according to the color theory of Goethe, this series of colors can be bent into a circle, and arranged in such a way that one sees not only the light from which the spectrum is formed, but also the darkness from which it is formed. In this case the color in the middle is not green but the peach-blossom color, and the other colors proceed from this. When I observe darkness I obtain the negative spectrum. And if I place the two spectra together, I have 12 colors that may be definitely arranged in a circle: red, orange, yellow, green, blue, indigo, and violet. On this side the violet becomes ever more and more similar to the peach blossom and there are two nuances between. On the other side there are two nuances between peach blossom and red. You have, if I may employ the expression, 12 color conditions in all. This shows that what is usually called the spectrum can be thought of as arising in this way: I can by any suitable means bring about this circle of color and can make it larger and larger, stretching out the upper five colors (peach blossom and the two shades on each side) until they finally disappear. The lower arc becomes practically a straight line, and I obtain the ordinary spectrum array of colors, having brought about the disappearance of the upper five colors. I finally bring these colors to the vanishing point. May it not be that the going off into infinity is somewhat similar to this thing that I have done to the spectrum? Suppose I ask what happens if that which apparently goes off into infinity is made into a circle and returns on itself. May I not be dealing here with another kind of spectrum that comprehends for me on the one hand the condition extending from heat to matter, but that I can close up into a circle as I did the color spectrum with the peach blossom color? We will consider this train of thought further tomorrow.

The Warmth Course

Lecture VIII

https://rsarchive.org/Lectures/GA321/English/MP1980/19200308p01.html

Stuttgart

8 Mar 1920

GA321-8

My dear friends, The fact that we have spoken of the transformation of energy and force assumed by modern physics makes it necessary for us to turn our attention to the problem of indicating what really lies behind these transformations. To aid in this, I wish to perform another experiment to be ranged alongside of yesterday's. In this experiment we will perform work through the use of another type of energy than the one that is immediately evident in the work performed. We will, as it were, bring about in another sphere the same sort of thing that we did yesterday when we turned a wheel, put it in motion and thus performed work. For the turning of the wheel can be applied in any machine, and the motion utilized. We will bring about the turning of a wheel simply by pouring water on these paddle, and this water by virtue of its weight will bring the paddle wheel into motion. The force that somehow or other exists in the running water is transformed into the rotational energy of the wheel. We will let the water flow into this trough in order to permit it to form a liquid surface as it did in previous experiments. What we show is really this, that by forming a liquid surface below we make the motion of the wheel slower than it was before. Now, it will slow down in proportion to the degree to which the lower level approaches the upper level. Thus we can say: if we indicate the total height of the water from the point \(a\) here where it flows onto the wheel by \(h\) and the perpendicular distance to the liquid surface by \(h'\) then we can state the difference as \(h-h'\). We can further state that the work available for the wheel is connected in some way with the difference between the two levels. (The sense in which this is so we will seek in our further considerations.) Yesterday in our experiment we also had a kind of difference in levels, \(t-t'\). For you will recollect we denoted the heat of the surroundings at the beginning of our experiments by \(t'\) and the heat we produced in order to do work to raise and lower a bell, this we denoted by \(t\). Therefore you can say: the energy available for work depends on the difference between \(t\) and \(t'\). Here too, we have something that can be denoted as a difference in level. I must ask you to note especially how both these experiments show that wherever we deal with what is called energy transformation, we have to take account of difference in level. The part played by this, what is really behind the phenomenon of energy transformation, this we will find only where we pursue further the train of thought of yesterday. As we do this we will illuminate so to speak, the phenomena of heat and take into account that which Eduard von Hartmann set aside before he attempted a definition of physical phenomena. In this connection we must emphasize again and again a beautiful utterance of Goethe's regarding physical phenomena. He gave utterance to this in various ways, somewhat as follows: what is all that goes on in outer physical apparatus as compared to the ear of the musician, as compared to the revelation of nature that is given us in the musician's ear itself. What Goethe wishes to emphasize by this is that we will never understand physical things if we observe them separately from man himself. According to his view, the only way to attain the goal is to consider physical phenomena in connection with the human being, the phenomena of sound in connection with the sense of hearing. But we have seen that great difficulties arise when we try in this way to bring the phenomena of heat in connection with the human being — really seek to connect heat with the being of man. Even the facts that have led to the discover of the so-called modern mechanical theory of heat support this view. Indeed, that which appears in this modern mechanical theory of heat took its origin from an observation made on the human organism by Julius Robert Mayer. Julius Robert Mayer, who was a physician, had noticed from blood-letting he was obliged to do in the tropical country of Java, that the venous blood of tropical people was redder than that of people in northern climes. He concluded correctly from this that the process involved in the coloration of blood varies, depending on whether man lives in a warmer or cooler climate, and is thus under the necessity of giving off less or more heat to his surroundings. This in turn involves a smaller or greater oxidation. Essentially he discovered that this process is less intense when the human being is not obliged to work so intensely on his environment. Thus, the human being of the tropics, since he loses less heat to his environment, is not obliged to set up so active a relation with the outer oxygen as when he gives off more heat. Consequently man, in order to maintain his life processes and exist at all on the earth in the cooler regions, is obliged to tie himself in more closely with his environment. He must take in more oxygen from the air in the colder regions where he works more intensely in connection with his environment than in the warmer zones where he labors more intensely in his inner nature. Right here you get an insight into the inner workings of the whole human organization. You see that it has only to become warmer and the human being then works more in his inner individuality than he does when his environment is colder and he is thereby obliged to link his activities more intimately with his outer environment. From this process in which we have represented a relation of man to his environment, there proceeded the observations that resulted in the theory of heat. These observations led Julius Robert Mayer to submit his small paper on the subject to the Poggnedorfschen Annalen . From this paper arose the entire movement in physics that we know about. This is strange enough since the paper that Mayer handed the Poggnedorfschen Annalen was returned as entirely lacking in merit. Thus we have the odd circumstance that physicists today say: we have turned physics into entirely new channels, we think entirely otherwise about physical things than they did before the year 1842. But attention has to be called to the fact that the physicists of that time, and they were the best physicists of the period, had considered Mayer's paper as entirely without merit and would not publish it in the Poggnedorfschen Annalen. Now you can see that it might be said: this paper in a certain sense brings to a conclusion the kind of view of the physical that was, as it were, incompletely expressed in Goethe's statement. After the publication of this paper, a physics arises which sees science advancing when physical facts are considered apart from man. This is indeed the principle characteristic of modern views on the subject. Many publications bring this idea forward as necessary for the advance of physics, stating that nothing must enter in which comes from man himself, which has to do with his own organic processes. But in this way we shall arrive at nothing. We will however continue our train of thought of yesterday, a train of thought drawn from the world of facts and one which will lead us to bring physical phenomena nearer to man. I wish once more to lay before you the essential thing. We start from the realm of solids and find a common property at first manifesting as form . We then pass through the intermediate state of the fluid showing form only to the extent of making for itself a liquid surface. Then we reach the gaseous bodies , where the property corresponding to form manifests itself as condensation and rarefaction . We then come to the region bordering on the gaseous, the heat region, which again, like the fluid, is an intermediate region, and then we come to our \(X\). Yesterday we saw that pursuing our thought further we have in \(X\) to postulate materialization and dematerialization . It is not difficult then to see that we can go beyond \(X\) to \(Y\) and \(Z\) just as, for instance, we go in the light spectrum from green to blue, from blue to violet and to ultra violet. And now it is a question of studying the mutual relations between these different regions. In each one we see appearing what I might call definitely characteristic phenomena. In the concrete realm we see a circumscribed for; in gas a changing form, so to speak, in condensations and rarefactions. This accompanies, and I am now speaking precisely, this accompanies the tone entity, under certain conditions. When we pass through the warmth realm into \(X\) realm, we see materialization and dematerialization. The question now arising is this: how does one realm work into another? Now I have already called your attention to the fact that when we speak of gas, the phenomena there enacted present a kind of picture of what goes on in the realm of heat. We can say therefore, in the gas we find a picture of what goes on in the heat realm. This comes about in no other manner than that we have to consider gas and heat as mutually interpenetrating each other, as so related that gaseous phenomena are seized upon in their spatial relationship by the heat entity. What is really taking place in the realm of heat expresses itself in the gas through the interpenetration of the two realms. Furthermore we can say, fluids show us a relationship of forces similar to that obtaining between gases and heat. Solids show the same sort of relationship to fluids do to gases and as gases do to heat. What then, comes about in the realm of solids? In this realm forms appear, definite forms. Forms circumscribed within themselves. These circumscribed forms are in a relative sense pictures of what is really active in fluids. Now we can pass here to a realm \(U\), below the solid, whose existence we at the start will merely postulate; and let us try to create concepts in the realm of the observable. By extending our thinking which you can feel is rooted in reality, we can create concepts and these concepts springing from the real bring into us a bit of the real world. What must take place if there is to be such a reality as the \(U\) realm? In this realm there must be pictured that which in solids is a manifested fact. In a manner corresponding to the other realms the \(U\) realm must give us a picture of the solids. In the world of solids we have bodies everywhere, everywhere forms. These forms are conditioned from within their own being, or at least conditioned according to their relation to the world. We will consider this further in the next few days. Forms come into being, mutually inter-related. Let us go back for a moment to the fluid state. There we have, as it were, the fluid throwing out a surface and thus showing its relation to the entire earth. In gravity therefore, we have to recognize a force related to the creation of form in solids. In the \(U\) realm we must find something that happens in a similar manner to the form-building in the world of solids, if we are to pursue our thinking in accordance with reality. And this must parallel the picturing of the fluid world by solids. In other words: in the \(U\) world we must be able to see an action which foreshadows the solid world. We must in some way be able to see this activity. We must see how, under the influence of forms related to each other something else arises. There must come into existence as a reality what further manifests as varying forms in the solid world. We really have today only the beginning of such an insight. For, suppose you take a suitable substance, such as tourmaline, which carries in itself the principle of form. You then bring this tourmaline into such a relation that form can act on form. I refer to the inner formative tendency. You can do this by allowing light to shine through a pair of tourmaline crystals. At one time you can see through them and then the field of vision darkens. This you can bring about simply by turning one crystal. You have brought their form-creating force into a different relation. This phenomena, apparently related to the passage of light through systems of differing constitution, shows us the polarization figures. Polarization phenomena always appear when one form influences another. There we have the noteworthy fact before our eyes that we look through the solid realm into another realm related to the solid as the solid is to the liquid. Let us ask ourselves now, how come it is that under the influence of the form-building force there arises in the \(U\) realm that which we observe in the polarization figures as they are called, and which really lies in the realm beneath the solid realm? For we do, as a matter of fact, look into a realm here that underlies the world of the solids. But we see something else also. We might look long into such a solid system, and the most varied forces might be acting there upon each other, but we would see nothing. It is necessary to have something playing through these systems, just as the U realm plays through the world of solids in order to bring out the phenomenon. And the light does this and makes the mutual inter-working of the form-building forces visible for us. What I have here expressed, my friends, is treated by the physics of the 19th century in such a way that the light itself is supposed to give rise to the phenomenon while in reality the light only makes the phenomenon visible. Looking on these polarization figures, one must seek for their origin in an entirely different source from the light itself. What is taking place has nothing whatever to do with the light as such. The light simply penetrates the \(U\) realm and makes visible what is going on there, what is taking place there as a foreshadowing of the solid form. Thus we can say we have to do with an interpenetration of different realms which we have simply unfolded before our eyes. In reality we are dealing with an interpenetration of different realms. And now the facts lead us to the same point which we reached, for instance, in the realm of the gaseous by means of the forces of form. Our concepts of what has been said will be better if we consider condensation and rarefaction in connection with the relation of tone to the organ of hearing. We must not feel it necessary to identify these condensations and rarefactions in a gaseous body entirely with what we are conscious of as tone. We must seek for something in the gas that uses the condensations and rarefactions as an agency when these are present in a suitable fashion. What really happens we must express as follows: that which we call tone exists in a non-manifested condition. But when we bring about in a gas certain orderly condensations and rarefactions, then there occurs what we perceive consciously as tone. Is not this way of stating the matter entirely as though I should say the following: we can imagine in the cosmos heat conditions where the temperature is very high — about 100°C. We can also imagine heat conditions where very low temperatures prevail. Between the two is a range in which human beings can maintain themselves. It is possible to say that wherever in the cosmos there is a passage from the condition of high temperature to a condition of low temperature, there obtains at some intermediate point a heat condition in which human beings may exist. The opportunity for the existence of man is there, if other necessary factors for human existence are present. But we would on no account say: man is the temperature Variation from high to low and the reverse variation. (For here the conditions would be right again for his existence.) We would certainly not say that. In physics, however, we are always saying, tone is nothing but the condensation and rarefaction of the air; tone is a wave-motion that expresses itself as condensation and rarefaction in the air. Thus we accustom ourselves to a way of thinking that prevents us from seeing the condensations and rarefactions simply as bearers of the tone, and not constituting the tone itself. And we should conceive for the gaseous something that simply penetrates it, but belongs to another realm, finding in the realm of the gaseous the opportunity so to manifest as to form a connection between itself and our higher organs. Concepts formed in this way about physical phenomena are really valid. If however, one forms a concept in which tone is merely identified with the air vibrations, then one is naturally led to consider light merely as ether vibrations. A person thus passes from what is not accurately conceived to the creation of a world of thought-out fantasies resulting simply from loose thinking. Following the usual ideas of physics, we bury ourselves in physical concepts that are nothing more than the creation of inaccurate thinking. But now we have to consider the fact that when we pass through the heat realm to the \(X\), \(Y\) and \(Z\) realms, we have to pass out into infinity and here from the U region we have also to step into the infinite. Recollect now what I told you yesterday. In the case of the spectrum also, when we try to get an idea of it as it exists ordinarily, we have to go from the green through the blue to the violet and then of to the infinite, or at least to the undetermined. So likewise at the red end of the spectrum. But we can imagine the spectrum in its completeness as a series of 12 independent colors in a circle, with green below and peach-blossom above, and ranged between these the other colors. When we can imagine the circle to become larger and larger, the peach blossom disappears above and the spectrum extends on the one hand beyond the red and on the other beyond the violet. In the ordinary spectrum therefore, we really have only a part of what would be there if the entire color series could appear. Only a portion is present. Now there is a very remarkable thing. I think, my friends, if you take as a basis the ordinary presentation of optics in the physic books and read what is there given as explanation of a special spectral phenomenon, namely the rainbow, you will be rather uneasy if you are a person who likes clear concepts. For the explanation of the rainbow is really given in such a manner that one has no foundation on which to stand. One is obliged to follow all sorts of things going on in the raindrop from the running together of extremely small reflections that are dependent on where one stands in relation to the rainbow. These reflections are said really to come from the raindrops. In brief you have in this explanation an atomistic view of something that occurs in our environment as unity. But even more perplexing is the fact that his rainbow or spectrum conjured up before us by nature herself, never occurs singly. A second rainbow is always present, although sometimes very completely hidden. Things that belong together cannot be separated. The two rainbows, of which one is clearer than the other, belong of necessity together, and if one is to explain this phenomenon, it is not possible to do so simply by explaining one strip of color. If we are to comprehend the total phenomenon we must make it clear to ourselves that something of a unique nature is in the center and that it shows two bands of color. The one band is the clearer rainbow, and the other band is the more obscure bow. We are dealing with a representation in the greatness of nature herself, which is an integral portion of the “All” and must be comprehended as a unity. Now, when we observe carefully we will see that the second rainbow, the accessory bow, shows colors in the reverse order from the first. It reflects, so to speak, the first and clearer rainbow. As soon as we go from the partial phenomenon as it appears in our environment, to a relatively more complete one, when we conceive of the whole earth in its relation to the cosmic system, we see in the rainbows a different aspect. I wish only to mention this here — we will go into it more completely in the course of our lecture. But I wish to say here that the appearance of the second bow converts the phenomenon into a closed system, so to speak. The system is only an open one so long as I limit my consideration to the special spectrum arising in the \(U\) portion of my environment. The phenomenon of the rainbow really leads me to think of the matter thus, that when I produce a spectrum experimentally, I grasp nature only at one pole, the opposite pole escapes me. Something has slipped into the unknown, and I really have to add to the seven-colored spectrum the accessory spectrum. Now hold in mind this phenomenon and the ideas that arise from it and recollect the previous ideas that we have brought out here. We are trying to close up the band of color that stretches out indefinitely on both sides, and bring the two together. If now, we do a similar things in this other realm, what happens? (See sketch at end of Chapter) Then we will pass from solids to the U region and beyond, but as we do this we also come back from the other end of the series and the system becomes a closed one. But now, when the downward path and the upward one come together to make a closed system, what does that form for us? What happens then? I will try as follows to lead you to an understanding of this: suppose you really go in one direction in the sense indicated in our diagrams. Let us say we go out from the sphere where, as we have explained in these lectures, gravity becomes negative. We have, let us say, arrived in one of the realms. From this realm, suppose we go downward, and imagine that we pass through first the fluid and then the solid realms. Now when we go further, we must really come back from the other side — it is difficult to show this diagrammatically. Since we come back from the other side, that which belongs to this other side has to insert itself into the realm from which we have just passed. That is to say, while I pass from the solid to the U region, if I want to represent the whole cycle I must bend what is at the other end of the series around and thrust it in here. I can picture it in this way. From the null sphere I go through the fluid into the solid and then into the U region. Returning then, I come to the same point from the other side. Or, I might say: I observe the gas, it extends to here where I have colored with blue (referring to the drawing at end of Chapter). But from the other side comes that which inserts itself, interpenetrates it from the cosmic cycle, but appearing there only as a picture. It impregnates the gas, so to speak, and manifests as a picture. The fluid in its essence interpenetrates the sphere of the solid, and attains a form. Similarly, form appears in the gas as tone and this we have indicated in our diagram. Turn over in your minds this returning and interpenetration in these world-processes. You will of necessity have to think not of a world-cycle only, but of a certain sort of world-cycle. You will have to think of a world cycle that moves from one realm to another, but in which any realm shows reflection of other realms. In this way we get a basis for thinking about these things that has a root in reality. This way of thinking will help you, for instance, to see how light arises in matter, light which belongs to an entirely different realm; but you will see that the matter is simply “overrun” by the light, as it were. And you will then, if you treat these things mathematically, have to extend your formulae somewhat. You may, if you will, consider these things under the symbol of ancient wisdom, the snake that swallows its own tail. The ancient wisdom represented these things symbolically and we have to draw nearer to the reality. This drawing nearer is the problem we must solve.

The Warmth Course

Lecture IX

https://rsarchive.org/Lectures/GA321/English/MP1980/19200309p01.html

Stuttgart

9 Mar 1920

GA321-9

My dear friends, Before we continue the observations of yesterday which we have nearly brought to a conclusion, let us carry out a few experiments to give support to what we are going to say. First we will make a cylinder of light by allowing a beam to pass through this opening, and into this cylinder we will bring a sphere which is so prepared that the light passes into it, but cannot pass through. What happens we will indicate by this thermometer (see drawing Fig. 1). You will note that this cylinder of energy, let us say, passing into the sphere reveals its effect by causing the mercury column to sink. Thus we are dealing with what we have formerly brought about by expansion. And indeed, in this case we have to assume also that heat passes into the sphere, causes an expansion and this expansion makes itself evident by a depression of the column of mercury. If we placed a prism in the path of the light we would get a spectrum. We do not form a spectrum in this experiment, but we catch the light — gather it up and obtain as a result of this gathering up of what is in the bundle of light, a very market expansion. You can see the definite depression of the mercury. Now we will place in the path of the energy cylinder, an alum solution, and see what happens under the influence of this solution. You will see after a while that the mercury will come to exactly the same level in the right and left hand tubes. This shows that originally heat passed through, but under the influence of the alum solution the heat is shut off, not more goes through. The apparatus then comes only under the influence of the heat generally present in the space around it and the mercury readjusts itself to equilibrium in the two tubes. The heat is stopped as soon as I put the alum solution in the path of the energy cylinder. That is to say, from this cylinder which yields for me both light and heat, I separate out the heat and permit the light to pass through. Let us keep this firmly in mind. Something still rays through. But we see that we can so treat the light-heat mercury that the light passes on and the heat is separated by means of the alum solution. This is one thing we must keep in mind simply as a phenomenon. There is another phenomenon to be brought to our attention before we proceed with our considerations. When we study the nature of heat we can do so by warming a body at one particular spot. We then notice that the body gets warm not only at the spot where we are applying the heat, but that one portion shares its heat with the next portion, then this with the next, etc. and that finally the heat is spread over the entire body (Fig. 2). And this is not all. If we simply bring another body in contact with the warm body, the second body will become warmer than it formerly was. In modern physics this is ordinarily stated by saying that heat is spread by conduction. We speak of the conduction of heat. The heat is conducted from one portion of a body to another portion, and it is also conducted from one body to another in contact with the first. A very superficial observation will show you that the conduction of heat varies with different materials. If you grasp a metallic rod in your fingers by one end and hold the other end in a flame, you will soon have to drop it, since the heat travels rapidly from one end of rod to the other. Metals, it is said, are good conductors of heat. On the other hand, if you hold a wooden stick in the flame in the same way, you will not have to drop it quickly on account of the conduction of heat. Wood is a poor conductor of heat. Thus we may speak of good and poor conductors of heat. Now this can be cleared up by another experiment. And this experiment we are unfortunately unable to make today. It has again been impossible to get ice in the form we need it. At a more favorable time the experiment can be made with a lens made of ice as we would make a lens of glass. Then from a source of heat, a flame, this ice lens can be used to concentrate the heat rays just as light rays can be concentrated (to use the ordinary terminology.) A thermometer can then be used to demonstrate the concentration by the ice lens of the heat passing through it. (See Fig. 4). Now you can see from this experiment that it is a question here of something very different from conduction even though there is a transmission of the heat, otherwise the ice lens could not remain an ice lens. What we have to consider is that the heat spreads in two ways. In one form, the bodies through which it spreads are profoundly influenced, and in the other form it is a matter of indifference what stands in the path. In this latter case we are dealing with the propagation of the real being of heat, with the spreading of heat itself. If we wish to speak accurately we must ask what is spreading, then we apply heat and see a body getting warmer gradually piece by piece, we must ask the question: is it not perhaps a very confused statement of the matter when we say that the heat itself spreads from particle to particle through the body, since we are able to determine nothing about the process except the gradual heating of the body? You see, I must emphasize to you that we have to make for ourselves very accurate ideas and concepts. Suppose, instead of simply perceiving the heat in the metal rod, you had a large rod, heated it here, and placed on it a row of urchins. As it became warm the urchins would cry out, the first one, then the second, then the third, etc. One after another they would cry out. But it would never occur to you to say that what you heard from the first urchin was conducted to the second, the third, the fourth, etc. When the physicist applies heat at one spot, however, and then perceives it further down the rod, he says: the heat is simply conducted. He is really observing how the body reacts, one part after another, to give him the sensation of warmth, just as the urchins give a yell when they experience the heat. You cannot, however, say that the yells are transmitted. Now we will perform also an experiment to show how the different metals we have here in the form of rods behave in respect to what we call the conduction, and about which we are striving to get valid ideas. We have hot water in this vessel (Fig. 3). By placing the ends of the rods in the water, they are warmed. Now we will see how this experiment comes out. One rod after another will get warm, and we will have a kind of graduated scale before us. We will be able to see the gradual spreading of the effect of the heat in the different substances. (The rods consisted of copper, nickel, lead, tin, zinc, iron.) The iodide of mercury on the rods (used to indicate rise in temperature) becomes red in the following order: copper, nickel, zinc, tin, iron and lead. The lead is, therefore, among these metals, the poorest conductor of heat, as it is said. This experiment is shown to you in order to help form the general view of the subject that I have so often spoken to you about. Gradually we will rise to an understanding of what the heat entity is in its reality. Now, from our remarks of yesterday we have seen that when we turn our attention to he realm of corporeality, we can in a certain way, set limits to the realm of the solids by following what it is essentially that takes on form. We have the fluids as an intermediate stage and then we go over to the gaseous realm. In the gaseous we have a kind of intermediate state, exactly as we would expect, namely the heat condition. We have seen why we can place it as we do in the series. Then we come, as I have said, into an X region in which we have to assume materialization and dematerialization, pass then to a Y and a Z. This is all similar to the manner in which we find in the light spectrum the transition from green through blue to violet and then apparently on to infinity. Yesterday we convinced ourselves that we have to continue below the solid realm into a U region. Thus we think of the world of corporeality as arranged in an order analogous to the arrangement in the spectrum. This is exactly what we do when we pursue our thinking in contact with reality. Now let us further extend the ideas of yesterday. In the case of the spectrum we conceive of what disappears at the violet end and at the red end in the straight line spectrum as bent into a circle. In exactly the same way we can, in this different realm of states of aggregation, imagine that the two ends of the series do not disappear into infinity. Instead, what apparently goes off into the indefinite on the one side and what goes off into indefiniteness on the other may be considered as bending back (Fig. 1) and then we have before us a circle, or at least a line whose two ends meet. The question now arises, what is to be found at the point of juncture? When we observe the usual spectrum, we can in that case find something at this point. In Goethe's sense you know that the spectrum considered as a whole with all its colors included shows as its middle color on one side green, when we make a bright spectrum. On the other side peach blossom which is also a middle color when we make a dark spectrum. Thus we have green, blue, violet extending to peach blossom. By closing the circle we note that at the point where it closes, there is the peach blossom color. If we then construct a similar circle in our thinking about the realm states of aggregation, what do we find at the point of juncture? This brings us to an enormously important consideration. What must we place in the spectrum of states of aggregation which will correspond to the peach blossom of the color spectrum? The idea that arises naturally from the facts here may perhaps be easier for you to grasp if I lead you to it as follows: What do we have in reality which disappears as it were in two opposite directions — just as in the color spectrum the tones shade off on the one side into the region beyond the violet and on the other side into the region beyond the red? Ask yourselves what it is. It is nothing more or less than the whole of nature. The whole of nature is included in it. For you cannot in the whole of nature find anything not included in the form categories we have mentioned. Nature disappears from us on the one hand when we go through corporeality into heat and beyond. She disappears from us on the other when we follow form through the solid realm into the sub-solid where we saw the polarization figures as the effect of form on form. The tourmaline crystals show us now a bright field, now a dark one. By the mutual effect of one form on another there appear alternately dark and light fields. It is essential for us to determine what we should place here when we follow nature in one direction until we meet what streams from the other side. What stands there? Man as such stands there. The human being is inserted at that point. Man, taking up what comes from both sides is placed at that point. And how does he take up what comes from the two sides? (Fig. 2) He has form. He is also formed within. When we examine his form among other formed bodies we are obliged to give him this attribute. Thus, the forces that give from elsewhere are within man. And now we must ask ourselves, are these forces to be found in the sphere of consciousness? No, they are not in the human consciousness. Think of the matter a moment. You cannot get a real understanding of the human form from what you can see in either yourselves or other men. You cannot experience it immediately in consciousness. We have a corporeality, but this form is not given in our immediate consciousness. What do we have in our immediate consciousness in the place of form? Now, my friends, that can be experienced only when one gradually and in an unbiased manner learns to observe the physical development of man. When the human being first enters physical existence, he must be related very plastically to his formative forces. That is, he must do a great deal of body building. The nearer we approach the condition of childhood, the greater the body building, and as we take on years there is a withdrawal of the body building forces. In proportion as the body building forces withdraw, conscious reasoning comes into play. The more the formative forces withdraw the more reasoning advances. We can create ideas in regard to form in proportion as we lose the ability to create form in ourselves. This considered in a matter of fact way, is simply an obvious truth. But now you see, we can say that we experience formative forces — forces that create form outside the body can be experienced. And how do we experience them? In this way, that they become ideas within us. Now we are at the point where we can bring the formative forces to the human being. These forces are not something that can be dreamed about. Answers to the questions that nature puts to us cannot be drawn from speculation or philosophizing, but must be got from reality. And in reality we see that the formative forces show themselves where, as it were, form dissolves into ideas, where it becomes ideas. In our ideas we experience what escapes us as a force while our bodies are building. When we place human nature before us in thought, we can state the matter as follows: man experiences as ideas the forces welling up from below. What does he experience coming down from above? What comes into consciousness from the realms of gas and heat? Here again when you look at human nature in an unprejudiced way, you have to ask yourselves: how does the will relate itself to the phenomena of heat? You need only consider the matter physiologically to see that we go through a certain interaction with the heat being of outer nature in order to function in our will nature. Indeed heat must appear if willing is to become a reality. We have to consider will related to heat. Just as the formative forces of outer objects are related to ideas, so we have to consider what is spread abroad as heat as related to that which we find active in our wills. Heat may be thus looked upon as will, or we may say that we experience the being of heat in our will. How can we define form what it approaches us from within-out? We see it, in this form, in any given solid body. We know that if conditions are such that this form can be seized upon by our life processes, ideas will arise. These ideas are not within the outer object. It is somewhat as if I observed the spirit separated from the body in death. When I see form in outer nature, what brings about the form is not there in the object. It is in truth not there. Just as the spirit is not within the corpse but has been in it, so is that which determines form not within the object. If I therefore turn my eyes in an unprejudiced way towards outer nature I have to say: Something works in the process of form building in objects, but in the corpse this something “has been active,” while in the object its activity is becoming. We will see that what is there active lives in our ideas. If I experience heat in nature, then I experience what works in a certain way as my will . In the thinking and willing man we have what meets us in outer nature as form and heat respectively. But now there are all possible intermediate stages between will and thought. A mere intellectual self-examination will soon show you that you never think without exercising the will. Exercise of the will is difficult for modern man especially. The human being is more prone to will unconsciously the course of his thoughts, he does not like to send will impulses into the realm of thought. Entirely will-free thought content is really never present just as will not oriented by thought is likewise not present. Thus when we speak of thought and will, of ideas and will, we are dealing with extreme conditions, with what from one side builds itself as thought and from the other side builds itself as will. We can therefore say that in experiencing will permeated by thinking and thinking permeated by will, we experience truly and essentially the outer forms of nature and the outer heat being of nature. There is only one possibility for us here and that is to seek in man for essential being of what meets us in outer nature. And now pursue these thoughts further. When you follow further the condition of corporeality on the one hand you can say that you proceed along a line into the indeterminate. The opposite must be the case here. And how can we state this? How must it be within man? We must indeed, find again here what goes off into infinity. Instead of it going off into infinity, so that we can no longer follow it, we must picture to ourselves that it moves out of space. What wells up in man from the states of aggregation we must think of as going out of space. That is, the forces that are in heat must so manifest themselves in man that they move out of space. Likewise, the forces that produce form, pass out of space when they enter man. In other words, in man we have a point where that which appears spatially in the outer world as form and heat, leaves space. Where the impossibility arises, that that which becomes non-spatial can still be held mathematically. I think we can see here in a very enlightening way how an observation of nature in accordance with facts obliges us to leave space when we approach man, provided we properly place him in the being of nature. We have to go to infinity above and below (the scale of that states of aggregation.) When we enter the being of man, we leave the realm of space. We cannot find a symbol which expresses spatially how the facts of nature meet us in the being of man. Nature properly conceived, shows us that when we think of her in relation to man, we must leave her. Unless we do, when we consider the content of nature in relation to man, we simply do not come to the human being. But what does this mean mathematically? Suppose you set down the lineal series among which you are following states of aggregation to infinity. The words one after another may be considered as positive. Then what works into the nature of man must be set down as negative. If you consider this series as positive, the effects in the human being have to be made negative. What is meant by positive and negative will be cleared up I think by a lecture to be given by one of our members during the next few days. We have to conceive, however, of what comes before our eyes plainly here in this way that the essential nature of heat, insofar as this belongs to the outer world, must be made negative when we follow it into the human being, and likewise the essentiality of form becomes negative when we follow it into man. Actually then, what lives in man as ideas is related to outside form as negative numbers are to positive numbers and vice versa. Let us say, as credits and debits. What are debits on the one hand are credits on the other and vice versa. What is form in the outside world lives in man in a negative sense. If we say “there in the outside world is some sort of a body of a material nature,” we have to add: “if I think about its form the matter must be negative, in a sense, in my thinking.” How is matter characterized by me as a human being? It is characterized by its pressure effects. If I go from the pressure manifestation of matter to my ideas about form, then the negative of pressure, or suction, must come into the picture . That is, we cannot conceive of man's ideas as material in their nature if we consider materiality as symbolized by pressure. We must think of them as the opposite. We must think of something active in man which is related to matter as the negative is to the positive. We must consider this as symbolized by suction if we think of matter as symbolized by pressure. If we go beyond matter we come to nothing, to empty space. But if we go further still, we come to less-than-nothing, to that which sucks up matter. We go from pressure to suction. Then we have that which manifests in us as thinking. And when on the other hand you observe the effects of heat, again you go over to the negative when it manifests in us. It moves out of space. It is, if I may extend the picture, sucked up by us. In us it appears as negative. This is how it manifests. Debits remain debits, although they are credits elsewhere. Even though our making external heat negative when it works within us results in reducing it to nothing, that does not alter the matter. Let me ask you again to note: we are obliged by force of the facts to conceive of man not entirely as a material entity, but we must think of something in man which not only is not matter, but is so related to matter as suction is to pressure. Human nature properly conceived must be thought of as containing that which continually sucks up and destroys matter. Modern physics, you see, has not developed at all this idea of negative matter, related to external matter as a suction is to a pressure. That is unfortunate for modern physics. What we must learn is that the instant we approach an effect manifest in man himself all our formulae must be given another character. Will phenomena have to be given negative values in contrast to heat phenomena; and thought phenomena have to be given negative values as contrasted to the forces concerned in giving form.

The Warmth Course

Lecture X

https://rsarchive.org/Lectures/GA321/English/MP1980/19200310a01.html

Stuttgart

10 Mar 1920

GA321-10

My dear friends, At this point I would like to build a bridge, as it were, between the discussions in this course and the discussion in the previous course. We will study today the light spectrum, as it is called, and its relation to the heat and chemical effects that come to us with the light. The simplest way for us to bring before our minds what we are to deal with is first to make a spectrum and learn what we can from the behavior of its various components. We will, therefore, make a spectrum by throwing light through this opening — you can see it here. (The room was darkened and the spectrum shown.) It is to be seen on this screen. Now you can see that we have something hanging here in the red portion of the spectrum. Something is to be observed on this instrument hanging here. First we wish to show you especially how heat effects arise in the red portion of the spectrum. Something is to be observed on this instrument hanging here. These effects are to be observed by this expanding action of the energy cylinder on the air contained in the instrument, which expanding action in turn pushes the alcohol column down on this side and up on this one. This depression of the alcohol column shows us that there is a considerable heat effect in this part of the spectrum. It would be interesting also to show that when the spectrum is moved so as to bring the instrument into the blue-violet portion, the heat effect is not noticeable. It is essentially characteristic of the red portion. And now, having shown the occurrence of heat effects in the red portion of the spectrum by means of the alcohol column, let us show the chemical activity of the blue-violet end. We do this by allowing the blue portion to fall on a substance which you can see is brought into a state of phosphorescence. From the previous course you know that this is a form of chemical activity. Thus you see an essential difference between the portion of the spectrum that disappears on the unknown on this side and the portion that disappears on this other side; you see how the substance glows under the influence of the chemical rays, as they are called. Moreover, we can so arrange matters that the middle portion of the spectrum, the real light portion, is cut out. We cannot do this with absolute precision, but approximately we can make the middle portion dark by simply placing the path of the light a solution of iodine in carbon disulphate. This solution has the property of stopping the light. It is possible to demonstrate the chemical effect on one side and the heat effect on the other side of this dark band. Unfortunately we cannot carry out this experiment completely, but only mention it in passing. If I place an alum solution in the path of the light the heat effect disappears and you will see that the alcohol column is no longer displaced because the alum, or the solution of alum, to speak precisely, hinders its passage. Soon you will see the column equalize, now that we have placed alum in the path, because the heat is not present. We have here a cold spectrum. Now let us place in the light path the solution of iodine in carbon disulphate, and the middle portion of the spectrum disappears. It is very interesting that a solution of esculin will cut out the chemical effect. Unfortunately we could not get this substance. In this case, the heat effect and the light remain, but the chemical effect ceases. With the carbon disulphide you see clearly the red portion — it would not be there if the experiment were an entire success — and the violet portion, but the middle portion is dark. We have succeeded partly in our attempt to eliminate the bright portion of the spectrum. By carrying out the experiment in a suitable way as certain experimenters have done (for instance, Dreher, 50 years ago) the two bright portions you see here can be done away with. Then the temperature effect may be demonstrated on the red side, and on the other side phosphorescence shows the presence of the chemically active rays. This has not yet been fully demonstrated and it is of very great importance. It shows us how that which we think of as active in the spectrum can be conceived in its general cosmic relations. In the course that I gave here previously I showed how a powerful magnet works on the spectral relations. The force emanating from the magnet alters certain lines, changes the picture of the spectrum itself. It is only necessary for a person to extend the thought prompted by this in order to enter the physical processes in his thinking. You know from what we have already said that there is really a complete spectrum, a collection of all possible twelve colors; that we have a circular spectrum instead of the spectrum spread out in one dimension of space. We have (in the circular spectrum) here green, peach blossom here, here violet and here red with the other shades between. Twelve shades, clearly distinguishable from one another. Now the fact is that under the conditions obtaining on the earth such a spectrum can only exist as a mental image. When we are dealing with this spectrum we can only do so by means of a mental picture. The spectrum we actually get is the well-known linear one extending as a straight line from red through the green to the blue and violet — thus we obtain a spectrum formed from the circular one, as I have often said, by making the circle larger and larger, so that the peach blossom disappears, violet shades off into infinity on one side and red shades off on the other, with green in the middle. We may ask the question: how does this partial spectrum, this fragmentary color band arise from the complete series of color, the twelve color series which must be possible? Imagine to yourselves that you have the circular spectrum, and suppose forces to act on it to make the circle larger and larger and finally to break at this point (see drawing). Then, when it has opened, the action of these forces would make a straight line of the circle, a line extending apparently into infinity in each direction. (Fig. 1). Now when we come upon this straight line spectrum here under our terrestrial conditions we feel obliged to ask the question: how can it arise? It can arise only in this way, that the seven known colors are separated out. They are, as it were, cut out of the complete spectrum by the forces that work into it. But we have already come upon these forces in the earth realm. We found them when we turned our attention to the forces of form. This too is a formative activity. The circular form is made over into the straight-line form. It is a form that we meet with here. And considering the fact that the structure of the spectrum is altered by magnetic forces, it becomes quite evident that forces making our spectrum possible are everywhere active. This being the case, we have to assume that our spectrum, which we consider a primary thing, has working within it certain forces. Not only must we consider light variation in our ordinary spectrum, but we have to think ofthis ordinary spectrum as including forces which render it necessary to represent the spectrum by a straight line . This idea we must link up with another, which comes to us when we go through the series, as we have frequently done before (Fig. 2), from solids, through fluids, to condensation and rarefaction, i.e. gases, to heat and then to that state we have called X, where we have materialization and dematerialization. Here we meet a higher stage of condensation and rarefaction, beyond the heat condition, just as condensation and rarefaction proper constitute a kind of fluidity of form. When form itself becomes fluid, when we have a changing form in a gaseous body, that is a development from form as a definite thing. And what occurs here? A development of the condensation-rarefaction condition Keep this definitely in mind, that we enter a realm where we have a development of the condensation-rarefaction state. What do we mean by a “development of rarefaction”? Well, matter itself informs us what happens to it when it becomes more and more rarefied. When I make matter more and more dense, it comes about that a light placed behind the matter does not shine through. When the matter becomes more and more rarefied, the light does pass through. When I rarefy enough, I finally come to a point where I obtain brightness as such. Therefore, what I bring into my understanding here in the material realm is empirically found to be the genesis of brightness or luminosity as a heightening of the condition of rarefaction; and darkening has to be thought of as a condensation, not yet intense enough to produce matter, but of such an intensity as to be just on the verge of becoming material. Now you see how I place the realm of light above the heat realm and how the heat is related to the light in an entirely natural fashion. But when you recollect how a given realm always gives a sort of picture of the realm immediately above it, then you must look in the being of heat for something that foreshadows, as it were, the conditions of luminosity and darkening. Keep in mind that we do not always find only the upper condition in the lower, but also always the lower condition in the upper. When I have a solid, it foreshadows for me the fluid. What gives it solidity may extend over into the non-solid realm. I must make it clear to myself, if I wish to keep my concepts real, that there is a mutual interpenetration of actual qualities. For the realm of heat this principle takes on a certain form; namely this, that dematerialization works down into heat from above (see arrow). From the lower side, the tendency to materialization works up into the heat realm. Thus you see that I draw near to the heat nature when I see in it a striving for dematerialization, on the one hand, and on the other a striving for materialization. (If I wish to grasp its nature I can do it only by conceiving a life, a living weaving, manifesting itself as a tendency to materialization penetrated by a tendency to dematerialization.) Note, now, what an essential distinction exists between this conception of heat based on reality and the nature of heat as outlined by the so-called mechanical theory of heat of Clausius. In the Clausius theory we have in a closed space atoms or molecules, little spheres moving in all directions, colliding with each other and with the walls of the vessel, carrying on an outer movement. (Fig. 3) And it is positively stated: heat consists in reality in this chaotic movement, in this chance collision of particles with each other and with the walls of the vessel. A great controversy arose as to whether the particles were elastic or non-elastic. This is of importance only as the phenomena can be better explained on the assumption of elasticity or on the assumption that the particles are hard, non-elastic bodies. This has given form to the conviction that heat is purely motion in space. Heat is motion. We must now say “heat is motion,” but in an entirely different sense. It is motion, but intensified motion . Wherever heat is manifest in space, there is a motion which creates the material state striving with a motion which destroys the material state. It is no wonder, my friends, that we need heat for an organism. We need heat in our organism simply to change continuously the spatially-extended into the spatially non-extended. When I simply walk through space, my will carries out a movement in space. When I think about it, something other than the spatial is present. What makes it possible for me as a human organism to be inserted into the form relationships of the earth? When I move over the earth, I change the entire terrestrial form. I change her form continually. What makes it possible that I am in relation to the other things of the earth, and that I can form ideas, outside of space, within myself as observer, of what is manifested in space? This is what makes it possible, my being exists in the heat medium and is thus continually enabled to transform material effects, spatial effects, into non-spatial ones that no longer partake of the space nature. In myself I experience in fact what heat really is, intensified motion. Motion that continually alternates between the sphere of pressure and the sphere of suction. Assume that you have here (Fig. 4) the border between pressure and suction forces. The forces of pressure run their course in space, but the suction forces do not, as such, act in space — they operate outside of space. For my thoughts, resting on the forces of suction, are outside of space. Here on one side of this line (see figure) I have the non-spatial. And now when I conceive of that which takes place neither in the pressure nor in the suction realms, but on the border line between the two, then I am dealing with the things that take place in the realm of heat. I have a continually maintained equilibrium tendency between pressure effects of a material sort and suction effects of a spiritual sort. It is very significant that certain physicists have had these things right under their noses but refuse to consider them. Planck, the Berlin physicist, has made the following striking statement: if we wish to get a concept of what is called ether nowadays, the first requisite is to follow the only path open to us, in view of the knowledge of modern physics, and consider the ether non-material. This from the Berlin physicist, Planck. The ether, therefore, is not to be considered as a material substance. But now, what we are finding beyond the heat region, the realm wherein the effects of light take place, that we consider so little allied to the material that we are assuming the pressure effects — characteristic of matter — to be completely absent, and only suction effects active there. Stated otherwise, we may say: we leave the realm of ponderable matter and enter a realm which is naturally everywhere active, but which manifests itself in a manner diametrically opposite to the realm of the material. Its forces we must conceive of as suction forces while material things obviously manifest through pressure forces. Thus, indeed, we come to an immediate concept of the being of heat as intensified motion, as an alternation between pressure and suction effects, but in such a way that we do not have, on the one hand, suction spatially manifested and, on the other hand, pressure spatially manifested. Instead of this, we have to think of the being of heat as a region where we entirely leave the material world and with it three-dimensional space. If the physicist expresses by formulae certain processes, and he has in these formulae forces, in the case where these forces are given the negative sign — when pressure forces are made negative — they become suction forces. Attention must be paid to the fact that in such a case one leaves space entirely. This sort of consideration of such formulae leads us into the realm of heat and light. Heat is only half included, for in this realm we have both pressure and suction forces. These facts, my dear friends, can be given, so to speak, only theoretically today in this presentation in an auditorium. It must not be forgotten that a large part of our technical achievement has arisen under the materialistic concepts of the second half of the 19 th century. It has not had such ideas as we are presenting and therefore such ideas cannot arise in it. If you think over the fruitfulness of the one-sided concepts for technology, you can picture to yourselves how many technical consequences might flow from adding to the modern technology, knowing only pressures — the possibility of also making fruitful these suction forces. (I mean not only spatially active suction which is a manifestation of pressure, but suction forces qualitatively opposite to pressure.) Of course, much now incorporated in the body of knowledge known as physics will have to be discarded to make room for these ideas. For instance, the usual concepts of energy must be thrown out. This concept rests on the following very crude notions: when I have heat I can change it into work, as we saw from the up and down movement of the flask in the experiment resulting from the transformation of heat. But we saw at the same time that the heat was only partly changed and that a portion remained over of the total amount at hand. This was the principle that led Eduard von Hartmann to enunciate the second important law of the modern physics of heat — a perpetuum mobile of the second type is impossible. Another physicist, Mach, well known in connection with modern developments in this field, has done quite fundamental thinking on the subject. He has thought along lines that show him to be a shrewd investigator, but one who can only bring his thinking into action in a purely materialistic way. Behind his concepts stands the materialistic point of view. He seeks cleverly to push forward the concepts and ideas available to him. His peculiarity is that when he comes to the limit of the usual physical concepts where doubts begin to arise, he writes the doubts down at once. This leads soon to a despairing condition, because he comes quickly to the limit where doubts appear, but his way of expressing the matter is extremely interesting. Consider how things stand when a man who has the whole of physics at his command is obliged to state his views as mach states them. He says (Ernst Mach, Die Prinzipien der Warme Lehre , p. 345): “There is no meaning in expressing as work a heat quantity which cannot be transformed into work.” (We have seen that there is such a residue.) “Thus it appears that the energy principle like other concepts of substance has validity for only a limited realm of facts. The existence of these limits is a matter about which we, by habit, gladly deceive ourselves.” Consider a physicist who, upon thinking over the phenomena lying before him, is obliged to say the following: “Heat exists, in fact, that I cannot turn into work, but there is no meaning in simply thinking of this heat as potential energy, as work not visible. However, I can perhaps speak of the changing of heat into work within a certain region — beyond this it is not valid.” And in general it is said that every energy is transformable into another, but only by virtue of a certain habit of thinking about those limits about which we gladly deceive ourselves. It is extremely interesting to pin physics down at the very point where doubts are expressed which must arise from a straightforward consideration of the facts. Does this not clearly reveal the manner in which physics is overcome when physicists have been obliged to make such statements? For, fundamentally, this is nothing other than the following: one can no longer hold to the energy principle put forth as gospel by Helmoltz and his colleagues. There are realms in which this energy principle does hold. Now let us consider the following: How can one make the attempt symbolically (for fundamentally it is symbolic when we try to set the outlines of something), how can we make the attempt to symbolize what occurs in the realm of heat? When you bring together all these ideas I have developed, and through which in a real sense I have tried to attain to the being of heat, then you can get a concept of this being in the following manner. Picture this to yourselves (Fig. 5). Here is space (blue) filled with certain effects, pressure effects. Here is the non-spatial (red) filled with suction effects. Imagine that we have projected out into space what we considered as alternately spatial and non-spatial. The red portion must be thought of as non-spatial. Using this intermediate region as an image of what is alternately spatial and non-spatial, you have in it a region where something is appearing and disappearing. Think of something represented as extended and disappearing. As substance appears, there enters in something from the other side that annihilates it, and then we have a physical-spiritual vortex continually manifesting in such a manner that what is appearing as substance is annihilated by what appears at the same time as spirit. We have a continual sucking up of what is in space by the entity which is outside of space. What I am outlining to you here, my dear friends, you must think of as similar to a vortex. But in this vortex you should see simply in extension that which is “intensive” in its nature. In this way we approach, I might say figuratively, the being of heat. We have yet to show how this being of heat works so as to bring about such phenomena as conduction, the lowering of the melting point of an alloy below the melting point of its constituents, and what it really means that we should have heat effects at one end of the spectrum and chemical effects at the other. We must seek the deeds of heat as Goethe sought out the deeds of light . Then we must see how knowledge of the being of heat is related to the application of mathematics and how it affects the imponderable of physics. In other words, how are real formulae to be built, applicable to heat and optics.

The Warmth Course

Lecture XI

https://rsarchive.org/Lectures/GA321/English/MP1980/19200311p01.html

Stuttgart

11 Mar 1920

GA321-11

My dear friends, The experiments we had anticipated carrying out today we will unfortunately have to postpone until tomorrow. At that time they will be arranged so as to show you what is necessary if I am to prove to you all that I wish to prove. Today, therefore, we will consider some things which, together with the experiments of tomorrow, will enable us to bring our observations to a conclusion the following day. As a help toward the understanding of the being of heat, I wish to call your attention to a certain fact. This fact is one which we must take into account in developing our ideas on this subject, and it is that there is a certain difficulty in understanding what is really involved in a transparent body. I am not now speaking of transparency in connection with heat. You will see, however, when we have finished that we can get helpful ideas for understanding heat from the realm of light. I said there was a certain difficulty in understanding what a relatively transparent body is and what an opaque body is as these reveal themselves under the influence of light. I have to express myself in a different way from that ordinarily used. The ordinary method of expression in physics would be as follows: an opaque body is one that by some peculiar property of its surface reflects the rays of light that fall on it and thus become a visible body. I cannot use this form of expression because it is not a reflection of the facts, it is a statement of a preconceived theory and is not by any means to be taken as self-evident. For to speak of rays, of light rays, is theoretical. I have dealt with that in my former course. What we meet in reality is not light rays, but an image and it is this we must hold firmly in mind. As a matter of fact, we cannot simply say: a transparent body is one that by virtue of its inner molecular properties passes light through, and an opaque body is one that throws the light back. For how can such a theory be substantiated? Recollect what I have said to you about the relations of the various realms of reality. We have solids, fluids, gaseous bodies, heat, \(X\), \(Y\), \(Z\) and below the solid and bordering on it the U region, and you can see that the light realm must have a relation to heat and so also must the realm of chemical activity. On the other side that which we meet, so to speak, as the fluid nature in heat or in gases must have a relation to the essence of tone. For tone appears alone with the occurrence of condensation and rarefaction in gases or aeriform bodies. We may therefore suspect that where we have assumed \(X\), \(Y\), \(Z\), we will find the essence of light. Now the question is whether we have to look for the explanation of transparency of certain bodies is not to be immediately derived from the nature of light, nor from the relation of light to these bodies. We have the \(U\) region and this \(U\) region must have a relation to the solids on the surface of the earth. We must first ask the question and seek to apply the answer to this question to our consideration of these things. What influence has the \(U\) region on solids and can we from the nature of this influence derive anything that will show use the difference between transparent bodies and the ordinary non-transparent metals? This question must be considered and the answer to it will appear when we extend further our ideas of yesterday in regard to heat by the addition of certain other conceptions. Note now, the warmth phenomena naturally are considered as belonging to the realm of physics. Such things as conduction have been included, thought of in the way I have described to you. This spreading of heat through conduction or flow of the heat condition either through a body or from one body to another one touching it has been observed. The flow has been conceived of as though a kind of fluid were involved, and the picture is of a liquid flow. It may be compared to something readily observable in the objective world, namely the water in a brook which is at one point now, and a moment later is at a distant point. Thus is pictured the flow of heat from one spot to another when the so-called conduction of heat takes place. The phenomenon are to be found in Fourrier (other investigators might also be cited.) Let us consider these a little from our own point of view and see if we can establish their validity. Imagine that we have a body bounded by a definite wall, say of metal (Fig. 1). Assume the wall to extend indefinitely above and below, and suppose it to consist of some sort of metal. Let us place boiling water in contact with the wall on one side holding it at a temperature \(U_1\) which in this case is 100°C. On the other side we place melting ice to hold the wall at a temperature \(U_2\) which in this special case will be 0°C. Considering the entire phenomenon you will see that we have to do with a difference, here \(U_1\), here \(U_2\) and \(U_1\) and \(U_2\) gives us the temperature difference. Upon this difference depends the fact that we have a conduction of heat. Obviously, this transfer of heat will proceed otherwise when the difference is small, a small quantity of heat is transferred to attain equilibrium, and when the difference is great a larger quantity is transferred. Thus I may say that the quantity of heat needed to attain a certain condition depends on this temperature difference, \(U_1 - U_2\). Furthermore, it will depend not only on the difference \(U_1 - U_2\), but on the thickness of the wall which I may denote by \(L\), becoming greater when this is large and less when it is small. That is, the amount of heat transferred is inversely proportional to \(L\). I may calculate for a given area that I will call \(Q\), how much heat I will need to get a certain degree of conduction. The greater \(Q\) is, the greater will be the amount. Thus the amount of heat is directly proportional to \(Q\) and I must multiply by this factor. Finally, the whole process is dependent upon time. A greater effect is produced by permitting a given amount of heat to act for a longer time, a smaller effect in a less time. Therefore I have to multiply by the time. Obviously then, I must multiply through by a constant representing the heat itself, by something involving heat, since none of the quantities so far mentioned include the heat and thus cannot by themselves give the quantity of heat, \(W\), which I wish to secure. This quantity of heat, \(W\), is directly proportional to \(L\). Now if you equate all the other factors with \(U_1\) and \(U_2\), you are expressing what really flows and this not a heat quantity, essentially, nor dependent directly on a heat quantity, but is a temperature fall, a difference in level. Please keep this in mind. Just as when we pour water through a sluice and turn a paddle wheel, and the motion is due to the energy arising from a different in level, so there we have to do with a drop from one level to another, and it is this we must keep our attention on. Now we have to take up another consideration of Fourrier's to draw nearer to the being of heat. We will work over the ordinary concepts as it were so as to move nearer to reality than the physicists of the 20th century. So far I have taken into consideration only what pertains to the conducting of heat from one spot to another, but I can assume that something goes on in the body itself. Let me now ask a question. Suppose we assume that the progress of heat instead of being uniform from left to right was non-uniform, then the formula would have to apply to the inner lack of uniformity. If the irregularity in the partition of heat is present I must bring it into my considerations in some way. I must bring in the differences that reveal themselves within, that is, what takes place in the body as the temperature effects equalize themselves. As you can easily see, my formula is applicable to the process. I can say $$W=\frac{U_1-U_2}{L} t c q$$ That represents what takes place here. I will not consider the whole thickness of the wall, but deal with small portions of it, and will consider what happens in these small portions, as over the entire distance it is expressed by the factor \((U_1-U_2)/l\) It is thus a question of dealing with minute distances within the body. To do this, I employ the differential ratio \(du\) where \(du/dx\) represents an infinitesimal movement of heat. If this is considered for an instant of time, I must multiply by \(dt\), this being left out of account if I do not consider the time. Thus we have W as an expression of the quantity of heat transferred through small distance in order to equalize the temperature within the body. The following formula expresses the effects of temperature fall within the body: $$W=c•q\frac{du}{dx} dt$$ In relation to this, I will ask you please to consider what we took up yesterday in a sketchy way, which will be clearer tomorrow when we have carried out the necessary experiments. Today, I will simply mention it, since we must keep it in mind. I refer to the relation between heat, light and chemical effect in the spectrum. Yesterday, your attention was called to the following fact: when we have an ordinary terrestrial spectrum, in the middle is the light effect proper, towards one end (Fig. 2, arrow) heat effects, toward the other end the chemical effects Now we have to consider the following. We have seen that when we construct a picture of this spectrum, we must not think of light, heat and chemical effects as stretched out in a straight line. We go toward the left to approach the warm end of the spectrum and toward the right to approach the chemically active end. (Fig. 2) thus, it is not possible to remain in the lane of the pure light effects if we wish to symbolize the heat effects; nor can we remain in this place if we wish to symbolize the chemical effects. We have to move out of this plane. Now to visualize the whole matter, let us make clear to ourselves how we must really represent a heat quantity working within a body by means of our formula. How must we represent qualitatively the relation between it and the chemical effect? We will not do this properly until we take into account the fact that we go one way to reach the heat and the opposite way to reach the chemical effects. This fact must be kept in mind if we would orient ourselves. So when we consider W as a positive quantity here (or we might consider it negative) then we have to consider the corresponding chemical effect as: $$W=-c•q\frac{du}{dx} dt$$ The foregoing equation corresponds to the chemical effect, and this one: $$W=+c•q\frac{du}{dx} dt$$ corresponds to the heat effect. As a matter of fact, these things demonstrate for us an important point. This point is that when we use formulae we cannot handle the mathematical quantities merely as such if we at the same time expect the formulae to express the relations within a field of actual effects, an observed realm, where heat and chemical action are manifesting themselves. In ordinary combustion, for instance, where we wish to bring heat and chemical effects into relation, we must, if we use formulae, set down as positive what represents heat and as negative what represents chemical effect . Now if you carry your considerations further, you may make the following statement: When we think of heat as extending in one direction, so to speak, and chemical action as extending in the opposite, then we have what is essential in light left in a plane at right angles to the imagined chemical action-heat lines and between them. But if you have reserved positivity for heat and negativity for chemical action, you cannot use either of these for light effects. At this point you have to apply to the light effects a set of facts which today are only vaguely felt and not by any means explained, namely the relation between positive and negative numbers and imaginary numbers. When you are dealing with light phenomena you have to say: $$w=\sqrt{-1}•c•q•\frac{du}{dx}•dt$$ That is to say, if you wish to deal with the relation of heat, chemical action and light working in the same phenomenological field at the same time, you have to use imaginary numbers — your calculation has to involve the mathematical relations expressed in imaginary numbers. But now we have already made the following statement. The spectral band that we can produce experimentally under terrestrial conditions is to be thought of actually as a circle that has been opened out. Furthermore, the complete spectrum has the peach blossom color above. If, by the employment of a sufficiently great force, you were able to bend the spectrum into a circle, you would bring together what apparently extends off into infinity in either direction. Now you can realize that this closing up cannot simply be thought of as being carried out in a circle in one plane. For as you go out into the heat region you also go off to one side (i.e. into something qualitatively different) and, proceeding into the chemical effect region, you go off to the other side. You are then in a situation where you must go first into the infinite on one side and then into the infinite on the other side and then into the infinite on the other side. You have first the awkward problem of going into infinity in a plane in one direction and then coming back from infinity and entering the plane on the other side. This implies that you reach the same infinite point no matter what direction you take. Moreover, you are confused unless you assume that you reach the same point as you go out in one direction and then in the other and you then have to come back from two different points at infinity. The way to discovery of the peach blossom color is thus a doubly complicated one. Not only must you bend the spectrum in one plane, but at right angles with, say an electromagnet, you will have to turn the magnet. That, however, lead to another point. If the magnet would have to be turned, then none of the mathematical expressions so far given would apply entirely. We then have to call in what was put before you yesterday in the discussion following the lecture by Messrs. Blumel and Strakesch, namely the super-imaginary number . You will doubtless recollect that we have to take into account that there is controversy about these super-imaginary numbers. They are readily handled mathematically and have, so to speak, more than one meaning. Some mathematicians even question whether there is any justification for them at all. Physics does not give us a definite formulation of the super-imaginary numbers. Nevertheless we put them into the series because we are led to see that they are necessary if we wish to formulate in an orderly manner what happens in the realm of chemical activity, light, heat, and what takes place in addition when we pass out in one direction through this series and come back into it from the other direction. One who has the organ to perceive these things finds something very peculiar. He finds something which, I believe, furnishes a real foundation for illuminating the basic facts of physical phenomena. What I mean my friends, is this. The same sort of difficulty that meets one in the consideration of super-imaginary numbers also meets one when the attempt is made to apply the science of the inorganic to the phenomena of life . It cannot be done with these concepts of the inorganic. They simply do not apply. What has been the result of this? On the one hand there are thinkers who say: “The organic things of the earth have arisen by a transformation out of the inorganic.” But with this view alone one can never enter the reality of the living. Other thinkers like Prayer, regard the organic as the source of the inorganic and come nearer the truth. They think of the earth as originally a living body and what is today inorganic they consider as something thrown off or as that which has died out of the organic. But these people do not make us an entirely satisfactory picture. The same difficulty that meets us in the phenomena of nature considered by and for themselves is met also when we attempt a comprehensive formulation of what is present in the realms of heat, light, and chemical activity and what is come upon when we attempt to close the color band in a natural manner. We must assume, of course, that this color band can be closed somewhere although it is obvious that it cannot be done under terrestrial conditions. It is necessary for us to recognize how the purely mathematical leads up to the problem of living. With the faculties at hand today you can handle the phenomena of light, heat and chemical action, let us say, but you cannot handle what is evidently connected with these, namely the opening up of the spectrum. This cannot be formulated in a manner corresponding to the others. It will be helpful to us at this stage if we set up a terminology. We can base this terminology on rather definite concepts. We say: Something real is at the basis of the formula for W. Let us speak of this as heat ether . Likewise something real is involved when we change the positive signs of the heat formula to negative ones, and here we speak of the chemical ether . Where our formulae involve imaginary numbers, we speak of the light ether . You see here an interesting parallelism between thinking in mathematics and thinking within science itself. The parallelism shows how we are really dealing not so much with an objective difficulty but rather with a subjective one. For the purely mathematical difficulty arises of itself, and independently of the science of external things. No one would think that a beautifully built lecture could be delivered on the limits of mathematical thinking, similar to the one du Bois-Reymond delivered on the limits of knowledge of nature. At least the conclusions would be different. Within mathematics, unless the matter slips us because it is too complicated, in this realm of the purely mathematical it must be possible to set up a completely formulated expression. The fact that one cannot do this hangs together with our own relative lack of maturity. It is unthinkable that we have here an absolute shortcoming or limit to human knowledge. It is extremely important that you hold this before your minds as a fundamental. For this shows us how we cannot apply mathematics if we wish to enter reality unless we keep in mind certain relations. We cannot simply say with the energeticists, for instance, “a given quantity of heat changes into a certain quantity of chemical energy and vice versa.” That we cannot do, but we must bring in certain other values when a process of this kind takes place. For the necessity of the case constrains us to see as essential not the quantitative mechanical change from one energy to another but rather the qualitative aspect of the transformation. This is indeed to be found along with the quantitative. If people turned their attention to these qualitative changes which are expressed by the numerical formulations, such ideas as the following would not be advanced: “Apparently heat is just heat because we experience it as such, mechanical energy is as we experience it, chemical energy is what we see as chemical processes; but within, these processes are all alike. Mechanical energy is manifesting everywhere and heat is nothing but a form of this energy.” This idea of a bombardment, of collisions between molecules and atoms or between these and the wall of the vessel — this struggle for an abstract unity of all energy which makes it into a mechanical motion and nothing more — such things as these would not have arisen if it had been seen that even when we calculate we must take into account the qualitative differences between various forms of energy. It is very interesting in this connection to see how Eduard von Hartmann was obliged to find definitions for physics that excluded the qualitative. Naturally, one cannot find this in the one-sided mathematics of physics, and aside from the cases where negative quantities arise from purely mathematical relations, physicists do not like to reckon with numerical quality differences. They use positive and negative signs, but only because of purely mathematical relationships. In the ordinary theory of energy, justification would never be found for making one energy positive and another negative on the basis of qualitative differences.

The Warmth Course

Lecture XII

https://rsarchive.org/Lectures/GA321/English/MP1980/19200312a01.html

Stuttgart

12 Mar 1920

GA321-12

My dear friends, We will today first carry out what I had in mind yesterday because it will lead us to a more prompt conclusion of our series. Tomorrow, I will try to conclude the lecture series being given during my present visit with you. We will now demonstrate to ourselves in a completely adequate fashion that within what we call the sun's spectrum or a light spectrum, there are wrapped up heat effects, light effects and chemical effects. Yesterday, also, we saw that the forces involved in the phenomena of life as well were hidden away here; only we are not able to bring these life-effects into the field of our investigations in the same manner as we can the chemical, light and heat effects. For, there is not a simple experimental method by which the reality of the twelve-fold spectrum can be shown in its objectivity. Just this thing will be the task of a Research Institute, working entirely within our movement. Such investigations will not only be undertaken but they must be followed out in detail. Now I would like to call your attention to something. When we consider the hypothetical inclusion of life effects or the fact that our series , as we think of it at least, has hidden away in it life, heat, light and chemical effects, an important realm escapes us. This realm is physically more definitely manifested than the ones we have named. The realm that escapes us in the acoustical realm. The realm of acoustics is manifested strikingly in the movements of the air, that is, in the movement of the gaseous or aeriform body. And now comes up an important fundamental question. How do we come in the one direction through the heat, light and chemical spectra to the life forces and on the other side to the acoustic forces ? This is the question that presents itself when we look over the whole field of phenomena and about which we can teach according to Goethe's views of the physical world, as we have done heretofore rather than simply theorizing about it. Now let us show our first experiment. When we place a solution of alum in the path of a light cylinder made into a spectrum by passage through a prism we remove the heat effects. Let us permit the thermometer to rise in consequence of the action of the spectrum. When we place the solution of alum in the path of the spectrum, we have to look for a fall in the column of the thermometer. (the thermometer that had been going up rapidly, rose more slowly and then stopped.) The effect is shown by the fact that the thermometer rises more slowly. Therefore, the alum solution removes heat from the spectrum. We may consider this as proven — it has been done times without number and is a well-known fact. The second experiment we will make is to insert into the light cylinder a solution of iodine in carbon disulphide. You will see, the central portion of the spectrum is thereby entirely blotted out and the other portions considerably weakened. From the previous course you will remember that we have to consider this central portion as the light-portion proper. Thus, the light-portion of this spectrum is stopped by the solution of iodine in carbon disulphide just as the heat portion is stopped by the solution of alum. The thermometer now rises rapidly because the heat effect is present again. The third thing we will do is to place a solution of esculin in the path of light. This has the peculiarity of stopping the chemical effect leaving the heat and light effects unchanged. We can, thus, so handle the spectrum that we can remove the heat effect by means of an alum solution, the light portion by a solution of iodine in carbon disulphide, and the chemical part by an esculin solution. We will establish the facts in regard to the chemical effect by showing that when the chemical portion is there, the phosphorescent body glows. You can see that this body has been in the light cylinder, because when I shut off the light momentarily, with my hand, it slows. Now we will place it again in the spectrum, but this time with the light cylinder passing through the esculin solution. The action is excellent. There is no phosphorescence visible. Now, place before yourselves the fact that we have first the realm of heat, then the realms of light and chemical action. From our considerations taken in their entirety, you can conclude with a fair degree of certainty, at least, that a relation must exist here similar to the ones I have in the past few days pointed out as the X and Y realms. It is in this way that we are approaching definitely the place where we can begin to identify these two realms: Z Y chemical effect X light heat gaseous fluid solid U Let us observe particularly the following: The heat realm, the X, Y, and Z realms, the gaseous, fluid, solid and the U realms are to be arranged as we have outlines. Recollect that there is a matter of fact a certain very loose relationship to be observed between heat effects and the phenomena manifested in a gaseous mass. We are able to observe that the gaseous body manifests in its material configuration, what is manifested otherwise in the case of heat. The nature of heat is set before us materially in the gas. Now if we will cultivate a vivid insight into what occurs in this interplay between gaseous matter and heat, we will be able to get a concept also of the difference between the realm of gases and the x-realm. We need only consider what we have many times seen in our lives. This is that light relates itself quite otherwise to gases than does heat. The gas does not follow changes in light by corresponding changes in its material configuration. When the light spreads, the gas does not do likewise, it does not show difference in pressure, etc. Therefore when light is playing through a gas, the relationship is different from the one existing between the gas and heat playing through it. Thus, when light is active through the gas, there is a different relation involved than when heat is active through the gas. Now, in the observations made previously, we said: fluids stand between gas and solids, heat between gases and the X realm. Also the solid realm foreshadows the gaseous, and the gaseous gives a picture of heat. So likewise we can say that heat gives a picture of the X realm while heat is itself pictured in the gaseous. We have, as it were, in the gaseous, pictures of pictures of the X realm. Imagine now, these pictured pictures are really present with light passes through the air. Considering how the air relates itself in various phenomena to light, one must say that we are not dealing with a picturing of the one realm by the other, but rather that the light has an independent status in the gas. The matter may be figuratively expressed as follows: Suppose we paint a landscape and hang the picture on the wall of this room and then photograph the room. By thus changing something in the room, I alter its whole appearance and this alteration shows on the photograph. If I were accustomed always to sit on this chair when giving a lecture, and some ill-disposed person removed it while I lectured without my noticing what he was doing, I would do what many have done under similar circumstances, namely, sit on the floor. The relation of things in the room suffers real changes when I alter something in it. But whether I hand the picture in one place or another the relationship between the various figures painted upon it do not change. What exists in the picture itself in the way of relationships is not changed by alterations that go on in the room. In the same way, my experiments with light are not affected by the air in the space in which they are carried out. Experiments with heat are, on the contrary, related to the space in which they are carried out as you can convince yourselves, and indeed, you are made aware of this by the whole room becoming warm. But my light experiments have an independent being. I can think of them by themselves. Now, when I build up a concept of the action of X in a gas-filled space by analogy, I find the same relationships as if I am experimenting with light. I can identify X with light. A further extension of this train of thought leads to the identification of Y with chemical effects, and of Z with vital effects. However, as you see, there is a certain autonomy of light acting in the gaseous realm. The same sort of relationships are found when we extend a train of thought. You can do it for yourselves, it would lead us too far to do it here today. For instance, we would expect to find chemical effects in fluids, and this is in fact the case. In order to have chemical action solutions are necessary. In these solutions chemical action is related to the fluid as light is to the gas. We then have to expect to find a Z associated with the solid. This may be stated so — if I indicate the three realms by Z, Y and X, with heat as the intermediate realm and put X′ for the gas, Y′ for the fluid and Z′ for the solid, I can represent the order: $$Z, Y, X, heat, X', Y', Z'$$ X in X′ represents light in gas, Y in Y′ represents chemical effect in fluids, Z in Z′ represents the Z effect in solid bodies. Formerly we knew these realms only as various types of manifested form. Now we meet interminglings as it were. These are representations of things that are very real in our lives. X in X′ is light-filled gas, Y in Y′ is fluid in which chemical processes are going on, Z in Z′, life acting in solids. After yesterday's talk, you can scarcely doubt that just as we proceed beyond heat to find chemical effects. This was spoken of yesterday in a preliminary way. Therefore Z in Z′ represents vital effects in solid bodies. But there is no such thing as vital effects in solid bodies. We know that under terrestrial conditions a certain degree of fluidity is necessary for life. Under terrestrial conditions life does not manifest in the purely solid state. But, these same conditions force us to set it up as a hypothesis that such a condition is not beyond the realms of possibility. For the order in which we have been able to think of these things necessarily leads to this. We find solid bodies, we find fluid bodies, we find gas. The solids we find without vitality. Vital effects in the terrestrial sphere we discover by unfolding themselves adjacent to solid bodies, in relation with them, etc. But we do not find an immediate coupling up of what we call solids with the living. We are led to this last member of the series, Z in Z′, the living in the solid realm by analogy from Y in Y′ and X in X′. Fluid bodies have the same relation to chemical activity although not so strong as do solid bodies to life. Gases, in the realm of the terrestrial, stand in the same relation to light that solids do to the living. Now, this leads us to recognize that solids, fluids and gases in their supplementary relations to light, chemical action and vital phenomena represent, as it were, something that has died out. These things cannot be made as obvious as people like to make most presentations of empirical facts. If you wish to make these facts really mean something to you, you must work them over within yourselves and then you will find that there is a relation between : The solid and the living The fluid and the chemical The gaseous and light That stands as it were set off by itself. These relations are not, however, under terrestrial conditions immediately active. The relations that actually exist point to something that was once there but is there no longer. Certain inner relationships of the things force us to ring time concepts into the picture. When you look at a corpse you are forced into time concepts. The corpse is there. Everything that makes possible the presence of the corpse, that gives it the appearance it has, all this you must consider as soul and spirit since the corpse has in itself no possibilities of self-determination. A human form would never arise except for the presence of soul and spirit. What the corpse presents to you, forces you to say the following: The corpse as it exists there has been abandoned by the living, the terrestrial fluid by the emanations of chemical effects and the terrestrial gaseous by the emanations of light effects. And just as we glance back from the corpse to the living, to the time when matter that is now the corpse was bound together with the soul and spirit, so we glance from the solid bodies of the earth back to a former physical condition, when the solid was bound up with the living and only occurred bound to the living; fluid existed only bound to chemical effect and gases only bound to the light. In other words, all gas had an inner glittering, or inner illumination, an illumination that showed a wave-like phosphorescence and darkening as the gas was rarefied or condensed. Fluids were not as they are today but were permeated by a continuous living chemical activity. And at the foundation of all was life, active in solidification (as it solidifies now in the horn formation in cattle, for instance) passing back again into fluid or gas, etc. In brief, we are forced by physics itself to admit a previous period of time when realms now torn apart existed together. The realms of the gaseous, the fluid and the solid are now found on the one hand, and on the other realms of light, chemical effects and vital activity. At that time they were within each other, not merely side by side, but actually within each other. Heat had an intermediate position. It did not appear to share this association of the more material and the more etheric natures. But since it occupied an intermediate position, it possessed an independence that was attributable to its not taking part in the two. If now we call the upper realm the etheric and the lower realm the region of ponderable matter, we obviously have to consider the heat realm as the equilibrium condition between them. Thus in heat we have found that which is the equilibrium condition between the etheric body and the ponderable material . It is ether and matter at the same time and indicates by its dual nature what we actually find in it, namely, a difference in level of transition. (Unless we understand this, we cannot understand or do anything in the realm of heat phenomena). If you take up this line of thinking, you will come to something much more fundamental and weighty than the so-called second law of thermodynamics: a perpetuum mobile of the second type is possible. For this second law really tears a certain realm of phenomena out of its proper connection. This realm is bound up with certain other phenomena and essentially and profoundly modified by them. If you make it clear to yourselves that the gaseous realm and light were once united, that the fluid realm and chemical activity were once one, etc. then you will also be led to think of the two polarically opposed portions of the heat realm, namely ether and ponderable matter, as originally united. That is to say, you must conceive of heat in former ages as quite different from the heat you know now. Then you will come to say to yourselves, the things we define as physical phenomena today, the things that bear the impress of physical entities, these considerations of ours are limited in their meaning by time . Physics is not eternal. In the case of certain types of reality physics has absolutely no validity . For the reality that gas was once illumined within is an entirely different reality from the condition where gas and light are together in a relatively independent condition. Thus, we come to see that there was a time when another type of physics was valid; and, looking forward, there will be a time when a still different type will be valid. Our modern physics must conform with the phenomena of the present time, with what is in our immediate environment. In order to avoid paradoxes, and not only these but absurdities, physics must be freed of the tendency to study terrestrial phenomena, build hypotheses based on them, and then apply these hypotheses to the whole universe. We do this, and forget that what we know as physical is time-limited on the earth. That it is space-limited, we have already seen . For the moment we move out to the sphere where gravity ceases and everything streams outward, at that moment our entire physical scheme ceases to apply. We have to say that our earth is spatially limited as a physical body and what is more, spatially limited in its physical qualities. It is nonsensical to suppose that beyond the null-sphere the terrestrial physical laws apply. Just as nonsensical is it to apply the present laws to former ages and infer the nature of earth evolution from what is going on at a particular time. The madness of the Kant-Laplace theory consists in the belief that it is possible to abstract something from contemporary physical phenomena and extend it without more ado backwards in time. Modern astrophysics also shows the same madness to the belief that what can be abstracted from terrestrial physical conditions can be applied to the constitution of the sun and that we can look upon the sun as governed by the laws of the earth. But a tremendously important thing unfolds for us when we take a general view over the phenomena we have considered and bring certain series of phenomena together. Your attention has been called to the fact that the physicists have come to a certain view so neatly expressed by Eduard von Hartmann. The second law of thermodynamics states that whenever heat is changed into mechanical work some heat remains unchanged, and thus, finally, all energy must change into heat and the earth come to a heat death. This view has been expressed by Eduard von Hartmann as follows: “The world process has the tendency to run down.” Now suppose we assume such a running down of the world-process does take place in the direction indicated. What happens then? When we make experiments to illustrate the second law of the mechanical theory of heat, heat appears. We see mechanical work used up and heat appearing. What we see appearing is susceptible to further change. For we can show likewise when we produce lights from heat that not all of the heat reappears as light, since heat simply reverses the mechanical process as it is understood in the sense of the second thermodynamic law of mechanical phenomena. This has, however, led us to say that we have to imagine the whole cosmic spectrum as closed into a circle . Thus if it were really true, as examination of a certain series of phenomena indicates, that the entropy of the cosmos is striving to the maximum, and that the world process is running down, provision is made for re-energizing it. It runs out here, but it runs in again here (indicating figure) on the other side, for we have to think of it as a circle. Thus even if the heat-death enters on one side, on the other side, there comes in that which re-establishes the equilibrium and which opposes the heat-death by a cosmic creating process . Physics can orientate itself according to this fact if it will no longer observe the world process as we usually look at the spectrum, going off into infinity in the past we go from the red and again into infinity in the future as we go from the blue. Instead the world process must be symbolized as a circle . It is only thus that we can draw near to this process. When now we have symbolized the world process as a circle then we can include in it what lies in the various realms. But we have had no opportunity in these realms to insert the acoustic phenomena. These, as it were, do not lie in the plane. In them we have something new and we will speak further of this tomorrow. ˂˂ Previous Table of Contents Next ˃˃ X in X′ represents light in gas, Y in Y′ represents chemical effect in fluids, Z in Z′ represents the Z effect in solid bodies. Formerly we knew these realms only as various types of manifested form. Now we meet interminglings as it were. These are representations of things that are very real in our lives. X in X′ is light-filled gas, Y in Y′ is fluid in which chemical processes are going on, Z in Z′, life acting in solids. After yesterday's talk, you can scarcely doubt that just as we proceed beyond heat to find chemical effects. This was spoken of yesterday in a preliminary way. Therefore Z in Z′ represents vital effects in solid bodies. But there is no such thing as vital effects in solid bodies. We know that under terrestrial conditions a certain degree of fluidity is necessary for life. Under terrestrial conditions life does not manifest in the purely solid state. But, these same conditions force us to set it up as a hypothesis that such a condition is not beyond the realms of possibility. For the order in which we have been able to think of these things necessarily leads to this. We find solid bodies, we find fluid bodies, we find gas. The solids we find without vitality. Vital effects in the terrestrial sphere we discover by unfolding themselves adjacent to solid bodies, in relation with them, etc. But we do not find an immediate coupling up of what we call solids with the living. We are led to this last member of the series, Z in Z′, the living in the solid realm by analogy from Y in Y′ and X in X′. Fluid bodies have the same relation to chemical activity although not so strong as do solid bodies to life. Gases, in the realm of the terrestrial, stand in the same relation to light that solids do to the living. Now, this leads us to recognize that solids, fluids and gases in their supplementary relations to light, chemical action and vital phenomena represent, as it were, something that has died out. These things cannot be made as obvious as people like to make most presentations of empirical facts. If you wish to make these facts really mean something to you, you must work them over within yourselves and then you will find that there is a relation between : The solid and the living The fluid and the chemical The gaseous and light That stands as it were set off by itself. These relations are not, however, under terrestrial conditions immediately active. The relations that actually exist point to something that was once there but is there no longer. Certain inner relationships of the things force us to ring time concepts into the picture. When you look at a corpse you are forced into time concepts. The corpse is there. Everything that makes possible the presence of the corpse, that gives it the appearance it has, all this you must consider as soul and spirit since the corpse has in itself no possibilities of self-determination. A human form would never arise except for the presence of soul and spirit. What the corpse presents to you, forces you to say the following: The corpse as it exists there has been abandoned by the living, the terrestrial fluid by the emanations of chemical effects and the terrestrial gaseous by the emanations of light effects. And just as we glance back from the corpse to the living, to the time when matter that is now the corpse was bound together with the soul and spirit, so we glance from the solid bodies of the earth back to a former physical condition, when the solid was bound up with the living and only occurred bound to the living; fluid existed only bound to chemical effect and gases only bound to the light. In other words, all gas had an inner glittering, or inner illumination, an illumination that showed a wave-like phosphorescence and darkening as the gas was rarefied or condensed. Fluids were not as they are today but were permeated by a continuous living chemical activity. And at the foundation of all was life, active in solidification (as it solidifies now in the horn formation in cattle, for instance) passing back again into fluid or gas, etc. In brief, we are forced by physics itself to admit a previous period of time when realms now torn apart existed together. The realms of the gaseous, the fluid and the solid are now found on the one hand, and on the other realms of light, chemical effects and vital activity. At that time they were within each other, not merely side by side, but actually within each other. Heat had an intermediate position. It did not appear to share this association of the more material and the more etheric natures. But since it occupied an intermediate position, it possessed an independence that was attributable to its not taking part in the two. If now we call the upper realm the etheric and the lower realm the region of ponderable matter, we obviously have to consider the heat realm as the equilibrium condition between them. Thus in heat we have found that which is the equilibrium condition between the etheric body and the ponderable material . It is ether and matter at the same time and indicates by its dual nature what we actually find in it, namely, a difference in level of transition. (Unless we understand this, we cannot understand or do anything in the realm of heat phenomena). If you take up this line of thinking, you will come to something much more fundamental and weighty than the so-called second law of thermodynamics: a perpetuum mobile of the second type is possible. For this second law really tears a certain realm of phenomena out of its proper connection. This realm is bound up with certain other phenomena and essentially and profoundly modified by them. If you make it clear to yourselves that the gaseous realm and light were once united, that the fluid realm and chemical activity were once one, etc. then you will also be led to think of the two polarically opposed portions of the heat realm, namely ether and ponderable matter, as originally united. That is to say, you must conceive of heat in former ages as quite different from the heat you know now. Then you will come to say to yourselves, the things we define as physical phenomena today, the things that bear the impress of physical entities, these considerations of ours are limited in their meaning by time . Physics is not eternal. In the case of certain types of reality physics has absolutely no validity . For the reality that gas was once illumined within is an entirely different reality from the condition where gas and light are together in a relatively independent condition. Thus, we come to see that there was a time when another type of physics was valid; and, looking forward, there will be a time when a still different type will be valid. Our modern physics must conform with the phenomena of the present time, with what is in our immediate environment. In order to avoid paradoxes, and not only these but absurdities, physics must be freed of the tendency to study terrestrial phenomena, build hypotheses based on them, and then apply these hypotheses to the whole universe. We do this, and forget that what we know as physical is time-limited on the earth. That it is space-limited, we have already seen . For the moment we move out to the sphere where gravity ceases and everything streams outward, at that moment our entire physical scheme ceases to apply. We have to say that our earth is spatially limited as a physical body and what is more, spatially limited in its physical qualities. It is nonsensical to suppose that beyond the null-sphere the terrestrial physical laws apply. Just as nonsensical is it to apply the present laws to former ages and infer the nature of earth evolution from what is going on at a particular time. The madness of the Kant-Laplace theory consists in the belief that it is possible to abstract something from contemporary physical phenomena and extend it without more ado backwards in time. Modern astrophysics also shows the same madness to the belief that what can be abstracted from terrestrial physical conditions can be applied to the constitution of the sun and that we can look upon the sun as governed by the laws of the earth. But a tremendously important thing unfolds for us when we take a general view over the phenomena we have considered and bring certain series of phenomena together. Your attention has been called to the fact that the physicists have come to a certain view so neatly expressed by Eduard von Hartmann. The second law of thermodynamics states that whenever heat is changed into mechanical work some heat remains unchanged, and thus, finally, all energy must change into heat and the earth come to a heat death. This view has been expressed by Eduard von Hartmann as follows: “The world process has the tendency to run down.” Now suppose we assume such a running down of the world-process does take place in the direction indicated. What happens then? When we make experiments to illustrate the second law of the mechanical theory of heat, heat appears. We see mechanical work used up and heat appearing. What we see appearing is susceptible to further change. For we can show likewise when we produce lights from heat that not all of the heat reappears as light, since heat simply reverses the mechanical process as it is understood in the sense of the second thermodynamic law of mechanical phenomena. This has, however, led us to say that we have to imagine the whole cosmic spectrum as closed into a circle . Thus if it were really true, as examination of a certain series of phenomena indicates, that the entropy of the cosmos is striving to the maximum, and that the world process is running down, provision is made for re-energizing it. It runs out here, but it runs in again here (indicating figure) on the other side, for we have to think of it as a circle. Thus even if the heat-death enters on one side, on the other side, there comes in that which re-establishes the equilibrium and which opposes the heat-death by a cosmic creating process . Physics can orientate itself according to this fact if it will no longer observe the world process as we usually look at the spectrum, going off into infinity in the past we go from the red and again into infinity in the future as we go from the blue. Instead the world process must be symbolized as a circle . It is only thus that we can draw near to this process. When now we have symbolized the world process as a circle then we can include in it what lies in the various realms. But we have had no opportunity in these realms to insert the acoustic phenomena. These, as it were, do not lie in the plane. In them we have something new and we will speak further of this tomorrow.

The Warmth Course

Lecture XIII

https://rsarchive.org/Lectures/GA321/English/MP1980/19200313a01.html

Stuttgart

13 Mar 1920

GA321-13

My dear friends, Today it is my object by giving you a few indications to bring these observations to a close for the time being. It is indeed obvious that what we have sought for in the former course and in this one can only come out fully when we are in a position to extend our treatment of the subject further. Today I will have a few remarks to make on this phase of the matter, at the conclusion of the lecture. Let me first give a general summary of what we have taken under consideration in connection with heat and the matter related to it. Out of the array of concepts you have got, I will draw your attention to certain ones. They are the following. When we bring before our eyes the realms of reality that we are able to distinguish in physics, we may list them as follows: The solid realm, which was have called \(Z'\) The fluid realm, which we have called \(Y'\) The gaseous or aeriform world, denoted by \(X'\) The realm of chemical effects, which we call \(Y\) And lastly, by \(Z\) we have denoted the life activity realm (see Table at end.) Moreover, we considered yesterday very definite conditions obtaining in regard to the heat state when we pass from X to \(X'\) and from \(Y\) to \(Y'\). We tried for example to bring before you the facts which showed how chemical effects could make themselves felt in the fluid element. One who strives to comprehend chemical processes finds the following: Wherever chemical processes are taking place, wherever chemical combinations and chemical dissociations occur, all that has a certain relation to the fluid element must enter in its own particular way into the solid or gaseous realms in order for the chemical effects to manifest themselves there. Thus when we consider our terrestrial chemistry we must keep before our eyes an interpenetration, and with this interpenetration, a kind of mutual binding of chemical effects and the fluid realm. Our terrestrial chemistry presents to us, as it were, the fluid element animated by chemical effects. But now, you will readily see that when we consider these various realms of reality it is impossible for us to think that this working of one realm in another is limited to the activity of heat in the gaseous realm. The other realms also work within each other. These call forth their appropriate effects in this or that field of action. We can indeed say the following: although chemical effects work primarily in the fluid medium since they have an inner relationship to is, we have also to visualize the working of the chemical on X′, that is to say a direct working on the chemical or gaseous or aeriform bodies. When I say “chemical effect” you must not think of that which comes to clear manifestation and is penetrated with an inner spirituality in the blue-violet portion of the spectrum. Here we have the chemical effect standing, as it were, by itself in a certain independence over against the material realm. When, however, we speak of chemical processes, we are really dealing with this effect as it interpenetrates physical bodies. We must conceive of something here in this chemical realm that, at the outset, has nothing to do with ponderable matter, but interpenetrates it, and in particular does it interpenetrate the fluid element owing to an inner relationship that I showed you yesterday. But let us now ask ourselves the question: What happens when the chemical effect picks out (figuratively speaking) the next realm, the gaseous, or its activities? Then it must happen, considering the matter simply from the external point of view, that something takes its rise in the gaseous which shows an inner relationship to the manifestation of this effect in fluids, which can be compared to this manifestation. In the fluid, the chemical effect seizes upon the material, as it were, and brings this material into such a condition that a mutual interaction sets in. When we put the fluid element before us in thought, we must conceive of it as in mutual reaction with the chemical effect. Let us assume, however, that the action does not go so far as to admit of this seizing of the chemical effect on the matter itself, but let us assume that it works on the matter from the outside only, that it is a stage removed from it as compared to its action on the fluid. Then we have as in the gaseous, a process in which the chemical effect accompanies the material, in one stage removed as compared to its action in fluids. Then there comes about a certain wide independence of the imponderable as compared to the material carrier. In chemical processes proper, the imponderable seizes definitely on the material. Here, however, we come upon a realm where there is not this definite linkage where the imponderable does not definitely insert itself into matter. This is the case in the acoustical realm, in the effect of tone; while in chemical processes in matter we have a complete submergence of the imponderable in matter, in tone we have a persistence of the imponderable as such , a preservation of it in gaseous or aeriform matter. This leads us to something further. It leads us to the point when we have to say: There must be some reason why in fluids the imponderable seizes directly on the material, while in tone effects in the gaseous realm, the imponderable is less able to do this. If we observe chemical activity and have a feeling for what is to be seen within the physically visible, then we will as a matter of course, understand that it belongs to the nature of matter that chemical phenomena go as they do. That is to say: the imponderable is there as something which is a characteristic of matter. It is not possible otherwise than in this way, that when we are dealing with terrestrial matter the seizing upon the imponderable matter takes place through the earth. By means of the forces of the earth, the chemical effect is, so to speak, seized upon and works within the fluids. You see the forces of form stretched out over the whole terrestrial realm and active by virtue of the fact that these forces of form get hold of the interpenetrating chemical effect. When we really understand correctly that we have here the forces of the earth, then we have understood something further, if we will grasp the meaning of tone in the air, namely that an opposite kind of force is involved in tone. That is, we have to think as active in tone a force passing into the earth in all directions from the cosmos, a tendency overcoming the earth forces, and thus striving to separate the imponderable from the earth. This is the peculiarity of the tone world. It is this which gives a certain characteristic to the physics of tone, of acoustics. For in this realm we can on the one hand study the material processes and on the other hand we can live in the world of tone by means of our sensations without paying the slightest attention to the acoustical side. What does acoustics matter to us perceiving men, when we live in tone with our sensations? Acoustics is a beautiful science; it reveals for us striking inner laws and an inner order, but that which lies before us as a subjective experience of tone is far, far removed from the physics of the tone as it is expressed in the material world. And this is really due to the fact that tone manifestation preserves a certain individuality. It takes its origin from the periphery of the cosmos, while such a process as we observe in the chemical forces active in fluids, for instance, proceeds from the earth as a center. Now there is one relation brought out also yesterday in Dr. Kolisko's lecture which shows itself only when we rise, as it were, to a universal point of view. This is that we can conceive of the periodic arrangement of the elements as octaves. In this we have an analogy between the inner laws of tone and the whole nature of matter as it demonstrates itself in chemical processes. Thus is established the fact that we may conceive of all the combinations and breaking down of material compounds as an outer reflection of an inner world music. This inner world music reveals itself to us outwardly as such in only one particular form, namely in our terrestrial music. Music should never be so conceived that we merely say, what is tone within us, subjectively, is only vibrating air outside of us. This must be looked upon as nonsense. It is to be considered just as nonsensical as if we were to say the following: What you are outwardly as a physical body that you are inwardly as a soul; such a statement leaves out the subject. Likewise we leave out the subject when we consider tone in its inner nature as identical with the condensations and rarefactions of the air that constitute, in the aerial medium, the carrier of tone. Now if you get a correct conception of this matter, you will see that we have in chemical processes to do with a certain relationship between \(Y\) and \(Y'\), and in tone we have to do with a certain relationship between \(Y\) and \(X'\) (See Table.) I have already indicated to you that when we stand within this or that realm, what we become aware of in the outer world always pertains to difference in level or potential differences. Please endeavor now, to trace what is similar to potential difference in this realm we are dealing with. Let us try to trace what is similar to the potential difference which becomes active in the case where gravity is used to furnish a driving force for a wheel through the falling water. Let us make clear to ourselves that we have differences in level involved in temperature, heat, tone and in the equalization of electric strains. Everywhere are potential differences, we meet them wherever we study forces. But what do we have, then? We have an inner relationship between what we perceive in the spectrum and liquid matter; and that which presents itself to us as chemical process is nothing but the result of the difference between chemical effects and the forces that are in the fluid. It is a \(Y-Y'\) potential difference. And in tone, a lower \(Y-X'\) potential difference is manifesting. Thus we can say: In relating a chemical process to the world of reality we are dealing with a potential difference between chemical effects and fluid forces. In the manifestation of tone and sound in the air, we are dealing with a potential difference between what is working formatively into chemical effects, what starts from the periphery into the world and the material of the gas, the aeriform body. Furthermore, what shows itself in this realm of reality manifests through potential differences. The matter rests on these differences in potential even though we remain in one element, in warmth, or even in gas or in water. But especially when we perceive distinctions between realms, do we deal with potential differences in the effects of these realms. Taking all of this together you come to the following: from a consideration of fluids and their boundary surfaces we are obliged to attribute the form of solids to earth forces. The extent to which gravity and the energies of configuration, to borrow a term from modern physics, are related, has been brought before you in past lectures. If we proceed from the forces that manifest in gravity, to those which result in liquid surfaces, apparently plane surfaces on account of the great size of the earth, we find we are really dealing with a sphere. Obviously the liquid levels of all the terrestrial bodies of water taken together constitute a sphere. Now you see, when we pass outwards from the center of the earth toward the surface of the sphere we meet successively certain sets of conditions. For terrestrial relations, within the solid realm we have forces which tend to close in, to delimit. Fluid forces, however, may perhaps be represented in their configuration by a line or plane tangential to the surface of the sphere. If we go further and observe the sphere from without we must put the matter in this way: beneath the sphere of liquid we have to deal with the formative forces of solids. In these formative forces which delimit solids we are dealing with a single body if we consider the earth as a whole. The many single bodies together form a single form like the fluid element of the earth. How must we then conceive of these various conditions? For we have passed beyond the formed, beyond what is shaped from within as the solid bodies are. How must we picture this to ourselves? Well, we must conceive of it as the opposite condition. Within the sphere we have solids filled with matter, and without we must think of space filled with negative matter. Within we have filled space (see figure). We must become accustomed to thinking of an emptying of space . The earth is indeed not influenced only by what happens on it, but by the other effects from all sides. If this were not so, the terrestrial phenomena themselves would be different. This can only be mentioned today; later we will go into it more thoroughly. For instance, it would not be possible for us to have a separations of continents from bodies of water, or a north and a south pole, if in the environment of the earth there were not empty spaces. These “matterless” spaces must work in from various directions. If we search for them we find them in what the older cosmic systems designated as the planets, to which we must add also the sun. Thus we are forced from the realm of the earth into the realm of the cosmos, and we are obliged to find the transition from the one condition of space to the opposite condition. We must learn to pass from a space filled positively with matter to one filled negatively with matter and this condition of negativity filled space so far as it acts on our earth we must think of as localized in the planets around the earth. Thus there is active at the point where terrestrial phenomena are going on a mutual interaction of the terrestrial proper and the cosmic, and this is due to the fact that from the negatively filled spaces, a suction-like action is going on while the formative forces are expressing themselves as pressures. This mutual interaction meets us in that particular force-configuration ordinarily sought for in molecular forces and attractions. We should conceive of these things as they were thought of by the intuitive knowledge of former times. Manifestations in matter, which are always accompanied by the imponderable, were then thought of as influenced by the whole cosmos instead of being misinterpreted fantastically as due to certain theoretical inner configurations. What the stars, like giants, do in the cosmos is reflected in the terrestrial dwarfs, the atoms and molecules. This indeed, is what we have to do; we must know that when we represent a terrestrial process or perform calculations on it, we are dealing with a picture of extra-terrestrial effects, with a mutual action of the terrestrial and the cosmic. Now you see here we have the force that fills space with matter (see drawing.) Also, here we still have this force that fills space with matter, but this force is attenuated. Ultimately we come to the condition where there is negative matter. There must be a region between where, so to speak, space is torn apart. We can put the matter in this way. Our space as it surrounds us constitutes a kind of vessel for physical manifestations, and has an inner relationship to these forces. Something in it corresponds to them. But when we go from the ponderable to the imponderable, space is torn apart. And in this tearing apart, something enters that was not there before it happened. Let us assume that we tear apart the three dimensional space. What is it that enters through the rift? When I cut my finger, blood comes out — it is a manifestation in three dimensional space. But when I tear apart space itself that which comes through is something that is otherwise non-spatial. Note how modern physical thinking is lost in the woods. Is it not true that when we make electrical experiments in the school room, our apparatus must be painstakingly dried, we must make it a good insulator, or our experiments will fail. If it is moist, the experiment will fail. But I have often called attention to the fact that the inner friction of clouds which are certainly moist is supposed to give rise to electricity which in turn produced lightning and thunder. This is one of the most impossible ideas that can be conceived. Now on the other hand, if we bring together these things we have considered as necessary for a real understanding, then we can see that space is torn apart the moment the flash appears. At that moment, what fills space as non-dimensional entity, intensively, comes forth like the blood when I cut my hand. This is indeed always the case when light appears accompanied by heat. Space is torn apart. Space reveals to us what dwells within, while it shows us only its exterior in the usual three dimensions that we have before us. Space then shows us its inner content. We may thus say: when we proceed from the ponderable to the imponderable and have to pass through the realm of heat as we go, we find heat welling out wherever we make the transition from the pressure effects of ponderable matter to the suction effects of the imponderable. At all such points of transition heat wells out. Now you will see that when we are constructing ideas about the processes which we spoke of several days ago as processes of conduction of heat, you have to relate to them the concept that the heat is bound to the ponderable matter. This is quite the opposite condition to that which we have considered as existing in radiating heat itself. This heat we find as the entity welling out when matter is torn apart. How will it affect matter? It will work from the intensive condition to the extensive. It will, so to speak, work from the inner portion of space into its outer portions. When heat and a material body mutually react on one another we see a certain thing occurring. What occurs is that the characteristic tendency of the heat is transformed. The suction effect is transformed into a pressure effect so that the cosmic tendency of the heat opposes the individualizing tendency of the material which, in solids, is the force that gives form. We thus have in heat, in phenomena of warmth, insofar as these manifest a conductivity, to seek, not for rays, but for a tendency to spread in all directions. We must look for a mirroring of the imponderable matter, or for the presence of the imponderable in the ponderable. Bodies that conduct heat bring it into manifestation by an intensive reflection of the impinging imponderable heat on their material portion This is in contracts to the extensive reflection characteristic of light. Now I wish to ask you to work over in your minds such concepts as we are accustomed to entertain and to work them over in the way we do here so that they become saturated with reality, as it were. Let me give you a picture in closing to recapitulate and show you how much reality-saturated concepts can lead us into a vital grasp of the being of the cosmos. I have already called your attention to the basis upon which rests the perception, the subjective experiences of temperature. We really experience the difference between our own temperature and the temperature of the environment, which, indeed, is what the thermometer does — I have drawn this to your attention. But perception depends precisely on this that we have within us a certain condition and that which lies outside this condition constitutes our perception. We cannot be a thing and perceive it at the same time . But we must always be other than the conditions we are experiencing. Suppose we consider tone. Insofar as we are tone, we cannot experience tone. If we would answer without prejudice the question: what are we as experiencers of tone, we come to the conclusion that we simply experience one potential difference while we are the other potential difference. We experience the \(Y-X'\) difference; we do not experience the \(Y-Y'\) difference because that is part of our being in time. It accompanies our perception of tone. It is an orderly inner chemical process in our fluid nature and is a part of our being. What causes chemical effects within us produces certain orderly effects in the world itself. It is by no means without interest to picture the following to yourselves. You know well that the human body consists only of a small degree of solid constituents. More than 90 percent of it is water, what plays through us as a delicate chemical process while we listen to a symphony is an inner continually phosphorescent marvel in this fluid nature. We are in our inner nature what these chemical processes reflect from tone. And we become aware of the tone world through the fact that we are chemically the tone world in the sense I have presented to you. Our understanding of man himself is really much broadened, you see, if we bring an understanding of physical problems to bear on the human body. But the thing we must strive for is not to form abstract concepts of which physics is so fond today Rather, we must force our way through the concepts really woven into the world, the objective world. Fundamentally everything that spiritual science is striving to bring into the conceptual world and especially what it is striving to do to promote a certain way of thinking, has for its object to bring back into human development thought permeated with reality. And it is indeed necessary for this to happen. For this reason we must prosecute vigorously such studies as have been presented here during the last few days. You can see, my friends, how everywhere around you something old is dying out. Is it not possible from examination of physical concepts, to see that something old is really dying out, for little is to be done with them? The very fact that we can build up a new physical concept even when we attempt it in such a limited way — for we can only give indications now — this fact shows that we stand today at a turning point in human development., We must, my friends, give thought to certain things. We must push forward the varied lines of endeavor which Dr. Baravalle, Dr. Blumel, Mr. Strakesch, and Dr. Kolisko have presented to you in order to give a new impulse to the development hitherto consummated by the human race. Thus we will lay foundations for progress. You must see that people the world over are asking for an extension of these things. We must found schools. What is happening in the world outside? People are encouraging schools, the Danish school movement is an example. What is characteristic of the old schools is being carried into the new ones. But nothing new will come of this. The whole people will simply have fastened on them the thing that up to now has been fastened on the learned. There is nothing sadder than to contemplate a future where the manner of thinking which has devastated the heads of the learned men in the fashion we have seen will be transmitted to the people of the whole earth through the school system. If we would found schools for the people, we must be sure that there will be something available to teach in them, something whose inner configuration represents an advance. We need first the science that can be given in these schools. People wish always to remain superficial, considering only what is obvious. Consequently, in a spiritual movement, they do not wish to do anything radical toward renewing their manner of thinking, but simply to bring to people the old, the disappearing. It is just in regard to physical facts that this tendency is most noticeable. You will certainly find many things in these lectures that are unsatisfactory, for they can only be suggestive at best. One thing however, is shown, and that is the necessity to build anew our whole physical, chemical, physiological and biological thought world. It must be rebuilt from the fundamental up. We will naturally accomplish this when we have reconstructed not only the schools, but also the science itself. And until we have succeeded in so arranging things that the academic side has been renewed along the lines started in these last few days, only then will we reach that which will and must be reached if European civilization is not to perish in a spiritual sense. Only consider the shocking trend in the modern academic world. We have long controversial papers read, completely divorced from real life. People sit in fine lecture halls and each reads his paper, but the others do not listen. For it is a noteworthy fact that one man is a specialist in one line, another man is a specialist in a different line. The mathematician reads but the medical man does not listen. And when the medical man reads the thoughts of the mathematician are busy elsewhere. This is indeed a well known sign. Something new must be injected. And this something must have its center in a spiritual striving. We must see this point. Therefore, one can say: if we can but bring together this striving towards a new kind of reality with a building up of the way of thinking in our schools, then we will attain what must be attained. You can see there is much to be done. We really learn how such is to be done only when we begin to go into details. For this reason it is so pathetic that people today who cling to the old way of thinking, for it has become old, it has had its day — coin phrases and accumulate great amounts of money to perpetuate their academic system in the world. It is especially difficult because we must become fundamentally convinced that a genuine new world is necessary. We must not deceive ourselves and simply say, “build schools.” We must live in reality and say, “first it is necessary to have something to teach in these schools for the people.” And I would like to say that while fruitful technological results have flowed from science, a still more fruitful technology will flow from a popularizing of science of such a nature as we have tried to indicate here in the realm of physics. We have in every case tried to emerge from the old theoretical point of view and enter into a point of view that is real, so that our concepts will be saturated with reality. This will yield technical results quite different from those attained up to the present. Practice and theory hang together inwardly. And when we see in any one case what reform is needed as in the case of physics, for instance, we can understand what must happen. Since the time has come when we must separate, I wish to emphasize that I have only indicated to you in these lectures what you are to see, to stimulate you to develop these things further. You will be able to develop them. Our mathematical physicists, whom we have among our number will be able to give new life to the old formulae. And they will find, when they apply to these old formulae the ideas I have indicated to you, that certain transformations can be made that are real metamorphoses. From these will grow much that will be of enormous importance technically for the further development of mankind. This is, of course, something which cannot be gone into in detail, but only can be indicated at this time. But these observations must now be brought to a close and their further progress will depend on your own work. It is this that I wish you to take especially to heart, for the things are now extremely pressing that have to be accomplished in the three paths of human endeavor. These things have become urgent in our era and there is no time to lose because chaos stands before the door. A second thing to remember is this: The end can only be attained satisfactorily through an orderly human working together. Thus we must try to work out further within ourselves the things that have been stimulated, and you will also find something arising in the work of the Waldorf School. The moment you really try to utilize in pedagogy the definite and valid ideas we have set forth here, they will be taken up at once, and you will also discover that they will go well if you find it necessary to apply them in the conduct of life. We could wish that one did not always have to speak about science to a public which while it takes in much, is always exposed to the opinions of “rigorous scientific thinkers,” to “authorities.” These authorities have no inkling that all we observe is very definitely shot through with the play of something else. We can see this even from language. Note that in language we have everything mutually related. We speak of an impact. Now it is only because we have ourselves brought about an impact and given a name to the phenomenon that we speak of an impact in a space free of human activity, and vice versa we speak of things that happen within us in words drawn from the outer world. But we do not realize that we should look into the outer world, that is the planetary world, if we will understand the terrestrial bodies, and because we not know this we cannot learn what is happening in the embryos of plants and animals or in any tiny cell upon which we turn our microscopes. We discover all sorts of interesting things, but the source of all this, the thing we long to know, we will only be able to see when we understand macroscopically these processes microscopically observed. We must see that the fertilization and the fruiting of outer nature takes place in a mutual interaction with the outer cosmos. We must study how to conceive of the planets as points of departure for the working of the imponderable in the physical world, as if we are to grasp the relation of the cosmos to plant and animal germ cells . If we can learn to see all these things on a grand scale without, these things that today we look for under the microscope where they are not really present, if we try to see these things in that which surrounds us (in the cosmos) then we will make progress. The way is now clear before us. Human prejudice makes for us a very, very serious barricade. This prejudice is hard to overcome. It is for us to do all that we can to overcome it. Let us hope that we can at some future time continue again these discussions.

The Warmth Course

Lecture XIV

https://rsarchive.org/Lectures/GA321/English/MP1980/19200314p01.html

Stuttgart

14 Mar 1920

GA321-14

The theme of this cycle of lectures was not chosen because it is traditional within academic or philosophical disciplines, as though we thought epistemology or the like should appear within our courses. Rather, it was chosen as the result of what I believe to be an open-minded consideration of the needs and demands of our time. The further evolution of humanity demands new concepts, new notions, and new impulses for social life generally: we need ideas which, when realized, can create social conditions offering to human beings of all stations and classes an existence that seems to them humane. Already, to be sure, it is being said in the widest circles that social renewal must begin with a renewal of our thinking. 1 “... that social renewal must begin with the renewal of our thinking.” The original German (“ ... dass die soziale Erneuerung vom Geiste ausgehen musse ”) might be translated alternately “that social renewal must proceed from the spirit.” The German word “ Geist ” — bane of all who would translate German into English — embraces two meanings that remain in English quite distinct “mind” and “spirit.” The translator must choose one, even though the German always implies both. If he chooses the former, he runs the risk of seriously distorting the author's intentions (as did the man who translated Hegel's Phanomenologie des Geistes as The Phenomenology of Mind ). If he chooses the latter, he flies in the face of the dubious connotations that “spirit” and “spiritual” convey — no doubt as a result of the basically empirical cast of English thought. Although “ Geist ” as Steiner uses it should almost invariably be translated “spirit” (which of course comprehends “wind”), here the context has led us to choose the more restricted meaning. Yet not everyone in these widest circles imagines something clear and distinct when speaking in this way. One does not ask: whence shall come the ideas upon which one might found a social economy offering man a humane existence? That portion of humanity which has received an education in the last three to four centuries, but particularly since the nineteenth century, has been raised with certain ideas that are outgrowths of the scientific world view or entirely schooled in it. This is particularly true of those who have undergone some academic training. Only those working in fields other than the sciences believe that natural science has had little influence on their pursuits. Yet it is easy to demonstrate that even in the newer, more progressive theology, in history and in jurisprudence — everywhere can be found scientific concepts such as those that arose from the scientific experiments of the last centuries, so that traditional concepts have in a certain way been altered to conform to the new. One need only allow the progress of the new theological developments in the nineteenth century to pass before the mind's eye. One sees, for example, how Protestant theology has arrived at its views concerning the man, Jesus, and the nature of Christ, because at every turn it had in mind certain scientific conceptions that it wanted to satisfy, against which it did not want to sin. At the same time, the old, instinctive ties within the social order began to slacken: they gradually ceased to hold human life together. In the course of the nineteenth century it became increasingly necessary to replace the instincts according to which one class subordinated itself to another, the instincts out of which the new parliamentary institutions, with all their consequences, have come with more-or-less conscious concepts. Not only in Marxism but in many other movements as well there has come about what one might call a transformation of the old social instincts into conscious concepts. But what was this new element that had entered into social science, into this favorite son of modern thought? It was the conceptions, the new mode of thinking that had been developed in the pursuit of natural science. And today we are faced with the important question: how far shall we be able to progress within a web of social forces woven from such concepts? If we listen to the world's rumbling, if we consider all the hopeless prospects that result from the attempts that are made on the basis of these conceptions, we are confronted with a dismal picture indeed. One is then faced with the portentous question: how does it stand with those very concepts that we have acquired from natural science and now wish to apply to our lives, concepts that — this has become clearly evident in many areas already — are actually rejected by life itself? This vital question, this burning question with which our age confronts us, was the occasion of my choosing the theme, “The Boundaries of Natural Science.” Just this question requires that I treat the theme in such a way that we receive an overview of what natural science can and cannot contribute to an appropriate social order and an idea of the kind of scientific research, the kind of world view to which one would have to turn in order to confront seriously the demands made upon us by our time. What is it we see if we consider the method according to which one thinks in scientific circles and how others have been influenced in their thinking by those circles? What do we see? We see first of all that an attempt is made to acquire data and to order it in a lucid system with the help of clear concepts. We see how an attempt is made to order the data gathered from inanimate nature by means of the various sciences — mechanics, physics, chemistry, etc. — to order them in a systematic manner but also to permeate the data with certain concepts so that they become intelligible. With regard to inanimate nature, one strives for the greatest possible clarity, for crystal-clear concepts. And a consequence of this striving for lucid concepts is that one seeks, if it is at all possible, to permeate everything that one finds in one's environment with mathematical formulae. One wants to translate data gathered from nature into clear mathematical formulae, into the transparent language of mathematics. In the last third of the nineteenth century, scientists already believed themselves very close to being able to give a mathematical-mechanical explanation of natural phenomena that would be thoroughly transparent. It remained for them only to explain the little matter of the atom. They wanted to reduce it to a point-force [ Kraftpunkt ] in order to be able to express its position and momenta in mathematical formulae. They believed they would then be justified in saying: I contemplate nature, and what I contemplate there is in reality a network of interrelated forces and movements wholly intelligible in terms of mathematics. Hence there arose the ideal of the so-called “astronomical explanation of nature,” which states in essence: just as one brings to expression the relationships between the various heavenly bodies in mathematical formulae, so too should one be able to compute everything within this smallest realm, within the “little cosmos” of atoms and molecules, in terms of lucid mathematics. This was a striving that climaxed in the last third of the nineteenth century: it is now on the decline again. Over against this striving for a crystal-clear, mathematical view of the world, however, there stands something entirely different, something that is called forth the moment one tries to extend this striving into realms other than that of inanimate nature. You know that in the course of the nineteenth century the attempt was made to carry this point of view, at least to some extent, into the life sciences. And though Kant had said that a second Newton would never be found who could explain living organisms according to a causal principle similar to that used to explain inorganic nature, Haeckel could nevertheless claim that this second Newton had been found in Darwin, that Darwin had actually tried, by means of the principle of natural selection, to explain how organisms evolve in the same “transparent” terms. And one began to aim for just such a clarity, a clarity at least approaching that of mathematics, in all explanations, proceeding all the way up to the explanation of man himself. Something thereby was fulfilled which certain scientists explained by saying that man's need to understand the causes of phenomena is satisfied only when he arrives at such a transparent, lucid view of the world. And yet over against this there stands something entirely different. One comes to see that theory upon theory has been contrived in order to construct a view of the world such as I have just described, and ever and again those who strove for such a view of the world called forth — often immediately — their own opposition. There always arose the other party, which demonstrated that such a view of the world could never produce valid explanations, that such a view of the world could never ultimately satisfy man's need to know. On the one hand it was argued how necessary it is to keep one's world view within the lucid realm of mathematics, while on the other hand it was shown that such a world view would, for example, remain entirely incapable of constructing even the simplest living organism in thought of mathematical clarity or, indeed, even of constructing a comprehensible model of organic substance. It was as though the one party continually wove a tissue of ideas in order to explain nature, and the other party — sometimes the same party — continually unraveled it. It has been possible to follow this spectacle — for it seems just that to anyone who is able to view it with an unprejudiced eye — within the scientific work and striving of the last fifty years especially. If one has sensed the full gravity of the situation, that with regard to this important question nothing but a weaving and unraveling of theories has taken place, one can pose the question: is not the continual striving for such a conceptual explanation of phenomena perhaps superfluous? Is not the proper answer to any question that arises when one confronts phenomena perhaps that one should simply allow the facts to speak for themselves, that one should describe what occurs in nature and forgo any more detailed accounting? Is it not possible that all such explanations show only that humanity is still tied to its mother's apron strings, that humanity in its infancy sought a kind of luxury? Would not humanity, come of age, have to say to itself: we must not strive at all for such explanation; we get nowhere in that way and must simply extirpate the need to know? Why not? As we become older we outgrow the need to play; why, if we were justified in doing so, should we not simply outgrow the need for explanations? Just such a question could already emerge in the most extraordinarily significant way when, on August 14, 1872, du Bois-Reymond stood before the Second General Meeting of the Association of German Scientists and Physicians to deliver his famous address, “The Boundaries of Natural Science” [“ Grenzen des Naturerkennens ”], an address still worthy of consideration today. Yet despite the amount that has been written about this address by the important physiologist, du Bois-Reymond, many still do not realize that it represents one of the important junctures in the evolution of the modern world view. In medieval Scholasticism all of man's thinking, all of his notional activity, was determined by the view that one could explain the broad realms of nature in terms of certain concepts but that one had to draw the line upon reaching the super-sensible. The super-sensible had to be the object of revelation. They felt that man should stand in a relation to the super-sensible in such a way that he would not even wish to penetrate it with the same concepts he formed concerning the realms of nature and external human existence. A limit was set to knowledge on the side of the super-sensible, and it was strongly emphasized that such a limit had to exist, that it simply lay within human nature and the order of the universe that such a limit be recognized. This placement of a limit to knowledge was then renewed from an entirely different side by thinkers and researchers such as du Bois-Reymond. They were no longer Schoolmen, no longer theologians, but just as the medieval theologian, proceeding according to his own mode of thinking, had set a limit to knowledge at the super-sensible, so these thinkers and researchers set a limit at the sensible. The limit was meant to apply above all to the realm of external sensory data. There were two concepts in particular that du Bois-Reymond had in mind, which to him established the limits natural science could reach but beyond which it could not proceed. Later he increased that number by five in his lecture, “The Seven Enigmas of the World,” but in the first lecture he spoke of the two concepts, “matter” and “consciousness.” He said that when contemplating nature we are forced, in thinking systematically, to apply concepts in such a way that we eventually arrive at the notion of matter. Just what this mysterious entity in space we call “matter” is, however, we can never in any way resolve. We must simply assume the concept “matter,” though it is opaque. If only we assume this opaque concept “matter,” we can apply our mathematical formulae and calculate the movements of matter in terms of the formulae. The realm of natural phenomena becomes comprehensible if only we can posit this “opaque” little point millions upon millions of times. Yet surely we must also assume that it is this same material world that first builds up our bodies and unfolds its own activity within them, so that there rises up within us, by virtue of this corporeal activity, what eventually becomes sensation and consciousness. On the one hand we confront a world of natural phenomena requiring that we construct a concept of “matter,” while on the other hand we confront ourselves, experience the fact of consciousness, observe its phenomena, and surmise that whatever it is we assume to be matter must also lie at the foundation of consciousness. But how, out of these movements of matter, out of inanimate, dead movement, there arises consciousness, or even simple sensation, is a mystery that we cannot possibly fathom. This is the other pole of all the uncertainties, all the limits to knowledge: how can we explain consciousness, or even the simplest sensation? With regard to these two questions, then — What is matter? How does consciousness arise out of material processes? — du Bois-Reymond maintains that as researchers we must confess: ignorabimus , we shall never know. That is the modern counterpart to medieval Scholasticism. Medieval Scholasticism stood at the limit of the super-sensible world. Modern natural science stands at the limit delineated in essence by two concepts: “matter,” which is everywhere assumed within the sensory realm but nowhere to be found, and “consciousness,” which is assumed to originate within the sense world, although one can never comprehend how. If one considers this development of modern scientific thought, must one not then say to oneself that scientific research is entangling itself in a kind of web, and only outside of this web can one find the world? For in the final analysis it is there, where matter haunts space, that the external world lies. If this is the one place into which one cannot penetrate, one has no way in which to come to terms with life. Within man one finds the fact of consciousness. Does one come at all near to it with explanations conceived in observing external nature? If in one's search for explanations one pulls up short at human life, how, then, can one arrive at notions of how to live in a way worthy of a human being? How, if one cannot understand the existence or the essence of man according to the assumptions one makes concerning that existence? As this course of lectures progresses it shall, I believe, become evident beyond any doubt that it is the impotence of the modern scientific method that has made us so impotent in our thinking about social questions. Many today still do not perceive what an important and essential connection exists between the two. Many today still do not perceive that when in Leipzig on August 14, 1872 du Bois-Reymond spoke his ignorabimus , this same ignorabimus was spoken also with regard to all social thought. What this ignorabimus actually meant was: we stand helpless in the face of real life; we have only shadowy concepts; we have no concepts with which to grasp reality. And now, almost fifty years later, the world demands just such concepts of us. We must have them. Such concepts, such impulses, cannot come out of lecture-halls still laboring in the shadow of this ignorabimus . That is the great tragedy of our time. Here lie questions that must be answered. We want to proceed from fundamental principles to such an answer and above all to consider the question: is there not perhaps something more intelligent that we as human beings could do than what we have done for the last fifty years, namely tried to explain nature after the fashion of ancient Penelope, by weaving theories with one hand and unraveling them with the other? Ah yes, if only we could, if only we could stand before nature entirely without thoughts! But we cannot: to the extent that we are human beings and wish to remain human beings we cannot. If we wish to comprehend nature, we must permeate it with concepts and ideas. Why must we do that? We must do that, ladies and gentlemen, because only thereby does consciousness awake, because only thereby do we become conscious human beings. Just as each morning upon opening our eyes we achieve consciousness in our interaction with the external world, so essentially did consciousness awake within the evolution of humanity. Consciousness, as it is now, was first kindled through the interaction of the senses and thinking with the outer world. We can watch the historical development of consciousness in the interaction of man's senses with outer nature. In this process consciousness gradually was kindled out of the dull, sleepy cultural life of primordial times. Yet one must only consider with an open mind this fact of consciousness, this interaction between the senses and nature, in order to observe something extraordinary transpiring within man. We must look into our soul to see what is there, either by remaining awhile before fully awakening within that dull and dreamy consciousness or by looking back into the almost dreamlike consciousness of primordial times. If we look within our soul at what lies submerged beneath the surface consciousness arising in the interaction between senses and the outer world, we find a world of representations, faint, diluted to dream-pictures with hazy contours, each image fading into the other. Unprejudiced observation establishes this. The faintness of the representations, the haziness of the contours, the fading of one representation into another: none of this can cease unless we awake to a full interaction with external nature. In order to come to this awakening which is tantamount to becoming fully human — our senses must awake every morning to contact with nature. It was also necessary, however, for humanity as a whole to awake out of a dull, dreamlike vision of primordial worlds within the soul to achieve the present clear representations. In this way we achieve the clarity of representation and the sharply delineated concepts that we need in order to remain awake, to remain aware of our environment with a waking soul. We need all this in order to remain human in the fullest sense of the word. But we cannot simply conjure it all up out of ourselves. We achieve it only when our senses come into contact with nature: only then do we achieve clear, sharply delineated concepts. We thereby develop something that man must develop for his own sake — otherwise consciousness would not awake. It is thus not an abstract “need for explanations,” not what du Bois-Reymond and other men like him call “the need to know the causes of things,” that drives us to seek explanations but the need to become human in the fullest sense through observing nature. We thus may not say that we can outgrow the need to explain like any other child's play, for that would mean that we would not want to become human in the fullest sense of the word — that is to say, not want to awake in the way we must awake. Something else happens in this process, however. In coming to such concepts as we achieve in contemplating nature, we at the same time impoverish our inner conceptual life. Our concepts become clear, but their compass becomes diminished, and if we consider exactly what it is we have achieved by means of these concepts, we see that it is an external, mathematical-mechanical lucidity. Within that lucidity, however, we find nothing that allows us to comprehend life. We have, as it were, stepped out into the light but lost the very ground beneath our feet. We find no concepts that allow us to typify life, or even consciousness, in any way. In exchange for the clarity we must seek for the sake of our humanity, we have lost the content of that for which we have striven. And then we contemplate nature around us with our concepts. We formulate such complex ideas as the theory of evolution and the like. We strive for clarity. Out of this clarity we formulate a world view, but within this world view it is impossible to find ourselves, to find man. With our concepts we have moved out to the surface, where we come into contact with nature. We have achieved clarity, but along the way we have lost man. We move through nature, apply a mathematical-mechanical explanation, apply the theory of evolution, formulate all kinds of biological laws; we explain nature; we formulate a view of nature — within which man cannot be found. The abundance of content that we once had has been lost, and we are confronted with a concept that can be formed only with the clearest but at the same time most desiccated and lifeless thinking: the concept of matter. And an ignorabimus in the face of the concept of matter is essentially the confession: I have achieved clarity; I have struggled through to an awakening of full consciousness, but thereby I have lost the essence of man in my thinking, in my explanations, in my comprehension. And now we turn to look within. We turn away from matter to consider the inner realm of consciousness. We see how within this inner realm of consciousness representations pass in review, feelings come and go, impulses of will flash through us. We observe all this and notice that when we attempt to bring the inner realm into the same kind of focus that we achieved with regard to the external world, it is impossible. We seem to swim in an element that we cannot bring into sharp contours, that continually fades in and out of focus. The clarity for which we strive with regard to outer nature simply cannot be achieved within. In the most recent attempts to understand this inner realm, in the Anglo-American psychology of association, we see how, following the example of Hume, Mill, James, and others, the attempt was made to impose the clarity attained in observation of external nature upon inner sensations and feelings. One attempts to impose clarity upon sensation, and this is impossible. It is as though one wanted to apply the laws of flight to swimming. One does not come to terms at all with the element within which one has to move. The psychology of association never achieves sharpness of contour or clarity regarding the phenomenon of consciousness. And even if one attempts with a certain sobriety, as Herbart has done, to apply mathematical computation to human mental activity [das Vorstellen], to the human soul, one finds it possible, but the computations hover in the air. There is no place to gain a foothold, because the mathematical formulae simply cannot comprehend what is actually occurring within the soul. While one loses man in coming to clarity regarding the external world, one finds man, to be sure — it goes without saying that one finds man when one delves into consciousness — but there is no hope of achieving clarity, for one swims about, borne hither and thither in an insubstantial realm. One finds man, but one cannot find a valid image of man. It was this that du Bois-Reymond felt very clearly but was able to express only much less clearly — only as a kind of vague feeling about scientific research on the whole — when in August 1872 he spoke his ignorabimus . What this ignorabimus wants to say in essence is that on the one hand, we have in the historical evolution of humanity arrived at clarity regarding nature and have constructed the concept of matter. In this view of nature we have lost man — that is, ourselves. On the other hand we look down into consciousness. To this realm we want to apply that which has been most important in arriving at the contemporary explanation of nature. Consciousness rejects this lucidity. This mathematical clarity is entirely out of place. To be sure, we find man in a sense, but our consciousness is not yet strong enough, not yet intensive enough to comprehend man fully. Again, one is tempted to answer with an ignorabimus , but that cannot be, for we need something more than an ignorabimus in order to meet the social demands of the modern world. The limit that du Bois-Reymond had come up against when he spoke [about] his ignorabimus on August 14, 1872 lies not within the human condition as such but only within its present stage of historical human evolution. How are we to transcend this ignorabimus ? That is the burning question.

The Boundaries of Natural Science

Lecture I

https://rsarchive.org/Lectures/GA322/English/AP1983/19200927p01.html

Dornach

27 Sep 1920

GA322-1

It must be answered, not to meet a human “need to know” but to meet man's universal need to become fully human. And in just what way one can strive for an answer, in what way the ignorabimus can be overcome to fulfil the demands of human evolution — this shall be the theme of our course of lectures as it proceeds. To those who demand of a cycle of lectures with a title such as ours that nothing be introduced that might interfere with the objective presentation of ideas, I would like, since today I shall have to mention certain personalities, to say the following. The moment one begins to represent the results of human judgment in their relationship to life, to full human existence, it becomes inevitable that one indicate the personalities with whom the judgments originated. Even in a scientific presentation, one must remain within the sphere in which the judgment arises, within the realm of human struggling and striving toward such a judgment. And especially since the question we want above all to answer is: what can be gleaned from modern scientific theories that can become a vital social thinking able to transform thought into impulses for life? — then one must realize that the series of considerations one undertakes is no longer confined to the study and the lecture halls but Stands rather within the living evolution of humanity. Behind everything with which I commenced yesterday, the modern striving for a mathematical-mechanical world view and the dissolution of that world view, behind that which came to a climax in 1872 in the famous speech by the physiologist, du Bois-Reymond, concerning the limits of natural science, there stands something even more important. It is something that begins to impress itself upon us the moment we want to begin to speak in a living way about the limits of natural science. A personality of extraordinary philosophical stature still looks over to us with a certain vitality out of the first half of the nineteenth century: Hegel. Only in the last few years has Hegel begun to be mentioned in the lecture halls and in the philosophical literature with somewhat more respect than in the recent past. In the last third of the nineteenth century the academic world attacked Hegel outright, yet one could demonstrate irrefutably that Eduard von Hartmann had been quite right in claiming that during the 1880s only two university lecturers in all of Germany had actually read him. The academics opposed Hegel but not on philosophical grounds, for as a philosopher they hardly knew him. Yet they knew him in a different way, in a way in which we still know him today. Few know Hegel as he is contained, or perhaps better said, as his world view is contained, in the many volumes that sit in the libraries. Those who know Hegel in this original form so peculiar to him are few indeed. Yet in certain modified forms he has become in a sense the most popular philosopher the world has ever known. Anyone who participates in a workers' meeting today or, even better, anyone who had participated in one during the last few decades and had heard what was discussed there; anyone with any sense for the source of the mode of thinking that had entered into these workers' meetings, who really knew the development of modern thought, could see that this mode of thinking had originated with Hegel and flowed through certain channels out into the broadest masses. And whoever investigated the literature and philosophy of Eastern Europe in this regard would find that the Hegelian mode of thinking had permeated to the farthest reaches of Russian cultural life. One thus could say that, anonymously, as it were, Hegel has become within the last few decades perhaps one of the most influential philosophers in human history. On the other hand, however, when one perceives what has come to be recognized by the broadest spectrum of humanity as Hegelianism, one is reminded of the portrait of a rather ugly man that a kind artist painted in such a way as to please the man's family. As one of the younger sons, who had previously paid little attention to the portrait, grew older and really observed it for the first time, he said: “But father, how you have changed!” And when one sees what has become of Hegel one might well say: “Dear philosopher, how you have changed!” To be sure, something extraordinary has happened regarding this Hegelian world view. Hardly had Hegel himself departed when his school fell apart. And one could see how this Hegelian school appropriated precisely the form of one of our new parliaments. There was a left wing and a right wing, an extreme left and an extreme right, an ultra-radical wing and an ultra-conservative wing. There were men with radical scientific and social views, who felt themselves to be Hegel's true spiritual heirs, and on the other side there were devout, positive theologians who wanted just as much to base their extreme theological conservatism on Hegel. There was a center for Hegelian studies headed by the amiable philosopher, Karl Rosenkranz, and each of these personalities, every one of them, insisted that he was Hegel's true heir. What is this remarkable phenomenon in the evolution of human knowledge? What happened was that a philosopher once sought to raise humanity into the highest realms of thought. Even if one is opposed to Hegel, it cannot be denied that he dared attempt to call forth the world within the soul in the purest thought-forms. Hegel raised humanity into ethereal heights of thinking, but strangely enough, humanity then fell right back down out of those heights. It drew on the one hand certain materialistic and on the other hand certain positive theological conclusions from Hegel's thought. And even if one considers the Hegelian center headed by the amiable Rosenkranz, even there one cannot find Hegel's philosophy as Hegel himself had conceived it. In Hegel's philosophy one finds a grand attempt to pursue the scientific method right up into the highest heights. Afterward, however, when his followers sought to work through Hegel's thoughts themselves, they found that one could arrive thereby at the most contrary points of view. Now, one can argue about world views in the study, one can argue within the academies, and one can even argue in the academic literature, so long as worthless gossip and Barren cliques do not result. These offspring of Hegelian philosophy, however, cannot be carried out of the lecture halls and the study into life as social impulses. One can argue conceptually about contrary world views, but within life itself these contrary world views do not fight so peaceably. One must use just such a paradoxical expression in describing such a phenomenon. And thus there stands before us in the first half of the nineteenth century an alarming factor in the evolution of human cognition, something that has proved itself to be socially useless in the highest degree. With this in mind we must then raise the question: how can we find a mode of thinking that can be useful in social life? In two phenomena above all we notice the uselessness of Hegelianism for social life. One of those who studied Hegel most intensively, who brought Hegel fully to life within himself, was Karl Marx. And what is it that we find in Marx? A remarkable Hegelianism indeed! Hegel up upon the highest peak of the conceptual world — Hegel upon the highest peak of Idealism — and the faithful student, Karl Marx, immediately transforming the whole into its direct opposite, using what he believed to be Hegel's method to carry Hegel's truths to their logical conclusions. And thereby arises historical materialism, which is to be for the masses the one world view that can enter into social life. We thus are confronted in the first half of the nineteenth century with the great Idealist, Hegel, who lived only in the Spirit, only in his ideas, and in the second half of the nineteenth century with his student, Karl Marx, who contemplated and recognized the reality of matter alone, who saw in everything ideal only ideology. If one but takes up into one's feeling this turnabout of conceptions of world and life in the course of the nineteenth century, one feels with all one's soul the need to achieve an understanding of nature that will serve as a basis for judgments that are socially viable. Now, if we turn on the other hand to consider something that is not so obviously descended from Hegel but can be traced back to Hegel nonetheless, we find still within the first half of the nineteenth century, but carrying over into the second half, the “philosopher of the ego,” Max Stirner. While Karl Marx occupies one of the two poles of human experience mentioned yesterday, the pole of matter upon which he bares all his considerations, Stirner, the philosopher of the ego, proceeds from the opposite pole, that of consciousness. And just as the modern world view, gravitating toward the pole of matter, becomes unable to discover consciousness within that element (as we saw yesterday in the example of du Bois-Reymond), a person who gravitates to the opposite pole of consciousness will not be able to find the material world. And so it is with Max Stirner. For Max Stirner, no material universe with natural laws actually exists. Stirner sees the world as populated solely by human egos, by human consciousnesses that want only to indulge themselves to the full. “I have built my thing on nothing”— that is one of Max Stirner's maxims. And on these grounds Stirner opposes even the notion of Providence. He says for example: certain moralists demand that we should not perform any deed out of egoism, but rather that we should perform it because it is pleasing to God. In acting, we should look to God, to that which pleases Him, that which He commands. Why, thinks Max Stirner, should I, who have built only upon the foundation of ego-consciousness, have to admit that God is after all the greater egoist Who can demand of man and the world that all should be performed as it suits Him? I will not surrender my own egoism for the sake of a greater egoism. I will do what pleases me . What do I care for a God when I have myself ? One thus becomes entangled and confused within a consciousness out of which one can no longer find the way. Yesterday I remarked how on the one hand we can arrive at clear ideas by awakening in the experience of ideas when we descend into our consciousness. These dreamlike ideas manifest themselves like drives from which we cannot then escape. One would say that Karl Marx achieved clear ideas — if anything his ideas are too clear. That was the secret of his success. Despite their complexity, Marx's ideas are so clear that, if properly garnished, they remain comprehensible to the widest circles. Here clarity has been the means to popularity. And until it realizes that within such a clarity humanity is lost, humanity, as long as it seeks logical consequences, will not let go of these clear ideas. If one is inclined by temperament to the other extreme, to the pole of consciousness, one passes over onto Stirner's side of the scale. Then one despises this clarity: one feels that, applied to social thinking, this clarity makes man into a cog in a social order modeled on mathematics or mechanics — but into that only, into a mere cog. And if one does not feel oneself cut out for just that, then the will that is active in the depths of human consciousness revolts. Then one comes radically to oppose all clarity. One mocks all clarity, as Stirner did. One says to oneself: what do I care about anything else? What do I care even about nature? I shall project my own ego out of myself and see what happens. We shall see that the appearance of such extremes in the nineteenth century is in the highest degree characteristic of the whole of recent human evolution, for these extremes are the distant thunder that preceded the storm of social chaos we are now experiencing. One must understand this connection if one wants at all to speak about cognition today. Yesterday we arrived at an indication of what happens when we begin to correlate our consciousness to an external natural world of the senses. Our consciousness awakens to clear concepts but loses itself. It loses itself to the extent that one can only posit empty concepts such as “matter,” concepts that then become enigmatic. Only by thus losing ourselves, however, can we achieve the clear conceptual thinking we need to become fully human. In a certain sense we must first lose ourselves in order to find ourselves again out of ourselves. Yet now the time has come when we should learn something from these phenomena. And what can one learn from these phenomena? One can learn that, although clarity of conceptual thinking and perspicuity of mental representation can be won by man in his interaction with the world of sense, this clarity of conceptual thinking becomes useless the moment we strive scientifically for something more than a mere empiricism. It becomes useless the moment we try to proceed toward the kind of phenomenalism that Goethe the scientist cultivated, the moment we want something more than natural science, namely Goetheanism. What does this imply? In establishing a correlation between our inner life and the external physical world of the senses we can use the concepts we form in interaction with nature in such a way that we try not to remain within the natural phenomena but to think on beyond them. We are doing this if we do more than simply say: within the spectrum there appears the color yellow next to the color green, and on the other side the blues. We are doing this if we do not simply interrelate the phenomena with the help of our concepts but seek instead, as it were, to pierce the veil of the senses and construct something more behind it with the aid of our concepts. We are doing this if we say: out of the clear concepts I have achieved I shall construct atoms, molecules — all the movements of matter that are supposed to ex-ist behind natural phenomena. Thereby something extraordinary happens. What happens is that when I as a human being confront the world of nature [see illustration], I use my concepts not only to create for myself a conceptual order within the realm of the senses but also to break through the boundary of sense and construct behind it atoms and the like I cannot bring my lucid thinking to a halt within the realm of the senses. I take my lesson from inert matter, which continues to roll on even when the propulsive force has ceased. My knowledge reaches the world of sense, and I remain inert. I have a certain inertia, and I roll with my concepts on beyond the realm of the senses to construct there a world the existence of which I can begin to doubt when I notice that my thinking has only been borne along by inertia. It is interesting to note that a great proportion of the philosophy that does not remain within phenomena is actually nothing other than just such an inert rolling-on beyond what really exists within the world. One simply cannot come to a halt. One wants to think ever farther and farther beyond and construct atoms and molecules — under certain circumstances other things as well that philosophers have assembled there. No wonder, then, that this web one has woven in a world created by the inertia of thinking must eventually unravel itself again. Goethe rebelled against this law of inertia. He did not want to roll onward thus with his thinking but rather to come strictly to a halt at this limit [see illustration: heavy line] and to apply concepts within the realm of the senses. He thus would say to himself: within the spectrum appear to me yellow, blue, red, indigo, violet. If, however, I permeate these appearances of color with my world of concepts while remaining within the phenomena, then the phenomena order themselves of their own accord, and the phenomenon of the spectrum teaches me that when the darker colors or anything dark is placed behind the lighter colors or anything light, there appear the colors which lie toward the blue end of the spectrum. And conversely, if I place light behind dark, there appear the colors which lie toward the red end of the spectrum. What was it that Goethe was actually seeking to do? Goethe wanted to find simple phenomena within the complex but above all such phenomena as allowed him to remain within this limit [see illustration], by means of which he did not roll on into a realm that one reaches only through a certain mental inertia. Goethe wanted to adhere to a strict phenomenalism. If we remain within phenomena and if we strive with our thinking to come to a halt there rather than allow ourselves to be carried onward by inertia, the old question arises in a new way. What meaning does the phenomenal world have when I consider it thus? What is the meaning of the mechanics and mathematics, of the number, weight, measure, or temporal relation that I import into this world? What is the meaning of this? You know, perhaps, that the modern world conception has sought to characterize the phenomena of tone, color, warmth, etc. as only subjective, whereas it characterizes the so-called primary qualities, the qualities of weight, space, and time, as something not subjective but objective and inherent in things. This conception can be traced back principally to the English philosopher, John Locke, and it has to a considerable extent determined the philosophical basis of modern scientific thought. But the real question is: what place within our systematic science of nature as a whole do mathematics, do mechanics — these webs we weave within ourselves, or so it seems at first — what place do these occupy? We shall have to return to this question to consider the specific form it takes in Kantianism. Yet without going into the whole history of this development one can nonetheless emphasize our instinctive conviction that measuring or counting or weighing external objects is essentially different from ascribing to them any other qualities. It certainly cannot be denied that light, tones, colors, and sensations of taste are related to us differently from that which we could represent as subject to mathematical-mechanical laws. For it really is a remarkable fact,a fact worthy of our consideration: you know that honey tastes sweet, but to a man with jaundice it tastes bitter — so we can say that we stand in a curious relationship to the qualities within this realm — while on the other hand we could hardly maintain that any normal man would see a triangle as a triangle, but a man with jaundice would see it as a square! Certain differentiations thus do exist, and one must be cognizant of them; on the other hand, one must not draw absurd conclusions from them. And to this very day philosophical thinking has failed in the most extraordinary way to come to grips with this most fundamental epistemological question. We thus see how a contemporary philosopher, Koppelmann, overtrumps even Kant by saying, for example — you can read this on page 33 of his Philosophical Inquiries [ Weltanschauungsfragen ]: everything that relates to space and time we must first construct within by means of the understanding, whereas we are able to assimilate colors and tastes directly. We construct the icosahedron, the dodecahedron, etc.: we are able to construct the standard regular solids only because of the organization of our understanding. No wonder, then, claims Koppelmann, that we find in the world only those regular solids we can construct with our understanding. One thus can find Koppelmann saying almost literally that it is impossible for a geologist to come to a geometer with a crystal bounded by seven equilateral triangles precisely because — so Koppelmann claims — such a crystal would have a form that simply would not fit into our heads. That is out-Kanting Kant. And thus he would say that in the realm of the thing-in-itself crystals could exist that are bounded by seven regular triangles, but they cannot enter our head, and thus we pass them by; they do not exist for us. Such thinkers forget but one thing: they forget — and it is just this that we want to indicate in the course of these lectures with all the forceful proofs we can muster — that the natural order governing the construction of our head also governs the construction of the regular polyhedrons, and it is for just this reason that our head constructs no other polyhedrons than those that actually confront us in the external world. For that, you see, is one of the basic differences between the so-called subjective qualities of tone, color, warmth, as well as the different qualities of touch, and that which confronts us in the mechanical-mathematical view of the world. That is the basic difference: tone and color leave us outside of ourselves; we must first take them in; we must first perceive them. As human beings we stand outside tone, color, warmth, etc. This is not entirely the case as regards warmth — I shall discuss that tomorrow — but to a certain extent this is true even of warmth. These qualities leave us initially outside ourselves, and we must perceive them. In formal, spatial, and temporal relationships and regarding weight this is not the case. We perceive objects in space but stand ourselves within the same space and the same lawfulness as the objects external to us. We stand within time just as do the external objects. Our physical existence begins and ends at a definite point in time. We stand within space and time in such a way that these things permeate us without our first perceiving them. The other things we must first perceive. Regarding weight, well, ladies and gentlemen, you will readily admit that this has little to do with perception, which is somewhat open to arbitrariness: otherwise many people who attain an undesired corpulence would be able to avoid this by perception alone, merely by having the faculty of perception. No, ladies and gentlemen, regarding weight we are bound up with the world entirely objectively, and the organization by means of which we stand within color, tone, warmth, etc. is powerless against that objectivity. So now we must above all pose the question: how is it that we arrive at any mathematical-mechanical judgment? How do we arrive at a science of mathematics, at a science of mechanics? How is it, then, that this mathematics, this mechanics, is applicable to the external world of nature, and how is it that there is a difference between the mathematical-mechanical qualities of external objects and those that confront us as the so-called subjective qualities of sensation, tone, color, warmth, etc.? At the one extreme, then, we are confronted with this fundamental question. Tomorrow we shall discuss another such question. Then we shall have two starting-points from which we can proceed to investigate the nature of science. Thence we shall proceed to the other extreme to investigate the formation of social judgments.

The Boundaries of Natural Science

Lecture II

https://rsarchive.org/Lectures/GA322/English/AP1983/19200928p01.html

Dornach

28 Sep 1920

GA322-2

We have seen that one arrives at two limits when one seeks either to penetrate more deeply into natural phenomena or, proceeding from the state of normal consciousness, to penetrate more deeply into one's own being in order to uncover the essential nature of consciousness. Yesterday we showed already what happens at the one limit to knowledge. We have seen that man awakes to full consciousness in coming into contact with an external, physical world of sense. Man would remain a more-or-less drowsy being, a being with a sleepy soul, if he could not awake in confronting external nature. And what has happened in the spiritual evolution of humanity, in man's gradual acquisition of knowledge about external nature, is actually nothing other than what happens every morning when we awake out of sleep or dream-consciousness by confronting an external world. This latter is a kind of moment of awakening, and in the course of the evolution of humanity we have to do with a gradual awakening, a kind of long, drawn-out moment of awakening. Now, we have seen that at this frontier a certain inertia on the part of the soul very easily comes into play, so that when we come up against the extended world of phenomena we do not proceed in the manner of Goethean phenomenology by halting at this frontier and ordering the phenomena according to the representations, concepts, and ideas we have already gained, describing them in a systematic, rational manner, and so forth. Instead, we roll on a bit farther beyond the phenomena with our concepts and ideas and thereby create a world, for example a world of metaphysical atoms, molecules, and so forth. This world, when it is so constituted, is merely a fabrication of the mind, a world into which there enters a creeping doubt, so that we have to unravel again the theoretical web we have spun. And we have seen that it is possible to guard against such a violation of this frontier of our knowledge through phenomenalism, through working purely with the phenomena themselves. We have also had to show that at this point in our striving for knowledge something emerges that commends itself to our use as an immediate necessity: mathematics and that part of mechanics that can be comprehended without any empirical observation, i.e., the entire compass of so-called analytical mechanics. If we call to mind everything comprehended by mathematics and analytical mechanics, we have before us the system of concepts that allows us to enter into phenomena with the utmost certainty. And yet, as I began to indicate yesterday, one should not deceive oneself, for the whole manner in which we call forth the notions of mathematics and analytical mechanics, this process within our souls, is entirely different from that employed when we experiment with or observe sensory data and then seek to comprehend them, when we try to gather knowledge from sensory experience. In order to arrive at the fullest clarity regarding these matters one must bring all one's mental energy to bear, for in this realm full clarity can be attained only with the greatest mental exertion. What is the difference between accumulating knowledge from sensory experience in a Baconian manner and the more inward mode of apprehension we find in mathematics and analytical mechanics? One can sharply differentiate the latter from those modes of apprehension that are not inward in this way by formulating clearly the concepts of the parallelogram of motion and the parallelogram of forces. One theorem of analytical mechanics states that two angular vectors proceeding from one point result in a third vector. To say, however, that a vector of a specific force here [see diagram: a] and a vector of a specific force here [b] result in a third force, which can also be determined according to the parallelogram — that is another notion altogether. The parallelogram of motion lies strictly within the province of analytical mechanics, for it is internally consistent and demands no external proof. In this it is like the Rule of Pythagoras or any other geometrical axiom, but the existence of the parallelogram of forces can be determined only by experience, by experimentation. In this case, we bring something into that which we work through inwardly: the force that can be given only empirically from without. Here we no longer have a pure, analytical mechanics but an “empirical mechanics.” One can thus differentiate sharply between that which is still actually mathematical — as we still conceive mathematics today — and that which leads over into conventional empiricism. Now one stands before this phenomenon of mathematics as such. We comprehend mathematical truths. We proceed from mathematical phenomena to certain axioms. We weave the fabric of mathematics out of these axioms and then stand before an architectonic whole apprehended by the mind's eye [ im inneren Anschauen ]. If we are able by means of energetic thinking to differentiate sharply this inner apprehension from anything that can be experienced outwardly, we must see in this fabric of mathematics something that arises through an activity of soul entirely different from that which underlies our experience of the outer objects of sensation. Whether or not we arrive at a satisfactory comprehension of the world depends to a tremendous extent on our being able to make this clear distinction out of inner experience. We thus must ask: where does mathematics originate? Nowadays this question is still not pursued rigorously enough. One does not ask: how is this inner activity of the soul that we need in mathematics, in the wonderful architecture of mathematics — how is this inner activity of the soul different from that whereby we grasp external nature through the senses? One does not pose this question and seek an answer with sufficient rigor, because it is the tragedy of the materialistic world view that, while on the one hand it presses for sensory experience, on the other hand it is driven unawares into an abstract intellectualism, into a realm of abstraction where one is isolated from any true comprehension of the phenomena of the material world. What kind of capacity is it, then, that we acquire when we engage in mathematics? We want to address ourselves to this question. In order to answer this question we must, I believe, have reached a complete understanding of one thing in particular: we must take fully seriously the concept of becoming as it applies to human life as well. We must begin by acquiring the discipline that modern science can teach us. We must school ourselves in this way and then, taking the strict methodology, the scientific discipline we have learned from modern natural science, transcend it, so that we use the same exacting approach to rise into higher regions, thereby extending this methodology to the investigation of entirely different realms as well. For this reason I believe — and I want this to be expressly stated — that nobody can attain true knowledge of the spirit who has not acquired scientific discipline, who has not learned to investigate and think in the laboratories according to the modern scientific method. Those who pursue spiritual science [ Geisteswissenschaft ] have less cause to undervalue modern science than anyone. On the contrary, they know how to value it at its full worth. And many people — if I may here insert a personal remark — were extremely upset with me when, before publishing anything pertaining to spiritual science as such, I wrote a great deal about the problems of natural science in a way that appeared necessary to me. So you see it is necessary on the one hand for us to cultivate a scientific habit of mind, so that this can accompany us when we cross the frontiers of natural science. In addition, it is the quality of this scientific method and its results that we must take very seriously indeed. You see, if we consider the simple phenomenon of warmth that appears when we rub two bodies together, it would be utterly unscientific to say, regarding this isolated phenomenon, that the warmth had been created ex nihilo or simply existed. Rather, we seek the conditions under which this warmth was previously latent and now appears by means of the bodies. We proceed from the one phenomenon to the other and thus take seriously this process of becoming [ das Werden ]. We must do the same with the concepts that we consider in spiritual science. So we must first of all ask: is that which manifests itself as the ability to perform mathematics present in man throughout his entire existence between birth and death? No, it is not always present. It awakes at a certain point in time. To be sure, we can, while still remaining empirical regarding the outer world, observe with great precision how there gradually arise out of the dark recesses of human consciousness faculties that manifest themselves as the ability to perform mathematics and something like mathematics that we have yet to discuss. If one can observe this emergence in time precisely and soberly, just as scientific research treats the phenomena of the melting or boiling point, one sees that this new faculty emerges at approximately that time of life when the child changes teeth. One must treat such a point in the development of human life with the same attitude with which physics, for example, teaches one to treat the melting or boiling point. One must acquire the ability to carry over into the complicated realm of human life the same strict inner discipline that one can acquire by observing simple physical phenomena according to the methods of modern science. If one does this, one sees that in the course of human development from birth, or rather from conception, up to the change of teeth, the soul faculties enabling one to perform mathematics manifest themselves gradually within the organism but that they are not yet fully present. Now we say that the warmth that manifests itself in a body under certain conditions was latent in that body beforehand, that it was at work within the inner structure of that body. In the same way we must be entirely clear that the capacity to perform mathematics, which becomes most evident at the change of teeth and reveals itself gradually in another sense, was also at work beforehand within the human organization. We thus arrive at an important and valuable insight into the nature of mathematics — mathematics taken, of course, in the very broadest sense. We begin to understand how that which is at our disposal after the change of teeth as a soul faculty worked previously within to organize us. Yes, within the child until approximately its seventh year there works an inner mathematics, an inner mathematics not abstract like our external one but full of active energy, a mathematics which, if I may use Plato's expression, not only can be inwardly envisioned [ angeschaut ] but is full of active life. Up to this point in time there exists within us something that “mathematicizes” us through and through. When we ask at first entirely superficially what can be seen by looking empirically at this “latent mathematics” in the body of the young child, we are led to three things resembling inner senses. In the course of these lectures we shall come to see that one can indeed speak of senses within as well. Today I want only to indicate that we are led to something that develops an inward faculty of perception similar to the outward perception developed by the eyes and ears, except that the former remains unconscious within us during these first years. And if we look within, look into our own inner organization not like nebulous mystics but with all our powers of apprehension, we can find within three functions similar to those of the outward senses. We find inner senses that exercise a certain activity, a certain inner mathematics, just in those first several years. One encounters first of all what I would like to call the sense of life. This sense of life manifests itself in later years as a perception of our inner state as a whole. In a certain way we feel either well or unwell. We feel comfortable or uncomfortable: just as we have a faculty for perceiving outwardly with the eyes, so also do we have a faculty for perceiving inwardly. This faculty is directed toward the whole organism and is for that reason dark and dull; yet it is there all the same. We shall have more to say about this later. For the moment I want to anticipate this later discussion only by remarking that this sense of life is — if I may use a tautology — especially active in the vitality of the child up until the change of teeth. Another inner sense that we must consider when we look within in this way is that which I would like to call the sense of movement. We must form a clear conception of this sense of movement. When we move our limbs, we are aware of this not only by viewing ourselves externally but also by means of an internal perception. Also when we walk: we are conscious that we are walking not only in that we see objects pass and our view of the external world changes but also in that we have an internal perception of the movements of the limbs, of changes within ourselves as we move. Normally we remain unaware of the inner experiences and perception that run parallel to the outer because of the strength of the external impressions, much as a dim light is “extinguished” by a bright one. And a third inward-looking faculty is the sense of balance. The sense of balance is what enables us to locate ourselves within the world, to avoid falling, to perceive in a certain way how we can bring ourselves into harmony with the forces in our environment. We perceive this process of bringing ourselves into harmony with our environment inwardly. We thus can truly say that we bear within ourselves these three inner senses: the sense of life, the sense of movement, and the sense of balance. They are especially active in childhood up to the change of teeth. Around this time of the change of teeth their activity begins to wane, but observe to take but one example, the sense of balance — observe how at birth the child has as yet nothing enabling it to attain the position of balance it needs in later life. Consider how the child gradually gains control of itself, how it learns at first to crawl on all fours, how it gradually achieves through its sense of balance the ability to stand and to walk, how it finally is able to maintain its own balance. If one considers the entire process of development from conception to the change of teeth, one sees therein the powerful activity of these three inner senses. And if one can attain a certain insight into what is happening there, one sees that there is at work in the sense of balance and the sense of movement nothing other than a living “mathematicizing” [ ein lebendiges Mathematisieren ]. In order for it to come to life, the sense of life is there to vitalize it. We thus see a kind of latent realm of mathematics active within man. This activity does not entirely cease at the change of teeth, but it does become at that time considerably less pronounced for the remainder of life. That which is inwardly active in the sense of balance, the sense of movement, and the sense of life becomes free. This latent mathematics becomes free, just as latent heat can become liberated heat. And we see how that which initially was woven through the organism as an element of soul becomes free. We see how this mathematics emerges as abstraction from a condition in which it was originally a concrete force shaping the human organism. And because as human beings we are suspended in the web of existence according to temporal and spatial relationships, we take this mathematics that has become free out into the world and seek to comprehend the external world by means of something that worked within us up until the change of teeth. You see, it is not a denial but rather an extension of natural science that results when one considers rightly what ought to live within spiritual science as attitude and will. We thus carry what originates within ourselves beyond the frontier of sense perception. We observe man within a process of becoming. We do not simply observe mathematics on the one hand and sensory experience on the other but rather the emergence of mathematics within the developing human being. And now we come to that which truly leads over into spiritual science itself. You see, that which we call forth out of our own inner life, this “mathematicizing,” becomes in the end an abstraction. Yet our experience of it need not remain an abstraction. In our time there is, to be sure, little opportunity for us to experience mathematics in a true light. Yet at a certain point in the development of Western civilization there does come to light something of this sense of a special spirit in mathematics. This comes to light at the point where Novalis, the poet Novalis, who underwent a good mathematical training in his studies, writes about mathematics in his Fragments. He calls mathematics a grand poem, a wonderful, grand poem. One really must have experienced at some time what it is that leads from an abstract understanding of the geometrical forms to a sense of wonder at the harmony that underlies this inner “mathematicizing.” One really must have had the opportunity to get beyond the cold, sober performance of mathematics, which many people even hate. One must have struggled through as Novalis had in order to stand in awe of the inner harmony and — if I may use an expression you have heard often in a completely different context — the “melody” [ Melos ] of mathematics. Then something new enters into one's experience of mathematics. There enters into mathematics, which otherwise remains purely intellectual and, metaphorically speaking, interests only the head, something that engages the entire man. This something manifests itself in such youthful Spirits as Novalis in the feeling: that which you behold as mathematical harmony, that which you weave through all the phenomena of the universe, is actually the same loom that wove you during the first years of growth as a child here an earth. This is to feel concretely man's connection with the cosmos. And when one works one's way through to such an inner experience, which many hold to be mere fantasy because they have not actually attained it themselves, one has some idea what the spiritual scientist [ Geistesforscher ] experiences when he rises to a more extensive grasp of this “mathematicizing” by undergoing an inner development of which I have yet to speak and which you will find fully depicted in my book, Knowledge of the Higher Worlds and Its Attainment . 2 Wie erlangt man Erkenntnisse der hoheren Welten ?, Berlin, 1909 ( Knowledge of the Higher Worlds and Its Attainment . Anthroposophie Press, Spring Valley, N.Y., reprinted 1983). For then the capacity of soul manifesting itself as this inner mathematics passes over into something far more comprehensive. It becomes something that remains just as exact as mathematical thought yet does not proceed solely from the intellect but from the whole man. On this path of constant inner work — an inner work far more demanding than that performed in the laboratory or observatory or any other scientific institution — one comes to know what it is that underlies mathematics, that underlies this simple faculty of the human soul which can be expanded into something far more comprehensive. In this higher experience of mathematics one comes to know Inspiration. One comes to understand the differences between what lives in us as mathematics and what lives in us as outer-directed empiricism. In this outer-directed empiricism we have sense impressions that give content to our empty concepts. In Inspiration we have something inwardly spiritual, the activity of which manifests itself already in mathematics, if we know how to grasp mathematics properly — something spiritual which in our early years lives and weaves within us. This activity continues. In doing mathematics we experience this in part. We come to realize that the faculty for performing mathematics rests upon Inspiration, and we can come to experience Inspiration itself by evolving into spiritual scientists. Our representations and concepts then receive their content in a way other than through external experience. We can inspire ourselves with the spiritual force that works within us during childhood. For what works within us during our childhood is spirit. The spirit, however, resides in the human body and must be perceived there through the body, within man. It can be viewed in its pure, free form if one acquires through the faculty of Inspiration the capacity not only to think in mathematical concepts but to view that which exists as a real force in that it organizes us through and through up until the seventh year. And that which manifests itself partially in mathematics and reveals itself as a much more expansive realm through Inspiration can be inwardly viewed, if one employs certain spiritual scientific methods about which — as I have said — I plan yet to speak. One thereby gains not merely new results to add to those acquired through the old powers of cognition but rather an entirely new mode of apprehension. One acquires a new “Inspirative” cognition. The course of human evolution has been such that these powers of Inspirative cognition have receded with the passage of time, after having been present earlier to a very high degree. One must come to understand how Inspiration arises within the inner being of man — that same Inspiration that survives in the West only in the diluted, intellectual experience of mathematics. The experience can be expanded, however, if only one comprehends fully the inner nature of that realm; only then does one begin to understand what lived in that earlier consciousness transmitted to us actually only from the East, from the Vedanta and the other Eastern philosophies that remain so cryptic to the Western mind. For what was it that actually lived within these Eastern philosophies? lt was something that arose through soul faculties of a mathematical nature. It was an Inspiration. It was not merely mathematics but rather something attained within the soul in a way similar to that in which one performs mathematics. Thus I would say that the mathematical atmosphere emanating from the Vedanta and similar ancient world views is something that can be understood from the perspective one attains in rising again to enter the realm of Inspiration. If one can raise to vivid inner life that which works unconsciously in mathematics and the mathematical sciences and can carry it over into another realm, one discovers the same mathematical element that Goethe viewed. Goethe modestly confessed that he did not have proficiency in mathematics in any conventional sense. Goethe has written on his relationship to mathematics in a very interesting series of essays, which you can find in his scientific writings under the heading “Relationship to Mathematics.” Extraordinarily interesting! For despite Goethe's modest confession that he had not acquired a proficiency in the handling of actual mathematical concepts and theories, he does require one thing: he calls for a phenomenalism such as he employed in his own scientific studies. He demands that within the secondary phenomena confronting us in the phenomenal world we seek the archetypal phenomenon [ Urphänomen ]. But just what kind of activity is this? He demands that we trace external phenomena back to the archetypal phenomenon, in just the same way that the mathematician traces the outward apprehension [ äusseres Anschauen ] of complex structures back to the axiom. Goethe's archetypal phenomena are empirical axioms, axioms that can be experienced. Goethe thus demands, in a truly mathematical spirit, that one inwardly permeate phenomena with mathematics. He writes that we must see the archetypal phenomena in such a way that we are able at all times to justify our procedures according to the rigorous requirements of the mathematician. Thus what Goethe seeks is a modified, transformed mathematics, one that suffuses phenomena. He demands this as a scientific activity. Goethe was able, therefore, to suffuse with light the one pole that otherwise remains so dark if we postulate only the concept of matter. We shall see how Goethe approached this pole; we modern must, however, approach the other, the pole of consciousness. We must investigate in the Same way how soul faculties manifest their activity in the human being, how they proceed from man's inner nature to manifest their activity externally. We shall have to investigate this. It shall become clear that we must complement the method of investigating the external world offered by Goethean phenomenology with a method of comprehending the realm of human consciousness. It must be a mode of comprehension justifiable in the sense in which Goethe's can be justified to the mathematician — a method such as I tried to employ in a modest way in my book, Philosophy of Freedom . 3 Die Philosophie der Freiheit , Berlin, 1894 ( The Philosophy of Freedom , Anthroposophic Press, Spring Valley, N.Y., 1964). Earlier translations of this book (1922, 1938, and 1963) bore the title The Philosophy of Spiritual Activity , following a suggestion given by Steiner himself. The English word “freedom” connotes a passive state; the German “Freiheit” (as is clean from the following lecture), an objective basis for moral action achieved through intense inner activity. At the pole of matter we thus encounter the results yielded by Goethean phenomenology and at the pole of consciousness those attained by pursuing the method that I sought to establish in a modest way in my Philosophy of Freedom . Tomorrow we will want to pursue this further. ˂˂ Previous Table of Contents Next ˃˃ At the pole of matter we thus encounter the results yielded by Goethean phenomenology and at the pole of consciousness those attained by pursuing the method that I sought to establish in a modest way in my Philosophy of Freedom . Tomorrow we will want to pursue this further.

The Boundaries of Natural Science

Lecture III

https://rsarchive.org/Lectures/GA322/English/AP1983/19200929p01.html

Dornach

29 Sep 1920

GA322-3

Yesterday's considerations led us to conclude that at one boundary of cognition we must come to a halt within phenomena and then permeate them with what the phenomena call forth within our consciousness, with concepts, ideas, and so forth. It became apparent that the realm in which these ideas are most pure and pellucid is that of mathematics and analytical mechanics. Our considerations then climaxed in showing how reflection reveals that everything present in the soul as mathematics, as analytical mechanics, actually rests upon Inspiration. Then we were able to indicate how the impulses proceeding from Inspiration are diffused throughout the ancient Indian Vedanta: the same spirit from which we now draw only mathematics and analytical mechanics was once the source of the delicate spirituality of the Vedanta. We were able to show how Goethe, in establishing his mode of phenomenology, always strives to find the archetypal phenomenon while remaining within the phenomena themselves and that his search for die archetypal phenomenon that underlies complex phenomena is, inwardly, the same as the mathematician's search for the axiom underlying complex mathematical constructs. Goethe, therefore, who himself admitted that he had no conventional mathematical training, nevertheless sensed the essence of mathematics so clearly that he demanded a method for the determination of archetypal phenomena rigorous enough to satisfy a mathematician. It is just this that the Western wind finds so attractive in the Vedanta: that in its inner organization, in its progression from one contemplation to the next, it reveals the same inner necessity as mathematics and analytical mechanics. That such connections are not uncovered by academic studier of the Vedanta is simply a consequence of there being so few people today with a universal education. Those who engage in pursuits that then lead them into Oriental philosophy have too little comprehension — and, as I have said, Goethe did have this — of the true inner structure of mathematics. They thus never grasp this philosophy's vital nerve. At the one pole, then, the pole of matter, we have been able to indicate the attitude we must assume initially if we do not wish to continue weaving a Penelope's web like the world view woven by recent science but rather to come to grips with something that rests upon a firm foundation, that bears its center of gravity within itself. On the other side there stands, as I indicated yesterday, the pole of consciousness. If we attempt to investigate the content of consciousness merely by brooding our way into our souls in the nebulous manner of certain mystics, what we attain are actually nothing but certain reminiscences that have been stored up in our consciousness since birth, since our childhoods. This can easily be demonstrated empirically. One need think only of a certain man well educated in the natural sciences who, in order to demonstrate that the so-called “inner life” partakes of the nature of reminiscences, describes an experience he once had while standing in front of a bookstore. In the store he saw a book that captured his attention by its title. It dealt with the lower form of animal life. And, seeing this book, he had to smile. Now imagine how astonished he was: a serious scientist, a professor, who sees a book title in a bookstore — a book on the lower animals at that! — and feels compelled to smile! Then he began to ponder just whence this smile might have come. At first he could think of nothing. And then it occurred to him: I shall close my eyes. And as he closed his eyes and it became dark all around him, he heard in the distance a musical motif. Hearing this musical motif in the moment reminded him of the music he had heard as a young lad when he danced for the first time. And he realized that of course there lived in his subconscious not only this musical motif but also a bit of the partner with whom he had hopped about. He realized how something that his normal consciousness had long since forgotten, something that had not made so strong an impression on him that he would have thought it possible for it to remain distinct for a whole lifetime, had now risen up within him as a whole complex of associations. And in the moment in which his attention had been occupied with a serious book, he had not been conscious that in the distance a music box was playing. Even the sounds of the music box had remained unconscious at the time. Only when he closed his eyes did they emerge. Many things that are mere reminiscences emerge from consciousness in this way, and then some nebulous mystics come forth to tell us how they have become aware of a profound connection with the divine “Principle of Being” within their own inner life, how there resounds from within a higher experience, a rebirth of the human soul. And thereby vast mystical webs are woven, webs that are nothing but the forgotten melody of the music box. One can ascribe a great deal of the mystical literature to this forgotten melody of the music box. This is precisely what a true spiritual science requires: that we remain circumspect and precise enough to refrain from trumpeting forth everything that arises out of the unconscious as reminiscences, as mysticism, as though it were something that could lay claim to objective meaning. For it is just the spiritual scientist who most needs inner clarity if he wishes to work in a truly fruitful way in this direction. He needs inner clarity above all when he undertakes to delve into the depths of consciousness in order to come to grips with its true nature. One must delve into the depths of consciousness itself, yet at the same time one must not remain a dilettante. One must acquire a professional competence in everything that psychopathology, psychology, and physiology have determined in order to be able to differentiate between that which makes an unjustifiable claim to spiritual scientific recognition and that which has been gained through the same kind of discipline, as, for example, mathematics or analytical mechanics. To this end I sought already in the last century to characterize in a modest way this other pole, the pole of consciousness, as opposed to the pole of matter. To understand the pole of matter requires that we build upon Goethe's view of nature. The pole of consciousness, on the other hand, was not to be reached so easily by a Goetheanistic approach, for the simple reason that Goethe was no trivial thinker, nor trivial in his feelings when it was a matter of cognition. Rather, he brought with him into this realm all the reverence that is necessary if one seeks to approach the springs of knowledge. And thus Goethe, who was by disposition more attuned to external nature, felt a certain anxiety about anything that would lead down into the depths of consciousness itself, about thinking elaborated into its highest, purest forms. Goethe felt blessed that he had never thought about thinking. One must understand what Goethe meant by this, for one cannot actually think about thinking. One cannot actually think thinking any more than one can “iron” iron or “wood” wood. But one can do something else. What one can do is attempt to follow the paths that are opened up in thinking when it becomes more and more rational, to pursue them in the way one does through the discipline of mathematical thinking. If one does this, one enters via a natural inner progression into the realm that I sought to consider in my Philosophy of Freedom. What one attains in this way is not a thinking about thinking. One can speak of thinking about thinking in a metaphorical sense at best. One does attain something else, however: what one attains is an actual viewing [ Anschauen ] of thinking, but to arrive at this “viewing of thinking,” it is necessary first to have acquired a concrete notion of the nature of sense-free thinking. One must have progressed so far in the inner work of thinking that one attains a state of consciousness in which one recognizes one's thinking to be sense-free merely by grasping that thinking, by “viewing” it as such. This is the path that I sought to follow — if only, as I have said, in a modest way — in my Philosophy of Freedom . What I sought there was first to make thinking sense-free and then to present this thinking to consciousness in the same way that mathematics or the faculties and powers of analytical mechanics are present to consciousness when one pursues these sciences with the requisite discipline. Perhaps at this juncture I might be allowed to add a personal remark. In positing this sense-free thinking as a simple fact, yet nevertheless a fact capable of rigorous demonstration in that it can be called forth in inner experience like the structure of mathematics, I flew in the face of every kind of philosophy current in the 1880s and 1890s. It was objected again and again: this “sense-free thinking” has no basis in any kind of reality. Already in my Theory of Knowledge Implicit in Goethes World Conception , 4 Grundlinien einer Erkenntnistheorie der Goetheschen Weltanschauung , Berlin and Stuttgart, 1886 (A Theory of Knowledge Implicit in Goethes World Conception , Anthroposophic Press, Spring Valley, N.Y.,1968). however, in the early 1880s, I had pointed to the experience of pure thinking, in the presence of which one realizes: you are now living in an element that no longer contains any sense impressions and nevertheless reveals itself in its inner activity as a reality. Of this thinking I had to say that it is here we find the true spiritual communion of humanity and Union with reality. It is as though we have grabbed the coat-tails of universal being and can feel how we are related to it as souls. I had to protest vigorously against what was then the trend in philosophy, that to which Eduard von Hartmann paid homage in 1869 by giving his Philosophy of the Unconscious the motto: “Speculative Results Following the Method of Scientific Induction.” That was a philosophical bow to natural science. I wrote to protest against this insubstantial metaphysics, which arises only when we allow our thinking to roll on beyond the veil of sense as I have described. I thus gave my Philosophy of Freedom the motto: “Observations of the Soul According to the Scientific Method.” I wished to indicate thereby that the content of a philosophy is not contrived but rather in the strictest sense the result of inner observation, just as color and sound result from observation of the outer world. And in experiencing this element of pure thought — an element that, to be sure, has a certain chilling effect on human nature — one makes a discovery. One discovers that human beings certainly can speak instinctively of freedom, that within man there do exist impulses that definitely tend toward freedom but that these impulses remain unconscious and instinctive until one rediscovers freedom in one's own thinking. For out of sense-free thinking there can flow impulses to moral action which, because we have attained a mode of thinking that is devoid of sensation, are no longer determined by the senses but by pure spirit. One experiences pure spirit by observing, by actually observing how moral forces flow into sense-free thinking. What one gains in this way above all is that one is able to bid farewell to any sort of mystical superstition, for superstition results in something that is in a way hidden and is only assumed on the basis of dark intimations. One can bid it farewell because now one has experienced in one's consciousness something that is inwardly transparent, something that no longer receives its impulses from without but fills itself from within with spiritual content. One has grasped universal being at one point in making oneself exclusively a theater of cognition; one has grasped the activity of universal being in its true form and observed how it yields itself to us when we give ourselves over to this inner contemplation. We grasp the actuality of universal being at one point only. We grasp it not as abstract thought but as a reality when moral impulses weave themselves into the fabric of sense-free thinking. These impulses show themselves to be free in that they no longer live as instinct but in the garb of sense-free thinking. We experience freedom — to be sure a freedom that we realize immediately man can only approach in the way that a hyperbola approaches its asymptote, yet we know that this freedom lives within man to the extent that the spirit lives within him. We first conceive the spirit within the element of freedom. We thereby discover something deep within man that weaves together the impulses of our moral-social actions — freedom — and cognition, that which we finally attain scientifically. By grasping freedom within sense-free thinking, by understanding that this comprehension occurs only within the realm of spirit, we experience that while performing this we are indeed within the spirit. We experience a mode of cognition that manifests itself simultaneously as an inner activity. It is an inner activity that can become a deed in the external world, something entirely capable of flowing over into the social life. At that time I sought to make two points absolutely clear, but at that time they were hardly understood. I tried above all to make clear that the most important thing about following such a cognitional path is the inner “schooling” [ Erziehung ] that we undertake. Yes, to have attained sense-free thinking is no small thing. One must undergo many inner trials. One must overcome obstacles of which otherwise one has hardly any idea. By overcoming these obstacles; by finally attaining an inner experience that can hardly be retained because it escapes normal human powers so easily; by immersing oneself in this essence, one does not proceed in a nebulous, mystical way, but rather one descends into a luminous clarity, one immerses oneself in spirit. One comes to know the spirit. One knows what spirit is, knows because one has found the spirit by traveling along a path followed by the rest of humanity as well, except that they do not follow it to its end. It is a path, though, that must be followed to its end by all those who would strive to fulfil the social and cognitional needs of our age and to become active in those realms. That is the one thing that I intimated in my Philosophy of Freedom . The other thing I intimated is that when we have found the freedom that lives in sense-free thinking to be the basis of true morality, we can no longer seek to deduce moral concepts and moral imperatives as a kind of analogue of natural phenomena. We must renounce everything that would lead us to ethical content obtained according to the method of natural science; this ethical content must come forth freely out of super-sensible experience. I ventured to use a term that was little understood at the time but that absolutely must be posited if one enters this inner realm and wishes to understand freedom at all. I expressed it thus: the moral realm arises within us in our moral imagination [ moralische Phantasie ]. I employed this term “moral imagination” with conscious intent in order to indicate that — just as with the creations of the imagination [ Phantasie ] — the requisite spiritual effort is expended within man, regardless of anything external, and to indicate on the other hand that everything that makes the world morally and religiously valuable for us — namely moral imperatives — can be grasped only within this realm that remains free from all external impressions and has as its ground man's inner activity alone. At the same time I indicated clearly in my Philosophy of Freedom that, if we remain within human experience, moral content reveals itself to us as the content of moral imagination but that when we enter more deeply into this moral content, which we bear down out of the spiritual world, we simultaneously enter the external world of the senses. If you really study this philosophy, you shall see clearly the door through which it offers access to the spirit. Yet in formulating it I proceed in such a way that my method could meet the rigorous requirements of analytical mechanics, and I placed no value on any concurrence with the twaddle arising out of spiritualism and nebulous mysticism. One can easily earn approbation from these sides if one wants to ramble on idly about “the spirit” but avoids the inner path that I sought to traverse at that time. I sought to bring certainty and rigor into the investigation of the spirit, and it remained a matter of total indifference to me whether my results concurred with all the twaddle that comes forth from nebulous mystical depths to represent the spirit. At the same time, however, something else was gained in this process. If one pursues further the two paths that I described on the basis of actual observation of consciousness in my Philosophy of Freedom , if one goes yet further, takes the next step — then what? If one has attained the inner experiences that are to be found within the sphere of pure thought, experiences that reveal themselves in the end as experiences of freedom, one achieves a transformation of the cognitional process with respect to the inner realm of consciousness. Then concepts and ideas no longer remain merely that; Hegelianism no longer remains Hegelianism and abstraction no longer abstraction, for at this point consciousness passes over into the actual realm of the spirit. Then one's immediate experience is no longer the mere “concept,” the mere “idea,” no longer the realm of thought that constitutes Hegelian philosophy — no: now concepts and ideas transform themselves into images, into Imagination. One discovers the higher plane of which moral imagination is only the initial projection; one discovers the cognitional level of Imagination. While philosophising, one remains caught within a self-created reality; now, after pursuing the inner path indicated by my Philosophy of Freedom, after transcending the level of imagination [ Phantasie ], one enters a realm of ideas that are no longer dream-images but are grounded in spiritual realities, just as color and tone are grounded in the realities of sense. At this point one attains the realm of Imagination, a thinking in pictures [ bildliches Denken ]. One attains Imaginations that are real, that are no longer merely a subjective inner experience but part of an objective spiritual world. One attains Inspiration, which can be experienced when one performs mathematics in the right way, when this performance of mathematics itself becomes an experience that can then be developed further into that which one finds in the Vedanta. Inspiration is complemented at the other pole by Imagination, and only through Imagination does one arrive at something enabling one to comprehend man. In Imaginations, in pictorial representations [ bildhafte Vorstellungen ] — representations that have a more concrete content than abstract thoughts — one finds what is needed to comprehend man from the point of view of consciousness. One must renounce proceeding further when one has reached this point and not simply allow sense-free thinking to roll on with a kind of inner inertia, nor believe that one can penetrate into the secret depths of consciousness through sense-free thinking. Instead one must have the resolve to call a halt and confront the “external world” of the spirit from within. Theo one will no longer spin thoughts into a consciousness that can never fully grasp them; rather, one will receive Imagination, through which consciousness can finally be comprehended. One must learn to call a halt at this limit within the phenomena themselves, and thoughts then reveal themselves to one as that within cognition which can organize these phenomena; one needs to renounce at the outward limit of cognition and thereby receive the spiritual complement to phenomena in the intellect. In just this way one must renounce in the process of inner investigation, one must come to a halt with one's thinking and transform it. Thinking must be brought inwardly to a kind of reflection [ Reflexion ] capable of receiving images that then unfold the inner nature of man. Let me indicate the soul's inner life in this way [see illustration]. If through self-contemplation and sense-free thinking I approach this inner realm, I must not roll onward with my thinking lest I pass into a region where sense-free thinking finds nothing and can call forth only subjective pictures or reminiscences out of my past. I must renounce and turn back. But then Imagination will reveal itself at the point of reflection. Then the inner world reveals itself to me as a world of Imagination. Now, you see, we arrive inwardly at two poles. By proceeding into the outer world we approach the pole of Inspiration; by proceeding into the inner world of consciousness we approach the pole of Imagination. Once one has grasped these Imaginations it becomes possible to collate them, just as one collates data concerning external nature by means of experiments and conceptual thinking. In this manner one can collate inwardly something real, something that is not a physical body but an etheric body informing man's physical body throughout his whole life, yet in an especially intensive manner during the first seven years. At the change of teeth this etheric body takes on a somewhat different configuration [ Gestalt ], as I described to you yesterday. By having attained Imagination one is able to observe the way in which the etheric or life-body works within the physical body. Now, it would be easy to object from the standpoint of some philosophical epistemology or other: if he wishes to remain logical, man must remain within the conceptual, within what is accessible to discursive thinking and capable of demonstration in the usual sense of the term. Fine. One can philosophise thus on and on. Yet however strong one's belief in such an epistemological tissue, however logically correct it may be, reality does not manifest itself thus; it does not live in the element of logical constructs. Reality lives in pictures, and if we do not resolve to achieve pictures or Imaginations, man's real nature shall elude our grasp. It is not at all a matter of deciding beforehand out of a certain predilection just what form knowledge must take in order to be valid but rather of asking reality in what form it wishes to reveal itself. This leads us to Imagination. In this way, then, what lives within moral imagination manifests itself as the projection into normal consciousness of a higher spiritual world that can be grasped in Imagination. And thus, ladies and gentlemen, I have led you, or at least sought to lead you, to the two poles of Inspiration and Imagination, which we shall consider more closely in the next few days in the light of spiritual science. I had to lead you to the portal, as it were, beforehand, in order to show that the existence of this portal is well founded in the normal scientific sense. For it is only upon such a foundation that we later can build the edifice of spiritual science itself, which we enter through that portal. To be sure, in traversing the long path, in employing the extremely demanding epistemological method I described to you today — which many may feel is difficult to understand — one must have the courage to come to grips not only with Hegel but also with “anti-Hegel.” One must not only pursue the Hegelianism that I sought to depict in my Riddles of Philosophy ; 5 Die Rätsel der Philosophie in ihrer Geschichte als Umriss dargestellt , Berlin, 1914 ( Riddles of Philosophy , Anthroposophie Press, Spring Valley, N.Y, 1973). one must also learn to give Stirner his due, for in Stirner's philosophy there lies something that rises out of consciousness to reveal itself as the ego. And if one simply gives rein to this ego that comes forth out of instinctive experiences, if one does not permeate it with that which manifests itself as moral imagination and Imagination, this ego becomes antisocial. As we have seen, Philosophy of Freedom attempts to replace Stirner's egoism with something truly social. One must have the courage to pass through the instinctive ego Stirner describes in order to reach Imagination, and one must also have the courage to confront face-to-face the psychology of association that Mill, Spencer, and other like-minded proponents have sought to promulgate, a psychology that seeks to comprehend consciousness in a bare concept but cannot. One must have the courage to realize and admit to oneself that today we must follow another path entirely. The ancient Oriental could follow a path no longer accessible to us, in that he formulated his experiences of an inner mathematics in the Vedanta. This path is no longer accessible to the West. Humanity is in a process of constant evolution. It has progressed. Another path, another method, must be sought. This new method is now in its infancy, and its immaturity is best revealed when one realizes that this psychology of association, which seeks to collate inner representations according to laws in the same way one collates the data of natural phenomena, is nothing but the inertia of thinking that wants to break through a boundary but actually enters a void. To understand this one must come to know this psychology of association for what it really is and then learn to lead it over through an inner contemplative viewing [ Schauung ] into the realm of Imagination. Just as the Orient once saw the Vedanta arise within an element of primal mathematical thought and was able to enter thus into the spirituality of the external world, so we must seek the spirit in the way in which it tasks us today: we must look within and have the courage to proceed from mere concepts and ideas to Imaginations, to develop this pictorial consciousness within and thereby to discover the spirituality within ourselves. Then we shall be able to bear this spirituality back out into the external world. We shall have attained a spirituality grasped by the inner being of man, a spirituality that thus can bear fruit within the social life. The quality of our social life shall depend entirely on our nurturing a mode of cognition such as this, which can at the same time embrace the social. That this is the case I hope to show in the lectures yet to follow.

The Boundaries of Natural Science

Lecture IV

https://rsarchive.org/Lectures/GA322/English/AP1983/19200930p01.html

Dornach

30 Sep 1920

GA322-4

Today it will be necessary to come to terms with a number of things that actually can be understood only if one is able to overcome certain prejudices that have long been cultivated and zealously inculcated right up to the present day. Much of what shall be said here today, and further substantiated tomorrow, must be comprehended through raising oneself up to an inner viewing [ Anschauung ] of the spirit. You must consider that when the results of a scientific investigation of the spirit are met with a demand for proof such as is recognized by contemporary science or jurisprudence, or even contemporary social science — which is so useless in the face of life itself — one does not get very far at all. For the true spiritual scientist must already bear this method of demonstration within himself. He must have schooled himself in the rigorous methods of contemporary science, even of the mathematical sciences. He must know what mode of demonstration is demanded in these circles, and he must suffuse the processes of his whole inner life with this method: therein he builds the foundation for a higher mode of cognition. For this reason it is usually the case that when the demands of normal consciousness are placed before the spiritual scientist, he is thoroughly at home in the field from which the question stems. He has long since anticipated the objections that can be raised. One could even go so far as to say that he is only a spiritual scientist in the true sense of the word — in the sense in which we characterized spiritual science yesterday — to the extent that he has subjected himself to the rigorous discipline of the modern scientific method and knows at least the tenor of modern scientific thought quite well. I must make this one preliminary remark and add one other. If one cannot transcend the manner of demonstration that experimentation has made scientific habit, one shall never attain knowledge that can benefit society. For in a scientific experiment one proceeds — even if one cherishes the illusion that it is otherwise — in such a way that one moves in a certain direction and allows phenomena to confirm what lives within the ideas one has formulated as a natural law, or perhaps mathematically. Now, when one is required to translate one's knowledge into social judgments, in other words, if the ideas that one has formulated as the natural laws of contemporary anthropology or biology or Darwinism — no matter how “progressive” this Darwinism might be — are to have validity; if one wants to translate them into a social science that can become truly practical, this knowledge obtained through experimentation is totally inadequate. lt is totally inadequate because one cannot simply sit in a laboratory and wait to see what one's ideas call forth when they are applied to society. Thereby thousands upon thousands of people could easily die or starve or be made to suffer in some other way. A great part of the misery in our society has been called forth in just this way. Because they have originated in pure experimentation, our ideas have gradually become too narrow and impoverished to subsist in reality, which they must be able to do if thought is ever to enrich the sphere of practical life. I have already indicated the stance the spiritual scientist must take regarding the two boundaries that arise within cognition — the boundaries at the poles of matter and consciousness — if he is to attain knowledge that can reflect light back into nature and at the same time forward into the social future. I have shown that at the boundary of the material world one must not allow one's thinking to roll on with its own inertia in order to construct mechanistic, atomistic, or molecular world conceptions tending toward the metaphysical but call a halt at the boundary and develop instead something that normally is not yet present as a faculty of cognition. One must develop Inspiration. On the other hand, I have shown you that if one wishes to come to an understanding of consciousness, one must not attempt, as Anglo-American associative psychology does, to penetrate into consciousness with ideas and concepts called forth by the natural world. It must be entirely clear in one's mind that consciousness is constituted such that these ideas culled from the external world can gain no access. We must abandon such ideas and seek rather to enter the realm of Imaginative cognition. In order to achieve self-knowledge we must permeate the concepts and ideas with content, so that they become images. Until the view of man which was born in the West and now has all of civilization in its grasp is transformed into Imaginative cognition, we shall never progress in coming to terms with this second boundary presenting itself to normal human cognition. At the same time, however, one can say that humanity has evolved from certain stages, now become historical, to the point that requires that it progress to Inspiration on the one hand and Imagination on the other. Whoever is able to perceive what humanity is undergoing at the present, what is just beginning to reveal its first symptoms, knows that forces are rising out of the depths of human evolution that tend toward the proper introduction of Imagination and Inspiration into human evolution. Inspiration cannot be attained except by exercising a certain faculty of mental representation in the way that I described in my book, Knowledge of the Higher Worlds and Its Attainment , and shall describe at least in outline in the coming lectures. When one has progressed far enough in a kind of inner self-cultivation, a schooling of the self in a certain form of mental representation [ Vorstellen ]; when one schools oneself to live within the realm of representations, ideals, and concepts that live within the mind — then one learns what it means to live in Inspiration. For when one exercises consciously the faculty that otherwise “mathematicizes” within us during the first seven years up to the change of teeth (in normal life and in conventional science this occurs unconsciously), when one enters into this “living mathematics,” into this “living mechanics,” it is as though one were to fall asleep, entering not into unconsciousness or nebulous dreams but into a new form of consciousness that I shall begin to describe to you today. One takes up into full consciousness what otherwise works within as the sense of balance, the sense of movement, and the sense of life. It is as though one were to wrest from oneself what otherwise lives within as sensations of balance, movement, and life so that one lives within them with the extended mathematical representations. Tomorrow I shall speak about this at greater length. One passes over into another consciousness, within which one experiences something like a toneless weaving in a cosmic music. I cannot describe it otherwise. One unites with this weaving in a toneless music in a way similar to that by which one makes the physical body one's own through the activity of the ego in childhood. This weaving in a toneless music provides the other, rigorously demonstrable awareness that one is now outside the body with one's soul-spirit. One begins to comprehend that even in normal sleep one's soul-spirit is outside the body. Yet the experience of sleep is not permeated with that which vibrates when leaving the body consciously through one's own initiative, and one experiences initially something like an inner unrest, an inner unrest that exhibits a musical quality when one enters into it with full consciousness. This unrest is gradually elucidated when the musical element one experiences there becomes a kind of wordless revelation of speech from the spiritual cosmos. These matters naturally appear grotesque and paradoxical to these who hear them for the first time. Yet much has arisen in the course of cosmic evolution that first appeared paradoxical and grotesque, and human evolution will not advance if one wishes to pass over these phenomena only half-consciously or unconsciously. Initially one has only a certain experience, an experience of a kind of toneless music. Then out of this experience of toneless music there arises something which, when experienced, enables us to comprehend inwardly a content as meaningful as that which is conveyed to us when we listen outwardly to a man who speaks to us via sensible words. The spiritual world simply begins to speak, and one has only to begin to acquire an experience of this. Then one comes to experience something at a higher level. One no longer only weaves and lives in a toneless music and no longer merely perceives the speech of the super-sensible spiritual world: one begins to recognize the contours of something that reveals itself within this super-sensible world, the contours of beings. Within this universal spiritual speech that one initially encounters there emerge individual spiritual beings, in the same way that we, listening at a lower level to the speech of another man, crystallize or organize — if I may use such trivial expressions — what reveals itself as his soul and spirit into something substantial. We begin to live within the contemplation and knowledge of a spiritual reality. This realm of the spirit replaces the vacuous, insubstantial, metaphysical world of atoms and molecules: it confronts us as the reality that lies behind the phenomena of the sense world. We no longer stand in the same relation to the boundary of the material world as when we allow conceptualizing to roll on with its own inertia, attempting to carry the kind of thinking developed through interaction with the sense world beyond the boundary. Now we stand in a relationship to this boundary of sense such that the spiritual content of the world suddenly stands revealed there. This is one boundary to cognition. Ladies and gentlemen, humanity at this point in its evolution is yearning to step out of itself, to step out of the body in this way, and one can see this tendency exemplified quite clearly in certain individuals. Human beings seek to withdraw from their bodies that which the spiritual scientist withdraws with full consciousness. The spiritual scientist withdraws this in a way analogous to the way in which he applies inwardly obtained concepts in a systematic, organized fashion to the natural world. As some of you will know, for some time now a great deal of attention has been paid to a remarkable illness. Psychologists and psychiatrists term this “pathological questioning or doubt” [ Grübelsucht; Zweifelsucht ]; it would perhaps better be termed “pathological skepticism.” One now encounters innumerable instances of this illness in the most remarkable forms, and it is already necessary that the study of this disease in particular be promoted within the cultural context of our time. This illness manifests itself — you can learn a great deal about it from the psychiatric literature — in these people, from a certain age onward, usually from puberty or the period immediately preceding puberty, no longer being able to relate properly to the external world. When confronted with their experiences in the external world, these people are overcome by an infinite number of questions. There are certain individuals who, though they remain otherwise fully rational, can pursue their duties to a great extent and are fully cognizant of their condition, must begin to pose the most extraordinary questions if they are but slightly withdrawn from what normally binds them to the external world. These questions simply intrude into their life and cannot be brushed aside. They intrude themselves especially strongly in individuals with healthy, or even conspicuously healthy, organizations — in individuals who have an open mind and a certain understanding for the manner in which modern scientific thinking proceeds. They experience modern science in this way, so that they cannot understand at all how such questions arise unconsciously thereby. Such phenomena are evident especially in women, who have less robust natures than men and who also tend to acquire their knowledge of natural science, if they undertake to do so, not so much through the highly disciplined scientific literature but rather through works intended for laymen and dilettanti. For if at this time immediately before puberty, or just when puberty is on the wane, there should occur an intense preoccupation with modern scientific thought in the way I have just described, among such people a high incidence of this disease can be observed. It manifests itself in these people having then to ask: where ever does the sun come from? And no matter how clever the answers one gives them, one question always calls forth another. Where does the human heart come from? Why does it beat? Did I not forget two or three sins at confession? What happened when I took Communion? Did a few crumbs of the Host perhaps fall to the ground? Did I not try to mail a letter somewhere and miss the slot? I could produce a whole litany of such examples for you, and you would see that all this is eminently suited to keeping one uneasy. Now, when the spiritual scientist comes to consider this matter he feels himself right at home. It is simply a manifestation of the element in which the spiritual scientist resides consciously when he achieves an experience of the toneless musical speech of spiritual beings through Inspiration. Those afflicted with pathological skepticism enter this region unconsciously. They have cultivated nothing that would enable them to comprehend the state into which they enter. The spiritual scientist knows that throughout the entire night, from falling asleep until waking, one lives in an element consisting entirely of such questions, that out of the sleeping state countless questions arise within one. The spiritual scientist knows this condition, because he can experience it consciously. Whoever approaches these matters from the standpoint of normal consciousness and seeks thus to comprehend them will perhaps make attempts at all kinds of rationalistic explanations, but he will not arrive at the truth, because he is unable to comprehend the matter through Inspirative cognition. Such a one sees that there are, for example, people who go to the theater in the evening and on leaving the theater are helpless to resist the countless questions that overcome them: what is this actress's relationship to the outer world? What was that actor doing some previous year? What are the relationships between the individual actors and actresses? How was this or that flat constructed? Which painter is responsible for each? and so on, and so on. For days on end such people are subject to the influence of this pesky questioner within. This is a pathological condition that one begins to understand only by realizing that these people enter a region the spiritual scientist experiences in Inspiration by approaching this realm differently from these afflicted with this pathological condition. Persons in this pathological state enter the same region as the spiritual scientist, but they do not take their egos with them; in a certain sense they lose their egos upon entering this realm. And it is just this ego that is the ordering faculty. It is the ego that is capable of bringing the same kind of order into this world as we are able to bring to our physical environment. The spiritual scientist knows that one lives in this same region between falling asleep and waking. Everyone who returns from the theater actually is deluged by all these questions in the night while he sleeps, but due to the operation of certain laws sleep normally spreads itself out over this interlocutor, so that one has finished with him by the time one awakes again. In order to perform valid spiritual research, one must bear into this region unimpaired judgment, complete discretion, and the full force of the human ego. Then we do not live in this region in a kind of super-skepticism but rather with just as much self-possession and confidence as in the physical world. And actually all the meditative exercises that I have given in my book, Knowledge of the Higher Worlds and Its Attainment , are intended in large part to result in a greater ability to enter this region preserving one's ego in full consciousness and in strict inner discipline. The purpose of a large part of the spiritual scientist's initial schooling is to keep him from losing the inner support and discipline of the ego while traversing this path. The finest example in recent times of a man who entered this region without full preparation is someone whom Dr. Husemann has characterized here in another context. The finest example is Friedrich Nietzsche. Nietzsche is, to be sure, an extraordinary personality. In a certain sense he was not an intellectual at all. He was not your conventional scholar. With the tremendous gifts of genius, however, he grew out of puberty into scientific research; with these tremendous gifts he was able to take in what the contemporary sciences can offer. That, despite having acquired this knowledge, he did not become a scholar of the conventional sort is shown quite simply by the polemics of so exemplary a modern scholar as Wilamowitz, who came out in opposition immediately after the appearance of the young Nietzsche's first publication. Nietzsche had just published his treatise, The Birth of Tragedy out of the Spirit of Music , in which there resounds a readiness to undergo initiation, to enter the musical, the Inspirative — even the title reveals his yearning for the realm that I have characterized — but he could not. The possibility did not exist. In Nietzsche's time a conscious spiritual science did not exist, but in giving his work the title, The Birth of Tragedy out of the Spirit of Music , he indicated that he wished to come to terms with a phenomenon such as Wagnerian tragedy out of this spirit of music. And he entered further and further into this realm. As I said, Wilamowitz immediately came out in Opposition and wrote his polemics against The Birth of Tragedy , in which he completely rejected from his academic point of view what Nietzsche, unschooled but yearning for knowledge, had written. From the point of view of modern science he was of course completely justified. And actually it is hard to understand how so excellent a thinker as Erwin Rohde could have believed a compromise was possible between this modern philology that Wilamowitz represented and what lived within Nietzsche as a dark striving, as a yearning for initiation, for Inspiration. What Nietzsche had acquired in this manner, had inwardly appropriated, grew out into the other fields of contemporary sciences. It grew into positivism, namely that of the Frenchman, Comte, and the German, Dühring. While cataloguing Nietzsche's library in the 1890s I saw with my own eyes all the marks Nietzsche had so conscientiously made in the margins of Dühring's works, from which he acquired his knowledge of positivism; I held all these books in my own hand. I could enter sympathetically right into the manner in which Nietzsche took positivism up into himself. I could well imagine how he then reverted to an extra-corporeal existence, where he experienced this positivism again without having penetrated into this region sufficiently with his ego. As a result, he produced works such as Human, All Too Human , exhibiting a constant oscillation between an inability to move within the world of Inspiration and a desire to remain there nonetheless. One notices this in the aphoristic progression of Nietzsche's style in these works. Nietzsche strives to bring his ego into this realm, but it tears itself away again and again: thus he produces not a systematic, artistic presentation but only aphorisms. It is just this constant self-interruption in aphorism that reveals the inward soul of this remarkable spirit. And then he rises to encounter that which has provided modern science, the contemporary physical sciences, with their greatest riddles. He rises up to encounter what lives in Darwinism, what lives in the theory of evolution, and attempts to demonstrate how the most complicated organisms have gradually arisen out of the most primitive. He penetrates into this realm, a realm into which I have sought in a modest way to bring inner structure and an inward mobility — you can follow this in the discussion of Haeckel in my book, The Riddles of Philosophy . Nietzsche enters this realm, and there emerges from his soul the notion of a kind of super-evolution [ Überevolutionsgedanke ]. He follows the course of evolution up to man, where this notion of evolution explodes to create his “super-man.” In following this self-progression of evolving beings he loses the content, because he is unable to obtain the true content through Inspiration: he is confined to the empty idea of “eternal recurrence.” Only by virtue of the inner integrity of his personality was Nietzsche able to avoid what the pathologist calls “pathological skepticism.” It was something within Nietzsche, a prodigious health that Nietzsche himself sensed underlying his debility, that asserted itself and kept him from falling prey to complete skepticism, leading him rather to contrive what later became the content of his most inspiring words. No wonder, then, that this excursion into the spiritual world, this striving to proceed from music to the inner word, to inner being, culminated in the most unmusical of ideas — that of “the eternal recurrence of the same”— and the empty, merely lyrical “superman.” No wonder that it had to end in the condition that his physician, for example, diagnosed as an “atypical case of paralysis.” Yes, this man who did not know Nietzsche's inner life, who was incapable of judging it from the standpoint of spiritual science and confronted the images and ideas of Nietzsche's inner life as a mere psychiatrist, without sympathetic understanding — this man found only an abstraction to answer the question posed by the concrete case before him. With regard to all nature du Bois-Reymond had said in 1872: ignorabimus . Confronted with exceptional cases, the psychiatrist says: paralysis, atypical paralysis. Confronted with concrete cases that reveal the essence of present human evolution, the psychiatrist can say only ignorabimus , or ignoramus . This is but a translation of what is clothed in the words “atypical case of paralysis.” This eventually destroyed Nietzsche's body. It produced the condition that makes Nietzsche such a revealing phenomenon within our contemporary cultural life. This is the other form of the debility appearing in certain highly cultivated individuals, which psychiatrists term pathological doubt or hyper-skepticism. And the phenomenon of Nietzsche — here I must be allowed a personal remark — stood before my eyes the moment that, trembling, I entered his room in Naumburg a few years after his illness. He lay upon the sofa after dinner, staring into space. He recognized nobody around him and stared at one like a complete idiot, but the light of his former genius still gleamed within his eyes. If one looked at Nietzsche knowing all one could about his world view, about the ideas and images that lived within his soul; if, unlike the mere psychiatrist, one stood before Nietzsche, this ruin of a man, this physical wreck, with this image in one's soul, then one knew: this man strove to view the world revealed by Inspiration. Nothing of this world came forth to him. And the part of him that desired to achieve Inspiration finally extinguished itself: for years the physical organism was filled by a soul-spirit devoid of content. From such a sight one can learn the whole tragedy of our modern culture, its striving for the spiritual world, its inclination toward that which can proceed from Inspiration. For me — and I do not hesitate in the slightest to introduce a personal remark here — this was one of those moments that can be interpreted in a Goethean manner. Goethe says that nature conceals no secret that she is not willing to reveal in one place or another. No, the entire world contains not a single secret that is not revealed in one place or another. The present stage of human evolution conceals the secret that humanity is giving birth to a striving, an inclination, an impulse that rumbles within the social upheavals our civilization is undergoing — an impulse that seeks to view the spiritual world of Inspiration. And Nietzsche was the one point where nature revealed its open secret, where the striving that exists within humanity as a whole could reveal itself. We must seek this if all those striving for education, seeking within modern science — and this shall be the entire civilized world, for education must become universal — if humanity as a whole is not to lose its ego and civilization fall into barbarism. That is one great cultural anxiety, one great threat to civilization, which must be faced by anyone who follows the contemporary progress of human evolution and seeks to develop a thinking that can grasp the realities of social life. Similar phenomena assert themselves on the other side as well, on the side of consciousness. And we shall have to study these phenomena on the side of consciousness at least in outline as well. We shall see how these other phenomena arise out of the chaos of contemporary life, phenomena that appear pathologically and have been described by Westphal, Falret, and others. It is no accident that these have been described only just in the most recent decades. On the other side, that of the boundary of consciousness, we encounter the phenomena of claustrophobia, astraphobia, and agoraphobia, 6 “Astraphobia” = morbid dread of storms; “agoraphobia” = morbid dread of crossing, or being in, open spaces. just as we encounter pathological skepticism on the side of matter. And in the same way (we shall discuss this further) in which pathological skepticism must be cured culturally-historically through the cultivation of Inspiration — one of the great talks of contemporary social ethics — we are threatened with the emergence of the phenomena that I shall describe tomorrow: claustrophobia, astraphobia, and agoraphobia. These emerge pathologically and can be overcome through Imagination, which, when civilization has acquired it, shall become a social blessing for all humanity.

The Boundaries of Natural Science

Lecture V

https://rsarchive.org/Lectures/GA322/English/AP1983/19201001p01.html

Dornach

1 Oct 1920

GA322-5

Yesterday I closed with a consideration of what reveals itself at one boundary of scientific thinking as a real and true mode of cognition: I closed with a characterization of Inspiration. I have brought to your attention the way in which man enters through Inspiration a spiritual world: he knows that he is in this world and feels also that he is outside the body. I have shown you how the transition from the experience of a “toneless” musical element to a merger with an individuated element of being occurs. It also became clear in the course of yesterday's considerations of pathological skepticism and hypercriticism that pathological conditions can arise within man if he takes this step out of the body without the accompaniment of the ego, if he does not suffuse the conditions he experiences in Inspiration with full self-consciousness. If one brings the ego into Inspiration, Inspiration represents a healthy, indeed a necessary, step forward in human cognition. Yet in a cultural epoch such as ours, in which man's being is striving to free itself from the physical organism, one cannot allow this condition to come about in an instinctive, unconscious, unhealthy way without the emergence of the pathological conditions we discussed yesterday. For, you see, there exist two poles in human nature. We can either turn to what opens a free, spiritual vision of the highest realities, or, by shunning this, by not summoning sufficient courage to penetrate into these regions with full consciousness but allowing ourselves to be driven by unconscious forces within ourselves, we can call forth illness in the physical organism. And it would be a grave error to believe that one could guard against this illness by electing not to strive into the actual spiritual world. Illness will occur anyway, if the instincts are allowed to drive the astral body, as we call it, out of the organism. Yet especially at the present time, even if we do not investigate the spiritual world ourselves, we are fully protected against the pathological states that I described yesterday — even against those arising only in the soul — by seeking to comprehend rationally the ideas of spiritual science. What is it, however, that we bear into the spiritual world when we take full consciousness with us? You need only follow somewhat man's development from birth to the change of teeth and beyond in Order to realize that, besides the development of speech, thinking, and so forth, an especially important element in this human development is the gradual emergence and transformation of memory. If you then look at the course of human life, you will come to see the tremendous importance of memory for a fully human existence. If, as a result of certain pathological conditions, the continuity of memory is interrupted, so that we cannot recall certain experiences we have had, then a serious illness befalls us, for we feel that the thread of the ego, which otherwise runs through our lives, has been broken. You can consult my book, Theosophy , 7 Theosophie. Einfuhneng in ubersinnliche Welterkenntnis und Menschenbestimmung , Berlin, 1904 ( Theosophy. An Introduction to the Supersensible Knowledge of the World and the Destination of Man , Anthroposophie Press, Spring Valley, N.Y., 1971). on this: memory is intimately connected with the ego. Thus in pursuing the path I have characterized we must take care not to lose what manifests itself in memory. We must take along with us into the world of Inspiration the power of soul that provides us with memory. Just as in nature everything changes, however — just as the plant, in growing, metamorphoses its green leaves into the red petals of the flower; just as everything in nature is in constant metamorphosis, so it is with everything concerning human existence. If we really bear the faculty of memory out into the world of Inspiration under the full influence of ego-consciousness, it metamorphoses itself. Then one comes to realize that in the moment of one's life in which one investigates the spiritual world in Inspiration, one does not have the normal faculty of memory at one's disposal. One has this faculty of memory at one's disposal in healthy life within the body; outside the body, this faculty is no longer available. This results in something extraordinary — something that, since I present it to your mind's eye for the First time, might seem paradoxical, yet that is fully grounded in reality. Whoever has become a true spiritual scientist, who enters and seeks to experience through Inspiration actual spiritual reality as I have described it in my books, must experience this reality each time anew if he wishes to have it present to consciousness. Thus whenever someone speaks out of Inspiration concerning the spiritual world — not from notes or from mere memory but when he expresses immediately what reveals itself to him in the spiritual world — he must perform the task of spiritual perception each time anew. The faculty of memory has transformed itself. One has retained only the power to call forth the experience again and again. For that reason the spiritual scientist does not have it so easy as one who relies on mere memory. He cannot simply communicate some information out of memory but must call forth anew each time what presents itself to him in Inspiration. In this matter it is essentially the same as it is in normal sense perception of the physical world. If you wish actually to perceive within the physical world of the senses, you cannot turn away from what you wish to perceive and still have the same perception in another place. You must return to the object. In the same way, the spiritual scientist must return to the Same spiritual content of consciousness. And just as in physical perception one must learn to move about in space in order to perceive this or that in turn, the spiritual scientist who has attained Inspiration must learn to move freely within the element of time. He must be able — if you will allow me to use a paradoxical expression — to swim within the element of time. He must learn to travel along with time itself, and when he has learned this, he finds that the faculty of memory has undergone a metamorphosis, that the faculty of memory has transformed itself into something else. What memory performed within the physical world of the senses must be replaced by spiritual perception. This transformed memory, however, gives the spiritual scientist perception of a more encompassing ego. Now the ego is recognized to be more encompassing. When one has transformed memory, which contains the power of the ego between birth and death, the content of the ego cracks the husk that circumscribes but one lifetime. Then the fact of repeated earthly incarnations, alternating with a purely spiritual existence between death and rebirth, emerges as something that can be grasped as a reality. On the other side, the side of consciousness, there emerges something different when one seeks to avoid what an ancient view of the spirit, that of the Vedanta, did not yet know. We in the West feel on the one hand the loftiness of the spiritual view when we steep ourselves in the ancient Oriental wisdom. We feel that in the Vedanta the soul was borne up into spiritual regions in which it could move in a way that the Westerner's normal consciousness can only in mathematical, geometrical, analytic-mechanical thinking. When we descend into the expansive realms that in the Orient were accessible to normal consciousness, however, we find something that we Westerners, because of our more advanced state of evolution, can no longer bear: we find an extensive symbolism, an allegorization of the natural world. It is this symbolism, this allegorization, this thinking about external nature in images, that makes us clearly aware that we are being led away from reality, away from a true investigation of nature. This has become part of certain religious confessions. Certain religious confessions are at a loss how to proceed with this act of symbolization, of mythologization, which has become decadent. For us in the West, that which the Oriental, living in an illusory world, applied directly in this way to external nature, that with which he believed himself capable of arriving at insights concerning the natural world — for us at present this has value only as an exercise preliminary to further spiritual research. We must acquire the soul faculty that the Oriental employed in symbolism and anthropomorphism. We must exercise this faculty inwardly and remain fully conscious thereby: we lapse into superstitions, into rhapsodic enthusiasm for nature, if we employ this faculty to any end but the cultivation of our soul. Later I shall have occasion to speak here about the particulars of this — which, by the way, you can find in my book, Knowledge of the Higher Worlds and Its Attainment . By taking this faculty that the Oriental turned outward and employing it inwardly, as an activity of inner schooling [ Kraft des Übens ], by first developing a pictorial representation in such a way within, one actually begins to arrive at new insights on the other side, on the side of consciousness. One gradually achieves a transformation of abstract, merely notional thinking into pictorial thinking. Then there arises what I can only call an experiential thinking [ erlebendes Denken ]. One experiences pictorial thinking. Why does one experience this? One experiences nothing other than what is active within the physical body during the first years of childhood, as I have described it to you. One experiences not the human organism that has taken static form in space but rather what lives and weaves within man. One experiences it in pictures. One gradually struggles through to a viewing of the life of the soul in its actuality. On the other side the content of consciousness gradually emerges within cognition: pictorial representation, a life within Imagination. And without entering into this life of Imaginations, modern psychology shall not progress. In this way, and in this way only, by entering into Imagination, there will arise again a psychology that is more than word-games, a psychology that actually looks into the soul of man. Just as the time has come in which, as a result of general cultural relationships, man is gradually excarnating from the physical body and striving for Inspiration, as we have seen in the example of Nietzsche, the time has come in which man, if he desires self-knowledge, should feel himself led toward Imagination. Man must descend deeper into himself than was necessary in the course of previous cultural history. If evolution is not to lapse into barbarism, humanity must attain a true image of itself [ Selbstschau ], and humanity can accomplish this only by accepting the knowledge offered by Imagination. That man is striving to descend deeper into his inner self than has been the case in evolution heretofore is shown, again, in the phenomena of pathological diseases of a particularly modern form. These have been described very recently by those who are able to study them from the point of view of medicine or psychiatry. It is shown above all in the emergence of agoraphobia, claustrophobia, and astraphobia — illnesses of a sort that arise especially frequently in our time. Even if they usually are observed only as pathological conditions requiring psychiatric treatment, the more acute observer can see something else altogether. He sees agoraphobia, astraphobia, and so forth already emerging from the soul-nature of humanity, just as he saw Inspiration arising pathologically in Friedrich Nietzsche. Above all, he can observe states of soul that often appear outwardly normal from which emerges agoraphobia — morbid dread of open spaces. He sees emerging something that appears as astraphobia, a state in which one fails to come to terms with an inner sensation. This inner feeling can grow to the extent that the Organs of digestion are attacked, and digestion is disturbed. He comes to know what might be called fear of isolation, agoraphobias, 8 The German edition gives “claustrophobia” here, which seems to be a mistake. in which one cannot remain atone but only where there is company assembled all around and so forth. Such things emerge. These things show that humanity is presently striving for Imagination and that an illness that must otherwise become an illness of the entire culture can be counteracted only by developing Imagination. Agoraphobia — this is an illness that manifests itself in many people in a frightening way. These people grow up, and from a certain point in their lives onward remarkable conditions manifest themselves. If such a person steps out of the house into a square devoid of people he is stricken with a fear that is entirely incomprehensible to him. He is afraid of something; he does not dare go a step further into the empty square, and if he does, it can happen that he falls down on his knees or perhaps even topples over in a faint. The moment that even a child comes, the sufferer grasps its arm or merely reaches out to touch the child: in this moment he feels himself inwardly strengthened again, and the agoraphobia subsides. One case that has been described in the medical literature is particularly interesting. A young man who felt himself strong enough even to become an officer is overcome by agoraphobia while on maneuvers as he is sent out to map some terrain. His fingers tremble; he is unable to draw. Wherever there is emptiness around him, or what he perceives as emptiness, he is beset with fears that he immediately senses to be pathological. He is in the vicinity of a mill. In order to be able to perform his duty at all, he must keep a small child at his side, and its mere presence is enough for him to be able to resume drawing. We ask ourselves: what is the cause of such phenomena? Why is it that there are, for example, people who, when they have somehow forgotten to leave open the door to their bedrooms at night — something that has perhaps long since become a habit with them — wake in the night dripping sweat and can do nothing but leap up to open the door, for they cannot stand to be in an enclosed space. There are such people. Some suffer to such an extent that they must have all the doors and windows open. If their house is on a square, they must leave open the door leading out, so that they know they are free and can get out into the open at any time. This claustrophobia is something that one sees emerging — even if it often does not emerge in so radical a form — if one is able to observe human states of soul more closely. And then there are people who feel, even to a physical degree, something inexplicable happening within them. What is it? It is an approaching thunderstorm or some other atmospheric condition. There are otherwise intelligent people who must draw the curtains whenever there is lightning or thunder. Then they must sit in a dark room, for only in this way can they protect themselves from what they experience in the atmospheric conditions. This is astraphobia, or morbid fear of thunderstorms. What is the cause of these states that we observe already very clearly in the souls of human beings today, especially in those who for a long time surrender themselves devoutly to a certain dogmatism? In these people one observes precisely these states of soul, even if they have not manifested themselves yet physically. These states are just beginning to appear. Their emergence works to upset a balanced, calm approach to life. They also emerge in such a way that they call forth all kinds of pathological conditions that are ascribed to every sort of thing, because the physical symptoms of claustrophobia, agoraphobia, or astraphobia are not yet manifest, while they must actually be ascribed to the particular configuration of soul arising within man. What is the cause of such conditions? They are the result of our need not only to experience the life of the soul discarnately but also to bring this experience of the discarnate soul down into the physical body. We must allow it to immerse itself consciously. Just as that which I have described to you in the course of these lectures gradually extricates itself from the body between birth and the change of teeth, so also that which is experienced externally, which we could call experience of the astral, immerses itself again in the physical organism between the change of teeth and puberty. And what takes place in puberty is nothing other than this immersion between approximately the seventh and fourteenth years. The independent soul-spirit that man has developed must immerse itself in the body again, and what then emerges as physical love, as sexual desire, is nothing other than the result of this immersion I have described to you. One must come to understand this immersion clearly. Whoever wishes to gain a true understanding of the basis of consciousness must be able to effect this in a fully conscious, healthy way, using such methods as I shall describe here later. That is to say, he must learn to immerse himself in the physical body. Then he attains an initial experience of what manifests itself as an Imaginative representation of the inner realm. Here a faculty of formal representation framed for an external, three-dimensional world of plastic forms is insufficient. To perform this inner activity one needs a mobile faculty of formal representation: one must be able to overcome gradually everything spatial in Imagination and to immerse oneself in the representation of something intensive, something that radiates activity. In short, one must immerse oneself in such a way that in descending one can still clearly differentiate between oneself and one's body. Whatever inheres in the subject cannot be known. If one can keep what one experiences outside from immersing unconsciously in the physical body, one descends into the physical body and experiences in descending the essence of this body up to the level of consciousness in Imagination, in pictures. Whoever fails to keep these pictures separate, however, and allows them to slip into the physical body, confronting the physical body not as an object but as something subjective, brings the sensation of space down into the physical body with him The astral thereby coalesces with the physical to a greater degree than should be allowed. The experience of the external world coalesces with man's inner life, and because he makes subjective what should have remained objective, he can no longer experience space normally. Fear of empty space, fear of lonely places, fear of the astrality diffused through space, of Storms, perhaps even of the moon and Stars, rise up within one. One lives too deeply within oneself. Thus it is necessary that all exercises leading to the life of Imagination protect one against descending too deeply into the body. One must immerse oneself in the body in such a way that the ego remains outside. One may not take the ego out into the world of Imagination in the way that one must carry the ego out into the world of Inspiration. Although one worked toward Imagination through a process of symbolization, through pictorial representation, in Imagination itself all pictures created by mere fantasy disappear. Now objective pictures emerge instead. Only that which actually lives within the human form ceases to confront one as an object. One loses the outward human form and there emerges a diversity of living forms from the human etheric. One now sees not the unified human form but the profusion of animal forms that interpenetrate and merge to create the human form. One comes to know in an inward way what lives within the realms of plants and minerals. One learns this through introspection. One learns what can never be learned through atomism and molecularism: one learns what actually lives within the realms of plants and minerals. And how is it that we avoid bringing the ego down into the physical body when we strive for Imagination? Only by developing the power of love more nobly than in normal life, where love is led by the powers of the bodily senses. Only by acquiring the selfless power of love, freedom from egotism not only regarding the realm of humanity but also regarding the realm of nature. Only by allowing all that leads to Imagination to be borne by love, by merging this power of love with every object of cognition that we seek in this manner. Again we have divergent tendencies: the healthy tendency to extend the power of love into Imagination or the pathological tendency to expose ourselves to fear of what is outside. We experience what lies outside with our ego and then, without restraining our ego, bear it down into the body, giving rise to agoraphobia, claustrophobia, and astraphobia. Yet we enjoy the prospect of an extremely high mode of cognition if we can develop in a healthy way what threatens humanity in its pathological form and would lead it into barbarism. In this way one attains a true knowledge of man. One surpasses all that anatomy, physiology, and biology can teach; one attains a true knowledge of man by actually seeing through the physical body. Oh, man comes to know himself in a way so different from that which nebulous mystics believe, who think that some abstract divinity reveals itself to them when they delve down within. Oh no, something rich and concrete reveals itself; something that provides insight into the human organism, into the nature of the lungs, the liver, and so forth. Only this can be the basis of a true anatomy, a true physiology; only this can serve as the basis for a true understanding of man and also for a true medical science. One has developed two faculties within human nature. On the side of matter is the faculty of Inspiration, developed by gradually discovering within matter a spiritual realm that expands out into the tableau Mr. Arenson has depicted for you here. The other faculty is developed by discovering within oneself the realms that I described as the basis of a true knowledge of man, of a true medical science, when I spoke here earlier this year before almost forty medical doctors. These two faculties, however, those of Inspiration and Imagination, can join together. The one can coalesce with the other, but it must happen in full consciousness and by comprehending the cosmos in love. Then there arises a third faculty, a confluence of Imagination and Inspiration in true, spiritual Intuition. Then we rise up to that which allows us to recognize the external material world to be a spiritual world, the inner realm of the soul and spirit with its material foundations as a continuous whole; we rise up to that which grants us knowledge of the expansion of human existence beyond earthly life, as I have described it to you here in other lectures. One comes thus on the one side to know the realms of plants, animals, and minerals in their inmost essences, in their spiritual content, through Inspiration. By coming to know the human organs through Imagination one creates the basis for a true organology, and by uniting in Intuition what one has learned about plants, animals, and minerals with what Imagination reveals concerning the human organs, one attains a true therapy, a science of medication that knows in a real sense how to apply the external to the internal. The true doctor must understand medications cosmologically; he must understand the human organs anthropologically, or actually anthroposophically. He must come to grasp the external world through Inspiration, the inner world through Imagination, and he must achieve a therapy based upon real Intuition. You see what a prospect opens before us if we are able to comprehend spiritual science in its true form. To be sure, this spiritual science still has to shed many externals and much that still adheres to it in the minds of those who believe they can nurture it with fantasies and dilettantism of every sort. Spiritual science must develop a method of research as rigorous as mathematics and analytical mechanics. On the other hand, spiritual science must rid itself of all superstitions. Spiritual science must truly be able to call forth in light-filled clarity the love that otherwise overcomes man if he can call it forth out of instinct. Then spiritual science will be a seed that will grow and send its forces out into all the sciences and thus into human life. For this reason, let me bring to a dose what I have had to say to you in these lectures with one more brief consideration. Beforehand I would like to say that there is, of course, still much that can be read between the lines of my descriptions. Some of this I shall make legible in two lectures this evening and tomorrow: they will elaborate what I could only intimate in the short time available to us for this course. Only what is gained by attaining Imagination on the one hand and Inspiration on the other, and then uniting Imagination and Inspiration in Intuition, gives man the inner freedom and strength enabling him to conceive ideas that can then be effected in social life. And only those who experience contemporary life with a sleeping soul can fall to see everything that is brewing in the most frightful way, threatening a horrific future. What is the spiritual cause of this? The spiritual cause of this is something one can perceive by studying attentively recent human evolution as it manifests itself in extremely prominent individuals. How human beings strove in the later nineteenth and early twentieth centuries to arrive at clear concepts, to arrive at truly inward, clear impulses for three concepts that are of the very greatest importance for social life: the concept of capital, the concept of labor, and the concept of commodities! Just look at the relevant literature from the nineteenth and the beginning of the twentieth centuries to see how human beings strove to understand what capital actually means within the social process, to see how that which human beings strove to understand in concepts has passed over into frightful struggles in the external world. Just look how intimately the particular feeling emerging within humanity in the present age corresponds to what they are able to feel and think concerning the function, the meaning of labor within the social organism. Then look at the hopelessly inadequate definition of “commodity”! Human beings strove to bring three practical concepts into clear focus. In the course of life in the civilized world today one Sees everywhere a lack of clarity regarding the triad, capital, labor, commodities. And one cannot rise up to answer the question: what function does capital have within the social organism? One is able to answer this question only when, out of a true spiritual science, by means of Imagination and Inspiration united in Intuition, one understands that a proper impulse for the functioning of capital can be found within the spiritual life as an independently subsisting part of the social organism. Only true Imagination can bring real comprehension of this part of the social organism. And one will come to realize something else as well. One will realize that one can come to understand labor's functioning within the social organism when one no longer understands what is produced by human labor in terms of the product, so that one no longer conceives commodities in the Marxist manner as congealed labor or even congealed time. Rather, one will realize that the results of human labor can be understood by arriving at a representation, at a free experience of that which can proceed from man. The concept of labor will become clear only to those who know what is revealed to man through Inspiration. And the concept of “commodity” is the most complicated imaginable. For no single man is able to comprehend what commodities are in their actual existence in life. Anyone who wishes to define commodities has not the slightest inkling what knowledge is. “Commodity” cannot be defined, for one can define in this sense or formulate conceptually only what concerns but one individual, what one man alone can comprehend with his soul. Commodities, however, always exist in the interaction between a number of human beings and a number of individuals of a certain type. Commodities exist in the interaction between producers, consumers, and those who mediate between them. The impoverished concepts of barter and purchase, products of a discipline that fails to recognize the limits of natural science, shall never prove adequate to an understanding of commodities. Commodities, the products of human labor, exist in the relationship between several individuals, and if a solitary man undertakes to understand commodities “as such,” he is on the wrong track. Commodities must be understood as a function of the socially contracted majority of human beings, of association. Commodities must be understood in terms of association; they must exist in association. Only when associations are formed that process what originates with the producers, businessmen, and consumers will there arise — not out of the individual but through association, through the worker associations — the social concept, the concept of “commodity,” that human beings must share before there can exist a healthy economic life. If human beings would only take the trouble to ascend to that which the spiritual scientist can convey from the realm of higher cognition, they would find concepts giving rise to the social forms we must develop if we wish to reverse the course of a civilization on the decline. It is thus no mere theoretical interest, no mere scientific need, that underlies all we shall strive for here. It is rather the most urgent need that the work and the research we do here make human beings mature enough that they can go forth from this place to all the corners of the earth, taking with them such ideas and social impulses as really can buoy up an age so rapidly sinking and reverse the course of a world so clearly in decline.

The Boundaries of Natural Science

Lecture VI

https://rsarchive.org/Lectures/GA322/English/AP1983/19201002a01.html

Dornach

2 Oct 1920

GA322-6

It is to be hoped that my discussions of the boundaries of natural science have been able to furnish at least some indications of the difference between what spiritual science calls knowledge of the higher worlds and the mode of knowledge proceeding from everyday consciousness or ordinary science. In everyday life and in ordinary science our powers of cognition are those we have acquired through the conventional education that carries us up to a certain stage in life and whatever this education has enabled us to make of inherited and universally human qualities. The mode of cognition that anthroposophically oriented spiritual science terms knowledge of the higher worlds has its basis in a further self-cultivation, a further self-development; one must become aware that in the later stages of life one can advance through self-education to a higher consciousness, just as a child can advance to the stage of ordinary consciousness. The things we sought in vain at the two boundaries of natural science, the boundaries of matter and of ordinary consciousness, reveal themselves only when one attains this higher consciousness. In ancient times the Eastern sages spoke of such an enhanced consciousness that renders accessible to man a level of reality higher than that of everyday life; they strove to achieve a higher development, similar to the one we have described, by means of an inner self-cultivation that corresponded to their racial characteristics and evolutionary stage. The meaning of what radiates forth from the ancient Eastern wisdom-literature becomes fully apparent only when one realizes what such a higher level of development reveals to man. If one were to characterize the path of development these sages followed, one would have to describe it as a path of Inspiration. For in that epoch humanity had a kind of natural propensity to Inspiration, and in order to understand these paths into the higher realms of cognition, it will be useful if First we can gain clarity concerning the path of development followed by these ancient Eastern sages. I want to make it clear from the start, however, that this path can no longer be that of our Western civilization, for humanity is in a process of constant evolution, ever moving forward. And whoever desires — as many have — to return to the instructions given in the ancient Eastern wisdom-literature in order to enter upon the paths of higher development actually desires to turn back the tide of human evolution or shows that he has no real understanding of human progress. In ordinary consciousness we reside within our thought life, our life of feeling, and our life of will, and we initially substantiate what surges within the soul as thought, feeling, and will in the act of cognition. And it is in the interaction with percepts of the external world, with physical-sensory perceptions, that our consciousness First fully awakens. It is necessary to realize that the Eastern sages, the so-called initiates of the East, cultivated perception, thinking, feeling, and willing in a way different from their cultivation in everyday life. We can attain an understanding of this path of development leading into the higher worlds when we consider the following. In certain ages of life we develop what we call the soul-spirit toward a greater freedom, a greater independence. We have been able to show how the soul-spirit, which functions in the earliest years of childhood to organize the physical body, emancipates itself, becomes free in a sense with the change of teeth. We have shown how man then lives freely with his ego in this soul-spirit, which now places itself at his disposal, while formerly it occupied itself — if I may express myself thus — with the organization of the physical body. As we enter into ever-greater participation in everyday life, however, there arises something that initially prevents this emancipated soul-spirit from growing into the spiritual world in normal consciousness. As human beings, we must traverse the path that leads us into the external world with the requisite faculties during our life between birth and death. We must acquire such faculties as allow us to orient ourselves within the external, physical-sensory world. We must also develop such faculties as allow us to become useful members of the social community we form with other human beings. What arises is threefold. These three things bring us into a proper relationship with other human beings in our environment and govern our interaction with them. These are: language, the ability to understand the thoughts of our fellow men, and the acquisition of an understanding, or even a kind of perception, of another's ego. At first glance these three things — perception of language, perception of thoughts, and perception of the ego — appear simple, but for one who seeks knowledge earnestly and conscientiously these things are not so simple at all. Normally we speak of five senses only, to which recent physiological research adds a few inner senses. Within conventional science it is thus impossible to find a complete, systematic account of the senses. I will want to speak to you an this subject at some later time. Today I want only to say that it is an illusion to believe that linguistic comprehension is implicit in the sense of hearing, of that which contemporary physiology dreams to be the organization of the sense of hearing. just as we have a sense of hearing, so also do we have a sense of language. By this I do not mean the sense that guides us in speaking — for this is also called a sense — but that which enables us to comprehend the perception of speech-sounds, just as the auditory senses enable us to perceive tones as such. And when we have a comprehensive physiology, it will be known that this sense of speech is analogous to the other and can rightfully be called a sense in and of itself. It is only that this sense extends over a larger part of the human constitution than the other, more localized senses. Yet it is a sense that nevertheless can be sharply delineated. And we have, in fact, a further sense that extends throughout virtually all of our body — the sense that perceives the thoughts of others. For what we perceive as word is not yet thought. We require other organs, a sensory organization different from that which perceives only words as such, if we want to understand within the word the thought that another wishes to communicate. In addition, we are equipped with an analogous sense extending throughout our entire bodily organization, which we can call the sense for the perception of another person's ego. In this regard even philosophy has reverted to childishness in recent times, for one can often hear it argued: we encounter another man; we know that a human has such and such a form. Since the being that we encounter is formed in the way we know ourselves to be formed, and sine we know ourselves to be ego-bearers, we conclude through a kind of unconscious inference: aha, he bears an ego within as well. This directly contradicts the psychological reality. Every acute observer knows that it is not an inference by analogy but rather a direct perception that brings us awareness of another's ego. I think that a friend or associate of Husserl's school in Göttingen, Max Scheler, is the only philosopher actually to hit upon this direct perception of the ego. Thus we must differentiate three higher senses, so to speak, above and beyond the ordinary human senses: the sense that perceives language, the sense that perceives thoughts, and the sense that perceives another's ego. These senses arise within the course of human development to the same extent that the soul-spirit gradually emancipates itself between birth and the change of teeth in the way I have described. These three senses lead initially to interaction with the rest of humanity. In a certain way we are introduced into social life among other human beings by the possession of these three senses. The path one thus follows via these three senses, however, was followed in a different way by the ancients — especially the Indian sages — in order to attain higher knowledge. In striving for this goal of higher knowledge, the soul was not moved toward the words in such a way that one sought to arrive at an understanding of what the other was saying. The powers of the soul were not directed toward the thoughts of another person in such a way as to perceive them, nor toward the ego of another in such a way as to perceive it sympathetically. Such matters were left to everyday life. When the sage returned from his striving for higher cognition, from his sojourn in spiritual worlds to everyday life, he employed these three senses in the ordinary manner. When he wanted to exercise the method of higher cognition, however, he needed these senses in a different way. He did not allow the soul's forces to penetrate through the word while perceiving speech, in order to comprehend the other through his language; rather, he stopped short at the word itself. Nothing was sought behind the word; rather, the streaming life of the soul was sent out only as far as the word. He thereby achieved an intensified perception of the word, renouncing all attempts to understand anything more by means of it. He permeated the word with his entire life of soul, using the word or succession of words in such a way that he could enter completely into the inner life of the word. He formulated certain aphorisms, simple, dense aphorisms, and then strove to live within the sounds, the tones of the words. And he followed with his entire soul life the sound of the word that he vocalized. This practice then led to a cultivation of living within aphorisms, within the so-called “mantras.” It is characteristic of mantric art, this living within aphorisms, that one does not comprehend the content of the words but rather experiences the aphorisms as something musical. One unites one's own soul forces with the aphorisms, so that one remains within the aphorisms and so that one strengthens through continual repetition and vocalization one's own power of soul living within the aphorisms. This art was gradually brought to a high state of development and transformed the soul faculty that we use to understand others through language into another. Through vocalization and repetition of the mantras there arose within the soul a power that led not to other human beings but into the spiritual world. And if, through these mantras, the soul has been schooled in such a way and to such an extent that one feels inwardly the weaving and streaming of this power of soul, which otherwise remains unconscious because all one's attention is directed toward understanding another through the word; if one has come so far as to feel such a power to be an actual force in the soul in the same way that muscular tension is experienced when one wishes to do something with one's arm, one has made oneself sufficiently mature to grasp what lies within the higher power of thought. In everyday life a man seeks to find his way to another via thought. With this power, however, he grasps the thought in an entirely different way. He grasps the weaving of thought in external reality, penetrates into the life of external reality, and lives into the higher realm that I have described to you as Inspiration. Following this path, then, we approach not the ego of the other person but the egos of individual spiritual beings who surround us, just as we are surrounded by the entities of the sense world. What I depict here was self-evident to the ancient Eastern sage. In this way he wandered with his soul, as it were, upward toward the perception of a realm of spirit. He attained in the highest degree what can be called Inspiration, and his constitution was suited to this. He had no need to fear, as the Westerner might, that his ego might somehow become lost in this wandering out of the body. In later times, when, owing to the evolutionary advances made by humanity, a man might very easily pass out of his body into the outer world without his ego, precautionary measures were taken. Care was taken to ensure that whoever was to undergo this schooling leading to higher knowledge did not pass unaccompanied into the spiritual world and fall prey to the pathological skepticism of which I have spoken in these lectures. In the ancient East the racial constitution was such that this was nothing to fear. As humanity evolved further, however, this became a legitimate concern. Hence the precautionary measure strictly applied within the Eastern schools of wisdom: the neophyte was placed under an authority, but not any outward authority — fundamentally speaking, what we understand by “authority” First appeared in Western civilization. There was cultivated within the neophytes, through a process of natural adaptation to prevailing conditions, a dependence on a leader or guru. The neophyte simply perceived what the leader demonstrated, how the leader stood firmly within the spiritual world without falling prey to pathological skepticism or even inclining toward it. This perception fortified him to such an extent on his own entry into Inspiration that pathological skepticism could never assail him. Even when the soul-spirit is consciously withdrawn from the physical body, however, something else enters into consideration: one must re-establish the connection with the physical body in a more conscious manner. I said this morning that the pathological state must be avoided in which one descends only egotistically, and not lovingly, into the physical body, for this is to lay hold of the physical body in the wrong way. I described the natural process of laying hold of the physical body between the seventh and fourteenth years, which is through the love-instinct being impressed upon it. Yet even this natural process can take a pathological turn: in such cases there arise the harmful afflictions I described this morning as pathological states. Of course, this could have happened to the pupils of the ancient Eastern sages as well: when they were out of the body they might not have been able to bind the soul-spirit to the physical body again in the appropriate manner. One further precautionary measure thus was employed, one to which psychiatrists — some at any rate — have had recourse when seeking cures for patients suffering from agoraphobia or the like. They employed ablutions, cold baths. Expedients of an entirely physical nature have to be employed in such cases. And when you hear on the one hand that in the mysteries of the East — that is, the schools of initiation, the schools that led to Inspiration — the precautionary measure was taken of ensuring dependence on the guru, you hear on the other hand of the employment of all kinds of devices, of ablutions with cold water and the like. When human nature is understood in the way made possible by spiritual science, customs that otherwise remain rather enigmatic in these ancient mysteries become intelligible. One was protected against developing a false sense of spatiality resulting from an insufficient connection between the soul-spirit and the physical body. This could drive one into agoraphobia and the like or to seek social intercourse with one's fellow men in an inappropriate way. This represents a danger, but one which can and should — indeed must — be avoided in any training that leads to higher cognition. It is a danger, because in following the path I have described leading to Inspiration one bypasses in a certain sense the path via language and thought to the ego of one's fellow man. If one then quits the physical body in a pathological manner — even if one is not attempting to attain higher cognition but is lifted out of the body by a pathological condition — one can become unable to interact socially with one's fellow men in the right way. Then precisely that which arises in the usual, intended manner through properly regulated spiritual study can develop pathologically. Such a person establishes a connection between his soul-spirit and his physical body: by delving too deeply into it he experiences his body so egotistically that he learns to hate interaction with his fellow men and becomes antisocial. One can often see the results of such a pathological condition manifest themselves in the world in quite a frightening manner. I once met a man who was a remarkable example of such a type: he came from a family that inclined by nature toward a freeing of the soul-spirit from the physical body and also contained certain personalities — I came to know one of them extremely well — who sought a path into the spiritual worlds. One rather degenerate individual, however, developed this tendency in an abnormal, pathological way and finally arrived at the point where he would allow nothing whatever from the external world to contact his own body. Naturally he had to eat, but — we are speaking here among adults — he washed himself with his own urine, because he feared any water that came from the outside world. But then again I would rather not describe all the things he would do in order to isolate his body totally from the external world and shun all society. He did these things because his soul-spirit was too deeply incarnated, too closely bound to the physical body. It is entirely in keeping with the spirit of Goetheanism to bring together that which leads to the highest goal attainable by earthly man and that which leads to pathological depths. One needs only slight acquaintance with Goethe's theory of metamorphosis to realize this. Goethe seeks to understand how the individual organs, for example of the plant, develop out of each other, and in order to understand their metamorphosis he is particularly interested in observing the conditions that arise through the abnormal development of a leaf, a blossom, or the stamen. Goethe realizes that precisely by contemplating the pathological the essence of the healthy can be revealed to the perceptive observer. And one can follow the right path into the spiritual world only when one knows wherein the essence of human nature actually lies and in what diverse ways this complicated inner being can come to expression. We see from something else as well that even in the later period the men of the East were predisposed by nature to come to a halt at the word. They did not penetrate the word with the forces of the soul but lived within the word. We see this, for example, in the teachings of the Buddha. One need only read these teachings with their many repetitions. I have known Westerners who treasured editions of the Buddha's teachings in which the numerous repetitions had been eliminated and the words of a sentence left to occur only once. Such people believed that through such a condensed version, in which everything occurs only once, they would gain a true understanding of what the Buddha had actually intended. From this it is clear that Western civilization has gradually lost all understanding of Eastern man. If we simply take the Buddha's teachings word for word; if we take the content of these teachings, the content that we, as human beings of the West, chiefly value, then we do not assimilate the essence of these teachings: that is possible only when we are carried along with the repetitions, when we live in the flow of the words, when we experience the strengthening of the soul's forces that is induced by the repetitions. Unless we acquire a faculty for experiencing something from the constant repetitions and the rhythmical recurrence of certain passages, we do not get to the heart of Buddhism's actual significance. It is in this way that one must gain knowledge of the inner nature of Eastern culture. Without this acquaintance with the inner nature of Eastern culture one can never arrive at a real understanding of our Western religious creeds, for in the final analysis these Western religious creeds stem from Eastern wisdom. The Christ event is a different matter. For that is an actual event. It stands as a fact within the evolution of the earth. Yet the ways and means of understanding what came to pass through the Mystery of Golgotha were drawn during the first Christian centuries entirely from Eastern wisdom. It was through this wisdom that the fundamental event of Christianity was originally understood. Everything progresses, however. What had once been present in Eastern primeval wisdom — attained through Inspiration — spread from the East to Greece and is still recognizable as art. For Greek art was, to be sure, bound up with experiences different from those usually connected with art today. In Greek art one could still experience what Goethe strove to regain when he spoke of the deepest urge within him: he to whom nature begins to unveil her manifest secrets longs for her worthiest interpreter — art. For the Greeks, art was a way to slip into the secrets of world existence, a manifestation not merely of human fantasy but of what arises in the interaction between this faculty and the revelations of the spiritual world revealed through Inspiration. That which still flowed through Greek art, however, became more and more diluted, until finally it became the content of the Western religious creeds. We thus must conceive the source of the primeval wisdom as fully substantial spiritual life that becomes impoverished as evolution proceeds and provides the content of religious creeds when it finally reaches the Western world. Human beings who are constitutionally suited for a later epoch therefore can find in this diluted form of spiritual life only something to be viewed with skepticism. And in the final analysis it is nothing other than the reaction of the Western temperament [Gemüt] to the now decadent Eastern wisdom that gradually produces atheistic skepticism in the West. This skepticism is bound to become more and more widespread unless it is countered with a different stream of spiritual life. Just as little as a creature that has reached a certain stage of development — let us say has undergone a certain aging process — can be made young again in every respect, so little can a form of spiritual life be made young again when it has reached old age. The religious creeds of the West, which are descendants of the primeval wisdom of the East, can yield nothing that would fully satisfy Western humanity again when it advances beyond the knowledge provided during the past three or four centuries by science and observation of nature. An ever-more profound skepticism is bound to arise, and anyone who has insight into the processes of world evolution can say with assurance that a trend of development from East to West must necessarily lead to an increasingly pronounced skepticism when it is taken up by souls who are becoming more and more deeply imbued with the fruits of Western civilization. Skepticism is merely the march of the spiritual life from East to West, and it must be countered with a different spiritual stream flowing henceforth from West to East. We ourselves are living at the crossing-point of these spiritual streams, and in the further course of these considerations we will want to see how this is so. But first it must be emphasized that the Western temperament is constitutionally predisposed to follow a path of development leading to the higher worlds different from that of the Eastern temperament. Just as the Eastern temperament strives initially for Inspiration and possesses the racial qualities suitable for this, the Western temperament, because of its peculiar qualities (they are at present not so much racial qualities as qualities of soul) strives for Imagination. It is no longer the experience of the musical element in mantric aphorisms to which we as Westerners should aspire but something else. As Westerners we should strive in such a way that we do not pursue with particular vigour the path that opens out when the soul-spirit emerges from the physical body but rather the path that presents itself later, when the soul-spirit must again unite with the physical organism by consciously grasping the physical body. We see the natural manifestation of this in the emergence of the bodily instinct: whereas Eastern man sought his wisdom more by sublimating the forces at work between birth and the seventh year, Western man is better fitted to develop the forces at work between the time of the change of teeth and puberty, in that there is lifted up into the soul-spirit that which is natural for this epoch of humanity. We come to this when, just as in emerging from the body we carry the ego with us into the realm of Inspiration, we now leave the ego outside when we delve again into the body. We leave it outside, but not in idleness, not forgetting or surrendering it, not suppressing it into unconsciousness, but rather conjoining it with pure thinking, with clear, keen thinking, so that finally one has this inner experience: my ego is totally suffused with all the clear thinking of which I have become capable. One can experience just this delving down into the body in a very clear and distinct manner. And at this point you will perhaps allow me to relate a personal experience, because it will help you to understand what I really mean. I have spoken to you about the conception underlying my book, Philosophy of Freedom . This book is actually a modest attempt to win through to pure thinking, the pure thinking in which the ego can live and maintain a firm footing. Then, when pure thinking has been grasped in this way, one can strive for something else. This thinking, left in the power of an ego that now feels itself to be liberated within free spirituality [ frei und unabhängig in freier Geistigkeit ], can then be excluded from the process of perception. Whereas in ordinary life one sees color, let us say, and at the same time imbues the color with conceptual activity, one can now extract the concepts from the entire process of elaborating percepts and draw the percept itself directly into ones bodily constitution. Goethe undertook to do this and has already taken the First steps in this direction. Read the last chapter of his Theory of Colors , entitled “The Sensory-Moral Effect of Color”: in every color-effect he experiences something that unites itself profoundly not only with the faculty of perception but with the whole man. He experiences yellow and scarlet as “attacking” colors, penetrating him, as it were, through and through, filling him with warmth, while he regards blue and violet as colors that draw one out of oneself, as cold colors. The whole man experiences something in the act of sense perception. Sense perception, together with its content, passes down into the organism, and the ego with its pure thought content remains, so to speak, hovering above. We exclude thinking inasmuch as we take into and fill ourselves with the whole content of the perception, instead of weakening it with concepts, as we usually do. We train ourselves specially to achieve this by systematically pursuing what came to be practiced in a decadent form by the men of the East. Instead of grasping the content of the perception in pure, strictly logical thought, we grasp it symbolically, in pictures, allowing it to stream into us as a result of a kind of detour around thinking. We steep ourselves in the richness of the colors, the richness of the tone, by learning to experience the images inwardly, not in terms of thought but as pictures, as symbols. Because we do not suffuse our inner life with the thought content, as the psychology of association would have it, but with the content of perception indicated through symbols and pictures, the living inner forces of the etheric and astral bodies stream toward us from within, and we come to know the depths of consciousness and of the soul. It is in this way that genuine knowledge of the inner nature of man is acquired, and not by means of the blathering mysticism that nebulous minds often claim to be a way to the God within. This mysticism leads to nothing but abstraction and cannot satisfy anyone who wishes to become a man in the full sense of the ward. If one desires to do real research concerning human physiology, thinking must be excluded and the picture-forming activity sent inward, so that the physical organism reacts by creating Imaginations. This is a path that is only just beginning in the development of Western culture, but it is the path that must be trodden if the influence that streams over from the East, and would lead to decadence if it atone were to prevail, is to be confronted with something capable of opposing it, so that our civilization may take a path of ascent and not of decline. Generally speaking, however, it can be said that human language itself is not yet sufficiently developed to be able to give full expression to the experiences that one undergoes in the inner recesses of the soul. And it is at this point that I would like to relate a personal experience to you. Many years ago, in a different context, I made an attempt to give expression to what might be called a science of the human senses. In spoken lectures I succeeded to some extent in putting this science of the twelve senses into words, because in speaking it is more possible to turn language this way and that and ensure understanding by means of repetitions, so that the deficiencies of our language, which is not yet capable of expressing these super-sensible things, is not so strongly felt. Strangely enough, however, when I wanted many years ago to write down what I had given as actual anthroposophy in order to put it into a form suitable for a book, the outer experiences an being interiorized became so sensitive that language simply failed to provide the words, and I believe that the beginning of the text — several sheets of print — lay for some five or six years at the printer's. It was because I wanted to write the whole book in the style in which it began that I could not continue writing, for the simple reason that at the stage of development I had then reached, language refused to furnish the means for what I wished to achieve. Afterward I became overloaded with work, and I still have not been able to finish the book. Anyone who is less conscientious about what he communicates to his fellow men out of the spiritual world might perhaps smile at the idea of being held up in this way by a temporarily insurmountable difficulty. But whoever really experiences and can permeate with a full sense of responsibility what occurs when one attempts to describe the path that Western humanity must follow to attain Imagination knows that to find the right words entails a great deal of effort. As a meditative schooling it is relatively easy to describe, and this has been done in my book, Knowledge of the Higher Worlds and Its Attainment . If one's aim, however, is to achieve definite results such as that of describing the essential nature of man's senses — a part, therefore, of the inner makeup and constitution of humanity — it is then that one encounters the difficulty of grasping Imaginations and presenting them in sharp contours by means of words. Nevertheless, this is the path that Western humanity must follow. And just as the man of the East was able to experience through his mantras the entry into the spiritual nature of the external world, so must the Westerner, leaving aside the entire psychology of association, learn to enter into his own being by attaining the realm of Imagination. Only by penetrating into the realm of Imagination will he acquire the true knowledge of humanity that is necessary in order for humanity to progress. And because we in the West must live much more consciously than the men of the East, we cannot simply say: whether or not humanity will gradually attain this realm of Imagination is something that can be left to the future. No — this world of Imagination, because we have passed into the stage of conscious human evolution, must be striven for consciously; there can be no halting at certain stages. For what happens if one halts at a certain stage? Then one does not meet the ever-increasing spread of skepticism from East to West with the right countermeasures but with measures that result from the soul-spirit uniting too radically, too deeply and unconsciously, with the physical body, so that too strong a connection is formed between the soul-spirit and the physical body. Yes, it is indeed possible for a human being not only to think materialistically but to be a materialist, because the soul-spirit is too strongly linked with the physical body. In such a man the ego does not live freely in the concepts of pure thinking he has attained. If one descends into the body with pictorial perception, one delves with the ego and the concepts into the body. And if one then spreads this around and suffuses it throughout humanity, it gives rise to a spiritual phenomenon well known to us — dogmatism of all kinds. Dogmatism is nothing other than the translation into the realm of the soul-spirit of a condition that at a lower stage manifests itself pathologically as agoraphobia and the like, and that — because these things are related — also shows itself in something else, which is a metamorphosis of fear, in superstition of every variety. An unconscious urge toward Imagination is held back through powerful agencies, and this gives rise to dogmatism of all types. These types of dogmatism must gradually be replaced by what is achieved when the world of ideas is kept within the sphere of the ego; when progress is made toward Imagination, the true nature of man is experienced inwardly, and this Western path into the spiritual world is followed in a different way. It is this other path through Imagination that must establish the stream of spiritual science, the process of spiritual evolution that muss make its way from West to East if humanity is to progress. It is supremely important at the present time, however, for humanity to recognize what the true path of Imagination should be, what path must be taken by Western spiritual science if it is to be a match for the Inspiration and its fruits that were attained by ancient Eastern wisdom in a form suited to the racial characteristics of those peoples. Only if we are able to confront the now decadent Inspiration of the East with Imaginations which, sustained by the spirit and saturated with reality, have arisen along the path leading to a higher spiritual culture; only if we can call this culture into existence as a stream of spiritual life flowing from West to East, are we bringing to fulfillment what is actually living deep within the impulses for which humanity is striving. It is these impulses that are now exploding in social cataclysms because they cannot find other expression. In tomorrow's lecture we will speak further of the path of Imagination and of how the way to the higher worlds is envisaged by anthroposophical spiritual science.

The Boundaries of Natural Science

Lecture VII

https://rsarchive.org/Lectures/GA322/English/AP1983/19201002p01.html

Dornach

2 Oct 1920

GA322-7

Yesterday I attempted to show the methods employed by Eastern spirituality for approaching the spiritual world and pointed out how anybody who wished to pursue this path into the super-sensible more or less dispensed with the bridge linking him with his fellow men. He chose a path different from that which establishes communication within society by means of language, thought, and perception of the ego. And I showed how it was initially attempted not to understand through the word what one's fellow man wished to say, what one wants to understand from him, but to live within the words. This process of living within the word was enhanced by forming the words into certain aphorisms. One lived in these and repeated them, so that the forces accrued in the soul by this process were strengthened further by repetition. And I showed how something was achieved in the condition of the soul that might be called a state of Inspiration, in the sense in which I have used the word, except that the sages of the ancient East were, of course, members of their race: their ego-consciousness was much less developed than in later epochs of human evolution. They thus entered into the spiritual world in a more instinctive manner, and because the whole thing was instinctive and thus resulted, in a sense, from a healthy drive within human nature, in the earliest times it could not lead to the pathological afflictions of which we have also spoken. In later times steps were taken by the so-called Mysteries to guard against the rise of such afflictions as I have described to you. I said that those Westerners who desire to gain knowledge of the spiritual world must approach this in another way. Humanity has progressed in the interim. Different soul faculties have evolved, so that one cannot simply renew the ancient Eastern path of spiritual development. Within the realm of spiritual life one cannot long to return in a reactionary manner to prehistoric or earlier historical periods of human evolution. For Western civilization, the path leading into the spiritual worlds is that of Imagination. This faculty of Imagination, however, must be integrated organically into the life of the soul as a whole. This can come about in the most varied ways, just as the Eastern path of development was not unequivocally predetermined but could take numerous different courses. Today I would like to describe the path into the spiritual world that conforms to the needs of Western civilization and is particularly suited to anyone immersed in the scientific life of the West. In my book, Knowledge of the Higher Worlds and Its Attainment , I have described an entirely safe path leading to the super-sensible, but I describe it in such a way that it applies for everybody, above all for those who have not devoted their lives to science. Today I shall describe a path into the super-sensible that is much more for the scientist. All my experience has taught me that for such a scientist a kind of precondition for this cognitional striving is to take up what is presented in my book, Philosophy of Freedom . I will explain what I mean by this. This book, Philosophy of Freedom , was not written with the same intent as most books written today. Nowadays books are written simply in order to inform the reader of the book's subject matter, so that the reader learns the book's contents in accordance with his education, his scientific training, or the special knowledge he already possesses. This was not my primary Intention in writing Philosophy of Freedom , and thus it will not be popular with those who read books only to acquire Information. The purpose of the book is to make the reader directly engage his thinking activity on every page. In a sense, the book is only a kind of musical score that one must read with inner thought activity in order to progress, as the result of one's own efforts, from one thought to the next. The book constantly presupposes the mental collaboration of the reader. Moreover, the book presupposes that which the soul becomes in the process of such mental exertion. Anyone who has really worked through this book with his own inner thinking activity and cannot confess that he has come to know himself in a part of his inner life in which he had not known himself previously has not read Philosophy of Freedom properly. One should feel that one is being lifted out of one's usual thinking [ Vorstellen ] into a thinking independent of the senses [ ein sinnlichkeitsfreies Denken ], in which one is fully immersed, so that one feels free of the conditions of physical existence. Whoever cannot confess this to himself has actually misunderstood the book. One should be able to say to oneself: now I know, as a result of the inner thought activity I myself have expended, what pure thinking actually is. The strange thing is that most Western philosophers totally deny the reality of the very thing that my Philosophy of Freedom seeks to awaken as something real in the soul of the reader. Countless philosophers have expounded the view that pure thinking does not exist but is bound to contain traces, however diluted, of sense perception. A strong impression is left that philosophers who maintain this have never really studied mathematics or gone into the difference between analytical and empirical mechanics. Specialization, however, has already grown to such an extent that nowadays philosophy is often pursued by people totally lacking any knowledge of mathematical thinking. The pursuit of philosophy is actually impossible without a grasp of at least the spirit of mathematical thinking. We have seen what Goethe's attitude was toward this spirit of mathematical thinking, even though he made no claim himself to any special training in mathematics. Many thus would deny the existence of the very faculty I would like those who study The Philosophy of Freedom to acquire. And now let us imagine a reader who simply sets about working through The Philosophy of Freedom within the context of his ordinary consciousness in the way I have described: he will, of course, not be able to claim that he has been transported into a super-sensible world. For I intentionally wrote The Philosophy of Freedom in the way that I did so that it would present itself to the world initially as a purely philosophical work. Just think what a disservice would have been accorded anthroposophically oriented spiritual science if I had begun immediately with spiritual scientific writings! These writings would, of course, have been disregarded by all trained philosophers as the worst kind of dilettantism, as the efforts of an amateur. To begin with I had to write purely philosophically. I had to present the world with something thought out philosophically in the strict sense, though it transcended the normal bounds of philosophy. At some point, however, the transition had to be made from a merely philosophical and scientific kind of writing to a spiritual scientific writing. This occurred at a time when I was invited to write a special chapter about Goethe's scientific writings for a German biography of Goethe. This was at the end of the last century, in the 1890s. And so I was to write the chapter on Goethe's scientific writings: I had, in fact, finished it and sent it to the publisher when there appeared another work of mine, called Mysticism at the Dawn of the Modern Age . The book was a bridge between pure philosophy and an anthroposophical orientation. When this work came out, my manuscript was returned to me by the publisher, who had enclosed nothing but my fee so that I would not make a fuss, for thereby the legal obligations had been met. Among the learned pedants, there was obviously no interest in anything — not even a single chapter devoted to the development of Goethe's attitude toward natural science written by one who had authored this book on mysticism. I will now assume that The Philosophy of Freedom has been worked through already with one's ordinary consciousness in the way described. Now we are in the right frame of mind for our souls to undertake in a healthy way what I described yesterday, if only very briefly, as the path leading into Imagination. It is possible to pursue this path in a way consonant with Western life if we attempt to surrender ourselves completely to the world of outer phenomena, so that we allow them to work upon us without thinking about them but still perceiving them. In ordinary waking life, you will agree, we are constantly perceiving, but actually in the very process of doing so we are continually saturating our percepts with concepts; in scientific thinking we interweave percepts and concepts entirely systematically, building up systems of concepts and so on. By having acquired the capacity for the kind of thinking that gradually emerges from The Philosophy of Freedom , one can become capable of such acute inner activity that one can exclude and suppress conceptual thinking from the process of perception and surrender oneself to bare percepts. But there is something else we can do in order to strengthen the forces of the soul and absorb percepts unelaborated by concepts. One can, moreover, refrain from formulating the judgments that arise when these percepts are joined to concepts and create instead symbolic images, or images of another sort, alongside the images seen by the eye, heard by the ear, and rendered by the senses of warmth, touch, and so on. If we thus bring our activity of perception into a state of flux, infusing it with life and movement, not as we do when forming concepts but by elaborating perception symbolically or artistically, we will develop much sooner the power of allowing the percepts to permeate us as such. An excellent preparation for this kind of cognition is to school oneself rigorously in what I have characterized as phenomenalism, as elaboration of phenomena. If one has really striven not to allow inertia to carry one through the veil of sense perception upon reaching the boundary of the material world, in order to look for all kinds of metaphysical explanations in terms of atoms and molecules, but has instead used concepts to set the phenomena in order and follow them through to the archetypal phenomena, one has already undergone a training that enables one to isolate the phenomena from everything conceptual. And if one still symbolizes the phenomena, turns them into images, one acquires a potent soul forte enabling one to absorb the external world free from concepts. Obviously we cannot expect to achieve this quickly. Spiritual research demands of us far more than research in a laboratory or observatory. It demands above all an intense effort of the individual will. If one has practiced such an inner representation of symbolic images for a certain length of time and striven in addition to dwell contemplatively upon images that one keeps present in the soul in a way analogous to the mental representation of phenomena, images that otherwise only pass away when we race from sensation to sensation, from experience to experience; if one has accustomed oneself to dwell contemplatively for longer and longer periods of time upon an image that one has fully understood, that one has formed oneself or taken at somebody else's suggestion so that it cannot be a reminiscence, and if one repeats this process again and again, one strengthens one's inner soul forces and finally realizes that one experiences something of which one previously had no inkling. The only way to obtain even an approximate idea of such an experience, which takes place only in one's inner being — one must be very careful not to misunderstand this — is to recall particularly lively dream-images. One must keep in mind, however, that dream-images are always reminiscences that can never be related directly to anything external and are thus a sort of reaction coming toward one out of one's own inner self. If one experiences to the full the images formed in the way described above, this is something entirely real, and one begins to understand that one is encountering within oneself the spiritual element that actuates the processes of growth, that is the power of growth. One realizes that one has entered into apart of one's human constitution, something within one; something that unites itself with one; something that is active within but that one previously had experienced only unconsciously. Experienced unconsciously in what way? I have told you that from birth until the change of teeth a soul-spiritual entity is at work structuring the human being and that this then emancipates itself to an extent. Later, between the change of teeth and puberty, another such soul-spiritual entity, which dips down in a way into the physical body, awakens the erotic drives and much else as well. All this occurs unconsciously. If, however, we use fully consciously such measures of soul as I have described to observe this permeation of the physical organism by the soul-spiritual, one sees how such processes work within man and how man is actually given over to the external world continually, from birth onward. Nowadays this giving-over of oneself to the external world is held to be nothing but abstract perception or abstract cognition. This is not so. We are surrounded by a world of color, sound, and warmth and by all kinds of sense impressions, By elaborating these with our concepts we create yet further impressions that have an effect on us. By experiencing all this consciously we come to see that in the unconscious experience of color- and sound-impressions that we have from childhood onward there is something spiritual that suffuses our organization. And when, for example, we take up the sense of love between the change of teeth and puberty, this is not something originating in the physical body but rather something that the cosmos gives us through the colors, sounds, and streaming warmth that reach us. Warmth is something other than warmth; light something other than light in the physical sense; sound is something other than physical sound. Through our sense impressions we are conscious only of what I would term external sound and external color. And when we surrender ourselves to nature, we do not encounter the ether-waves, atoms, and so on of which modern physics and physiology dream; rather, it is spiritual forces that are at work, forces that fashion us between birth and death into what we are as human beings. Once we tread the path of knowledge I have described, we become aware that it is the external world that forms us. We become best able to observe consciously what lives and embodies itself within us when we acquire above all a clear sense that spirit is at work in the external world. lt is of all things phenomenology that enables us to perceive how spirit works within the external world. It is through phenomenology, and not abstract metaphysics, that we attain knowledge of the spirit by consciously observing, by raising to consciousness, what otherwise we would do unconsciously, by observing how, through the sense world, spiritual forces enter our being and work formatively upon it. Yesterday I pointed out to you that the Eastern sage in a way disregards the significance of Speech, thought, and the perception of the ego. He experiences these things differently and cultivates a different attitude of soul toward these things, because language, perception of thoughts, and perception of the ego initially tend to lead us away from the spiritual world into social contact with other human beings. In everyday physical existence we purchase our social life at the price of listening right through language, looking through thoughts, and feeling our way right through the perception of the ego. The Eastern sage took upon himself not to listen right through the word but to live within it. He took upon himself not to look right through the thought but to live within the thought, and so forth. We in the West have as our task more to contemplate man himself in following the path into super-sensible worlds. At this point it must be remembered that man bears a certain kind of sensory organization within as well. I have already described the three inner senses through which he becomes aware of his inner being, just as he perceives what goes on outside him. We have a sense of balance by means of which we sense the spatial orientation appropriate to us as human beings and are thereby able to work inside it with our will. We have a sense of movement by means of which we know that we are moving even in the dark: we know this from an inner sensing and not merely because we perceive our changing relationship to other objects we pass. We have an actual inner sense of movement. And we have a sense of life, by means of which we can perceive our general state of well-being, the constant changes in the inner condition of our life forces. These three inner senses work together with the will during man's first seven years. We are guided by our sense of balance, and a being who initially cannot move at all and later can only crawl is transformed into one who can stand upright and walk. This ability to walk upright is effected by the sense of balance, which places us into the world. The sense of movement and the sense of life likewise contribute toward the development of our full humanity. Anybody who is capable of applying the standards of objective observation employed in the scientist's laboratory to the development of man's physical body and his soul-spirit will soon discover how the forces that worked formatively upon man principally during the fast seven years emancipate themselves and begin to assume a different aspect from the time of the change of teeth onward. By this time a person is less intensively connected to that within than he was as a child. A child is closely bound up inwardly with human equilibrium, movement, and life. Something else, however, is evolving simultaneously during this emancipation of balance, movement, and life. There takes place a certain adjustment of the three other senses: the senses of smell, taste, and touch. It is extremely interesting to observe in detail the way in which a child gradually finds his way into life, orienting himself by means of the senses of taste, smell, and touch. Of course, this can be seen most obviously in early life, but anybody trained to do so can see it clearly enough later on as well. In a certain way, the child pushes out of himself balance, movement, and life but at the same time draws more into himself the qualities of the sense of smell, the sense of taste, and the sense of touch. In the course of an extended phase of development the one is, so to speak, exhaled and the other inhaled, so that the forces of balance, movement, and life, which press from within outward, and the qualitative orientations of smell, taste, and touch, which press from without inward, meet within our organism. This is effected by the interpenetration of the two sense-triads. As a result of this interpenetration, there arises within man a firm sense of self; in this way man First experiences himself as a true ego. Now we are cut off from the spirituality of the external world by speech and by our faculties of perceiving thoughts and perceiving the egos of others — and rightly so, for if it were otherwise we could never in this physical life become social beings — in just the same way, inasmuch as the qualities of smell, taste, and touch encounter balance, movement, and life, we are inwardly cut off from the triad life, movement, and balance, which would otherwise reveal itself to us directly. The experiences of the senses of smell, taste, and touch place themselves, as it were, in front of what we would otherwise experience through our sense of balance, our sense of movement, and our sense of life. And the result of this development toward Imagination of which I have spoken consists in this: the Oriental comes to a halt at language in order to live within it; he halts at the thought in order to live there; he halts at the perception of the ego in order to live within it. By these means he makes his way outward into the spiritual world. The Oriental comes to a halt within these; we, by striving for Imagination, by a kind of absorption of external percepts devoid of concepts, engage in an activity that is in a way the opposite of that in which the Oriental engages with regard to language, perception of thoughts, and perception of the ego. The Oriental comes to a halt at these and enters into them. In striving for Imagination, however, one wends one's way through the sensations of smell, taste, and touch, penetrating into the inner realm so that, by one's remaining undisturbed by sensations of smell, taste, and touch, the experiences stemming from balance, movement, and life come forth to meet one. It is a great moment when one has penetrated through what I have described as the sense-triad of taste, smell, and touch, and one confronts the naked essence of movement, balance, and life. With such a preparation behind us, it is interesting to study what Western mysticism often sets forth. Most certainly, I am very far from decrying the elements of poetry, beauty, and imaginative expression in the writings of many mystics. I most certainly admire what, for instance, St. Theresa, Mechthild of Magdeburg, and others have to tell us, and indeed Meister Eckhart and Johannes Tauler. But all that arises in this way reveals itself to the true spiritual scientist as something that arises when one traverses the inward-leading path yet does not penetrate beyond the region of smell, taste, and touch. Read what has been written by individuals who have described with particular clarity what they have experienced in this way. They speak of a tasting of that within, of a tasting regarding what exists as soul-spirit in man's inner being; they also speak of a smelling and, in a certain sense, of a touching. And anybody who knows how to read Mechthild of Magdeburg, for instance, or St. Theresa, in the right way will see that they follow this inward path but never penetrate right through taste, smell, and touch. They use beautiful poetic imagery for their descriptions, but they are speaking only of how one can touch, savor, and sniff oneself inwardly. For it is far less agreeable to see the true nature of reality with senses that are developed truly spiritually than to read the accounts given by voluptuous mysticism — the only term for it — which in the final analysis only gratifies a refined, inward-looking egotism of soul. As I say, much as this mysticism is to be admired — and I do admire it — the true spiritual scientist must realize that it stops halfway: what is manifest in the splendid poetic imagery of Mechthild of Magdeburg, St. Theresa, and the others is really only what is smelt, tasted, and touched before breaking through into the actual inner realm. Truth is occasionally unpleasant, and at times perhaps even cruel, but modern humanity has no business becoming rickety in soul by following a nebulous, imperfect mysticism. What is required today is to penetrate into man's true inner nature with strength of spirit, with the same strength we have achieved in a much more disciplined way for the external world by pursuing natural science. And it is not in vain that we have achieved this. Natural science must not be undervalued! Indeed, we must seek to acquire the disciplined and methodical side of natural science. And it is precisely when one has assimilated this scientific method that one appreciates the achievements of a nebulous mysticism at their true worth, but one also knows that this nebulous mysticism is not what spiritual science must foster. On the contrary, the task of spiritual science is to seek clear comprehension of man's own inner being, whereby a clear, spiritual understanding of the external world is made possible in turn. I know that if I did not speak in the way that truth demands I could enjoy the support of every nebulous, blathering mystic who takes up mysticism in order to satisfy his voluptuous soul. That cannot be our concern here, however; rather, we must seek forces that can be used for life, spiritual forces that are capable of informing our scientific and social life. When one has penetrated as far as that which lives in the sense of balance, the sense of life, and the sense of movement, one has reached something that one experiences initially as the true inner being of man because of its transparency. The very nature of the thing shows us that we cannot penetrate any deeper. But then again one has more than enough at this initial stage, for what we discover is not the stuff of nebulous, mystical dreams. What one finds is a true organology, and above all one finds within oneself the essence of that which is within equilibrium, of that which is in movement, of that which is suffused with life. One finds this within oneself. Then, after experiencing this, something entirely extraordinary has occurred. Then, at the appropriate moment, one begins to notice something. An essential prerequisite is, as I have said, to have thought through The Philosophy of Freedom beforehand. This is then left, so to speak, to one side, while pursuing the inner path of contemplation, of meditation. One has advanced as far as balance, movement, and life. One lives within this life, this movement, this balance. Entirely parallel with our pursuit of the way of contemplation and meditation but without any other activity on our part, our thinking regarding The Philosophy of Freedom has undergone a transformation. What can be experienced in such a philosophy of freedom in pure thinking has, as a result of our having worked inwardly on our souls in another sphere, become something utterly different. lt has become fuller, richer in content. While on the one hand we have penetrated into our inner being and have deepened our power of Imagination, on the other hand we have raised what resulted from our mental work on The Philosophy of Freedom up out of ordinary consciousness. Thoughts that formerly had floated more or less abstractly within pure thinking have been transformed into substantial forces that are alive in our consciousness: what once was pure thought is now Inspiration. We have developed Imagination, and pure thinking has become Inspiration. Following this path further, we become able to keep apart what we have gained following two paths that must be sharply differentiated: on the one hand, what we have obtained as Inspiration from pure thinking — the life that at a lower level is thinking, and then becomes a thinking raised to Inspiration — and on the other hand what we experience as conditions of equilibrium, movement, and life. Now we can bring these modes of experience together. We can unite the inner with the outer. The fusion of Imagination and Inspiration brings us in turn to Intuition. What have we accomplished now? Well, I would like to answer this question by approaching it from another side. First of all I must draw attention to the steps taken by the Oriental who wishes to rise further after having schooled himself by means of the mantras, after having lived within the language, within the word. He now learns not only to live in the rhythms of language but also in a certain way to experience breathing consciously, in a certain way to experience breathing artificially by altering it in the most varied ways. For him this is the next highest step — but again not something that can be taken over directly by the West. What does the Eastern student of yoga attain by surrendering himself to conscious, regulated, varied breathing? Oh, he experiences something quite extraordinary when he inhales. When inhaling he experiences a quality of air that is not found when we experience air as a purely physical substance but only when we unite ourselves with the air and thus comprehend it spiritually. As he breathes in, a genuine student of yoga experiences something that works formatively upon his whole being, that works spiritually; something that does not expend itself in the life between birth and death, but, entering into us through the spirituality of the outer air, engenders in us something that passes with us through the portal of death. To experience the breathing process consciously means taking part in something that persists when we have laid aside the physical body. For to experience the breathing process consciously is to experience the reaction of our inner being to inhalation. In experiencing this we experience something that preceded birth in our existence as soul-spirit — or let us say preceded our conception — something that had already cooperated in shaping us as embryos and then continued to work within our organism in childhood. To grasp the breathing process consciously means to comprehend ourselves beyond birth and death. The advance from an experience of the aphorism and the word to an experience of the breathing process represented a further penetration into an inspired comprehension of the eternal in man. We Westerners must experience much the same thing — but in a different sphere. What, in fact, is the process of perception? It is nothing but a modified process of inhalation. As we breathe in, the air presses upon our diaphragm and upon the whole of our being. Cerebral fluid is forced up through the spinal column into the brain. In this way a connection is established between breathing and cerebral activity. And the part of the breathing that can be discerned as active within the brain works upon our sense activity as perception. Perception is thus a kind of branch of inhalation. In exhalation, on the other hand, cerebral fluid descends and exerts pressure on the circulation of the blood. The descent of cerebral fluid is bound up with the activity of the will and also of exhalation. Anybody who really studies The Philosophy of Freedom , however, will discover that when we achieve pure thinking, thinking and willing coincide. Pure thinking is fundamentally an expression of will. Thus pure thinking turns out to be related to what the Oriental experienced in the process of exhalation. Pure thinking is related to exhalation just as perception is related to inhalation. We have to go through the same process as the yogi but in a way that is, so to speak, pushed back more into the inner life. Yoga depends upon a regulation of the breathing, both inhalation and exhalation, and in this way comes into contact with the eternal in man. What can Western man do? He can raise into clear soul experiences perception on the one hand and thinking on the other. He can unite in his inner experience perception and thinking, which are otherwise united only abstractly, formally, and passively, so that inwardly, in his soul-spirit, he has the same experience as he has physically in breathing in and out. Inhalation and exhalation are physical experiences: when they are harmonized, one consciously experiences the eternal. In everyday life we experience thinking and perception. By bringing mobility into the life of the soul, one experiences the pendulum, the rhythm, the continual interpenetrating vibration of perception and thinking. A higher reality evolves for the Oriental in the process of inhalation and exhalation; the Westerner achieves a kind of breathing of the soul-spirit in place of the physical breathing of the yogi. He achieves this by developing within himself the living process of modified inhalation in perception and modified exhalation in pure thinking, by weaving together concept, thinking, and perceiving. And gradually, by means of this rhythmic pulse, by means of this rhythmic breathing process in perception and thinking, he struggles to rise up to spiritual reality in Imagination, Inspiration, and Intuition. And when I indicated in my book The Philosophy of Freedom , at first only philosophically, that reality arises out of the interpenetration of perception and thinking, I intended, because the book was meant as a schooling for the soul, to show what Western man can do in order to enter the spiritual world itself. The Oriental says: systole, diastole; inhalation, exhalation. In place of these the Westerner must put perception and thinking. Where the Oriental speaks of the development of physical breathing, we in the West say: development of a breathing of the soul-spirit within the cognitional process through perception and thinking. All this had to be contrasted with what can be experienced as a kind of dead end in Western spiritual evolution. Let me explain what I mean. In 1841 Michelet, the Berlin philosopher, published posthumously Hegel's works on natural philosophy. Hegel had worked at the end of the eighteenth century, together with Schelling, at laying the foundations of a system of natural philosophy. Schelling, as a young firebrand, had constructed his natural philosophy in a remarkable way out of what he called “intellectual Intuition” [ intellektuale Anschauung ]. He reached a point, however, where he could make no further progress. He immersed himself in the mystics at a certain point. His work, Bruno, or Concerning the Divine and Natural Principle in Things , and his fine treatise on human freedom and the origin of evil testify so wonderfully to this immersion. But for all this he could make no progress and began to hold back from expressing himself at all. He kept promising to follow up with a philosophy that would reveal the true nature of those hidden forces at which his earlier natural philosophy had only hinted. When Michelet published Hegel's natural philosophy in 1841, Schelling's long-expected and oft-promised “philosophy of revelation” had still not been vouchsafed to the public. He was summoned to Berlin. What he h ad to offer, however, was not the actual spirit that was to permeate the natural philosophy he had founded. He had striven for an intellectual intuition. He ground to a halt at this point, because he was unable to use Imagination to enter the sphere of which I spoke to you today. And so he was stuck there. Hegel, who had a more rational intellect, had taken over Schelling's thoughts and carried them further by applying pure thinking to the observation of nature. That was the origin of Hegel's natural philosophy. And so one had Schelling's unfulfilled promise to bring forth nature out of the spirit, and then one had Hegel's natural philosophy, which was discarded by science in the second half of the nineteenth century. It was misunderstood, to be sure, but it was bound to remain so, because it was impossible to gain any kind of connection to the ideas contained in Hegel's natural philosophy with regard to phenomenology, the true observation of nature. It is a kind of wonderful incident: Schelling traveling from Munich to Berlin, where great things are expected of him, and it turns out that he has nothing to say. It was a disappointment for all who believed that through Hegel's natural philosophy revelations about nature would emerge from pure thinking. Thus it was in a way demonstrated historically, in that Schelling had attained the level of intellectual intuition but not that of genuine Imagination and in that Hegel showed as well that if pure thinking does not lead on to Imagination or to Inspiration — that is, to the level of nature's secrets ... it was shown that the evolution of the West had thereby run up against a dead end. There was as yet nothing to counter what had come over from the Orient and engendered skepticism; one could counter with nothing that was suffused with the spirit. And anyone who had immersed himself lovingly in Schelling and Hegel and has thus been able to see, with love in his heart, the limitations of Western philosophy, had to strive for anthroposophy. He had to strive to bring about an anthroposophically oriented spiritual science for the West, so that we will possess something that works creatively in the spirit, just as the East had worked in the spirit through systole and diastole in their interaction. We in the West can allow perception and thinking to resound through one another in the soul-spirit [ das geistig-seelische Ineinanderklingenlassen ], through which we can rise to something more than a merely abstract science. It opens the way to a living science, which is the only kind of science that enables us to dwell within the element of truth. After all the failures of the Kantian, Schellingian, and Hegelian philosophies, we need a philosophy that, by revealing the way of the spirit, can show the real relationship between truth and science, a spiritualized science, in which truth can really live to the great benefit of future human evolution.

The Boundaries of Natural Science

Lecture VIII

https://rsarchive.org/Lectures/GA322/English/AP1983/19201003p01.html

Dornach

3 Oct 1920

GA322-8

To-day I should like to make some introductory remarks to what I am going to lay before you in the coming days. My reason for doing this is that you may know the purpose of these talks from the outset. It will not be my task during the following days to deal with any narrowly defined, special branch of science, but to give various wider viewpoints, having in mind a quite definite goal in relation to science. I should therefore like to warn people not to describe this as an ‘Astronomical Course’. It is not meant to be that. But it will deal with something that I feel is especially important for us to consider at this time. I have therefore given it the title “The relation of the diverse branches of Natural Science to Astronomy,” and today in particular I shall explain what I actually intend with the giving of this title. The fact is that in a comparatively short time much will have to be changed within what we call the sphere of science, if it is not to enter upon a complete decline. Certain groups of sciences which are now comprised under various headings and are permitted to be represented under these headings, in our ordinary schools, will have to be taken out their grooves and be classified from quite other aspects. This will necessitate a far reaching regrouping of our sciences. The grouping at present employed is entirely inadequate for a world-conception based upon reality, and yet our modern world holds so firmly to such traditional classification that it is on this basis that candidates are chosen to occupy the professorial chairs in our Universities. People confine themselves for the most part to dividing the existing, circumscribed fields of Natural Science into yet further special branches, and they then look to the specialists or experts as they are called. But a change must come into the whole scientific life by the advent of quite different categories, within which will be united, as in a whole new field of science, things that today are dealt with in Zoology or Physiology, or again, let us say, in the Theory of Knowledge. The older forms of scientific classification, often extremely abstract, must die out, and quite new scientific combinations must arise. This will meet with great obstacles at first, because people today are trained in the specialized branches of science and it will be difficult for them to find an approach to what they will urgently need in order to bring about a combination of scientific material in accordance with reality. To put in concisely, I might say: We have today a science of astronomy, of Physics, of Chemistry, of Philosophy, we have a science of Biology, of Mathematics, and so on. Special branches have been formed, almost, I might say, so that the various specialists will not have such hard work in order to become well grounded in their subject. They do not have too much to do in mastering all the literature concerned, which, as we know, exists in immense quantities. But it will be a matter of creating new branches which will comprise quite different things, including perhaps at the same time something from Astronomy, something from Biology, and so on. For this, a reshaping of our whole life of science will of course be essential. Therefore, what we term Spiritual Science, which does indeed aim to be of a universal nature, must work precisely in this direction. It must make it its special mission to work in this direction. For we simply cannot get any further with the old grouping. Our Universities confront the world today, my dear friends, in a way that is really quite estranged from life. They turn out mathematicians, physiologists, philosophers, but none of them have any real relation to the world. They can do nothing but work in their narrowly confined spheres, putting before us a picture of the world that becomes more and more abstract, less and less realistic. It is the change here indicated — a deep necessity for our time — to which I want to do justice in these lectures. I should like you to see how impossible it will be to continue the older classifications indefinitely, and I therefore want to show how other branches of science of the most varied kinds, which, in their present way of treatment, take no account of Astronomy, have indeed definite connections with Astronomy, that is, with a true knowledge of universal space. Certain astronomical facts must perforce be taken into account in other branches of science too, so that we may learn to master these other fields in a way conformable to reality. The task of these lectures is therefore to build a bridge from the different fields of scientific thought to the field of Astronomy, that astronomical understanding may appear in the right way in the various fields of science. In order not to be misunderstood, I should like to make one more remark about method. You see, the manner of presenting scientific facts which is customary nowadays must undergo considerable change, because it actually arises out of the scientific structure which has to be overcome. When today facts are referred to, which lie somewhat remote from man's understanding, — remote, just because he does not meet with them at all in his scientific knowledge, — it is usual to say: “That is stated, but no proved.” Yet in scientific work is often quite inevitable that statements must be made at first purely as results of observation, which only afterwards can be verified as more and more facts are brought to support them. So it would be wrong to assume, for instance, that right at the beginning of a discourse someone could break in and say, “That is not proved.” It will be proved in the course of time, but much will first have to be presented simply from observation, so that the right concept, the right idea, may be created. And so I beg of you to take these lectures as a whole, and to look in the last lectures for the plain proof of many things which seem in the first lectures to be mere statements. Many things will then be verified which I shall have to handle at first in such a way as to evoke the necessary concepts and ideas. Astronomy as we know it today, even including the domain of Astrophysics, is fundamentally a modern creation. Before the time of Copernicus or Galileo men thought about astronomical phenomena in a way which differed essentially from the way we think today. It is even extraordinarily difficult to indicate the way in which man still thought of Astronomy in, say, the 13th and 14th centuries, because this way of thinking has become completely foreign to modern man. We only live in the ideas which have been formed since the time of Galileo, Kepler, Copernicus; and from a certain point of view that is perfectly right. They are ideas which treat of the distant phenomena of universal space, in so far as they are concerned with Astronomy, in a mathematical and mechanical way. Men think of these phenomena in terms of mathematics and mechanics. In observing the phenomena, men base their ideas upon what they have acquired from an abstract mathematical science, or an abstract science of mechanics. They calculate distances, movements and forces. But the qualitative outlook still in existence in the 13th and 14th centuries, which distinguished Individualities in the stars, an Individuality of Jupiter, of Saturn ... this has become completely lost to modern man. I will make no criticism of the things at the moment, but will only point out that the mechanical and mathematical way of treating what we call the domain of Astronomy has become the exclusive one. Even if we acquaint ourselves with the stars in a popular fashion without understanding mathematics or mechanics, we still find it presented, even if in a manner suitable for the lay-mind, entirely in ideas of space and time, of a mathematical and mechanical kind. No doubts of any kind exist in the minds of our contemporaries — who believe that their judgment is authoritative — that this is the only way in which to regard the starry heavens. Anything else, they are convinced, would be merely amateurish. Now, if the question arises as to how it has actually come about that this view of the starry heavens has emerged in the evolution of civilization, the answer of those who regard the modern scientific mode of thought as absolute, will be different from the reply which we are able to give. Those who regard the scientific thought of today as something absolute and true, will say: Well, you know, among earlier humanity there were not yet any strictly scientifically formed ideas; man had first to struggle through to such ideas, i. e., to the mathematical, mechanical mode of regarding celestial phenomena of the Universe, a later humanity has worked through to a strictly scientific comprehension of what does actually correspond to reality. This is an answer that we cannot give, my dear friends. We must take up our position from the standpoint of the evolution of humanity, which in the course of its existence, has introduced various inner forces into its consciousness. We must say to ourselves: The manner of observing the celestial phenomena which existed among the ancient Babylonians, the Egyptians, perhaps even the Indian people, was due to the particular form which the development of the human soul-forces was taking in those times. Those human soul-forces had to be developed with the same inner necessity with which a child between the 10th and 15th year must develop certain soul-forces, while in another period it will developing other faculties, which lead it to different conclusions about the world. Then came the Ptolemaic system. That arose out of different soul-forces. Then our Copernican system. That arose from yet other soul-forces. The Copernican system did not develop because humanity had happily struggled through to objectivity, whereas before they had all been as children, but because humanity since the middle of the 15th century needed precisely the mathematical, mechanical faculties for its development. That is why modern man sees the celestial phenomena in the picture formed by the mathematical, mechanical faculties. And he will some day see them again in a different way, when in his development he has drawn up out of the depths of the soul other forces, — to his own healing and benefit. Thus it depends upon humanity what form the world-concept takes . But it is not a question of looking back in pride to earlier times when men were “more childlike,” and then thinking that in modern times we have at last struggled through to an objective understanding which can now endure for all future ages. There is something which has become a real necessity to later humanity and has given color to the requirements of the scientific mind. It is this: Men strive on the one hand for ideas that are clear and easy to control — namely, mathematical ideas — , and on the other hand they strive for ideas through which they can surrender most strongly to an inner compulsion. The modern man at once becomes uncertain and nervous when he does not feel the strong inner compulsion presented, for instance, by the argument of the Pythagorean theorem, but realizes, let us say, that the figure which is drawn does not decide for him, but that he must develop an activity of soul and decide for himself. Then he at once becomes uncertain and nervous and is no longer willing to continue the line of thought. So he says: That is not exact science; subjectivity comes into it. Modern man is really dreadfully passive; he would like to be led everywhere by a chain of infallible arguments and conclusions. Mathematics satisfies this requirement, at least in most cases; and where it does not, where man have interposed their own opinion in recent times, — well, my dear friends, the results are according! Men still believe that they are being exact, while they hit upon the most incredible ideas. Thus in mathematics and mechanics men think they are being led forward by leading-strings of concepts which are linked together through their own inherent logic. They feel then as if they had ground under their feet, but the moment they step off it they do not want to go on any further. Concepts which are easy to grasp on the one hand, and the element of inner compulsion on the other: this is what modern man needs for his “safety.” Fundamentally, it is on this basis that the particular form of world-conception, supplied by the modern science of Astronomy, has been built up. I am not at the moment speaking of the single facts, but merely of the world-conception as a whole. This attitude towards a mathematical, mechanical conception of the world has so penetrated the consciousness of humanity, my dear friends, that people have come to regard everything that cannot be treated in this way as more or less unscientific. From this feeling proceeded such a phrase as that of Kant, who said: In every domain of science there is only so much real science as there is mathematics in it; one ought really to bring Arithmetic or Geometry into all the sciences. But this idea, as we know, breaks down when we think how remote the simplest mathematical ideas are to those, for instance, who study Medicine. Our present division of the sciences gives to a medical student practically nothing in the way of mathematical ideas. And so it comes about that on the one hand what is called astronomical knowledge has been set up as an ideal. DuBois-Raymond has defined this in his address on the limits of the knowledge of Nature by saying: We only grasp truths in Nature and satisfy our need of causality inasmuch as we can apply the astronomical type of knowledge. That is to say, we regard the celestial phenomena in such a way that we draw the stars upon the chart of the sky and calculate with the material which is there given us. We can state exactly: There is a star, it exercises a force of attraction upon other stars. We begin to calculate, having the different things, to which our calculations apply, visibly before us. This is what we have brought into Astronomy in the first place. Now we observe, let us say, the molecule. Within the complex molecule we have the atoms, exercising a force of attraction on one another, moving around each other, — forming, as it were, a little universe. We observe this molecule as a small cosmic system and are satisfied if it all seems to fit. But then there is the great difference that when we look out into the starry sky all the details are given to us. We can at most ask whether we understand them rightly, whether after all, there might not be some other explanation than the one given by Newton. We have the given details and then we spin a mathematical, mechanical web over them. This web of thought is actually added to the given facts, but from a scientific point of view it satisfies the modern need of man. And now we carry the system, which we have first thought out and devised, into the world of the molecule and atom. Here we add in thought what in the other case was given to us. But we satisfy our so-called need of causality by saying: What we think of as the smallest particle, moves in such and such a way, and it is the objective counterpart of what we experience subjectively as light, sound, warmth etc. We carry the astronomic form of knowledge into every phenomenon of the world and thus satisfy our demand for causality. Du-Bois Raymond has expressed it quite bluntly: “When one cannot do that, there is no scientific explanation at all.” Yes, my dear friends, what is here claimed should actually imply that if, for example, we wished to come to a rational form of therapy, that is to say, to understand the activity of a remedy, we should have to be able to follow the atoms in the substance of the remedy as we follow the movements of the Moon, the Sun, the planets and the fixed stars. They would all have to become little cosmic systems. We should have to be able to calculate how this or that remedy would work. This was actually an ideal for some people not so very long ago. Now they have given up such ideals. Such an idea collapses not only in reference to such a far off sphere as a rational therapy, but in those lying more within reach, simply because our sciences are divided as they are today. You see, the modern doctor is educated in such a way that he masters extraordinarily little of pure mathematics. We may talk to him perhaps of the need for a knowledge of astronomy but it would be of no use to speak of introducing mathematical ideas into his field of work. But as we have seen, everything outside mathematics, mechanics and astronomy should be described, according to the modern notion, as being unscientific in the strict sense of the word. Naturally that is not done. People regard these other sciences too as exact, but this is most inconsistent. It is, however, characteristic of the present time that the demand should have been made at all for everything to be understood on the model of mathematical Astronomy. It is hard today to talk to people in a serious way about such thing; how hard this is I should like to make clear to you by an example. You know of course that the question of the form of the human skull has played a great role in modern biology. I have also spoken of this matter may times in the course of our anthroposophical lectures. Goethe and Oken put forward magnificent thoughts on this question of the human skull-bones. The school of Gegenbauer also carried out classical researches upon it. But something that could satisfy the urge for a deeper knowledge in this direction does not in fact exist today. People discuss, to what extent Goethe was right in saying that the skull-bones are metamorphosed vertebrae, bones of the spine. But it is impossible to arrive at any really penetrating view of this matter today, because in the circles where these things are discussed one would scarcely be understood, and where an understanding might be forthcoming these things are not talked of because they are not of interest. You see, it is practically impossible today to bring together in close working association a thoroughly modern doctor, a thoroughly modern mathematician, — i.e., one who is master of higher mathematics —, and a man who could understand both of them passably well. These three men could scarcely understand one another. The one who would sit in the middle, understanding both of them slightly, would be able at a pinch to talk a little with the mathematician and also with the doctor. But the mathematician and the doctor would not be able to understand each other upon important questions, because what the doctor would have to say about them would not interest the mathematician, and what the mathematician would have to say — or would say, if he found words at all, — would not be understood by the doctor, who would be lacking the necessary mathematical background. This is what would happen in an attempt to solve the problem I have just put before you. People imagine: If the skull-bones are metamorphosed vertebra, then we ought to be able to proceed directly, through a transformation which it is possible to picture spatially, from the vertebra to the skull. To extend the idea still further to the limb-bones would, on the basis of the accepted premises, be quite out of the question. The modern mathematician will be able, from his mathematical studies, to form an idea of what it really means when I turn a glove inside out, when I turn the inside to the outside. One must have in mind a certain mathematical handling of the process by which what was formerly outside is turned inward, and what was inside is turned to the outside. I will make a sketch of it (Fig. 1) — a structure of some sort that is first white on the outside and red inside. We will treat this structure as we did the glove, so that it is now red outside and white inside (Fig. 2). But let us go further, my dear friends, and picture to ourselves that we have something endowed with a force of its own that does not admit of being turned inside out in such a simple way as a glove which still looks like a glove after being inverted. Suppose that we invert something which has different stresses of force on the outer surface from those on the inner. We shall then find that simply through the inversion quite a new form arises. The form may appear thus before we have reversed it (Fig. 1): we turn it inside out and now different forces come into consideration on the red surface and on the white, so that perhaps, purely through the inversion, this form arises (Fig. 3). Such a form might arise merely in the process of inversion. When the red side faced inward, forces remained dominant which are developed differently when it is turned outward. And so with the white side; only when turned towards the inside can it develop its inherent forces. It is of course quite conceivable to give a mathematical presentation of such a subject, but people are thoroughly disinclined nowadays to apply to reality what is arrived at conceptually in such a way. The moment, however, we learn to apply this to reality, we become able to see in our long bones or tubular bones (that is, in the limb bones), a form which, when inverted, becomes our skull bones! In the drawing, let the inside of the bone, as far as the marrow, be depicted by the red, the outside by the white ( Fig. 4 ). Certain forms and forces, which can of course be investigated, are turned inward, and what we see when we draw away the muscle from the long bone is turned outward. But now imagine these hollow bones turned inside out by the same principle as I have just given you, in which other conditions of stress and strain are brought into play; then you may easily obtain this form (Fig. 5). Now it has the white within, and what I depicted by the red comes to the outside. This is in fact the relationship of a skull-bone to a limb-bone , and in between lies the typical bone of the back — the vertebra of the spinal column. You must turn the tubular bone inside out like a glove according to its indwelling forces; then you obtain the skull-bone. The metamorphosis of the bones of the limbs into the skull-bones is only to be understood when keeping in mind the process of inversion, or ‘turning inside-out’. The important thing to realizes is that what is turned outward in the limb-bones is turned inward in the skull. The skull-bones turn towards a world of their own in the interior of the skull. That is one world. The skull-bone is orientated to the world, just as the limb-bone is orientated outward, towards the external world. This can be clearly seen in the case of the bones. Moreover, the human organism as a whole is so organized that it has on the one hand a skull organization, and on the other a limb-organization, the skull-organization being oriented inward, the limb-organization outward. The skull contains an inner world, the limb-man an outer world, and between the two is a kind of balancing system which preserves the rhythm. My dear friends, take any literature dealing with the theory of functions, or, say, with non-Euclidean geometry, and see what countless ideas of every kind are brought forward in order to get beyond the ordinary geometrical conception of three-dimensional space; — to extend the domain — widen out the concept of geometry. You will see what industry and ingenuity are employed. But now suppose that you have become an expert at mathematics, who knows the theory of functions well and understands all that can be understood today of non-Euclidean geometry. I should like now to put a question concerning much that tends in this direction (Forgive me if it seems as if one did not value them highly, speaking of these things in such trivial terms. And yet I must do so, and I beg the audience, especially trained mathematicians, to turn it over in their minds and see if there is not truth in what I say.) The question could be put as follows: What is the use of all this spinning of purely mathematical thoughts? What is it worth to me, so to speak, in pounds, shillings and pence? No one is interested in the spheres in which it might perhaps find concrete application. Yet if we were to apply to the structure of the human organism all that has been thought out in non-Euclidean geometry, then we should be in the realm of reality, and applying immeasurably important ideas to reality, not wandering about in mere speculations. If the mathematician were so trained as to be interested also in what is real, — in the appearance of the heart, for example, so that he could form an idea of how through a mathematical process he could turn the heart inside out, and how thereby the whole human form would arise, — if he were taught to use his mathematics in actual life, then he could be working in the realm of the real. It would then be impossible to have the trained mathematician on the one hand, not interested in what the doctor learns, and on the other, the physician, understanding nothing of of how the mathematician — though in a purely abstract element — is able to change and metamorphose forms. This is the situation we must alter. If not, our sciences will fall into decay. They grow estranged from one another; people no longer understand each other's language. How then is science to be transformed into a social science, as is implied in all that I shall be telling you in these lectures? A science which leads over into social science is not yet in existence. On the one hand we have Astronomy, tending more and more to be clothed in mathematical forms of thought. It has become so great in its present form just because it is a purely mathematical and mechanical science. But there is another branch of science which stands, as it were, at the opposite pole to Astronomy, and which cannot be studied in its real nature without Astronomy. It is however, impossible, as science is today, to build a bridge between Astronomy and this other pole of science, namely, Embryology. He alone is studying reality, who on the one hand studies the starry skies and on the other hand the development of the human embryo. How is the human embryo generally studied today? Well, it is stated: The human embryo arises from the interaction of two cells, the sex-cells or gametes, male and female. These cells develop in the parent organism in such a way as to attain a certain state of independence before they are able to interact. They then present a certain contract, the one cell, the male, calling forth new and different possibilities of development in the other, the female. The question is put: What is a cell? As you know, since about the middle of the 19th century, Biology has largely been built upon the cell theory. The cell is described as a larger or smaller, spherule, consisting of albuminous or protein-like substances. It has a nucleus within it of a somewhat different structure and around the whole is an enclosing membrane. As such, it is the building-stone for all that arising by way of living organisms. The sex-cells are of a similar nature but are formed differently according to whether they are male or female, and from such cells every more complicated organism is built up. But now, what is actually meant when it is said that an organism builds itself up from these cells? The idea is that substances which are otherwise in Nature are taken up into these cells and then no longer work in quite the same way as before. If oxygen, nitrogen or carbon are contained in the cells, the carbon, for instance, does not have the effect upon some other substance outside, that it would have had before; such power of direct influence is lost to it. It is taken up into the organism of the cell and can only work there as conditions in the cell allow. That is to say, the influence is exerted not so much by the carbon, but by the cell, which makes use of the particular characteristics of carbon, having incorporated a certain amount of it into itself. For example, what man has within him in the form of metal — iron for instance — only works in a circuitous way, via the cell. The cell is the building-stone. So in studying the organism, everything is traced to the cell. Considering at first only the main bulk of the cell, without the nucleus and membrane, we distinguish two parts: a transparent part composed of this fluid, and another part forming sort of framework. Describing it schematically, we may say that there is the framework of the cell, and this is embedded, as it were, in the other substance which, unlike the framework, is quite unformed. (Fig. 6) Thus we must think of the cell as consisting of a mass which remains fluid and unformed and a skeleton or framework which takes on a great variety of forms. This then is studied. The method of studying cells in this way has been pretty well perfected; certain parts in the cell can be stained with color, others do not take the stain. Thus with carmine or saffron, or whatever coloring matter is used, we are able to distinguish the form of the cell and can thus acquire certain ideas about its inner structure. We note, for instance, how the inner structure changes when the female germ-cell is fructified. We follow the different stages in which the cell's inner structure alters; how it divides; and how the parts become attached to one another, cell upon cell, so that the whole becomes a complicated structure. All this is studied. But it occurs to no-one to ask: With what is this whole life in the cell connected? What is really happening? It does not occur to anyone to ask this. What happens in the cell is to be conceived, my dear friends, in the following way, — though to be sure, it is still a rather abstract way. There is the cell. For the moment let us consider it in its most usual form, namely the spherical form. This spherical form is partially determined by the thin fluid substance, and enclosed within it is the delicate framework. But what is the spherical form? The thin fluid mass is as yet left entirely to itself and therefore behaves according to the impulses it receives from its surroundings. What does it do? Well, my dear friends, it mirrors the universe around it! It takes on the form of the sphere because it mirrors in miniature the whole cosmos, which we indeed also picture to ourselves ideally as a sphere. Every cell in its spherical form is no less than an image of the form of the whole universe . And the framework inside, every line of the form, is conditioned by its relationship to the structure of the whole cosmos. To express myself abstractly to begin with, think of the sphere of the universe with its imaginary boundary ( Fig. 7 ). In it, you have here a planet, and there a planet (a,a 1 ). They work in such a way as to exert an influence upon one another in the direction of the line which joins them. Here (m) let us say — diagrammatically, of course, — a cell is formed; its outline mirrors the sphere. Here, within the framework it has a solid part which is due to the working of the one planet on the other. And suppose that here there were another constellation of planets, working upon each other along the line joining them (b,b 1 ). And here again there might be yet another planet (c), this one having no counterpart; — it throws the whole construction, which might otherwise have been rectangular, out of shape, and the structure takes on a somewhat different form. And so you have in the whole formation of the framework of the cell a reflection of the relationships existing in the planetary system, — altogether in the whole starry system. You can enter quite concretely into the formation of the cell and you will reach an understanding of this concrete form only if you see in the cell an image of the entire cosmos. And now take the female ovum, and picture to yourselves that this ovum has brought the cosmic forces to a certain inner balance. They have taken on form in the framework of the cell, and are in a certain way at rest within it, supported by the female organism as a whole. Then comes the influence of the male sex-cell. This has not brought the macrocosmic forces to rest, but works in the sense of a very specialized force. It is as though the male sex-cell works precisely along this line of force (indicated by Dr. Steiner on the blackboard) upon the female ovum which has come to a condition of rest. The cell, which is an image of the whole cosmos, is thereby caused to relinquish its microcosmic form once more to a changing play of forces. At first, in the female ovum, the macrocosm comes to rest in a peaceful image. Then through the male sex-cell the female is torn out of this state of rest, and is drawn again into a region of specialized activity and brought into movement. Previously it had drawn itself together in the resting form of the image of the cosmos, but the form is drawn into movement again by the male forces which are, so to speak, images of movement. Through them the female forces, which are images of the form of the cosmos and have come to rest, are brought out of this state of rest and balance. Here we may have some idea, from the aspect of Astronomy, of the forming and shaping of something which is minute and cellular. Embryology cannot be studied at all without Astronomy, for what Embryology has to show is only the other pole of what is seen in Astronomy. We must, in a way, follow the starry heavens on the one hand, seeing how they reveal successive stages, and we must then follow the process of development of a fructified cell. The two belong together, for the one is only the image of the other. if you understand nothing of Astronomy, you will never understand the forces which are at work in Embryology, and if you understand nothing of Embryology, you will never understand the meaning of the activities with which Astronomy has to deal. For these activities appear in miniature in the processes of Embryology. It is conceivable that a science should be formed, in which, on the one hand, astronomical events are calculated and described, and on the other hand all that belongs to them in Embryology, which is only the other aspect of the same thing. Now look at the position as it is today: you find that Embryology is studied on its own. It would be regarded as madness if you were to demand of a modern embryologist that he should study Astronomy in order to understand the phenomena in his own sphere of work. And yet it should be so. This is why a complete regrouping of the sciences is necessary. It will be impossible to become a real embryologist without studying Astronomy. It will no longer be possible to educate specialists who merely turn their eyes and their telescopes to the stars, for to study the stars in that way has no further meaning unless one knows that it is out of the great universe that the minute and microscopical is fashioned. All this, — which is quite real and concrete, — has in scientific circles been changed into the utmost abstraction. It is reality to say: We must strive for astronomical knowledge in cellular theory, especially in Embryology. If DuBois-Raymond had said that the detailed astronomical facts should be applied to the cell-theory, he would have spoken out of the sphere of reality. But what he wanted corresponds to no reality, namely that something thought-out and devised — the atoms and molecules — should be examined with astronomical precision. He wanted the astronomical type of mathematical thoughts, which have been added to the world of the stars, to be sought for again in the molecule. Thus you see, upon the one hand lies reality: movement, the active forces of the stars and the embryonic development in which there lives, in all reality, what lives in the starry heavens. That is where the reality lies and that is where we must look for it. On the other hand lies abstraction. The mathematician, the mechanist, calculates the movements and forces of the heavenly bodies and then invents the molecular structure to which to apply this kind of astronomical knowledge. Here he is withdrawn from life, living in pure abstractions. These are the things about which we must think, remembering that now we must renew, in full consciousness, something which was in a certain sense present in earlier times. Looking back to the Egyptian Mysteries, we find astronomical observations such as were made at that time. These observations, my dear friends, were not used merely to calculate when an eclipse of the Sun or Moon would take place, but rather to arrive at what should come about in social evolution. Men were guided by what they saw in the heavens, as to what must be said to the people, what instructions should be given, so that the development of the whole social life should take its right course. Astronomy and Sociology were dealt with as one . We too, though in a different way from the Egyptians, must again learn how to connect what happens in social life with the phenomena of the great universe. We do not understand what came about in the middle of the 15th century, if we cannot relate the events of that time to the phenomena which then prevailed in the universe. It is like a blind man talking about color to speak of the changes in the civilized world in the middle of the 15th century without taking all this into account. Spiritual Science is already a starting point. But we shall not succeed in bring together the complicated domain of Sociology — social science — with the observations of natural phenomena, unless we first begin by connecting Astronomy with Embryology, linking the embryonic facts with astronomical phenomena.

Astronomy as Compared to Other Sciences

Lecture I

https://rsarchive.org/Lectures/GA323/English/LR81/19210101p01.html

Stuttgart

1 Jan 1921

GA323-1

Yesterday I showed a connection between two branches of science which according to our modern ideas are widely separated. I sought to show that the science of Astronomy should provide certain items of knowledge which must then be turned to account in quite a different branch of science, from which the study and method of Astronomy is completely excluded nowadays. In effect, I sought to show that Astronomy must be linked with Embryology. It is impossible to understand the phenomena of cell-development, especially of the sex-cells, without calling to our aid the realities of Astronomy, which lie apparently so far removed from Embryology. I pointed out that there must come about a regrouping of the sciences, for a man specializing nowadays along certain lines finds himself hemmed in by the circumscribed divisions of science. He has no possibility of applying his specialized knowledge and experience to spheres which may lie near to hand but which will only have been presented to him from certain aspects, insufficient to give him a deeper understanding of their full significance. If it is true, as will emerge in these lectures, that we can only understand the successive stages in human embryonic development when we understand their counterpart, the phenomena of the Heavens; if this is a fact — and it will turn out to be so — then we cannot work at Embryology without working at Astronomy. Nor can we occupy ourselves with Astronomy without bringing new light to the facts of Embryology. In Astronomy we are studying something which reveals its most important activity in the development of the human embryo. How, then, shall we explain the meaning and reason of astronomical facts, if we bring into the kind of connection with these facts the very realm in which this meaning and reason are revealed? You see how necessary it is to come to a reasonable world-conception, out of the chaos in which we are today in the sphere of science. If, however, one only accepts what is fashionable nowadays, it will be very difficult to grasp, even as a general idea, anything like what I said yesterday. For the evolution of our time has brought it about that astronomical facts are only grasped through mathematics and mechanics, while embryological facts are recorded in such a way that in dealing with them anything of the nature of mathematics or mechanics is discarded. At most, even if the mathematical-mechanical is brought into some kind of relation to Embryology, it is done in a quite an external way, without considering where lies the origin of what, in embryonic development, might truly be expressed in mathematical and mechanical terms. Now I need only point to a saying of Goethe's, uttered out of a certain feeling — a ‘feeling knowledge’ I might call it — but indicating something of extraordinary significance. (You can read of it in Goethe's “Spruche in Prosa”, and in the Commentary which I added to the publication in the Kurschner edition of the Deutsche National-Literatur, where I spoke in detail about this passage.) Goethe says there: People think of natural phenomena so entirely apart from man that they are tending ever more and more to disregard the human being in their study of the phenomena of Nature. He, on the contrary, believed that natural phenomena only reveal their true meaning if they are regarded in full connection with man — with the whole organization of man. In saying this, Goethe pointed to a method of research which is well-nigh anathematized nowadays. People today seek an 'objective' understanding of Nature through research that is completely separated from the human being. This is particularly noticeable in such a science as Astronomy, where no account at all is taken of the human being. On the contrary, people are proud that the apparently ‘objective’ facts have shown that man is only a grain of dust upon an Earth which has somehow been fused into a planet, moving first round the Sun and then, in some way or other, moving with the Sun in space. They are proud that one need pay no attention to this ‘grain of dust’ which wanders about on Earth, — that one need only pay attention to what is external to the human being in considering the great celestial phenomena. Now the question is, whether any real results are to be obtained by such a method. I should like once more to call attention, my dear friends, to the path we must pursue in these lectures. What you will find as proof will only emerge in the further course of the lectures. Today we must take a good deal simply from observation in order to form certain preliminary ideas. We must first build up certain necessary concepts; only then shall we be able to pass on to the verification of these concepts . From what source, then, can we gain a real perception of the celestial phenomena merely through the mathematics which we apply to them? The course of development of human knowledge can disclose — if one does not take up the proud position of thinking how ‘wonderfully advanced’ we are today and how all that went before was childish — the course of human development can teach us how the prevailing points of view can change. From certain aspects one can have great reverence for the celestial observations carried out, for instance, by the ancient Chaldeans. The ancient Chaldeans made very exact observations concerning the connection of human time-reckoning with the heavenly phenomena. They had a highly develop ‘Calendar-Science’. Much that appears to us today as self-evident really dates back to the Chaldeans. Yet the Chaldeans were satisfied with a mathematical picture of the Heavens which portrayed the Earth more or less as a flat disc, with the hollow hemisphere of the heavenly vault arched above, the fixed stars fastened to it, and the planets moving over it. (Among the planets they also included the Sun.) They made their calculations with this picture in the background. Their calculations for the most part were correct, in spite of being based upon a picture which the science of today can only describe as a fundamental error, as something ‘childish’. Science, or more correctly, the scientific tendency and direction, then went on evolving. There was a stage when men pictured that the Earth stood still, but that Venus and Mercury moved round the Sun. The Sun formed the central point, as it were, for the motions of Venus and Mercury, while the other planets — Mars, Jupiter and Saturn — moved round the Earth. Thereafter, men progressed to making Mars, Jupiter and Saturn also revolved around the Sun, but the Earth was still supposed to stand still, while the Sun with its encircling planets as well as the starry Heavens revolved round the Earth. This was still the fundamental view of Tycho Brahe, whereas his contemporary Copernicus established the other concept, namely, that the Sun was to be regarded as standing still and that the Earth was to be reckoned among the planets revolving round the Sun. Following hard one upon the other in the time of Copernicus were the two points of view, one which existed in ancient Egypt, of the stationary Earth with the other planets encircling the Sun, still represented by Tycho Brahe; the other, the Copernican concept, which broke radically with the idea of the center of coordinates being in the center of the Earth, and transferred it to the center of the Sun. For in reality the whole alteration made by Copernicus was nothing else than this, — the origin of coordinates was removed from the center of the Earth to the center of the Sun. What was actually the problem of Copernicus? His problem was, how to reduce to simple lines and curves these complicated apparent motions of the planets, — ; for so they appear as observed from the Earth. When the planets are observed from the Earth, their movements can only be described as a variety of looped lines, such as these (Fig. 1). So, when taking the center of the Earth as the center of coordinates it is necessary to base the planetary movements on all sorts of complicated curves. Copernicus said, in effect: ‘as an experiment, I will place the center of the whole coordinate system in the center of the Sun.’ Then the complicated planetary curves are reduced to simple circular movements, or as was stated later, to ellipses. The whole thing was purely the construction of a world-system which aimed at being able to represent the paths of the planets in the simplest possible curves. Now today we have a very remarkable fact, my dear friends. This Copernican system, when employed purely mathematically, supplies the necessary calculations concerning the observed phenomena as well as and no better than any of the earlier ones. The eclipses of the Sun and Moon can be calculated with the ancient Chaldean system, with the Egyptian, with the Tychonian and with the Copernican. The outer occurrences in the Heavens, in so far as they relate to mechanics or mathematics, can thus be foretold. One system is as well suited as another. It is only that the simplest thought-pictures arise with the Copernican system. But the strange thing is that in practical Astronomy, calculations are not made with the Copernican system. Curiously enough, in practical Astronomy, — to obtain what is needed for the calendar, — the system of Tycho Brahe is used! This shows how little that is really fundamental, how little of the essential nature of things, comes into question when the Universe is thus pictured in purely mathematical curves or in terms of mechanical forces. Now there is another very remarkable fact which I will only indicate today, so that we shall understand each other about the aim of these lectures. I shall speak further about it in succeeding lectures. Copernicus in his deliberations bases his cosmic system upon three axioms. The first is that the Earth rotates on its own North-South axis in 24 hours. The second principle on which Copernicus bases his picture of the Heavens is that the Earth moves round the Sun. In its revolution round the Sun the Earth itself, of course, also revolves in a certain way. This rotation, however, does not occur round the North-South axis of the Earth, which always points to the North Pole, but round the axis of the Ecliptic, which, as we know, is at an angle with the Earth's own axis. Therefore the Earth goes through a rotation during a 24-hour day round its own N. S. Axis, and then, inasmuch as it performs approximately 365 such rotations in the year, there is added another rotation, an annual rotation, if we disregard the revolution round the Sun. The Earth, then, if it always rotates thus, and then again revolves round the Sun, behaves like the Moon as it rotates round the Earth, always turning the same side towards us. The Earth does this too, inasmuch as it revolves round the Sun, but not on the same axis as the one on which it rotates for the daily revolution. It revolves through this 'yearly day' on another axis; this is an added movement, besides the one taking place in the 24-hour day. Copernicus' third principle is that not only does such a revolution of the Earth take place round the North-South axis, but that there is yet a third revolution which appears as a retrograde movement of the North-South axis round the axis of the Ecliptic. Thereby, in a certain sense, the revolution round the axis of the Ecliptic is canceled out. By reason of this third revolution the Earth's axis continuously points to the North celestial Pole (the Pole-Star). Whereas, by virtue of revolving round the Sun, the Earth's axis would have to describe a circle, or an ellipse, round the pole of the Ecliptic, its own revolution, which takes the opposite direction (every time the Earth proceeds a little further its axis rotates backwards), causes it to point continually to the North Pole. Copernicus adopted this third principle, namely: The continued pointing of the Earth's axis to the Pole comes about because, by a rotation of its own — a kind of ‘inclination’ (?) — it cancels out the other revolution. This latter therefore has no effect in the course of the year, for it is constantly being annulled. In modern Astronomy, founded as it is on the Copernican system, it has come about that the first two axioms are accepted and the third is ignored. This third axiom is lightly brushed aside by saying that the stars are so far away that the Earth-axis, remaining parallel to itself, always points practically to the same spot. Thus it is assumed that the North-South axis of the Earth, in its revolution, remains always parallel to itself. This was not assumed by Copernicus; on the contrary, he assumed a perpetual revolving of the Earth's axis. Modern Astronomy is therefore not really based on the Copernican system, but accepts the first two axioms because they are convenient and discards the third, thus becoming lost in the prevarication that it is not necessary to suppose that the Earth's axis itself must move in order to keep pointing to the same spot in the Heavens, but that the place itself is so far away that even if the axis does move parallel to itself it will still point to the same spot. Anyone can see that this is a prevarication. To-day therefore we have a ‘Copernican system’ from which a most important element has actually been discarded. The development of modern Astronomy is presented in such a way that no one notices that an important element is missing. Yet only in this way is it possible to describe it all so neatly: “Here is the Sun the Earth goes round in an ellipse with the Sun in one of the foci.” (Fig. 2) As time went on it became no longer possible to hold to the starting-point of the Copernican theory, namely that the Sun stands still. A movement is now attributed to the Sun, which is said to move forward with the whole ellipse, perpetually creating new ellipses, so to speak (Fig. 3). It became necessary to introduce the Sun's own movement, and this was done simply by adding something new to the picture they had before. A mathematical description is thus obtained which is admittedly convenient, but few questions are asked as to its possibility or its reality. It is only from the apparent movement of the stars that the Earth's movement is deduced by this method. As we shall presently see, it is of great significance whether or no one assumes a movement — which indeed must be assumed — namely the aforesaid ‘inclination’ (?) of the Earth's axis, perpetually annulling the annual rotation. Resultant movements, after all, are obtained by adding up the several movements. If one is left out, the whole is no longer true. Thus the whole theory that the Earth moves round the Sun in an ellipse comes into question. You see, purely from these historical facts, that burning questions exist in Astronomy today, though it is seemingly a most exact science because it is mathematical. The question arises: Why do we live in such uncertainty with regard to a real astronomical science? We must then ask further, turning the question in another direction: Can we reach any real certainty through a purely mathematical approach? Only think that in considering a thing mathematically we lift the observation out of the sphere of external reality. Mathematics is something that ascends from our inner being; in mathematics we lift ourselves out of external reality . It must therefore be understood from the outset that if we approach an external reality with a method of investigation that lifts itself out of reality, we can, in all probability, only arrive at something relative. To begin with, I am merely putting forward certain general considerations. We shall soon come to the realities. The point is that in regarding things purely from the mathematical standpoint, man does not put reality into his thought with sufficient energy, in order to approach the phenomena of the outer world rightly. This, indeed, demands that the celestial phenomena be brought nearer to man; they must not be regarded as quite apart from man, but must be brought into relationship with man. It was only one particular instance of this associating of the heavenly phenomena with the human being, when I said that we must see what takes place out there in the starry world in its reflection in the embryonic process. But let us look at the matter at first somewhat more generally. Let us ask whether we cannot perhaps find another approach to the celestial phenomena than the purely mathematical one. We can indeed bring the celestial phenomena, in their connection with earthly life, somewhat nearer to man in a purely qualitative way. We will not disdain to form a basis today with seemingly elementary ideas, these ideas being just the ones that are excluded from the foundations of modern Astronomy. We will ask the following question: How does man's life on Earth appear, in relation to Astronomy? We can regard the external phenomena surrounding man from three different points of view . We can regard them from the standpoint of what I will call the solar life , the life of the Sun; the lunar life ; and the terrestrial, the tellurian life . Let us think first in quite a popular, even elementary way how these three domains play around man and upon him. Clearly there is something on the Earth which is in complete dependence upon the Sun-life, including also that aspect of the Sun's life which we shall have to look for in the Sun's movement or state of rest, and so on. We will leave aside the quantitative aspect and today merely consider the qualitative. Let us try to be clear as to how, for instance, the vegetation of any given region depends upon the solar life. Here we need only call to mind what is very well known with regard to vegetation, namely, the difference in the vegetation of spring, summer, autumn and winter; we shall be able to say that we see in the vegetation itself an imprint of the solar life. The Earth opens herself in a given region to what is outside her in heavenly space, and this reveals itself in the unfolding of vegetative life. If the Earth closes herself again to the solar life, the vegetation recedes. There is, however, an interplay of activity between the terrestrial or tellurian and the solar life. There is a difference in the solar life according to the variation of tellurian conditions. We must here bring together quite elementary facts and you will see how they lead us further. Take, for example, Egypt and Peru, two regions in the tropical zone. — Egypt, a low-lying plain, Peru a table land, and compare the vegetation. You will see how the tellurian element, simply the distance from the center of the Earth in this instance, plays its part in conjunction with the solar life. You only need study the vegetation over the earth, regarding the Earth, not as mere mineral but as incorporating plant-nature as well, and in the picture of vegetation you have a starting-point for an understanding of the connection of the earthly with the celestial. But we perceive the connection most particularly when we turn our attention to mankind. We have, in the first place, two opposites on the Earth: the Polar and the Tropical . The Polar and the tropical form a polarity, and the result of this polarity shows itself very clearly in human life. Is it not so that life in the polar regions brings forth in man a condition of mind and spirit which is more or less a state of apathy: The sharp contrast of a long winter and a long summer which are almost like one long day and one long night, produces a certain apathy in man; it is as though the setting in which man lives makes him apathetic. In the Tropics, man also lives in a region which makes him apathetic. But the apathy of the polar region is based upon a sparse external vegetation — sparse and meager in a peculiar way even where it develops to some extent. The tropical apathy of man is caused by a rich, luxuriant vegetation. Putting together these two pictures of environment one can say that the apathy which affects man in polar regions is different from that affecting him in tropical regions. He is apathetic in both regions, but the apathy results from different causes. In the Temperate Zone lies the balance. Here the human capacities are developed in a certain equilibrium. No-one will doubt that this has something to do with the solar life. But what is the connection: (I will, as I said, first make a few remarks based on observation and in this way arrive at essential concepts.) Going to the root of things, we find that in the life around the Poles there is a very strong working-in of the Sun-forces upon man. In those regions the Earth tends to withdraw from the life of the Sun; she does not let her activity shoot upward from below into the vegetation. But the human being is exposed in these parts to the true Sun-life (you must not only look for the Sun-life in mere warmth). That this is so, the vegetation itself bears witness. We have, then, a preponderance of solar influence in the Polar zones. What kind of life predominates in the Tropical? There it is the tellurian, the Earth-life. This shoots up into the vegetation, making it rich and luxuriant. This also robs man of a balanced development of his capacities, but the causes in the North and in the Tropics come from different directions. In Polar regions the sunlight represses man's inner development. In the Tropics, what shoots up from the Earth represses his inner powers. We thus see a certain polarity, the polarity shown in the preponderance of the Sun-life around the Poles, and of the tellurian life in tropical regions — ; in the neighborhood of the Equator. If we then observe man and have in mind the human form, we can say the following. (Please do not object at once if it seems paradoxical, but wait a little. We shall be taking the human form seriously.) The head, the part of the human form which in its outer configuration copies universal space, — namely the sphere, the spherical shape of the Universe as a whole — the head is exposed by life in polar regions to what comes from the Cosmos outside the Earth. In the Tropics, the metabolic system in its connection with the limbs is exposed to the Earth-life as such. We come to a special relationship, you see, of the human head to the cosmic life outside the Earth and of the human metabolic and limb-system to the Earth-life. Man is so placed in the Universe as to be more co-ordinated with the cosmic surroundings of the Earth in his head, his nerve-senses system, and with the Earth-life in his metabolic system. And in the temperate zones we shall have to look for a kind of perpetual harmonizing between the head-system and the metabolic system. In the temperate zones there is a primary development of the rhythmic system in man. You see then that there exists a certain connection between this threefold membering of man — nerves-and-senses system, rhythmic system, metabolic system — and the outer world. The head-system is more related to the whole Cosmos, the rhythmic system is the balance between the Cosmos and the earthly world, and the metabolic system is related to the earth itself . Then we must take up another indication, which points to a working of the solar life upon mankind in a different direction. The connection of the solar life with the life of man which we have just been considering can only be related to the interplay of the earthly and extra-earthly life in the course of the year . But as a matter of fact, in the course of the day we are also concerned with a kind of repetition, even as in the yearly course. The yearly course is determined by the relation of the Sun to the Earth, and so is the daily course. In the language of purely mathematical astronomy we speak of the daily rotation of the Earth on its axis, and of the revolution of the Earth round the Sun in the course of the year. But we are then confining ourselves to very simple aspects. We have then no justification for assuming that we are really starting from adequate premisses, giving an adequate basis for our investigations. Let us call to mind all that we have considered with regard to the yearly course. I will not say ‘the revolution of the Earth round the Sun’, but the course of the year with its alternating conditions. This must have a connection with the three-fold being of man. Since through the earthly conditions it finds different expression in the Tropics, in the Temperate Zones and at the Poles, this yearly course must be connected in some way with the whole formation of man — with the relations of the three members of the threefold man. When we bring this into consideration, we acquire a wider basis from which to proceed and can perhaps arrive at something quite different from what we reach when we merely measure the angles which one telescopic direction makes with another. It is a matter of finding broader foundations in order to be able to judge the facts. Speaking of the daily course , we speak in the astronomical sense of the rotation of the Earth on its axis. But something rather different is here revealed. There is revealed a far-reaching in dependence of man upon this daily course. The dependence of man on the yearly rhythm, namely on what is connected with the yearly course, the shaping of the human form in the various regions of the Earth, shows us a very great dependence of man on the solar life, — on the changes that appear on Earth in consequence of the solar life. The daily course shows it far less. True, very much of interest will also be revealed in connection with the daily course, but as regards the life of mankind as a whole it is relatively insignificant. The differences appear in individual human beings. Goethe, who can be regarded in a certain respect as a normal type of man, felt himself best attuned to production in the morning; Schiller at night. This points to the fact that the daily rhythm has a definite influence upon certain subtler parts of human nature. A man who has a feeling for such things, will tell us that he has met many persons in his life who have confided to him that their really important thoughts were worked out in the dusk, that is, in the temperate period of the day-to-day rhythm, not at midday nor at midnight, but in the temperate time of the day. It is however, a fact that man is in a way independent of the daily course of the Sun. We have still to go into the significance of this independence and to show in what way a certain dependence does nevertheless exist. A second element is the lunar life, the life that is connected with the Moon. It may be that a great deal of what has been said on this subject in the course of human evolution appears today as mere fantastic nonsense. But in one way or another we see that the Earth-life as such, for example in the phenomena of tidal ebb and flow, is connected quite evidently with the movement of the Moon. Nor must it be overlooked that the female functions, although they do not coincide in time with the Moon's phases, coincide with them in their periodicity, and that therefore something essentially concerned with human evolution is shown to be dependent in time and duration upon the phases of the Moon. It is as though this process of the female function were lifted out of the general course of Nature, but has remained a true image of Nature's process; it is accomplished in the same period of time as the corresponding natural phenomenon. Just as little must it be overlooked — only people do not make rational, exact observations of these things if they turn aside from them at the very outset — just as little must it be overlooked that as a matter of fact, man's life of fancy and imagination is extraordinarily bound up with the phases of the Moon. If anyone were to keep a calendar-record of the upward and downward flow of his life of imagination, he would notice how much it had to do with the Moon's phases. The fact that the Moon-life, the lunar life, has an influence upon certain lower organs should he studied in the phenomenon of the sleep-walker. In the sleep-walker, interesting phenomena can be studied; phenomena which are overlaid by normal human life, but are present in the depths of human nature and point in their totality to the fact that the lunar life is just as much connected with the rhythmic system of man as is the solar life with his nerves-and-senses system. This gives a sort of crossing of influences. We have seen how the solar life, in its interplay with the forces of the Earth, works on the rhythmic system in the temperate zones. Crossing this influence, we now have the direct influence of the lunar life upon the rhythmic system. When we now look at the tellurian, the Earth-life as such, we must not disregard a domain in which the earthly influence makes itself felt; though, to be sure, this is not ordinarily taken into account. I ask you to turn your attention to such as phenomenon as home-sickness. It is difficult to from any clear ideas about home-sickness. It can no doubt be explained from the point of view of habit, custom, and so on. But I ask you to note that real physiological effects can be produced entirely as a result of this so-called home-sickness. Home-sickness can go so far as to make a man ill. It can express itself in such phenomena as asthma. Study the complex of the phenomena of home-sickness with its consequences, asthmatic conditions and general ill-health, a kind of emaciation, and it is possible to come to the following conclusion. One comes to see that ultimately the feeling of home-sickness results from an alteration of the metabolism — the whole metabolic system. Home-sickness is the reflection in consciousness of changes in the metabolism — changes entirely due to the man's removal from one place, with its tellurian influences from below, to another place, with different influences coming from below. Please take this in connection with other things which, unfortunately, Science as a rule leaves unconsidered. Goethe, I said, felt most inspired to poetry, to the writing of his works in the morning. If he needed a stimulant however, he took that stimulant which in its nature takes least hold of the metabolic system, but only stirs it up via the rhythmic system, namely wine. Goethe took wine as a stimulant. In this respect he was, indeed, altogether a Sun-man; he let the influence of the solar life work upon him. With Schiller or Byron this was reversed. Schiller preferred to write his poetry when the Sun has set, that is to say when the solar life was hardly active any more. And he stimulated himself with something which takes thorough hold of the metabolic system — with hot punch. The effect was quite different from that obtained by Goethe from wine. It worked into the whole metabolism. Through the metabolism the Earth works upon man; so we can say that Schiller was essentially tellurian — an Earth-man. Earth-men work more through the emotions and what belongs to the will; the Sun-man works rather through calm and contemplation. For those persons, therefore, who could not endure the solar element, but only liked the tellurian, only what is of the Earth Goethe increasingly became “the cold literary Greybeard” as they called him in Weimar — “the cold, literary greybeard with the double chin.” That was the name which was so often given to Goethe in Weimar in the 19th century. Now I should like to bring something rather different to your notice. We have observed how man is set into the universal connections of Earth, Sun, Moon: the Sun working more on the nerves-and-senses system; the Moon working more on the rhythmic system; the Earth, inasmuch as she gives man of her substance as nourishment and makes substance directly active in him, working upon the metabolic system, working tellurically. We see something in man through which we can perhaps find starting-point for an explanation of the Heavens as they exist outside man, upon broader foundations than merely through the measurement of angles by the telescope and so on. This is especially so if we go yet further, if we now consider Nature outside of man, — but consider it so as to see more in it than a mere register of external data. Look at the metamorphosis of insects. In the course of the year it is a complete reflection of the external solar life. I would say that with man we must make our researches more in the inner being in order to follow what is solar, lunar and tellurain in him, whereas in the insect-life with its metamorphoses, we see the direct course of the year expressed in the successive forms the insect assumes. We can now say to ourselves: Maybe we have not to only proceed quantitatively, but should also take into account the qualitative impression which such phenomena make upon us Why always merely ask what a phenomenon of the outer Universe looks like in the objective of the telescope? Why not ask what relation is given, not merely by the objective of the telescope, but by the insect? How does human nature react? Is anything revealed to us through human nature regarding the celestial phenomena? Are we not led in this way to broader foundations, making it impossible that on the one hand, theoretically, we should be Copernicans when desiring to explain the world philosophically, while on the other we use Tychonic System as our basis for calculating the calendar etc., as practical Astronomy still does to this day. Or that we are Copernicans, but set aside the most important part of his theory, namely his third axiom Can we not overcome the uncertainties which create burning problems even in the most fundamental realms of Astronomy today, by working on a broader basis — working in this sphere too from the quantitative to the qualitative? Yesterday I sought to point out the connection of the celestial with the embryonic phenomena; today, the connection with fully developed man. Here you have an indication towards a necessary regrouping of the sciences. Now take another thing to which I have also referred to in the course of today's remarks. I indicated the connection of human metabolism with the Earth-life. In man we have the faculties of sense-perception mediated through the nerves-and-senses system, connected as a whole with the solar and cosmic life. We have the rhythmic system connected with what lies between Heaven and Earth. We have the metabolism related especially to the Earth, so that in contemplating metabolic man we should be able to get nearer to the real essence of the tellurian. But what do we do today if we want to approach the tellurian realm? We behave as we habitually do, and investigate things from the outside. But things have an inner side also! Will they perhaps only show it in its true form when they pass through the human being? It has become an ideal nowadays to regard the relationship of substances quite apart from man and to rest there; to observe by experimentation in chemical laboratories the reciprocal actions of substances in order to arrive at their nature. But if the substances only disclosed their nature within the human being, then we should have to practice Chemistry in such a way as to reach man. Then we should have to form a connection between true Chemistry and the processes undergone by matter within man, just as we see a connection between Astronomy and Embryology, or between Astronomy and the whole human form — the threefold being of man. Thus do the things work into one another. We only come to real life when we perceive them in their interpenetration. On the other hand, inasmuch as the Earth is poised in cosmic space, we shall have to see the connection between the tellurian and the starry realm. Now we have seen a connection between Astronomy and the substances of Earth; also between the Earth and human metabolism; and again a direct influence of the solar and celestial events upon man himself. In man we have a kind of meeting of what comes directly from the Heavens and what comes via earthly substance. Earthly substances work on the human metabolism, while the celestial influences work directly upon man as a whole. In man there meet the direct influences for which we are indebted to the solar life, and those influences which, passing indirectly through the Earth, have undergone a change by reason of the Earth. Thus we can say: The interior of the human being will become explicable even in a physical, anatomical sense as a resultant of cosmic influences coming directly from the Universe outside the Earth, and cosmic influences which have first passed through the earthly process. These flow together in man (Fig. 4). You see how, contemplating man in his totality, the whole Universe comes together. For a true knowledge of man, it is essential to perceive this. What then has come about by scientific specialization? It has led us away from reality into a purely abstract sphere. In spite of its 'exactness', Astronomy — to calculate the calendar — cannot help using in practice something other than it stands for in theory. And then again, Copernican though it is in theory, it discards what was of great importance to Copernicus, namely the third axiom. Uncertainty creeps in at every point. These modern lines of research do not lead to what matters most of all, — to perceive how Man is formed from the entire Universe .

Astronomy as Compared to Other Sciences

Lecture II

https://rsarchive.org/Lectures/GA323/English/LR81/19210102p01.html

Stuttgart

2 Jan 1921

GA323-2

I have brought to your notice on the one hand how problematical it is to conceive the celestial phenomena in their mathematical and geometrical aspect alone. This is now being recognized by many people and from diverse angles. Only quite unadvanced thinkers still maintain that the world-picture of Copernicus and Galileo represents downright reality. Increasingly, we hear the voice of those who find this way of thinking of the celestial phenomena useful and practical, no doubt, for purposes of calculation, yet emphasize that it represents only a certain mode of understanding, and that quite other syntheses might be conceived. There are even those who say, somewhat as Ernst Mach used to say: In the last resort, one can uphold the Ptolemaic just as well as the Copernican world-system, and a third system might equally well be devised. These are but practical ways of correlating the observed facts. The entire realm should now be confronted with a far freer kind of outlook. You see from this that the problematical nature of the celestial charts, described but a short time ago as replicas of the real facts, is now conceded by the widest circles. On the other hand an escape from the manifest problems and uncertainties of this realm can only be found through such views as were brought forward in outline yesterday, — views which no longer remove Man from the whole cosmic background, but on the contrary, put him into it from the outset. We have to recognize the processes within Man himself in their connection with solar phenomena, lunar phenomena and terrestrial phenomena, thus taking as a starting-point all that goes on in Man, in order to find the way to what is going on out there in the Cosmos, the latter being in some sense the cause of the processes in Man. A path like this can of course only be trodden from the standpoint of Spiritual Science. Precisely when we try to bring Astronomy into connection with the most varied spheres of life, we shall find that we are being led through Astronomy itself into the views of Spiritual Science. Bear in mind that the visible celestial phenomena, perceptible to our senses and also to our re-inforced senses, appear at first a manifestation of something outside of man. Man confronts and, as it were, arrests with his senses whatever approaches him, introducing it into his conscious world-picture. But the impulses streaming towards us from all sides, certainly do not come to a standstill before our senses. All that goes on without being held up by man's senses and brought into consciousness, all that lives in the celestial influences that stream towards us from all sides, must be sought for within our bodily organism. The organism must in a certain way reflect it all, and it does this in the unconscious and subconscious processes which can only be raised into consciousness in more complicated ways. We will now continue in a certain direction what we began yesterday. Only an abstraction of our earthly world is dealt with in Geology or Mineralogy; the Earth as described by Geology consists of minerals has evolved in the mineral sphere; true as it is that forces are there in the Earth by virtue of which it brings forth the minerals; yet is is equally true that all that is living in plants, animals and physical human beings also belongs to the Earth. We only see the Earth in its totality when we do not simply cast aside what lives in plant, animal and man and have in mind the mere abstraction "mineral earth ", but bring it all into our consciousness. The living beings and entities that grow up out of the Earth are also part and parcel of the whole. Of all that belongs in this way to the Earth, let us first take the plant kingdom. We will approach it in order then to find the transition to what meets us in man. Whereas the mineral kingdom to a certain extent carries on an independent Earth-existence and is only related to the Cosmos outside the Earth in such a way as is shown, for example, in the changing of water into ice in winter, the plant kingdom retains a much greater inner connection with the cosmic surroundings of the Earth — with all that enters the Earth from the Cosmos. Through the plant-world the life of the Earth as it were opens itself to the Universe. In geographical regions where in a given season an intensive interaction is taking place between Earth and Cosmos. We must pay heed to a phenomenon like this, for it will lead us into the realm of Astronomy not only quantitatively, but qualitatively. We must be able to derive our ideas from such a thing as this, even as the astronomers of our time derive their ideas from angles, parallaxes and so on. Then we shall say to ourselves, for example: — The plant-life, covering a given region of the Earth, is a kind of sense-organ, sensitive to all that is revealed towards the Earth out of the Cosmos. At seasons when the interplay is more intense between a portion of the Earth's surface and the Universe, it is as though a human being were opening his eyes to the outer world to receive sense-impressions. And when the interplay is less intense between the Earth and the Cosmos, the consequent decline and inward closure of the vegetative life is like a closing of the eyes to the Cosmos. It is more than a mere comparison to say that through its vegetation a given territory opens its eyes to the Universe in spring and summer and shuts its eyes in autumn and winter, and as by opening and closing of our eyes we do in a way converse with the outer world, so too it is a kind of information or revelation from the Universe which the Earth receives by the opening and closing of its eyes through the life of plants. And to describe it a little more precisely, we may consider the vegetation of a given region of the Earth when exposed, as it were, so to speak, to the most vivid interplay with the solar life, and we may then turn our attention to the state of vegetation in this region when it is not thus exposed. The winter, I need hardly say, does not interrupt the vegetative life of the Earth. It goes without saying that the vegetative life continues through the winter. But it expresses itself in quite another way than when exposed to the intensive working of the Sun's rays — or, shall we say, of the Cosmos. Under the influence of the solar life, the vegetative life of the Earth shoots outward into form. The leaves unfold and grow more complex; flowers develop. But when this is followed by the closing of the eyes to the Universe, if we may call it so, the vegetative life goes back into itself — into the seed. Withdrawing from the outer world, it no longer shoots into outward form; it concentrates, if I may put it so, into a point; it becomes centered in itself. We may describe this contrast truly as a law of Nature. The interplay between the earthly and the solar life reveals itself in the Earth's vegetation. Under the solar influence the vegetative life shoots outward into form; under the influence of the earthly life it closes up into a plant, — it becomes seed or germ. In all this there is a quality of expansion and contraction or gathering into a center. Here we begin to apprehend the relationships of space itself in a directly qualitative aspect. This is the very thing which we must practice in the development of our ideas, if we would attain to really fruitful notions and perceptions in this sphere. And now we pass from plant-life to the life of man. Naturally, what comes to expression in the life of plants will find expression in man too. In what way will it do so? What we somehow perceive, my dear Friends, so outwardly and evidently in the life of plants — what we have visibly before our eyes if only we are attentive to the qualitative aspect — this we can recognize in man, properly speaking, only in the first years of childhood. Let us then trace the interaction of the solar and terrestrial life for man in the age of childhood, as we have just been doing for the plant kingdom. The little child opens through the senses to receive the impressions of the outer world. In doing so, the human being is really opening to receive the solar life. You only need see things in the proper light to recognize that what pours in upon our senses is inherently connected with what is brought about in the terrestrial sphere by the Cosmos. You can reflect upon the special case of light. When light and darkness succeed each other in the alternation of day and night, impressions are made upon our eyes by day, and no impressions are made by night. You can apply this also to other perceptions, though it is more difficult to make it clear. You will then say that a certain effect of the daily alternations, solar and earthly, expresses itself in man's soul-life. Man has an activity of soul through what arises in the rhythm of the day. What the Sun here brings to the Earth comes to expression in the soul-life of man. But if we follow the growth of the child, particularly until the 7th year — the change of teeth — and go into all the details, we find how, notably in the first years of the child's development (less and less, the older the child becomes), it is plainly perceptible that the changing seasons, year by year, have just as much significance for human growth as for the sprouting and dying-down of the vegetation. We will represent it diagrammatically. If, for example, we study carefully and intelligently the development of the human brain in the earliest stages from year to year, we shall find the following. We have the human skull with its brain-content. (Fig. 1) It remodels itself, and one can follow how it remodels itself through what in the course of the changing year. Something which works formatively and creatively upon the human head, molding it from outside in a corporeal, physical sense, — we find this intimately connected with the forces playing between Earth and Sun in the course of the year. In the daily rhythm we find what enters through the senses, independent of growth, to work on the soul and spirit of man. We see how what takes place in man by reason of the Sun's activity in the daily rhythm, has an inner effect which frees itself from the external world and becomes of a soul-and-spirit nature; it is what the child learns, what it assimilates through observation, what takes place in effect, in soul and spirit. Then we see how in a totally different tempo — from a different aspect — the brain remodels itself, organizes itself, and grows. That is the other activity, the yearly activity of the solar forces. We will say nothing yet of the changes occurring in the Universe between Sun and Earth; we will consider manifestations in man himself which are united with certain changes in the solar and terrestrial life. We consider the day and find the soul- and spirit-life of man connected with the course of the Sun. We consider the change of seasons through the year and find man's life of growth, the physical, corporeal life, connected with the course of the Sun. We can say: The change taking place between Earth and Sun in 24 hours has certain effects on the spirit and soul of man. What happens between Earth and Sun in the course of the year has certain effects on the physical, corporeal part of man . We shall have to bring these effects into connection with others and thence arrive at a world-concept which can no longer be deceptive, for it speaks to us of real processes within ourselves, no longer dependent on illusory sense-impressions or the like. Thus we must gradually draw near to what can give us a sure basis for the astronomical world-conception. We can only take our start from what appears in man himself. So we can say: the day is something in man's connection with the Cosmos that expresses itself in soul and spirit; the year is something in man's connection with the Cosmos that expresses itself in the physical-corporeal life, as for example in growth, and so on. Now let us look at another complex of facts, referred to yesterday. With human reproduction we must relate certain ideas referring to the life of the Cosmos. We indicated yesterday that the female organism shows in a striking manner how the monthly functions connected with the sex-life — though not, to be sure, coinciding with the Moon's phases — are yet a reflection of them in their time rhythm. The process wrests itself free from the Cosmos, as it were, but still reflects the Cosmic Moon-process in its periodic course. We have here an indication, my dear friends, of inner processes in the human organism which we can study better if we turn our attention to more familiar phenomena, such as may make these more remote phenomena easier to understand. There is something in the soul-life which actually reproduces in miniature the organic processes to which we have just alluded. Let us say, we have an outer experience which affects us through the senses and the mind, — perhaps also through our feelings. We retain a memory of the experience. The recollection — the retention of the experience — leads to the possibility of the picture of it emerging again at a later time. Anyone who considers these facts, not on the basis of fanciful theories, but with sound qualitative observation, will have to admit that in all that arises within us by way of memory, our physical bodily organization plays a part. The remembering itself is no doubt an event in the life of soul, but it needs the inner basis of the physical body in order to come into being. The activity of remembering is directly interrelated with bodily processes; though this has not yet been investigated sufficiently by external science. Comparing what occurs in the female organism in the monthly periods (it occurs in the male organism too, only it is less evident; it can be observed more in the etheric organism and this is not usually done) — comparing this with what happens in ordinary experience when we remember something, one will certainly find a difference. Yet if with sound inner perception one recreates the process in one's consciousness, one cannot but say that the activity of remembering, this soul-occurrence arising out of the physical organism, is similar to what takes place in the monthly functions of the female organism, only is in miniature and is more drawn into the realm of soul, less impressed upon the body. From this point of view you will be able to say: Inasmuch as man individualizes himself from the Cosmos, he develops the faculty of memory; inasmuch as he still lives within the Cosmos, developing more his sub-conscious functions, something in the nature of a common experience with the Cosmos arises, connected with the Moon-processes in the Cosmos. This experience remains, just as a past experience remains in our memory, and later it emerges in an inner constitutional process, like a remembrance which has been drawn into the body and has become organic. There is no other way, my dear friends, of understanding these matters than by thus proceeding from the simpler to the more complex. Just as it is not necessary for a recollection to coincide with a fresh outer experience, so it is not necessary for what appears in the female organism, as a memory of an earlier cosmic connection of the human organism with the phases of the Moon, to coincide in time with these phases. Nevertheless, it is connected with the Moon's phases no less essentially than is the recollection of an earlier experience with the experience itself. Here then we have an activity in the human organism, more on the psychological side and yet not unlike the effects — precipitated, as it were, into the life of time — of influences due originally to the Moon. For the organic periodicity of which we have been speaking embraces about 28 days, as you know. Now take the following. If we consider the daily influence of the Sun, we find an inner activity of soul and spirit; if we consider the yearly influence of the Sun, then we find laws of growth belonging to the outer physical body. Thus we can say, for the Sun life : 1. Soul and Spirit: Day 2. Physical bodily nature: Year And now we come to the Lunar activity . We pass on to consider the lunar life, the life of the Moon. What I have just described as taking place in rhythm of 28 days belongs indeed to the soul and spirit; it has only impressed itself deeply into the body. Physiologically, there is really no difference, in a finer sense, between what takes place in the body on the arising of a memory with respect to the event to which the memory refers, and what takes place in the monthly periods of the female body with respect to what the female organism experienced long ago in conjunction with the phases of the Moon. Only the latter is a stronger, a more intensive experience, — a soul spiritual experience pressed more intensively into the body. Thus, for the Lunar life : Soul and Spirit: 28 day's activity Let us now seek the corresponding phenomena for the physical body. What will they be? You can find it for yourselves by deduction. We will have bodily, physical effects with a 28-year period. As a day here corresponds to a year, we shall have 28 years. Physical bodily nature: 28 year's activity You need only remember that 28 years is the period bringing us to our full inner maturity of growth. It is then that we first cease to be in the ascending scale of growth. Just as the Sun works upon us from outside in its yearly activity, in order to complete in us an outward process corresponding to the daily process in the inner life o soul and spirit, so something works in the Cosmos in a 28-year period, organizing us from outside even as the female human being is organized inwardly. (In her it is more obvious than in the male, for in the man the corresponding daily rhythm is more withdrawn into the etheric.) Here then a 28-day period impresses itself inwardly in the realm of the soul and spirit, and we can say: As the daily Sun-life is related to the yearly Sun-life in regard to man, so the 28-day Moon-life related to the 28-year Moon-life with respect to the whole man (the former belonging, in effect, more to the human head ). You see how we place man, and rightly place him, into the whole Cosmos. We leave off speaking of Sun and Moon merely as if we stood isolated here on Earth, and only looked out with our eyes or with our telescopes to Sun and Moon. We speak of Sun and Moon as of something inwardly united with our very life, and we perceive the connection in the special configurations of our life in time. Until we place man again, my dear friends, into the picture of the doings of Sun and Moon, we shall not have evolved a firm foundation for true Astronomy. Thus a new science of Astronomy must be built upon a spiritual-scientific basis. It must be evolved out of a more intimate knowledge of man himself. We shall only be able to find a meaning in what is taught by the external Astronomy of today, when we are in a position to base our hypotheses on man himself. We shall then be able profitably to study the rather schematic statements made in Astronomy today and we shall also be able to make essential corrections in this external Astronomy. What follows from all this? It follows that in these processes — no matter, for the moment, what the underlying basis of them is — a universal life reveals itself. Whether it be (and we will speak of this later) that the daily and yearly rotations of the Earth underlie what I have here described as solar life with respect to the soul and spirit for the day, and to the physical bodily nature for the year; whether it be the movements of the Moon described by modern Astronomy or something very different; — we shall never reach an understanding of it merely by setting up the well-known picture taught in the Schools. But we must understand all that is expressed in this picture as being in reality a continuing, enduring universal life — a life which cannot be approached in its fullness by a mere series of diagrammatic pictures. We will now set to work in another way. We will begin to work from the standpoint offered us in the Astronomical ideas of a man who still had very much from the past. We do not want to return to the older ideas; we must work out of new ideas This man, however, still had much of the old qualitative virtues in his ideas. I refer to Kepler. Astronomy has become more and more quantitative in modern time, and it would be a delusion to look on Astrophysics as the entry of a qualitative element into Astronomy; of an universal life that lay behind the work of Kepler. In him a feeling still persisted that behind all that is manifest to ordinary astronomical observation there lies hidden something like the gesture of a vast cosmic life — a cosmic life that here reveals its presence. If we have a man before us and see him move a hand or an arm, we do not merely calculate the mechanics of the movement; we recognize it as the outer revelation of an inner life of soul and spirit. We understand as an expressive gesture something that can, after all, also be looked on from a purely spatial, mathematical point of view. The further back one goes in the history of man's approach to Astronomy, the more one find men conscious that the pictures they conceived of the path of the Sun or of the stars were no mere passive pictures of indifferent events but that these pictures were gestures of life and being. It is quite easy to discern in olden times this feeling of the gesture-like nature of the movements of the heavenly bodies. When my hand moves through the air I shall not merely calculate its path, but in this path I see an expression of the soul . So did the earlier observer see in the path of the Moon an expression. of a life of soul. In all the movements of the heavenly bodies he saw expressions of a soul-nature lie pictures it somewhat in this s way — If I could held an umbrella here so that only my hand were seen, my hand would make an inexplicable movement, for I am there behind the umbrella; only the hand is to be seen. Somewhat in this way the men of ancient times pictured that the movement of the Moon up in the sky was but the outer expression — a sort of terminal ‘limb’ — end that the really active being stood behind it. So too in earlier times men did not speak of isolated heavenly bodies of the planets; they spoke of planetary spheres . They spoke of the several spheres, belonging to the heavenly bodies. Thus they distinguished the Moon-sphere, the Mercury-sphere, the Venus-sphere, the Sun-sphere, the Mars-sphere, the Jupiter-sphere, the Saturn-sphere, and then the eighth sphere — the Heaven of Fixed Stars They distinguished these eight spheres and saw in them something which expressed itself in outer gestures, so that a certain sphere expressed itself by lighting up now here, now there, and so on. The reality, for instance, was the sphere of the Moon. The Moon itself was not a separate entity, — only the gesture. Where the Moon appeared, the Moon-sphere was making a definite gesture I am relating this to show you the living nature of the old conceptions. Kepler still retained in his whole consciousness a feeling for this universal life in space Only on this account was he able to draw up his three famous Laws For modern Astronomy the three famous Laws of Kepler are purely of a quantitative nature, to be regarded simply from the aspect of spatial and temporal concepts. For a man who still worked out of such a life of ideas as Kepler did, this was not the case. Let us now call to mind these Laws of Kepler. They are: The First Law: The Planets move in ellipses round the central body, which is situated in one of the foci of the ellipse. The Second Law: The Radius-vector of a Planet describes equal sectors, equal areas, in equal periods of time. The Third Law: The squares of the periods of revolution of the different Planets are proportional to the cubes of the major semi-axes Now as we said, to the modern, purely quantitative view these laws too are purely quantitative To anyone like Kepler, the very expression ‘elliptical’ and the corresponding curve signified a greater livingness when it only moves in a circle, for it must use an inner impulse in order continually to alter the radius. When something simply moves in a circle it need do nothing to alter the radius. A more intense inner life must be employed in the radius-vector is continually altered. The simple. statement: “The Planets move in ellipses round the central body and the central body is not in the mid-point but in one of the foci of the ellipse”, implied an element of greater livingness than when something moves in a perfect circle. Further: “The radius-vector describes equal sectors in equal periods of time”. We have here the transition from the line to the surface, to the plane. Please notice this.’ Inasmuch as at first only the ellipse is described, we remain in the line — the curve. When we are directed to the path that the radius-vector describes, we are led to the surface — the area. A more intensive condition in the planetary movement is disclosed, When the planet ‘rolls along’ — if I may express so myself — it is not only expressing something within itself, but draws its tail after it, as it were. The whole area which the radius-vector describes belongs to it spiritually. Moreover, in equal periods of time equal areas are described, Special attention is thus drawn to the quality, the inherent character of the movement of the planets. The third Law above all relates to the life that plays its part between the various planets. This Law assumes a more complicated form. “The squares of the periods of revolution of the Planets are in proportion to the cubes of the semi-major axes” (or of the mean distance from the central body). This Law, you see, contains a great deal if one still understands it in Kepler's living way. Newton then killed the law. He did this in a very simple fashion. Take Kepler's Third Law. You can write it thus: or written differently: Now write it in a somewhat different form. Write it thus: (I might of course also have written it in the reverse order.) What have we on the left-hand side of the equation, here in the left-hand ratio? No less than what is expressed by one half of Newton's Law, and on the other side the other half, the forces of Newton's Law. You need only write Kepler's Law thus differently and you can say: “The forces or attraction are inversely proportional to the squares of the distances.” Here then you have the Newtonian Law of Gravity deduced from the Law of Kepler. The force of gravity between the planets, the celestial bodies, is in inverse proportion to the squares of their distances apart. It is nothing else than the killing of Kepler's Third Law. In principle that is what it is. But now take the matter actively and livingly. Do not set before yourself the dead product “force of gravity” — “the forces of attraction decrease with the squares of the distances”, — but take what is living still in Kepler's form, the squares of the periods of time. Fill out the caput mortum of the Newtonian force of attraction, which is a mere external concept, with what is implied in the square of the period of time, and you will fill with inner life of the Newtonian concept, which is really the corpse of an idea! For inner life has to do with time. And here you have before you not only time in its simple course, you have time squared — time to the second power! We shall yet have to come back to what it means to speak of ‘time squared’ But you can realize that to speak of time to the second power is to speak or something of an inward nature. It is, indeed, time which in the life of man actually represents the course of his inner soul-life. The point is that we should look right through it dead concept of the Newtonian force of attraction to that which suddenly darts into the center, bringing time into it and therewith bringing in an element of inner life. Now look at the matter from another point of view. Notice that Kepler's first Law also has reference to the Earth. Not only does the Earth describe an ellipse, but you , since you are on the Earth, describe an ellipse together with it. What takes place outwardly is in you an inner process. Thus the arising of the ellipse from the circle, in the living way in which Kepler still conceived it, corresponds to a process in your own inner being. And inasmuch as you move in the line which is formed by the radius-vector describing equal sectors in equal times, it is you who continually relate yourself to the central body, placing yourself in relation to your own Sun. You, together with the curve, are describing a path in time, along which you are in continual relation to the Sun. If I may put it a little quaintly You must take care all the time that you do not ‘skid’ or side-slip, that you do not go too fast, — that your radius-vector does not describe too great an area. This outer point which moves in the ellipse must be continuously in the right relation to the Sun. There you have the movement you yourselves make, characterized as a pure line in space. The relation to the Sun is characterized in the Second Law. And if we pass on to the Third Law, you have an inner experience of the relation to the other planets — your own living connection with the other planets. Thus we not only have to find, in man himself, processes that lead us out again into the Cosmos. If we interpret rightly the mathematical pictures presented to us by the cosmic process, we also turn into an inner experience what is apparently external and quantitative. For the cosmic Mathematics indwells man. Man is himself in the midst of the living Mathematics. Of this we shall speak more tomorrow.

Astronomy as Compared to Other Sciences

Lecture III

https://rsarchive.org/Lectures/GA323/English/LR81/19210103p01.html

Stuttgart

3 Jan 1921

GA323-3

If I had the task of presenting my subject purely according to the methods of Spiritual Science, I should naturally have to start from different premises and we should be able to reach our goal more quickly. Such a presentation, however, would not fulfill the special purpose of these lectures. For the whole point of these lectures is to throw a bridge across to the customary methods of scientific thought. Admittedly, I have chosen just the material which makes the bridge most difficult to construct, because the customary mode of thought in this realm is very far from realistic. But in contending against an unreal point of view, it will become apparent how we can emerge from the unsatisfying nature of modern theories and came to a true grasp of the facts in question. Today, then, I should like to consider the whole way in which ideas have been formed in modern times about the celestial phenomena. We must, however, distinguish two things in the formation of these ideas. First, the ideas 1 Note by translators : In the first few pages of this lecture, the word Vorstellungen has been translated, either as “mental pictures” or “thought-pictures”, or by the word “ideas” as in Prof. Hoernle's original English edition of Dr. Steiner's Philosophie der Freiheit . In other translations, including the later editions of this book, the word is rendered “representations”, or again, “Mental presentations”. Dr. Steiner's use of Vorstellung corresponds, we believe, to the colloquial, work-a-day meaning of the word “idea” in current English. (Where Idea is meant in its deeper, more spiritual meaning — German Idee — it can be distinguished by the use of a capital.) are derived from observation of the celestial phenomena, and theoretical explanations are then linked on to the observations. Sometimes very far-reaching, spun-out theories have been linked on to relatively few observations. That is the one thing, namely, that a start is made from observations out of which certain ideas have been developed. The other is that, the ideas having been reached, they are further elaborated into hypotheses. In this creating of hypotheses, — a process which ends in the setting up of some definite cosmology, — much arbitrariness prevails, since in the setting-up of theories, any preconceived ideas existing in the minds of those who put forward the theory, make themselves strongly felt. I will therefore first call your attention to something which will perhaps strike you as paradoxical, but which, when carefully examined, will none the less prove fruitful in the further course of our studies. In the whole mode of thought of modern Science there prevails what might be called, and indeed has been called, the ‘Regula philosophandi’. It consists in saying: What has been traced to definite causes in one realm of reality, is to be traced to the same causes in other realms. In setting up such a ‘regula philosophandi’ the starting-point is as a rule apparently self-evident. It will be said — scientists of the Newtonian school will certainly say — that breathing must have the same causes in man as in the animal, or again, that the ignition of a piece of wood must have the same cause whether in Europe or in America. Up to this point the thing is obvious enough. But then a jump is made which passes unnoticed, — is taken tacitly for granted. Those who are wont to think in this way will say, for example, that if a candle and the Sun are both of them shedding light the same causes must surely underlie the light of the candle and the light of the Sun. Or again, if a stone falls to Earth and the Moon circles round the Earth, the same causes must underlie the movement of the stone and the movement of the Moon. to such an explanation they attach the further thought that if this were not so, we should have no explanations at all in Astronomy. The explanations are based on earthly things. If the same causality did not obtain in the Heavens as on Earth, we should not be able to arrive at any theory at all. Yet when you come to think of it, this regula philosophandi is none other than a preconceived idea. Who in the world will guarantee that the causes of the shining of a candle and of the shining of the Sun are one and the same? Or that in the falling of a stone, or the falling of the famous apple from the tree by which Newton arrived at his theory, there is the same underlying cause as in the movements of the heavenly bodies? This would first have to be established. As it is, it is a mere preconceived idea. Prejudices of this kind enter in, when, having first derived theoretical explanations and thought — pictures inductively from the observed phenomena, people rush headlong into deductive reasoning and construct world-systems by deductive methods. What I am now describing thus abstractly has, however, become a historical fact. There is a continuous line of development from what the great thinkers at the opening of the modern age — Copernicus, Kepler, Galileo — concluded from comparatively few observations. Of Kepler — notably of his third Law, quoted yesterday — it must be said that his analysis of the facts which were available to him is a work of genius. It was a very great intensity of spiritual force which Kepler brought to bear when, from the little that lay before him, he discovered this ‘law’ as we call it, or better, this ‘conceptual synthesis’ of the phenomena of the universe. Then however, by way of Newton a development set in which was not derived from observation but from theoretical constructions, including concepts of force and mass and the like, which we must simply omit if we only want to hold to what is given. The development in this direction reaches a culminating point — conceived, admittedly, with genius and originality — in Laplace, where it leads to a genetic explanation of the entire cosmic system (as you will convince yourselves if you read his famous book Exposition du Systeme du Monde ), or again in Kant, in his Natural History and Theory of the Heavens . In all that has followed in this trend we see the effort constantly made to come to conclusions based on the thought pictures that have thus been conceived of the connections of the celestial movements, and resulting in such explanations of the origin of the universe as the nebular theory and so on. It must be noted that in the historical development of these theories we have something which is put together from inductions made, once again, with no little genius in this domain — and from subsequent deductions in which the special predilections of their authors were included. Inasmuch as a thinker was imbued with materialism it was quite natural for him to mingle materialistic ideas with his deductive concepts. Then it was no longer the facts which spoke, for one proceeded on the basis of the theories which had emerged from the deductions. Thus, for example, inductively men first arrived at the mental pictures which they summed up in the notion of a central body, the Sun, with the planets revolving around it in ellipses according to a certain law, namely: the radius-vectors describe equal areas in equal periods of time. By observing the different planets of a solar system, it was moreover possible to summarize their mutual relations in Kepler's third law: ‘For different planets the squares of the periods of revolution are proportional to the cubes of the radius-vectors’. Here was a certain picture. The question, however, was not decided, whether this picture completely fitted the reality. It was in truth an abstraction from reality; to what extent it related to the full reality, was not established. From this picture — not from reality, but from this picture — people deduced what then became a whole genetic system of Astronomy. All this must be borne in mind. Modern man is taught from childhood as if the theories which have been reached in the past few centuries by deductive reasoning were the real facts. We will therefore, while taking our start from what is truly scientific, disregard as far as is possible all that is merely theoretical and link on to those ideas which only depart from reality to the extent that we shall still be able to discover in them a connection with what is real. It will be my task, in all that I give to-day, to follow the direction of modern scientific thought only up to those ideas and concepts which still permit one to find the way back again into reality. I shall not depart so far from reality that the concepts become crude enough to allow of the deduction of nebular hypotheses. Proceeding in this way, — pursuing the modern method of forming concepts in this particular field, — we must first form a concept which presented itself inductively to Kepler and was then developed further I repeat expressly, I will only go so far in these concepts that even if the picture in the form in which it was conceived should be mistaken, it has departed only so far from reality that it will be possible to eliminate the mistake and return to what is true. We need to develop a certain flair for reality in the concepts we entertain. We cannot proceed in any other way if we wish to throw a bridge across from the reality to the spun-out theories of modern scholarship and science. Here then, to begin with, is a concept which we must examine. The planets have eccentric orbits, — they describe ellipses. This is something with which we can begin. The planets have eccentric orbits and describe ellipses, in one focus of which is the Sun. They describe the ellipses in accordance with the law that the radius — vectors describe equal areas in equal periods of time. A second essential for us to hold to is the idea that each planet has its own orbital plane. Although the planets carry out their evolutions in the neighborhood of each other, so to speak, yet for each planet there is the distinct plane of its orbit, more or less inclined to the plane of the Sun's equator: If this depicts the plane of the Sun's equator (Fig.1), an orbital plane of a planet would be thus; it would not coincide at all with the plane of the Sun's equator. 2 Note by Editor : This plane is inclined at an angle of about seven degrees to the plane of the ecliptic. These are two very significant mental pictures, to be formed from the facts of observation. And yet, in the very forming of them we must take note of something in the real world-picture, which as it were, rebels against them. For instance, if we are trying to understand our solar system in its totality, and only base it upon the picture of the planets moving in eccentric orbits, the orbital planes being inclined at varying degrees to the plane of the solar equator, we shall be in difficulties if we also take into account the movements of the comets . The moment we turn our attention to the cometary movements, the picture no longer suffices. The outcome will be better understood from the historical facts than from any theoretical explanations. Upon these two thought-pictures, — that the orbital planes of the planets lie in the proximity of the plane of the Sun's equator, and that the orbits are eccentric ellipses, — Kant, Laplace and their successors built up the nebular hypothesis. Follow what emerges from this. At a pinch, and indeed only at a pinch, it is a way of imagining the origin of the solar system. But the astronomical system thus constructed contains no satisfactory explanation of the part played by the cometary bodies. They always fall out of the theory. This discordance of the comets with the theories which were formed, as described, in the course of scientific history, proves that the cometary life somehow rebels against a concept formed, not from the whole but only from a part of the whole. We must be clear, too, that the paths of the comets frequently coincide with those of other bodies which also play into our system and present a riddle precisely through their association with the comets. These are the meteoric swarms, whose paths very frequently — perhaps even always — coincide with the cometary paths. Here, my dear friends, taking into account the totality of our system, we are led to say: A sea of ideas has gradually been formed from the study of our planetary system as a whole, — ideas with which we cannot do justice to the seemingly irregular and almost arbitrary paths of the comets and meteoric swarms. They simply refuse to be included in the more abstract pictures that have been reached. I should have to give you long historical descriptions to show in detail how many difficulties have arisen in connection with the concrete facts, when the investigators — or rather, thinkers — approached the comets and meteoric swarms with their astronomical theories. I wish only to point out the directions in which a sound understanding can be sought. We shall come to such an understanding if we pay attention to yet another aspect. Starting in this way from concepts which still have a remnant of reality in them, we will now try to go back a little towards what is real. It is indeed always necessary to do this in relation to the outer world, in order that our concepts may not stray too far from reality, — for this is a strong propensity of man. We must go back again and again to the reality. There is already no little danger in forming such a concept as that the planets move in ellipses, and then beginning at once to build a theory upon this concept. It is far better, after forming such a concept, to turn back to reality in order to see if the concept does not need correcting, or at least modifying. This is important. It is very clearly seen in astronomical thinking. Also in biological and especially in medical thought, the same failing has led people very far astray. They do not take into account, how necessary it is directly they have formed a concept, to go back to reality in order to make sure that there is no reason to modify it. The planets, then, move in ellipses. But these ellipses vary; they are sometimes more circular, sometimes more elliptical. We find this if we return to reality with the ellipse idea. In the course of time the ellipse becomes more bulging, more like a circle, and then again more like an ellipse. So I by no means include the whole reality if I merely say, ‘the planets move in ellipses’. I must modify the concept and say: The planets move in paths which continually struggle against becoming a circle or remaining one and the same ellipse. If I were now to draw the elliptic line, to be true to the reality I should have to make it of india-rubber, or form it flexibly in some way, continually altering it within itself. For if I had formed the ellipse which is there in one revolution of the planet, it would not do for the next revolution, and still less for the following one. It is not true that when I pass from reality to the rigid concept I still remain within the real. That is the one thing. The other is: We have said that the planes of the planetary orbits are inclined to the plane of the Sun's equator. Where the planets cross the point of intersection of their orbits (with the Ecliptic) in an upward or downward direction, they are said to form Nodes. The lines, joining the two Nodes (K-K 1 in Fig. 1), are variable. So too are the inclinations of the planes to one-another, so that even these inclinations, if we try to express them in a single concept, bring us to a rigid concept which we must immediately modify in face of the reality. For if an orbit is inclined at one time in one way, and at another time in another way, the concept we deduce in the first instance must afterwards be modified. To be sure, once such a point has been reached, we can take an easy line and say that there are ‘disturbances’ and that the reality is only grasped ‘approximately’ with our concepts. We then go on swimming comfortably in further theories. But in the end we swim so far that the fanciful and theoretic pictures we are constructing no longer correspond to the reality, though they are meant to do so. It is easy to agree that this mutability of the eccentric orbits, and of the mutual inclination of the planes of the orbits, must somehow or other be connected with the life of the whole planetary system, or shall we say, with its continuing activity. It must be connected in some way with the living activity of the whole planetary system. That is quite evident. Starting from this, one might again try to form the concept, saying: Well now, I will bring such mobility into my thoughts that I picture the ellipses continually bulging out and contracting, the planes of the orbits ascending, descending and rotating, and then from this starting-point I will build up a world-system according to reality. Good. But if you think the idea through to the end, then precisely as the outcome of such logical thought, the result is a planetary system which cannot possibly go on existing. Through the summation of the disturbances which arise especially through the variability of the Nodes, the planetary system would move towards its own ultimate death and rigidity. Here there comes in what philosophers have pointed out again and again. While such a system can be thought out, in reality it would have had ample time to reach the ultimate finale. There is no reason why it should not. The infinite possibility would have been fulfilled; rigidity would long ago have set in. We enter here into a realm where thought apparently comes to a standstill. Precisely by following my thinking through to the very last, I arrive at a world-system which is still and rigid. But that is not reality. Now, however, we come to something else, to which we must pay special attention. In pursuing these things further — you can find the theory of it in the work of Laplace; I will only relate the phenomena — one finds that the reason why the system has not actually reached rigidity under the influence of the disturbances — the variability of the Nodes, etc., — is that the ratios of the periods of revolution of the planets are not commensurable. They are incommensurable quantities, numbers with decimals to an infinite number of places. Thus we must say: If we compare the periods of revolution of the planets in the sense of Kepler's Third Law, the ratios of these periods cannot be given in integers, nor in finite fractions, but only in incommensurable numbers. Modern Astronomy is clear on this. It is to the incommensurability of the ratios between the periods of revolution of the several planets (in Kepler's third Law) that the planetary system owes its continued mobility. Otherwise, it must long ago have come to a standstill. Observe now, what has happened. In the last resort, we are obliged to base our thoughts about the planetary system upon numbers which in the end elude our grasp. This is of no little importance. We are therefore led, by the very requirements of scientific development, to think of the planetary system mathematically in such a way that the mathematical results are no longer commensurable. We are at the place, where in the mathematical process itself we arrive at incommensurable numbers . We have to let the number stand, — we come to a stop. We can write it in decimals no doubt, but only up to a certain place. Somewhere or other we must leave off when we come to the incommensurable. The mathematicians among you will be clear about this. You will see that in dealing with incommensurable number I reach the point where I must say: I calculate up to here and then I can go no further. I can only say (forgive my using a somewhat amusing comparison for a serious subject) that this coming to an inevitable halt in mathematics reminds me of a scene in which I was once a participator in Berlin. A fashion in Variety-entertainment came about through certain persons, one of whom was Peter Hill. He had founded a kind of Cabaret and wanted to read his own poems there. He was a very lovable person, in heart and soul a Theosophist, he had rather gone to seed in Bohemian circles. I went to a performance in which he read his own poems. The poem had got so far that single lines were finished, and so he read it aloud: The Sun came up. ... etc. (The first line.) The Moon rose. ... etc. (That was the second line.) At each line he said ‘etc.’ That was a reading I once attended. As a matter of fact it was most stimulating. Everyone could finish the line as he chose! Admittedly with incommensurable numbers [you] cannot do this, yet here too you can only indicate the further process. You can say that the process continues in a certain direction, but nothing is given by which you might form an idea as to what numbers may yet be coming. It is important that precisely in the astronomical field we are led into incommensurabilities. We are forced by Astronomy to the very limits of mathematising; here the reality escapes us. Reality escapes us, we can say nothing else; reality eludes our grasp. What does this mean? It means that we apply the most secure of our sciences, Mathematics, to the celestial phenomena, and in the last resort the celestial phenomena do not submit; the moment comes where they elude us. Precisely where we are about to reach their very life, they slip away into the incommensurable realm. Here then, our grasp of reality comes to an end at a certain point and passes over into chaos. We cannot say without more ado, what this reality, which we are trying to follow mathematically, actually does when it slides away into the incommensurable. Undoubtedly this is related to its power of continued life. To enter the full astronomical reality we must take leave of what we are able to master mathematically. The calculation plainly shows this; the very history of science shows it. Such are the points which we must work towards, if we would proceed in a realistic spirit. Now I would like to set before you the other pole of the matter. If you follow it physiologically you can begin from any point you like in embryonic development , whether it be from the development of the human embryo in the third or second month, — or the embryo of some other creature. You can follow the development back as far as ever you can with the means of modern science. (it is in fact only possible to a limited extent, as those of you who have studied it will know.) You can trace it back to a certain point, from which you cannot get much further, namely to the detachment of the ovum — the fertilized ovum. Picture to yourselves how far you can go back. If you wished to go still further back you would be entering the indeterminate realm of the whole maternal organism. This means that in going back you come into a kind of chaos. You cannot avoid this, and the fact that it cannot be avoided is shown by the course of scientific development. Think of such scientific hypotheses as the theory of “Panspermia” for instance, where they speculated as to whether the single germ-cell was prepared out of the forces of the whole organism, which was more the point of view of Darwin, or whether it developed in a more segregated way in the purely sexual organs. You will see when you study the course of scientific development in this field that no little fantasy was brought to bear on the attempt to explain the underlying genesis, when tracing backward the arising of the germ cell from the maternal organism. You come into a completely indeterminate realm. There is little but speculation in the external science of today as to the connection between the germ-cell and the maternal organism. Then at a certain point in its development this germ appears in a very definite way, in a form which can be grasped at least approximately by mathematical or at any rate geometrical means. Diagrams can be made from a certain point onward. Many such diagrams exist in Embryology. The development of the germ-cell and other cells can be delineated more or less exactly. So one begins to picture the development in a geometrical way, representing it in forms similar to purely geometrical figures. Here we are following up a reality which in a way is the reverse of what we had in Astronomy. There we pursued a reality with our cognitional process and came to incommensurable numbers; the whole thing slips into chaos through the process of knowledge itself. In Embryology we slip out of chaos. From a certain moment onward we can grasp what emerges from chaos through forms that are like purely geometrical forms. Thus in effect, in employing Mathematics in Astronomy we come at one point into chaos. And by pure observation in Embryology we have at a certain point nothing before us but chaos; it all seems chaotic at first, observation is impossible. Then we come out of chaos into the realm of Geometry. It is therefore an ideal of certain biologists — a very justifiable ideal — to grasp in a geometrical form what presents itself in Embryology; not merely to make illustrations of the growing embryo naturalistically, but to construct the forms according to some inherent law, similar to the laws underlying geometrical figures. It is a justifiable ideal. Now therefore we can say: When in Embryology we try to follow up the real process by observation, we emerge out of a sphere which lies about as near to our understanding as that which is beyond the incommensurable numbers. In Astronomy on the one hand, we proceed with our understanding up to the point where we can no longer follow mathematically. In Embryology on the other hand our understanding begins at a certain point, where we are first able to set to work with something resembling Geometry. Think the thought through to its conclusion. You can do so, since it is a purely ‘methodological’ thought, that is to say the reality of it is in our own inner life. If in arithmetic we reach the incommensurable numbers, — that is, we reach a point where the reality is no longer represented by a number that can be shown in its complete form — then we should also begin to ask whether the same thing may not happen with geometrical form as with arithmetical analysis. (We shall speak more of this in the next lecture.) The analytical process leads to incommensurable number. Now let us ask: How do geometrical forms image the celestial movements? Do not these images perhaps lead us to a certain point. Similar to that to which arithmetical analysis is leading when we reach incommensurable number? Do we not in our study of the heavenly bodies — namely the planets — come to a boundary, at which we must admit we can no longer use geometrical forms as a means of illustration; the facts can no longer be grasped with geometrical forms? Just as we must leave the region of commensurable numbers, it may well be that we must leave the region where reality can still be clothed in geometrical (or again arithmetical, algebraic, analytical) forms, such as in drawings of spirals and other figures derived from Geometry. So, in Geometry too, we should be coming into the incommensurable realm. In this sense it is indeed remarkable that in Embryology, though arithmetical analysis is not yet of much use, Geometry makes its presence felt pretty strongly the moment we begin to take hold of the embryological phenomena as they emerge from chaos. Here we are dealing, not indeed with incommensurable number but with something that tends to pass from incommensurable into commensurable form . We have thus sought to grasp reality at two poles: On the one hand where the process of cognition leads through analysis into the incommensurable, and on the other where observation leads out of chaos to a grasping of reality in ever more commensurable forms. It is essential that we bring these things before our minds with full clarity, if we would add reality to what is presented by the external science of today. In no other way can we reach this end. I should now like to add a methodical reflection, from which we can tomorrow make our way into more realistic problems. In all that we have spoken of hitherto, we have been taking it for granted that the cosmic phenomena have been approached from the standpoint of Mathematics. It appeared that at one point the mathematician comes up to a limit — a limit he encounters too in purely formal Mathematics. Now there is something underlying our whole way of thinking in this realm, which perhaps passes unnoticed because it always wears the mask of the ‘obvious’ and we therefore never really face the problem. I mean the whole question of the application of mathematics to reality. How do we proceed? We develop Mathematics as a formal science and it appears to us absolutely cogent in its conclusions; then we apply it to reality, without giving a thought to the fact that we are really doing so on the basis of certain hypotheses. Today however, sufficient ground has already been created for us to see that Mathematics is only applicable to outer reality on the basis of certain premises. This becomes clear when we try to continue Mathematics beyond certain limits. First, certain laws are developed, — laws which are not obtained from external facts, as for example are Kepler's Laws, but from the mathematical process itself. They are in fact inductive laws, developed within Mathematics. They are then employed deductively ; highly elaborate mathematical theories are built upon them. Such laws are those encountered by anyone who studies Mathematics. In lectures given recently in Dornach by our friend Dr. Blumel, significant indications were given of this line of mathematical research. One of the laws in question is termed the Commutative Law . It can be expressed in saying: It is obvious that \(a+b\) equals \(b+a\), or \(a•b\) equals \(b•a\). This is a self-evident fact so long as one remains within the realm of real numbers: But it is merely an inductive law derived from the use of the implicit postulates in the arithmetic of real numbers. The second law is the Associative Law . It is expressed as \((a + b) + c = a + (b + c)\). Again this is a law, simply derived by working with the implicit postulates in the arithmetic of real numbers. The third is the so-called Distributive Law , expressible in the form: \(a (b + c) = ab + ac\). Once more, it is a law obtained inductively by working with the implicit postulates in the arithmetic of real numbers. The fourth law may be expressed as follows: ‘A product can only equal zero if at least one of the factors equals zero .’ This law again is only an inductive one, derived by working with the implicit postulates in the arithmetic of real numbers. We have, then, these four laws; the commutative law, the associative law, the distributive law, and this law about the product being equal to zero. These laws underlie the formal Mathematics of today, and are used as a basis for further work. The results are most interesting, there is no question of that. But the point is this: These laws hold good so long as we remain in the sphere of real numbers and their postulates. But no thought is ever given to the question, to what extent the real facts are in accord with them. Within our ordinary formal modes of experience it is true, no doubt that \(a + b = b + a\), but does it also hold good in outer reality? There is no ascertainable reason why it should. We might be very astonished one day to find that it did not work if we applied to some real process the idea that \(a + b\) equals \(b + a\). But there is another side to it. We have within us a very strong inclination to cling to these laws; with them therefore. We approach reality and everything that does not fit in escapes our observation. That is the other side. In other words: We first set up postulates which we then apply to reality and take them as axioms of the reality itself. We ought only to say: I will consider a certain sphere of reality and see how far I get with the statement \(a + b = b + a\). More than that, I have no right to say. For by approaching reality with this statement we meet what answers to it, and elbow aside anything that does not. We have this habit too in other fields. We say for example, in elementary physics: Bodies are subject to the law of inertia. We define ‘inertia’ as consisting in the fact that bodies do not leave their position or alter their state of motion without a definite impelling force. But that is not an axiom; it is a postulate. I ought only so say: I will call a body which does not alter its own state of motion ‘inert’, and now I will seek in the real world for whatever answers to this postulate. In that I form certain concepts, I am therefore only forming guiding lines with which to penetrate reality, and I must keep the way open in my mind for penetrating other facts with other concepts. Therefore I only regard the four basic laws of number in the right way if I see them as something which gives me a certain direction, something which helps me regulate my approach to reality. I shall [be] wrong if I take Mathematics as constituting reality, for then in certain fields, reality will simply contradict me. Such a contradiction is the one I spoke of, where incommensurability enters in, in the study of celestial phenomena.

Astronomy as Compared to Other Sciences

Lecture IV

https://rsarchive.org/Lectures/GA323/English/LR81/19210104p01.html

Stuttgart

4 Jan 1921

GA323-4

For the further progress of our studies I must today insert a kind of interlude, for we shall then understand more easily the real nature of our task. From a particular point of view we will reflect on the cognitional theory of Natural Science altogether. Let us link on to yesterday's lecture by calling to mind once more the provisional conclusions to which we came. The verification of them will emerge in the further course. We have seen that in the study of celestial phenomena, in so far as these are expressed by our Astronomy in geometrical forms and arithmetical figures, we are led to incommensurable qualities. There is a moment in our process of cognition — in the attempt to understand the celestial phenomena — when we must come to a standstill, as it were, and can no longer declare the mathematical method to be competent. From a certain point onward, we simply cannot continue merely to draw geometrical lines, tracing the movements of the heavenly bodies. We can no longer employ mathematical analysis; we can only admit that analysis and geometry take us up to a certain point, whence we can go no further. At least provisionally, we come to the very significant conclusion that in reflecting on what we see, whether with the naked eye or with the aid of instruments, we can never fully compass it was geometrical figures or mathematical formulae. We do not contain the whole of the phenomena in algebra, analysis and geometry. Think of the significance of this. If we are claiming to include the totality of the celestial phenomena, we must no longer imagine that we can do so by thinking of the Sun as moving in such a way that its movement can be represented by a definite geometry line, or that the Moon's movement can be so represented. Precise our most ardent wish must be renounced when we confront the phenomena in their totality. This is the more significant, since nowadays, the moment someone says ‘The Copernican System works no more satisfactorily than the Ptolemaic’, someone else will answer, ‘Let us then design another system’. We shall see the in the further course of these lectures, what must be put in the place of mere geometrical designs in order to comprehend the phenomena in their totality. I must put this negative aspect before you first, before we can enter into the positive, for it is most important that we clear our thought in this respect. On the other hand, we saw yesterday that what confronts us in Embryology emerges as if from indefinite, chaotic regions, and from a certain point onward can be grasped in picture-form, or even geometrically. As I said yesterday, in studying the celestial phenomena, through the very process of cognition we come to a point where we must recognize that the world is different from what this process of cognition might at first have led us to believe. And in the embryonic phenomena we are led to see that there must be something which preceeds the facts to which we still have access. Now among other things there recently appeared a certain divergence of outlook among embryologists. (I will only give a rough description.) On the one hand there were the strict followers of biogenetic law, which states, as you know, that the development of the individual embryo is a kind of shortened recapitulation of the development of the race. These people wished to trace the cause of the development of the embryo to the development of the race. On the other hand, others came forward who would not hear of the derivation of the individual from the racial development, but held to a more or less mechanical conception of embryonic development saying that it was only necessary to take into account the forces directly present in what takes place in the embryo itself. For example, Oscar Hertwig left the strict biogenetic school of Haeckel and changed over to the more mechanical school. Now the mechanical needs to be grasped in a way that is at least similar to mathematics even though it be not pure mathematics. We therefore see, from the very history of Science, how front a certain stage onward (something as I said, must be presumed to have gone before this stage) embryological development is taken hold of by a mechanical, mathematical method of research. It is the history of these things to which I now wish to point. All this appears in the field which one might call the theory of knowledge. On the one hand we are driven to a boundary in the cognitional process, where we can get no further with our favorite modern method of approach. On the other hand, in studying the embryonic life our only possibility of grasping it with ordinary methods is to start from a certain point: what goes before this has to be taken fro granted. We must admit that we find something in the realm of reality, the beginnings of which we must leave vague and unexplored; then from a certain point onward we can set to work, describing what we observe in terms of diagrams, formulas and relationships which are at least similar to those of mathematics and mechanics. Bearing these things in mind, I deem it necessary in today's lecture to insert a kind of general reflection. As I have often pointed out, it is the ideal of modern scientific research to observe outer Nature as independently of man as possible, — to establish the phenomena in pure objectivity, as it were, excluding man altogether from the picture. We shall see that precisely through this method of excluding, it is impossible to transcend such barriers as we have now observed from two distinct sides. This is connected with the fact that the principle of metamorphosis , which, as you know,was first conceived and presented in an elementary way by Goethe, ha so far hardly been followed up at all. It has no doubt been used to some extent in morphology, yet even here, as we saw yesterday, one essential principle is lacking. Morphology today cannot yet recognize the form and construction of a tubular or long bone, for example, in its relation to that of a skull-bone. To do this, we should have to reach a way of thinking whereby we should first study what is within, say, the inner surface of a tubular bone and then relate this to the outer surface of a skull-bone. This means a kind of inversion, as when a glove is turned inside-out; but at the same time there is an alteration of the form, an alteration of the surface-tensions through the reversing or turning of inside outward. Only if we follow the metamorphosis of forms in this way, though it may seem complicated, shall we reach true conclusions. But when we leave the morphological and enter more into the functional domain, there are but the barest indications, in the existing ways of thought, towards a true pursuit of the idea of metamorphosis in this domain. Yet this is what is needed. A beginning was made in my book, “Riddles of the Soul”, wherein I indicated at least sketchily — the three-foldness of the being of man, recognized as a sum-total of interrelated functions. At least in outline, I explained how we must first distinguish those functions and processes in man which may be regarded as belonging to the nerves and senses; how we then have to recognize, as relatively independent processes, all that is rhythmical in the human organism; and how again we must recognize the metabolic processes as distinct. I pointed out that in these three forms of processes all that is functional in man is included. Anything else which appears functional in the human organism is derivable from these three. It is essential to see that all phenomena in the organic realm although appearing outwardly side by side, are related to one-another through the principle of metamorphosis. People today are disinclined to look at things macroscopically. We must find our way back to the macroscopic aspect. Otherwise, through the very lack of synthetic understanding of what is living, problems will arise which are not inherently insoluble, but are made so by our methodical prejudices and limitations. You see, in learning to understand man in this threefold aspect we must observe that he is connected with the outer world in a three fold way His life of nerves and senses is one way in which man is related to the outer world; through all rhythmic processes he is related to it in another way. It lies in the very nature of the rhythmical processes that they cannot be considered as isolated within man, apart from the rest of the world, for they depend upon the breathing, — a process of perpetual interchange between the human body and the outer world. Again, in the metabolism there is a very obvious process of interchange between man and the outer world. Also the nerves-and-senses process may be regarded as a continuation of the outer world into the inner man. This becomes easier to understand if the distinction is made between the actual perceptions, given to us through the senses, and the accompanying process of cognition — the forming of ideas and mental pictures. It is unnecessary here now to go into these things more deeply, for it is evident enough. In relation between man and the outer world during sense-perception the emphasis is more on the outer world, while the forming of ideas and mental pictures takes us more into the inner man. (I am referring to the bodily processes, not to the life of soul.) Again, leaving aside for the moment the rhythmic system — breathing and blood-circulation — the metabolic system brings us to something else, which is in definite contrast to this inward-leading process from sense perception to ideation. A thorough study of the metabolic system establishes a connection between the inner metabolic processes and the functions of the human limbs. The limb-functions are connected with the metabolism. If people would proceed more rationally than they are wont to be they would discover the essential connection between the metabolism, situated as it is more deeply within the body, and the processes by means of which we move our limbs. These too are metabolic. The actual organic functions which underlie the movements of the limbs are processes of metabolic. Consumption of material substances is what we find if we examine the organic functions here. But we must not stop short at the metabolic process as such. There is a way in which this process leads as much from man towards the outer world, as sense-perception leads from the outer world towards the interior of the human body. (Such methods of research, which are really fundamental, need to be undertaken, otherwise no progress will be made in certain essential directions.) What is it that is directed outward from the metabolism even as something is directed inward from sense-perception to the creating ideas and mental pictures? It is the process of fertilization . Fertilization points in the opposite direction, — from the bodily organism outward. Representing it diagrammatically ( Fig.1 ): In sense-perception the direction is from without inward; this in — coming process of sense-perception is then ‘fertilized’ by the organism and we get the forming of ideas. (Please do not take offense at the expression ‘fertilized’; we shall soon replace, what may look like a symbolical way of speaking, by the reality it indicates.) In the metabolic process the direction is from within outward, and we get actual fertilization. In what is manifested therefore at the two poles of threefold human nature, we are led in two opposite directions. In the middle is all that belongs to the rhythmic system. Now we may ask, what in the rhythmic system is directed outward and what inward? Here it is not possible to find such precise distinctions as between the inner metabolism and fertilization, or between perception and ideation. The processes in the rhythmic system rather merge into one-another. In the in-breathing and out breathing the process is more of a unity. It cannot be distinguished quite so sharply, yet it is still possible to say (Fig.1): As sense perception comes from outside and fertilization goes outward, so too in inspiration and expiration there is a going inward and outward. Breathing is intermediate. Here is a true example of metamorphosis: a single entity, underlying threefold human nature, organized now in one way, now in another. In the upward direction this can be followed to some extent physiologically. (Some of you already know what I Shall now refer to.) Observe the breathing process. The intake of air influences the organism in a certain way; namely, in in-breathing, the cerebro — spinal fluid, in which the spinal cord and brain are stepped, is pressed upward. You must remember that the brain is in fact floating in cerebral fluid, and is thus buoyed up. We should not be able to live at all without this element of buoyancy. We will not go into that now, however, but only draw attention to the fact that here is an upward movement of the cerebral fluid in in-breathing and a downward movement in out-breathing. So that the breathing process actually plays into the skull, into the head. In this process we have a real interplay and co-operation of the nerves-and-senses system with the rhythmic system. You see how the organs work, to bring about what we may call metamorphosis of functions . Then we can say, however hypothetical or only as a postulate: perhaps something similar will be found as regards metabolism and fertilization. But in this realm of the body we shall less easily reach a conclusion. This is indeed characteristic of the human organism; it is comparatively easy to understand the interpenetrating relation between the rhythmic system and the nerves-and-senses system in process accessible to thought, but we cannot so easily find an evident relation between the rhythmic system and the processes of metabolism and fertilization. Call to your aid the physiological knowledge at your disposal, and the more exactly you go into the matter the better you will perceive this. Moreover it is quite obvious why it is so. Consider the regular alternation of sleeping and waking. Through sense-perception you are open to the outer world, continuously exposed to the outer world. Then you set to work with your thinking and ideation and bring a certain order and orientation into what you see around you in your waking life. It becomes ordered through an activity which works from within outward; the orientation comes from within. Actually we can say: We confront an external world which is already ordered according to its own laws, and we ourselves bring another order into it out of our own inner being. We think about the outer world, we put together the facts and phenomena according to our own liking — unhappily, often a very bad liking! From our inner being, something is introduced into the outer world which by no means necessarily corresponds to this outer world. If this were not so, we should never fall a victim to error. Out of our own inner being comes an arbitrary remolding of the world around us. But now, looking at the other pole of human nature, you will agree that the disordering comes from without, both in metabolism and fertilization. For it is left very largely to our own arbitrary choice and free will, how we sustain our metabolism by taking food, and even more so, how we behave as regards fertilization. But here the arbitrary element has much to do with the outer world, which in the first place is foreign to us. We do at least feel at home in the arbitrary element we introduce, out of our own inner being, into the process of perception. But we do not feel familiar with all that we bring into ourselves from the outer world. We have, for instance but a very slight idea — at least, most people have very little idea of what actually happens in our relationship with the world when we eat or drink. And as to what happens in the intervals of time between our meals, — to this we pay very little attention, and even if we did it would not help as much. Here we come into an indefinite, impalpable region, I would say. Thus at the one place of man's being we have the ordered Cosmos which extends its gulfs, as it were, in our sense organs (Fig.2). (The world ‘ordered’ must not be misunderstood, it is only used to characterize the facts; we will not lose ourselves in philosophical arguments as to whether the Cosmos is really ordered or not, we want only o characterize the given facts.) The pole is in contrast to the other, which, we are bound to admit, is an un-ordered Cosmos , considering all that comes into us from without all that we stuff into ourselves, or again, how the process of fertilization is entered into in quite irregular intervals of time and so on. Contemplating this invasion of the metabolism by the outer world, we must admit that we are here confronted by an unordered Cosmos — un-ordered at least to begin with, so far as we are concerned. And now we may put the question — from the more general aspects of the theory of human knowledge: How and to what extent are we really connected with the starry Heavens? In the first place, we see them. But you will have a vivid feeling by this time of the uncertainties which assail us when we being to think about the starry Heavens. Not only have the men of different ages felt convinced of the truth of the most diverse astronomical world — systems. As we saw yesterday, we have to face the fact that we cannot contain the totality of the starry Heavens in the mathematical and mechanical forms of thought in which we feel most secure. Not only must we admit that we cannot trust to mere sensory appearances as regards the Heavens, but we must recognize that when we take our start from what we see and then work upon it with the life of thought, which, as we saw, belongs more to the inner man,we cannot ever really get at this world of stars. It is the truth, it is no mere comparison to say: The starry Heavens only present themselves to us in their totality — a relative totality, of course — through sense perception. Taking our start from sense-perception, when we as man try to go farther inward, to understand the starry Heavens, we feel somewhat foreign to them. We get a strong feeling of our inadequacy. And yet we feel that something intelligible must be there in the phenomenon which we behold. Outside us, then , is the ordered Cosmos; it only presents itself to our senses. It most certainly does not at once reveal itself to our intellectual understanding. We have this ordered Cosmos on the one hand; with it, we cannot enter into man. We try to lead on from outer sense-perception of the Cosmos towards the inner man — the life of thought and ideation — and find we cannot enter. We must admit: Astronomy will not quite go into our head. This is not said in the least metaphorically. It is a demonstrable fact in the theory of knowledge. Astronomy will not go into the human head; it simply will not fit there. What do we see now at the other pole — that of the unordered Cosmos? Let us but look at the facts; we do not want to set up theories or hypotheses, but only to see the facts clearly. Look for what is in contrast, in the outer Universe to the astronomical domain, and in man to the processes of perception and ideation (the continuation of the ‘ordered Cosmos’ into man). In man you come into the realm of metabolism and fertilization — and Astronomy (Fig.2) and look downward in an analogous way, into what realm are you led? You are led into Meteorology — all the phenomena of the outer world once more, relating to Meteorology. For if you try to understand meteorological phenomena in terms of ‘natural law’, the amount of law you can bring in is to the ordered Cosmos of Astronomy in just the same proportion as is the temperamental region of metabolism and fertilization in man to the realm of sense perception, into which the whole starry Heaven sheds its light, — which only begins to get into disorder in our own inner life, namely in our forming of ideas. If therefore we regard man not as an isolated being, but in connection with the whole of Nature, then we can place him into the picture in the following way. Through his head, he takes part in the astronomical, through his metabolism in the meteorological domain. Man is thus interwoven with the Cosmos on either hand. Let us here add another thought. Yesterday we spoke of those processes which may be looked upon as an inner organic imagining of Moon-events, namely the processes in the female organism. In the female organism there is something like an alternation of phases, a succession of events, taking their course in 28 days. Although, as things are now, these events are not at all dependent on any actual Moon-events, yet they are somehow an inner reflection of the moon. I also drew your attention to the following psycho-physiological fact. If we really analyze human memory and take into account the underlying inner organic process, we cannot but compare it with this functioning of the female body. Only that in the latter the bodily nature is taken hold of more intensely than it is when holding fast in memory some outer experience which it has undergone. What comes to expression in these 28 days as a result of erstwhile our impressions is no longer contained within the individual life between birth and death, whereas the experiencing of outer events and the memory of them comes into a shorter period and takes its course between birth and death, within the single life of the individual. Considered in their psychological-physiological aspect, the two processes are however essentially the same — a functional reexperiencing of an external process or event. (In my ‘Occult Science’ I clearly hinted at this kind of experience in relation to the outer world.) Now, study the functions of the ovum before fertilization and you will find that they are entirely involved in this 28-day inner rhythm; they belong to this process. But as soon as fertilization takes place, the processes in the ovum immediately fall out of this inner rhythmic life of the human being. A mutual relation with the outer world is at once established. Observing the process of fertilization, we are led to see that what is happening in the ovum from then onward no longer has to do with mere inner processes in the human body. Fertilization tears the ovum out of the purely inner organic process and leads it over into the realm of those processes which belong in common to the inner being of man and to the Cosmos, — a realm in which there are no barriers between what takes place within man and in the Cosmos. Therefore, what occurs after fertilization, — all that happens in the forming of the embryo, — must be studied in connection with external cosmic events, and not merely in terms of developmental mechanisms within the ovum itself in its successive stages. Think what this means. All that goes on in the ovum before fertilization is, so to speak, within the domain of the human being's own inner organic process. But in what happens after fertilization and is brought about thereby — the human being opens himself to the Cosmos. Cosmic influences here prevail. Thus on the one hand we have the Cosmos working in upon us up to the point where the life of ideas begins. We have, in sense — perception, a mutual relation, between man and the Cosmos. We investigate this relation, for example, by means of the laws of perception. The physiology of the senses and so on. The way in which we see an object must be investigated through such laws. Suppose we watch a railway-train traveling past us. We see the whole movement lengthwise. If, however, we are at a point directly in front of the train far enough away — however fast the train is going, we see it as if it were stationary. Pictorially, therefore, what takes place in us depends on the relation of the cosmos to us. We are in the midst of pictures and we ourselves belong to the picture. However, we become entangled in something chaotic, — for ultimately, our world systems are chaotic, — if we try to draw conclusions as to the real events from what we see externally. On the other hand, in regard to fertilization, man is involved not in pictorial but in real cosmic processes. Thus at the one role man is immersed in the Cosmos in a pictorial , and at the other in a real way. The very thing that eludes him when he looks out into the Cosmos, works in upon him when he undergoes the process of fertilization. Here therefore something, in itself a whole, is drawn apart into two members. In the one case a mere picture is before us and we cannot strike through to the reality. In the other the reality confronts us; through it a new man comes into being. But it does not become clear picture; it remains for us as devoid of law as do the manifestations of the weather, or meteorological conditions generally. Here we are face to face with a duality — here are two poles. From either side we receive half thrilled. It is as though we received the picture from the one side and the reality which underlies it from the other. You see, the way man confronts the world is not as simple as one might assume in saying: The sensory picture of the world is given; now let us devise the reality by philosophical methods. This problem of finding the underlying reality in sense-perception is, of course, fundamental in the philosophic theory of cognition. But man is curiously balanced between the picture and reality in quite other ways than by mere philosophic speculation. Now in the course of world-evolution, men have already tried to approach this secret through an experience of the intermediary realm: in-breathing and out-breathing. The ancient Indian wisdom which, as I often say, it would be wrong for us to imitate today — proceeded more or less instinctively from the following hypotheses. Sense-perceptions are of no use in the striving for reality; nor are the sexual processes or those of fertilization, for they give no clear picture. Therefore, let us keep to the middle region, which is metamorphosed at one time towards picture-forming and at another time towards reality. We must keep to the middle region, for through it the approach to reality and yet at one and the same time to the picture must in some way be possible. This is why the special breathing exercises of the Yoga system were perfected by the wisdom of Ancient India. Men sought to reach reality by experiencing the breathing process consciously, thus grasping at the same time both picture and reality. And if one asks why this should be, the answer is given: Breathing unites picture and reality. (The answer may be more or less instinctive, though not entirely so, as you can see if you will study, in the Indian philosophy itself, how this strange system of breathing-exercises arose.) Breathing unites picture and reality. The picture is experienced in its relation to the reality, if once the breathing process is lifted out of the unconscious into consciousness. We shall never understand what thus appeared in the historic evolution of mankind, unless we regard it from the point of view of the inner physiology of man. Looking at it in this light, you can say: There was a time when men sought to comprehend reality by turning to man himself. For pictures of the world, we have the senses; for the reality, something quite different. Therefore men turned to that part of the world human being which is neither shutoff in finished pictures, nor on the other hand in the mere experiencing of reality; they turned to what is not yet differentiated or divided — to the breathing process. And in so doing, they brought man into the Cosmos. They did not contemplate a world separate from man like the world of our Natural Science; they beheld a world for which man, as rhythmic man, became a real organ of perception. This world, they said, can be grasped neither by the nerves-and-senses man, nor by the metabolic man. In his life of nerves and senses, man becomes conscious in such a way that what presented itself to nerves and senses is thinned out to a mere picture; in the metabolism, reality meets him in such a way as not to be raised into consciousness at all. The interweaving of the real but unconscious experience with what is thinned out to a picture was sought by the wise men of ancient India in the regulated breathing process. Nor shall we ever understand the ancient cosmic systems, previous to the Ptolemaic, till we are able to divine how the Universe appears to man when in this was a synthesis, however undifferentiated, is achieved between the process of cognition on the one hand, and on the other the intense realty of the reproduction-process. Consider now from this point of view the teachings about the creation of the world which are to be met with particularly in the Bible: teachings which, as things are today, are not so easy to see through. Consider the Bible story of the Creation, particularly as interpreted by those who still had the old traditions. Fundamentally, the Biblical story of Creation can only be understood if we are able to combine the genesis of the world which we derive by looking at the outer Universe, with that which we derive by Embryology. What is set forth in the Book of Genesis is in fact compounded of Embryology and of what is seen in the outward glory of the sense world. Hence the repeated attempts to interpret the Biblical story of Creation, even word for word, by embryological facts. Truly, it calls for such interpretation. I introduced this today, my dear friends, for quite a definite reason. You see, if our present studies — intended, as they are, to form a bridge between the external Science of today and Spiritual Science — are to have any meaning at all, we must first acquire a quite definite feeling and must permeate ourselves with this feeling otherwise we can get no further. We must become able to feel that certain modern ways of thought are superficial and external, — to feel this in a thoroughly deep way. We must learn to see the superficiality, on the one hand, of setting up pictures of the Universe which only try to make some slight corrections in the Copernican System, and on the other hand, of researching into the embryonic life in the ways which are customary today. One might say that Nietzsche's dictum: “The world is deeply thought and wrought; more deeply than the passing day”, proceeded from such a feeling. The impulses must be acquired not to seek explanations in the mere superficial acceptance of what presents itself directly, even if it be to the enhanced sight of telescope or microscope or X-ray apparatus. We must learn to have respect for explanations of another nature, aspiring to other faculties of knowledge, such as were sought by the old Indian sages in the Yoga System, so as to penetrate into reality and find the means of forming an adequate picture of reality. Since we have now outgrown the Yoga system, we must feel impelled towards a new way of penetrating into the Universe by processes which still remain to be developed — which are not to be derived so simply from the habitual methods of today. For man is placed in the midst between the picture of the world, — a picture which presents itself to him in an overwhelmingly forceful way in the starry Heavens, the secrets of which will never be disclosed through the mere intellectual faculties, — and what meets him with ever — changing mood and temperament in the processes of reproduction, by virtue of which the human race exists. Into the midst of this great whole which is thus separated for him into two halves, man is placed. to find a connection between the two, he must look for a way of spiritual development, even as he did in an older form in the Yoga system, — a form no longer possible today. Astronomy, practiced as hitherto, will never lead to a grasp of reality; it will only give us pictures. And Embryology, though in this realm we seize reality, will no enable us to penetrate the reality with ideas and mental pictures. Astronomical pictures of the world are poor in reality; embryological pictures are poor in idea — we fail to penetrate the facts with clear ideas. Thus in the theory of knowledge too we must approach the human being as a whole, instead of merely indulging in philosophical and psychological speculations about sense-perception. We must take our start from the whole of man. We must learn how to place man as a whole into the Universe. That is our task today. It is very evident today, how on the one hand in Astronomy the ground of knowledge is being lost. And it is evident how on the other hand in Embryology, where knowledge fails to reach the well-springs of reality, all that results is a mere talking round and round the given facts, whether in terms of the biogenetic law or of developmental mechanisms. Amplification of our fundamental methods is quite evidently needed in both of these directions. I had to put all this before you, so that we might understand each other better in what follows. For it will help you see that it would be no use if I were simply to add another formal picture of the Universe to the existing ones, although admittedly that is the kind of thing which people nowadays desire.

Astronomy as Compared to Other Sciences

Lecture V

https://rsarchive.org/Lectures/GA323/English/LR81/19210105p01.html

Stuttgart

5 Jan 1921

GA323-5

You will have seen, from what has been said so far, that in the explanation of natural phenomena we need to find a path leading beyond the intellectually mathematical domain. That we do not dispute the justification of a mathematical approach is implicit in the whole spirit of these lectures. But we were able sharply to define the point beyond which it is impossible to go with mathematical thought-forms, in the celestial spaces on the one hand, and in the realm of embryology on the other. We must hew out a path to other methods of cognition. It is the purpose of these lectures to show the scientific need of other methods. I shall try to show that what is looked for nowadays merely by gazing outward into celestial space — whether with the unaided eye or with the help of optical instruments — needs to be put on a far wider basis, so that not only a part but the whole of man becomes the ‘reagent’ for a deeper penetration of the Heavens. Today I shall try, if not to prove, at least to indicate the validity of such a widening of method, by approaching the problem from quite another side. It may seem paradoxical in relation to our present theme, but the reason will soon become plain. In studying the evolution of mankind on Earth we must surely find something within human evolution itself to guide us to the essential source of the celestial phenomena. For otherwise we should be assuming that what goes on in the Universe beyond the Earth is without influence on man, — on human evolution. No-one will make such an assumption, although admittedly the influences may be over-estimated by some and under-estimated by others. It will therefore be plausible — at least from a methodic point of view — to put the question: ‘Can we find anything in the evolution of mankind itself to indicate ways of access to the secrets of celestial space?’ Asking this question, we will take our start, not from Spiritual Science, but from the facts which anyone can gather for himself by empirical, historical research. Looking back in the evolution of mankind in the realm where human thoughts, the human faculties of knowledge find expression, where, so to speak, the relation of man to the world takes on the most highly sublimated forms — we are led back, to begin with (as you may gather from my ‘Riddles of Philosophy’), only a few centuries into the past. Indeed I have often pointed to a certain moment during the 15th century, one of the most essential in the more recent phase of human evolution. The indication is of course approximate. We have to think of the period about the middle of the Middle Ages. Needless to say, we are referring only to what was going on within civilized mankind. It is not generally seen clearly or sharply enough, how deep and incisive a change was then taking place in human thought and cognition. There has unfortunately for some time been a downright aversion — among philosophers especially — to a real study and appreciation of the epoch in European civilization which may be called the Age of Scholasticism . During that age, deeply significant questions came to the surface of man's life of knowledge. It one goes into them deeply enough, one feels that these questions did not merely spring from the realm of logical deduction — the form in which the Middle Ages used to clothe them — but from the very depths of man's being. One need only recall what then became a fundamental question in human knowledge — the question of Nominalism and Realism. Or again, what it betokened in the spiritual development of Europe that attempts were made to prove the existence of God. There was for instance the so-called ontological proof of the existence of God. From thought itself — from the pure concept — men wanted confirmation of God's existence. Think what it means in the whole evolution of human knowledge. Something was stirring in the inmost depths of human being; in the philosophical deductions of the time it only found fully conscious expression. Men were perplexed as to whether the concepts and ideas, which man forms and puts into words, in some way stand for a reality, or whether they are merely formal summarizations of the external sensory data. The Nominalists regarded the general concepts which man creates for himself as a mere formal summary, having no significance for the external reality but only helping man to find his way about — to orientate himself in an otherwise confusing outer world. The Realists (an expression used in a rather different sense than today) declared that something real is to be found in general or universal concepts, — that in these concepts man in his inner life takes hold of something real , — that they are no mere convenient generalizations or abstractions from the world. Often in more public lectures I have related how my old friend Vinsenz Knauer — a latter-day scholastic, though he would not have claimed to be one — showed himself very clearly, in his interesting work “The Central Problems of Philosophy, from Thales to Robert Hamerling”, to be thoroughgoing Realist. The Nominalists, he said, assert that the concept ‘lamb’ is nothing but a convenient generalization arising in the human mind; so too the concept ‘wolf’. Matter is only put together in a different way in the lamb and in the world. We only summarize it in the convenient abstraction, ‘lamb’ or ‘wolf’ as the case may be. Well, he suggested, try for some time to keep a wolf away from all other food and give it only lambs to eat, after the necessary lapse of time the matter in the wolf will be nothing but lamb, and yet it will not have lost its wolfishness. Therefore the wolf-nature, expressed in the general concept ‘wolf’ must be something real. Now the fact that the so-called ‘ontological’ proof of God's existence could arise at all, bears witness to a deep and thorough going change then taking place in human nature. Quite a short time before, it simply would not have occurred to anyone within European culture to want to prove God's existence, for this was felt to be self-evident. Only when this feeling was no longer alive in men, did they begin to crave for proof. If you have living inner certainty about a thing, you do not want to prove it. But at that time something was slipping away from man, which until then had been alive in him quite as a matter of course, and the human spirit was thus led into quite other channels — quite other needs. I could adduce many another example, showing precisely at the highest levels of thought and knowledge (though you may take the word 'highest' with a grain of salt) what a deep stirring and rumbling was going on in human nature during that period of the Middle Ages. Now we can surely not deny that there must be some connection between what is going on in the life of mankind and the phenomena in the Heavens beyond the Earth. In the most general sense, we must assume that there is some connection; what it is in detail, we shall discover in due course. Hence we may ask — we want to proceed very carefully, so we need only ask — ‘How were these inner experiences which man on Earth was undergoing at that time, connected with the evolution of the Earth-plant altogether?’, — a question which may obviously lead us into realms beyond the earth. Was it perhaps a special moment in the evolution of the Earth a such? Is there anything that we can point to as a more definite criterion of what this moment was in human evolution? We can indeed point to something of significance in this connection. There was another time which made a deep incision in the name regions of the Earth where in the Middle Ages these events were taking place in the most highly sublimated realm of human life the spiritual life of thought. The medieval time, when this deep moving and stirring of humanity took place, lies in the very midst between two end-points, as it were, in the scale of time. For European regions these ‘end-points’ do not represent the kind of times in which intense activity of human life and culture would be possible at all. In effect, if from this medieval moment, which I will call A (Fig. 1), we go backward and forward an equal length of time into a fairly distant past and future, we come to points of time representing a certain barrenness and death of civilization in the very regions where this deep stirring of human life was going on in the 13th, 14th, and 15th centuries. About 10,000 years forward and 10,000 years back from this moment (A in Figure 1) we reach the maximum development of the Ice Ages in these very regions Ice Ages certainly would not allow of any outstanding development in human life and culture. Surveying therefore the evolution of these European regions we find an Ice Age — a laying-waste of civilization — 10,000 years before the Christian era, and we should find the same again 10,000 years after this time. The deep stirring of human life, of which we have been speaking, happened midway between two such barren epochs. As I said just now, there is a certain reluctance to pay attention to this period in the development of philosophy — the 13th and 14th centuries; — it is not seen clearly and accurately for what it is. Yet if one has a feeling for the evolution of the life of knowledge in mankind, one is aware that to this day our philosophic history is influenced by the after-effects of what was stirring and rumbling in the life of mankind at that time. It showed itself in other domains of civilization too; it only came to expression most clearly and symptomatically in this phase of development of the life of thought and knowledge. Now as you know, this phase of development — appearing about the middle of the Middle Ages — was an incisive one in European civilization. I have often spoken of it in anthroposophical lectures. It was an incision. Something was changed in the whole trend of human evolution. It had been beginning long before — in the 8th century B.C. We may describe it as a most intense development of human intellectuality . Since then, in the life and civilization of mankind, we have been looking especially at the development of Ego-consciousness. All aberrations and all wisdom gained in the general life of humanity since that medieval time are really due to this Ego-development to the ever-growing elaboration of the consciousness of “I” in man. The consciousness of the ancient Greeks and even of the Latins (both the ancient Latins and their descendants, the Latin peoples of today) did not lay so much stress on the Ego. Even in language for the most part, in grammar and syntax, they do not pronounce the “I” so outspokenly, but still include it in the verb. The “I” is not yet so blatantly set forth. Take Aristotle and Plato, and above all the greatest philosopher of antiquity, Heraclitus. Throughout their work the Ego is not yet so prominent. The way in which they take hold of the world-phenomena with the intellectual reasoning principle is as yet rather more selfless. (Please do not over stress this, but in a relative sense the word ‘selfless’ may be used.) There is not yet so sharp a dissociation of the self from the world-phenomena as there tends to be in the new age — the Age of Consciousness in which we are now living. Going still farther back — beyond the 8th century B.C. — we come into the Egyptian and Chaldean Age as I have called it (you will find the details in my “Occult Science”). Once again, the condition of the human soul was different. During this age — which like the others, lasted for over 2,000 years — man was not yet relating external phenomena to one-another by intellectual reasoning at all. He apprehended the world — the Heavens too — rather in feeling and direct sensation. It is mistaken and fruitless to approach what is still extent of the Astronomy of Egypt and Chalden with present-day intellectual judgments — the kind of judgment which we ourselves have inherited from the Graeco-Latin Age. We must achieve a certain metamorphoses or soul so as to enter into the quite different soul-condition then prevailing, where man took hold of the world in simple feeling and sensation (where the concept was not yet separated from the sensation). Even in the realm of actual sensations or sense-impressions — as can be shown historically and philologically — they attached no great importance to the precise description of the blue and violet shades of color, whereas (they had a very keen sensation of the red and yellow regions of the spectrum. Indeed the sensation of the dark colors can be seen to have arisen simultaneously with the capacity for intellectual concepts. The Egypto-Chaldean Age — from 747 B.C. about 2160 years into the past, — takes us to the beginning of the third millennium BC. Still earlier, say in the fourth or fifth millennium BC, we come into an age when man's whole outlook and mode of perception were so different from ours today that it is hard for us, without recourse to spiritual-scientific methods, to transplant ourselves at all into the way in which the man of that time was the world around him. It was not only a feeling and sensing, — it was a living with the outer happenings, being right in them. Man felt himself a part and member of all Nature around him, much as my arm, if it were conscious, would feel itself a member of my body. Here therefore was an altogether different trend and quality in man's relation to the world. And if we go still farther back, we find this union of man with the surround world even more enhanced. In those very early times, civilizations were only able to develop where special geographical conditions made it possible. I mean the time described in my Occult Science as the Ancient Indian civilization — much earlier than the culture of the Vedas, which was but a later echo of it. The Ancient Indian epoch comes very near to the time when glacial conditions prevailed in our regions of the Earth. A culture like the Ancient Indian could only develop when such climatic conditions, more or less, as we enjoy in the Temperate zone today, extended to what is now the Equator. You can deduce it simply from the relative advance or retreat of the ice; tropical conditions did not come about in India until a must later time, when in more northerly regions the ice had receded. We see therefore how the inner evolution of mankind undergoes modifications hand in hand with changing terrestrial conditions — changing conditions, that is to say, on the Earth's surface. Only those who take a very short-term view of mankind's evolution upon Earth will imagine that the scientific ideas we entertain today have any absolute validity — that we have now at last got through to the scientific truth, so to speak. To anyone who looks more deeply into these regions of the Earth which are today enjoying certain forms of cultural and spiritual life will at some future time inevitably be laid waste again; they will be desolate once more. From the past length of time you may reckon out how long ahead it will be till a new glacial age overtakes our present civilization. Moreover assuming that we can find some connection between the celestial phenomena and these facts of earthly evolution — the successive Ice-ages and the mid-point between them — this will lead on to a further insight. That which take place on Earth in the most highly sublimated realms of cultural life — in the life of thought and knowledge — will be related now not only to these changing conditions on the Earth itself, but to conditions in the outer Cosmos. Purely empirical reflection shows that man is what he is by virtue of conditions on the planet Earth and in the Universe beyond. Once more then taking the facts empirically as is usual in Science, only with a somewhat wider range, our vision is extended until we recognize such a relationship as we have just been describing. Now in a sense, even in present time we can perceive how the quality and trend of human spiritual life is brought about by the relation between the Earth and the celestial bodies. In an earlier lecture it was pointed out how different the spiritual configuration of mankind tends to be in Equatorial and in Polar regions. Investigating this more closely, the different relation of the Earth to the Sun proves to be the determining factor. It makes man in the Polar regions less free of his bodily nature. Man in the Polar regions is less able to lift himself out of the bodily organism, — to pain free use and manipulation of his life of soul (As to the different mutual relations of Earth and Sun, there will be more in it than that, as we shall find in due course; but to begin with we can take our start from the conventional notions.) We need only picture to ourselves how differently the men of Polar regions are taken hold of by something which in ourselves keeps more in the background. We of the Temperate zone have the quick alternation of day and night. Think how long this alternation becomes as you approach the Polar zone. It is as though the day were to lengthen out into a year. I told you of what works in the little child, deep in the bodily nature from year to year, from birth to the change of teeth, and of how the independent working of the life of soul, given up as it is to the quicker rhythm of the day, gradually frees and detaches itself from this more bodily working. This is not possible to the same extent in Polar regions. It is the yearly rhythm which will there tend to make itself felt. The emphasis is more on the bodily side. The human being will not wrest himself free to the same extent from what works within the body. Think now of the scanty relics that have been preserved from the civilization of very early times, — that have survived the Ice Age. Then you will see that there were times in which a kind of ‘Polarization’ (giving the word its proper meaning in this context) extended right across the present Temperate zone, so that conditions were prevailing here not unlike those in the present Polar regions. You can use this comparison for what was working in the Ice Age; you can truly say: What is now pressed back towards the North Pole, extended then over a considerable part of the Earth. (Please keep this free of present-day explanations and ideas, for otherwise the pure phenomenon will be obscured. Take only the pure phenomenon as such.) Conditions on the Earth today are such that we have the three types; the human beings of the Tropical, the Temperate and the Polar zones respectively. Of course they influence each other, so that in outer reality the phenomenon does not appear quite so purely. Nevertheless, what you here have in a spatial form — you find it again in time as you go backward. Going back in time, we come to a ‘North Pole’, as it were, in time — in the history of civilization. Going forward, we come to a Pole again. Remembering that the Polar influence on man is connected with the mutual relations between Earth and Sun. We must conceive that the change which has taken place since the Ice Age — the de-polarization, so to speak — is connected with a changed relation between Earth and Sun. Something must have happened as regards the mutual relation between Earth and Sun. What was it then? The facts themselves suggest the question. What is the source of this in the celestial spaces? Consider it more nearly. Of course these things will be different in the Northern and Southern hemispheres, but the facts remain. We shall at most have to extend our picture, adapting it to the real facts. We can only take our start from the empirically given data. What is revealed then, if we approach the phenomena without preconceived ideas? The Earth and the events on Earth appear as an expression of cosmic happenings — cosmic happenings which manifest themselves in certain rhythms. Something that showed itself about the tenth millennium before the origin of Christianity, will show itself again about the eleventh millennium after. What is in between, will also in a sense be repeated. What we here have between the two Ice Ages, will undoubtedly have been there before — in former cycles. It is a rhythm; our attention is drawn to a rhythmic process. And now look out into the celestial phenomena. To emphasize one fact especially, which I have often pointed to in my lectures, you have the following. (I will only characterize it roughly.) You know that the vernal point — where the Sun rises in spring-time gradually moves through the Ecliptic. Today the vernal point is in the constellation of Pisces; before, it was in Aries; still earlier in Tauraus, — that was the time of the cult of the Bull among the Egyptians and Chaldeans. Still earlier, it was in the constellation of Gemini, and then in Cancer; in Leo. This already brings us very nearly to the last Ice Age. Thinking it through to a conclusion, we know that the vernal point goes all the way round the Ecliptic, and that the time it takes is called the Platonic Year — the great Cosmic Year, lasting approximately 25,920 years. A whole number of processes are comprised in these 25,920 years, involving among other things this rhythmic alternation on the Earth; Ice Age., intermediate period, Ice Age, intermediate period, and so on. At the time we spoke of, when there was that deep stirring of the spiritual life in mankind, the vernal point was entering the sign of Pisces. In the Graeco-Latin Age it had been in the sign of Aries, previous to that in Taurus, and so on. We get back to Leo or Virgo, more or less, during the time when glacial conditions prevailed over the greater part of Europe and in America too. Looking into the future, there will be another Ice Age in these regions when the vernal point reaches the sign of Scorpio. This rhythm is contained within what takes its course in 25,920 years. Although admittedly of vast extent, it is a true rhythm none the less. Now as I have often mentioned, this rhythm is reminiscent — purely numerically — of another rhythm. If it is simply a question of rhythms and the rhythms are expressible in numbers, if the numbers are the same the rhythms too are the same. You know that the number of breaths man takes — in breathing and out breathing — is approximately 18 to the minute. Reckon out the number of breaths in a 24-hour day and you get the same number as before — 25,920. Man therefore shows in his daily life the same periodicity, the same rhythm, as is revealed by the movement of the vernal point in the great Cosmic Year. Now it is in the day that man shows this rhythm. A day therefore, with respect to breathing, corresponds to the Platonic Year. The vernal point — connected as it is with the Sun — goes round apparently in 25,920 years. But there is also the apparent movement of the Sun through the 24 hour day, while man is taking 25,920 breaths. It is the same picture here as in the great Universe. If then there were a Being who breathed in and out once a year (a simple-minded hypothesis no doubt, but we will use it for comparison), — such a Being, if living long enough, would undergo in 25,920 years the same process as man does in a day. Man reproduces, as it were in miniature, what is manifested in the great cosmic process. These things make little impression on the people of today, for they are not accustomed to look at the qualitative aspect of the world. Quantitatively, the mere rhythm appears less important. Therefore the scientists are out to find other relations between numbers than these that find expression in pure rhythms. They pay less heed to the latter: But in the epochs when man experienced more nearly the relation between himself and the Universe — when he felt himself more immersed in the phenomena of the Cosmos — these things made a deep impression on him. As we go back in the history of mankind — beyond the second or third millennium B.C. — we find great attention paid to the Platonic Year. I mentioned yesterday not to explain it, but by way of illustration — the ancient Indian Yoga system. Man entered deeply into a living inner experience of the breathing process, trying to make it conscious. In doing so there dawned upon him this relation between the rhythm that goes on in man — breathed, as it were, into man in a concentrated and contracted form — and the phenomena of the great Universe. Therefore he spoke of his own in- and out-breathing and of the mighty in- and out-breathing of Brahma, a single breath spanning an entire year, for which 25, 920 years are a day — a day of the Great Spirit. I do not wish to make an unkind remark, my dear friends, but we do here begin to get some notion of the great distance which men at one time felt between themselves and the Spirit of the Macrocosm whom they revered. Man felt himself about as far beneath the Spirit of the Macrocosm as a day is beneath 25,920 years. It was indeed a great Spirit — a very great Spirit — whom man conceived in this way and whose relation to himself he experienced with due modesty. It would not be uninteresting to compare how great is the distance often felt by modern man between himself and his God. Does he not often conceive the Deity as little more than a slightly idealized human being? This may not seem very relevant to our subject, but in fact it is. If we want to develop real means of knowledge in this sphere, we must find our way from what is merely calculable into quite other realms. Indeed our study of Kepler's Laws and all that followed from them showed how our very calculations, leading as they do to incommensurable numbers, impel us of their own accord into a realm beyond mere calculation.

Astronomy as Compared to Other Sciences

Lecture VI

https://rsarchive.org/Lectures/GA323/English/LR81/19210106v01.html

Stuttgart

6 Jan 1921

GA323-6

You will have seen how we are trying in these lectures to prepare the ground for an adequate World-picture. As I have pointed out again and again, the astronomical phenomena themselves impel us to advance from the merely quantitative to the qualitative aspect. Under the influence of Natural Science there is a tendency, in modern scholarship altogether, to neglect the qualitative side and to translate what is really qualitative into quantitative terms, or at least into rigid forms. For when we study things from a formal aspect we tend to pass quite involuntarily into rigid forms, even if we went to keep them mobile. But the question is, whether an adequate understanding of the phenomena of the Universe is possible at all in terms of rigid, formal concepts. We cannot build an astronomical World-picture until this question has been answered. This proneness to the quantitative, abstracting from the qualitative aspect, has led to a downright mania for abstraction which is doing no little harm in scientific life, for it leads right away from reality. People will calculate for instance under what conditions, if two sound-waves are emitted one after the other, the sound omitted later will be heard before the other. All that is necessary is the trifling detail that we ourselves should be moving with a velocity greater than that of sound. But anyone who thinks in keeping with real life instead of letting his thoughts and concepts run away from the reality, will, when he finds them incompatible with the conditions of man's co-existence with his environment, stop forming concepts in this direction. He cannot but do so. There is no sense whatever in formulating concepts for situations in which one can never be. To be a spiritual scientist one must educate oneself to look at things in this way. The spiritual scientist will always want his concepts to be united with reality. He does not want to form concepts remote from reality, going off at a tangent, — or at least not for long. He brings them back to reality again and again. The harm that is done by the wrong kinds of hypothesis in modern time is due above all to the deficient feeling for the reality in which one lives. A conception of the world free of hypotheses, for which we strive and ought to strive, would be achieved far more quickly if we could only permeate ourselves with this sense of reality. And we should then be prepared, really to see what the phenomenal world presents. In point of fact this is not done today. If the phenomena were looked at without prejudice, quite another world-picture would arise than the world-pictures of contemporary science, from which far-fetched conclusions are deduced to no real purpose, piling one unreality upon another in merely hypothetical thought-structures. Starting from this and from what was given yesterday, I must again introduce certain concepts which may not seem at first to be connected with our subject, though in the further course you will see that they too are necessary for the building of a true World-picture. I shall again refer to what was said yesterday in connection with the Ice-ages and with the evolution of the Earth altogether. To begin with however, we will take our start from another direction. Our life of knowledge is made up of the sense-impressions we receive and of what comes into being when we assimilate the sense-impressions in our inner mental life. Rightly and naturally, we distinguish in our cognitional life the sense-perceptions as such and the inner life of ‘ideas’ — mental pictures. To approach the reality of this domain we must being by forming these two concepts: That of the sense-perception pure and simple, and of the sense-perception transformed and assimilated into a mental picture. It is important to see without prejudice, what is the real difference between our cognitional life insofar as this is permeated with actual sense-perceptions and insofar as it consists of mere mental picture. We need to see these things not merely side by side in an indifferent way; we need to recognize the subtle differences of quality and intensity with which they come into our inner life. If we compare the realm of our sense-perceptions — the way in which we experience them — with our dream-life, we shall of course observe an essential qualitative difference between the two. But it is not the same as regards our inner life of ideas and mental pictures. I am referring now, not to their content but to their inner quality. Concerning this, the content — permeated as it is with reminiscences of sense-perceptions — easily deludes us. Leaving aside the actual content and looking only at its inner quality and character — the whole way we experience it, — there is no qualitative difference between our inner life in ideas and mental pictures and our life of dreams. Think of our waking life by day, or all that is present in the field of our consciousness in that we open our senses to the outer world and are thereby active in our inner life, forming mental pictures and ideas. In all this forming of mental pictures we have precisely the same kind of inner activity as in our dream-life; the only thing that is added to it is the content determined by sense-perception. This also helps us realize that man's life of ideation — his forming of mental pictures — is a more inward process than sense-perception. Even the structure of our sense-organs — the way they are built into the body — shows it. The processes in which we live by virtue of these organs are not a little detached from the rest of the bodily organic life. As a pure matter of fact, it is far truer to describe the life of our senses as a gulf-like penetration of the outer world into our body (Fig. 1) than as something primarily contained within the latter. Once more, it is truer to the facts to say that through the eye, for instance, we experience a gulf-like entry of the outer world. The relative detachment of the sense-organs enables us consciously to share in the domain of the outer world. Our most characteristic organs of sense are precisely the part of us which is least closely bound to the inner life and organization of the body. Our inner life of ideation on the other hand — our forming of mental pictures — is very closely bound to it. Ideation therefore is quite another element in our cognitional life than sense-perception as such. (Remember always that I am thinking of these processes such as they are at the present stage in human evolution.) Now think again of what I spoke of yesterday — the evolution of the life of knowledge from one Ice-Age to another. Looking back in time, you will observe that the whole interplay of sense-perceptions with the inner life of ideation — the forming of mental pictures — has undergone a change since the last Ice-Age. If you perceive the very essence of that metamorphosis in the life of knowledge which I was describing yesterday, then you will realize that in the times immediately after the decline of the Ice-Age the human life of cognition took its start from quite another quality of experience than we have today. To describe it more definitely; whilst our cognitional life has become more permeated and determined by the senses and all that we receive from them, what we do not receive from the senses — what we received long, long ago through quite another way of living with the outer world — has faded out and vanished, ever more as time went on. This other quality — this other way of living with the world — belongs however to this day to our ideas and mental pictures. In quality they are like dreams. Fro in our dreams we have a feeling of being given up to, surrendered to the world around us. We have the same kind of experience in our mental pictures. While forming mental pictures we do not really differentiate between ourselves and the world that then surrounds us; we are quite given up to the latter. Only in the act of sense-perception do we separate ourselves from the surrounding world. Now this is just what happened to the whole character of man's cognitional life since the last Ice-Age. Self-consciousness was kindled. Again and again the feeling of the “I” lit up, and this became ever more so. What do we come to therefore, as we go back in evolution beyond the last Ice-Age? (We are not making hypotheses; we are observing what really happened.) We come to a human life of soul, not only more dream-like than that of today, but akin to our present life of ideation rather than to our life in actual sense-perception. Now ideation — once again, the forming of mental pictures — is more closely bound to the bodily nature than is the life of the senses. Therefore what lives and works in this realm will find expression rather within the bodily nature than independently of the latter. Remembering what was said in the last few lectures, this will then lead you from the daily to the yearly influences of the surrounding world. The daily influences, as I showed, are those which tend to form our conscious picture of the world, whereas the yearly influences affect our bodily nature as such. Hence if we trace what has been going on in man's inner life, as we go back in time we are led from the conscious life of soul deeper and deeper into the bodily organic life. In other works; before the last Ice-Age the course of the year and the seasons had a far greater influence on man than after. Man, once again, is the reagent whereby we can discern the cosmic influences which surround the Earth. Only when this is seen can we form true ideas of the relations — including even those of movement — between the Earth and the surrounding heavenly bodies. To penetrate the phenomena of movement in the Heavens, we have to take our start from man — man, the most sensitive of instruments, if I may call him so. And to this end we need to know man; we must be able to discern what belongs to the one realm, namely the influences of the day, and to the other, the influences of the year. Those who have made a more intensive study of Anthroposophical Science may be reminded here of what I have often described from spiritual perception; the conditions of life in old Atlantis, that is before the last Ice-Age. For I was there describing from another aspect — namely from direct spiritual sight — the very same things which we are here approaching more by the light of reason, taking our start from the facts of the external world. We are led back then to a kind of interplay between the Earth and its celestial environment which gave men an inner life of ideation — mental pictures — and which was afterwards transmuted in such a way as to give rise to the life of sense-perception in its present form. (The life of the senses as such is of course a much wider concept; we are here referring to the form it takes in present time.) But we must make a yet more subtle distinction. It is true that self-consciousness or Ego-consciousness, such as we have it in our ordinary life today, is only kindled in us in the moment of awakening. Self-consciousness trikes in upon us the moment we awaken. It is our relation to the outer world — that relation to it, into which we enter by the use of our senses — to which we owe our self-consciousness. But if we really analyze what it is that thus strikes in upon us, we shall perceive the following. If our inner life in mental pictures retained its dream-like quality and only the life of the senses were added to it, something would still be lacking. Our concepts would remain like the concepts of fantasy or fancy (I do not say identical with these, but like them). We should not get the sharply outlined concepts which we need for outer life. Simultaneously therefore with the life of the senses, something flows into us from the outer world which gives sharp outlines and contours to the mental pictures of our every-day cognitional life. This too is given to us by the outer world. Were it not for this, the mere interplay of sensory effects with the forming of ideas and mental pictures would bring about in us a life of fantasy or fancy and nothing more; we should never achieve the sharp precision of every-day waking life. Now let us look at the different phenomena quite simply in Goethe's way, or — as has since been said, rather more abstractly — in Kizchhoff's way. Before doing so I must however make another incidental remark, Scientists nowadays speak of a “physiology of the senses”, and even try to build on this foundation a “psychology of the senses”, of which there are different schools. But if you see things as they are, you will find little reality under these headings. In effect, our senses are so radically different from one-another that a “Physiology of the senses”, claiming to treat them all together, can at more be highly abstract. All that emerges, in the last resort, is a rather scanty and even then very questionable physiology and psychology of the sense of touch, which is transferred by analogy to the other senses. If you look for what is real, you will require a distinct physiology and a distinct psychology for every one of the senses. Provided we remember this, we may proceed. With all the necessary qualifications, we can then say the following. Look at the human eye. (I cannot now repeat the elementary details which you can find in any scientific text-book.) Look at the human eye, one of the organs giving us impressions of the outer world, — sense-impressions and also what gives them form and contour. These impressions, received through the eye, are — once again — connected with all the mental pictures which we then make of them in our inner life. Let us now make the clear distinction, so as to perceive what underlies the sharp outline and configuration which makes our mental images more than mere pictures of fancy, giving them clear and precise outline. We will distinguish this from the whole realm of imagery where this clarity and sharpness is not to be found, — where in effect we should be living in fantasies. Even through what we experience with the help of our sense-organs — and what our inner faculty of ideation makes of it — we should still be floating in a realm of fancies. It is through the outer world that all this imagery receives clear outline, finished contours. It is through something from the outer world, which in a certain way comes into a definite relation to our eye. And now look around. Transfer, what we have thus recognized as regards the human eye, to the human being as a whole. Look for it, simply and empirically, in the human being as a whole. Where do we find — though in a metamorphosed form — what makes a similar impression? We find it in the process of fertilization . The relation of the human being as a whole — the female human body — to the environment is, in a metamorphosed form, the same as the relation of the eye to the environment. To one who is ready to enter into these things it will be fully clear. Only translated, one might say, into the material domain, the female life is the life of fantasy or fancy of the Universe, whereas the male is that which forms the contours and sharp outlines. It is the male which transforms the undetermined life of fancy into a life of determined form and outline. Seen in the way we have described in today's lecture, the process of sight is none other than a direct metamorphosis of that of fertilization; and vice-versa. We cannot reach workable ideas about the Universe without entering into such things as these. I am only sorry that I can do no more than indicate them, but after all, these lectures are meant as a stimulus to further work. This I conceive to be the purpose of such lectures; as an outcome, every one of you should be able to go on working in one or other of the directions indicated. I only want to show the directions; they can be followed up in diverse ways. There are indeed countless possibilities in our time, to carry scientific methods of research into new directions. Only we need to lay more stress on the qualitative aspects, even in those domains where one has grown accustomed to a mere quantitative treatment. What do we do, in quantitative treatment? Mathematics is the obvious example; ‘Phoronomy’ (Kinematics) is another. We ourselves first develop such a science, and we then look to find its truths in the external, empirical reality. But in approaching the empirical reality in its completeness we need more than this. We need a richer content to approach it with, than merely mathematical and phoronomical ideas. Approach the world with the premises of Phoronomy and Mathematics, and we shall naturally find starry worlds, or developmental mechanisms as the case may be, phoronomically and mathematically ordered. We shall find other contents in the world if once we take our start from other realms than the mathematical and phoronomical. Even in experimental research we shall do so. The clear differentiation between the life of the senses and the organic life of the human being as a whole had not yet taken place in the time preceding the last Ice-Age. The human being still enjoyed a more synthetic, more ‘single’ organic life. Since the last Ice-Age man's organic life has undergone, as one might say, a very real ‘analysis’. This too is an indication that the relation of the Earth to the Sun was different before the last Ice-Age from what it afterwards became. This is the kind of premise from which we have to take our start, so as to reach genuine pictures and ideas about the Universe in its relation to the Earth and man. Moreover our attention is here drawn to another question, my dear Friends. To what extent is ‘Euclidean space’ — the name, of course, does not matter — I mean the space which is characterized by three rigid directions at right angles to each other. This, surely, is a rough and ready definition of Euclidean space. I might also call it ‘Kantian space’, for Kant's arguments are based on this assumption. Now as regards this Euclidean — or, if you will, Kantian — space we have to put the question: Does it correspond to a reality, or is it only a thought-picture, an abstraction? After all, it might well be that there is really no such thing as this rigid space. Now you will have to admit; when we do analytical geometry we start with the assumption that the X-, Y- and Z-axes may be taken in this immobile way. We assume that this inner rigidity of the X, Y and Z has something to do with the real world. What if there were nothing after all, in the realms of reality, to justify our setting up the three coordinate axes of analytical geometry in this rigid way? Then too the whole of our Euclidean Mathematics would be at most a kind of approximation to the reality — an approximation which we ourselves develop in our inner life, — convenient framework with which to approach it in the first place. It would not hold out any promise, when applied to the real world, to give us real information. The question now is, are there any indications pointing in this direction, — suggesting, in effect, that this rigidity of space can not, after all, be maintained? I know, what I am here approaching will cause great difficulty to many people of today, for the simple reason that they do not keep step with reality in their thinking. They think you can rely upon an endless chain of concepts, deducing one thing logically from another, drawing logical and mathematical conclusions without limit. In contrast to this tendency in science nowadays, we have to learn to think with the reality, — not to permit ourselves merely to entertain a thought-picture without at least looking to see whether or not it is in accord with reality. So in this instance, we should investigate. Perhaps after all, by looking into the world of concrete things, there is some way of reaching a more qualitative determination of space. I am aware, my dear Friends, that the ideas I shall now set forth will meet with great resistance. Yet it is necessary to draw attention to such things. The theory of evolution has entered ever more into the different fields of science. They even began applying it to Astronomy. (This phase, perhaps, is over now, but it was so a little while ago.) They began to speak of a kind of natural selection. Then as the radical Darwinians would do for living organisms, so they began to attribute the genesis of heavenly bodies to a kind of natural selection, as though the eventual form of our solar system had arisen by selection from among all the bodies that had first been ejected. Even this theory was once put forward. There is this p to the whole Universe the leading ideas that have once been gaining some particular domain of science. So too it came about that man was simply placed at the latter end of the evolutionary series of the animal kingdom. Human morphology, physiology etc. were thus interpreted. But the question is whether this kind of investigation can do justice to man's organization in its totality. For, to begin with, it omits what is most striking and essential even from a purely empirical point of view. One saw the evolutionists of Haechel's school simply counting how many bones, muscles and so on man and the higher animals respectively possess. Counting in that way, one can hardly do otherwise than put man at the end of the animal kingdom. Yet it is quite another matter when you envisage what is evident for all eyes to see, namely that the spine of man is vertical while that of the animal is mainly horizontal. Approximate though this may be, it is definite and evident. The deviations in certain animals — looked into empirically — will prove to be of definite significance in each single case. Where the direction of the spine is turned towards the vertical, corresponding changes are called forth in the animal as a whole. But the essential thing is to observe this very characteristic difference between man and animal. The human spine follows the vertical direction of the radius of the Earth, whereas the animal spine is parallel to the Earth's surface. Here you have purely spatial phenomena with a quite evident inner differentiation, inasmuch as they apply to the whole figure and formation of the animal and man. Taking our start from the realities of the world, we cannot treat the horizontal in the same way as the vertical. Enter into the reality of space — see what is happening in space, such as it really is, — you cannot possibly regard the horizontal as though it were equivalent or interchangeable with the vertical dimension. Now there is a further consequence of this. Look at the animal form and at the form of man. We will take our start from the animal, and please fill in for yourselves on some convenient occasion what I shall now be indicating. I mean, observe and contemplate for yourselves the skeleton of an mammal. The usual reflections in this realm are not nearly concrete enough; they do not enter thoroughly enough into the details. Consider then the skeleton of an animal. I will go no farther than the skeleton, but what I say of this is true in an even higher degree of the other parts and systems in the human and animal body. Look at the obvious differentiation, comparing the skull with the opposite end of the animal. If you do this with morphological insight, you will perceive characteristic harmonies or agreements, and also characteristic diversities. Here is a line of research which should be followed in far greater detail. Here is something to be seen and recognized, which will lead far more deeply into realty than scientists today are wont to go. It lies in the very nature of these lectures that I can only hint at such things, leaving out many an intervening link. I must appeal to your own intuition, trusting you to think it out and fill in what is missing between one lecture and the next. You will then see how all these things are connected. If I did otherwise in these few lectures, we should not reach the desired end. Diagrammatically now (Fig. 2), let this be the animal form. If after going into an untold number of intervening links in the investigation, you put the question: ‘What is the characteristic difference of the front and the back, the head and the tail end due to?’, you will reach a very interesting conclusion. Namely you will connect the differentiation of the front end with the influences of the Sun. Here is the Earth (Fig. 3). You have an animal on the side of the Earth exposed to the Sun. Now take the side of the Earth that is turned away from the Sun. In one way or another it will come about that the animal is on this other side. Here too the Sun's rays will be influencing the animal, but the earth is now between. In the one case the rays of the Sun are working on the animal directly; in the other case indirectly, inasmuch as the Earth is between and the Sun's rays first have to pass through the Earth (Fig. 3). Expose the animal form to the direct influence of the Sun and you get the head. Expose the animal to those rays of the Sun which have first gone through the Earth and you get the opposite pole to the head. Study the skull, so as to recognize in it the direct outcome of the influences of the Sun. Study the forms, the whole morphology of the opposite pole, so as to recognize the working of the Sun's rays before which the Earth is interposed — the indirect rays of the Sun. Thus the morphology of the animal itself draws our attention to a certain interrelation between Earth and Sun. For a true knowledge of the mutual relations of Earth and Sun we must create the requisite conditions, not by the mere visual appearance (even though the eye be armed with telescopes), but by perceiving also how the animal is formed — how the whole animal form comes into being. Now think again of how the human spine is displaced through right angle in relation to the animal. All the effects which we have been describing will undergo further modification where man is concerned. The influences of the Sun will therefore be different in man than in the animal. The way it works in man will be like a resultant (Fig. 4). That is to say, if we symbolize the horizontal line — whether it represent the direct or the indirect influence of the Sun — by this length, we shall have to say; here is a vertical line; this also will be acting. And we shall only get what really works in man by forming the resultant of the two. Suppose in other words that we are led to relate animal formation quite fundamentally to some form of cosmic movement — say, a rotation of the Sun about the Earth, or a rotation of the Earth about its own axis. If then this movement underlies animal formation, we shall be led inevitably to attribute to the Earth or to the Sun yet another movement, related to the forming of man himself, — a movement which, for its ultimate effect, unites to a resultant with the first. From what emerges in man and in the animal we must derive the basis for a true recognition of the mutual movements among the heavenly bodies. The study of Astronomy will thus be lifted right out of its present limited domain, where one merely takes the outward visual appearance, even if calling in the aid of telescopes, mathematical calculations and mechanics. It will be lifted into what finds expression in this most sensitive of instruments, the living body. The forming forces working in the animal, and then again in man, are a clear indication of the real movements in celestial space. This is indeed a kind of qualitative Mathematics. How, then, shall we metamorphose the idea when we pass on from the animal to the plant? We can no longer make use of either of the two directions we have hitherto been using. Admittedly, it might appear as though the vertical direction of the plant coincided with that of the human spine. From the aspect of Euclidean space it does, no doubt (Euclidean space, that is to say, not with respect to detailed configuration but simply with respect to its rigidity.) But it will not be the same in an inherently mobile space. I mean a space, the dimensions of which are so inherently mobile that in the relevant equations, for example, we cannot merely equate the \(x\)- and the \(y\)-dimensions: \(y = ƒ(x)\). (The equation might be written very differently from this. You will see what I intend more from the words I use than from the symbols; it is by no means easy to express in mathematical form.) In a co-ordinate system answering to what I now intend, it would no longer be permissible to measure the ordinates with the same inherent measures as the abscissae. We could not keep the measures rigid when passing from the one to the other. We should be led in this way from the rigid co-ordinate system of Euclidean space to a co-ordinate system that is inherently mobile. And if we now once more ask the question: How are the vertical directions of plant growth and of human growth respectively related? — we shall be led to differentiate one vertical from another. The question is, then, how to find the way to a different idea of space from the rigid one of Euclid. For it may well be that the celestial phenomena can only be understood in terms of quite another kind of space — neither Euclidean, nor any abstractly conceived space of modern Mathematics, but a form of space derived from the reality itself. if this is so, then there is no alternative; it is in such a space and not in the rigid space of Euclid that we shall have to understand them. Thus we are led into quite other realms, namely to the Ice-Age on the one hand and on the other to a much needed reform of the Euclidean idea of space. But this reform will be in a different spirit than in the work of Minkowski and others. Simply in contemplating the given facts and trying to build up a science free of hypotheses, we are confronted with the need for a thoroughgoing revision of the concept of space itself. Of these things we shall speak again tomorrow.

Astronomy as Compared to Other Sciences

Lecture VII

https://rsarchive.org/Lectures/GA323/English/LR81/19210107p01.html

Stuttgart

7 Jan 1921

GA323-7

To lead our present studies to a fruitful conclusion we must still pursue the rather subtle course I have been adopting, bringing together a great variety of ideas from different fields. For this reason we shall have to continue with this course also while the other course 1 Examples of the relation of Spiritual Science to the different branches of Science. Four lectures to students, Stuttgart, 11th to 15th January, 1921. Published (in the original German) in the Swiss periodical “Gegenwart”, Vol. 14, nos. 2 to 8, Berne, 1952. is going on — between the 11th and 15th January. We must arrange the times by agreement with the Waldorf School. There is so much to bring in that we shall need these days too. Now I am also well aware how many queries, doubts and problems may be arising in connection with this subject. Please prepare whatever questions you would like to put, if you need further elucidation. I will then try to incorporate the answers in one of next week's lectures, so as to make the picture more complete. Working in this way we shall be able to continue as heretofore, bringing in what I would call the subtler aspects of our theme. Let us envisage once again the course we have been pursuing. Our aim is to gain a deeper understanding of Astronomy — the science of the Heavens — in connection with phenomena on Earth. To begin with, we pointed out that as a rule the Astronomy of our time only takes into account what is observed directly with the outer senses aided, no doubt, by optical instruments and the like. Such, in the main, were all the data hitherto adduced when seeking to explain and understand the phenomena of the Heavens. They took their start from the ‘apparent movements’, as they would now be called, or the celestial bodies. First they considered the apparent movement of the starry Heavens as a whole around the Earth and the apparent movement of the Sun. Then they observed the very strange paths described by the Planets. Such, in effect, is the immediate visual appearance; portions of the planetary paths look like loops (Fig. 1) the planet moves along here, reverses and goes back, and then forward again, here ... And now they reasoned; if the Earth itself is moving and we have no direct perception of this movement, the real movements of the heavenly bodies cannot but be different from the visual appearance. Interpreting along these lines — applying mathematical and geometrical laws — they arrived at an idea of what the ‘real’ movements might be like. So they arrived at the Copernican system and at its subsequent modifications. Such, in the main, were the methods of cognition used; first, what our senses when looking out into the Heavens, and then the intellectual assimilation, the reasoned interpretation of these sense-impression. We then pointed out that this procedure can never lead to the adequate penetration of the celestial phenomena, if only for the reason that the mathematical method itself is insufficient. We begin our calculations along certain lines and are then brought to a stop. For as I was reminding you, the ratios between the periods of revolution of the several planets are incommensurable numbers, — incommensurable magnitudes. By calculation therefore, we do not reach the innermost structure of the celestial phenomena. Sooner or later we have to leave off. It follows that we must adopt a different method. We have to take our start not only from what man observes when he looks out into the Universe with his senses; we must take man as a whole in his connection with the Universe, and perhaps not only man, but other creatures too, — the kingdoms of Nature upon Earth. All these things we pointed out, and I then showed how the whole organization of man can be seen in relation to certain phenomena in the evolution of the Earth, namely the Ice-Ages in their rhythmical recurrence. They also have to do with the inner evolution of man and of mankind. This too, I said, will give us indications of what the real movements in celestial space may be. These are the kind of things we must pursue. Before continuing the rather more formal lines of thought with which we ended yesterday's lecture, let us consider once again this connection of man's evolution with the evolution of the Earth through the Ice-Ages. We saw that the special kind of knowledge or of cognitional life which the man of present time calls his own has only come into being since the last Ice-Age. Moreover all the civilization-epochs, of which I have so often told, have taken place since then — namely the Ancient Indian, the Persian, the Egypto — Chaldean, the Graeco-Latin and then the epoch in which we are now living. Before the last Ice-Age, we said, there must have been developing in human nature what in the man of today is more withdrawn, less at the surface of his nature, namely his power of ideation — the forming of mental pictures. The inner quality, we said, of this part of our inner life is truly to be understood only if we compare it with our dream-life. It is through sense-perception that our mental pictures receive clear and firm configuration and, as it were, a fully saturated content. The mental pictures are being formed in a more inward region of our bodily organic life — farther back, as it were behind the sense-perceptions, — and this activity is dim and hazy like our dream-life. Our forming of mental pictures would be as dim as it is in dreams, if the experiences of the senses did not strike in upon us every time we awaken. (We may allow the supposition, to help explain what is meant.) More dim and hazy than our life in sense-perception, this inner life of ideation, mental imagery, is related to those earlier phases in the evolution of man's nature which preceded the last glacial epoch, or which — to speak in anthroposophical terms — belonged to old Atlantis. What must it then have been like for man? In the first place he must have had a far more intimate inner connection with the surrounding world than he has today through sense-perception. We can control our sense-perception with our will. It is with our will at any rate that we direct the vision of our eyes, and by deliberate attention we can go even farther in governing our sense-perception by our own will. At all events, our will is very much at work in our sense — perceptions, making us to a large extent independent of the outer world. We orientate ourselves by our own arbitrary choice. Now this in only possible because as human beings we have in a way emancipated ourselves from the Universe. Before the last Ice-Age we cannot have been thus emancipated. (I say ‘cannot have been’ since I am wanting now to speak from the empirical aspect of external Science.) During that time, as we have seen, the power of ideation — the forming of mental images — was especially developed, and in his inner conditions man must have been far more dependent on all that was going on around him. Today we see the world around us shining in the sunlight, but the way we see it is considerably subject to the inner culture and control of our own life of will. In Atlantean time the way man was given up to the outer world must have been somehow dependent on the illumined Earth and its illumined objects, and then again — at night-time when the Sun was not shining — on the darkness, the gloaming. He must in other words have experienced periodic alternations in this respect. His inner life of mental imagery, which as we saw was then in process of development must alternately have been lighting up and ebbing down again. This inner periodicity, brought about by man's relation to the surrounding Universe, was indeed not unlike the peculiar periodicity of woman's organic functions of which we spoke before, which is related to the Lunar phases though only as regards length of time. This inner functioning of the woman's nature (I said, you will remember, it is there in man too but in a more inward way and therefore less easily perceived) was at one time actually linked with the corresponding events in the outer Universe. It then became emancipated — a property of human nature on its own, — so that what now goes on in the human being in this respect need not coincide with the outer events. yet the periodicity — the sequence of phases — remains the same as it was when the one coincided with the other. Something quite similar is true of the rhythmic alternation in our inner life — in our ideation, our forming of mental images. The whole way we are organized in this respect, implanted in us in a far distant past, is to this day more or less independent of the life of the outer senses. Day by day we undergo an inner rhythm, our powers of mental imagery alternately lighting up and growing more dim; it is a daily ebb and flow. We only fail to notice it, since it is far less intense than that other periodicity which runs parallel to the Lunar phases. Nevertheless, in our head-organization to this day we have an alternation between a brighter and a dimmer kind of life. We carry in our head a rhythmic life. We are at one time more and at another less inclined to meet our sense-perceptions actively from within. It is a 24-hour rhythmic alteration. It would be interesting to observe — it might even be recorded in graphically — how human being vary as regards this inner period of the head, the forces of ideation and mental imagery alternating between brighter and more lively and then again dimmer and more sleepy times. The dim and sleepy times represent, so to speak, the inner night of the head, the brighter ones the inner day, but it does not coincide with the external alternation of day and night. It is an inner alternation of light and darkness, or relatively bright and dim conditions. And people vary in this respect. One human being has this inner alternation of light and dark in such a way that he tends rather to connect the lighter period of his mental image-forming power with his sense-perceptions. Another tends to it with the darker. Individuals are organized in one way or the other, and differ accordingly as to their power of observing the outer world. One human being will be inclined sharply to focus the phenomena of the outer world; another tends to do so less, — is more inclined to an inner brooding. All this is due to the alternating conditions I have been describing. Notably as educators, my dear Friends, we should cultivate the habit of observing things like this. They will be valuable signposts, indicating how we should treat the individual children both in our teaching and in education generally. What interests us however here and now is the fact that man thus makes inward, as it were, what he once underwent in direct mutual relation with the outer world; so that it now works in him as an inner rhythm, the phases no longer coinciding with the outer yet still retaining the periodicity Before the Ice-Age, man's periods of brighter and more intimate participation in the surrounding Universe,. and then of dim withdrawal into himself, will have coincided regularly with the processes of the outer world. He still retains an echo of this rhythm, which in those long-ago times proceed from his living-together with the Universe around him, where at one moment his consciousness was lightened and filled with pictures while at another he withdrew into himself, brooding over the pictures. It is an echo of this latter state whenever we today are inclined to brood more or less melancholically in our own inner life. Once again therefore, what man experienced in and with the world in those older times has been driven farther back into his inner bodily nature, while at the outer periphery a new development has taken place in his faculties of sense-perception. He had these faculties, of course in earlier epochs too, but not developed in the way they now are. While looking thus at what has taken place in man through his connection with the phenomena of the world around him, we are in fact looking into the Universe itself. Man then becomes the reagent for a true judgment of the phenomena of the Universe. But to complete this we need the other kingdoms of Nature too. Here I should like to draw your attention to something well-known and evident to everyone, the essential significance of which, however, remains unrecognized. Consider the annual plant, — the characteristic cycle of its development. We see in it quite evidently what I was mentioning yesterday — the direct and indirect influences of the Sun. Where the Sun works directly, the flower comes into being; where the Sun works in such a way that the Earth comes in between, we get the root. The plant too makes manifest what we were speaking of yesterday as regards the animal and then applied in another way to man. Yet we shall only see the full significance of this if we relate it to another fact. There are perennial plants too. What is the relation of the perennial plant to the annual, as regards the way in which plant-growth belongs to the Earth as a whole? The perennial retains its stem or trunk, and the truth is: Year by year a new world of plants springs, so to speak, from the trunk itself. Of course it is modified and metamorphosed, yet it is a vegetation growing on the trunk, which in its turn grows out of the Earth (Fig. 2). If you have morphological perception you will see it as clearly as can be, — it almost goes without saying. Here on the left I have the surface of the Earth, and the annual plant springing from it. Here on the right is the stem or trunk of the perennial, from which new vegetation, new plant-growth springs in each succeeding year. I must image something or other (to leave it vague, for the moment) continued from the Earth into the trunk. I must say to myself — what this plant here (Fig. 2 on the left) is growing on, must somehow be there in the trunk too (on the right). In other words there must be some element of the Earth — whatever it may be — entering into the trunk. I have no right to regard the trunk of the perennial as a thing apart, not belonging to the Earth; rather must I regard it as a modified portion of the Earth itself. Only then shall I be seeing it rightly; only then shall I discern the inner relationships, such as they really are. Something is there in the perennial plant, which otherwise is only in the Earth. It is through this that the plant becomes perennial. In effect, precisely by taking something of the Earth into itself it frees itself from dependence on the yearly course of the Sun. For we may truly say: The perennial wrests itself away from its dependence on the Sun's yearly course. it emancipates itself from the yearly course of the Sun, in that it forms the trunk, receiving into its own Nature — becoming able, as it were, to do for itself what otherwise could only come about through the working of the whole cosmic environment. Do we not here see prefigured in the plant world, what I was just describing with regard to man in preglacial times? For in those times, as I was showing, the inner rhythm of the man's ideation — his life in mental pictures — developed by relation to the surrounding world. What then lived in the mutual relation between man and the surrounding world has since become a feature of his own inner life. There is an indication of the same kind of change in the plant kingdom, in that the annual is changed to a perennial. This is indeed a universal tendency in evolution; the living entities are on the way to emancipation from their original connections with the surrounding world. Seeing the perennials arising, we have to say: It is as though the plant, when it becomes perennial, had learned something it you will allow the expression — learned from the time when it depended on cosmic environment, something which it can now do for itself. Now it is able of itself to bring forth fresh plant-shoots year by year. We do not reach an understanding of the phenomena of the world by merely staring at the things that happen to be side by side, or that are crowded into the field of view under the microscope. We have to see the larger whole and recognize the single phenomena in their connection with it. Look at it all once more. The annual plant is given up to the cycle of the year, with all the changing relations to the Cosmos which this involves. This influence of the Cosmos beings to fade away in the perennial. In the perennial, what would otherwise vanish in the further course of the year is, as it were, preserved. In the trunk we see springing from the ground the working of the year, made permanent and lasting. This transition of what was first connected with the outer Universe into a more inward way of working we see it throughout the whole range of Nature's phenomena, in so far as they are cosmic. Hence too there are phenomena in which we can more quickly find the living connections between our Earth and the wider Cosmos, whilst there are others in which the cosmic influences are more concealed. We need to find out which of them are sensitive reagents, telling of the cosmic influences. The annual plant will tell us of the Earth's connection with Cosmos, the perennial will not be able to tell us much. Again, the relation of the animal to man can give us an important clue. Look at the animal's development. (Though we might also include it, we will for the moment disregard the embryonic life.) The animal is born and grows up to a certain limit. It reaches puberty. Look at the animal's whole life, until puberty and beyond. Without any added hypotheses — taking the simple facts — you must admit that it is strange, what happens to the animal once puberty has been attained. For in a way the animal is finished then, so far as the earthly world is concerned. Any such statement is of course an approximation to the truth, needless to say; yet in the main we must admit that in the animal no further progression is to be seen, not after puberty. Puberty is the important goal of animal development. The immediate consequence of puberty — all that happens as an outcome of it — is there of course, but we cannot allege that anything takes place thence forward, deserving to be called a true progression. With man it is different. Man remains capable of development far beyond puberty; but the development becomes more inward. Indeed it would be very sad for man if in his human nature he were to end his development at puberty in the way animals do. Man goes beyond this. He holds something in reserve by means of which he can go farther, — can undertake quite other journeys, unconnected with sexual maturity or puberty. This again is not unlike the “inwarding” of the cycle of the year in the perennial as against the annual plant. What is in evidence in the animal when puberty is reached, we see it transmuted into a more inward process in man, from puberty onward. Something therefore is at work in man, that is related to a cosmic process in his development from birth until puberty, and that then gets emancipated from the Cosmos — just as it does in the perennial plant — when puberty has been outgrown. Here then you have a subtler way of estimating the phenomena among the kingdoms of Nature; so will you presently find signposts, indicating the connections between the creatures upon Earth and the Cosmos. We see how, when the cosmic influences cease as such, they are transplanted into the inner nature of the several creatures. We will take note of this and set it on one side for the moment; later we shall find the synthesis between this and quite another aspect. Let us now take up again what I have frequently mentioned: The incommensurable ratios between the periods of revolution of the planets of the solar system. We may ask, what would the outcome be if they were commensurable? Cumulative disturbances would arise, whereby the planetary system would be brought to a standstill. This can be proved by calculation, though it would lead too far afield to do it now. Only the incommensurability between the periods of revolution enables the planetary system, so to speak, to stay alive. In other words, the solar system contains among other things a condition even tending to a standstill. It is precisely this condition which we are calculating. When in our calculations we get to the end of our tether, there is the incommensurable — and there, withal, is the very life of the planetary system! We are in a strange predicament when calculating the planetary system. If it were such that we could fully calculate it, it would die, — nay, as I said before, would have died long ago. It lives by virtue of the face that we can not calculate it fully. What is alive in the planetary system is precisely what we cannot calculate. Now upon what do we base these calculations, from which once more, if we could pursue them to the end, we must deduce the inevitable death of the whole system? We base them on the force of gravitation — universal gravitation. Suppose we take our start from gravitation and nothing more, and think it out consistently. We get the picture of a planetary system subject to the force of gravitation. Then indeed we do arrive at commensurable ratios. But the planetary system would inevitably die. We calculate, in other words, to the extent that death prevails in the planetary system, basing our calculations on the force of gravity. In other words there must be something in the planetary system — different from gravitation — to which the incommensurability is due. The planetary orbits can be brought into accord with the force of gravity very nicely, even as to their genesis, but their periods of revolution would then have to be commensurable. Now there is something which cannot be brought into accord with the force of gravitation, and which moreover does not so tidily fit into our planetary system. I mean what reveals itself in the cometary bodies. The comets play a very strange part in the system, and they have recently been leading scientists to some unusual ideas. I leave aside the kind of explanations which often tend to arise, where anything most recently discovered is seized on to explain phenomena in other fields. In physiology for instance there was a time when they were fond of comparing the so-called sensory nerves to telegraph-wires leading in from the periphery. Through some central switch or commutator the impulse was supposed to be transmitted, leading to impulses and acts of will. From the centripetal nerves it was supposed to be switched over to the centrifugal; they compared it all to a telegraphic system. Maybe one day something quite different from telegraph-wires will be invented and by this way of thinking quite another picture will be applied to the same thing. So do the scientific fashions change. Whatever happens to have been discovered is quickly seized on as a handy way of explaining the phenomena in other fields. Much as they do in medicine! Scarcely has any new thing been found, — it is “discovered” to be a valuable remedy, though little thought is given to the inner reasons. Now that we have X-rays, X-rays are the remedy to use; we only use them because we happen to have found them. It is as though men let themselves be swept along chaotically, willy-nilly by whatever happens to turn up from time to time. So for the comets: By spectroscopic investigation and by comparison with the corresponding results for the planets, the idea arose that the phenomena might be explained electromagnetically. Such ideas will at most lead to analogies, which may no doubt have some connection with the reality, but which will certainly not satisfy us if we are looking into it more deeply. Yet as I said, leaving this aside, there was one thing which emerged quite inevitably when the phenomena of comets were studied in more detail. While for the rest of the planetary system they always speak of gravitational forces, the peculiar position of the comet's tail in relation to the Sun inevitably drove the scientists to speak of forces of repulsion from the Sun — forces, as it were of recoil. The terminology is not the main point; it will of course vary with the prevailing fashion. The point is that science was here obliged to look for something in addition to — and indeed opposite to gravity. In effect, with the comets something different enters our planetary system, — something which in its nature is in a way opposite to the inner structure of the planetary system as such. Hence it is understandable that for long ages the riddle of the comets gave rise to manifold superstitions. Men had a feeling that in the courses of the planets laws of Nature, inherently belonging to our planetary system, find expression, while with the comets something contrary comes in. Here something disparate and diverse makes its way into our planetary system. Thus they inclined to see the planetary phenomena as an embodiment of normal laws of Nature, and to regard the cometary apparitions as something contrary to these normal laws. There were times — though not the most ancient times — when comets were associated, as it were, with moral forces flying through the Universe, scourges for sinful man. Today we rightly look on that as superstition. Yet even Hegel could not quite escape associating the comets with something not quite explicable or only half explicable by ordinary means. The 19th century, of course, no longer believed the comets to appear like judges to chastise mankind. Yet in the early 19th century they had statistics purporting to connect them with good and bad vintage years. These too occur somewhat irregularly; their sequence does not seem to follow regular laws of Nature. And even Hegel did not quite escape this conclusion. He though it plausible that the appearance or non-appearance of comets should have to do with the good and bad vintage years. The standpoint of the people of today — at least, of those who share the normal scientific outlook — is that our planetary system has nothing to fear from the comets. Yet the phenomena which they evoke within this planetary system somehow have little inner connection with it. Like cosmic vagrants they seem to come from very distant regions into the near neighborhood of our Sun. Here they call forth certain phenomena, indicating forces of repulsion from the Sun. The phenomena appear, was and wane, and vanish. There was a man who still had a certain fund of wisdom where by he contemplated the Universe not only with his intellect but with the whole human being. He still had some intuitive perception of the phenomena of the Heavens. I refer to Kepler. He was the author of a strange saying about the comets — a saying which gives food for thought to anyone who is at all sensitive to Kepler; way of though and mood of soul. We spoke of his three Laws — a work of genius, when one considers the ideas and the data which were accessible in his time. Kepler arrived at his Laws out of a feeling for the inner harmony of the planetary system. For him it was no mere dry calculation; it was a feeling of harmony. He felt has three planetary Laws as a last quantitative expression of something qualitative — the harmony pervading the whole planetary system. And out of this same feeling he made a statement about the comets, the deep significance of which one feels if one is able to enter into such things at all. Kepler said: In the great Universe — even the Universe into which we look by night — there are as many comets as there are fishes in the ocean. We only see very, very few among them, while all the rest remain invisible, either because they are too small or for some other reason. Even external research has tended to confirm Kepler's saying. The comets seen were recorded even in olden time and it is possible to compare the number. Since the invention of the telescope ever so many more have been seen than before. Also when looking out into the starry Heavens under different conditions of illumination — that is to say, making provision for extreme darkness — a larger number of comets are recorded than otherwise. Even empirical research therefore comes near to what Kepler exclaimed, inspired as he was by a deep feeling for Nature. Now if one speaks at all of a connection between the Cosmos and what happens on the Earth, it surely is not right to dwell one-sidedly on the relation to our Earth of the other planets of our system and to omit the heavenly bodies which come and go as the comets do. It is especially one-sided since we must now admit that the comets give rise to phenomena indicating the presence of quite other forces — forces opposite in kind to those to which we usually attribute the coherence of our planetary system. The comets do in fact bring something opposite into our system, and if we follow it up we must admit that this too is of great significance. Something in some way opposite in nature to the force which holds it together, comes with the comets into our planetary system. In an earlier lecture-course about natural phenomena I drew attention to something of which I must here remind you. Those who were present — the course was mainly about Heat or Warmth 2 Stuttgart, 1st to 14th March 1920, generally known as the “Second Scientific Lecture-Course”. Issued (in the original German) by the Science Section of the Goetheanum, Dornach, Switzerland, 1925. — will no doubt recall it. I said that when we look at the phenomena of warmth in their relation to other phenomena of the Universe we are obliged to form a far more concrete idea of the Ether, of which the physicists generally speak in rather hypothetical terms. I said that in the formulae of Physics, wherever the force of pressure occurs as regards ponderable matter, we have to replace it by a force of suction as regards the ether. In other words, if we insert a plus sign for the intensity of a force in the realm of ponderable matter, we must give a minus sign to the corresponding intensity in the ether. I suggested that the well-known formulae should be looked through with this end in view; for one would see how remarkably, when this is done, they harmonize with the phenomena of Nature. Take for example that whole game of thought, if I may call it so, the Kinetic Theory of Gases, of of Heat itself, — the molecules impinging on each other and on the walls of the containing vessel. Take all this brutal play of mutual impact and recoil which is supposed to represent the thermal condition of gas. Instead of this phenomena will become clear and penetrable the moment we perceive that within warmth itself there are two conditions. akin to the conditions that prevail in ponderable matter ; the other must be thought of as akin to the ether . Warmth is in this respect different from Air or Light. For light, if we are calculating truly we must use the negative sign throughout. Whatever in our formulae is to represent the effects of light, must bear a negative sign. For air or gas the sign must be positive. For warmth on the other hand, the positive and negative will have to alternate. What we are wont to distinguish as conducted heat, radiant heat and so on will only then become clear and transparent. Within the realm of matter itself, these things reveal the need for a qualitative transition from the positive to the negative in characterizing the different kinds of force. And we now see, very significantly, how for the planetary system we also have to pass from the positive — that is, gravitation — to the corresponding negative, the repelling force. One more thing I will say today, if only to formulate the problem. For the moment I will carry it no further, but only put the problem; we shall have time to go into these things in later lectures. Now that we have ascertained all this about the cometary bodies, let me compare the relation between our planetary system and the comets to what is there in the ovum, the female germ-cell, in its relation to the male element, the fertilizing sperm. Try to imagine, try to visualize the two processes, as you might actually see them. There is the planetary system; it receives something new into itself, namely the effects of a comet. There is the ovum; it receives into itself the fertilizing effect of the male cell, the spermatozoid. Look at the two phenomena side by side without prejudice, as you might do in ordinary life when you see two things obviously comparable, side by side. Do you not find plenty of comparable features when you contemplate these two? I do not mean to set up any theory or hypothesis, I only want to indicate what you will see for yourselves if you once look at these things in their true connection. Taking our start from this, tomorrow we may hope to enter into more concrete and more detailed aspects.

Astronomy as Compared to Other Sciences

Lecture VIII

https://rsarchive.org/Lectures/GA323/English/LR81/19210108p01.html

Stuttgart

8 Jan 1921

GA323-8

We have now reached a point in our studies from which we must proceed with extreme caution, in order to see where there is a danger of allowing our thought to depart from reality and to see also when we are avoiding this danger, by keeping within the bounds of what is real. Last time, we suggested the comparison of two facts: The appearance within the planetary system of the cometary phenomena, and, alas within the planetary system, though perhaps not bearing quite the same relationship to it, all that we observe in the phenomena of fertilization. In order, however, to come to ideas about this which are at all justified, we must first see whether it is indeed possible to find connections between two so widely separated things, with which we are confronted in the external world of facts. In scientific method, we shall not make real progress, unless we can refer from one realm of facts to another, manifesting something of a similar nature and thus leading us on. We have seen how on the one hand we have to use the element of figure and form, the mathematical, and then how we are again and again impelled to come to terms in one way or another with the qualitative aspect, in some way to find a qualitative approach. And so today we will bring in something which arises in regard to man if one really studies this man, who is, after all, in some way an image of the heavenly phenomena, — as the many statements in these lectures may enable us to deduce. Yet we still have to establish in what way he is this image. If this is what he is, we must first of all gain a clear understanding of man himself. We must understand the picture from which we intend to take our start, — understand its inner perspective. Just as in looking at a painting one must know what a foreshortening means, and so on, in order to pass from the picture to the real spatial relationships and to relate the picture to what it represents in reality, so, if we would approach reality in the universe, interpreting it through man, we must first be clear about man. Now it is, extraordinarily difficult, as a human being, to come near to the human being with palpable ideas. Therefore, I should like today to bring before your souls what I might call “palpably impalpable” thought-pictures arising from quite simple foundations, ideas with which most of you are probably already well acquainted, but which we must nevertheless bring before our minds in a certain connection. These ideas, which seem in part to be quite easy to grasp and yet again, beyond certain limits, to elude our comprehension, will afford us a means of orientation in the striving to take hold of the outer world through ideas. It may appear somewhat forced to keep emphasizing the necessity of referring back to man's life of pictorial imagination in order to understand the phenomena of the heavens. But after all it is obvious that however carefully we may describe the heavenly phenomena, we have, to begin with, nothing more than a form of optical picture, permeated with mathematical thoughts. What Astronomy gives us has fundamentally the character of a picture . To be on the right path, we must therefore concern ourselves with the arising of the picture in man, otherwise we shall gain no true relationship to what Astronomy can say to us. And so I should like today to proceed from some quite simple mathematics and to show you how, in a different domain from that to which we were led through the ratios of the periods of revolution of the planets, there appears within Mathematics itself this element of the incomprehensible, the impalpable. We meet with it when in a certain connection we study quite familiar curves. (As I said, many of you already know what I am about to describe, I only want to elucidate the subject today from a particular aspect.) Consider the Ellipse , with its two foci \(A\) and \(B\), and you know that it is a definition of the ellipse that for any point \(M\) of the curve, the sum of its distances \((a + b)\) from the two foci remains constant. It is characteristic of the ellipse, that the sum of the distances of any one of its points from two fixed points, the two foci, remains constant (Fig. 1). Then we have a second curve, the Hyperbola (Fig. 2). You know that it has two branches. It is defined in that the difference of the distances of any point of the curve from the two foci, \((b - a)\) is a constant magnitude. In the ellipse, then, we have the curve of the constant sum, in the hyperbola, the curve of constant difference, and we must now ask: What is the curve of constant product? I have often drawn attention to this: The curve of constant product is the so-called Curve of Cassini (Fig. 3). We find it when, having two points, \(A\) and \(B\), we consider a point M in regard to its distances from \(A\) and \(B\), and establish the condition that the two distances \(AM\) and \(BM\) multiplied together should equal a constant magnitude. For the sake of simplicity in the calculation, I will call the constant magnitude \(b^2\) and the distance \(AB\), \(2a\). If we take the mid-point between \(a\) and \(b\) as the center of the axes of a co-ordinate system and calculate the ordinates for each point that fulfills these conditions, — take \(C\) as the center of the co-ordinate system and let the point whose ordinate we will call y move round so that for each point of the curve \(AM•BM = b^2\), we get the following equation. (I will only give you the result, for the simply reason that everyone can easily work out the calculation for himself; it is to be found in any mathematical text-book relating to the subject.) We find for \(y\) the value: Taking here into account that we cannot use the negative sign because we should then have an imaginary y, and considering therefore taking only the positive sign, we have: If we then draw the corresponding curve, we have a curve, rather like but not identical with an ellipse, called the curve of Cassini (Fig. 4). It is symmetrical to the left and right of the ordinate axis and about and below the abscissa axis. But now, this curve has various forms, and for us at any rate this is the important thing about it. The curve has different forms, according to whether b, as I have taken it here, is greater than a, equal to a, or less than a. The curve I have just drawn arises when b ˃ a, and furthermore when another condition is fulfilled, namely, that b is also greater than or equal to a √2. Moreover, when b ˃ a√2, there is a distinct curvature above and below, If b = a√2, then at this point above and below, the line of the curve becomes straightened,m it flattens so much that it almost becomes a straight line (Fig. 4). If, however, b ˂ a√2, then the whole course of the curve is changed and it takes on this form (Fig. 5). And if b = a, the curve passes over into a quite special form, it changes into this form (Fig. 6). It runs back into itself, cuts through itself and comes out on the other side, and we obtain the special form of the Lemniscate . The lemniscate, then, is a special form of Curve of Cassini — these curves are so named after their discoverer. The particular form assumed by the curve is determined by the ratio between the constant magnitudes which appear in the equation characterizing the curve. In the equation, we have only these two constant magnitudes, b and a, and the form of the curve depends on the ratio between them. Then the third case is possible, that b ˂ a. If b ˂ a, we can still find values for the curve. We can always solve the equation and obtain values for the curve, ordinates and abscissae, even when b is smaller than a, only the curve then undergoes yet another metamorphosis. For when b ˂ a, we find two branches of the curve, which look something like this (Fig. 7). We have a discontinuous curve. And here we come to the point where the mathematics itself confronts us with what I called the “palpably impalpable”, something that is difficult to grasp in space. For in the sense of the mathematical equation, this is not two curves, but one; it is a single curve in exactly the same way as all these are single curves (Figs. 3 through 5). In this one (the lemniscate) there is already a transition. The point which describes the curve takes this path, goes round underneath, cuts its previous path here and continues on here (Fig. 7). Here, we must picture the following: If we let the point M move along this line, it does not simply cross over from one side to the other, — it does not do this. It runs along the path just as in the other curves, describes a curve here, but then manages to turn up again here (Fig. 7) You see, that which carries the point along the line disappears here in the middle. If you want to understand the curve you can only imagine that it disappears in the middle. If you try to form a continuous mental picture of this curve, what must you do? It is quite easy, is it not, to imagine curves such as thes. (I only say this in parenthesis for the ordinary philistine!) You can go on imagining points along the curve and you do not find that the picture breaks off. Here (in the lemniscate) admittedly, you have to modify the comfortable way of simply going round and round, but still it goes on continuously. You can keep hold of the mental picture. But now, when you come to this curve (Fig. 7), which is not so commonplace, and you want to image it, then, in order to keep the continuity of the idea you will have to say: Space no longer gives me a point of support. In crossing over to the other branch in my imagination, unless I break the continuity and regard the one branch as independent of the other, I must go out of space; I cannot remain in space. So you see, Mathematics itself provides us with facts which oblige us to go out of space, if we would preserve the continuity of the idea . The reality itself demands of us that in our ideas we go out of space. Even in Mathematics therefore we are confronted with something which shows us that in some way we must leave space behind, if the pure idea is to follow its right path. Having ourselves and going the idea is beginning to think the process through, we must go on thinking in such a way that space is no longer of any help to us. If this were not so, we should not be able to calculate all possibilities in the equation. In pursuing similar line of thought, we meet with other instances of this kind. I will only draw your attention to the next step, which ensures if one things as follows. The ellipse is the locus of the constant sum, — it is defined by the fact that is is the curve of constant sum. The hyperbola is the curve of constant difference. The curve of Cassini in its various forms is the curve of constant product. There must then be a curve of constant quotient also, if we have here A, here B, here a point M, and then a constant quotient to be formed through the division of BM by AM. We must be able to find different points, M 1, M 2, etc., for which etc. are equal to one another and always equal to a constant number. This curve is, in fact, the Circle . If we look for the points M1, M2 etc. we find a circle which has this particular relationship to thee points A and B (Fig. 8). So that we can say: Besides the usual, simple definition of a circle, — namely, that it is the locus of a point whose distance from a fixed point remains constant, — there is another definition. The circle is that curve, very point of which fulfills the condition that its distances from two fixed points maintain a constant quotient. Now, in considering the circle in this way there is something else to be observed. For you see, if we express this (it could of course be expressed in some other way), we always obtain corresponding values in the equation, and we can find the circle. In doing this we find different forms of the circle (that is, different proportions between the radius of the circle and the length of the straight line AB), according to the proportion of m to n. These different forms of the circle behave in such a way that their curvature becomes less and less. When \(n\) is much greater than m, we find a circle with a very strong curvature; when n is not so much greater, the curvature is less. The circle becomes larger and larger the smaller the difference between n and m. And if we follow this proportion of m to n still further, the circle gradually passes over into a straight line. You can follow this in the equation. It passes over into the ordinate axis itself. The circle becomes the ordinate axis when \(m=n\), that is, when the quotient \(m/n=1\). In this way the circle gradually changes into the ordinate axis, into a straight line. You need not be particularly astonished at this. It is quite possible to imagine. But something very different happens it we wish to follow the process still further. The circle has flattened more and more, and through becoming flatter from within, as it were, it changes into a straight line. It does this because the constant ratio in the equation undergoes a change. Through this the circle becomes a straight line. But this constant ratio can of course grow beyond \(1\), so that the arcs of the circles appear here (on the left of the \(y\)-axis). What must we do, however, if we try to follow it in our imagination? We have to do something quite peculiar. We have, in fact, to think of a circle which is not curved towards the inside, but is curved towards the outside. Of course, I cannot draw this circle, but it is possible to think of a circle which is curved towards the outside. 1 If it were drawn it would look like an ordinary circle, only one would have to bear in mind that “outside” and “inside” had changed places. (Editor's note.) In an ordinary circle the curvature is towards the inside, it is not? If we follow the line round it returns into itself. But defining the circle in this other way, if we use the necessary constant, we obtain a straight line. The curvature is still on this side (right of the \(y\)-axis). But it now makes things not nearly so comfortable for us as before! Previously, the curvature always turned towards the center of the circle, while now (in the case of the straight line), we are shown that the center is somewhere in the infinite distance, as one says. Following on from this, there arises for us the idea of a circle which is curved towards the outside. Its curvature is then no longer as it is here (Fig. 9a) — that would be the ordinary, commonplace, philistine circle, — but its curvature is here (Fig. 9b). Therefore, the inside of this circle is not here; this is the outside; the inside of this circle (Fig. 9c) is to the right. Now compare what I have just put before you. I have described the curve of Cassini, with its various forms, the lemniscate and the form in which there are two branches. And now we have pictured the circle in such a way that at one time it is curved in the familiar way, with the inside here and the outside here; while in a second form of circle (in drawing it we are only indicating what is meant) we find that the curvature is this way round, with an inside here and an outside here. Comparing it with the Cassini curve, the first form of the circle would correspond to the closed forms, as far as the lemniscate. After this we have another kind of circle, which must be thought of in the other direction, being curved this way, with the inside here and the outside here. You see, when we are concerned with the constant product we find forms of the curve of Cassini where, it is true, we are thrown out of space, yet we can still draw the other branch on the other side. The other branch is once more in space, although in order to pass from the one to the other we are thrown out of space. Here, in the case of the circle, however, the matter becomes still more difficult. In the transition from circle to straight line we are, indeed, thrown out of space, and moreover, we can no longer draw a self-contained form at all. This we are unable to do. In passing over from the curve of constant product to the curve of constant quotient, we are only just able to indicate the thought spatially. It is extraordinarily important that we concern ourselves with the creating of ideas which, as it were, will still slip into such curve-forms. I am convinced that most people who concern themselves with mathematics take note of such discontinuities, but then make the thought more comfortable by simply holding to the formula and not passing on to what should accompany the mathematical formula in true continuity of thought. I have also never seen that in the treatment of Mathematics as subject matter for education any great value is laid upon the forming of such thoughts in imagination. — I do not know, — I ask the mathematicians present, Herr Blümel, Herr Baravalle, if this is so; whether in modern University education any importance is attached to this? (Dr. Unger here mentioned the use of the cinema.) Yes, but that is a pretense. It is only possible to represent such things within empirical space by means of the cinema or in similar ways, it some sort of deception is introduced. It cannot be pictured fully in real space without the effect being achieved through some form of deception. The point is, whether there is anywhere in the sphere of reality something which obliges us to think realistically in terms of such curves. This is the question I am now asking. Before passing on, however, to describe what might perhaps correspond to these things in the realm of reality, I should like to add something which may perhaps make it easier for you to pass transition from these abstract ideas to the reality. It is the following. You can set another problem in the sphere of theoretical Astronomy, theoretical Physics. You can say: Let us suppose that here as \(A\), is a source of light, and this source of light in a illumines a point \(M\) (Fig. 10). The strength of the light shining from \(M\) is observed from \(B\). That is, with the necessary optical instruments, observation is made from \(B\) of the strength of the light shining from the point \(M\), which is illumined from \(A\). And of course, the strength of the light would vary, according to the distance between \(B\) and \(M\). But there is a path which could be described by the point \(M\), such that, being illumined from A, it always shines back to \(B\) with the same intensity. There is such a path; and we can therefore ask: What must be the locus of a point, illumined from a fixed point \(A\), such that, seen from another fixed point \(B\), its light is always of the same intensity? This curve — the curve in which such a point would have to move — is the curve of Cassini! From this you see that something which takes on a qualitative nature is set into spatial connection, fitting into a complicated curve. The quality that we must see in the beam of light — for the intensity of light is a quality — depends in this case on the element of form in the spatial relationships. I only wished to bring this forward for you to see that there is at least some way of leading over from what can be grasped in geometrical form to what is qualitative. This way is a long one, and what we will now discuss is something to which I want to draw your attention, although it would take months to present in all detail. You must be fully aware that I only intend to give you guiding lines; it is left to you to develop them further and to go into all the details which would testify to the truth of what is said. For you see, the connection which must be formed between spiritual science and empirical sciences of today demands very far-reaching and extensive work. But when lines of direction are once given, this work can to some extent be undertaken and carried forward. It is at all events possible. One must only be able in a quite definite way to penetrate into the empirical phenomena. If we now tackle the problem from quite another angle, — we have sought to some degree to understand it from the mathematical aspect, then, to anyone who is studying the human organism, there is something which cannot escape unnoticed, something which has often been brought forward in our circle, especially in the talks which accompanied the course of lectures on Medicine in Dornach in the spring of 1920. It is not to be overlooked that certain relationships exist between the organisation of the head and the rest of the human organisation , for example the metabolism. There is indeed a connection, indefinable to begin with, between what takes place in the third system of the human being — in all the organs of metabolism — and what takes place in the head. The relationship is there, but it is hard to formulate. Clearly as it emerges in various phenomena, — for example, it is obvious that certain illnesses are connected with skull or head deformities and the like, and these things can easily be traced by one who tries to follow them with biological reasoning, — it nevertheless difficult to grasp this relationship in imagination. People do not usually get beyond the point of saying that there must be some sort of connection between what takes place in the head, for instance, and in the rest of the human organism. It is a picture which is difficult to form, just because it is so very hard for people to make the transition from the quantitative aspect to the qualitative. If we are not educated through spiritual-scientific methods to find this transition, quite independently of what outer experience offers, — to extend to what is qualitative the kind of thought we use for what is quantitative, if we do not methodically train ourselves to do this, then, my dear friends, there will always be an apparent limit to our understanding of the external phenomena. Let me indicate but one way in which you can train yourselves methodologically to think the qualitative in a similar way as you think the quantitative . You are all acquainted with the phenomenon of the solar spectrum, the usual continuous spectrum. You know that we have there the transition of colour from red to violet. You know, too, that Goethe wrestled with the problem of how this spectrum is in a sense the reverse of what must arise if darkness be allowed to pass through the prism in the same way as is usually done with light. The result is a kind of inverted spectrum, and as you know Goethe arranged this experiment also. In the ordinary spectrum, the green passes over on the one side towards the violet and on the other towards the red; whereas in the spectrum obtained by Goethe in applying a strip of darkness to the prism there is peach-blossom in the middle and then again red on the one side and violet on the other (Fig. 11). The two colour bands are obtained, the centres of which are opposite to one another, qualitatively opposite, and both bands seem to stretch away as it were into infinity. But now, one can imagine that this axis, the longitudinal axis of the ordinary spectrum, is not simply a straight line, but a circle, as indeed every straight line is a circle. If this straight line is a circle, it returns into itself, and we can consider the point where the peach-blossom appears to be the same point as the one in which the violet, stretching to the right, meets the red, which stretches to the left. They meet in the infinite distance to the right and left. If we were to succeed — maybe you know that one of the first experiments to be made in our newly established physical laboratory is to be in this direction — if we were to succeed in bending the spectrum in a certain way into itself, then even those who are not willing to grasp the matter to begin with in pure thought will be able to see that we are here concerned with something real and of a qualitative nature. We come to certain limiting ideas in Mathematics, where — as in Synthetic Geometry — we are obliged to regard the straight line as a circle in a quite real though inner sense; where we are obliged to admit of the infinitely distant point of a straight line as being only one point; or to understand as bounding a plane, not some line above and then again below, but a single straight line; or to think of the boundary of infinite space, not in the nature of something spherical, but as a plane. Such ideas, however, also become, in a way, limiting ideas for sense-perceptible empirical reality, and we are made to realise it if we insist on restricting ourselves to sense-perceptible reality. This brings us to something which would otherwise always remain perpetually in the dark. I have already mentioned it. It invites us really to think-through the thought-pictures to which we come when we allow the lemniscate-form of the Cassini curve to pass over into the double-branched form, — the form with the two branches for which we must go out of space, — and them compare this with what confronts us in the empirical reality. You are indeed already doing this, my dear friends, when you apply Mathematics in one way or another to the empirical reality. You call a triangle a triangle, because you have first constructed it mathematically. You apply to the outer form what has been evolved in an inner constructive way within you. The process I have just described is only more complicated, but it is the same process when you think of the two branches of that particular form of the Cassini curve as one. Apply this thought to the correspondence between the human head and the rest of the human organism and you will have to realise that in the head there is a connection with the remaining organism of precisely such a character as is expressed by the equation which requires, not a continuous curve, but a discontinuous one. This cannot be followed anatomically; you must go out beyond what the body comprises physically, if you would find the connection of what comes to expression in the head with what comes to expression in the metabolic system. It is essential to approach the human organism with thoughts which are quite unattainable if for every element of the thought you insist on an entire correspondence within the sense-perceptible empirical realm. We must reach out to something else, beyond the sense-perceptible empirical realm, if we are to find what this relationship really is within the human being. Such a study, if one really gives oneself up to it and carried it out methodically, is extraordinarily rich in its results. The human organisation is of such a nature that it cannot be embraced by the anatomical approach alone. Just as we are driven out of space in the Cassini curve, so in the study of man we are driven out of the body, by the method of study itself . You see, it is quite possible to understand in the first place in thought, that in a study of the whole man we are driven out of the realm of what can be grasped in a physical-empirical sense. To put forward such things is no offence against scientific principles. Such ideas are far removed from the purely hypothetical fantasies which are often entertained in connection with natural phenomena, for they refer to the whole way in which man is membered into the universe. You are not looking for something which is otherwise non-existent, but rather for something which is exactly the same as what is expressed in the relationship between a man thinking mathematically and the empirical reality. It is not a question of looking for hypotheses which in the end are unjustifiable; it is a question, since the reality is obviously complicated, of looking for other cognitive relations to the inner reality, in addition to the simple relation of mathematical man to empirical reality. When once you have accepted such thoughts, you will also be led to ask whether what takes place outside the human being in other domains besides the astronomical, — for example, in those phenomena which we call the chemical and physical, — whether those same phenomena, which we regard as chemical phenomena outside of man, take the same course within man, when he is alive, as they do outside him, or whether here, too, a transition is necessary which leads in some way out of space. Now consider the important question arising out of this. Suppose we have here some kind of chemical phenomena and here the boundary leading over to the inside of the human being (Fig. 13). Supposing that this chemical phenomenon were able to call forth another, so that the human being reacted here (inside); then, if we remain in the field of the empirical, space would of course be the mediator. If, however, the continuance of this phenomenon within the human being comes about by virtue of the fact, say, that the human being is nourished by food, and the processes already taking place outside him continue inside him, then the question arises: Does the force which is at work in the chemical process remain in the same space when it taking place within man as when it is taking its course outside him? Or must we perhaps go out of space? And there you have what is analogous to the circle which changes over into a straight line. If you look for its other form, where what is usually turned outward is now turned inward, you are entirely outside of space. The question is, whether we do not need such ideas as these, thought-pictures which, while remaining continuous, go right out of space, — when we follow the course of what happens outwardly, outside of man, into the interior of the human being. The only thing to be said against such things, my dear friends, is that they certainly impose greater demands on the human capacity of understanding than the ideas with which he phenomena are approached today. They might therefore be rather awkward in University education. They are, no doubt, thoroughly awkward, for they imply that before approaching the phenomena we must awaken in ourselves what will enable us to understand them. Nothing like this exists in our educational system today; but it must come, it must certainly come, otherwise simply in speaking of a phenomenon we get into the greatest disparities, without in any way seeing the reality. Just think what happens when someone observes the circle as it curves to this side (Fig. 9a), and then sees how it curves to this side (Fig. 9b), but then remains a philistine and simple does not conceive that the circle now curves towards the other side. He says: This is impossible, the circle cannot curve this way; I must put the curvature this way round, I must simply place myself on the other side. What he is speaking about seems to be one and the same thing; but he has changed his point of view. In this way today we make matters simple, in describing what is within the human being in comparison with what takes place in Nature outside him. We say: What is within man does not exist at all; I must simply place myself within man and say that the curvature is facing this way (Fig. 9c). I will then consider what is inside, without taking into account that I have reversed the curvature. I will make the interior of the human being into an outer Nature. I simply imagine outer Nature to continue through the skin into the interior. I turn myself round, because I am not willing to admit the other form of curvature, and then I theorise. That is the trick which is performed today, only in order to adhere to more comfortable motions. There is no desire to accent what is real; in order not to have to do so, we simply turn ourselves round, and — this is now a comparison — instead of looking at the human from in front, we look at Nature from behind and thus arrive in this way at all the various theories concerning man. We will continue, then, tomorrow.

Astronomy as Compared to Other Sciences

Lecture IX

https://rsarchive.org/Lectures/GA323/English/LR81/19210109p01.html

Stuttgart

9 Jan 1921

GA323-9

Taking my start yesterday from certain considerations in the realm of form, I showed how the connections should be thought of between the processes of the human metabolic system and the processes of the head, the nervous system, or whatever you wish to call it in the sense of the indications given in my book Riddles of the Soul ( Von Seelenrätseln ). It would be regarded as quite out of the question to study the movements of a magnet-needle on the Earth's surface in such a way as to try to explain these movements solely out of what can be observed within the space occupied by the needle. The movements of the magnet-needle are, as you know, brought into connection with the magnetism of the Earth. We connect the momentary direction of the needle with the direction of the Earth's magnetism, that is, with the line of direction which can be drawn between the north and south magnetic poles of the Earth. When it is a question of explaining the phenomena presented by the magnetic needle, we go out of the region of the needle itself and try to enter, with the facts that have been collected towards an explanation, into the totality which alone affords the opportunity to explain phenomena, the manifestations of which belong to this totality. This rule of method is certainly observed in regard to some phenomena, — to those, I should say, the significance of which is fairly obvious. But it is not observed when it is a question of explaining and understanding more complicated phenomena. Just as it is impossible to explain the phenomena of the magnetic needle from the needle itself, it is equally and fundamentally impossible to explain the phenomena relating to the organism from out of the organism itself, or from connections which do not belong to a totality, to a whole. And just for this reason, because there is so little inclination to reach the realm of totalities in order to find explanations, we arrive at those results put forward by the modern scientific method in which the wider connections are almost entirely left out of the picture. This method encloses the phenomena, whatever they may be, within the field of vision of the microscope; while the celestial phenomena are restricted to what is observable externally, with the help of instruments. In seeking for explanations, no attempt is made to consider the necessity of reaching out to the surrounding totality within which a phenomenon is localised. Only when we become familiar with this quite indispensable principle of method, are we in a position to bring our judgment to bear upon such things as I was describing to you yesterday. Only in this way shall we grow able to estimate how such realms of phenomena as are met within the human organism will appear, when truly recognised in the totality to which they properly belong. Remember what I described at the very beginning of this course of lectures. I drew your attention to the fact that the principle of metamorphosis as it appeared first in the work of Goethe and Oken must be modified if it is truly to be applied to man. The attempt was made — and it was made with genius on the part of Goethe — to derive the formation of the bones of the skull from that of the vertebrae. These investigations were continued by others in a way more akin to 19th-century method, and the progress of the method of investigation (I will not now decide whether it was a step forward or not) can be studied by comparing how this problem of the metamorphosis of one form of bone into another was conceived on the one hand by Goethe and Oken and on the other, for example, by the anatomist Gegenbauer. These things are only to be set on a real basis, if one knows (as I said, I have already mentioned this in the course of these lectures, but we will now link on to it again) how two types of bone in the human organism (not the animal, but the human organism), most widely separated from the point of view of their morphology, are actually related to one another. Bones far removed from one another in the aspect of their form would be a tubular or long bone — femur or humerus, for example, — and a skull-bone. To make a superficial comparison, without really entering into the inner nature of the form and bringing a whole range of phenomena into connection with it, is not enough to reveal the morphological relationship between two polar opposite bones — polar opposite, once more, in regard to their form. We only begin to perceive it if we compare the inner surface of a tubular bone with the outer surface of a skull-bone. Only thus do we get the true correspondence (Fig. 1) which we must have in order to establish the morphological relation. The inner surface of the tubular bone corresponds morphologically to the outer surface of the skull-bone. The skull-bone can be derived from the tubular bone if we picture it as being reversed, to begin with, according to the principle of the turning-inside-out of a glove. In the glove, however, when I turn the outer surface to the inside and the inner to the outside, I get a form similar to the original one. But if in the moment of turning the inside of the tubular bone to the outside, certain forces of tension come into play and mutual relationships of the forces change in such a way that the form which was inside and has now been turned outward alters the shape and distribution of its surface, then we obtain, through inversion on the principle of the turning-inside-out of a glove, the outer surface of the skull bone as derived from the inner surface of the tubular bone. From this you can conclude as follows. The inner space of the tubular bone, this compressed inner space, corresponds in regard to the human skull to the entire outer world. You must consider as related in their influence upon the human being: The outer universe, forming the outside of his head, and what works within, tending from within toward the inner surface of the tubular bone. These you must see to belong together. You must regard the world in the inside of the tubular bone as a kind of inversion of the world surrounding us outside. There, for the bones in the first place, you have the true principle of metamorphosis ! The other bones are intermediary forms; morphologically, they mediate between the two opposite extremes, which represent a complete inversion, accompanied by a change in the forces determining the surface. The idea must however be extended to the entire human organism. In one way, it comes to expression most clearly in the bones; but in all the human organs we must distinguish between two opposing factors, — that which works outward from an unknown interior, as we will call it for the moment, and that which works inward from without. The latter corresponds to all that surrounds us human beings on the planet Earth. The tubular bone and the skull-bone represent indeed a remarkable polarity. Take the tubular bone and think of this centre-line (Fig. 2). This line is in a way the place of origin of what works outward, in a direction perpendicular to the inner surface of the bone (Fig. 3). If you now think of what envelops the human skull, you have what corresponds to the central line of the tubular bone. But how must you draw the counterpart of this line? You must draw it somewhere as a circle, or more exactly, as a spherical surface, far way at some indeterminate distance (Fig. 4). All the lines which can be drawn from the centre-line of the tubular bone towards it inner surface (Fig. 3). correspond, in regard to the skull-bone, to all the lines which can be drawn from a spherical surface as though to meet in the centre of the Earth (Fig. 4). In this way you find a connection — approximate, needless to say — between a straight line, or a system of straight lines, passing through a tubular bone and bearing a certain relation to the vertical axis of the body, the direction of which coincides, in fact, with that of the Earth's radius and a sphere surrounding the Earth at an indeterminate distance. In other words, the connection is as follows. The radius of the Earth has the same cosmic value in regard to the vertical posture of the human organism, perpendicular to the surface of the Earth, as a spherical surface, a cosmic spherical surface has in regard to the skull organisation. This, however, is the same contrast which you experience within yourself if you make yourself aware of the feeling of being inside your own organism and experiencing of the outer world at the same time. This is the polarity you reach if you compare your feeling of self — that feeling of self which is really based on the fact that in normal life you can depend upon your bodily organisation, that you do not become giddy, but keeping a right relation to the force of gravity — with all that is present in your consciousness in connection with what you see around you through the senses, even as far away as the stars. Putting all this together, you will be able to say: There is the same relation between this feeling of being in yourself and the feeling of consciousness you have in perceiving the outer world as there is between the structure of your body and of your skull. We are thus led to the relationship between what we might call: Earthly influence upon man , of such a character that it works in the direction of the Earth's radius , and what we might call: The influence which makes itself felt in the entire circumference of our life of consciousness , and which we must look for in the sphere , in what really is for us the inner wall, the inner surface, of a hollow sphere. This polarity prevails in our normal day-waking conscious life. It is this polarity which, roughly speaking — if we leave out of account what is in our consciousness as a result of observating our earthly environment — we may look upon as the contrast between the starry sphere and earthly consciousness, earthly feeling of ourselves, — Earth-impulse living in us. If we compare this impulse of Earth, this radial Earth-impulse, to our consciousness of the vast sphere, — if we observe how this polarity, prevails in normal waking consciousness, we shall perceive that it is always there, living in us, playing its part in our conscious life. We live far more in this polarity than we are wont to think. It is always present and we live within it. The connection between the forming of mental images and the life of will can be really studied in no other way than by considering the contrast between ‘sphere’ and ‘radius’. In psychology, too, we should come to truer results with regard to the connection of our world of ideas and mental pictures, manifold and extensive as it is, with the more unified world of our will, if a similar relationship were sought between them as is symbolised in the relation of the surface-area of a sphere with the corresponding radius. Now, my dear friends, let us look at all this which is at work in our day-waking consciousness, forming the content of our soul-life, let us now consider how it takes its course when we are in quite a different situation. In effect, how does it work upon us during the time of the embryonic life? We can well imagine, indeed we must imagine that the same polarity will be at work here too, only in another way. During the embryonic period, we do not direct towards the outer world the same activity which afterwards dims down this polarity to a pictorial one; at this time, the polarity affects all that is formative in our organisation, in a much more real way than when, in picture form, it becomes active in our life of mind and soul. If therefore we project the activity of consciousness back in time to the embryonic period, then one might say that in the embryonic life we have what we otherwise have in the activity of consciousness, but we have it at a more intensive, more realistic stage. Just as we clearly see the relation of sphere and radius in our consciousness, so to reach any real result, we must look for this same polarity of heavenly sphere and earthly activity in what happens in the embryonic life. In other words, we must look for the genesis of human embryonic life by finding a resultant between what takes place out in the starry world — an activity in the ‘sphere’ — and what takes place in man as a result of the radial Earth-activity. What I have just described must be taken into account with the same inner necessity of method as the Earth's magnetism is in connection with the magnetic needle. There may be much that is hypothetical even in this, but I will not go into it now. I only wish to point out: We have no right to restrict our considerations to the embryo alone, — to explain the processes taking place within it simply out of the embryo itself. In just the same way as we have no right too explain the phenomenon of the magnet out of itself alone, so too, we have no right to explain the form and development of the embryo purely on the basis of the embryo itself. In attempting to explain the embryo we must take these two opposites into account. As we take the Earth's magnetism into account in connection with the magnet, so must we observe the polarity of sphere and radial activity, in order to understand what is developing in the embryo, — which, when the embryo is born, fades into the pictorial quality of the experience of consciousness. The point is, we must learn to see the relationship which exists in man between tubular or long bone and skull-bone in the other systems too — in muscle and nerve, and so on; — and when we do study this polarity, we are led out into the life of the Cosmos. Consider how closely related (as described in my book “Riddles of the Soul”) is the whole essence and content of the human metabolic system with what I have now characterised as being under the influence of the ‘radial’ element, and how closely related is the head system to what I have just described as being under the influence of the ‘sphere’. Then you will say: We must distinguish in the human being what conditions his sensory nature and what conditions his metabolic life; moreover, these two elements are related to one another as heavenly sphere to earthly activity. We must therefore look for the product of the celestial activity in what we bear in our head organisation and for what unites to a resultant with this, the activity belonging to the Earth — tending, as it were, towards the centre of the Earth — in our metabolism. These two realms of activity and influence fall apart in man; it is as thought they represent two Ice Ages, and the middle realm, the rhythmic realm, mediates between them. In the rhythmic system we actually have something, — if I may so express myself, — which is a realm of mutual interplay between Earth and Heaven. And now if we wish to go further, we must consider various other relationships which reveal themselves to us in the realm of reality. I will now draw your attention to something very intimately connected with what I have just been describing. There is the familiar membering of the outer world which surrounds us and to which we as physical man belong; we divide it into mineral kingdom, plant kingdom, animal kingdom, and regard man as the culmination of this external world of Nature. Now, if we would obtain a clearer view of what we have described in connection with the working of the celestial phenomena, we must turn our attention to yet another thing. It is not to be denied — it is indeed quite obvious to any prejudiced observer — that with our human organisation as it is now, in the present phase of the cosmic evolution of humanity, we are, in regard to our capacities of knowledge, entirely adapted to the mineral kingdom. Take the kind of laws we seek in Nature; and you will agree that we are certainly not adapted to all aspects of our environment. To put it curtly, all that we really understand is the mineral kingdom. Hence all the efforts to refer the other kingdoms of Nature back to the laws of the mineral domain. After all, it is because of this that such confusion has arisen with regard to mechanism and vitalism. To the ordinary view which is ours toady, life remains either a vague hypothesis, as it was in earlier times, or else its manifestations are explained in terms of the mechanical, the mineral. The ideal, to reach an understanding of life, is unaccompanied by any recognition of the fact that life must be understood as life; on the contrary, the fundamental aim is to refer life back to the laws of the mineral realm. Precisely this betrays a vague awareness of the fact that man's faculties of knowledge are only adapted to understand the mineral kingdom and not the plant nor animal. Now when we study on the one hand the mineral kingdom itself and on the other hand its counterpart, namely, our own knowledge of the mineral kingdom, in that these two correspond to one another, we shall be compelled, — since as explained just now we must relate all our life of knowledge to the heavenly sphere, also to bring into connection with the heavenly sphere, in some way, that to which our knowledge is related, namely the mineral kingdom. We must admit: In regard to our head organisation, we are organised from the celestial sphere; therefore what underlies the forces of the mineral kingdom must also be organised from the celestial sphere in some way. Compare then what you have to your sphere of understanding — the whole compass of your knowledge of the mineral kingdom — with what is actually there in the mineral kingdom in the outer world, and you will be led to say: What is thus within you relates to what is in the mineral kingdom outside you, as picture to reality. Now we must think of this relationship more concretely than in the form of picture and reality, and we are helped to do so by what I said before. Our attention is drawn to what underlies the human metabolic system and to the forces active there, forces which are connected with the pole of earthly activity, typified by the radius. In seeking for the polar opposite, within ourselves, to that part of our organisation which forms the basis for our life of knowledge, we are directed from the encompassing Sphere to the Earth. The radii converge to the middle point of the Earth. In the radial element we have something by which we feel ourselves , which gives us the feeling of being real. This is not what fills us with pictures in which we are merely conscious; this is what gives us the experience of ourselves as a reality . When we really experience this contrast, we come into the sphere of the mineral kingdom. We are led from what is organised only for the picture to what is organised for the reality. In other words: In connection with the cause and origin of our life of knowledge, we are led to the wide, encompassing sphere, — we concave it in the first place as a sphere, — whereas, in following the radii of the sphere towards the middle of the Earth, we are led to the middle point of the Earth as the other pole. Thinking this out in more detail, we might say: Well, according to the Ptolemaic conception for example, out there is the blue sphere, on it a point (Fig. 5) — we should have to think of a polar point in the centre of the Earth. Every point of the sphere would have its reflected point in the Earth's centre. But, or course, it is not to be understood like that. (I shall speak more in detail later on; to what extent these things correspond exactly is not the question for the moment.) The stars, in effect, would be here (Fig. 6). So that in thinking of the sphere concentrated in the centre of the Earth, we should have to think of it in the following way: The pole of this star is here, of this one here, and so on (Fig. 6). We come, then, to a complete mirroring of what is outside in the interior of the Earth. Picturing this in regard to each individual planet, we have, say, Jupiter and then a polar Jupiter’ within the Earth. We come to something which works outward from within the Earth in the way that Jupiter works in the Earth's environment. We arrive at a mirroring (in reality it is the opposite way round, but I will now describe it like this), a mirroring of what is outside the Earth into the interior of the Earth. And if we see the effect of this reflection in the forms of the minerals then we must also see the effect of what works in the cosmic sphere itself in forming our faculty of understanding the minerals. In other words: We can think of the whole celestial sphere as being mirrored in the Earth: We conceive the mineral kingdom of the Earth as an outcome of this reflection, and we conceive that what lives within us, enabling us to understand the mineral kingdom, comes from what surrounds us out in the celestial space . Meanwhile the realities we grasp by means of this faculty of understanding come from within the Earth. You need only follow up this idea and then cast a glance at man, at the human countenance, and, if you really look at this human countenance, you will hardly be able to doubt that in it something is expressed of the celestial sphere, and that there also appears in it what is present as pictorial experience in the soul, namely the forces which rise up into the realm of soul activity from the realm of bodily activity, after having been at work more intensively in this bodily realm during embryonic life. Thus we find a connection between what is out side us in outer reality, and our own organisation for the understanding of this outer reality. We can say: The cosmos produces the outer reality, and our power to understand this outer reality is organised physically by virtue of the fact that the cosmic sphere is only active in us now for our faculty of knowledge. Therefore we must distinguish, in the genesis of the Earth as well, between two phases: One in which active forces work in such a way that the real Earth itself is created, and then a later phase of evolution, in which the forces work so as to create the human faculty for understanding the realities of the Earth. Only in this way, my dear friends, do we really come near to an understanding of the Universe. You may say: Well and good, but this method of understanding is less secure than the method used today with the aid of microscope and telescope. It may be that to some people it appears less secure. But if things are so constituted that we cannot reach the realities with the methods in favour today, then we are faced with the absolute necessity of comprehending the reality with other modes of understanding and we shall have to get used to developing those other methods. It is of no avail to say, you will have nothing to do with such lines of thought, since they appear too uncertain. What if this degree of certainty alone were possible! However, if you really follow up this line of thought, you will see that the degree of certainty is just as great as in your conception of a real triangle in the outer world when you take hold of it in thought with the inner idea of construction of a triangle. It is the same principle, the same manner of comprehending outer reality in the one case as in the other. This should be borne in mind. Certainly, the question arises: Taking these thoughts, as I have here developed them, it is possible to become clear in a general way about such connections, but how can one reach a more definite comprehension of these things? For only in a much more definite form can they be of use in helping us to grasp the realm of reality. In order to go into this, I must draw your attention to something else. Let us return to what I aid yesterday, for example, in regard to the Cassini curve. We know that this curve has three, or, if you like, four forms. You remember, the Cassini curve is determined as follows. Given two points \(A\) and \(B\), I will call the distance between them \(2a\); then any point of the curve will be such that \(AM-MB=b2\), that is, a constant. And I obtain the various forms of the Cassini Curve according to whether \(a\), that is, half the distance between the foci, is greater than, equal to, or less than \(b\). I obtain the lemniscate when \(a=b\), and the discontinuous curve when a is greater than \(b\). Imagine now that I wanted not only to solve this geometrical problem, assuming two constant magnitudes a and b and then setting up equations to determine the distances of M from A and B. Suppose I wanted to do more than this, namely, to move in the plane from one form of line or curve to another by treating as variable magnitudes those magnitudes which remain constant for a particular curve. In the picture (Lecture IX, Fig. 3) after all, we only envisaged certain limiting positions with a greater or smaller than b. Between these there are an infinite number of possibilities. I can pass over quite continuously to the construction of one form of the Cassini curve after another. And I shall obtain these different forms if, let us say, to the variability of the first order, say between \(y\) and \(x\). I add a variability of the second order; that is, if I allow my construction of the curves as they pass over from one to the other continuously, to take its course in such a way that a remains a function of \(b\). What am I doing when I do this? I am constructing curves in such a way that I create a continuous, moving system of Cassini curves passing over via the lemniscate into the discontinuous forms, not at random, but by basing it on a variability of the second order, in that I bring the constants of the curves themselves into relationship with one another so that a is a function of \(b\), \(a=φ(b)\). Mathematically, it is of course perfectly feasible. But what do we obtain by it? Just think, by means of it I obtain the condition for the character of a surface such that there is a qualitative difference even mathematically speaking, in all its points. At every point another quality is present. I cannot comprehend the surface obtained like this in the same way as I comprehend some abstract Euclidean plane. I must look upon it as a surface which is differentiated within itself. And if by rotation I create three-dimensional forms then I should obtain bodies differentiated within themselves. If you think of what I said yesterday, namely, that the Cassini Curve is also the curve in which a point must move in space if, illuminated from a point \(B\), it reflects the light to a point \(A\) with constant intensity; and if you also bear in mind that the constancy underlying the curve here brings about a relation between the effects of light at different points; then, just as in this instance certain light-effects result from the relation of the constants, so one can also imagine that a system of light-effects would follow if a variability of the second order were added to the variability of the first. In this way you can create, even in mathematics itself, a process of transition from the quantitative to the qualitative aspect. These attempts must indeed be made in order to find a way of transition from quantity to quality, — and this endeavour we must not abandon. For a start can be made from what it is that we are really doing when we form an inner connection between the function within the variability of the second order and the function within variability of the first order. (It has nothing to do with the expression “order”, as it is familiarly used; but you will understand me, as I have explained the whole thing from the beginning.) By turning our attention to this relationship between what I have called first and second order, we shall gradually come to see that our equations must be formed differently, according to whether we are taking into account, for example, what in an ordinary bodily surface lies between the surface and our eye, or what lies behind the surface of the body. For a relationship not unlike this between the variability's of the first order and of the second order, exists between what I must consider as being between myself and the surface of a quite ordinary body and what lies behind the surface of the body. For example, suppose we are trying to understand the so-called reflection of the rays of light, — what we observe when there is a reflecting surface. It is a process taking place, to begin with, between the observer and the surface of the body. Suppose that I conceive this as a confluence of equations taking their course between me and the surface of the body in a variability of the first order, and then, in this connection consider what is at work behind the surface so as to bring about the reflection as an equation in the variability of the second order. I shall arrive at quite other formulae than are now applied according to purely mechanical laws, — omitting phases of vibration and so on — when dealing with reflection and refraction. In this way the possibility would be reached of creating a form of mathematics capable of dealing with realities; and it is essential for this to happen, if we would find explanations particularly in the realm of astronomical phenomena. In regard to the external world, we have before us what takes place between the surface of the Earth-body and ourselves. When, however, we contemplate the celestial phenomena — say, a loop of Venus — trivially speaking we also have before us something which takes place between us and some other thing; yet the reality confronting us in this case is in fact like the realm beyond the sphere in its relation to what is within the central point. However we look to the phenomena of the heavens, we must recognise that we cannot study them simply according to the laws of centric forces, but that we must regard them in the light of laws which are related to the laws of centric forces as is the sphere to the radius. If, then, we would reach an interpretation at all of the celestial phenomena, we must not arrange the calculations in such a way that they are a picture of the kind of calculations used in mechanics in the development of the laws of centric forces; but we must formulate the calculations, and also the geometrical forms involved, so that they relate to mechanics as sphere relates to radius. It will then become apparent (and we will speak about this next time) that we need: In the first place, the manner of thinking of mechanics and phoronomy, which has essentially to do with centric forces, and secondly, in addition to this system, another, which has to do with rotating movements, with shearing movements and with deforming movements. Only then, when we apply the meta-mechanical, meta-phoronomical system for the rotating, shearing and deforming movements, just as we now apply the familiar system of mechanics and phoronomy to the centric forces and centric phenomena of movement, only then shall we arrive at an explanation of the celestial phenomena, taking our start from what lies empirically before us.

Astronomy as Compared to Other Sciences

Lecture X

https://rsarchive.org/Lectures/GA323/English/LR81/19210110p01.html

Stuttgart

10 Jan 1921

GA323-10

We have now gained the most essential premises for a study of some aspects at least of celestial and also of earthly-physical phenomena. In human nature, once again, we have the very significant contrast (to ascertain which, as you will readily understand, we must leave the animal out of account to begin with) — the contrast between the organisation of the head and that of the metabolic system including the limbs. As we have seen, if we wish to relate Man to the Cosmos, we must assign the metabolic system to what is earthly, — what comes to man in a radial direction. Whereas we must assign the forming of the head to all that derives from the great Sphere, — that sends its lines of influence, as it were from the celestial Sphere towards the centre of the Earth, even as the radius reaches outward with its lines of influence to its surroundings. We saw this in the construction of the typical long bones or tubular bones by contrast to the skull-bones, the latter being sphere-like, or like a sector of a sphere. Envisaging this difference, we must relate it, to begin with, to what appears to us in the relation of the Earth to the Celestial Sphere. You are of course aware, how the scientific consciousness of our time departs from what the naive human being, untouched by any learning, would judge of the appearance of the celestial sphere, the movements of the stars upon it, and so on. We speak of the ‘Apparent aspect’ of the celestial vault. In contrast to it, as you know, we have a picture — a World-picture — gained in a fairly complicated way by interpreting the apparent movements, and so on. Upon this picture — the form of picture which has evolved through the great changes in cosmology since the Copernican era — we are wont to base all our considerations of celestial phenomena. Today I take it to be generally realised that this World-picture does not represent absolute reality. We can no longer maintain: What is presented to us by this picture, say, as the planetary movements or as the Sun's relation to the Planets, is the true form of the underlying reality, while what the eye beholds is mere appearance. I hardly think any competent person would adopt this standpoint nowadays. Yet he will still have a feeling that he at least gets nearer to a true conception when he proceeds from the apparent picture of the celestial movements — fraught, he will say with illusionary factors (yet after all, we must admit, objectively observed) — to the interpretation of it by mathematical Astronomy. The question now is, do we really gain a comprehensive view of the phenomena in question if we only base our picture of the World on this, the customary kind of interpretation. As we have seen, when we do so we are in fact only basing it on what the head-man ascertains, so to speak. We base it on the aspect which emerges for man's powers of observation, aided perhaps by optical instruments. But as we saw, for a more comprehensive interpretation of the World-picture we must have recourse to all that is knowable by man, of man. We emphasised how to this end the form of man must be seen in the light of a true science of metamorphosis. Then too we must bring in the evolution of man and of mankind. In a word, concerning the celestial phenomena, or some of them at least, we cannot look for enlightenment till in our efforts to interpret them we go as far as this, calling to our aid whatever can be known of man. Let us then presuppose what we arrived at in former lectures — the kind of qualitative mathematics, learned from the human form and growth and evolution. With this in the background let us take our start from what meets the eye — from what is said to be the mere appearance of the Heavens — asking ourselves how we may find the way to reality? Let us then ask, dear friends: What does the eye behold, what do we learn empirically, by simple observation? Then we can try to fill in the picture with what is given by the whole structure of man, both in morphology and evolution. First we will ask the question as regards those stars which are commonly described as fixed stars. I shall no doubt be repeating what is well-known to most of you, yet we must call it to mind for only by so doing, only from the facts as seen, taking them all together, shall we be able to advance to the ideas. What then do we see as to the movement of the fixed stars, so-called? We must consider longer periods of time, since in short periods the Heaven of fixed stars presents practically the same picture year by year. Only when taking longer epochs do we find that it no longer presents the same uniform picture, but that the whole configuration changes. We can envisage it by taking one example; what we shall find in one region of the Heavens would be found in other regions too. Take then this constellation, which you know so well, the “Great Bear” or “Plough” in the Northern sky. Today it looks like this (Fig. 2). Acquaint yourselves with the minute displacements of the so-called fixed stars which have been ascertained, and which agree with what is shown by very ancient star-maps, although the latter are not always reliable. Sum up the minute displacements and calculate what the constellation will have looked like very long ago, and you get this appearance (Fig. 1). You see, the fixed stars, so-called, have undergone considerable displacements. About 50,000 years ago, if we may reckon it from the minute changes observed, the constellation will have looked like this. If we continue to sum up the ascertainable displacements for the future, — assuming, as we surely may do, that they will continue at least approximately in the same direction — we may conclude that 50,000 years from now the constellation will have this appearance (Fig. 3). Just as this constellation changes in the course of years — for we have only chosen it as an example — so do the others. Thus when we make our drawings, of the Zodiac for instance in its present form, we must be clear that the form of it changes in the course of time — if we may thus include time in our calculations and in interpreting them. We must therefore regard the celestial sphere as undergoing changes within itself, ever changing its configuration, — changing the aspect of the starry Heavens which we behold in the fixed stars, — though the perpetual change is scarcely perceptible in shorter periods. Naturally, our observations here cannot go very far, nor can we do very much by way of interpretation, though as some of you will know, modern experiments enable us to ascertain even those movements of the stars which are along the line of sight, — towards us or away from us. Yet it remains very difficult to interpret the ever-changing aspect of the starry heavens. In the further course we shall be asking, what human value and significance is to seek in the interpretation. Having considered the movements of the fixed stars, let us now ask after the movements of the planetary stars. The movement of the planetary stars as we behold it is indeed complicated. The movement we observe is such that if we follow the path of a planet, in so far as it is visible, we see it moving in a curve of peculiar shape — different for the different planets and different too for the same planet at different times. From this we have to take our start. Take for example the planet Mercury. Precisely when it is nearest to us, its path is of peculiar form. In a certain direction it seems to move across the Heavens. Study it daily when visible, we see it moving thus; but them it turns and makes a loop, and then goes on as I am showing (Fig. 4). 1 In Figures 4 to 7 only one of the many varieties of loop which actually occur is shown in each case. It makes one such loop in a so-called synodical period of revolution. This then we may describe as the movement of Mercury — to begin with at least, so far as observation is concerned. The rest of the path is simple, only at certain places do the loops occur. Passing to Venus we have a similar phenomenon, though somewhat different in shape and form. Venus moves onward thus, then turns and then moves on, thus (Fig. 5). Here as a rule there is only one loop in the course of a year, and, once again, when the planet — as we conclude from other astronomical data — is nearest to us. Now to Mars: Mars has a similar path, only flatter. We may draw it somewhat like this (Fig. 6). In this case, you see, the loop is more compressed, but the appearance is still that of a loop, — distinctly so. Often however the path (both of this and other planets) is so formed that the loop is completely dissolved, flattened away until it is no more. The path is loop-like, though not an actual loop. (Fig. 7) We will pass by the planetoids, interesting though they are, and look at Jupiter and Saturn. We find them too describing loops or loop-like paths. They again do it when nearest the Earth — and only once a year. As a general rule they make a single loop each year. We have then to consider certain movements on the part of the fixed stars, and the movements of planets. The movements of fixed stars occupy gigantic periods, judged by our standards of time. The movements of the planets comprise a year or fractions of a year and reveal from time to time strange deviations from their ordinary path, loop-lines of movement, in effect. The question now is, what are we to make of these two kinds of movement? How to interpret the loop-movement for example? It is a very big question. Only the following reflection can lead towards any kind of interpretation of the loop-movements. In all our human observation the fact is that we are quite differently related to our own conditions and to those things which are not our own; — which take place apart from us, outside us, so to speak. You need only recall how it is with objects: The enormous difference between your relation to any object of the so-called outer world and to an object inside yourself, which you, so to speak, are sharing-in with your own inner experience. If you have any object before you, you see it, you observe it. What you yourself are living in — your liver, your heart, even your sense-organs to begin with you can observe. There is the same contrast, though not quite so strongly marked, with regard to the conditions in which we are living in the outer world. If we ourselves are in movement and if it is possible for us to remain unconscious of how we bring about the movement, then we may well be unaware of our own movement and therefore leave it out of account in judging outer movements. That is to say, though we ourselves are in movement, we leave this out; we deem ourselves at rest and envisage only the external movement. It is on this reflection, in the main, that the interpretation of movements amid the celestial phenomena has been based. You are aware, it has been argued: Man, at a certain point on Earth, shares of course in the spatial movement of his earthly habitation (eg the circling movement of his latitude) but knows it not and hence regards, what he sees happening in the Universe outside him, as a real movement in the opposite direction. The argument has been abundantly made use of! The question now is: How might this principle be modified if we take into account that in man's organized (if I may so express it) radially, whilst in our head-man we are oriented spherically. If it were then a fundamental feature of our own state of movement that we relate ourselves differently to the Radius and to the encompassing Sphere, this fact would somehow make itself felt in what appears to us in the outer Universe. Imagine what I have said to be in some way true. Suppose for instance that you yourself were moving thus (Fig. 8), — you were describing a Lemniscate. Let us assume however that the Lemniscate you were describing was not exactly like this, but that by variation of the constants the form of Lemniscate were brought about in which the lower branch did not close (Fig. 9). Assume then that a Lemniscate arises which by a certain variation of the constants is open on one side. The curve is mathematically feasible, and if you find the right way, you can certainly draw it into the human form and figure. Say now that this were the surface of the Earth (Fig. 10). We should have to draw, somehow in relation to the Earth, what passes through our limb-nature and then in some way turns, goes through our head-nature and then back again into the Earth. Say you could truly draw into the nature and organisation of man such an open Lemniscate; we should be justified in saying: There is an open Lemniscate of this kind in man's nature. The question is, is it of real significance to speak of such an open Lemniscate in human nature? It is indeed. You need only make a deeper morphological study; you will find the Lemniscate, either in this or in some modified form, in diverse ways inscribed in human nature. These things have not been gone into with due method. I advise you, try it. (As I said, we are only giving indications for further work; diligent research is needed.) Try it; investigate the curve that arises if you trace the middle line of a left-hand rib, then go past the junction into the vertebra, then turn and go back along the right rib (Fig. 11). Bear in mind what it must signify that as you go along this line — rib-vertebra-rib — various inner relationships of growth must play their part, not only quantitatively but qualitatively; then you will find in the Lemniscate with its loop-formation a morphological key to the whole system. Going upward from thence to the head-organisation, the farther you go upward, the more will you find it necessary to modify the form of Lemniscate. At a certain point you must imagine it transformed; the transformation is already indicated in the forming of the sternum, where the two come together. When you get up into the head there is a far-reaching metamorphosis of the lemniscatory principle. Study the whole human figure — the contrast above all of the nerves-and-senses organisation and the metabolic, — you get a Lemniscate tending to open out as you go downward and to close as you go upward. You also get Lemniscates — though highly modified, with the one loop extremely small — if you follow up the pathway of the centripetal nerves, through the nerve-centre and outward again to the termination of the centrifugal nerve. Follow it all in the right way: Again and again you will find this Lemniscate inscribed in man's nature, — man's above all. Then take the animal organisation with its manifestly horizontal spine. You will find it differing from the human, in that the Lemniscates, whether the downward loop be open or closed to some extent, are far less modified, less varied than they are in man. Moreover in the animal their planes are more parallel, whereas in man they are variedly inclined and askew to one another. It is an immense and very promising field of work, — this ever-deepening elaboration of morphological study. And as you apprehend these tasks, you will appreciate the outlook of such men — of whom there have always been a few — as Moritz Benedikt for instance, whom I have mentioned before. Benedikt had many fruitful thoughts and good ideas. As you may read in his memoirs, he regretted how little possibility there is of speaking to doctors of medicine from a mathematical standpoint or with the help of mathematical notions. In principle he is quite right, only we have to go still farther. Ordinary mathematics, reckoning in the main on rigid forms of curve in a rigid Euclidean space, would help us little if we tried applying it to organic forms. Only by seeking, as it were, to carry life itself into the realms of mathematics and geometry as such, by thinking of the independent and the dependent variable in an equation as being subject to an organic and inherent variation, as illustrated yesterday for the Cassini curves (Variability of the first and of the second order), only thus shall we make progress. But if you do this immense possibilities will be opened up. It is indeed already indicated in the principles applied when constructing cardioid or cycloid curves; you must only not fall back again into rigidity of treatment. Apply this principle — the inner mobility, as it were, of movement in itself — to Nature. Try to express in equations, this that ‘moves the moving’. You will then find it possible, mathematically to penetrate what is organic. You will come to say, for it can well be formulated thus: The axioms of rigid space — space immobile in itself — lead to an understanding of inorganic Nature. Conceive a space that is inherently mobile — or algebraic equations whose very functionality is in itself a function — and you will find the transition to a mathematical understanding of organic Nature. This incidentally is the method which should accompany the efforts now being made to investigate the transition-forms from inorganic Nature to organic, as regards shape and form at least. Valueless apart from this, they have a future if this method be applied. Take now the presence of the loop-making tendency in the human body and compare it with what confronts us, admittedly in a more irrational form, in the forms of movement of the planets. You will then realise: The 'apparent movements’ of the planets, as we are wont to call them, in a most striking way inscribe, in forms of Movement in the Heavens, what in the human body is a Form as such — a characteristic, fundamental figure. Therefore, to say the least, we must in some way correlate this basic form in the human body and these phenomena in the Heavens. And we shall now be able to say: Behold the loop. It always appears when the planet is relatively near the Earth, — therefore when we, being on the Earth, are in a special relation to the planet. Consider the position of the Earth in its yearly course and our position on the Earth. (We must refer it back to our own formative period, the embryo-period of our life, needless to say.) Consider in effect how we are alternating between a position relative to the planet wherein we turn our head towards the planetary loop and a position where we take leave of the loop and at length turn our head away from it. We in our process of formation are thus related to the planet: We are exposed at one time to the planet's loop and at another to the remainder of its path. We can therefore relate, what lies nearer to our head, to the loop, and what belongs more to the remainder of our body, to the planetary path outside the loop. Take in addition what I said before, I said, with regard to the morphological relation of the tubular or long bone to the skull-bone: Try how you would have to draw it. Here, throughout the long bone, is the radius; then as you pass to the skull-bone you will have to turn, like this (Fig. 12). Project this turn, in relation also to the Earth's movement, outward into the Heavens. It is the loop and the rest of the planet's path! If we develop a feeling for morphology in the higher sense, we can do no other than assign the human form and figure to the planetary system. And now the movement of the fixed stars themselves: — The movements of the fixed stars will naturally be less concerned with the several movements of individual human beings. Think on the other hand of the whole evolution of mankind on Earth. Bear in mind all we have said in these days of the relation of the great Sphere to the human head-formation. You cannot but divine that there will be some relation between the metamorphoses of aspect of the starry Heavens, and of the evolution of mankind in soul and spirit. There is the vault of the great Sphere above us. It reveals only that part of the movements which would correspond to the loop among the planets (nay more, as it would seem, only to part of the loop; Fig. 13, dotted line). In the movements of fixed stars, the rest of the path is omitted. Our attention is drawn to this great differentiation: The planets must somehow correspond to the whole man; the fixed stars only to what forms the head of man. Now we begin to get some guidance, how to interpret the loop. We human beings are in some way with the Earth. We are at some point on Earth and we move with it. We cannot but refer, what appears to us in projection on the vault of heaven, to the movements we ourselves are making with the Earth. For, as we move with the Earth (we ,must project this backward, once more, backward in time to the embryo-period of our life), — as we move with the Earth, what we have in us comes into being, formed as indeed it is by the very forces of movement. In the movements we see up yonder in their seeming forms and pictures, we have to recognise the cosmic movements we ourselves are making in the year's course. We realise it as we approach the true aspect of the loop-curve. (Downward of course we always see the loop still open. In the immediate aspect, it does not close at all. Looking at this alone, we should never get a complete path. We only get the complete path when contemplating the entire revolution.) I am relating all this rather quickly. You must reflect on it in detail and try to see the different things together. The more minutely and scrupulously you do so, the more will you find that the planetary movements are, to begin with, images — images of — movements you yourself accomplish, with the Earth, in the year's course. (We shall see in time, how a synthesis arises from the different planetary movements.) If then we see the human being as a whole and his projection to the Cosmos, we are led to recognise that the true form of movement of the Earth in the year's course will be the loop-curve or Lemniscate. We shall have to study it more closely during the next few days, but at this stage we are already led to conceive the path of the Earth itself as a loop-curve — quite apart now from its relation to the Sun or any other factor. What is projected then, for our perception, the planetary paths with the loops they make, — we must regard as the projection by the planets of the loop-path of the Earth on to the vault of Heaven, if we may formulate thus simply a very complicated set of facts. As to why, when the planet draws near the loop, we have to leave the rest of the path open during a relatively short space of time, — the reason lies in the fact that under certain conditions the projection of a closed curve may appear open. For example, if you were to make a Lemniscate, say of a flexible rod, and project the shadow of it on to a plane, you could easily make it so that the projection of the lower part appeared divergent and unclosed, whilst the upper part alone was closed; so the entire projection would become not unlike a planetary path. Quite simply in the shadow-figure, you could construct the likeness of a planet's path.

Astronomy as Compared to Other Sciences

Lecture XI

https://rsarchive.org/Lectures/GA323/English/LR81/19210111p01.html

Stuttgart

11 Jan 1921

GA323-11

I will begin today by pointing out that our studies hitherto have led us to a specific result. We have drawn attention on the one hand to the movements of the heavenly bodies, and, though it still remains for us to do it in more detail, we have at least gained some conception: Here are a number of cosmic bodies in movement, in a certain order and configuration. Meanwhile we have also been drawing attention to the form of man, and incidentally, from time to time, to the forms of animal and plant-nature; this we shall have to do still more, to gain the necessary supports from diverse realms. In the main however, it is the human form and figure we have contemplated, and in so doing we have divined that the formation of man is in some way related to what finds expression in the movement of celestial bodies. We want to formulate it with great care. Yesterday I showed that wheresoever we may look in the human body, we shall find the formative principle of the looped curve or Lemniscate, save for the two outermost polarities — the Radius and the Sphere. Thus in the human body we perceive three formative principles (Fig. 1): The Sphere, with its activity primarily going inward, the Radius, and between these the looped curve or Lemniscate. Truly to recognise these formative principles in the human organism, you must imagine the Lemniscate as such with variable constants, if I may use the paradox. Where a curve normally has constants in its equation, we must think variables. The variability is most in evidence in the middle portion of the human body. Take as a whole the structure of the pairs of ribs and the adjoining vertebrae. True as it is then that in the vertebra the one half of the Lemniscate is very much condensed and pressed together, whilst in the pair of ribs the other half is much extended and drawn apart (Fig. 2), we must not be put off my this. The underlying formative principle is the Lemniscate, none the less. We simply have to imagine that where the ribs are (the drawing indicated those that are joined in front via the sternum) the space is widened, matter being as it were extenuated, while, to make up for this, the matter is compressed and the space lessoned in the vertebra. Let us now follow the human form and figure upward and downward from this middle portion. Upward we find the vertebra as it were bulged out into a wide cavity (Fig. 3), while the remaining branches of the Lemniscate seem to vanish, nestling away, so to speak, in the internal formative process, becoming hidden and undefined. Going downward from the middle portion, we contemplate for instance the attachment of the lower limbs to the pelvis. In all that opens downward from this point, we find the other half of the loop fading away. We have therefore to contemplate a fundamental loop-curve, mobile and variable in itself. This dominates the middle part of man. Only, the formative forces of it must be so imagined that in the one half (Fig. 2) the material forces become, as it were, more attenuated and the loop widens, while in the other it contracts. Further we must imagine that from this middle region upward the portion of the Lemniscate which in the vertebra was drawn together, bulges and widens out, while the other, downward-opening portion vanishes and eludes us. On the other hand, as you go downward from the middle part of man, the closed loop grows minute and fades away, while those portions of the curve which disappear as you go towards the head, run out into the radial principle and are here prolonged. (Fig. 4) We should thus find our way into it, till we are able to see the only moving Lemniscate with perceptive insight. Also we think how the formative principle of the moving Lemniscate is combined with forces which are spheroidal on the one hand and on the other radial — radial with respect to the Earth's centre. We then have a system of forces which we may conceive as being fundamental to the form and figure, to the whole forming and configuration of the human body. (By the word “forces” I mean nothing hypothetical; — purely and simply what is made manifest in the forming of it.) Answering to this , in cosmic space, in the movement of celestial bodies, we also find a peculiar configuration, — configuration of movements. In yesterday's lecture, we recognised in the planetary loops the very same principle outside us which is the principle of form within us. Let us now follow this loop-forming principle in greater detail. Is it not interesting that Mercury and Venus make their loops when the planets are in inferior conjunction, i.e., when they are roughly between the Earth and the Sun? In other words, their loop occurs when what the Sun is for man — so to express it — is enhanced by Venus and Mercury. As against this, look for the loops of Mars, Jupiter and Saturn. These loops we find occurring when the planets are in opposition to the Sun. This contrast too, of oppositions and conjunctions, will in some way correspond to a contrast in the building forces of man. For Saturn, Jupiter and Mars, because their loops appear in opposition, the loops as loops will be most active and influential. Thinking along these lines, we shall indeed relate the loop-formation of Saturn, Jupiter and Mars to that in man which is little influenced by the Sun; for it takes place, once more, when the planet is in opposition. Whilst, inasmuch as Venus and Mercury form their loops when in conjunction, their loop-formation must in some way be related to what is brought about, amid the formative principles of man, by the Sun — or by what underlies the Sun. We shall therefore conceive the Sun's influence to be in some sense reinforced by Venus and Mercury, while it withdraws, as it were, in face of the superior planets, so-called. The latter, precisely during loop-formation, bring to expression something that bears directly, not indirectly, upon man. If we pursue this line of thought and bear in mind that there is the contrast between Radius and Sphere, then we need but recall the form that comes to manifestation in these movements, and we shall say: In Mays, Jupiter and Saturn the essential phase must be when they are forming their loops, that is to say, when, in a manner speaking, the sphere-forming process comes into evidence. Mars, Jupiter and Saturn (not to speak of further planets) will show their influence upon that element in man which is assigned to the sphere-forming process, namely the human head. In contrast to this — they are indeed the polar opposite — the movements of Venus and Mercury will somehow find expression in what in man too is the opposite pole, opposite to the forming of the head, — i.e., what abandons parallelism with the spherical formation and becomes parallel to the radial. Where the one part of the Lemniscate becomes minute and the other grows into the limbs, into a purely radial development, we have to look for the relation to Venus and Mercury. This in turn will lead us on to say: In the superior planets, which make their loop when in opposition, it is the loop that matters; they develop their intensity while they form the loop. Whilst in the inferior planets Venus and Mercury — it is essential that they wield their influence by virtue of what is not the loop, — i.e., in contrast to the loop, by the remainder of the planet's path. Think of a Lemniscate like this (Fig. 5), say in the case of Venus (I draw it diagrammatically). You will understand it if you imagine this part (dotted line) ever less in evidence, the farther you go downward. That is to say, whilst in the path of Venus it closes, in its effects it no longer does so, but, as it were, runs out into parabolic branches, answering precisely to what happens in the human limb, where the vertebra form fades away and loses character (to put it very briefly, omitting details). This loop of the Lemniscate is represented by the path's fading away, not being fully maintained; it only indicates the direction but cannot hold it. So, where it closes in the path of Venus in the Heavens, in man's formation it falls asunder. Thus, to sum up, the building principle of the human form, howsoever modified, is based on this; the metamorphosis emerges between head and limbs — the limbs with the metabolism which belongs to them — and in the great Universe this answers to the contrast between those planets that form them in opposition to the Sun. Between the two is then the Sun itself. Now, my dear friends, something quite definite results from this Namely, we see that also with respect to the qualitative effects we have just referred to, we have to recognise in the Sun's path, even as to its form, something midway between what we find in the forms movement of the superior and of the inferior planets respectively. We must therefore assign, what finds expression in the path and movement of the Sun, to all that in man which is midway between the forming of the head and the metabolism, In other words, we must attribute to the rhythmic system some relation to the path of the Sun. We therefore have to imagine a certain contrast between the paths of the superior and of the inferior planets; and in the Sun's path a quality midway between the two. There is now a very evident and significant fact, regarding both the Sun's path and the Moon's. Follow the movements of the two heavenly bodies; neither of them makes any loop. They have no loop. Somehow therefore we must contrast the relation to man, and to Earth nature generally, of Sun and Moon on the one hand and of the loop-forming planetary paths on the other. The planetary paths with their characteristic loops quite evidently correspond to what makes vortices and vertebrae, — to what is lemniscatory in man. Look simply at the human form and figure and think of its relation to the Earth; we can do no other than connect what is radial in human form and stature with the path of the Sun, even as we connect what is lemniscatory in form with the typical planetary path. You see then what emerges when we are able to relate to the starry Heavens the entire human being, not only the human organ of cognition. This in effect emerges: In the vertical axis of man we must in some way seek what answers to the Sun's path, whilst in all that is lemniscatory in arrangement we have to seek what answers to the planetary paths, — lemniscatory as they are too, though in a variable form. Important truths will follow from this, We must conceive, once more, that through his vertical axis man is related to the Sun's path. HOW then shall we think of the other path which also shows no loops, namely the Moon's? Quite naturally — you need only look with open mind at the corresponding forms on Earth — we shall be led to the line of which we spoke some days ago, the line that runs along the spine of the animal. There we must seek what answers to the Moon's path. And in this very fact — the correspondence of the human spinal axis to the Sun's path and of the animal spinal axis to the moon's _ we shall have to look for the essential morphological difference between man and animal. Precisely therefore when we are wanting to discover what is essential in the difference of man and animal, we cannot stay on Earth. A mere comparative morphology will not avail us, for we must first assign what we there find to the entire Universe. Hence too we shall derive some indication of what must be the relative position of the Sun's path and the Moon's — shall we say, what is their mutual situation, to begin with, in perspective (for here again we must express it with great caution). They must be so situated that the one path is approximately perpendicular to the other. The human vertical therefore — or, had we better say, what answers to the main line and direction of the spine in man — is related to the Sun's path. The rational morphology we are pursuing makes this coordination evident. Mindful of this, we must surely relate the Sun's path itself to what in some way coincides with the Earth's radius. Admittedly, the Earth may move in such a way that many of her radii in turn coincide with the Sun's path. The relation indicated will need defining more precisely in coming lectures. Yet this at least gives us a notion of it: the direction of the Sun's path must be radial in relation to the surface or the Earth. We have no other alternative. In no event can the Earth be revolving round the Sun. What has been calculated — quite properly and conscientiously, of course — to be the revolution of the Earth around the Sun must therefore be a resultant of some other kind of movements. To this conclusion we are driven. The many relevant details as regards human form and growth are so very complicated that in this brief lecture-course not everything can be gone into. But if you really concentrate upon the morphological descriptions given (though they are only bare indications of a qualitative morphology), you will be able to read it in the human form itself: The Earth is following the Sun! The Sun speeds on ahead, the Earth comes after. This then must be the essence of the matter: the earthly and the solar orbit in some way coincide, and the Earth somehow follows the Sun, making it possible as the Earth rotates for the Earth's radii to fall into the solar path, or at the very least to be in a certain relation to it. Now you may very naturally retort that all this is inconsistent with the accepted Astronomy. But it is not so, — it really isn't! As you are well aware, to explain all the phenomena, Astronomy today must have recourse not only to the primary notion of a stationary Sun supposed to be at the focus of an ellipse along which the Earth is moving — but to a further movement, a movement of the Sun itself towards a certain constellation. If you imagine the direction of this movement and other relevant factors, then from the several movements of Sun and Earth, you may well be able to deduce a resultant path for the Earth, no longer coincident with the ellipse in which the Earth is said to be going round the Sun, but of a different form which need not be at all like the supposed ellipse. All these things I am gradually leading up to; for the moment I only wish to point out that you need not think what I am telling you so very revolutionary as against orthodox Astronomy. Far more important is the method of our study, — to bring the human form and figure into the system of the starry movements. My purpose here is not to propound some astronomical revolution, nor is it called for. Look, for example: say this or something like it (Fig. 6) is the Earth's movement, and the Sun too is moving, You can well imagine, if the Earth is following the Sun in movement, it is not absolutely necessary for the Earth always to be running past the Sun tangentially. It may well be that the Sun has already gone along the same path and that the Earth always to be running past the Sun tangentially. It may well be that the Sun has already gone along the same path and that the Earth is following, Nay, it is possible, envisaging the hypothetical velocity that has been calculated for the Sun's proper movement, you may work out a very neat arithmetical result. Work out the resultant of the assumed Earth-movement and the assumed Sun-movement; you may well get a resultant movement compatible with present-day Astronomy, — velocity and all. Let me then emphasise once more: What I am here propounding is not unrelated to present-day Astronomy, nor do I mean it not be. Quite on the contrary, it is related to it more thoroughly and deeply than theories which are so frequently presented, nicely worked out in theoretic garb, selecting certain movements and omitting others. I am not therefore instigating an astronomical revolution in these lectures; let me say this again to prevent fairy-tales arising. What I intend is to co-ordinate the human form — inward and outward form, figure and formation — with the movements of the heavenly bodies, nay, with the very system of the Cosmos. For the rest, may I call your attention to this: It is not so simple to bring together in thought our astronomical observations of the heavenly bodies and the accepted constructions of the orbits. For as you know from Kepler's Second Law, an essential feature, on which the forms of the orbits depend, are the radius-vectors, — their velocity above all. The whole form of the path depends on the functionality of the radius vectors. If this be so, does it not also reflect upon the forms of the paths which actually confront us? May it not be that we are cherishing illusions after all, at the mere outward aspect of them? It is quite possible: What we here calculate from the velocity and length of the radius vectors might not be primary magnitudes at all. They might themselves be only the resultants of the true primary magnitudes. If so, then the seeming picture which emerges must refer back to another and more deeply hidden. This too is not so far afield as you might think. Suppose that in the sense of present-day Astronomy you wished to calculate the Sun's exact position at a given time of day and on a given date. Then it will not suffice you to take your start from the simple proposition, 'the Earth moves round the Sun'. People have thought it strange that in the ancient Astronomy (that of the Mysteries, not the exoteric version) they spoke of three Suns instead of one. So they distinguished three Suns. I must confess, I do not find it so very striking. Modern Astronomy too has its three Suns. There is the Sun whose path is calculated as the apparent counterpart of the Earth's movement round the Sun. This Sun occurs, does it not , in modern Astronomy? The path of it is calculated. Astronomy then has another Sun — an imagined one of course — with the help of which certain discrepancies are corrected. And then it has a third Sun, with the help of which it re-corrects discrepancies that persist after the first correction. Modern Astronomy too therefore distinguishes three: the real Sun and two imagined ones. It needs the three, for what is calculated to begin with does not accord with the Sun's actual position. It is always necessary to apply corrections. This alone should be enough to show you that we should not build too confidently on mere calculation. Other means are needed to arrive at adequate conceptions of the starry movements; others than the science of our time derives from sundry premises of calculation. The broad ideas of planetary paths we have been laying out, it I may put it so, call now for great definition. Yet we shall only come to this if we contrive first to go further in out study of Earth-nature, to see their mutual relation in a certain aspect. The Kingdoms of Nature are commonly thought of in a straight line: mineral kingdom, plant kingdom, animal kingdom, and I will add, human kingdom. (Some authorities would not admit the fourth, but that need not detain us.) The question now is: Is this arrangement sensible at all? Undoubtedly it is implicit in many of our modern lines of thought; at least it was so in the golden age of the mechanical outlook upon Nature. Today I know, in these wider realms of Science, there is a certain atmosphere of resignation, not to say despair. The habits of mind however remain the same as at their heyday, 20 or 30 years since. The scientists of that time would have been content, had they been able to follow up this series — mineral kingdom, plant kingdom, animal kingdom, man, — with the mineral kingdom as the amplest, deriving therefrom, by some combination of mineral structure, the structure of the plant, then by a further combination of plant structure the structure of the animal, and so on to man. The many thoughts that were pursued about the primal generation of living things, generatic aequivocs, — were they not eloquent of the tendency to derive animate living Nature from inanimate and at long last from inorganic or mineral? To this day, I believe, many scientiste would doubt if there is any other rational way of conceiving the inner connection in the succession of Nature's Kingdoms than by deriving them all ultimately from the Inorganic, even where they culminate in Man. You will find countless papers, books, lectures and so on, including highly specialised ones claiming to be strictly scientific, the authors of which — as though hypnotised — are always looking at it from this angle. How, they inquire, can it have happened, somewhere at some time in the course of Nature, that the first living creature came into being from some molecular distribution, i.e. from something purely mineral in the last resort? The question now is, is it true at all to put the kingdoms of Nature in series in this way? Can it be done? Or, if we do, are we doing justice to their most evident and essential features? Compare a creature of the plant kingdom with an animal to begin with. Taking together all that you observe, you will not find in the forming of the animal anything that looks like a mere continuation or further elaboration of what is vegetable. If you begin with the simplest plant, the annual, you may well conceive its formative process to be carried further in the perennial. But you will certainly not be able to detect, in the organic principles of plant form and growth, anything that suggests further development towards the animal. On the contrary, you will more likely ascertain a polarity, a contrast between the two. You apprehend this polarity in the most evident phenomenon, namely the contrasting processes of assimilation: the altogether different relation of the plant and of the animal to carbon, and the characteristic use that is made of oxygen. I may remark, you must be careful here, to see and to describe it truly. You cannot simply say, the animal breathes-in oxygen while the plant breathes oxygen out and carbon in. It is not so simple as that. Nevertheless, the plant-forming process taken as a whole, in the organic life, reveals an evident polarity and contrast (as against the animal) in its relation to oxygen and carbon. The easiest way to put it is perhaps to say: What happens in the animal, in that the oxygen becomes bound to carbon and the carbonic acid is expelled, is for the animal itself and for man too. — an un-formative process, the very opposite of formative, a process which must be eliminated if the animal is to survive. And now the very thing which is undone in the animal, has to be done, has to be formed and builded in the plant. Think of what in the animal appears in some sense as a process of excretion, what the animal must get rid of makes for the forming and building process in the plant. It is a tangible polarity. You cannot possibly imagine the plant-forming process prolonged in a straight line, so as to derive therefrom the animal-formation. But you can well derive from the plant-forming process what has to be prevented in the animal. From the animal the carbon has to be taken away by the oxygen in the carbonic acid. Turn it precisely the other way round, and you will readily conceive the plant-forming process. You therefore cannot get from plant to animal by going on in a straight line. On the other hand you can without false symbolism imagine here an ideal mean or middlepoint, on the one side of which you see the plant — and on the other the animal — forming process. It forks out from here (Fig. 7). What is midway between, — let us imagine it as some kind of ideal mean. If we now carry the plant forming process further in a straight line we arrive not at the animal but at the perennial plant. Imagine now the typical perennial. Carry the stream of development which leads to it still further; in some respects at least you will not fail to recognise in it the way that leads toward mineralisation. Here then you have the way to mineralisation, and we may justly say; In direct continuation of the plant forming process there lies the way that leads to mineralisation. Now look what answers to it at the contrasting pole, along the other branch (Fig. 7). To proceed by a mere outward scheme, one would be tempted to say: this branch too must be prolonged. There would be no true polarity in that. Rather should you think as follows: In the plant-forming process I prolong the line. In the animal-forming process I shall have to proceed negatively, I must go back, I must turn round; I must imagine the animal-forming process not to shoot out beyond itself but to remain behind — behind what it would otherwise become. Observe now what is already available in scientific Zoology, in Selenka's researches for instance on the difference between man and animal in the forming of the embryo and in further development after birth, — comparing man and the higher animals. You will then have a more concrete idea of this "remaining behind". Indeed we owe our human form to the fact that in embryo-life we do not go as far as the animal but remain behind. Thus if we study the three kingdoms quite outwardly as they reveal themselves, without bringing in hypotheses, we find ourselves obliged to draw a strange mathematical line, that tends to vanish as we prolong it. This is what happens at the transition from animal to men, whilst on the other side we have a line that really lengthens (Fig. 8). Here is a fresh extension of mathematics. You are led to recognise a distinction — a purely mathematical one — when you draw this diagram. Namely there are lines which when continued grow longer, and there are lines which when continued grow shorter. It is a fully valid mathematical idea. If then we want to set out the Kingdoms of Nature in a diagram at all, we must do it thus. First we must have some ideal point to start from. Thence it forks out: plant kingdom, animal kingdom on either hand. Thereafter we must prolong the two lines. Only, the plant-kingdom-line must be so prolonged that it grows longer; the animal-kingdom-line so that it grows shorter as we prolong it. I say again, this is a genuine, mathematical idea. We thus arrive at real relationships between the Kingdom of Nature, though we begin by simply placing them side by side. The question now is — and we will only put it as a question, — What in reality corresponds to the ideal point in our diagram? We may divine that as the forming of the Kingdoms of Nature is related to this ideal point, so too must there be movements in the great Universe which relate to something somehow corresponding to it, — to this ideal mean. Let us reflect on it until tomorrow.

Astronomy as Compared to Other Sciences

Lecture XII

https://rsarchive.org/Lectures/GA323/English/LR81/19210112p01.html

Stuttgart

12 Jan 1921

GA323-12

In popular works, as you are well aware, the evolution of astronomical ideas is thus presented — Until Copernicus, they say the Ptolemaic system was prevailing. Then through the work of Copernicus the system we accept — though with modifications — to this day, became the intellectual property of the civilised world. Now for the thoughts we shall pursue in the next few days it will be most important for us to be aware of a certain fact in this connection. I will present it simply by reading, to begin with, a passage from Archimedes . Archimedes describes the cosmic system or starry system as conceived by Aristarchus of Samos , in these words — “In Aristarchus' opinion the Universe is far, far greater. He takes the stars and the Sun to be immobile, with the Earth moving around the Sun as centre. He then assumes that the sphere of the fixed stars, — its centre likewise in the Sun, — is so immense that the circumference of the circle, described by the Earth in her movement, is to the distance of the fixed stars as is the centre of a sphere to the surface thereof.” Taking these words to be a true description of the spatial World-conception of Aristarchus of Samos, you will admit: Between his spatial picture of the Universe and ours, developed since the time of Copernicus, there is no difference at all. Aristarchus lived in the third Century before the Christian era. We must therefore assume that among those who like Aristarchus himself were leaders of cultural and spiritual life in a certain region at that time, fundamentally the same spatial conception of the World held good as in the Astronomy of today. Is it not all the more remarkable that in the prevailing consciousness of men who pondered on such things at all, this work-conception — heliocentric, as we may call it, — thereafter vanished and was supplanted by that of Ptolemy? Till, with the rise of the new epoch in civilisation, known to us as the Fifth post-Atlantean, the heliocentric idea comes forth again, which we have found prevailing among such men as Aristarchus in the 3rd Century B.C. ! (For you will readily believe that what held good for Aristarchus, held good for many people of this time.) Moreover if you are able to study the evolution of mankind's spiritual outlook — though it is difficult to prove by outer documents — you will find this heliocentric conception of the World the more widely recognised by those who counted in such matters, the farther you go back from Aristarchus into more distant times. Go back into the Epoch we are wont to call the Third post-Atlantean, and it is true to say that among those who were the recognised authorities the heliocentric conception prevailed during the Epoch. The same conception prevailed which Plutarch says was held by Aristarchus of Samos. Plutarch moreover described in such terms that we can scarcely distinguish it from that of our own time. This is the noteworthy fact. The heliocentric conception of the World is there in human thought, the Ptolemaic system supplants it, and in the Fifth post-Atlantean Epoch it is re-conquered. In all essentials we may aver that the Ptolemaic system held good for the Fourth post-Atlantean Epoch and for that alone. Not without reason do I bring this in today, after speaking yesterday of an ‘ideal point’ in the evolution of the Kingdoms of Nature. As we shall see in due course, there is an organic relationship between these diverse facts. But we must first enter more fully into the one adduced today. What is the essence of the Ptolemaic cosmic system? The essence of it is that Ptolemy and his followers go back again to the idea of an Earth at rest, with the fixed-star Heavens moving around the Earth; likewise the Sun moving around the Earth. For the movement of the planets, the apparent forms of which we have been studying, he propounds peculiar mathematical formulae. In the main, he thinks in this way: Let this be the Earth (Fig. 1). Around it he conceives the Heaven of fixed stars. Then he imagines the Sun to be moving in an eccentric circle round the Earth. The planets also move in circles. But he does not imagine them to move like the Sun in one circle only. No; he assumes a point (Fig. 1) moving in this eccentric circle which he calls the ‘Deferent’, and he makes this point in its turn the centre of another circle. Upon this other circle he lets the planet move, so that the true path of the planet's movement arises from the interplay of movements along the one circle and the other. Take Venus for example. Says Ptolemy: around this circle another circle is rotating; the centre of the latter circle moves along the former. The actual path of Venus would then be, as we should say, a resultant of the two movements. Such is the planet's movement around the Earth; to comprehend it we must assume the two circles, the large one, called the “deferent”, and the small one, know as the ‘epicyclic’ circle. Movements of this kind he attributes to Saturn, Jupiter, Mars, Venus an Mercury, only not to the Sun. The Moon he conceives to move in yet another small circle, — an epicyclic circle of its own. These assumptions were due to the Ptolemaic astronomers having calculated with great care the positions on the Heavens at which the planets were at given times. They computed these circling movements so as to understand the fact that the planets were at given places at given times. It is astonishing how accurate were the calculations of Ptolemy and his followers, — relatively speaking at least. Draw the path of any planet — Mars, for instance — from modern astronomical data. Compare this 'apparent path', so-called, of Mars, drawn as observed today, with the path derived from Ptolemy's theory of deferent and epicyclic circles. The two curves hardly differ. The difference, relatively trifling, is only due to the still more accurate results of modern observation. In point of accuracy these ancients were not far behind us. That they assumed this queer system of planetary movements, which seems to us so complicated, was not due therefore to any faulty observation. Of course the Copernican system is simpler, — that will occur to everyone. There is the Sun in the midst, with the planets moving in circles or ellipses round it. Simple, is it not? Whereas the other is very complicated: a circular path superimposed upon another circle, and an eccentric one to boot. The Ptolemaic system was adhered to with a certain tenacity throughout the Fourth post-Atlantean epoch, and we should ask ourselves this question: Wherein lies the essential difference in the way of thinking about cosmic space and the contents of cosmic space, such as we find it in the Ptolemaic school on the one hand and in Aristarchus and those who thought like him in the other? What is the real difference between these ways of thinking about the cosmic system? It is difficult to describe popularly, for many things seem outwardly alike, whilst inwardly they can be very different. Reading Plutarch's description of Aristarchus system, we shall say: This heliocentric system is fundamentally no different from the Copernican. Yet if we enter more deeply into the spirit of the Aristarchian world-picture, we find it different. Aristarchus too, no doubt, follows the outer phenomena's with mathematical lines. In mathematical lines he represents to himself the movements of the heavenly bodies. The Copernican's do likewise. Between the two there intervenes this other system — the strange one of the Ptolemaic school. Here it cannot be said that the forming of mathematical pictures coincides in the same way with what is observed. The difference in this respect is all-important. In the Ptolemaic school, the mathematical imagination does not directly rest upon the sequence of observed points in space. It is rather like this: In order ultimately to do justice to them it goes right away from the observed phenomena and works quite differently, not merely putting the observed results together. Yet in the end it is found that if one does admit the mathematical thought-pictures of the Ptolemaic school, one thereby comprehends what is observed. Suppose a man of today were to make a model of the planetary system. Somewhere he would attach the Sun, them he would draw wires to represent the orbits of the planets; he would really think of them as representing the true orbits. In purely mathematical lines he would comprise the logic of the planets' paths. Ptolemy would not have done so. He would have had to construct his model somewhat in this fashion (Fig. 2). Here would have been a pivot, fixed to it a rod, leading to the rim of a rotating wheel, upon this again another wheel rotating. Such would be Ptolemy's model. The model he makes, the mathematical picture living in his thought, is not in the least like what is outwardly seen. For Ptolemy the Mathematical picture is quite detached from what is seen externally. And now, in the Copernican system we return to the former method, simply uniting by mathematical lines the several places, empirically observed, of the planet. These mathematical lines correspond to what was there in Aristarchus's system. Yet is it really the same? This is the question we must now be asking: Is it the same? Bearing in mind the original premises of the Copernican system and the kind of reasoning by which it is maintained, I think you will admit: It is just like the way we relate ourselves, mathematically, to empirical reality in general. You may confirm it from his works. Copernicus began by constructing his planetary system ideally, much in the same way as we construct a triangle ideally and then find it realised in empirical reality outside us. He took his start from a kind of a priori mathematical reasoning and them applied it to the empirically given facts. What then is at the bottom of this complicated Ptolemaic system, to make it so complicated? You remember the well-known anecdote. When it was shown to Alphonso of Spain, he from his consciousness of royalty declared: Had God asked his advice at the Creation of the World, he would have made it more simply than to require so many cycles and epicycles. Or is there something in it after all — in this construction of cycles and epicycles — related to a real content of some kind? I put the question to you: Is it only fantasy, only a thing thought-out, or does this thought out system after all contain some indication that it relates to a reality? We can only decide the question by entering into it in greater detail. It is like this. Suppose that with the Ptolemaic system taking you start from Ptolemaic theories — you follow the movements, or, as we should say, the apparent movements of the Sun, and of Mercury, Venus, Mars, Jupiter, and Saturn: to begin with you will have angular movements of a certain magnitude each time. You can therefore compare the movements indicated by the successive positions of these heavenly bodies in the sky. The Sun has no epicyclic movement. The epicyclic daily movement of the Sun is therefore zero. For Mercury on the other hand we must put down a number, representing his daily movement along his epicyclic circle, which we shall them compare with that of other planets. Let us call the epicyclic daily movements — \(x_1\) for Mercury, \(x_2\) for Venus, \(x_3\) for Mars, \(x_4\) for Jupiter, \(x_5\) for Saturn, \(x_2\) for Venus, \(x_3\) for Mars, \(x_4\) for Jupiter, \(x_5\) for Saturn, \(x_3\) for Mars, \(x_4\) for Jupiter, \(x_5\) for Saturn, \(x_4\) for Jupiter, \(x_5\) for Saturn, \(x_5\) for Saturn, Now take the movements Ptolemy attributes to the centres of the epicycles along their different circles. Let the daily movement be y for the Sun. It is then remarkable that if we seek the corresponding value for Mercury we get precisely the same figure. The movement of the centre of Mercury's epicycle equals the movement of the Sun. We must write y again, and so for Venus. This then holds good of Mercury and Venus. The centres of their epicycles move along paths which correspond exactly to the Sun's path, — run paralleled to it. For Mars, Jupiter and Saturn on the other hand the movements of the centres of the epicycles are diverse, — shall we say \(x'\) for Mars, \(x''\) for Jupiter, \(x'''\) for Saturn. Yet the remarkable fact is that by taking the corresponding sums, namely: $$x3 + x' + x4 + x'' , x5 + x''',$$ adding the movements along the several epicycles to the movements of the centres of these epicycles, — I get the same magnitude for all three planets. Nay more, it is the identical which we obtained just now for the movement of the Sun and of the centres of the epicycles of Mercury and Venus — A noteworthy regularity, you see. This regularity will lead us to attribute a different cosmic significance to the centres at the epicycles of Venus and Mercury, the planets near the Sun as they are called, and of Jupiter, Mars, Saturn etc. called distant from the Sun. For the distant planets, the centre of the epicycle has not the same cosmic meaning. Something is there, by virtue of which the whole meaning of the planet's course is different than for the planets near the Sun. The fact was well-known in the Ptolemaic school and helped determine the whole idea — the peculiar construction of cycles and epicycles in the mind, detached from the empirically given facts. This very fact obliged them, as they saw it, to propound their system, and is implicit in it. The human being of today would scarcely recognise it there; he listens more or less obtusely when told how they set up their cycles and epicycles. To their way of thinking on the other hand the thought was palpable and eloquent???. If Mercury and Venus have the same values as Jupiter, Saturn and Mars, yet in another realm, we cannot treat the matter so simply, with an indifferent circling motion or the like. A planet, in effect, is of significance not only within the space it occupies but outside it. We have not merely to stare at it, fixing its place in the Heavens and in relation to other celestial bodies; we must go out of it to the centre of the epicycle. The centre of its epicycle behaves in space even as the Sun does. Once more, translated into modern forms of speech, the Ptolemaists said: For Mercury and Venus the centres of the epicycles so far as movement is concerned behave in cosmic space as the Sun itself behaves. Not so the other planets — Mars, Jupiter and Saturn. They claim another right. In effect, only when we add their epicyclic movements to their movements along the deferent, only then do they grow like the Sun in movement. They therefore are differently related to the Sun. This difference of behaviour in relation to the Sun was what they really built on in the Ptolemaic system. This among others was an essential reason for its development. Their aim was not merely to join the empirically given places in the Heavens by mathematical lines, building it all into a system of thought in this way. They were at pains to build a thought-system on another basis, and what is more, a piece of true knowledge under-lay their efforts; it is undeniable if we go into it historically. Modern man naturally says: We have advanced to the Copernican system, why bother about these ancient thinkers? He bothers not, but if he did, he would perceive that this was what the Ptolemaists meant. 'Truth is', they said to themselves, Mars, Jupiter and Saturn have quite another relation to Man than Mercury and Venus. What corresponds to them in Man is different. Moreover they connected Jupiter, Saturn and Mars with the forming of the human head, Venus and Mercury with the forming of what is beneath the heart in man. Rather than speak of the head, perhaps I should put it in these words: they related Jupiter, Saturn and Mars with the forming of all that is above the heart; Venus and Mercury with what is situated below the heart in man. The Ptolemaists did indeed relate to man, what they were trying to express in their cosmic system. What under-lay it really? To gain true judgement on this question, my dear Friends, I think you should read and mark the inmost tone and essence of my Riddles of Philosophy, in writing which I tried to show how very different was the way man met the world in his life or knowledge before the 15th Century and after. Since then, if I may use this image we unpeel ourselves from the world, — we detach ourselves completely. Before the 15th Century we did not do so. I must admit, at this point it is difficult to make oneself understood in the modern world. Man of to-day says to himself: “I think thus and thus about the world. I have my sense perceptions, thus or thus. In modern times we have become enlightened; the men of former times were simple, with many childish theories.” And as to our enlightenment and their simplicity the modern man's idea of it amounts to this, or something very like it: "If only our ancestors had tried hard enough, they might have grown just as clever as we are. But it took time, this eduction of mankind; it evidently had to take some time for men to get as enlightened as they afterwards became.” What is today left unconsidered, is that man's very seeing of the world, his seeing and his contemplating, his whole relation to the world was different. Compare the different stages of it, described in my Riddles of Philosophy. Then you will say: Through the whole time from the beginning of the Fourth Epoch until the end, the sharp distinction we now have, of concept and idea on the one hand and sense-perceived data on the other, did not exist. They coincided rather. In and with the sensory quality, men saw the quality of thought, the idea. And it was ever more so, the farther we go back in them. In this respect we need more real notions as to the evolution of mankind. What Dr. Stein has written for example in his book, upon the essence of sense-perception, is true of our time and excellently stated. I he had had to write a dissertation on this subject in the School of Alexandria in olden time, he would have had to write very differently of sense-perception. This is what people of today persist in disregarding; they will have everything made absolute. And if we go still farther back, for example into the time when the Egypto-Chaldean Epoch was at its height, we find an even more intensive union of concept and idea with sense-perceptible, outward and physical reality. It was from this moreover — from this more intensive union — that the conceptions arose which we still find in Aristarchus of Samos. They were already decadent in his time; they had been entertained even more vividly by his predecessors. The heliocentric system was simply felt, when with their thoughts and mental pictures men lived in and with the outer sense-perceptible reality. Then, in the Fourth post-Atlantean Epoch, man had to get outside the sense-world; he had to wean himself of this union of his inner life with the sense-world. In what field was it easiest to do so? Obviously, in the field where it would seem most difficult to bring the outer reality and the idea in the mind together. Here was man's opportunity to wrest himself away — in his life of ideas — from sense-impressions. Look at the Ptolemaic system from this angle; see in it an important means toward the education of mankind; then only do we recognise the essence of it. The Ptolemaic system is the great school of emancipation of human thoughts from sense-perception. When this emancipation had gone far enough when a certain degree of the purely inner capacity of thought had been attained — then came Copernicus. A little later, I may add, this attainment became even more evident, namely in Galileo and others, whose mathematical thinking is in the highest degree abstracted and complicated. Copernicus presented to himself the facts of which we have been speaking — the observation of the equality of y at diverse points in the equation, and, working backward from these mathematical results, was able to construct his cosmic system. For the Copernican system is based on these results. It represents a return, from the ideas now abstractly conceived, to the external, physically sense-perceptible reality. It is most interesting to witness, how in the astronomical world-picture above all, mankind gets free of the outer reality. And in perceiving this, my dear Friends, we also gain a truer estimate of the returning pathway, — for in a wider sense we must return. Yet how? Kepler still had a feeling of it. I have often quoted his rather melodramatic saying, to the effect: I have stolen the sacred vessels of the Egyptian Temples to bring them back again to modern man. Kepler's planetary system, as you know, grew from a highly romantic conception of how the Universe is built. In deed he feels it like a renewal of the ancient heliocentric system. Yet the truth is, the ancient heliocentric system was derived, not from a mere looking outward with the eyes, but from an inner awareness, an inner feeling of what was living in the stars. The human being who originally set up the cosmic system, making the Sun the centre with the Earth circling round it after the manner of Aristarchus of Samos, felt in his heart the influences of the Sun, felt in his head the influences of Venus and Mercury. This was experience, direct experience throughout the human being, and out of this the system grew. In later time this all-embracing experience was lost. Perceiving still with eyes and ears and nose, man could no longer perceive with heart or liver. To have perception from the Sun with one's heart, or from Jupiter with one's nose, seems like sheer madness to the people of today. Yet it is possible and it is exact and true. Moreover one is well aware why they think it madness. This living with the Universe, intensively and all-awarely, was lost in course of time. Then Ptolemy conceived a mathematical world-picture still with a little of the old feeling to begin with, yet in its essence already detached from the world. The earlier disciples of the Ptolemaic school still felt, though very slightly, that it is somehow different with the Sun than with Jupiter for instance. Later they felt it no more. In effect the Sun reveals his influence comparatively simply through the heart. Jupiter, we must admit, spins like a wheel in our head, — it is the whirling epicycle. Whilst in a different sense, here indicated (Fig. 1), Venus goes through beneath our heart. In later Ptolemaic times, all they retained of this was the mathematical aspect, the figure of the circle: the simple circle for the Sun's path and the more complicated for the planets. Yet in this mathematical configuration there was at least some remnant of relation to the human being. Then even this was lost and the high tide of abstraction came. Today we must look for the way back, — to re-establish once again from the entire Man an inner relation to the Cosmos. We have not to go on from Kepler, as Newton did, into still further abstractions. For Newton put abstractions in the place of things more real; he introduced mass etc. into the equations — a mere transformation, in effect, yet there is no empirical fact to vouch for it. We need to take the other road, whereby we enter reality even more deeply then Kepler did. And to this end we must include in our ambit what after all is in its life connected with the rising of the stars across the Heavens, namely the Kingdoms of external Nature in all their variedness of form and kind. Is it not worthy of note that we find a contrast between the superior planets so-called and the inferior, with the Earth-entity between the mineral and plant kingdoms along the one branch, the animal and man along the other? And, that in drawing the two branches of the forked line, we must put plant and mineral in simple prolongation, while animal and man must be so drawn as to show the formative process returning upon itself? (Fig. 3) We have put two things and of different kind before us: on the one hand the paths of the epicycle-centres and of the points on the epicyclic circumference, revealing a quite different relation to the Sun for the superior and inferior planets respectively; on the other hand the prolongation of the plant-forming process speeding on into the mineral, whilst the animal-forming process turns back upon itself to become man. (The symbolism of our diagram is justified; as I said yesterday, to recognise it you need only make a study of Selenka's work.) These two things side by side we put as problems, and we will try from thence to reach a cosmic system true to reality.

Astronomy as Compared to Other Sciences

Lecture XIII

https://rsarchive.org/Lectures/GA323/English/LR81/19210113p01.html

Stuttgart

13 Jan 1921

GA323-13

Today we will develop the different notes we touched on, — the notes which we were striking yesterday. From the material at our disposal, consisting as it does in the last resort of things observed, the true aspect of which we seek to divine, — from this observed material we shall try to gain ideas, to lead us into the inner structure of the celestial phenomena. I will first point to something that will naturally follow on the more historical reflections of yesterday. We realise that in the last resort both the Ptolemaic system and that used by modern Astronomy are attempts to synthesise in one way or another, what is observed. The Ptolemaic system and the Copernican are attempts to put together in certain mathematical or kindred figures what has in fact been perceived. (I say “perceived”, for in the light of yesterday's lecture it would not be enough to say “seen”.) All our geometry in this case, all of our measuring and mathematizing, must take its start from things perceived, observed. The only question is, are we conceiving the observed facts truly? We must really take it to heart — we must take knowledge of the fact — that in the scientific life and practice of our time what is observed, what is perceivable, is taken far to easily, too cursorily for a true conception to be gained. Here for example is a question we cannot escape; it springs directly from the observable facts — (In the shortness of time these lectures have to be in bare outline and I have not been able to discuss or even to bring forward all the details. I could do little more than indicate directions.) Now among other things I have tried to show that the movements of heavenly bodies in celestial space must in some way be co-ordinated with what is formed in the living human body, and in the animal too in the last resort, we should by now perceive from the whole way the facts have been presented. And I assure you, the more deeply you go into the facts, the more of the connection you will see. Nevertheless, I have not done nor claimed to do any more than indicate the pathway (let me say again), the pathway along which you will be led to the result: The human living body, also the animal and plant body, are so formed that if we recognise the characteristic lines of form (as for example we did in tracing the Lemniscate in various directions though the human body) we find in them a certain likeness to the line-systems which we are able to draw amid the movements of the celestial bodies. Granted it is so, the question still remains however: What is it due to? How does it come about? What prospect is there for us not merely to ascertain it but to find it cogent and transparent, inherent in the very nature of things? To get nearer to this question we must once more compare the kind of outlook which under-lay the Ptolemaic system and the kind that underlies the Copernican world-system of today. What are we doing when we set to working the spirit of the latter system, and by dint of thinking, calculating and geometrising, figure out a world-system? What do we do in the first place? We observe. Out in celestial space we observe bodies which, from the simple appearance of them, we regard as identical. I express myself with caution, as you see. We have no right to say more than this . From the appearance of them to our eye, we regard these bodies (in their successive appearance) as identical. A few simple experiments will soon oblige you to be thus cautious in relating what you see in the outer world. I draw your attention to this little experiment; of no value in itself, it has significance in teaching us to be careful in the way we form our human thoughts. Suppose it trained a horse to trot very regularly, — which, incidentally, a horse will do in any case. Say now I photograph the animal in twelve successive positions. I get twelve pictures of the horse. I put them in a circle, at a certain distance from myself, the onlooker. Over it all I put a drum with an aperture, and make the drum rotate so that I first see one picture of the horse, then, when the drum has totalled, a second picture, and so on. I get the appearance of a running horse, I should imagine a little horse to be running round in a circle. Yet the fact is not so. No horse is running round; I have only been looking in a certain way at twelve distinct pictures of a horse, each of which stays where it is. You can therefore evoke an appearance of movement not only by perspective but in purely qualitative ways. It does not follow that what appears to be a movement is really a movement. He then who wants to speak with care, who wants to reach the truth by scrupulous investigation, must begin by saying, whimsical as this may seem to our learned contemporaries: I look at three successive positions of what I call a heavenly body, and assume what underlies them to be identical. So for example I follow the Moon in its path, with the underlying hypothesis that it is always the same Moon. (That may be right without question, with such a “Standard” phenomenon, keeping so very regular a time-table!) What do we do then? We see what we take to be the identical heavenly body, in movement as we call it; we draw lines to unite what we thus see at different places, and we then try to interpret the lines. This is what gives the Copernican system. The school from which the Ptolemaic system derived did not proceed in this way, not originally. At that time the whole human being still lived in his perceiving, as I said yesterday. And inasmuch as man was thus alive and aware, perceiving with all his human being, the idea he then had of a heavenly body was essentially different from what it afterwards became. A man who still lived thus perceivingly amid the Ptolemaic system did not say. There is the Moon up yonder. No, he did not; the people of today only attribute that idea to him, nor does it do the system justice. If he had simply said, "Up yonder is the Moon", he would have been relating the phenomenon to his whole human being, and in so doing the following was his idea: — Here am I standing on the Earth. Now, even as I am on the Earth, so too am I in the Moon, — for the Moon is here (Figure 1, lightly shaded area). This (the small central circle in the Figure) is the Earth, whilst the whole of that is the Moon, — far greater than the Earth. The diameter (or semi-diameter) of the Moon is as great as what we now call the distance of the Moon (I must not say, of the Moon's centre) from the centre of the Earth. So large is the Moon, in the original meaning of the Ptolemaic system. Elsewhere invisible, this cosmic body at one end of it develops a certain process by virtue of which a tiny fragment of it (small outer circle in the Figure) becomes visible. They rest is invisible, and moreover of such substance that one can live in it and me permeated by it. Only at this one end of it does it grow visible. Moreover, in relation to the Earth the entire sphere is turning, (Incidentally it is not a perfect sphere, but a spheroid or ellipsoid-of-rotation. The whole of it is turning and with it turns the tiny reagent that is visible, i.e. the visible Moon. The visible Moon is only part of the full reality of it. The idea thus illustrated really lived in olden time. The form at least, the picture it presents, will not seem so entirely remote if you think of an analogy, — that of the human or animal germ-cell in its development (Fig. 2). You know what happens at a certain stage. While the rest of the germinal vesicle is well-nigh transparent, at one place it develops the germinative area, so called, and from this area the further development of the embryo proceeds. Eccentrically therefore, near the periphery, a centre forms, from which the rest proceeds. Compare the tiny body of the embryo with this idea of the Moon which underlay the Ptolemaic system and you will have a notion of how they conceived it for it was analogous to this. In the Ptolemaic conception of the Universe, we may truly say, quite another reality was ‘Moon’ — mot only what is contained in the Moon's picture, the illuminated orb we see. This, then, is what happened to man after the time when the Ptolemaic system was felt as a reality. The inner experience, the bodily organic feelings of being immersed in the Moon was lost. Today man has the mere picture before him, the illuminated orb out yonder. Man of the Fifth post-Atlantean Epoch cannot say, for he no longer knows it: “I am in the Moon, — the Moon pervades me”. In his experience the Moon is only the little illuminated disc or sphere which he beholds. It was from inner perceptions such as these that the Ptolemaic system of the Universe was made: These perceptions we can henceforth regain if we begin by looking at it all in the proper light: we can re-conquer the faculty whereby the whole Moon is experienced. We must admit however, it is understandable that those who take their start from the current idea of ‘the Moon’ find it hard to see any such inner relation between this “Moon” and life inside them. Nay, it is surely better for them to reject the statement that there are influences from the Moon affecting man than to indulge in so many fantastic and unfounded notions. All this is changed if in a genuine way we come again to the idea that we are always living in the Moon, so that what truly deserves the name of 'Moon' is in reality a realm of force, a complex of forces that pervades us all the time. Then it will no longer be a cause of blank astonishment that this complex of forces should help form both man and beast. That forces working in and permeating us should have to do with the forming and configuration of our body, is intelligible. Such then are the ideas we must regain. We have to realise that what is visible in the heavens is nor more than a fragmentary manifestation of cosmic space, which in reality is ever filled with substance. Develop this idea: you live immersed in substance — substances manifold, inter-related. Then you will get a feeling of how very real a thing it is. The accepted astronomical outlook of our time has replaced this 'real' by something merely thought-out, namely by 'gravitation' as we call it. We only think there is a mutual force of attraction between what we imagine to be the body of the moon and the body of the Earth respectively. This gravitational line of force from the one to the other — we may imagine it as it turns to get a pretty fair picture of what was called the 'sphere' in ancient astronomical conceptions — the Lunar sphere or that of any planet. This, then, has happened: What was once felt to be substantial and can henceforth be experienced in this way once more, has in the meantime been supplanted by mere lines, constructed and thought-out. We must then think of the whole configuration of cosmic space — manifoldly filled and differentiated in itself — in quite another way than we are wont to do. Today we go by the idea of universal gravitation. We say for instance that the tides are somehow due to gravitational forces from the Moon. We speak of gravitational force proceeding from a heavenly body, lifting the water of the sea. The other way of thought would make us say: The Moon pervades the Earth, including the Earth's hydrosphere. In the Moon's sphere, something is going on which at one place it manifests in a phenomenon of light. We need not think of any extra force of attraction. All we need think is that this Moon-sphere, permeating the Earth, is one with it, one organism all together , an organic whole. In the two kinds of phenomenon we see two aspects of a single process. In yesterday's more historical lecture my object was to lead you up to certain notions, — essential concepts. I could equally well have tried to present them without recourse to the ideas of olden time, but to do so we should have had to take our start from premises of Spiritual Science. This would have led us to the very same essential concepts. Imagine now (Fig. 3): Here is the Earth-sphere, — the solid sphere of Earth. And now the Lunar sphere: I must imagine this, of course, of very different consistency and kind of substance. And now I can go further. The space that is permeated by these two spheres, — I can imagine it permeated by a third sphere and a fourth. Thus in one way or another I imagine it to be permeated by a third sphere. It might for instance be the Sun-sphere, — qualitatively different form the Moon-sphere. I then say I, am permeated — I, man, am permeated by the sun — and by the Moon-sphere. Moreover naturally there is a constant interplay between them. Permeating each other as they do, they are in mutual relation. Some element of form and figure in the human body is then an outcome of the mutual relation. Now you will recognise how rational it is to see the two things together: On the one hand, these different cosmic substantialities permeating the living body; and on the other hand the organic forms in which you can well imagine that they find expression. Form and formation of the body is then the outcome of this permeation. And what we see in the heavens — the movement of heavenly bodies — is like the visible sign. Certain conditions prevailing, the boundaries of the several spheres become visible to us in phenomena of movement. What I have now put before you is essential for the regaining of more real conceptions of the inner structure of our cosmic system. Now you can make something of the idea that the human organisation is related to the structure of the cosmic system. You never gain a clear notion of it if you conceive the heavenly bodies as being far away yonder in space. You do gain a clear notion, the moment you see it as it really is. Though, I admit, it gets a little uncanny to feel yourself permeated by so many spheres, — just a little confusing! And there is worse to come, for the mathematician at least. In effect, we are also permeated by the Earth-sphere itself, in a wider sense. For to the Earth belongs not only the solid ball on which we stand but all the volume of water; also the air, — this is a sphere in which we know ourselves to be immersed. Only the air is still very coarse, compared to the effects of heavenly phenomena. Think then of this: Here we are in the Earth-sphere, in the Sun sphere, in the Moon-sphere, and in others too. But let us single out the three, and we shall say to ourselves: Something in us is the outcome of the substantialities of these three spheres. Here then is qualitatively, what in its quantitative form is the mathematician's bugbear — the “problem of three bodies”, as it is called! It is working in us. In us is the outcome of it, in all reality. We must face the truth: to read the hieroglyphic of reality is not so simple. That we are wont to take it simply and think it so convenient of access, springs after all from our fond comfort, — human indolence of thought. How many things, held to be "scientific", have their origin in this! Let go the springs of comfortableness, and you must set to work with all the care which we have tried to use in these lectures. If now and then, they do not seem careful enough, it is again because they are given in barest outline; so we have often had to jump from one point to another and you yourselves must look for the connecting links. The links are surely there. Now you must set to work with equal care to tackle the same problem from another aspect to which I have referred before, namely the body of man compared to the creatures of the remaining Nature-kingdoms. We can imagine, I said, a line that forks out on either hand from an ideal starting-point. Along the one branch we put the plant-world, along the other the animal. If we imagine the evolution of the plant-world carried further in a real Kingdom of Nature, we find it tending towards the mineral. How real a process it is, we may recall by the most obvious example. In the mineral coal, we recognised a mineralised plant-substance. What should detain us from turning attention to the analogous processes which have undoubtedly taken hold of other realms of vegetable matter? Can we not also derive the siliceous and other mineral substances of the Earth in the same way, recognising in them the mineralisation of an erstwhile plant-life? Not in the same way (I went on to say) can we proceed if we are seeking the relation of the animal to the human kingdom. Here on the contrary we must imagine it somewhat as follows. Evolution moves onward through the animal kingdom; then however it bends back, returns upon itself, and finds physical realisation upon a higher than animal level. We may perhaps put it this way: Animal and human evolution begin from a common starting — point, but the animal goes farther before reaching outward physical reality. Man on the other hand keeps at an earlier stage, man makes himself physically real at an earlier stage. It is precisely by virtue of this that he remains capable of further evolution after birth, incomparably more so then the animal. (For, once again, the processes of which we speak relate to embryo-development.) That man retains the power to evolve, is due to his not carrying the animal-forming process to extremes. Whilst in the mineral, the plant-forming process has overreached itself; in man on the contrary the animal-forming process has stopped short of the extreme. It has withheld, kept back, and taken shape at an earlier stage amid external Nature. We have then this ideal point from which it branches (Fig. 6). There is the shorter branch and the longer. The longer is of undetermined length; the other, we may say, no less so, but negatively speaking. So then we have the mineral and plant kingdoms, and animal and human. Now we must seek to gain a more precise idea: What is it that really happens, in this formation of man as compared to the animal? The process of development, once more, is kept back in man. It does not go so far; that which is tending to realisation is, as it were, made real before its time. Now think how it must be imagined according to what I have told you in these lectures. Study the share of the Solar entity in the forming of the animal body, — via the embryo-development, of course. You then know that the direct sunshine (so to describe it) has to do with the configuration of the animal head, whilst the indirect aspect of the sunlight, as it were the Sun's shadow by relation to the Earth, has in some way to do with the opposite pole of the creature. Strictly envisage this permeation of animal form and development with cosmic Sun-substantiality. Look at the forms as they are. Then you will gain a certain idea, which I shall try to indicate as follows. Assume to begin with, — assume that in some way the forming of the animal is really brought about by relation to the Sun. And now, apart from the constellation that will be effective in each case as between Sun and animal, let us ask, quite in the sense of the Sun's light in the cosmos, not so immediately connected with the Sun itself? There is indeed. For every time the Full Moon, or the Moon at all, shines down upon us, the light is sunlight. The cosmic opportunity is being made then, so to speak, for the Sun's light to ray down upon us. It is so of course also when the human being comes into life — in the germinal and embyonal period. In earlier stages of Earth-evolution the influence was most direct; today it is a kind of echo, inherited from then. Here then again we have an influence, in the other it is indirect, through the raying back of the Sun's light by the Moon. Now think the following. I will again draw it diagrammatically. Suppose the development of the animal were such that it comes into being under the Sun's influence according to this diagram (Fig. 4). This then, to put it simply, would be the ordinary influence of day and night — head and the opposite pole of the creature. This, for the animal, would be the ordinary working of the Sun. Now take that other working of the Sun's light which occurs when the Moon is in opposition, i.e. when it is Full Moon, — when the Sun's light, so to speak works from the opposite side and by reflection counteracts itself. If we conceive this downward arrow (Fig. 5). to represent the direction of the direct Sun-rays, animal formations, we must imagine animal-formation going ever farther in the sense of this direct Sun-ray. The animal would become animal, the more the Sun was working on it. If on the other hand the Moon is counteracting from the opposite direction — or if the Sun itself is doing so via the Moon, — something is taken away again from the animal-becoming process. It is withdrawn, drawn back into itself (Fig. 5a). Precisely this withdrawal corresponds to the shortening of the second branch in Figure 6. We have found a true cosmic counterpart of the characteristic difference between man and animal of which we spoke before. What I have just been telling you can be perceived directly by anyone who gains the faculty for such perception. Man really owes it to the counteracting of the Sunlight via the Moon. — owes it to this that his organisation is withheld from becoming animal. The influence of the Sun-light is weakened in its very own quality (for it is Sun-light in either case), in that the Sun places its own counterpart over against itself, namely the Moon and the Moon's influence. Were it not for the Sun meeting and countering itself in the Moonlight — influences, the tendency that is in us would give us animal form and figure. But the Sun's influence reflected by the Moon counteracts, it. The forming process is held in check, the negative of it is working; the human form and figure is the outcome. Now, on the other branch of the diagram, let us follow up the plant and the plant-formative process. That the Sun is working in the plant, is palpably evident. Let us imagine the Sun's effect in the plant, not to be able to unfold during a certain time. During the Winter, in fact, the springing and sprouting life in the plant cannot unfold. Nay, you can even see the difference in the unfolding of the plant by day and night. Now think of this effect in oft-repeated rhythm, repeated endless times, — what have we then? We have the influence of the Sun and the influence of the Earth itself; the latter when the Sun cannot work directly but is hidden by the Earth. At one time the Sun is working, at another it is not the Sun but the Earth, for the Sun is working from below and the Earth is in the way. We have the rhythmic alternation: Sun-influence predominant, Earth-influence predominant in turn. Plant-nature therefore is alternately exposed to the Sun, and then withdrawn, figuratively speaking, into the Earth — drawn by the earthly, as it were, into itself. This is quite different from what we had before. For in this case the Sun-quality, working in the plant, is potently enhanced. The solar quality is actually enhanced by the earthly, and this enhancement finds expression in that the plant gradually falls into mineralization. Such then is the divergence of two ways, as indicated once again in Figure 6. In the plant we have to recognize the Sun's effect, carried still further by the Earth, to the point of mineralization. In the animal we have to recognize the Sun's effect, which then in man is drawn back again, withdrawn into itself, by virtue of the Moon's effect. I might also draw the figure rather differently, like this (Fig. 6a), — here receding to become human, here on the other hand advancing to become mineral, which of course ought to be shown in some other form. It is no more than a symbolic figure, but this symbolic figure, tends to express more clearly than the first, made of mere lines, the bifurcation — as again I like to call it — with the mineral and plant kingdoms upon the one hand, the human and animal upon the other. We never do justice to the true system of Nature with all her creatures and kingdoms if we imagine them in a straight line. We have to take our start from this other picture. In the last resort, all systems of Nature which begin with the mineral kingdom and thence going on to the plant, thence to the animal and thence to man as if in a straight line, will fail to satisfy. In this quaternary of Nature we are face to face with a more complex inner relationship than a mere rectilinear stream of evolution, or the like, could possibly imply. If one the other hand we take our start from this, the true conception, then we are led, not to a generatic aequivoca or primal generation of life, but to the ideal centre somewhere between animal and plant — a centre not to be found within the physical at all, yet without doubt connected with the problem of three bodies, Earth, Sun and Moon. Though perhaps mathematically you cannot quite lay hold on it, yet you may well conceive a kind of ideal centre-of-gravity of the three bodies — Sun, Moon and Earth. Though this will not precisely solve you the 'problem of three bodies', yet it is solved, namely in Man. When man assimilates in his own nature what is mineral and animal and plant, there is created in him in all reality a kind of ideal point-of-intersection of the three influences. It is inscribed in man, and that is where it is beyond all doubt. Moreover inasmuch as it is so, we must accept the fact that what is thus in man will be empirically at many places at once, for it is there in every human being, — every individual one. Yes, it is there in all men, scattered as they are over the Earth; all of them must be in some relation to Sun and Moon and Earth. If we somehow succeeded in finding an ideal point-of-intersection of the effects of Sun and Moon and Earth, if we could ascertain the movement of this point for every individual human being, it would lead us far indeed towards an understanding of what we may, perhaps, describe as movement, speaking of Sun and Moon and Earth. As I said just now, the problem grows only the more involved, for we have so many points, — as many as there are men on Earth, — for all of which points we have to seek the movement. Yet it might be, might it not, that for the different human beings the movements only seemed to differ, one from another ... We will pursue our conversations on these lines tomorrow.

Astronomy as Compared to Other Sciences

Lecture XIV

https://rsarchive.org/Lectures/GA323/English/LR81/19210114p01.html

Stuttgart

14 Jan 1921

GA323-14

Today I will deal with some of the things that may be causing you difficulty in understanding what we have done hitherto. I will lead over from these difficulties into a realm of ideas which will show up the inadequacy of those lines of thought on which the people of our time, with all their comfortable mental habits, would gladly found their understanding of universal phenomena. We have been studying the universal phenomena in their relation to man. We have done so in manifold directions. Again and again we have indicated how a relationship reveals itself between the forming of man and what appears in the celestial phenomena. Whether we go by some ancient cosmic system of by the Copernican theories in forming our pictured synthesis of the movements of heavenly bodies, we must relate the picture to man in diverse ways of course, accordingly. This we have seen. For a true Science we must accept that there is this relation. Yet the difficulties are formidable. Earlier in these lectures we drew attention to one such difficulty. The moment we try to form ratios between the periods of revolution of the planets of our system we come to incommensurable numbers. Arithmetic runs out, as we might say; we get no farther with it, for where incommensurable numbers enter in there is no palpable unit. Thus, when we look for a synthesis of the phenomena of cosmic space with our accustomed mathematical method and way of thinking, the phenomena themselves are such that we find ourselves driven farther and farther from reality. We may not therefore take for granted that we shall ever be able to explain the cosmic phenomena on the accustomed basis of our Geometry, that is to say, within a rigid three-dimensional space. Nay more, another difficulty has emerged. Yesterday we found ourselves obliged to assume a certain relationship of Sun and Moon and Earth, finding expression in some way in man — in man's very structure. We would fain grasp how the relation is. Yet if we posit this working-together of the Three*, we get into formidable difficulties in spatial calculation. All these things we have mentioned. Now we can reach a certain starting-point at least, through pure Geometry — yet a Geometry of a higher kind. Thence we may gain an idea of where the difficulties come from when we are trying by dint of spatial calculation to grasp the inter-connection of celestial phenomena. Let us recall our precious attempts to comprehend the form of man himself. We are then let to this:- We can and we should try to take seriously that 'memberment' of the human being of which we have also spoken in these lectures. The human head-organization, we may truly say, centring as it does in the nerves-and-senses system, is relatively independent. So is the rhythmic system with all that belongs to it. The metabolic system too, and all that goes with it in the organization three independent systems are revealed. Taking our start now in an intelligent way from the principle of metamorphosis, as we must always do when dealing with organic Nature, we can try to form ideas upon this question: How are the three members of the three-fold human system related to each other, according to this principle of metamorphosis? Understand me rightly, my dear friends. We want to gain an idea-though it be only pictorial to begin with — of how the three members of the human system are related to each other. On the face of it, it will of course be difficult. Such organs as are met with in the human head, it will be difficult to recognise in them at all clearly the metamorphosis of those organs which are fundamental to the metabolic and lymph system. But if we go into the morphology of man deeply enough, we can find our way. We only have to think most thoroughly along the lines already indicated. Namely, the essence of the mutual relation of the long bone to the skull-bone and vice-versa is a complete turning-inside-out. The inner surface of the bone becomes the one turned outward. It is the principle by which you turn a glove inside-out, provided only that the turning-inside-out involves a simultaneous change in the inherent relationships of inner forces. If I should turn a tubular bone or long bone inside-out like a mere glove, I should again get the form of a tubular bone, needless to say. But it will not be so if we take our start, as we must do, from the inherent configuration of the bone. As I described before, in its inherent configuration the long bone is oriented inward towards the radial quality that runs right through it. It is obliged therefore to subject its material structure and arrangement to the radial principle. When I have "flipped" it, so that the inner side opens outside, in its configuration it will no longer follow the radial but the spheroidal principle. The "inner side", now turned outward towards the Sphere, will then receive this form (Fig. 1). What was outside before, is now inside, and vice-versa. Take this into account for the extreme metamorphosis-tubular bone into skull-bone and you will say: The outermost ends of human memberment — lymph-system and skull system — represent opposite poles in man's organization. But we must not think of "opposite poles" in the mere trivial, linear sense of the word. In that we go from one pole to the other, we must adopt the transition which this involves, namely from Radius to surface of a Sphere. Without the help of such ideas and mental pictures, intricate as they may seem, it is quite impossible to gain a just or adequate notion of what the human body is. We come now to what constitutes the middle, in a certain sense, — the middle member of man's organization. This will be all that belongs to the rhythmic system, and it will somehow form the transition from radial structure to spheroidal. In the threefold system thus presented we have the key to the morphological understanding of the entire human organism. Of course we need to realise how it will be. Suppose we have some organ in the metabolic system — the liver for example — or any one of the organs mainly assigned to the metabolism. (We must qualify it with the word 'mainly' for there is always an overlapping and interlocking of these things). Suppose then we begin with such an organ and seek what answers to it in the head. We try to find which of the organs in the head-nature of man m ay be connected with it by the metamorphosis of turning-inside-out. We shall then have to recognise the organ when entirely transformed, de-formed; only by so doing shall we understand it. It will therefore not be easy to take hold of mathematically. Yet without finding some mathematical way of access we shall never adequately grasp it. And if you call to mind (even if you only take this as a picture) — if you call to mind that the real understanding of the human form and figure will lead us out among the movements of celestial bodies, you will divine what must be needful also when we wish to comprehend the latter. For a true synthesis of the phenomena of movement among the heavenly bodies, it will be quite inadequate to think of them as if these movements were accessible to a Geometry that simply reckons with ordinary rigid space and therefore cannot master the turning-inside-out. For when we speak of a turning-inside-out in the way we have been doing, we can no longer be thinking of ordinary space. Ordinary space holds good where we can calculate volumes, cubicle contents in the conventional way. We cannot do so if obliged to make the inner outer. We can no longer go on calculating them with the same conceptions which hold good in ordinary space. If then in thinking of the human form and figure I need the turnings-inside-out, in thinking of the movements of heavenly bodies I shall need them too. I cannot proceed like the current Astronomy which tries to comprehend the celestial phenomena within an ordinary rigid form of space. Take, to begin with, simply the head-organization and the metabolic organization of man. To pass from one to the other you must imagine, once again, a turning-inside-out — and, what is more, one that involves variations of form. Let us at least try to get a picture of the kind of think involved. We did preliminary work in this direction when speaking of the Cassini curves, and of the circle differently conceived. Ordinarily the circle is defined as a curve, all of whose points are equidistant from one central point. We were speaking of the circle as a curve, all of whose points are at measured distances from two fixed points, and so that the quotient of the two distances is constant. This was our other conception of the circle. Speaking of the Cassini curve, we showed that it has three essential forms. One, not unlike an ellipse: — this form arose when the parameters of the curve bore a certain relation, the which we indicated. The second form was the lemniscate. The third form is that while in the idea of it — and also analytically — it is a single entity, to look at it is not. It has two branches (Fig. 2), yet the two branches are one curve. To draw the line, we should somehow have to go out of space, coming back into space again when we draw the second branch. Conceptually, our hand would be drawing a continuous line when drawing the two regions which look separate. We cannot draw the line continuously within ordinary space, and yet conceptually what is here above and what is here below (the inner curve in Figure 2) is a single line. Now as I also mentioned, the same curve can be thought of in another way. You can ask what will be the path of a point which when illumined from a fixed point A appears with constant intensity of illumination, seen from another fixed point B. Answer: a Cassini curve. A curve a Cassini will be the focus of all points through which a point must run, if when illumined from a fixed point A it is seen ever with the same intensity of light from another fixed point B (Fig. 2 again). Now it will not be hard for you to imagine that if something shines from A to C (Fig. 2) and thence by reflection from C to B, the intensity of light will be the same as if reflected from D instead. But it gets rather more difficult to imagine when you come to the Lemniscate. The ordinary geometrical constructions by the laws of reflection and so on, will not be quite so easy to carry through. And it gets still more difficult to imagine with the two-branched curve, that the same intensity of light should always be observed from the point B, inside the one branch of the curve, when the original point-source of light is in A. You would have to imagine (as you pass from the one branch to the other) that the ray of light goes out of space and then shines into space again. You are up against the same difficulty as before, when you were simply asked to draw the two branches as one — with a single sweep of the hand through space. Yet if we do not develop these conceptions we shall be unequal to the other task, namely of finding the transmutation — or even the mere relationship of form — as between any organ in the head of man and the corresponding organ in the metabolism. To find the connection you simply must go out of space. Once again — strange as it may sound — if with your understanding of any form in the human head you wish to make a transition to the understanding of a form in the human metabolic system then you will not be able to remain in space. You must get out of space. You must get right out of yourself , looking for something that is not there in space. You will find something that is as little inside ordinary space as is what intervenes between the upper and lower branches of a two-branched Cassini curve. This is in fact only another way of expressing what was said before that the metamorphosis must be so conceived as to turn the form completely inside out. In thinking thus of the connection between the upper and lower branches of the discontinuous curve of Cassini (as shown in Fig. 3) we are still presupposing actual constants, rigid and unchanged, in the equation. Now if we vary the constants themselves as in an earlier lecture, forming equations of twofold variability, we shall be able to imagine the upper branch say, in this form and the low one in this (Fig. 3). The upper branch will take this form eventually. If then you alter the curve of Cassini by taking variables in place of constants — so that you start with equations instead of starting with invariable constants — you will get two different kinds of branches. Then there will also be the possibility for one of the two branches to come in as it were from the infinite and go out to the infinite again. This is precisely the relationship from which you should take your start when following certain forms within the human head, comprising them in curves and lines, and then relating them to the forms of organs or of complexes of organs in the metabolic system, which in their turn you will comprise in curves and lines. Such is the intricacy of the human form. To make it still less simple, you must imagine the one line (Fig. 3a) with an outward tendency and the other with its tendency turned inward. You will be prone to say (I hope without insisting on it, but as a passing impression): If this be so, the human organization is so complicated that one would almost prefer to do without such understanding and fall back on the ordinary philistine idea of the body, as in the present-day Anatomy and Physiology. There we are not called upon to make such prodigious efforts, as to let mental pictures vanish and yet again not vanish, or turn them inside-out, and all the rest! May be; but then you never really understand the human form; your understanding is, at most, illusionary. Now, to go on: Suppose you thus look into it and recognize that there is something in the human organization which falls right out of space, is not in space at all, but obliges you for instance to imagine spatially separated line-systems, inherently united with each other and yet united by another principle than three dimensional space affords. Thinking in this way, you will no longer be too far removed from what I shall now bring forward. You will at least be able to entertain the thought in a formal sense. No-one, I mean can validly object to thinking it as a pure form of thought. For to begin with, all we are called upon to do is to conceive a clear idea, as in mathematics generally. It cannot be objected that the thing is unproved, or the like. We are only concerned to reach a self-contained and consistent idea. Think therefore for a moment that you had to do not only with ordinary space, conceived in its three dimension, but with a "counter-space" or anti-space". Let me call it so for the moment, and I will try to evoke an idea of it, as follows. Suppose I form the thought of ordinary, three-dimensional, rigid space. I form the first dimension, I form the second dimension and I form the third dimension (Fig. 4). Then I have, so to speak, filled-in in thought — in the idea and mental presentation of it — three-dimensional space with which I am ordinarily confronted. Now as you know, in any such domain you can not only advance up to a certain degree of intensity; you can subtract from it too, and as you go on subtracting — taking away — you come at last to the negation of ti. As you are well aware, there is not only wealth but debt. Likewise I cannot only make the three dimensions to arise in thought but I can also make them vanish. Only I now imagine the arising and vanishing to be a real process, — something hat is really there. Of course it is possible to think only two dimensions instead of three, but that is not my meaning. What I now mean is this: The reason why I only have two dimensions (Fig. 4a) is not that I never had a third. The reason is, I had a third and it has vanished. The two dimensions are an outcome of the coming-into being and vanishing-again of the third. I now have a space, which, though it outwardly shows only two dimensions, must inwardly be conceived as having two third dimensions, one positive and the other negative. The negative dimension springs from a source that can no longer be there in my three-dimensional space at all. Nor must I think of it as a "fourth dimension" in the conventional sense. No, I must think of it as being, to the third dimension, as positive to negative (Fig. 4a once more). And now suppose that what I have been indicating is really there in the Universe; yet, as things generally are in the real world, approximately so. It would then be not a pedantically accurate but an approximate rendering of what I have here drawn. This need not cause you any great surprise, for in outer sense-perceptible reality you never find mathematical figures reproduced in any other way, always approximately. If then I claim that the picture represents something real, you will only expect it to do so in an approximate sense. To represent a reality corresponding to it, I need not repeat exactly the same drawing, but I should have to draw something flattened; that would answer to it. The fact that something has been there and has then vanished, I may perhaps suggest in this way: I will suppose that the density of an effect, indicated by the dark shading, came into being and then partly faded out again, drew weaker (Fig. 5). You are then left with a sphere that has a denser portion in the middle region. I beg you know, compare what is here drawn with the real cosmic system, such as we see it with our eyes, — the cosmic sphere with all the stars widely dispersed, and then the stars more densely packed in the region of the Milky Way, or what we call the Galactic System. Yet you may also compare it with something else. Take any popular star-map. The picture we have shown (Fig. 5a) — let us still take it simply as a picture — is fundamentally equivalent to what is always being shown: the passage of the Sun or of the Earth through the Zodiac, with the with the North and South poles of the ecliptic somewhere out yonder. The idea we have been forming is, as you see, not so very remote from what is there in the outer Universe. In coming lectures we shall of course still have to look for more detailed relations. Now for an understanding of what was said before about the human being we have not yet gone for enough. We must go farther and make the second dimension also vanish; so then we shall be left with only one, — with a straight line. But this is no ordinary straight line drawn into three-dimensional space. It is the line that has remained when we have made the third and also the second dimension vanish. And now we make the last remaining one to vanish. Then we are left with a mere point. Bear in mind however that we have arrived at the point by the successive vanishing of three dimensions. Now let us suppose that this point were to present itself to us in reality, — as having existence in itself. If it is there, and making itself felt, how then shall we imagine its activity? We cannot relate its activity to any point in the space determined by the x-axis. The x-axis is not there, since it has vanished. Nor can we relate it to anything with an x — and a y-coordinate, for all of this has gone; all this has vanished out of space. Nor can we relate it in its activity to the third dimension of space. What then shall we say? When it reveals its activity we shall have to relate it to what is quite outside three-dimensional space. What then shall we say? When it reveals its activity we shall have to relate it to what is quite outside three-dimensional space. Consistently with the procedure we have been through in our thinking, we cannot possibly relate it to anything that could still be included in this space. We can only relate it to what is outside it three-dimensional space altogether. We can relate it neither to "x deleted" nor to "y deleted" not to "z deleted", but only to what deletes all three of them, z, y, and z together, and is therefore into within three-dimensional space at all. We put this forward to begin with as a purely formal, mathematical notion. Yet is soon grows real. It grows exceedingly real when we begin to enter into things more deeply than with the easy-going notions with which Science nowadays would gladly master them. Look, with this deeper tendency of understanding, — look at the process of sight and the whole organisation of the eye. You are perhaps aware (in other lectures I have often spoken of it) of how the eye is not merely to be regarded as a thing formed from within the body outward; for it is largely organized into the body from outside. You an trace the forming of it from without inward by studying the phylogenetic development of lower animals and then considering the act of sight itself. You will contrive to understand how the process of sight is stimulated from without and how the organ too is adapted to this stimulation from without. Then as the process works on inward to the optic nerve and farther in, it vanishes at length, — vanishes as it were into the organisation as a whole. I know you can find the termination of the optic nerves, and yet — this too comes to expression approximately — if you go into the inner organisation you will have to admit that it there vanishes. So much for the process of sight and the associated organs. And now compare with this the process of secretion of the kidneys. Go into it conscientiously. and you will have to relate the duct that leads outward, for the secretion of the kidneys, to what is working from without inward where the eye passes into the optic nerve. If you then look for ideas whereby the two things can be related, so that their mutual relation will help you understand the phenomena of either process, you will find indispensable such forms of thought as we have just been indicating. If you conceive the ideas of three-dimensional space as applying to the process of sight (we might also replace the one by the other, but if you do it in this way. ...), then, if you seek what answers to it in the secretion of the kidneys, you must realize that what is there enacted takes you right out of three-dimensional space. You must go through the same procedure in your thinking as I did just now in extinguishing the spatial dimensions. Otherwise you will not find your way. In like manner you must proceed if you are trying to understand the curves formed in the Heavens by the apparent paths of Venus and Mercury on the one hand, Jupiter and Mars on the other, I mean quite simply the apparent paths as we observe them with our eyes, — the loops and all. If you use polar coordinates for example, then for the loop of Venus you may make the origin of your coordinate system in three-dimensional space. Here you can do so. But you will not come to terms with reality if you adopt the same principle when examining the curve of Mars. In this case you must start from the ideal premise that the origins of any relevant system of polar coordinates will be outside three-dimensional space. You are obliged to take the coordinates in this way. In the former case you may start from the pole of the coordinate system, taking coordinates in the normal way, as in Figure 6. But if you do this for the one planetary curve — say for the path of Venus with its loop — you will do equal justice to the paths of Jupiter or Mars with their loops, only by saying to yourself: This time I will not pre-suppose a polar-coordinate system with an origin such that I always have to add a piece to get the polar-coordinates, as in Figure 6. No, I will take as origin of my polar-coordinate system the encompassing Sphere (Fig. 6a), i.e. what is there behind it, indeterminately far. Then I get such coordinates as these (dotted lines), where in each case, instead of adding, I must leave so much out. The curve I then obtain also has something like a centre, but the centre is in the infinite sphere. It might prove necessary then, for more profound research into the paths of the planets, that we make use of this idea: In constituting the paths of the inner planets we must indeed attribute to these paths some centre or other within ordinary space. But if we want to think of centres for the path of Jupiter, the path of Mars and so on, we must go right outside this ordinary space. In fine, we have to overcome space; we must transcend it . There is no help for it. If you are conscientious in your efforts to comprehend the phenomena, the mere ideas of three-dimensional space will not suffice you. You must envisage the interplay of two kinds of space. One of them, with the ordinary three dimensions, may be conceived as issuing radially from a central point. The other, which is all the time annulling and extinguishing the first, may not be thought of as issuing from a point at all. It must be thought of as issuing from the encompassing Sphere — that is, the Sphere infinitely far away. While in the former case the "point" is of zero areas which it turns outward, and a point with the area of an infinite spherical surface which it turns inward. Geometrically it may suffice to conceive the notion of a point abstractly. In the realm of reality it will not. We shall not do justice to reality with the mere notion of an abstract point. In every instance we must ask whether the point we are conceiving has its curvature turned inward or outward; its field of influence will be according to this. But you must think still farther, my dear friends; there is a another thing. Of course you may imagine that you had somewhere caught this point which is really a Sphere. To begin with, since it is in the infinite far spaces you need not imagine it just here (s, Fig. 7). You can equally well imagine it a little farther out, (b, or c). You can imagine it to be anywhere out there; you only have to leave this sphere free (strongly drawn sphere in Fig. 7). For this is hollowed out, so to speak; this is the inverted circle or the inverted sphere, if you like. But now suppose the following might be the case. Think of what is within this peculiar circle (namely at a, b, c, etc,) Think of this point that has its curvature turned inward. For in effect, the entire space outside this spherical surface is then a point with its curvature turned inward. And now imagine that this space had, after all, its limit somewhere. You might be able to go far away out, — very far. Suppose however the reality were such that you could not just go anywhere, but somewhere after all there was a limit of quite another kind (dotted circle in Figure7). What there would appear, as if by inner necessity, what in effect belongs to the realm beyond the limit. An equivalent sphere would have to arise within, belonging to what is there outside. You would then have to realize: Out there, beyond a certain sphere, something is still existing, it is true, but if I want to see it I must look in here (P), for here it re-appears. The continuation of what is faraway out there make itself felt in here. What I am looking for as I go out into infinite distances, makes its appearance within, and becomes manifest to me from this centre. These are the kind of ideas you should develop to an adequate extent. In a formal sense they look sound enough. As forms of thought there can surely be no objection to them. Truly remarkable results will be obtained however, if with their help you try to penetrate outer reality. Think for example that there might be a phenomenon in celestial space, — we may call it "Moon" to begin with, — yet this phenomenon were not to be understood simply by saying: "This Moon is a body, here is its central point; we will investigate it on the understanding that it is a body and that its central point is here." Assume (and please forgive my saying, I put it euphemistically) assume that this way of thinking did not fit the reality, but that I ought to express it quite differently. I ought rather to say: "If I, in my Universe, start from a certain point and go farther and farther out, I come at length to where I shall no longer find heavenly bodies. Yet neither shall I find a mere empty Euclidean space. No, I shall find something, the inherent reality of which obliges me to recognize the continuation of it here (at P)." I should then be obliged to conceive the space contained within the Moon as a portion of the entire Universe with the exception of all that exists by way of stars, etc., outside the Moon. I should have to think on the one hand of all the stars here are in cosmic space. These, I am now assuming I have to treat in one way, according to a single principle; but the inside of the Moon — the space contained within the Moon — could not be treated in this way. It would require me to think as follows: There on the one hand I go out into the far spaces. Somewhere out there, I presume, is the celestial Sphere. Though it be only the "apparent" Sphere to begin with; something effective, something real must be conceived to underlie it. Yet whatsoever realities I find out there, the space within the spherical surface of the Moon has nothing whatever to do with it. It only has to do with what begins where the stars come to an end. It is a fragment, in some strange way, belonging not to my Universe but to that Universe to which all the stars do not belong. If there is such a thing within a Universe, it is a thing inserted in this Universe, occluded as it were, — thing of altogether different nature and revealing different inner properties from all that is there around it. And we may then compare the relation of such Moon to its surrounding Heavens with the relation which obtains for instance between the secretions of the kidneys — with the organic structure that underlies them — and on the other hand the structure and functioning of the eyes. From this we shall proceed tomorrow. It is not due to me that I must try to form, and to acquaint you with, such complicated notions of how the Universe is built. Truth is, equipped with any other notions you will not make headway, save on the convention: "Let us comprise the phenomena with our given range of ideas, and if we come to a limit somewhere, well then we do, and we go no further". Ascribe it then to the reality and not to any craving for remote ideas, if in the effort to impart an understanding of how the Universe is built I have unfolded complicated notions.

Astronomy as Compared to Other Sciences

Lecture XV

https://rsarchive.org/Lectures/GA323/English/LR81/19210115p01.html

Stuttgart

15 Jan 1921

GA323-15

What we are doing, as you will have seen, is to bring together the diverse elements by means of which in the last resort we shall be able to determine the forms of movement of the heavenly bodies, and — in addition to the forms of movement — what may perhaps be described as their mutual positions. A comprehensive view of our system of heavenly bodies will only be gained when we are able to determine first the curve-forms (inasmuch as forms of movement are called curves), i.e. the true geometrical figures, and then the centres of observation. Such is the task before us along our present lines of study, which I have formed as I have done for very definite reasons. The greatest errors that are made in scientific life consist in this: they try to make syntheses and comprehensive theories when they have not yet established the conditions of true synthesis. They are impatient to set up theories — to gain a conclusive view of the thing in question, — they do not want to wait till the conditions are fulfilled, subject to which alone theories can properly be made. Our scientific life and practice needs this infusion badly, — needs to acquire a feeling of the fact that you ought not to try and answer questions when the conditions for an intelligent answer are not yet achieved. I know that many people (present company of course excepted) would be better pleased if one presented them with curves all ready made, for planetary or other movements. For they would then be in possession of tangible answers. What they are asking is in effect to be told how such and such things are in the Universe, in terms of the ideas and concepts they already have. What if the real questions are such as cannot be answered at all with the existing ideas and concepts? In that case, theoretic talk will be to no purpose. One's question may be set at rest, but the satisfaction is illusionary. Hence, in respect to scientific education, I have attempted to form these lectures as I have done. The results we have gained so far have shown that we must make careful distinctions if we wish to find true forms of curves for the celestial movements. Such things as these, for instance, we must differentiate: the apparent movements seen in the paths of Venus and of Mars respectively, — Venus making a loop when in conjunction, Mars when in opposition to the Sun. We came to this conclusion when trying to perceive how diverse are the forms of curves that arise in man himself through the forces that build and form him. We ascertained quite different forms of curve in the region of the head-nature and in the organization of the metabolism and the limbs. The two types of form are none the less related, but the transition from one to the other must be sought for outside of space, — at least beyond the bounds of rigid Euclidean space. Then comes a further transition, which still remains for us to find. We have to pass from what we thus discover in our own human frame, to what is there outside in Universal Space, which only looks to us plainly Euclidean. We think it nicely there, a rigid space, but that is mere appearance. As to this question, we only gain an answer by persevering with the same method we have so far developed. Namely we have to seek the real connection of what goes on in man himself and what goes on outside in Universal Space, in the movements of the celestial bodies. Then we are bound to put this fundamental question: What relation is there, as to cognition itself, between those movements that may legitimately be considered relative and those that may not? We know that amid the forming and shaping forces of the human body we have two kinds: those that work radially and those which we must think of as working spherically. The question now is, with regard to outer movements: How, with our human cognition do we apprehend that element of movement which takes its course purely within the Sphere, and how do we apprehend that element which takes its course along the Radius? A beginning has been made in Science as you know, even experimentally, in respect of these two kinds of spatial movement. The movements of a heavenly body upon the Sphere can of course be seen and traced visually. Spectrum analysis however also enables us to detect those movements that are along the line of sight, spectrum analysis enables us to recognise the fact. Interesting results have for example been arrived at with double stars that move around each other. The movement was only recognizable by tackling the problem with the help of Doppler's principle, — that is the experimental method to which I am referring. For us, the question now is whether the method which includes man in the whole cosmic system will give us any criterion — I express myself with caution — any criterion to tell whether a movement may perhaps only be apparent or whether we must conclude that it is real. Is there anything to indicate that a given movement must be a real one? I have already spoken of this. We must distinguish between movements that may quite well be merely relative and on the other hand such movements as the “rotating, shearing and deforming movements” (so we described them), the very character of which will indicate that they cannot be taken in a merely relative sense. We must look for a criterion of true movement. We shall gain it in no other way than by envisaging the inner conditions of what is moving. We cannot possibly confine ourselves to the mere outer relations of position. A trite example I have often given is of two men whom I see side by side at 9 am and again at 3 in the afternoon. The only difference is, one of them stayed there while the other went on an errand lasting six hours. I was away in the meantime and did not see what happened. At 3 pm I see them side by side again. Merely observing where they are outwardly in space, will never tell me the true fact. Only by seeing that one is more tired than the other — taking account of an inner condition therefore — shall I be able to tell, which of them has been moving. This is the point. If we would characterize any movement as an inherent and not a merely relative movement, we must perceive what the thing moved has undergone in some more inward sense. For this, a further factor will be needed, of which tomorrow. Today we will at least approach the problem. We must in fact get hold of it from quite another angle. If we in our time study the form and formation of the human body and look for some connection with what is there in cosmic space, the most we can do to begin with is in some outward sense to see that the connection is there. Man is today very largely independent of the movements of cosmic space; everything points to the fact that this is so. For all that comes to expression in his immediate experience, man has emancipated himself from the phenomena of the Universe. We therefore have to look back into the time when what he underwent depended less upon his conscious life of soul than in his ordinary, by which I mean, post-natal life on Earth. We must look back into the time when he was an embryo. In the embryo the forming and development of man does indeed take place in harmony with cosmic forces. What afterwards remains is only what is carried forward, so to speak. Implanted in the whole human organization during the embryonal life it then persists. We cannot say it is "inherited" in the customary sense, for in fact nothing is inherited, but we must think of some such process, where entities derived from an earlier period of development stay on. We must now look for an answer to the question: Is there still anything in the ordinary life we lead after our birth — after full consciousness has been attained — is there still any hint of our connection with the cosmic forces? Let us consider the human alternation of waking and sleeping. Even the civilized man of today still has to let this alternation happen. In its main periodicity, if he would stay in good health, it still has to follow the natural alternation of day and night. Yet as you know very well, man of today does lift if out of its natural course. In city life we no longer make it coincide with Nature. Only the country folk do so still. Nay, just because they do so, their state of soul is different. They sleep at night and wake by day. When days are longer and nights shorter they sleep less; when nights are longer the sleep longer. These aspects however can at most lead to vague comparisons; no clear perception can be derived from them. To recognize how the great cosmic conditions interpenetrate the subjective conditions of man, we must go into the question more deeply. So shall we find in the inner life of man some indication of what are absolute movements in the great Universe. I will now draw your attention to something you can very well observe if only you are prepared to extend your observation to wider fields. Namely, however easily man may emancipate himself from the Universe in the alternation of sleeping and waking as regards time, he cannot with impunity emancipate himself as regards spatial position. Sophisticated folk — for such there are — may turn night into day, day into night, but even they, when they do go to sleep, must adopt a position other than the upright one of waking life. They must, as it were, bring the line of their spine into the same direction as the animal's. One might investigate a thing like this in greater detail. For instance, it is a physiological fact that there are people who in conditions of illness cannot sleep properly when horizontal but have to sit more upright. Precisely these deviations from the normal association of sleep with the horizontal posture will help to indicate the underlying law. A careful study of these exceptions — due as they are to more or less palpable diseases (as in the case of asthmatic subjects for example) — will be indicative of the true laws in the domain. Taking the facts together, you can quite truly put it in this way: To go to sleep, man must adopt a position whereby his life is enabled in some respects to take a similar course, while he is sleeping, to that of animal life. You will find further confirmation in a careful study of those animals whose spinal axis is not exactly parallel to the Earth's surface. Here again I can only give you guiding lines. For the most part, these things have not been studied in detail; the facts have not been looked at in this manner, or not exhaustively. I know they have never been gone into thoroughly. The necessary researches have not been undertaken. And now another thing: You know that what is trivially called “fatigue” represents a highly complex sequence of events. It can come about by our moving deliberately. When we move deliberately, we move our centre of gravity in a direction paralleled to the surface of the Earth. In a sense, we move about a surface parallel to the Earth's surface. The process which accompanies our outward and deliberate movements takes its course in such a surface. Now here again we can discover what belongs together. On the one hand we have our movement and mobility parallel to the surface of the earth, and our fatigue, — becoming tired. Now we go further in our line of thought. This movement parallel to the surface of the Earth, finding its symptomatic expression in fatigue, involves a metabolic process — an expenditure of metabolism. Underlying the horizontal movement there is therefore a recognizable inner process in the human body. Now the human being is so constituted that he cannot well do without such movement — including all the concomitant phenomena, the metabolic expenditure of substance and so on. He needs all this for bodily well-being. If you're a postman, your calling sees to it that you move about horizontally; if you are not a postman you take a walk. Hence the relationship, highly significant for Economics, between the use and value of that mobility of man which enters into economic life and that which stays outside it — as in athletics, games and the like. Physiological and economic aspects meet in reality. In my critique of the economic concept of Labour, you may remember I have often mentioned this. It is at this point that the relation emerges between a purely social science and the science of physiology, nor can we truly study economics if we disregard it. For us however at the present moment, the important thing is to observe this parallelism of movement in a horizontal surface with a certain kind of metabolic process. Now the same metabolic process can also be looked for along another line. We think once more of the alternation of sleeping and waking. But there is this essential difference. The metabolic transformation, when it takes place with our deliberate movements, makes itself felt at once as an external process, even apart from what goes on inside the human being. If I may put it so, something is then going on, for which the surface of the human body is no exclusive frontier. Substance is being transformed, yet so that the transformation takes place as it were in the absolute; the importance of it is not only for the inside of man's body. (The world “absolute” must of course again be taken relatively!) That we get tired is, as I said, a symptomatic concomitant of movement and of the metabolic process it involves. Yet we also get tired if we have only lived the life-long day while doing nothing. Therefore the same entities which are at work when we move about with a will, are also at work in the human being in his daily life simply by virtue of his internal organization. The metabolic transformation must also be taking place when we just get tired, without our bringing it about by any deliberate action. We put ourselves into the horizontal posture so as to bring about the same metabolism which takes place when we are not acting deliberately, — which takes place simply with the lapse of time, if I may so express it. We put ourselves into the horizontal posture during sleep, so that in this horizontal position our body may be able to carry out what it also carries out when we are moving deliberately in waking life. You see from this that the horizontal position as such is of great significance. It is not a matter of indifference, whether or not we get into this position. To let our inner organism carry out a certain process without our doing anything to the purpose, we must bring ourselves into the horizontal position in which there happens in our body something that also happens when we are moving by our deliberate will. A movement must therefore be going on in our body, which we do not bring about by our deliberate will. A movement which we do not bring about by our deliberate will must be of significance for our body. Try to observe and interpret the given facts and you will come to the following conclusion, although again — for lack of time — in saying this I must leave out many connecting links. Human movement, as we said just now, involves an absolute metabolic process or change of substance, so that what then goes on in our metabolism has, so to speak, real chemical or physical significance, for which the limits of our skin are in some sense non-existent; — so that the human being in this process belongs to the whole Cosmos. And now the very same metabolic change of substance is brought about in sleep, only that then its significance remains inside the human body. The change of substance that takes place in our deliberate movement takes place also in our sleep, but the outcome of it is then carried from one part of our body to another. During sleep, in effect, we are supplying our own head. We are then carrying out or rather, letting the inside of our body carry out for us — a metabolic process of transformation for which the human skin is an effective frontier. The transmutation so takes place that the final process to which it leads has its significance within the bodily organization of man. Once more then, we may truly say: We move of our own will, and a metabolic process (a transformation of substance) is taking place. We let the Cosmos move us; a transformation of substance is taking place once more. But the latter process goes on in such a way that the outcome of it — which in the former metabolic process takes its course, so to speak, in the external world — turns inward to make itself felt as such within the human head. It turns back and does not go flowing outward and away. Yet to enable it to turn back, nay to enable it to be there at all, we have to bring ourselves into the horizontal posture. We must therefore study the connection between those processes in the human body that take place when we move deliberately and those that take place when we are sleeping. And from the very fact that we are obliged to do this at a certain stage of our present studies, you may divine how much is implied when in the general Anthroposophical lectures I emphasize — as indeed I must do, time and gain, — that our life of will, bound as it is to our metabolism, is to our life of thought and indeation even as sleeping is to waking. In the unfolding of our will, as I have said again and again, we are always asleep. Here now you have the more exact determination of it. Moving of his own will and in a horizontal surface, man does precisely the same as in sleep. He sleeps by virtue of his will. Sleep, and deliberate or wilful movement, are in this relation. When we are sleeping in the horizontal posture, only the outcome is different. Namely, what scatters and is dispersed in the external world when we are moving deliberately, is received and assimilated, made further use of, by our own head-organisation when we are asleep. We have then these two processes, clearly to be distinguished from one another: — the outward dispersal of the metabolic process when we move about deliberately in day-waking life, and the inward assimilation of the metabolic process by all that happens in our head when we are sleeping. And if we now relate this to the animal kingdom, we may divine how much it signifies that the animal spends its whole life in the horizontal posture. This turning-inward of the metabolism to provide the head must be quite different in the animal. Also deliberate movement must be quite different in the animal from what it is in man. This is the kind of thing so much neglected in the Science of today. They only speak of what presents itself externally, failing to see that the same external process may stand for something different in the one creature and in the other. For example — quite apart now from any religious implication — man dies and the animal dies. It does not follow that this is psychologically the same in either case. A scientist who takes it to be the same and bases his research on this assumption is like a man who would pick up a razor and declare: This is a kind of knife, therefore the same function as any other knife; so I will use it to cut my dumpling. Put on this simple level, you may answer: No-one would be so silly. Yet have a care, for this is just what happens in the most advanced researches. This then is what we are led to see. In our deliberate movements we have a process finding its characteristic expression in curves that run parallel to the surface of the Earth; we cannot but make curves of this direction. What have we taken as fundamental now, in this whole line of thought? We began with an inner process which takes its course in man. In sleep this is the given thing, yet on the other hand we ourselves bring a like process about by our own action. Through what we do ourselves, we can therefore define the other. The possibility is given, logically. What is done to our bodily nature from out of cosmic space when are sleeping, this we can treat as the thing to be defined, — the nature of which we seek to know. And we can use as the defining concept what we ourselves do in the outer world — what is therefore well-known to as to its spatial relations. This is the kind of thing we have to look for altogether, in scientific method: Not to define phenomena by means of abstract concepts, but to define phenomena by means of other phenomena. Of course it presupposes that we do really understand the phenomena in question, for only then can we define them by one-another. This characteristic of Anthroposophical scientific endeavour. It seeks to reach a true Phenomenalism, — to explain phenomena by phenomena instead of making abstract concepts to explain them. Nor does it want a mere blunt description of phenomena, leaving them just as they are in the chance distributions of empirical fact and circumstance, where they may long be standing side by side without explaining one-another. I may digress a moment at this point, to indicate the far-reaching possibilities of this “phenomenological” direction in research. The empirical data are at hand, for us to reach the right idea. There is enough and to spare to empirical data. What we are lacking in is quite another thing, namely the power to synthesize them, — in other words, to explain one phenomenon by another. Once more, we have to understand the phenomena before w can explain them by each other. Hence we must first have the will to proceed as we are now trying to do, — to learn to penetrate the phenomenon before us. This is so often neglected. In our Research Institute we shall not want to go on experimenting in the first place with the old ways and methods, which have produced enough and to spare of empirical data. (I speak here not from the point of view of technical applications but of the inner synthesis which is needed.) There is no call for us to go on experimenting in the old ways. As I said in the lectures on Heat last winter, we have to arrange experiments in quite new ways. We need not only the usual instruments from the optical instrument makers; we must devise our own, so as to get quite different kinds of experiments, in which phenomena are so presented that the one sheds light on the other. Hence we shall have to work from the bottom upward. If we do so, we shall find an abundance of material for fresh enlightenment. With the existing instruments our contemporaries can do all that is necessary; they have acquired admirable skill in using them in their one-sided way. We need experiments along new lines, as you must see, for with the old kind of experiment we should never get beyond certain limits. Nor on the other hand will it do for us merely to take our start from the old results and then indulge in speculation. Again and again we need fresh experimental results, to bring us back to the facts when we have gone too far afield. We must be always ready to find ways of means, when we have reached a certain point in our experimental researches, not just to go on theorising but to pass on to some fresh observation which will help elucidate the former one. Otherwise we shall not get beyond certain limits, transient though they are, in the development of Science. I will here draw attention to one such limit, which, though not felt to be insurmountable by our contemporaries, will in fact only be surmounted when fresh kinds of experiment are made. I mean the problem of the constitution of the Sun. Careful and conscientious observations have of course been made by all the scientific methods hitherto available, and with this outcome: First they distinguish the inner most part of the Sun; what it is, is quite unclear to them. They call it the solar nucleus, but none can tell us what it is; the methods of research do not reach thus far. To say this is no unfriendly criticism; everyone admits it. They then suppose the Sun's nucleus to be surrounded by the so-called photo-sphere, the atmosphere, the chromosphere and the corona. From the photosphere onward they begin to have definite ideas abut it. Thus they are able to form some idea about the atmosphere, the chromosphere. Suppose for instance that they are trying to imagine how Sun-spots arise. Incidentally, this strange phenomenon does not happen quite at random; it shows a certain rhythm, with maxima and minima in periods of about eleven years. Examine the Sun-spot phenomena, and you will find they must in some way be related to processes that take place outside the actual body of the Sun. In trying to imagine what these processes are like, our scientists are apt to speak of explosions or analogous conditions. The point is that when thinking in this way they always take their start from premisses derived from the earthly field. Indeed, this is almost bound to be so if one has not first made the effort to widen out one's range of concepts, — as we did for instance when we imagined curves going out of space. If one has not done something of this kind for one' s own inner training, one has no other possibility than to interpret on the analogy of earthly conditions such observations as are available of a celestial body that is far beyond this earthly world. Nay, what could be more natural — with the existing range of thought — than to imagine the processes of the solar life analogous to the terrestial, but for the obvious modifications. Yet in so doing one soon encounters almost insuperable obstacles. That which is commonly thought of as the physical constitution of the Sun can never really be understood with the ideas we derive from earthly life. We must of course begin with the results of simple observation, which are indeed eloquent up to a point; then however we must try to penetrate them with ideas that are true to their real nature. And in this effort we shall have to come to terms with a principle which I may characterize as follows. It is so, is it not? Given some outer fact or distribution which we are able thoroughly to illumina with a truth of pre Geometry we say to ourselves: how well it fits: we build it up purely by geometrical thinking and now the outer reality accords with it. It hinges-in, so to speak. We feel more at one with outer reality when we thus find again and recognize what we ourselves first constructed, (yet the delight of it should not be carried too far. Somehow or other, one must admit, it always “hinges-in” even for those theorists who get a little unhinged themselves in the process: They too are always finding the ideas they first developed in their mind in excellent agreement with the external reality. The principle is valid, none the less.) The following attempt must now be made. We may begin by imagining some process that takes place in earthly life. We follow the direction of it outward from some central point. It takes its course therefore in a radial direction. It may be a kind of outbreak, such for example as a volcanic eruption, or the tendency of deformation in an earthquake or the like. We follow such a process upon Earth in the direction of a line that goes outward from the given centre. And now in contrast to this you may conceive the inside of the Sun, as we are want to call it, to be of such a nature that its phenomena are not thrust outward from the centre, but on the contrary; they take their course from the corona inward, via the chromosphere, atmosphere and photosphere, — not from within outward therefore, but from without inward. You are to conceive , once more, — if this (Fig. 2) is the photosphere, this the atmosphere, this the chromosphere and this the corona, — that the processes go inward and, so to speak, gradually lose themselves towards the central point to which they tend just as phenomena that issue from the Earth lose themselves outward in expanding spheres, into the wide expanse. You will thus gain a mental picture which will enable you to bring some kind of synthesis and order into the empirical results. Speaking more concretely, you would have to say: If causes on the Earth are such as to bring about the upward outbreak for example of an active crater, the cause on the Sun will be such that if there is anything analogous to such an outbreak, it will happen from without inward. The whole nature of the phenomenon holds it together in quite another way. While on the Earth it tends apart, dispersing far and wide, here this will tend together, striving towards the centre. You see, then what is necessary. First you must penetrate the phenomena and understand them truly. Only then can you explain them by one-another. And only when we enter thus into the qualitative aspect, — only when we are prepared, in the widest sense of the word, to unfold a kind of qualitative mathematics, — shall we make essential progress. Of this we shall speak more tomorrow. Here I should only like to add that there is a possibility, notably for pure mathematicians, to find the transition to a qualitative mathematics. Indeed this possibility is there in a high degree, especially in our time. We need only consider Analytical Geometry, with all its manifold results, in relation to Synthetic Geometry — to the real inner experience of Projective Geometry. True, this will only give us the beginning, but it is a very, very good beginning. You will be able to confirm this if you once begin along this pathway, — if for example you really enter into the thought and make it clear to yourself that a line has not two infinitely distant points (one in the one and one in the opposite direction) but only one, — fact of which there is no doubt. You will then find truer and more realistic concepts in this field, and from this starting-point you will find your way into a qualitative form of mathematics. This will enable you to conceive the polarities of Nature no longer merely in the sense of outwardly opposite directions, where all the time the inner quality would be the same; whereas in fact the inner quality, the inner sense and direction, is not the same. The phenomena at the anode and the cathode for example have not the same inner direction; an inherent difference underlies them, and to discover what the difference is, we must take this pathway. We must not allow ourselves to think of a real line as though it had two ends. We should be clear in our mind that a real line in its totality must be conceived not with two ends but with one. Simple by virtue of the real conditions, the other end goes on into a continuation, which must be somewhere. Please do not underestimate the scope and bearing of these lines of thought. For they lead deep into many a riddle of Nature, which, when approached without such preparation, will after all only be taken in such a way that our thoughts remain outside the phenomena and fail to penetrate.

Astronomy as Compared to Other Sciences

Lecture XVI

https://rsarchive.org/Lectures/GA323/English/LR81/19210116p01.html

Stuttgart

16 Jan 1921

GA323-16

May I first refer to a matter from which misunderstandings might arise in future if some of you are thinking further along the lines we have been indicating. 1 The beginning of this lecture arose out of a mistaken remark by one of those present, which is omitted. Dr. Steiner's explanations, important for a general understanding of the lemniscatory curves, are reproduced apart from this. This is essential: You must imagine the plane in which I am drawing the Lemniscate (Fig. 1) to be rotating about the Lemniscate axis, ie. about the line joining the two foci, — call it what you will. I should therefore have to draw the Lemniscate in space. This (Fig. 1) is the projection of it. Such is the drawing of the Lemniscate which you must have in mind with regard to all that I have been saying, — so for example when you are tracing the bony system or the nervous system in man. Even the blood-circulation can be traced in this way. You must imagine it all, not in a plane but in space. The figure eight — the Lemniscate — is therefore legitimate, but as I said before, you are really dealing with geometrical figures of rotation. This also underlies what I have just been saying. The forms of our inner organisation, in the nerves-and-senses system and in the metabolic and limb-system respectively, are mutually related upon the principle of a lemniscate of rotation. We were obliged to seek the criterion of the true spatial movements of our Earth in changes that go on in man himself. We human beings are, after all, in some way spatially united with the Earth. So long as we merely look at the movements from outside, — then, as I said before, we never get beyond the relativity of movements. If we ourselves however are taking part in the movements and by so doing we perceive internal changes in the moving body, then in these inner changes we can, as it were, read the movements and know them to be real. This is the thing that matters. We pointed out that in the processes of human metabolism we have an inner criterion of man's deliberate movement, wherein he may be said to move his centre of gravity parallel to the surface of the Earth. Then there are processes very similar to these metabolic processes, which accompany our deliberate movements. They give us a criterion of a true movement which we undoubtedly describe in cosmic space together with the Earth. I referred to the phenomena of fatigue occurring in the course of the day, — i.e. while the Sun changes its position in the heavens. We may formulate it thus: — That which takes place between the head and the rest of man in a vertical direction when man is upright, takes place in a direction parallel to the surface of the Earth — that is, in the direction characteristics of the animal spine — when man is sleeping. Comparing human metabolism in sleeping and in waking respectively, we have indeed a kind of reagent for the relations of movement of Sun and Earth. Thence we can now pass on to the other kingdoms of Nature. We see the plant, maintaining a radial direction, — the same direction we human beings have in waking life. We must be clear however, when comparing our own vertical direction with that of plant growth, that it is not permissible to think of them with the same sign. We must give opposite signs to the two. Many are the compelling reasons for us to do this: to give to man's vertical direction the opposite sign to that of plant growth. I will refer only to one such reason, mentioned before. The process of plant growth, culminating as it does in the organic deposition of carbon, is so to speak cancelled-out in man: It must, as it were, be negatived. The very thing the plant consolidates into itself, man must get rid of. This and other considerations will oblige us, if we put the direction of plant-growth from year to year, so long as we are growing. It represents therefore, a process in us, similar to that in the plant. Hence, my dear Friends, we only find our way alright if we think thus: The plant grows radially upward from the Earth, up onto cosmic space. Ourselves we must imagine in a different way. There is our physically visible growth, but we must think of something super-physical, invisible, growing down to meet it — growing into us as it were, from above downward. Herein we have to seek an understanding of the human form, — its vertical direction. We must imagine that while man no doubt grows upward, a kind of invisible plant-formation grows down to meet him. It is a plant-form with its roots unfolding up towards the head and its flowers downward. It is a negative plant-forming process, opposite to the man-forming process. In this sense we must recognize, which movements are alike in kind. As the plant grows away from the Earth, so have we to imagine this super-physical man-plant growing in from cosmic space, even from the Sun, towards the centre of the Earth. This then is what we have. (I say again, I can only indicate general directions: you will be able to follow them up in the light of empirical phenomena) In what we here see (Fig. 2) as a line of like direction — a line of growth, but in the one case striving positively outward, in the other negatively back and downward — in this we have to seek the connecting line of Earth and Sun. You cannot think of it in any other way. Nay, to imagine it thus is comparatively simple, even trivial. You will perceive in this very line the line of movement both of Earth and Sun. The lines of movement both of Earth and Sun are to be looked for in the line that joins the two. Moreover, the line will always prove to be vertical in relation to the surface of the Earth. What I have here been putting forward ought really to be the theme of many lectures. I do however still want to give you something more substantial as it were, for you to get to grips with. I want to lead you to a more tangible result, though it will have to follow rather abruptly on the more methodical reflections we have hitherto pursued. We have been led to realize that Earth and Sun must be thought of as moving in a certain sense in the identical orbit and yet again in a way opposite to one another. You will get a more substantial line of what this means if you recall what was said yesterday. The constitution of the Sun, I said, — with the Sun's nucleus and then the photosphere, atmosphere, chromosphere and corona — can be imagined in no other way than this: While on the Earth craters are formed by outward thrusts and movements, and we think therefore of processes that work from within outward (fundamentally the same is true even of the tides); in the Sun on the contrary we have to go from without inward. The Sun releases its streams and currents from the surrounding periphery inward to the interior, to the solar nucleus. In a sense therefore, we see what is going on the Sun's environment as we should see things going on Earth if we were situated in the Earth's centre and looking outward, — only we should then have bank the convex into the concave. Looking into the Sun, it is as though we should be witnessing earthly processes from the Earth's centre; only for this comparison the Earth's inner surface which is concave must be bent convex, so that the interior of the Earth becomes the exterior of the Sun. Taking your start from this idea you will be able to realize the polar-opposite character of Earth and Sun. This too is most important: to realize how the Sun' s constitution derives from the Earth's once more by a turning inside-out, — by the same process I explained for the relation of the human metabolic and limb-system with the skull-bone. The coordination of Man and the Cosmos is the more thoroughly revealed. The polarity in man is in its inner quality and process like the polarity of Sun and Earth. I shall now pursue a line of thought which may look problematical to some of you, yet you would feel it to be thoroughly sound if we had time to go into all the connecting links. However as I said just now, I want to give you something more substantial. We have to look for a curve which makes it possible or us to imagine the movements of Sun and Earth taking their course in one and the same path and yet in some sense contrariwise. The curve can be determined, unambiguously. If you envisage all the relevant geometrical positions which are to be found in this way, the curve, I say again, will be uniquely determined. You must imagine it like this (Fig. 3), — a rotating lemniscate which at the same time moves on through space, resulting in a lemniscatory screw of spiral (as indicated in the Figure). Imagine the Earth to be at some point of this curve and the Sun at another, with the Earth following the Sun in movement. So then you have the movement of the Earth up here, the Sun down here. They go past each other. Taking all the valid criteria into account, this is the only way to conceive the real underlying movements both of the Earth and of the Sun. There is no other alternative than to imagine it arising on this basis: Earth and Sun are moving, following one another, along a lemniscatory spiral; what is projected into space arises out of this. Here is the line of sight (ES, Fig. 3). You are projecting the Sun in this position (S); thereafter, you may assume, the Sun has gone up here (S 1 ). You get the apparent position, including all the relevant and necessary factors, simply as the resulting projection when Earth and Sun move past each other along this line. But I repeat, you must include the manifold corrections, — the Bessel equations and so on, — if you expect your calculation to come true. You must include in the geometrical loci all that is really given. So too you must take into account what I mentioned before, how the Astronomy of today uses three Suns in its calculations: the real Sun, the Dynamical Mean Sun and the Astronomical Mean Sun. Two of them are of course imaginary; only the real Sun is actually there. For our determination of Time however, we reckon first with the Dynamical Mean Sun which coincides with the true Sun at perigee and apogee and no-where else. And then we have the third Sun which only coincides with the other at the equinoxes. You only need correct, according to all this, the accepted notion of the Sun's apparent path. Take all of this together and work it out; then you will certainly get this result, — in full agreement with what we also found observing Man's relation to the Cosmos. We now need to relate this curve in the right way to our solar system. I will begin by drawing the ordinary hypothetical form of solar system (Fig. 4), omitting the two outermost planets for today, for they are not essential in this connection. Here (disregarding the relative measures) are the orbit of Saturn, the orbit of Jupiter, the orbit of Mars, the orbit of the Earth with the Moon, the orbit of Venus, the orbit of Mercury, and the Sun. Somewhere along these orbits we should then find the respective planets. Let us assume to begin with what this is a valid perspective from some aspect or other. The question then is how the path of Sun and Earth as we have now described it fits in with this picture. Work out the calculation in the way indicated and you will find that it fits in as follows. We have to draw the path of the Earth with the Earth tending in a sense, towards the place where the Sun has been, and then again the Sun towards the place where the Earth has been. We thus get the one self of the Lemniscate — Earth, Sun, Earth, Sun. When this has been gone round, then it goes on (Fig. 5). They move past each other, as you see. Thus we obtain the true path of Earth and Sun if we alternately imagine the Earth to be at the place where in our usual drawings we are wont to put the Sun, and the Sun at the place where we are wont to put the Earth. The fact is, we do not get the true relation of movement as between Earth and Sun if we assume either the one or the other to be at rest. We must imagine both to be in movement, whereby the one follows the other, yet at the same time they go past each other. So then we have to picture it. Seen in perspective, the Sun is alternately in the middle point of our planetary system and then again the Earth is where we normally conceive the Sun to be. They change places, taking turns as it were. But it is complicated, for in the meantime the planets too, needless to say, have changed their situation, which brings in no little complication. However, if I take this, to begin with, to be a true perspective, I shall draw it thus (Sun in the middle point). Then as it were I get the other valid order by drawing the ideal sequence of the planets with the Earth here (Earth in the centre) and then Moon, Mercury, Venus, Sun Mars, Jupiter and Saturn. You see, we are in a way misled by the perspective's, to the establishment of an extremely simple system, whereas in fact it is by no means simple. It is as though, with respect to the planets, Earth and Sun were taking turns, alternately being in the centre of the system. I confess it is not at all easy for me to be telling you these things, which at the present stage might still be thought fantastic. We cannot not now bring all the mathematical paraphernalia to bear on them, but I assure you they can be calculated in all detail. The desire was for me to explain the relations of Astronomy to other branches of Science; hence at the end of these lectures I must try to give a resume as clear and as complete as possible. Tracing the path of Earth and Sun (now, once again, apart from the planetary system as a whole) we have then to imagine a Lemniscate in which the Earth is following the Sun. Here is it, projected (Fig. 6). Incidentally, you may also see in this a possibility of giving meaning to the idea of Gravitation. The one draws the other after it: that is the underlying principle. Think of it in this way, and you will no longer need the somewhat questionable quality of gravitational and tangential forces, for they are here reduced to a single force. Think it through thoroughly and you will find it so. You must admit, it is a rather problematical feature in the Newtonian conception. We are to think of the Sun in the centre and the Planets around it — endowed, one and all, with a kind of “shove” in the tangential direction, one and all, without presupposing which the Newtonian system would break down. Taking this then (Fig. 5) to be the path of Earth and Sun, — if you wish to bring out in perspective, along with the course of Earth and Sun, the path-forms of the other planets, you must imagine the paths of the inferior planets somewhat in this way (small Lemniscates in Figure 6). This will enable you — if this be the line of sight — to get the perspective of a planetary loop, for a certain position of the planet along its path. The line of sight is here (v). In this position (s) we get the loop, while these two branches (u) will appear to run out into the infinite. On the other hand, taking this once more to be the path of Earth and Sun and this the path of the inferior planets, you must imagine the corresponding paths of the superior planets to be Lemniscates like this (Fig. 7). I should now have to go on drawing upward, but the nearest part would be like this. And now this Lemniscate 2 Namely the lemniscate of Sun and Earth. moves on, makes its way through, — through the Lemniscate of the superior planets. It is a system of Lemniscates in determined order and relation. Such are the paths of the planets; such also is the path of Earth and Sun. Now you will easily harmonise what I have here presented in the grammatic outline, with the fact that we see the loops of Venus and Mercury in conjunction and those of Jupiter, Mars and Saturn in opposition. In our perspective it is the necessary outcome. Above all, you will recognize once more what the connection is between the planes and the human being. You need but look at this picture and you will say to yourselves: What you have here, in Mercury and Venus, is near in direction to the path of Earth and Sun. It is in the cosmic neighbourhood, so to speak, of the path of Earth and Sun. It is therefore in this relation: It has to do with the radial line — fundamentally, the connecting line of Earth and Sun. As against this, the other paths — those of the outer or upper planets — work more by virtue of their lateral or spherical direction. In their effects, they more approach what is peripherical in movement. We may then also formulate it thus: What we behold in Venus and Mercury is far more akin to what is living as a cosmical reality in us ourselves. Whilst, what we see in the paths of the superior planets is more akin to the fixed-star Heavens in general. Here too we reach a kind of qualitative valuation of what is taking place in the Cosmos. Of course the lines I have been drawing are only meant diagrammatically. It should really be put this way: An inferior planet has a path, making a lemniscate loop-curve the centre of which is the Earth-and-Sun path itself. A superior planet, on the other hand, embraces the Earth-and-Sun path in its own lemniscate-loop . Such is the essence of the matter; the thing itself is so complicated that the mental pictures we can form scarcely be more than diagrammatic. You see from this however, my dear Friends, — unwelcome as the news may be to some, — we need to get away from a principle that crept into the explanations of nature with the beginning of modern time. I mean the overriding principle of simplicity. It grew to be the accepted tendency. The simple explanation is the right one! Even today one is severely censured if one puts forward what is not simple enough. Yet Nature is not simple. On the contrary, it would be true to say: Nature the real World — is that which, looking simple proves on examination to be complex. What appears simple on the surface, is as a rule only the outward glory, only the outward semblance of it. It was not by any means my prime intention to let these lectures culminate in this way. I am not pre-disposed on principle to put forward things out of keeping with the accepted notions. We only want to get at the truth. As it is is however, the assumptions of the modern astronomical world-picture involves so many contradictions that in the end, having studied the current astronomy, one comes away dissatisfied. Hypothetically, it begins by assuming the world-picture I have also indicated in this sketch (Fig. 4), — the elliptic orbits of the planets, the Sun in one focus, and so on. The planetary orbits are then assumed to be in different planes, inclined to one another. For there is no alternative at this stage; the different inclinations are given by the perspective. The complications of it are complications of perspective. Yet the real calculations are not done to the basis of this simple solar system which people have explained to them at school and then retain for life. In practice, they take their start from the Tychonic system. Then one correction after another has to be applied. From the accepted formulae, one calculates, say, the position of the Sun at given time, and it does not come true. Instead of the real Sun being there, it will be the Dynamical of Astronomical Mean Sun, — something fictitious therefore. So it is time and again: Imagined entities are there, and more corrections must be introduced to get to what is real. In these corrections there lies hidden that which would lead to the truth. Instead of holding fast to the conventional formulae and being led to fictitious entities, one should bring movement into the formulae themselves — make them inherently mobile — and then draw curves accordingly. If one did so, one would soon reach the system here drawn, though I repeat, the drawings are diagrammatic. What I have sought for above all is that a picture should arise in you of the harmony there is between the organisation of Man and the constitution of the Cosmos. If you have really been following thus far, you cannot possibly regard this as offending against the scientific spirit. When the transition emerged from the Ptolemaic to the Copernican World-picture, a profound change was taking place in the whole way of interpreting the connection of man with the celestial phenomenal. In very ancient times — though from a different perspective so to speak, as mentioned a few days ago — man still had clear and penetrating ideas of the harmony between the movements in the Heavens and the form of Man. What they then had was more instinctive; raised into consciousness however, it becomes the true spirit of modern science, to which we too must be faithful, — the more so when venturing upon this problematic ground. Fundamentally there is no difference between the way of applying mathematics in general and the way we are applying this qualitative mathematic (which we have first had to develop) to man and the celestial phenomena. There is another thing however, you need to recognise in this connection. In the same period when the transition was developing between the old heliocentric system and the new heliocentric, the evolution of mankind suffered a certain break in the life of knowledge, Namely the bridges were demolished between the physically sense-perceptible or natural world-order and the ethical or moral. I have often mentioned in other lectures, how we in our time are thus torn asunder. On the one hand our theoretical ideas about Nature lead us to conceive some primeval cosmic entity in the beginning, from which the Universe was to unfold by purely natural events. So then evolved the Earth on which we are. So it goes on again by dint of purely natural laws and it will one day reach its end. In the midst of it are we. Out of our inner life there arise ethical impulses; no-one knows where they come from. And if one thinks according to this dualism, one cannot doubt that at some future time even these impulses will suffer burial in the universal grave. This is the way one thinks when failing to build a bridge between the natural world-order and the ethical. I have indicated on other occasions how the transition is to be looked for. It can indeed be found throughout Anthroposophical spiritual science. Here I would only draw your attention to a specific aspect of it, — for the rift between the natural world-order and the moral makes itself felt in diverse realms, and among others it affects our present subject. Here too, in the evolution of mankind the natural aspect and the ethical have in a certain way fallen asunder. The ethical has been cultivated in Astrology; the natural in an Astronomy bereft of spiritual values. There is no need for me to insist that Astrology as pursued today is scientifically unacceptable. I need not prove to you that this is an aberration on the one side. Yet on the other side our Astronomical world-system, as we call it, also involves an abberaction. All these perspective lines — or if you will, projective lines — that are conventionally drawn to represent our solar system, are not to be conceived as realities at all. Nor even are the lines that arise when we observe a further resultant movement, built up again of many components, namely the Sun's proper movement, the whole solar system going with it. All these things are built up of very many components; we are in the midst of relativities and we need some criterion to hold to. The criterion may seem vague to many people, yet it is there and it can lead us to an understanding of the curves in question. We have to penetrate the secret: Why is it man has an inner need to lie down horizontally in sleep, — thus to escape in sleep from the connecting line of Earth and Sun? Just as he can only carry out his voluntary movements while moving his centre of gravity at right angles to the line joining Earth and Sun, so with his involuntary movements: He can only carry them out by lying down, putting himself in a direction at right angles to the path of Earth and Sun. If he wants to escape from the effects of voluntary movement — if he wants, what would otherwise work itself out in voluntary movement, to work inside him and bring about a metabolic interchange between his body and his head — he must lie down, he must align himself in this way. In like manner you will be able to find other directions that are at work in man. From the directions ascertainable in man — derivable from man's own form and stature — you will be able to compose the curves that are really there in the movement of heavenly bodies. Granted, it is not so easy as what is done with mere telescopes and measured angles. Yet it is the way, the only way, to find the relationship between the human being and the celestial phenomena.

Astronomy as Compared to Other Sciences

Lecture XVII

https://rsarchive.org/Lectures/GA323/English/LR81/19210117p01.html

Stuttgart

17 Jan 1921

GA323-17

If we recall what I said yesterday about the opposite character of Earth and Sun, we shall perceive that in answering such questions it is all-important to follow up the empirical facts in the right way. We cannot form true ideas of what we see if we do not recognize from the outset that radical differences may be called for in the whole way we interpret what is seen in one case and in another. The phenomena that present themselves to us when looking at the so-called body of the Sun will only find their true interpretation if we start from such premises as we were indicating, for example, when we put this question: — On Earth there are many phenomena the characteristic of which is that they work outward from the given center to the wide circumference, — out into cosmic space We interpret them accordingly. How must we then interpret similar phenomena — or rather, phenomena that seem superficially similar — when we are looking, with or with-out the help of optical instruments, towards the Sun? Truth is, the empirically observed phenomena will only reveal themselves in their true light if we then take our start from some such idea as this: whilst on the surface of the Earth an eruption or the like will naturally be interpreted as tending up and outward (Fig. 1a), a process on the Sun — a Sun-spot for example — must be interpreted rather as tending from without inward (Fig. 1b). Continuing this line of thought: Just as we have to imagine that if we went through and beneath the surface of the Earth we should get into dense matter, so shall we have to imagine that if we moved from outside the Sun towards the Sun's interior we should come into an ever more attenuated state of matter. And we may truly say: Look at the Earth and the whole way it is placed into the Universe. It manifests as so much ponderable matter in the Universe. Not so the Sun. Here we shall only come near the truth if we imagine that as we go from the circumference towards the interior we get ever mere remote from ponderable matter and ever more and more into the imponderable. We have precisely the opposite behavior as we draw near the middle point. The Sun must be conceived as a hollowing-out, shall we say, of cosmic matter, a hollow space, a hollow sphere, — a sphere enveloped by matter, — in contrast to the Earth where we have denser matter enveloped by more attenuated. As to the Earth, we think of air around it. Air is outside and denser matter inside. For the Sun it is the opposite; as we go inward we go from relatively denser matter into more attenuated and at long last into the very negation of matter whoever takes the phenomena with open mind and puts them all together will be obliged to recognize that this is so. The Sun is not only a more attenuated heavenly body, of a materiality less dense than earthly matter, but if we call the Earth's materiality positive, then in the Sun — in the Sun's interior — we shall have negative matter in a certain sense. We only do justice to the phenomena if we conceive that there is negative matter in the inner space of the Sun. Now, my dear friends, as compared with positive matter negative matter is suctional. Positive matter exerts pressure, negative suction. And if you now conceive the Sun as a collection of suctional force, you need no further explanation of Gravitation. This is the explanation, Now think of it as I explained it yesterday. The movement of Earth and Sun is such that the Earth follows the Sun in the same path, in the same direction. Here then you have the cosmic relation between Sun and Earth. The Sun as a gathering of suctional forces goes on in front, and by this suctional force the Earth is drawn on after, moving through cosmic space in the same course and in the same direction in which the Sun thrusts forward. You thus perceive and understand what you would otherwise fall short of in your thinking. In no other way will you reach an adequate idea, to comprise all the phenomena. You have to start from such ideas as these. You must imagine that in the realm of matter there is a positive and a negative intensity. Matter itself, — that is, earthly matter — is positive; it is of positive intensity. Solar matter on the other hand is negative — of negative intensity — and is therefore not only empty in relation to matter-filled space, but even “less than empty”. It is a hollowing-out of space itself. This may be difficult to conceive. Yet if you are accustomed to having mathematical ideas, why should you not think of a certain degree of the fullness of space as a corresponding magnitude, say +a ? Empty space would then be Zero, and a space less than empty would be conceivable as -a . This granted, you will be able to conceive a truly mathematical relation — or at least, a relation analogous to mathematical — between the different intensities of matter, as in this instance between terrestrial and solar matter. As it were in parenthesis I may add the following: No matter how you think of the relation of positive and negative real numbers to imaginary numbers (I will not go into this question now), some interpretation of the so-called imaginary numbers must be discoverable, and since they too emerge in the solution of equations and the like. If in the way we have been saying you recognize a positive and a negative of intensity, you may well conceive that there is also an imaginary [intensity]. You must then have which would enable you to add to positive matter and negative the kind of matter for example (or if you will, the kind of spirituality) which Anthroposophy describes as the Astral. Thus you would find a mathematical way of approach to the Astral too. However, as I said before, this only in parenthesis. Once again take the connection of what I have been saying with man himself. You will admit: without any doubt the human physical body is related to ponderable earthly matter, and since it is as waking man — upright in his physical body — that man is related to earthly matter, we may compare man's relation to earthly matter with the upright direction of the plant, following what was said in preceding lectures. However, yesterday we saw that the plant must be imagined with the very opposite direction in the human being, while the outer plant must naturally be conceived as growing upwards from below, the plant we have to think of in the human being moves in a manner speaking, from above downward (Fig. 2). What is it then that grows from above downwards? Certainly nothing visible; it must be something invisible. Now we related this to the Sun. It there fore in relating the forces of plant-growth to the path of the Sun and Earth we think of them as tending from the Earth towards the Sun, we must needs think of what grows in the reverse direction in the human being as growing, in effect, in his etheric body. This force of suction therefore, proceeding from the Sun, works also in the human being. permeating his etheric body from above downward. Upon the human being — the human body in this instance — two opposite entities are at work; Sun-entity, Earth-entity. We should be able to prove in detail that these things are there, and we can indeed, once we perceive the true interpretation. This that is working in the human being from above downward may resolve itself in very many ways. For if we have a force, say, in the direction a - b, we can trace it not only in this direction but also in an imaginary sense. Namely if this (Fig. 3) is its intensity, we need only imagine it resolved into two components. Thus we can every where form components of forces in the direction of the path of Earth and Sun. If I press here with my finger, there will arise over this surface the force or pressure whereby the ponderable matter presses against me. The counter-pressure will then correspond to the force of the Sun that is working through me — through my etheric body, that is to say. Imagine a surface here pressing against the human being, — or against which he is pressing. Here you already have the opposition — the working of the ponderable and of the imponderable able force. It is the interplay of the ponderable pressure from without inward and of the imponderable from within outward (Fig. 4) which gives you the conscious sensation of pressure. If in our mind we see all these things clearly and comprehensively, we may truly say that the polarity of Sun end Earth into the midst of which the human being is placed, is felt by us in every sense-perception. In like manner, everything about the human being can be traced in such a way as to perceive the cosmic realities that are involved. Cosmic forces work into the human being upon every hand. It is of untold importance for us to overcome the method that excludes the human being and that is always haloing fast to isolated things, see it without any connection with their surroundings. You will remember, I used the same comparison before. If we place man into the world in such a way as to study head, limbs, etc., one by one and in a merely outward sense, it is as though we were to study a magnet-needle, tending as it does ever in the same direction, and seek the cause of this behaviour not in the magnetic pole of the Earth but inside the needle. To understand any fact or object, we must go to the totality from which alone it can be understood. What matters is in every case to look for the totality in question. Precisely this, alas, is foreign to the habitual ways or thought in our time. Before attempting to decide a problem, look first for the totality on which it all depends. You take a crystal of salt into your hand. You may regard it as a totality, just as it is. Even this is only relatively true, but at least relatively you can so regard it. It is , in a sense, a self-contained entity. Not so if you have picked and place a rose before you. Placed there before you in this way, the rose is not a self-contained entity at all. It could not be there in the same way as salt-crystal can. The crystal, it is true, must also have been formed in a surrounding medium; nevertheless it is a totality, the rose can only be looked upon as a totality when seen in connection with the shrub on which it grew. Only there has it the kind or totality which the crystal-cube of salt has on its own. Likewise if we look at man with respect to his full being, we cannot stop short at the limits of his skin, we must regard him in connection with the great universe that is visible to us; only in this connection is he to be understood. Such then must be our method, and as we persevere in it we become able to see a deeper meaning in the phenomenon that present themselves to us, — that can indeed be mastered by our cognition. During these lectures we haves recalled the fact that in comparing the periods of revolution of the planets incommensurable magnitudes emerge. For if they were commensurable, the planetary paths would presently come into such relation to one another that the whole system would rigidify. Our planetary system does indeed also contain this tendency to become rigid and dead. We can express what confronts us in the planetary system by means of certain curves — and arithmetical formulae. Yet as we saw, these curves and formulae are never in full agreement with reality. We must therefore admit that if we try to contain the phenomena of the Heavens in succinct formulae or geometrical figures the phenomena elude us. Time and again they elude us. This then is true: — look outward on the one hand and behold the given picture of the celestial phenomena. Look on the other hand at what we are able to make of it by dint of calculation. We never do contrive a formula that coincides entirely with the phenomena. We may devise such a drawing as I was sketching yesterday — the system of lemniscates. We can do so indeed. Even this system however, — we only understand it rightly if we admit the following. Suppose I managed to draw this lemniscatory system in a precise and finished form; it would at most be true of present time. Even a time comparatively near our own — the time I indicated when speaking of the coming ice-age — would require me to modify the system not a little. The constants of the curves must themselves be taken as variable. The very constants would therefore be curves of some complexity by virtue of their variations. Thus I can never draw staple straightforward curves, but only complicated ones. Even when drawing these lemniscate-curves (Fig. 5) I should have to say: Good and well, — I draw a path for some heavenly body. (As we saw yesterday, it will always be a lemniscatory path.) I draw the path. Yet when a certain time has elapsed I must disqualify it; it is no longer valid. I must make the Lemniscate a little broader. And then again after a time I must draw such a Lemniscate (Fig. 5 once more), and so on. In effect, my dear friends, if I were to trace the paths of the heavenly bodies, I should really have to go out into the Universe and trace them ever anew, varying them all the time. There is no constant path which I may draw. Whatever path I may work out, I must remember in so doing that I ought really to be changing it all the time, since every lapse of time involves a change of path, however slight. To apprehend the heavenly bodies and their paths of movement in any adequate way, I cannot draw ready-made lines at all. Ready-made lines, if I do draw them, will only be lines of approximation, and I shall have to bring in corrections. Whatever finished lines I may devise, the phenomena in the Heavens will presently elude them, No matter what mathematical curve I may devise, once it is fixed and finished the reality will certainly escape me; my finished curve will not contain it, yet in the very act of saying this, I am giving voice to an important reality. Namely, a planetary system has this essential feature: It tends in both directions, — on one hand towards rigidity and on the other hand to the forming of ever-mobile Lemniscates. In the solar Saturn or planetary system there is this contrast between the tendency to become rigid and the tendency to be ever variable, ever escaping from its established form. If we now follow up this very contrast, not in the way of speculation but in the actual seeing and contemplating of the phenomena, we shall be led to recognize that what we call a comet , a cometary body, is not a body at all in the same sense that a planet is. (What I am giving her, I give once more as guiding lines which you can verify for yourselves. You need only observe the empirical data. Observe them with the greatest possible precision, but do not cling to the theories with which so many scientists would fetter them — theories that lie like shackles upon the facts, You will convince yourselves: what I am about to say is verifiable. It will be verified increasingly, the more the given facts are put together.) Truth is that in studying the cometary phenomena we get into difficulties if we conceive the cometary body too in the same way as we are wont to think of a planetary body. The planetary body (I refer again to the same question of principle and method as in an earlier lecture), — the planetary body you may represent as though it were a self-contained body moving on in space. You will not go much against the facts in so conceiving it. Not so a cometary body. Again and again you will find yourself in contradiction to the phenomena if you conceive it after the same pattern as the planetary body. You will never understand the cometary body, in the way it moves — or seems to move — through cosmic space, if you regard it as you are accustomed to regard the planetary body. See what becomes of it on the other hand it you regard it as I shall now describe. Take all the empirical facts that are available and try to thread them on this line of thought. Imagine that in this direction (Fig. 6) — towards the Sun, as we may say — the comet comes into being at every moment. It is for ever coming into existence in this direction. It pushes towards its cometary nucleus, or what appears as such. Behind, it melts away again. In this way it thrusts forward — for ever coming into being on the one hand, passing away again upon the other. It is not a body in the same sense as a planet is, — not at all. It is perpetually coming into being and passing away again — renewed in front, accruing all the time in this direction; losing the old at its tail. It pushes forward like a mere effulgence, a mere phenomenon of light; but please, I do not say that that is all it is. And now remember what we were saying a few days ago. There is not merely the Moon up there and the Earth here (Fig. 7), but every planet has a certain sphere, and what we see is only a point at the periphery of the said sphere. The true Moon is the sphere, bounded by the lunar orbit. We, with the Earth, are in the Lunar Sphere. So also, in a certain sense, are we in the Solar Sphere and in the spheres of all the planets. The planets are not merely what is out there, moving in lemniscates, — what is at yonder point or yonder at any given moment. The visible point is only a specialized part of the whole; it is, as I was saying, like the ares of germination in the germinal vesicle of the human embryo. If you remember this, then you will say to yourselves: Here now I have the Earth and the Sun. In fact, two spheres are interpenetrating, thrusting into each other, — spheres which are really due to materialities of opposite tendency and kind. The one comes from the centre of the Sun, towards which negative matter is tending; the other from the centre of the Earth, from which positive matter is raying out. Positive and negative materialities are interpenetrating here. Naturally, the interpenetration will not everywhere be homogeneous. Not even clouds that move through one another would interpenetrate homogeneously. It is essentially inhomogeneous. Imagine how, in this mutual penetration, the different densities will impinge on one another. Then, in the penetration of the one substantiality by the other you have the requisite conditions for such phenomena as comets to arise. Comets are ever-nascent phenomena, perpetually coming into being, passing away again; and if we draw our ideal picture of a planetary system, say the Copernican picture, with the Sun here and Uranus and Saturn here (Fig. 8), we have not to imagine that the comet is arriving there from some great distance and then making its departure. Out there — outside the system — we need not imagine it to exist at all, It is not there to begin with, but becomes; then, at the perihelion, changes the gesture of its form, which is in fact ever-becoming, ever-nascent. Out there at last it melts away again and is no more, The comet comes into being and passes away; that is its very nature. Hence it can sometimes have apparent paths that are not closed at all — parabolic paths or hyperbolic, — for there is nothing moving round such as would have to move in a closed path. All that there is comes into being, and may well do so in a parabolic direction and then vanish and be no more. Altogether, we must look upon the comet as a fleeting thing. In relation to Sun and Earth, it is a phenomenon of compensation between ponderable and imponderable matter, — a meeting of the two kinds of matter, which do not immediately balance-out as when light extends in air. For in the latter instance too, there is a meeting of the ponderable and the imponderable; here however they spread continuously, homogeneously as it were, — do not impinge on one another. Take for example air, with light of a certain intensity passing through it. The light spreads homogeneously; but if so be the light does not adapt itself to the air quickly enough, a kind of inner friction will ensue between the ponderable and imponderable matter; only I beg you not to understand this in a mechanical sense but as an inward process (Fig. 9). Follow the comet in its movement. It is a mutual friction of ponderable and imponderable matter that moves on through space. It comes into being at every moment and passes away again. What I have tried to give you in these studies, my dear friends, was meant to bear on scientific method above all. Although the shortness of time has obliged me to deal with some of these things in bare outline, scarcely more than hinting at them, yet if you follow up the thoughts and indications of these lectures you will see that this is what I have been pointing to: It is a transmutation of method, in the whole way of scientific thinking and research. It would be most important for such lectures to become a starting-point for real work. I can only give general directions, as it were; and yet again and again, where we may only seem to have been working with mathematical curves and the like, you will find inspiration for empirical research and experiment. On every hand, both in the coarser and in the finer aspects, you may attempt to verify what has here been presented in seemingly mathematical and geometrical guise. You may take one of those blue or red toy balloons and examine the effect when you forcibly indent it from without inward, where the indentation will of course follow certain laws. See then what form is taken by the same type or phenomenon when in another experiment you make the forces work from within outward radially. Whether, I say, you are examining only this crude phenomenon of stress and deformation or whether you follow the lines along which the heating effect will spread when you heat certain substances — from within outward in one case, from the periphery inward in another, — or again whether you try your hand it optical, magnetic or other phenomena, in every instance you will find that what has here been said about the contrast of Sun and Earth (to mention only this example) can be detected experimentally. Above all, if such experiments are carried out, you will begin to penetrate the realities quite differently than has been done before. For you will meet with conditions, factual distributions, which have not hitherto been met with, or have been overlooked. From the realms of light and heat and so on, quite other effects will be derivable than hitherto, for the simple reason that the phenomena have not yet been approached in such a way as to become fully manifest. Such, my dear Friends, are the developments which I would like to have suggested to you. May-be in future lectures, before very long, we can continue and make actual experiments. It will depend on how our physical and other laboratories prosper, — whether you will have reached experimental methods or real value for the future. Let us not pursue the ideal of equipping our new laboratories with the most costly and perfect apparatus from the scientific instrument makers and then experimenting in the same way as other people do. For on these lines they have done splendid work on every hand. What we must do, as I said before, is to devise new kinds of experiment. We should begin therefore, not with a fully equipped Physics Laboratory, but as far as may be with an empty room, which we go into with the thoughts of a new Physics growing in our minds and souls, not with the usual instruments all ready-made. The emptier our laboratories and the fuller our own heads, the better experimenters we shall grow to be in course of time, my dear Friends. This is what matters most in the present connection, and in this sense we must do justice to the tasks of our time. Think only of the fetters that are cast around you in the different experimental sciences in the normal course of study nowadays; you had no opportunity to see or to set out the phenomena in any other form than was provided for by the accustomed apparatus. With these instruments, how can you expect to study the spectrum in Goethe's sense? You can not possibly. Given these instruments, nothing else can emerge than what you read of in your text books. You cannot even see why we reject the artificial insertion of “light-rays” in the interpretation of the phenomena of light, where in fact, there are no rays at all. We say to ourselves: There is a vessel filled with water (Fig. 10); on the bottom of it lies a coin. The coin seems to be at a different place. We hardly begin to think of this phenomenon, and we have already drawn our diagram with the normal and sundry other lines and rays (Fig. 10). We follow the whole process with such lines, where from the very outset we ought not to be pursuing such an isolated thing at all. Nowhere in reality are we confronted with such isolated things. If this (Fig. 11) is the bottom of the vessel and a coin is lying here, we only begin to see how the coin is to be treated when we think as follows. Imagine on the bottom of the vessel, not an isolated coin, but a circle, for example, made of paper (as in Fig. 12). The phenomenon is, that when seen through a surface of water the paper circle appears lifted and enlargerd. That is the pure phenomenon, — that you can draw. If then at the bottom of the vessel you have not the whole circle but only a little bit of it, you have no right to treat it differently. The coin in effect is like a little fragment of the paper circle. You have not to draw all manner of lines into the picture but to treat it as a portion of the circle, nay of the bottom of the vessel as a whole, — of what is there all the time even if not made visible by differentiation. The mere fact that I have made one point visible at the bottom of the vessel does not justify me theoretically, in treating this visible point as a point by itself. It has not the significance of a point, but only of a part of the larger circle (Fig. 13). Likewise a magnet-needle: In its reality I may not treat it as though there were a centre here, and here a north pole and a south pole; but I must realize that purely and simply by virtue of this arrangement the whole of it is one unlimited line, with forces working peripherally on the one hand and centrically on the other (Fig. 14). In the electrical phenomena this finds expression in that we set the cathode on the one hand, the anode on the other. On the one hand we can only explain the luminous phenomenon by regarding it at a portion of a sphere, the radius of which is given by the direction in which the electricity is working; whereas the other pole is given as a tiny portion of the radius itself. It Is not justifiable to speak of a simple polarity of poles. We should speak in quite another way. Namely, wherever anode and cathode make their appearance, this will belong to an entire system; purely and simply by virtue of the simple arrangement it belongs to an entire system. Only by speaking in this way shall we attain true understanding of the phenomena. Now, my dear Friends, I have been reading through the written questions; but I believe, if those concerned will reflect a little, they will find the necessary elements of an answer to their questions in what I have set forth. They should but try, in every case, to find the way from what I have been saying to their several questions. We shall advance in this bit by bit. Only one question I should like to deal with briefly. It is as follows: — “In representing a Science of this kind to the outer world the question may easily arise, to what extent the higher powers of cognition — Imagination, Inspiration and Intuition — are needed for the discovery of these relations between phenomenon. What will be the answer to this question?” Well, my dear Friends, and if it were the fact that Imagination, Inspiration and Intuition are needed for the discovery of certain things? How then are we to do without Imagination,Inspiration and Intuition, if the fact is that ordinary, “objective”, intellectual cognition will not reveal the truth and the reality? What else are you to do than to proceed to higher 'modes of knowledge — Imagination, Inspiration and Intuition? That there is still this possibility — If it is really so that one is quite reluctant to advance to higher modes of knowledge — there is the possibility of simply taking the results of such research and testing them by what is found in the field of external empirical fact. One will always find them verified, of that you may be sure. Yet in our time these things are not so remote as is commonly supposed. If only the path were really taken, from the ordinary analytical treatment of mathematics to the projective treatment — to a projective form of mathematics and beyond it — if one would cultivate and pay more heed to the idea from which I took my start some days ago, speaking or curves for which one has to go right out of space, one would not find it so very difficult to press forward to Imagination. It is indeed simply a question of inner courage — courage of soul. Today you need this inner courage of the soul for scientific work. Hence it is needful to maintain, for it is true: to the ordinary forms of observation and reflection the full reality will not reveal itself. But if one does not shrink from developing the latent forces of the human soul, depths of reality which would otherwise remain concealed will become ever more unveiled. This I would like to have said to you in conclusion. For the rest, I would express the wish that all these things, which I can only claim to have imparted by way of stimulus and suggestion and in the barest outline, may stimulate you to research, experimental above all. For this is what we need. We need empirical verification of these truths, which must be taken hold of to begin with in the way we have been doing here. Sooner or later we must get beyond the old foundations of judgment, which have so long been responsible for such conditions as in the instance I shall now relate. I say again, we must get beyond them. I was speaking to a Professor of Physics about Goethe's Theory of Color. The man has even published an edition of it, with his own commentary. When we had been discussing Goethe's Theory of Color for some time the man declared himself a strict Newtonian. He said, it is in fact impossible for any man to get a clear conception or Goethe's Theory of Color; no physicist can set a clear idea of what it means. You see, his education as a physicist had brought him to this point; he could get no real notion of Goethe's Theory of Color. I for my part could understand it. The modern physicist if he is candid, will have to admit that he cannot. He must first transcend the accepted foundations of present-day physical thinking; he must somehow be able to get away from these old foundations. If he succeeds in this, then he will find the way — for it can be found — from the actual phenomena to that interpretation which is contained in Goethe's Theory of Color and which can also provide an important starting-point for other physical researches, extending even to Astronomy. Consider without bias the warmth-region of the spectrum and the chemical region of the spectrum, their quite different behavior towards a number of reagents. Even in the spectrum you will detect the contrast I have been describing — the contrast of terrestrial effects and solar. In the spectrum itself we have a picture of the contrast of Earth end Sun, — the same contrast which finds expression in the whole bodily organization of man. Every time you touch another body, perceiving it with your sensation of touch, Sun and Earth are at work. So too, in the spectrum, Sun and Earth are at work. Taking it as the solar spectrum you cannot truly think of it as being put into space just arbitrarily here or there. You must be clear that it is always in the real space — the space that is between Sun and Earth. Indeed you never have to do with space in the abstract where real phenomena are concerned, for the real things are always there and have to be included. If you do not bear this in mind, you will at last be explaining the origin of the celestial system on the good old pattern — a little drop of oil floating in water, bearing a disk of paper with a pin stuck through it as a pivot, which you begin to turn. The drop of oil gets flattened and little drops detach themselves. A planetary system has arisen: You explain it to your audience: “You see, it is a planetary system”. You compare it with the solar system in the Universe outside — the Copernican conception, — it is the very same! Well and good. Yet you must not forget: There were you the teacher, turning the pin, and therefore — not to be untrue — you should also add the demon giant in the universe outside, turning the cosmic axis, for only so can there arise what you have been alleging. You have no right to use this illustration if you do not include the giant demon. In scientific explanation too, we need to be more scrupulous and careful. Upon these inner and methodical conditions above all, I have been wanting to lay stress in the present lectures. Next time then we will speak again from other points of view, of certain realms of Science.

Astronomy as Compared to Other Sciences

Lecture XVIII

https://rsarchive.org/Lectures/GA323/English/LR81/19210118p01.html

Stuttgart

18 Jan 1921

GA323-18

The spiritual science that underlies this course in anthroposophy, must fight for its validity in the truest sense of the word. This can seem strange to one who has become familiar with the motivating forces of this anthroposophically-oriented spiritual science, for it stands solidly on a common ground with scientific and other cultural demands of our time. It deals with all that is necessary and basic for spiritual life in these times. One can see, however, that spiritual science must fight, if one takes into consideration the many prejudices that exist at present. Spiritual science is in some ways a natural adversary of certain reactionary forces that remain and can be observed in the souls of human beings of our time. In these lectures it will be my task to present to you in a direct and scientific manner the significance of what we understand here as spiritual science. I will gradually proceed from relatively elementary things to a real knowledge of man from the point of view of this anthroposophically-oriented spiritual science. I will take pains to introduce some chapters and some special questions by speaking of the methodology, and by the choice of special examples indicate their significance. Today in this first lecture I would like to point out how present-day scientific thinking has increasingly come to rely on the experiment for its main support. In this regard present-day scientific thinking stands in a certain polarity to older kinds of knowledge acquisition, especially to those which start from simply observing nature and the world as it presents itself. One can start by observing the established facts of nature and the world, or — as we often do today — by first creating the conditions of an event and then, with the knowledge of these conditions, observing a fact and being led by this to certain scientific results. Along with this methodology, one can see the tendency of this newer scientific thinking to observe the entire field of natural science through mathematics, and with these mathematical thoughts, arrive at mathematical results. You all know the saying by Kant: In every individual science there is only so much real knowledge as there is mathematics. It is thought that in observation, as well as in experimentation, mathematics must be introduced. Through this, one feels oneself in a secure element, one feels in a position to have an overview of a series of facts with the use of mathematical formulas. This is a totally different relationship to knowledge than when such facts are simply described in their natural state. This feeling of certainty which one has in treating knowledge mathematically, has been characteristic of scientific thinking for a long time. One cannot say we have today a really clear idea of the reasons why one feels so certain and safe with the mathematical handling of the natural world. A clear knowledge of the feeling of certainty accompanying the use of mathematics will lead us to acknowledge the necessity that a spiritual science must come about with an equivalent degree of certainty. This spiritual science does not have to beg for acceptance from natural science or any other special field. This spiritual science will conform in every discipline to the scientific conscientiousness of modern times; it will, in addition, oppose all that is brought forward by modern science that is suspect, and it will answer questions that often go unanswered. Spiritual science will be on a very sure mathematical foundation. I only have to ask a very simple question for you to see that this feeling of certainty derived from the mathematical treatment of certain subjects leads quickly to uncertainty. What would we do with a science like history if in every science there were only so much real knowledge as there is mathematics? How shall we understand and get the facts straight in matters of the human soul if we have to struggle to understand what modern psychology, by the use of mathematics, has developed in order also to secure certainty of understanding? One must come to recognize that in this field it is not possible to introduce mathematics into actual knowledge. One of the first questions that must occupy us is this: What is the significance of this mathematical certainty in the context of human cognition? It is in approaching an answer to this question that we will be led to the justification for spiritual-scientific investigation. I have also said that the newer science prefers the experiment, where one knows the conditions of a process exactly, to outer observation where the determining conditions are more hidden; even in the case of psychology and also the field of education, attempts are made to go over from mere observation to experiment. In saying this, I must emphasize that spiritual science has nothing against the correct use of experimentation in psychology and education. The point I wish to call attention to is this: What draws the scientists in these fields to obtain knowledge by the use of experiment? In these areas we can actually find reasons for the inclination toward the use of experimentation. Let us therefore explore the transition to experimentation in the fields of psychology and education. We can see how until recently investigators in psychology and education have carefully observed the details of the daily life of man, be it fully mature men and women or the transitional developmental life. We might ask: What is fundamentally necessary for an observation of the soul life of the grownup or the developing child? It is to acquire a certain inner relationship to what one observes. Try to put yourselves into the observational methods of olden times, in the fields of psychology and education. You will find that the inner relationship that once existed between human beings has diminished in recent times. We are not so intimately connected in an objective way with the soul life of another human being as was the case in the past. We are no longer aware when our own soul vibrates in sympathetic reverberation with what lives in the soul of another. We are more removed from the objective soul life of the other; formerly it could be directly observed. We are becoming more and more estranged from any really intimate contact with the soul of the other, where in a directly intuitive way one takes part with one's own inner nature in the inner nature of the other soul. Now an effort is made to approach the human soul from the outside through the use of instruments. There is an effort to explore the human soul through the use of apparatus in an external way. This effort is in the character of our time and must be acknowledged as being partially justified. If one has become estranged from a direct perception of the inner activity, then one must accept the outer expression of the inner activity, and at the same time be content with the outer use of experimentation. It is especially true that when we are estranged from the spirit and soul elements of our fellow man, and yet our experiments are the material expression of this soul-spiritual element, these experiments must be explained in a spiritual sense. They should be wrought throughout with the results of spiritual research. I do not want to speak against experiments as such, but there is a need (I will speak today only in an introductory way) to illuminate the results of these experiments spiritually from within. To explain this properly, I will give you the following example. Investigations have established that the rate of growth differs between boys and girls. In the development of a boy, it has been shown that in certain phases he grows more slowly, while in the same time period the girl grows faster. One can take notice of these facts even if one only looks at the outer expression of the soul life. But to explain such facts one must know how the soul motivates the growing process, how the soul of the boy is inwardly different, and how the force of the soul expresses itself in different phases of life. Then one will be able to see how the difference of growth rates between boys and girls permits a comprehension of what goes on in the soul of a boy and what goes on in the soul of a girl. It is just here that one can know that a human being who develops very rapidly during the period of 14 to 17 years, develops different forces than those of a human being who grows rapidly in a somewhat earlier period of life. Especially in our age, in which there is real proficiency in the handling of facts in an outer experimental way, especially now if we are not to be drawn into superficiality, into externalities, what is investigated experimentally must be permeated with the results of spiritual research. This consciousness is opposed to the more mathematical type of consciousness that gives the researcher such a feeling of extraordinary sureness. If one wishes to examine the different ways of research, one might ask oneself the question: How does one actually know things mathematically when one applies mathematics to the facts of the outer sense-accessible world? And what distinguishes this mathematical approach from other modes of dealing with the facts given to us? Let us start with the fact that the outer objects and events of the world are given to man through his senses. From childhood on, the outer factual world presents itself to us as a kind of chaos. But as time passes we strengthen ourselves inwardly with all kinds of mental images and concepts. (I have set this forth in detail in my booklet Truth and Science.) Through the process of making mental pictures of the outwardly perceived world, we take what may lie far apart in observation and we bring the mental pictures of these observations close together within us. Through this activity we thus create, in our mental life, a certain order in what otherwise is chaotic in the purely sense-perceptible. We must, however, look very exactly at how we treat the perceptual facts of the world when we do not use our mathematical knowledge. We might ask what happens when we simply observe the outer world and make mental pictures about the connections between the observable facts — for instance, when we use the familiar law of cause and effect. We must acquire some thoughts about what we are doing when we simply observe the facts of the outer world. What do we really do when we bring order into the sense-perceptible chaos? It appears to me that in relation to this question David Hume has spoken quite correctly; however, his fault lies in that he has taken to apply to the universal field of human cognition what is meant only for this particular field, namely, the “observation of outer nature free of mathematics.” Most errors and one-sidednesses are based an the application of very correct thinking in one field to the totality of human cognition. This makes it so difficult to take the assertions considered to be universally true. Arguments can be raised for the universal truth being applicable to specific areas, and arguments can also be raised for the opposite point of view. David Hume says: We observe the outer world and we arrange it in a lawful way through our own mental pictures. However, what we then have in our soul as law is not directly representative of something in the objective world. We cannot say that the outer world is always going to follow the course predicted by such a law. We can only say, according to David Hume, that until today we have been able to see the sun rise every morning. That is a statement that fits the facts. We can put these facts into the form of a general law. But in doing so we have no guarantee that we have anything other than a series of events that have happened in the past, of which we made a comprehensive mental picture. What is it really in us that brings about these lawful connections between the sense-perceptible occurrences? What kind of significance do these lawful connections have for the field which we are considering? Is David Hume correct when he says: It lies in the habit of our souls to gather together in a lawful manner the facts as they present themselves to us and, because we respond to this soul habit, we create for ourselves various natural laws? These natural laws are nothing else than what has been gathered together from individual facts through habit of our souls. Thus one can say: Above all, man develops a practical life by bringing order and harmony into the otherwise chaotic stream of everyday facts; and the more one advances in this knowledge, in this special kind of knowledge, the more one inclines to this characteristic soul habit. This being the situation, one is not inclined to preserve individual phenomena as such; one wants to respond to the soul habit of bringing into uniformity what faces one as sense-perceptible, empirical manifoldness. If one is honest, one has to admit that all the knowledge obtained in this way stands as a closed door to the outer world in that it does not allow the essence of this outer world to enter our cognition. In this kind of cognition we must say: Out there are the material facts; we arrange them habitually into our system of mental pictures, and thus have a comprehensive view of them. We know when a series of facts have happened, that this series will happen a second time in a similar way when the same facts appear again before us. But as long as we remain in this field of knowledge, we cannot see through the outer appearances; we also, of course, do not claim to do so. When we want to present rash metaphysical hypotheses concerning matter, that it consists of this or that, we are attempting to change the state of affairs in which we do not deal with the material itself. We say to ourselves: We cannot see through matter to find out what it really is in its inner being, so what we are inclined to do is to arrange sequences of mental pictures and put these in the form of laws. By doing so, we remain outside what appears as outer reality; we only create pictures of the external material happenings. Basically, we need this kind of knowledge to maintain our normal human consciousness, and to this end, we concern ourselves with these pictures. Try to think for a moment what it would mean for human consciousness if we were not able to give ourselves up to the kind of knowledge consisting only of pictures of the external world — if every time we wished to know something of the outer world, this world had to flow into us, as it does when we eat or drink, if it had to become part of our soul's apprehension before we could know anything. Just imagine how incompatible such a uniting of the material existence and our inner life would be with what our soul-constitution must be in acquiring knowledge of the outer world! We are in the position where we must tell ourselves: In our activity of knowing, nothing flows into our soul life from the outer world; we form pictures of what we experience in the outer world and these pictures really have nothing to do with the outer world. Permit me to make an analogy out of the field of art to explain what I have been saying. Suppose I am painting something. The outer world is completely unconcerned about anything I might paint on a canvas. Take, for example, a couple of trees we see out there of which, let's say, I have painted a likeness on a canvas: the trees are completely indifferent as to how I have painted them, or if I do paint them. My picture is added to what is out there as something foreign, something that has nothing directly to do with that outer reality. In the field of theoretical and psychological knowledge it is basically the same as I have just described with the example of painting. If we were not separated from the world as just described, and were to take the content of the world into our soul in a way similar to when we eat or drink, our soul would grow together with, be one with, the world around us, and we would be unable to distinguish ourselves from our surroundings. We will take up the subject of human freedom at a later time and show that it can only be understood if the way of knowing the material world is as I have characterized it. This, however, is not so when I know something mathematically. Let's start by imagining how you know something of a mathematical nature, whether it is in the field of arithmetic, algebra, higher mathematics, or in the field of analytical or synthetic geometry. There we are not confronted by an outer world, we live directly and immediately in the objects of our mathematical knowledge. We form mathematical objects inwardly with all their interconnections and relationships, and when at times we sketch these forms, it is only for our own ease and comfort. What we refer to as mathematical is never some part of the outer world which we perceive with the senses, it is always something inwardly constructed. It is something that only lives in the part of our soul life that is not concerned with the senses as such. We build up, we inwardly construct, the mathematical content of our soul. There is a radical difference between the field of knowledge concerned with the empirical outer world presenting itself to the senses and that of the mathematical. In the external given world the objects of our knowledge remain strictly outside of us. In mathematical knowledge we stand with our whole soul within the objects of our knowledge, and what is observed as substance is the result of an experience in our soul of what we ourselves constructed. Here we have a significant problem which forms, as it were, the first stage to what will be the next higher stage of considerations: How does one arrive at the anthroposophical spiritual science when starting from the familiar science of the present day? I don't believe anyone will be able to answer this question in a truly scientific way who cannot first answer the question: How is our knowledge of a purely observational kind raised to the kind of knowledge of nature that is permeated with mathematics? — how is this knowledge related to mathematical knowledge as such? Now a further question arises which the scientist can answer himself, out of his own experience with scientific work. I have already mentioned what Kant called our attention to, that in every science there is only so much knowledge as there is mathematics contained in it. And, I repeat, this is a one-sidedness, because it is only applicable to a certain field. Kant's error lies in the fact that he takes a specialized truth and tries to make it into a universal law. We have a tendency not to want to leave the facts alone as they are presented to us, but rather to color them with what we have created as mathematical formula, so that we may measure and compare them. What really lives in us when we strive in this direction, when we don't want to remain standing still, habitually combining the outer facts with general rules, when we permeate the given facts with what we have formulated in full consciousness mathematically as objects in our soul life? It is clear that anyone who has experience in the field of objective observation will admit that the whole of nature surrounding his own being is felt, in regard to its materiality, as something foreign. Please notice that, in a sense, we can submerge ourselves into what we feel as a foreign material element, with the help of what we have ourselves inwardly constructed as mathematical formulas. What we describe in a mathematical way actually seems as if what happens in nature has occurred according to the mathematical formula that we have constructed. What is at the basis of this perception? It is the fact that we desire above all else to become one with what we perceive at first as foreign surroundings. We group what is presented to us externally in order to be able to reconstruct it in the same way that we construct something in the purely mathematical realm. We strive to experience what presents itself to us externally in an inwardly exact manner. This internalization of the outer world with the wish to experience exactness is what motivates a mathematical explanation of nature. This is especially characteristic of our present-day scientific efforts in the direction of technology. Today's science has an intense longing to penetrate outer occurrences with mathematical concepts. This means that we bring something we have created in our own soul out into what presents itself to us in raw perception. We do this so that we may understand what is perceived, but in doing so we can have the impression that the outer occurrence actually proceeds in the way we portray it mathematically. When we have gone so far that we have achieved this ideal, as we have in the field of optics and light theory, where every phenomenon is represented in terms of a formula, what really have we done? What really is the content of our soul when instead of plain external appearances a sum of mathematical formulas seem to present themselves? What does our soul receive from this? We look at this edifice, the world portrayed as mathematical relationships, and then we turn our gaze to the actual outer world and we find something strange. We find that all that we look at, all that we consider outer material world, appears inwardly dark until it is brightened by the introduction of mathematical concepts. But at the same time we cannot deny the fact that the picture we have created of the outer world no longer contains reality, no longer the reality which presented itself to us originally. Take, for example, optical appearances, the whole field as it presents itself to our eyes; contrast this with what we have, to a certain extent, correctly constructed as mathematical geometric optics, full of rules. If one uses just a little objectivity, it is clear that in what is constructed as a mathematical picture there is nothing left of the abundance of color. Everything that our senses first offered us, namely, actual outer reality, has been pressed out of the picture. The picture of the outer world is in sharp contrast to what is really out there; it lacks reality, it lacks the tremendous abundance that actually exists in the world. In the coming lectures I will be speaking of a comparison, that to begin with I would like you to consider as an analogy. When we permeate empirical facts with mathematics, our activity consists of two stages: First we must look at the empirical facts, let's say the facts of the eye. The second is the arrangement of these percepts into mathematical formulas. In a certain way, as a result of this we have essentially an experience of mathematical formulating. We no longer view the empirical world of phenomena. This process can be compared to our inhaling life-sustaining oxygen; we saturate our whole organism with it. The oxygen then combines with carbon and we exhale carbon dioxide, which is no longer the life-sustaining air. But the combined process was necessary for our inner life. We had to inhale the life-strengthening oxygen and combine it with something in us. What is produced in this way is something killing; we can contrast it with what was inhaled, which was life-sustaining. For the time being, this should only be considered as a picture of the way in which we pursue the knowledge of nature. We take something into ourselves that is presented to the senses and try to unite it intimately with something we produce only in ourselves, with mathematical construction. We feel that something is created by this union. Nature is not contained in what we have created; the living quality is not there, just as the life force is no longer in the air we exhale. We can say that our perception of the outer world is like an inhaling by the soul of what then is changed into the opposite. If one looks closely at this process of striving for mathematical knowledge of nature, it is proof of the fact that mathematical knowledge is something completely different from the merely perceptual knowledge of nature. This mere perceptual knowledge of nature contrasts with the habitual state of our soul, which consists of a feeling of competence derived from the use of inwardly formed mathematical knowledge. This state of soul wishes to have something that will explain the outer world in accordance with our own being, to unite something inner with something outer. When one realizes how the longing for mathematical explanations of nature are based on this soul habit of longing to take inner possession of the outer world, then it will also be clear that what one attains by this is completely different from the content of sense experience. One goes more deeply into human inner life with mathematical knowledge. One believes that one gets correspondingly closer to the outer world through an inner representation of the nature of the outer world. One has an inner experience of what has been changed into mathematical formulas; at the same time, one has basically lost the fullness of the outer world. One must, however, be conscious of the fact that what the outer world has given has been connected with something constructed purely inwardly. One must really experience what goes on in one's soul when one makes mathematical formulas; one must experience this correctly. One must see that a mathematical formula actually is constructed within us. One must realize that this inner human construction has been achieved apart from the outer world, and yet in a sense it has brought one closer to the outer world. Even so, this inner mathematical construction cannot be regarded as inner reality as compared to what we find in the outer world. If this were not true, we would have the feeling that this mathematical construction contained true reality instead of a bland version of the outer world which it does actually present to us. Think what the situation would be if in our spiritual contemplation of a mathematical construction we had the whole content of the eyes' original experience in all its color intensity. If this were the case, we would experience in the formula itself the lighting up, the intensity of colors, when considering the wave theory, or “interference phenomena,” in mathematical form. This we certainly do not see. The fact that we do not see this proves that with our mathematical formulas we penetrate only to some degree into the outer world. We do come closer to it, but at the same time we no longer have the full reality of it. We have shown a progression from an ordinary sense-based knowledge to a knowledge of inner mathematical construction. The question then arises: Can this progression be continued further in human soul life? First, we have an outer world before us; then we confront it in such a way that the laws which we create, based on observation, are entirely different from it in form. We go through this and we can do so because we become inwardly separated from the outer world. We are inwardly completely separated from the outer world while experiencing these mathematical formulas. We do gain a certain penetration through these mathematical formulas, but it is obvious that they are not filled with reality or we would see the whole outer reality recreated in the formulas. When we take a closer look we see that not only are they not real in themselves but in fact they have the effect of destroying reality. The question now arises: would it be possible to strengthen our capacity to make these inner mathematical constructions by which we then penetrate the sense-perceptible world? Is it possible that what is first experienced mathematically as pale abstractions can be made stronger? In other words, could the force which we have to use to attain a mathematical knowledge of nature be used more effectively? — with the result not just a mathematical abstraction, but something inwardly, spiritually concrete? In that case, we would not just see a re-created version of the outer world or an abstract mathematical picture, but we would have something formed in an entirely different manner. We would have gained something with the full character of reality, but obtained similarly to the way we obtain mathematical pictures. We would then have before us spiritually a reality that shines out toward us in the same way that the outer sense-perceptible world streams toward us. But we would have this from pictures filled with reality, not from mathematically abstract pictures. We would have lifted ourselves, through strengthening our mathematical capacity, to a higher level, and in doing so we would reveal more of our own inner reality. This we can see as a third step in our attainment of knowledge. The first step would be the familiar grasping of the real outer world. The second step would be the mathematical penetration of the outer world, after we have first learned inwardly to construct the purely mathematical aspect. The third would be the entirely inner experience, like the mathematical experience but with the character of spiritual reality. So we have before us: The ordinary outer empirical knowledge of nature, then mathematical knowledge, and finally, spiritual knowledge. We have, as the last step, through an inwardly creative activity, spiritual worlds before us . As preparation for viewing these worlds as real, we start by creating mathematical, pictorially-abstract elements. We use this mathematics in relation to the outer world, but if we are honest we must say: What we construct mathematically is still not a reality in itself; it does not bring reality up out of the depths of our souls, rather it is a picture of reality. In spiritual science we gain the ability to bring out of the depths of our souls what is not just a picture of the outer existence, but reality itself, true reality. The three levels of human knowledge are: Knowledge of physical nature, mathematical knowledge, and spiritual knowledge. This is not just taking spiritual science out of thin air with the purpose of constructing a spiritual science method; rather, it arises naturally. Starting from merely empirical research we come to a mathematical approach, and the continuation of this leads us to study an anthroposophically-oriented spiritual science. This, my dear friends, is what I wanted to say today as an introduction to this course of lectures. I wanted to show you that this anthroposophical spiritual science knows where its place is in the whole system of sciences. It is not born out of some kind of subjective caprice, some kind of dilettantism; it is born out of an exact theory of knowledge. It is born out of the knowledge that must be used even to understand the correct use of mathematics. It was not for nothing that Plato demanded of his pupils that they must first of all have a good grounding in the knowledge of geometry and mathematics. Plato did not require an arithmetical or geometric knowledge of some particular kind, but rather a sound understanding of what really happens in a man when he does mathematics or geometry. This is based an a seemingly paradoxical but deeply meaningful saying of Plato: “God geometrizes.” He did not mean by this that God just created with mathematics, or with five- or six-sided figures; rather, He creates with the force of which we can only make pictures to ourselves, in our mathematical abstract thinking. Therefore I believe that he who understands the place of mathematics in the whole field of the sciences, will also understand the correct place of spiritual science. Spiritual science will battle for its right to exist, no matter what adversaries it may have, for it builds on an exact foundation thoroughly in accord with historical necessity. Therefore I can say: We welcome any and all opponents who will seriously enter into what spiritual science has to say; we welcome any serious dialogue. Spiritual science has no fear of opposition because it is well supplied with all the scientific weapons of ordinary science and it knows how to use them. It would only not like to be continuously interrupted by those who don't understand it, due to their dilettantism and uninformed opinions. Spiritual science as we mean it here is actually a necessity for the other special sciences. The borders of these other special sciences must be crossed over with the help of spiritual science. We must inwardly resolve at least to confront those who, without reason, oppose this spiritual science, and sometimes even be a bit rude with them. There is a fundamental need for humanity to adopt this spiritual science as quickly as possible, and in all seriousness. This can really happen if only we bring good will to the understanding of it.

Anthroposophy and Science

Lecture I

https://rsarchive.org/Lectures/GA324/English/MP1991/19210316p01.html

Stuttgart

16 Mar 1921

GA324-1

I pointed out yesterday in my introductory lecture that we can observe a transition from the ordinary knowledge of the world around us to mathematical knowledge, and that this is the beginning of a path of knowledge. This path when continued will lead to an understanding of the spiritual scientific method, as we mean it here, and ultimately to acceptance of it. It will be my special effort in these lectures to characterize the spiritual scientific method in such a way as to completely justify it. To accomplish this task will take the remaining seven lectures. Today, once again, I would like to consider in greater depth the first stage. I would like to place before you today something which as normal scientific thinking appears here and there in fragments. As these fragments are not always found in the same place and are not seen as a whole, we have the situation that it is not possible to rise in a methodical way from a science that is free of mathematics to one that includes it. We will also have difficultly following in an entirely methodical way the transition from a mathematical penetration of the objective world to a spiritual-scientific penetration into reality. I shall also, as I have already mentioned, try to reach this last phase in a methodical way. We will start today by observing the human being as he experiences himself when he looks at the outer world. You will know from my lectures, also my book Riddles of the Soul , 1 See The Case for Anthroposophy , Anthroposophic Press. that one cannot reach a comprehensive observation of man without splitting the entire human organization into three distinctly different members. Naturally we have eventually to deal with the complete human being. This complete man is however a most complicated organism and its members have a certain independence. Finally we will see how what is contained independently in these members combines into a whole. First we have to look at what I have named in Riddles of the Soul as the nerve-sense man: The member of the human organism that has its primary expression in the head, although from there it extends over the entire organism. Despite this extension we can clearly differentiate this member from the rest of the organism. This physical member is the mediator of our conceptual life. As human beings we make mental pictures and we are able to take the life of these mental pictures to ourselves through our sense organs. From the senses it flows toward our inner organism. The way we are connected with our life of feeling is similar to the way our mental pictures are related to our nervous system. The present-day psychological approach to these things is quite inexact. Our feeling life is not directly connected to our nerve-sense system, only indirectly. It is directly connected to what we call the rhythmic system in the human organism, consisting mainly of breathing, pulse, and blood circulation. The mistaken idea that the life of feeling, as part of the soul life, is directly connected to our nervous system originates from the fact that what we experience as feeling is always accompanied by mental pictures. The physical expression of this is that the rhythmic system is connected throughout the organism with the nerve-sense system. The fact that our life of feeling is always accompanied by a mental picture of some kind is related organically to the fact that the rhythmic system works back onto the nervous system. This can give the appearance that the life of feeling is directly connected to the nerve-sense system. I have pointed out in Riddles of the Soul that if one studies what occurs in us when we listen to music, one can see the relationship correctly between feeling and the forming of mental pictures. Besides these two systems, the nerve-sense system which provides the mental image, and the rhythmic System which mediates the life of feeling, we have the metabolic system. Every function of the human organism is contained in these three systems. The metabolic system is the expression of the will, and the real connection between willing and the human organism will become clear only if you study how a metabolic transformative action comes about in us when there is an act of will or even an impulse of will. Every metabolic activity is consciously or unconsciously the physical basis of some act of will or impulse of will. Our capacity for movement is also connected with our will activity and therefore is connected with some kind of metabolic activity. One must be clear about the fact that when we complete a movement in space, this is a primitive activity of the will. To use a saying of Goethe, the “ur-phenomenal” activity of the will can be seen as expressed by the physical transformations that occur in the organism. And, as in the case of feeling, the will activities are indirectly connected with the nerve-sense system through our following our will activities with mental pictures. So we can say, to start with, that our soul life and also our physical life can be divided in three ways organically as well as into three soul aspects. Let us try today to look at man from a certain point of view so that we may see how these three members of our physical organism and our soul organization relate to one another. We must also go into some detail to achieve our task of showing that spiritual science is a continuation of the familiar scientific way of considering things. First of all, let us consider what I have named the nerve-sense organism. This nerve-sense organism is contained mainly in the head, as I have already mentioned, but from there it extends over the rest of the organism, in a certain way impregnating it. This is not obvious if one looks at just the outer form of a human being, but it does in fact extend inwardly through the whole organism. Take the sense of warmth as an example, which extends over the entire organism. This can be seen as a part of our nerve-sense organization that for the most part is concentrated in the head, in the life of the senses, and yet is extended over the whole organism, making the whole human being into a kind of head in regard to this particular sense of warmth. For most people it is distasteful nowadays to try to understand this kind of problem. Because we have become so used to an outer way of considering things, the three members of the human organism are considered spatially, as separate from one another. There is a professor of anatomy who takes this view, who has asserted that anthroposophy separates the human organism spatially into head system, chest system, and abdominal system. This is clearly erroneous. It is of course not what we have said; we wish to approach these things precisely, not in dilettante fashion. One must know these things correctly, especially if one also wants to understand how three elements flow into one another and compose the threefold social organism. To begin with it is empirically evident that it is the head organization that has most to do with cognition, at least mathematical cognition, as it approaches man in the outer world. In relation to this head organizatiion we can now empirically establish that what we can call “dimensionality” confronts us initially as a kind of intimation. You will see best what I mean if we consider the three modes of human activity. The first of these I would like to call the total act of seeing, observation of the world with our own two eyes. Secondly, I would mention man's arms and hands. Even though they are attached to man's trunk and are therefore in a certain way connected with the metabolic system, they also have an inner relationship to the rhythmic system. Through their attachment near the rhythmic system, they are influenced by the life and functioning of this system. The fact that they are located beside the rhythmic system, which is more hidden, allows them to reveal the nature of what would normally be hidden. Please listen carefully; I repeat: The arms and hands, because of their specific location on the human body and through their life functions, can be seen as belonging to the rhythmic system. The most obvious demonstration of this connection is the way they are used freely in gestures to express feelings. When they are used in this way, they are lifted to a higher function than serving merely the body. In the case of animals, the corresponding members, the legs, are used only to serve the body, but in human beings the arms are freed for a higher function. Through the fact that they are used for gestures in connection with speech, they have the higher function of making the invisible aspects of speech visible. The third mode is the activity of walking, an activity primarily of the limb system. Let us consider the activities of seeing, arm movement, and walking from a scientific point of view. In general, what you see with both eyes presents itself to you in two dimensions and these dimensions are independent of any mental activity. I can represent these two dimensions by these perpendicular coordinates. I will draw these as dotted lines for the purpose of later references I wish to make. With these dotted lines representing two dimensions, I want to express the fact that our mental activity of comprehension is not really involved when we look only at these two dimensions. The third dimension is in sharp contrast to this. The third dimension of depth does not stand ready-made before our soul independent of any mental activity. It confronts us as something we undergo as an inner operation of the mind when we supplement what we normally see as the surface of things with the depth dimension and thus obtain a three-dimensional body. Roughly speaking, what we actually do in this case is not brought to consciousness. But when we enter into the activity more precisely, we see that one experiences the depth dimension in a different way from width and height dimensions. We can become aware, for instance, how we are able to guess how distant something is from us. In ordinary observation something is added to the mere observation of the eyes when we progress from a surface-picture consciousness to a full-bodied three-dimensional consciousness. So long as we remain within our consciousness, we cannot say how height perception and width perception are achieved. We simply have to accept the height and width dimensions; for the activity of seeing they are simply given. This is not true of the depth dimension. For this reason I will draw it in perspective; I will draw a solid line to represent the difference. In this third dimension of depth, we are able to have the act of perceiving enter our consciousness in a slightly conscious way. Thus we recognize when we examine the act of seeing, that the height and width dimensions are given to us purely in thought; that is, if we penetrate the act of seeing with our thoughts. The depth dimension, however, is based an an activation of consciousness, a kind of half-conscious mental operation. Therefore, what you may already have heard as the physiological and anatomical interpretation of the total act of seeing must be accepted only in reference to the physical components of the act of seeing, to that aspect which does not involve an operation of the mind; only the perception of surface can be attributed to the act of seeing. In contrast, when considering the depth dimension, it is not sufficient to merely consider the activity of the corpora quadrigemina, the organ in the human body upon which the visualizing activity of the eyes depends, the bodily aspect of seeing — here the cerebrum must serve a mediating function, the cerebrum being that part of the brain to which are attributed the anatomical-physiological aspects of the volitional operation of the intellect. Thus we can grasp this depth dimension when we examine it carefully, using both analytical and synthetic means. The matter of depth perception belongs into the realm of what I would like to call “conscious activation through the human head.” When we turn our attention from the act of seeing to that activity which may be seen externally through the movement of the arms and hands, we immerse ourselves in an element that is very difficult to grasp consciously. Even so, we can follow what takes place in our life of feeling when we gesture with our arms and hands, which are free for this kind of activity, and we can become aware of the way this action is related to depth perception with our two eyes. What is it really that depth perception mediates to us? It is the exact position of the left and the right eye. It is the convergence of the left axis and right axis of sight. The mental judgment of the distance of some object from us depends upon the distance at which the lines of sight cross each other. Very little of this convergence activity of the eyes lying at the basis of the judgment of depth is outwardly perceptible. When we turn to the activity of our arms and hands, we find we are able to distinguish more exactly, with little effort of consciousness, what is happening inwardly when we move our arms in the horizontal plane, in the dimension of right-left, in the width dimension. If we look carefully, our judgment in relation to the width dimension is connected with the feeling we have when we consciously move our arms in a horizontal gesture expressing how wide something is. We have a feeling experience of what we call symmetry. This experience takes place particularly in the width dimension, through the feeling that is mediated to us through our left and right arm movements. Through the corresponding movements of our left and right arms we can actually feel our own symmetry. Our grasping in feeling of the width dimension is translated for us chiefly through the medium of symmetry into mental pictures, and we then also evaluate symmetry in our mental life. But we must not overlook the fact that this judging of the symmetry of the width dimension is something secondary: If we only looked at the symmetry without having the accompanying feelings that correspond to the symmetrical aspects of left and right, our experience would be pale, dry and wanting in its full reality. You can understand all that symmetry shows us if you can feel the symmetry. But you can really only feel the symmetry through the delicate process of becoming conscious of the fact that the movements of the left and right arms belong together, and in the same way the movements of the hands belong together. What we experience in feeling thus supports everything we can experience in relation to the width dimension. But also what we have called the depth dimension in relation to the act of seeing enters our consciousness through something to be found in the activity of our arms. The way the axes of our vision intersect is similar to the way our arms can intersect. When our arms intersect, we have a certain equivalent to the act of seeing. When we cross our arms, first close to us and then farther away, if we follow the points of intersection we can get a sense of depth dimension by trying to experience what is going on in our arms. In these moments we don't experience the width dimension as fully as we do — with no effort on our part — in the act of seeing. But if I would represent symbolically what is expressed in relation to the dimensions by the arms and hands, I would have to sketch the width dimension and the depth dimension as full lines and the height dimension as a dotted line. That is all that I can experience through my arms. The height dimension remains unconscious to us when we make gestures, because we connect our gestures consciously with a surface which is made up of depth and width dimensions. When does the third dimension show itself in a distinct, conscious way? Actually, it only appears to our consciousness in the act of walking. When we move from one place to another, then the line which is this third, vertical dimension changes continually, and although our consciousness of this third dimension while we walk is almost imperceptible, we must not overlook it. In fact, the half-conscious intellectual awareness we can experience is related to this height dimension. Figure 3 Certainly in our casual outer consciousness we don't take into account the changes in position of this line representing the height dimension. But in general when we walk and exercise this walking as an act of will, we continually reestablish the line. We have to say: The delicate consciousness of what is happening in the third dimension when we walk is similar in kind to the delicate consciousness of depth in our act of seeing. If I want now to draw the dimensional aspect of what happens in the activity of the body through the legs and feet, we can say: In the act of walking we can experience an intellectual awareness of activity going on in all three dimensions. So I have to draw the act of walking with three full lines. Therefore, when we examine the act of seeing, which obviously belongs to the head organization, we realize that in the act of seeing there is given ready-made a two-dimensional activity, and in addition we must establish an activity that creates the third dimension — depth. In the action which we have described as representative of the rhythmic system, namely, the free movement of the arms and hands, we can have an inner experience of two spatial dimensions. The third spatial dimension — height — is given to our consciousness in the same way that width and breadth are given for the head organization in the act of seeing. Only in the metabolic-limb system (the connection between these two is only recognized when we study the metabolic activity in the act of walking) is everything open to our consciousness that gives us the full measure of three dimensions. If you consider the following, you will have something extraordinarily important. The only content of our fully alert consciousness is the life of mental pictures. In contrast to this, our life of feeling does not come into our consciousness with the same clarity. As we shall see later, our feelings by themselves have no greater intensity in our consciousness than our dreams. Dreams are rendered from the clear content of daily life, from the fully alert life of mental pictures; in this way they become distinct mental pictures in our consciousness. In the same way, our feelings in daily life are continually accompanied by the mental pictures representing them during our waking hours. In this way our feelings, which otherwise only possess the intensity of dream life, are brought to the distinct, fully conscious life of mental pictures. The will-movements remain completely in the subconscious. How do we know anything of the will? Basically, in our everyday consciousness we know nothing of the real nature of the will. This is made clear in the psychology of Theodor Ziehen, for instance, who in his Physiological Psychology speaks only of the life of mental pictures or the representational life of the mind. He says: As psychologists we can only follow the life of mental images, but we find certain mental images to be tinged with feeling. The fact that the life of feeling, as I explained to you just now, is bound up with the rhythmic system and only shines up into the life of mental pictures, this is unknown to Theodor Ziehen. In his view, feelings are only an aspect of the life of mental pictures. This psychologist simply has no insight into the actual organization of the human being, which I have now to describe to you. Because feelings are bound up with the rhythmic system, they remain in the half-conscious realm of dreaming. And the will activity remains completely unconscious. That's the reason why the average psychologist does not write about it. Just read Theodor Ziehen's strange explanations concerning the activity of the will, and you will see that its real nature is completely missed by such psychologists. When we observe the result of an act of will, this is only something we are able to look at externally. We do not know what has happened inwardly when a will impulse moves our arm. We only see the arm move; that is, we observe the outer happening afterward. Thus we accompany the manifestations of our will with mental images; they are mediated organically through the metabolic system and the limb system related to it. So it is only in part of the human organism, in the metabolic system — which is the bodily aspect of the soul's will activity — that we experience the reality of all three dimensions of space. In our ordinary process of knowing the reality of the three dimensions cannot be grasped. It cannot be grasped, as we will see, until we are able to look with the same clarity into our will activity as we normally do into our mental activity. It cannot come about in our ordinary way of knowing but only with spiritual-scientific knowledge. It is through the activation of the entire man, of the entire limb-and-metabolic system, that our subconscious experience of the three dimensions comes about. What happens is that what is contained in the metabolic-limb system is lifted into the rhythmic system. There it is experienced in its two-dimensional aspect, not in its total reality. When experienced in two dimensions, the height dimension has already become abstract. Only in the subconscious do we normally experience the height dimension. You can see how reality becomes an abstraction in the human organization through the human activity itself. In the working of the human organization, the height or vertical dimension already becomes an abstraction, appearing as a mere line, a mere thought in the region of the rhythmic system. Following this up into the nerve-sense system, what occurs? Both height and width become abstraction. We can no longer experience them; they can only be thought by the intellect as we approach the subject afterward. So in the head, the region of our ordinary knowledge, we only have the possibility of expressing the two dimensions abstractly. It is only the depth dimension for which we still have a faint consciousness in the head. So you can see, it is only due to a delicate perception of the depth dimension that we are able to know anything at all in our normal consciousness of the spatial dimensions. Please now consider: With our present constitution, what if depth perception should become equally abstract? Then we would be left with just three abstract lines — and it would never even occur to us to search for the realities represented by those abstract lines. In this way I have pointed you toward reality. In Kantianism this reality appears in an unreal form. Kantianism speaks of the three dimensions being contained a priori in the human organization, and of the human organization transposing its subjective experience out into space. How is it that Kant came to this one-sided view? He arrived at this because he did not know that what is brought into consciousness in the delicate experience of the depth dimension, and otherwise abstractly, is experienced in its reality in our subconscious. As it is pushed up into consciousness, it is made into an abstraction, with only a small remainder in the case of depth dimension. We experience the reality of the three dimensions through our individual human organization. The reality is present in actuality in the realm of the will, and physiologically in the metabolic-limb system. Initially in this system we are unconscious of reality in our ordinary mind, but we become conscious of it, at first in the thought abstractions of mathematical-geometrical space. With this subject of the three dimensions I wished to give an example of the ways and means by which spiritual science can penetrate human activity. We don't have to remain on the abstract level — where, for example, Kant regards space and time as a priori — but we can progress to a discovery of the concrete aspects of the reality of the human being. I wanted to use this particular example of the actual meaning of space because it will be useful in the future in leading us to an exact understanding of the mathematical facts from all sides. We will speak further of this tomorrow.

Anthroposophy and Science

Lecture II

https://rsarchive.org/Lectures/GA324/English/MP1991/19210317p01.html

Stuttgart

17 Mar 1921

GA324-2

In yesterday's lecture I tried to consider what the origin is, in the human being, of the mental images of the three dimensions. For the moment I would like to leave this subject alone. When trying to illuminate physical facts with spiritual-scientific reflections, it is best to view things from many sides and I wish to do this in these lectures. Today I want to add something to yesterday's view, in order to bring these separate considerations together. We will then raise the whole to the level of a spiritual-scientific point of view. The objection is often heard that spiritual-scientific considerations interest only those who can relate to such ideas. In a certain way one may admit this, but only in a very narrow sense can one have such a feeling. The important question is whether or not it is possible for the results of spiritual-scientific investigation to be understood without special capacities of higher vision. It is precisely this question that I would like to answer in the affirmative. The results of spiritual-scientific investigation are indeed intelligible to a sound human understanding. The only essential element is an openness to what spiritual science has to say, justifying itself from various points of view. One of the attempted refutations of spiritual science, which cannot really stand, is this: that the natural world around us, just as given to us in outer experience, can be explained completely out of itself and there is no possibility of rising from this self-explanatory condition to some more satisfactory explanation. From a certain point of view I would be the first to emphasize that the outer sense world is explicable in itself. On one occasion I tried to make this clear, using an admittedly trivial comparison. I said: when someone examines the mechanism of a clock, he has no need for explanation originating from the world outside the clock if his desire is only to understand the mechanism itself. The clock is from a certain point of view explicable in itself. But of course this does not prevent us from wishing for complete clarity from some other point of view, such as knowledge about the clockmaker and other such things. Naturally these other aspects are outside the mechanism of the clock. Some things cannot be learnt so quickly as is sometimes thought — and for this reason: if one wishes to judge the real inner nature of spiritual-scientific investigation, it is necessary to venture into specifics. One must be willing to observe the way this science actually obtains results originating in the super-sensible realm and applies them in the field of ordinary sensory observation. I would like to speak to you today an this very subject. It must first become clear that real investigation in the field of spiritual science leads to a different kind of knowledge — I might also say a different condition of soul in relation to reality — than is normally present in everyday life, or in ordinary scientific life. The first level of this super-sensible knowledge I have named the imaginative level. Later I will describe the way in which this imaginative level of knowledge is reached through certain work performed in the soul. Today I would like to develop an understanding of what this imaginative level of cognition actually is. For this we must return to an earlier explanation of the nature of mathematical thinking. I attempted to characterize the difference in consciousness between an absorption in something which the external sense world presents to us, which we then penetrate with our intellectual activity (and of course with feeling and will impulses also), and on the other hand the absorption in mathematical thought. We can see that what takes place in the soul in the observation of the sense world is — if expressed purely externally — a kind of interaction, an immediate interaction between the human being and some form or other of the outer world. Please take what I am saying quite literally. It is not my intention to put forward some hypothesis — to speak of some reality hidden behind the phenomena. For the moment I wish only to indicate what is there as content of our completely ordinary consciousness when we confront the world on this level of knowing. There would be absolutely no meaning to this ordinary type of knowledge if we did not assume an immediate relationship to some sort of external world. In contrast to this, in mathematical thought, in the activity of pure mathematical thinking, things are different. The difference is there when we dwell in geometrical, arithmetical, or algebraic regions without any concern for external, concrete sense content. What we bring to inner clarity in this domain, whether it is in some elementary area such as the Pythagorean theorem or in some advanced theory of functions, is something that lives entirely within the creative activity of the soul. What is experienced is the continuity of the activity and the visualization of one's own activity. This “high” mathematical thinking — if I may call it that — which takes place entirely within the soul, is then found in today's mathematically-oriented science being applied to the outer world. What had been a process of inner work experienced purely inwardly, is then applied to our outer sense world. This should indicate that our mathematics can be characterized as purely pictorial. One can say: what we experience mathematically has as such no content, it has none of the content that we observe in our natural surroundings. In this regard, mathematical thinking is devoid of content, it is mere image. Yesterday, when we spoke of the spatial dimensions, I showed how what mathematical thinking only makes images of, is actually real and full of content; but mathematical thinking itself is merely imagery. If this were not so, we could not apply it as we do today to natural science. If this thinking were not just something pictorial, some reality would have to merge into the act of cognition. And the fact that something real does not merge with the act of cognition becomes conscious experience for us if we really enact this act of cognition. As we recognize the pictorial character of mathematical thought, we can realize that we experience these mathematical pictures vividly as a content of consciousness. In fact, we are able to experience this content so vividly just because we see that certain things are hidden there which we must assume to exist from the evidence of our senses, in contrast to what we experience as the mathematical thinking itself. In mathematical thinking we are right inside what actually takes place; we can say that we are entirely bound up with what takes place. This, along with the pictorial character of mathematical activity, permits us to have a clear consciousness of what we are actually experiencing. That is why we really know that when we work in mathematics we are in a realm where certainties of knowledge hold sway. Someone may have noticed the difference in the experience one has studying external sense realities or if one is active in the field of pure mathematics. Most important is the fact that in the process of mathematical thinking, one is assured of continually following everything one does with full, clear consciousness. I believe I am not exaggerating when I say that clarity of consciousness can be measured against mathematical thought, its highest standard. In fact, when we engage in mathematical thinking, there is no possibility to doubt that each single manipulation we perform is accompanied by our inner conscious activity — for each is inwardly visible. We have ourselves in complete control, so to speak, when we think mathematically. And, dear friends, the condition of consciousness present in mathematical thinking is in fact what a person strives for who strives toward what I call imaginative knowledge. When we think mathematically, what is really the content of our soul? It is the numerical world, the spatial world, and so on. I will speak of this later. Thus we have in our soul the content of a particular field with a certain pictorial representation. To work in a similar condition of soul but toward another pictorial content, is what constitutes the development of imaginative cognition. And this brings me to the following. When we apply mathematics to outer nature (at first we can hardly do otherwise if we are accustomed to this approach), we apply it to only one part of nature, which we call the mineral world. In the mineral world we are presented with something that in a certain way is fully suited to a pure mathematical approach. But the moment we rise from the merely mineral to the plant or other kingdoms of nature, then the mathematical approach to which we are accustomed is of no use to us. A person who strives to rise to the imaginative level of knowledge desires to gain something more in his soul life than geometrical constructs or numerical relationships. He would like to gain forms that will live in his soul in exactly the same way as these mathematical forms, but which go beyond the mathematical in their content. He would like to gain forms that he can apply in the same way to the plant kingdom as he applies purely mathematical forms to the mineral kingdom. I will speak later concerning exact methods which lead in the direction of imaginative forms. Our first concern must be that everything that leads to an imaginative level of knowledge shall take place in a condition of soul that is absolutely equivalent to mathematical cognition. Actually, the best preparation for the development of imaginative cognition is to have dealt as much as possible with mathematics — not so much in order to reach particular mathematical insights as to be able to experience clearly what the human soul does when it moves in the realm of mathematical structures. This activity of the human soul, this fully conscious activity, is now to be applied to another area. It is to be applied in such a way that out of our inner constructs — if I may use the expression in a wider sense — we form further constructs which enable us to penetrate plant life in the same way that we penetrate mineral nature, chemical-physical nature with mathematical constructs. I must raise all this into particularly sharp relief because of the way the word “clairvoyance” is normally used, and the way this incorrect usage is applied to the supersensory vision exercised in spiritual science. Frequently, what can quite correctly be designated as clairvoyance is confused with phenomena that can arise in the human constitution when conscious functions are suppressed so that they fall below the level of everyday consciousness — as in hypnosis, under the influence of suggestive mental images, and so forth. This suppression of consciousness, this entering into a subconscious realm, has absolutely nothing to do with what is meant here by the attainment of imagination. For in the case of imagination we have an enhancement of consciousness, we go in exactly the opposite direction from what is often called clairvoyance when the term is used in a trivial sense. As it is commonly used, the word is not given its correct meaning (“clear vision,” or “seeing in the light”), but rather “a reduced vision” or “dim vision.” At the risk of being misunderstood, it would not be incorrect to describe the upward striving toward imaginative knowledge as a striving toward clairvoyance. From the few words I have said on this subject, the difference should be clear to you between “dim vision” and a truly “clear vision.” Everything we encounter in a state of soul more or less inclined toward mediumship, shows us a reduction of consciousness. It may entail an artificial lowering of the consciousness, or it may be that the human being was somewhat feeble-minded in the first place, making his consciousness easily suppressible. In no case is it ever what you could compare to an inner state as luminous and clear as a mathematically-attuned state should be. What is widely called clairvoyance today — no doubt you have experienced this — has extremely little to do with a striving toward a mathematical clarity of soul. Quite the contrary, what is usually found is the desire to plunge as deeply as possible into the darkness of confusion. Imaginative vision is the opposite of this, as I will now describe to you. To begin with, imaginative vision is something that can only be present in the soul after being developed. After all, a five-year-old child is not yet a mathematician; the mathematical pictorial capacity must first be developed. It is also not strange that a development of soul from a pre-mathematical capacity to a mathematical capacity can be continued further in a certain way. That is, what has already been brought to a certain clarity of inner experience in mathematical thought can be developed further. Now, however, we must ask ourselves if someone is correct who says, "Yes, but the relationship must be established to ordinary sense-perceptible observation." In one way he is quite correct, and it is important to pursue this relationship in a detailed way. For this purpose let us consider once again what I called yesterday the nerve-sense system of the human being. The nerve-sense system is concentrated primarily in the head, as I said yesterday, but it extends throughout the human organism. This head organization can also be looked at in the following way. As our starting point let us take something that has proved difficult for modern science for a long time. I have dealt with this in my book Riddles of Philosophy , in the chapter entitled, "The World as Illusion." For the modern way of thinking, it is difficult to establish a proper relationship between the content of sensation itself and what is actually experienced by the human being in his pictorial representation of this content or in his feeling. Indeed, this difficulty has led some to say: What takes place in the world outside us cannot become the content of our consciousness. In fact, they say, the content of our consciousness is the reaction of the soul to the impressions of the outer world; the actual impressions are beyond the perceptible. The domain of the perceptible only consists of what is a reaction of the soul to the sense-world. For quite a while people imagined the situation in a rather crude way, saying — and many still say so even today: Outside in the world are vibrations from some kind of medium, extremely rapid vibrations, and these vibrations somehow make an impression on us. Our soul then reacts to this impression and we conjure up the whole world of color out of our soul, the whole world that can be called the visual realm. What to our consciousness seems spread out all around us — the entire world of color — is in fact only the reaction of the soul to what exists out there, completely in the realm of the unknowable, as some sort of vibrations of a medium that fills space. I offer this only as an example of how such things are pictured, and I would now like to describe what at first is intended as an alternative way of looking at the matter. Let us return to what I spoke of yesterday as the total act of seeing. This may serve as a basis for regarding the same process in the other senses. Let us consider external sense perception: what does it represent for the human being? To make this clear let us think of the realm of the eye. If we consider the eye in a descriptive way, even though it must really be regarded as a living member of a living organism, we can note processes in it that can be followed in the same way as processes in the extemal mineral world. Even though the eye is something living, we can construct a model to show how light falls into it. Through the way the eye is formed, the effect is similar to when we let light pass through a small hole in a wall and then fall on a screen, producing a picture. In short, it is possible to apply to the eye the interpretation that we feel justified in applying to the external, mechanical, mineral world. This can be carried further into the human organism. In spite of differences in the various senses, the eye can be regarded as offering an example for a series of phenomena also occurring in the other senses. You see, what takes place with our model does in fact take place in the eye and thus in our whole organism. And the question is: can we learn what really takes place in our organism? If one insists on a purely external approach, one will say something like this: Well, some sort of unknown outer world exerts an impression on the eye. In the eye something or other happens; this in turn exerts an impression on the optic nerve, and so on up to the central nerve organs. Then, inexplicably, a reaction to all this comes about in the soul. Out of our soul we conjure up the whole world of color as a reaction to this impression. There is no doubt that such an approach leads to an abyss. Indeed, it is already openly admitted by many scientists today that with such a method of investigation, in which we simply look externally — first, at what stands before the eye, then at the process in the eye, then at processes in the nerves and further back, even in the brain — we will never get beyond material processes. The point will never be found where some reaction of a soul nature to the external stimulus occurs. With this approach we never examine our actual experience of the outer world. For the spiritual investigator who develops in himself what I call imaginative cognition, the whole problem is transformed. He reaches a point where, when he looks at the eye, he is no longer obliged to see merely an aspect of the physical-mineral world: he can apprehend something else in the eye through his faculty of imagination. In a mathematical way of thinking we permeate the outer physical-mineral world with geometrical and arithmetical pictures, and feel that what we have imagined comes to meet the outer processes. For one who has developed imaginative cognition, it is not only what he develops mathematically that he experiences coinciding with the process in the eye, but also the imaginative images developed in accordance with imaginative cognition coincide with it. In other words, with these imaginative pictures of the eye one has additional content, so that one knows that with the faculty of imagination a reality is grasped, just as in contemplating external nature a reality is grasped when working with mathematical thought. So now let us understand this properly: in spiritual research, initially the same methods are applied in investigating the eye as are usually applied with the help of mathematics to the external investigation of nature. However, until we have developed imaginative cognition we do not really recognize — especially in regard to the eye — that we are in possession of a reality which is lacking when we confront only the external world. For someone who has advanced to imaginative cognition, outer physical matter is not altered from what it is for ordinary consciousness. Let us keep this firmly in mind. You may have developed imaginative cognition to the highest degree, but if you have developed it correctly and if you maintain the right condition of soul during an imagination, you will not be able to claim, when looking at a physical or chemical or purely mechanical process, that you see more than anyone else who is in full possession of his senses and normal understanding. If someone claims that he sees something different in the inorganic realm from one who has not developed higher vision, then he is on a deviant path of spiritual cognition. He may see all kinds of specters, but the spiritual entities of the world will not reveal their true form to him. On the other hand, the moment one undertakes in imagination to observe the human eye, one has exactly the same experience as one has in mathematical thought when applied to external nature. In other words, when we observe the living human eye with developed imagination, we find ourselves for the first time confronting a complete reality, for now we are not only able to extend our mathematical thought to the eye but we can also extend what we have apprehended in the imaginative realm, What follows from this? I can construct a model of the process that happens in the eye exactly similar to the process that happens in the outer world. I know that it is quite possible to reproduce this process in a darkroom or something similar in the mineral, mechanical world. But I also know that this whole domain which I can reproduce physically contains something else, which, if I want to proceed in the same manner as with mathematics in the inorganic realm, I can penetrate only with imaginative cognition. What does that mean? There is something in the eye that is not present in inorganic nature, and that is only recognized as a reality when one becomes one with it in the same way that one becomes one with inorganic nature through a mathematical approach. When one achieves this, one has reached the human etheric body. Through imaginative activity one has grasped the etheric nature of the human being, in the same way that one grasps the external inorganic world through a mathematical approach. Thus it is possible to indicate quite exactly what one does in order to discover the etheric within a sense organ through imagination. It is not true that the idea of an etheric body is arrived at in any kind of fantastic way. One arrives at this idea by first developing imagination and then — at first for oneself — demonstrating with a suitable object that the content of imaginative cognition can unite with its object in the same way that mathematical thought unites with its object. What light does this throw on the human constitution? Something living in us, the human etheric body, is brought into view in such a way that it joins with what is observed as outer inorganic nature. And what we can assert for the eye holds true, if slightly altered, for the other senses as well. Thus we can say: when we consider one of our senses, what we have is primarily a kind of empty space in our organism (if I may express myself crudely). In the case of the eye, the “organism” is those parts of the brain and of the face that connect with the eye. The outer world has sent “gulfs” into the organism. As the ocean creates gulfs in the Land, so the outer world makes gulfs in our organism and in these gulfs simply continues its inorganic processes. We can reconstruct the inorganic processes that take place there. It is not only outside the eye that we find the inorganic and deal with it mathematically, but we can follow these processes right into the eye. Thus with the eye we can use the same approach as we do to the inorganic realm. What we apprehend through imagination, however, reaches the boundary of the eye and goes beyond it. (I will not speak of this today.) Thus outer nature, which streams in as into a gulf, comes together with a member of the human organism, which does not consist of flesh and blood but nonetheless belongs to the organism and can be known through imaginative cognition. In the eye and the other senses our etheric organization penetrates what streams into these gulfs from the outer world. There is actually an encounter between something of a higher, super-sensible nature — allow me to use this expression; I will explain it in due course — between what can be called our etheric organization and what comes into us from the outer world. We become one with the process in our eye, which we can reconstruct purely geometrically. In the realm of our senses we actually experience the inorganic within us. This is the significant finding to which imaginative cognition brings us. It leads to the solution of a problem that is central for modern physiology and for what is called epistemology. It is central to such investigations because it discloses the fact that we possess an etheric organism, known only through imaginative cognition, that this organism unites with what is thrust into us by the outer world and completely penetrates it. We are now able to see the problem in a new light. Imagine that the human being could direct his etheric body through a photographic apparatus: he would regard what takes place in the photographic apparatus as connected with his own being. Similarly he regards what happens in the eye as connected with his own being. The problems dealt with in anthroposophical spiritual science are truly not fanciful ones. They are precisely the problems over which one can inwardly bleed to death — if I may express it in such a way — when one has no choice but to accept what modern science is in a position to offer in this field. Whoever has gone through all that one can inwardly go through when in striving for the truth one acknowledges the illusionary development of the outer world; whoever has suffered the uncertainty that immediately arises when one wants to comprehend — solely from one's physical understanding — what takes place in the process of sense perception: only such a person will know how strong the forces are that draw one to strive toward a higher development of our faculties of knowledge. I have spoken today of the first stage of imaginative cognition and described its similarity to, and some of its differences from, mathematical thinking. What we experience at this level influences our view of the boundaries of knowledge that are accepted by today's science. If we really approach existence and the world conscientiously as they pose their riddles for us; if we have recognized how helpless ordinary logic and ordinary mathematics are in the face of what is taking place in us at every moment when we are seeing, hearing, and so forth; if we see how helpless we are in our usual approach to knowledge in the face of what normally confronts us in our waking consciousness, then truly a deep longing can arise to widen and deepen our knowledge. A scientist in our modern culture would certainly not claim to be a researcher in some field other than his own; he accepts what a trained investigator in another field has to say to him. The same attitude might well prevail for a while — in a limited sense — toward the spiritual researcher. But it must be repeated again and again: above all, the world does have a right to require the spiritual scientist to tell how he arrives at his results. And this can be shown in every detail. When I look back at the way I have tried to do this for more than twenty years — to report to the world in purely anthroposophical language — I think I am justified in saying the following: If I have still not succeeded in finding a response in the world to this anthroposophical spiritual science; if again and again it has been necessary to speak for those less capable of going into detail because they are not scientifically trained; and if it has not been possible to any great extent to speak for the scientifically trained: then this, as experience has shown, is really due to the scientific schooling. Until now, the scientific community has shown small desire to hear what the spiritual investigator has to say about his methods. Let us hope that this will change in the future. For without a doubt, it is necessary that we progress through the use of deeper forces than those which have shown so clearly that they are of no value. In the last analysis it is those very forces that have led us into a cultural decline. We will speak further about this tomorrow.

Anthroposophy and Science

Lecture III

https://rsarchive.org/Lectures/GA324/English/MP1991/19210318p01.html

Stuttgart

18 Mar 1921

GA324-3

Yesterday I tried to show how, by developing the ability to form imaginative vision, it is possible to gain a different kind of insight into human sense perception than can be gained when we approach it with the logic of the mind. I emphasized especially that this imaginative picturing that lives in the soul — as I said, I will describe its development in due course — has to be built up the way mathematical imagery is built up, the way mathematical constructs are developed, analyzed, and so on. From this, the rest of what I said will also be clear: how we apply the results of our inner mathematical activity to the outer mineral-physical realm; and how in a similar way we apply our imaginative activity to the human senses. In this way we may know what takes place in those "gulfs" — as I called them yesterday — which the physical sense world sends into the human organism. The fact is that with the development of such an imaginative faculty and of knowledge of the real nature of the senses — of what is mainly the head organization — we also gain something else. We become able, for example, to form mental pictures of the plant kingdom. I indicated this yesterday. When we use only spatial and algebraic mathematics to approach plant growth and plant formation, we do not find that this mathematical form of consciousness is able to penetrate into the plant kingdom as it can penetrate into the mineral kingdom. When on the other hand we have developed imaginative cognition, at first just inwardly, then we become able to form mental images applicable to the plant kingdom just as we found it possible with the mineral kingdom. At this point, however, something peculiar appears: we now approach the plant world in such a way that the individual plant appears to us as only part of a great whole. In this way, for the first time we have a clear picture of what the plant nature in the earthly world really is. The picture we receive allows us to see the entire plant kingdom of the earth forming a complete unity with the earth-world. This is given purely empirically to the imaginative view. Of course, with our physical make-up we cannot possibly hold more than part of the earth's plant life in our consciousness. We observe only the plant world of a particular territory. Even if we are botanists, our practical knowledge of the plant world will always remain incomplete in the face of the entire plant world of the earth. This we know by the most simple thought. We know we do not have a whole, we have only part of the whole, something that belongs together with the rest. The impression we have in looking at the partial plant world is very much like being confronted by someone who is completely hidden from view except for a single arm and hand. We know that what is before us is not a complete whole, but just part of a whole, and that this part can only exist by virtue of being connected with the whole. At the same time we arrive at a concept that is completely unlike that of the physicist, mineralogist, or geologist: we see that the forces in the plant world are just as integral a part of the earth as those in the geological realm. Not in the sense of a vague analogy but as a directly perceived truth, the earth becomes a kind of organic being for us — an organic being that has cast off the mineral kingdom in the course of its various stages of development, and has in turn differentiated the plant kingdom. The thoughts I am developing here for you can, of course, be arrived at very easily by mere analogy, as we see happening in the case of Gustav Theodor Fechner. Such conclusions arrived at by analogy have no value for the spiritual science intended here — what we value is direct perception. For this reason it must always be emphasized that in order to speak of the earth as an organism, for example, one must first speak of imaginative mental pictures. For the earth as an integral being reveals itself only to the imaginative faculty, not to the logical intellect with its analogies. There is something else that one acquires in this process, and I wish especially to mention it because it would be most useful to students as regards methodology. In present-day discussions on the subject of thinking and also on how we apprehend the world in general, there is a great lack of clarity. Let us take an example. A crystal is held up to view — a cubic salt crystal, for instance — with the idea of illustrating something or other: perhaps something about its relation to human knowledge, its position in nature as a whole, or something similar. Now it could happen that in the same way that the salt cube is used, a single rose is held up for illustration. The person who holds up the rose feels it is acceptable to ascribe objective life to the rose in the same way as to the salt cube. To someone who does not strive for just a kind of formal knowledge, but who aspires to an experience of reality, it is clear that there is a difference. It is clear that the salt cube has an existence within its own limits. The plucked rose, on the other hand, even on its stem is not living its life as a rose. For it cannot develop independently to the same degree (please note the word) as the salt does. It must develop on the rosebush. The whole bush belongs to the development of the rose; separated from the bush, the rose is not quite real. An isolated rose only appears to have life. I say all this in an effort to be clear. In all observations that we make, we must take care not to theorize about the observations before we have grasped them in their totality. It is only to the entire rosebush that we can attribute an independent existence in the same sense as to the salt cube. When we rise to imaginative mental Images, we acquire the ability to experience reality in a certain completeness.Then what I have just said about the plant world can be accepted. We see it as a whole only if our consciousness is able to apprehend it as a whole, if we can regard everything confronting us separately — all the different families and species — as part of the entire plant organism which covers the earth, or better said, which grows out of the earth. Thus through imaginative mental images one not only gains understanding of the sense world, one also has important inner experiences of knowledge. I would like to speak of these inner experiences of knowledge in purely empirical terms. As human beings we are in a position to look back with our ordinary memory to what took place in our waking life, back to a certain year in our childhood; with our power of memory we can call up one or another event in pictorial form out of the stream of our experiences. Still, we are clearly aware that to do this we must exert a distinct effort to raise individual pictures out of the past stream of time. As this imaginative vision develops further, however, we arrive gradually at a point where time takes on the quality of space. This comes about very gradually. It should not be imagined that the results of something like imaginative vision come all at once. It is pointless to think that the acquisition of the imaginative method is easier than the methods employed in the clinic, the observatory, and so on. Both require years of work: one, mental work; the other, inner work in the soul. The result of this inner work is that the individual pictorial experiences join one another. At this point, time — which we usually experience as “running” when we look over the course of our experiences and draw up one or another memory experience — now time, at least to some extent, becomes spatial to us. All that we have lived through in life — almost from birth — comes together in a meaningful memory picture. Through this exertion of imaginative life, of “looking back,” of remembering back, individual moments appear before the soul. These moments are more than a mere remembering. We have a subjective experience of viewing our life lived here on earth. This, as I said, is a practical result of imaginative mental imaging. What kind of inner experience arises parallel to this inner viewing, this panorama of our experiences? We are quite clear that the strength of our soul which brings these memory pictures to consciousness is related to our ordinary bright, clear power of understanding. It is not itself the power of understanding, but it is related to it. One can say: What we have been striving to attain — that our consciousness will be illuminated by this imaginative cognition in all our activities as it is in mathematical activity — happens for us when we come to these memory pictures. We have images and we hold them as tightly as we hold the content of our intellect. Thereby we come to a definite kind of self-knowledge, a knowledge of how the power of understanding works. For we do not merely look back at our life: our life presents itself to us in mirror images. It shows itself in such a way that this comparison with a mirror really holds true. We can extend the comparison and speak of understanding reflected images in a mirror by applying optical laws. Similarly, when we come to inner imaginative perceptions, we can recognize the power of the soul that we usually think of as our mental capacity becoming enhanced, so that we experience our intellect creating not only abstract pictures but concrete pictures of our experiences. At first a kind of subjective difficulty arises, but once we understand it we can proceed. We experience clarity as in mathematics when we experience these pictures. But the feeling of being free — not in a behavioral sense, but in one's intellectual activity — is not present in this kind of imagining. Please do not misunderstand me. The entire imaginative activity is just as voluntary as our ordinary intellectual activity. The difference is that in intellectual activity one always has a subjective experience (I say "experience" because it is more than a mere sensation), one is really in a realm of imagery, a realm that means nothing from the point of view of the outer world. We do not have this feeling in relation to the content of the imaginative world. We have the very definite experience that what we are producing in the form of imaginations is at the same time really there. We find ourselves living and weaving in a reality. To be sure, at first this is a reality which does not have an especially strong grip on us and yet we can really feel it. What we can gather from this reality, what we become aware of as we think back from our life panorama to the inner activity that created it, acquaints us inwardly, "mathematically," with something that is similar to the formative force of the human being. Just as mathematical mental images match and explain outer physical-mineral reality, so this something coincides with what is contained in the human formative force or growth force. (It also coincides with the formative force of other living beings, but I will not speak of that now.) We begin to see a certain inner relation between something that lives purely in the soul — namely, imagination — and something that weaves through the human being as the force of growth, the force that makes a child grow into an adult, that makes limbs grow larger, that permeates the human being as an organizing power. In short, we experience what is really active in the growth principle of the human being. This insight appears first in one definite area: namely, the nerves. The life panorama and the experiences described in connection with it give us insight at first into the growth principle in the human nerve organism — that is, the creative principle which continues inward in the nerve-sense organism. We receive a mental picture of an imaginative kind that enables us to begin to understand what our sense organs actually represent. This also gives us the possibility of seeing the entire nervous system as a synthetic sense organ that is in the process of becoming, and as embracing the present sense organs. We learn to realize that at birth, though our sense organs are not fully mature, they are complete with regard to their inner forces; this may be evident from the way I spoke about the relation of imagination to the sense world. At the same time we can see that what lives in our nerve organism is permeated by the same force as are the sense organs, but that it is in the process of becoming. It is really one large sense organ in the process of becoming. This image comes to us as a real perception. The different senses as they open outward and continue inward in the nerve organism — during our whole life up to a certain age — are organized by the power we have come to know in imagination. You see what we are striving to accomplish. We wish to make transparent the forces that work in the human being which would otherwise remain spiritually opaque. For what does the human being know of the way in which these forces are active within him? Something that cannot be mastered by ordinary knowledge, something that can be characterized as ordinarily opaque to the soul and spirit, now begins to be clear. One has the possibility, through a higher kind of qualitative mathematics — if I may use such a phrase — of penetrating the world of the senses and the world of our nerve organism. One might think that when we reach this point we would become arrogant or immodest, but just the contrary, we learn true modesty through knowledge of the human being. For what I have described to you in a very few words is really acquired over a long period of time. For one, the knowledge comes quickly; for another, much more slowly. And often someone who applies the methods of spiritual research with patient inner work is surprised by the extraordinary results. The results that such inner work brings to light, if they are properly described, can be grasped by a healthy human understanding. But to draw these results forth from the recesses of the soul requires persistent and energetic soul work. And what especially teaches us modesty is the recognition that after much hard work, the results of imaginative cognition acquaint us only with our nerve-sense organism. We can realize how shrouded in darkness is the rest of the human organism. Then, however, to reach beyond mere self-knowledge regarding the nerve-sense system, we must attain a higher level of knowledge. (The word "higher" is of course just a term.) Above all I must emphasize (I will go into it in more detail later) that the attainment of imaginative knowledge is based on meditation — not a confused, but a clear methodically-exercised meditation (to repeat the phrase I used in my book Knowledge of the Higher Worlds and its Attainment ), in which over and over again we set before our soul easily surveyable images. What is essential is that they shall be easy to view as a well-defined whole, not some vague memories, reminiscences or the like. Vague memories would lead us away from a clear mathematical type of experience. Easily pictured mental images are required, and preferably symbolic images, for these are most easily viewed as a whole. The important thing is what we experience in our soul through these images. We seek to bring them into clear consciousness in such a manner that they are like a clear memory image. Thus through voluntary activity mental images we have evoked are taken into our soul in the same way that we take memory images into the soul. In a way, we imitate what happens in our activity of remembering. In remembering, certain experiences are continually being made into pictures. Our aim is to get behind this activity of the human soul; how we do this, I will describe in due course. In our effort to get behind the way remembering takes place, we gain the ability to hold easily-surveyable images in our consciousness (just as we hold memory images) for a certain length of time. As we become used to this activity, we are able to extend the time from a few seconds to minutes. The particular images themselves are of no importance. What is important is that through the effort of holding these self-chosen images, we develop a certain inner power of soul. We can compare the development of the muscles of the arm through exertion to the way certain soul forces are strengthened when mental images (of the kind I have described) are repeatedly held in our consciousness by voluntary effort. The soul must really exert itself to bring this about, and it is this exertion of soul that is crucial. As we practice on the mental images we ourselves have made, something begins to appear in us that is the power of imagination. This power is developed similarly to the power of memory, but it is not to be confused with the power of memory. We will come to see that what we conceive of as imaginations (we have already partly described this) are in fact outer realities, and not just our own experiences as is the case with memory images. That is the basic difference between imaginations and memory images. Memory images reproduce our own experiences in pictorial form, while imaginations, although they arise in the same way as memory images, show through their content that they do not refer merely to our own experiences but can refer to phenomena in the world that are completely objective. So you see, through the further development of the memory capacity, we form the imaginative power of the soul. And now, just as the power of remembering can be further developed, so it is also possible to develop another capacity. It will seem almost comical to you when I name it — but the further development of this capacity is more difficult than that of memory. In ordinary life there are certain powers by which we remember, but also by which we forget. It seems sometimes that we do not need to exert ourselves in order to forget. But the situation changes when we have developed the power of memory in meditation. For oddly enough, this power to hold onto certain imaginations brings it about that the imaginations want to remain in our consciousness. Once there, they are not so easily got rid of — they assert themselves. This fact is connected with what I said earlier, that in this situation we have to deal with actually dwelling in a reality. The reality makes itself felt; it asserts itself and wishes to remain. We succeeded in forming the power of imagination (in a manner modeled on mathematical thought); now through further exertion we must be able voluntarily to throw these imaginative pictures out of our consciousness. This capacity of the voluntarily developed "enhanced forgetting" must be especially cultivated. In the forming of these inner cognitive powers — enhanced memory and enhanced forgetting — we must be careful to avoid causing actual harm to the soul. However, just to point out the dangers involved would be like forbidding certain experiments in a laboratory for the reason that something might explode someday. I myself once had a professor of chemistry at the university who had lost an eye while conducting an experiment. Happenings of this nature are of course not a valid reason for preventing the development of certain methods. I think I can correctly say that if all the precautionary measures are applied which I have described in my books regarding the inner development of soul forces, then dangers cannot arise for the soul life. To continue — if we do not develop the capacity to obliterate the imaginative pictures again, then there is a real danger that we could be tethered to what we have given rise to in our meditations. If this happened, we would not be able to go further. The development of enhanced forgetting is really necessary for the next stage. There is a certain way in which we can help ourselves achieve this enhanced power of forgetting. Perhaps those who are involved in any of the present-day epistemological studies will find this discussion quite dilettante and I am fully aware of all the objections, but I am obliged to present the facts as they happen to be. So — to continue — one can gain help in enhancing the power of forgetting if we further develop, through self-discipline, a quality which appears in ordinary life as the ability to love. Naturally it can be said: love is not a cognitive power, it does not concern knowledge. Perhaps this is true today because of the way cognition is understood. But here it is not a matter of keeping the power of love just as it appears in ordinary life. Here the power to love is to be developed further through work an oneself. We can achieve this by keeping the following in mind. Is it not so? — living our lives as human beings, we must admit that with each passing year we have actually become a slightly different person. When we compare ourselves at a certain age with what we were, say, ten years earlier — if we are honest — we are sure to find that certain things have changed in the course of time. The content of our soul life has changed — not just the particular form of our thoughts, feelings, or life of will, but the whole make-up of our soul life. We have become a different person “inside.” And if we search for the factors through which we have changed inwardly, we will find the following: We may notice first of all what has happened to our physical organism — for this is always changing. In the first half of life it changes progressively through growth; in the second half it is changing through regression. Then we must look at our outer experiences: what confronts us as our own mental world; all those things that leave pain, suffering, pleasure, and joy in the soul; the forces we have tried to develop in our will life. These are the things that make us a different person again and again in the course of life. If we want to be honest about what is really taking place, we have to say we are just swimming along in the current of life. But whoever wishes to become a spiritual scientist must take his development in hand through a certain self-discipline. He might, for instance, take a habit — little habits are sometimes of tremendous importance — and within a certain time transform it through conscious work. In this way we can transform ourselves in the course of our life. We are transformed through being in the current of life, as well as through the work we do on ourselves with full consciousness. Then when we observe our life panorama, we can see what has changed in our life as a result of this self-discipline. This works back in a remarkable way on our soul life. It does not have the effect of enhancing our egotism, rather it enhances our power to love. We become more and more able to embrace the outer world with love, to enter deeply into the outer world. Only someone who has made efforts in such self-discipline can judge what this means. If one has made such efforts, one can appreciate what it means to have the thoughts we form about some process or some thing accompanied by the results of such self-discipline. We enter with a much stronger personal involvement into whatever our thoughts penetrate. We even enter into the physical-mineral world with a certain power of love — that world which if approached only mathematically leaves us indifferent. We feel clearly the difference between penetrating the world with just our weak power of mental imaging, and penetrating it with a developed power of love. You may take offense at what I am saying about the developed power of love: you may want to assert that the power of love has no place in a quest for knowledge of the outer world, that the only correct objective knowledge is that which is obtained by logical intellectual activity. Certainly there is need for a faculty that can penetrate the phenomena of the outer world by means of the bare sober intellect alone, excluding all other powers of the soul. But the outer world will not give us its all if we try to get it in this manner. The world will only give us its all if we approach it with a power of love that strengthens the mind's mental activity. After all, it is not a matter of commanding and expecting that nature will unveil herself to us through certain theories of knowledge. What is really important is to ask: How will nature reveal herself to us? How will she yield her secrets to us? Nature will reveal herself only if we permeate our mental powers with the forces of love. Let me return to the enhancement of forgetting: with the power of love the exercises in forgetting can be practiced with greater force, and the results will be more sure, than without it. By practicing self-discipline, which gives us a greater capacity for love, we are able to experience an enhanced faculty of forgetting, just as surely a part of our volition as the enhanced faculty of remembering. We gain the ability to put something definite, something of positive soul content, in the place of what is normally the end of an experience. Normally when we forget something, this marks the end of some sequence of experiences. Thus in place of what would normally be nothing, we are able to put something positive. In the enhanced power of forgetting, we develop actively what otherwise runs its course passively. When we have come this far, it is as if we had crossed an abyss within ourselves and reached a region of experience through which a new existence flows toward us. And it is really so. Up to this point we have had our imaginations. If in these imaginations we remain human beings equipped with a mathematical attitude of soul, and are not fools, we will see quite clearly that in this imaginative world we have pictures. The physiologists may argue whether or not what our senses give us are pictures or reality. (I have dealt with this question in my Riddles of Philosophy .) The fact is, we are well aware that these are pictures, pictures that point to a reality, but still they are just pictures. Indeed, to achieve a healthy experience in this region we must know that they are pictures — images — confronting us. However, at the moment when we experience something of the enhanced power of forgetting, these images fill with something coming from the other side of life, so to say. They fill with spiritual reality. And we go to meet this reality. We begin, as it were, to have perceptions of the other side of life. Just as through our senses we perceive one side of life, the physical-sensible side, so we learn to look toward the other side and become aware of a spiritual reality flowing into the images of imaginative life. This flowing of spiritual reality into the depth of our soul this is what in my book Knowledge of the Higher Worlds and its Attainment I have called “inspiration.” Please do not take exception to the name — just listen to how the word is being used. Do not try to remember instances where you have met the word before. We have to find words for what we want to say, and often we must use words that already have older meanings. So for the phenomenon just described, I have chosen the word inspiration. Through developing inspiration we finally gain insight into the human rhythmic system, which is bound up in a certain way with the realm of feeling. This leads us to something I must emphasize: the method leading to inspiration which I have just described can actually be followed only by modern man. In earlier periods of human evolution, this faculty was developed more instinctively — for example, in the Indian yoga system. This, however, is not renewable in our age. It goes against the stream of history. And in the spiritual-scientific sense, one could be called a dilettante if one wanted to renew the yoga system in these modern times. Yoga set into motion certain human forces that were appropriate only for an earlier stage of human evolution. It had to do with the development of certain rhythmic processes, with conscious respiratory processes. By breathing in a certain manner, the yogi worked to develop in a physical way what modern man must develop in a soul-spiritual way — as I have described. Nevertheless, there is something similar in the instinctive inspiration we find running through the Vedanta philosophy and what we achieve through fully conscious inspiration. The way we choose to achieve this, leads us through what I have described. As modern human beings, we approach this from above downwards, so to say. Purely through soul-spiritual exercises we work to develop the power within us that then finds its way in to the rhythmic system as inspiration. The Indian worked to find his way into the rhythmic system directly through yoga breathing. He took the physical organism as his starting-point; we take the soul-spiritual being as ours. Both ways aim to affect the human being in his middle system, the rhythmic system. We shall see how what we are given in imaginative cognition (which combines the sense system and nervous system) is in fact enhanced when we penetrate the rhythmic system through inspiration. We shall also see how the ancient, more childlike, instinctive forms of higher knowledge (for example, yoga) come to new life in the present day in the consciously free human being. Next time I will speak further on the relation of the earlier yoga development of the rhythmic system and the modern approach which leads through inner soul-spiritual work to inspiration.

Anthroposophy and Science

Lecture IV

https://rsarchive.org/Lectures/GA324/English/MP1991/19210319p01.html

Stuttgart

19 Mar 1921

GA324-4

I have tried to show how it is possible to rise to supersensory modes of cognition, how through them we gain access to new realms of experience — realms that are completely accessible only to a super-sensory approach. I spoke of the development of imaginative cognition — how by means of it we can understand what takes place in the activity of the human senses, and also understand the nature of the plant world. We learn these things through imaginative cognition as we understand the physical-mineral phenomena of the world through a mathematical approach. Further, I pointed out that through a continuation of these exercises we can attain to a higher form of knowledge — namely, inspired cognition. This opens the way to certain realms of experience through which we can begin to understand what I have called the human rhythmic system. I would like to look at the whole problem once again from a certain angle. When one tries to gain a real understanding of what is included in the sphere of human rhythmic activity, one sees — if one is honest — that the processes taking place here elude the kind of comprehension by which physical processes are understood through mathematics. Nor will one find that they can be comprehended through what I have called imaginative cognition. Everything that has to do with the senses and which is developed in the nervous system in the course of life as I have described — thus also providing a basis for the experience of the life panorama when imaginative cognition has been developed: all of this only clarifies the term, nerve-sense organization. In fact, our sensory organization can only be fully understood when this capacity of imaginative cognition has been acquired by us. Even external natural science has noticed that it is not really possible to understand a particular human sense when it is explained in terms of the general human organization. You will find, if you study what individual scientists have to say in this regard, that the facts themselves — in external phylogeny, or embryology, or ontology — simply point to the necessity of accepting the eye, for instance, as being formed from without. The structure of the eye cannot be understood in terms of the rest of the human organism — as, for example, the structure of the liver or the stomach. It can only be understood as brought about through outer influences, through action from without. But how do we grasp this process of "in-forming from without" in the human organism? Only imaginative cognition makes it comprehensible to us, as a mathematical approach makes physical phenomena comprehensible. From all this you may now begin to see why external science gives us essentially a deficient physiology of the senses. Before I myself was able through imaginative cognition to develop a physiology of the senses, something in me always resisted any wish to subject the realm of the human senses to the sort of measures applied by conventional physiology and psychology. I always found that what they offered to explain the senses was incomplete for the sense of hearing or sight, for example. Particularly the psychological explanations are deficient in this respect. Basically they always start by asking: how are the human senses constructed in general? Then, having given a general characterization, they proceed to specialize for the various senses. But it never occurs to them that their customary descriptions, particularly in the psychology text books, are really only applicable to the sense of touch. There is always something in their theories that does not fit when one tries to apply them unchanged to any other sense. We can understand this when we remember that the physiologies and psychologies use exclusively the ordinary logic of the intellect to put together the facts which external research presents. However, for someone who is examining the question carefully, it is simply impossible to do justice to the sensory phenomena by only the putting together of physical facts. When we apprehend each separate sense with imaginative cognition (when doing this, I was forced to extend the number of senses to twelve) and not just intellectually, we arrive at their true individual forms. We see that each separate sense is built into the human being from certain entities, certain qualities of the outer world. This reveals again — to one who will see it — the bridge that is thrown across from what I have called clairvoyant research to what is given by empirical observation. Certainly it can be said that a person endowed with healthy human understanding may still have no inclination to give up a certain point of view, and therefore may find no reason to be interested in clairvoyant research. But there really is an objection to this. When we subject the facts to a thorough analysis, there is a point at which we reach an impasse when we apply only sense observation and the ordinary logic of the intellect. We simply cannot clear up the problems. They leave an unsolved remainder. For this reason we must develop our logical thinking further to imaginative perception. Part of what imaginative perception discloses to us is the individual forms of the various human senses, as well as the gradual formation of the human nervous system. There is something to add to this — I will explain with a short story. Once I was at a meeting of the society that at that time called itself the Giordano Bruno Association. The first to speak at the meeting was a stalwart materialist who elaborated on the physiology of the brain; by this he believed he had given sufficient explanation for the association of mental images and in fact for everything that takes place in mental life. He made drawings for the different parts of the brain and showed how they are assigned different functions — one to seeing, another to hearing, and so on. Then he tried to show how it might be possible, following the neurologist Meynert, to see the connecting paths as physical formations responsible for connecting the individual sensory impressions, the individual mental pictures, and so on. Whoever wishes to learn about this can read about these extremely interesting investigations by the important neurologist Meynert, for they are still significant even for the present day. Well, after this materialistically tinged but still quite ingenious explanation, in which the brain was presented not as the mediator but as the producer of mental life, another man stepped forward, just as stalwart an Herbartian as the man before him was a materialist. This man said the following: Figure 1 Yes, I see what you have sketched, the various parts of the brain, their connections, and so forth. We Herbartians, the philosophers, could actually make the same diagrams. I could draw exactly the same thing. Only I would never intend it to represent parts of the brain and neuronal tracts. Rather, I would draw the mental images directly — thus, and the soul forces that are active in this picturing activity as they go from image to image. The drawing actually comes out the same, he said, whether I, an Herbartian, draw the psychic processes, or you, a physiologist, draw the parts of the brain and their connections. And it was truly interesting how one drew his diagram —I will draw it here schematically — and then the other drew his. The drawings were identical. The one drew to symbolize the life of the soul, while the other drew brain processes, which he also symbolized. In this way the two of them then disputed the matter — of course, without one convincing the other — but they actually drew two altogether different things in exactly the same way. This is in fact a characteristic experience in the field of knowledge, because when one tries to illustrate mental pictures symbolically through diagrams, as Herbart did (it can also be done in other ways), one actually arrives at something very similar to what one gets when one sketches processes and parts of the brain. How does this happen? This is something that becomes clear only to imaginative cognition, when we see in the retrospective life panorama how the independence of the soul life develops. We see how the etheric body actually organizes — and, in fact, has already at birth to some extent organized — the brain. It permeates the brain in its organization. Then we are not surprised to find out that the brain grows similar in formation to the entity which permeates it. But we do not come to real insight in the matter until we are able to perceive that there is an activity of soul working on the organization of the brain. This is similar to when someone paints a picture and what he paints resembles what he is copying. It is similar because the image he has in his mind works on in his painting and brings about the similarity. In the same way, what is found in the brain — actually in the entire nervous system — as the consequence of a forming activity on the part of the soul, will be similar to the soul's forming activity, or to the soul content itself. But if we wish to understand the activity that works itself into the nervous system, we must simply say: in its origin and development, the whole nervous system is an expression of a reality that may only be viewed imaginatively. The brain and the entire nervous system are, of course, external physical formations. But we do not really grasp them unless we comprehend them as imaginations that have become physical. Thus what the spiritual investigator generally calls imagination is not, as one might suppose, absent from the phenomenal world — it is indeed present, but in its physical image. This fact occasionally makes itself manifest in a striking way, as in the case of those two men, the one a physiologist, the other a philosopher, who portrayed two different things in the same way. But this has still another aspect. I have already referred to the research of the psychiatrist, physiologist, and psychologist Theodor Ziehen. Theodor Ziehen undertook to explain mental life in such a way that he replaced it by brain activity in every particular. His explanation is essentially the following: he contemplates mental life; he then considers the brain and nervous system anatomically and physiologically (to the extent that present empirical research permits) and shows which processes, in his opinion, are present in the brain for a particular mental activity (including memory). I have pointed out, however, that his explanation — which is truly valuable for the study of mental life and brain activity — is forced to come to a standstill before our life of feeling and our life of will. You will find this in Ziehen's Physiologische Psychologie ( Physiological Psychology ). There is, however, a shortcoming in this psychology. Although he makes everything so enticing by explaining mental life in terms of processes in the brain, in the end he does not completely account for such things as the forms that are present in the brain. To do this it is necessary to bring in an artistic principle; and this again is nothing else than the outward expression of imaginative cognition. Were Ziehen to consider this, his explanation of mental life through brain processes would not be fully satisfying to him either. When he wants to move on to the realm of feeling, he finds himself completely at sea. He is not able to account for feelings at all. So he tacks a “feeling coloration” onto the mental images. This is nothing but a word; when one cannot go any further, one makes do with a word. He says: Yes, in certain cases we are dealing not just with mental images, but with feeling-tinged mental images. He comes to this because he is unable to fit feeling into the brain, where it might enter into mental life. Also he does not find an organic basis for feeling that would permit him to make a link to mental life similar to that of the brain and nerves. In the case of brain and nerve activity it is easier because researchers like Theodor Ziehen are — most of them — extremely clever when it comes to an intellectual or mathematical understanding of the entire natural realm. I mean that exactly — without irony. In science these days an extraordinary amount of intellectual acumen has been applied in this direction. If you should decide to become better acquainted with the whole anthroposophical movement, it would become clear to you that in no way do I favor dilettante talk about abstruse nebulous anthroposophical conceptions while arrogantly disputing what present-day science presents, or that I approve when a speaker does not know present-day science well enough to acknowledge it in all its proper significance. I hold firmly to the standpoint that one can pass judgment on present-day science from an anthroposophical point of view only if one is really familiar with this science. I have had to suffer continually from the actions of anthroposophists who, without having an idea of the importance and task of contemporary science, talk loosely about it. They think a few fine anthroposophical phrases they have learned entitle them to pass judgment on what has been achieved through years of painstaking, conscientious, and methodical work. This stage we must of course leave behind us. Now, to continue, what actually happens is this: one arrives at the point of finding the relation between mental life and nerve-sense activity. But something is always left unexplained. Something always eludes one's attention. One swims slowly from the point of view of rational, logical, mathematical construction into a realm where things become unclear. One examines the senses and sees their continuation in the nervous system — and that is where one should take the next step into imaginative thought. But to some degree every human being has a dim feeling of the transformation of well-defined mathematically constructible figures into something that cannot be grasped mathematically and yet manifests itself clearly in the brain and nervous system. As a result of this feeling it is said that someday we shall also succeed in penetrating those parts of sensory life and nerve life that evade direct, purely mathematical construction. In other words, something is put off as a future ideal that is in fact attainable now if one will simply admit that it is not possible to penetrate the realm of the senses and nerves merely by rational cognition. This must be led over to something pictorial, something evoked just as consciously as a mathematical figure, but going beyond the mathematical. I mean, of course, imagination. Perhaps for some of you it would be helpful to make an exact picture of how ordinary analytic geometry relates to so-called synthetic or projective geometry. I would like to say a few words on this subject. In analytic geometry we discuss some equation of the kind y=ƒ(x) . If we stay, for instance, in the x-y coordinate system, then we say that for every x there is a y , and we look for the points of the y -coordinate, which are the results of the equation. What is actually occurring here? Here we have to say that in the way we manipulate the equation, we always have our eye on something that lies outside of what we ultimately seek, because what we are really looking for is the curve. But the curve is not contained in the equation — only the possible x and y values are contained in the equation. When we proceed in this manner, we are actually working outside the curve; and what we get as values of the y -coordinate in relation to the x -coordinate we consider as points belonging to the curve. With our analytic equation, we never really enter the curve itself, its real geometric form. This fact has significant implication as regards human knowledge. When we do analytic geometry, we perform operations which we subsequently look for spatially; but in all our figuring we actually remain outside of a direct contemplation of geometrical forms. It is important to grasp this because when we consider projective geometry, we arrive at a very different picture of what we are doing. Here, as most of you know, we don't calculate, we really only deal with the intersection of lines and the projection of forms. In this manner we get away from merely calculating around the geometrical forms, and we enter — at least to some degree — the geometrical forms themselves. This becomes evident, for example, when you see how projective geometry goes about proving that a straight line does not have two, but only one point at infinity. If we set off in a straight line in front of us, we will come back from behind us (this is easily understood from a geometrical point of view), and we can show that we travel through exactly one point at infinity on this line. Similarly, a plane has only one line at infinity, and the whole of three-dimensional space has only one plane at infinity. These ideas — which I am only mentioning here — cannot be arrived at by analytical means. It is not possible. If we already have projective-geometric ideas, we may imagine we can do it; but we cannot really. However, projective geometry does show us that we can enter into the geometrical forms, which is not possible for analytic geometry. With projective geometry it is really possible. When we move out of mere analytic geometry into projective geometry, we get a sense of how the curve contains in itself the elements of bending, or rounding, which analytic geometry describes only externally. Thus we penetrate from the environment of the line, the surroundings of the spatial form, into its inner configuration. This gives us the possibility of taking a first step along the way from purely mathematical thinking — of which analytic geometry is the prime representative — to imagination. To be sure, with projective geometry, we do not actually have imagination yet, but we approach it. When we go through the processes inwardly, it is a tremendously important experience — an experience which can actually be decisive in leading us to an acknowledgment of the imaginative element. Also, this experience leads us to affirm the path of spiritual research, inasmuch as we can form a real mental picture of what the imaginative element is. When I was reading the memoirs of Moriz Benedict — a good natural scientist and physician of our day — I found them in general to be unpleasant, blase and arrogant, but at one point I felt real sympathy. There he says something which seems to me quite correct; he finds that medical doctors lack the preparation that the study of mathematics can give. Of course, it would be a very good thing indeed if physicians had more mathematical preparation, but in this regard we must just register the shortcomings in contemporary training. From my point of view, however, while reading his memoirs, I could not help feeling: No matter how good their mathematical conceptions, doctors would still not be in a position with them to properly account for the kinds of forms that exist, for example, in the sense and nervous systems. There one can only succeed by transforming mathematical knowledge and advancing to imaginative knowledge. Only then does the specific nerve or sense structure reveal itself to us in a similar manner as a physical-mineral structure reveals itself to the mathematical representation. Matters such as these allow you to see how, in every area, the doors stand open for contemporary science to enter into what spiritual research wishes to give. In the coming days, if we manage to enter, even a little bit, into medical-therapeutic aspects, you will see how wide open the doors really are for spiritual research to enter and throw light on all that cannot be revealed through the usual methods of investigation. Let us now suppose we proceed on this path, but we do not wish to proceed any further than imagination, which I will describe further tomorrow. Let us suppose we do not wish to move forward to inspiration. We will then not have the slightest possibility of even recognizing something in the human organism as the approximate image or bodily realization of a soul-spiritual nature — so that two men with completely opposite ways of thinking will draw these structures similarly. Only through inspired cognition will we have our first opportunity to become aware in the human being of the rhythmic system, encompassing primarily the processes of respiration and blood circulation. Only at this point are we able to tolerate — if I may express it thus — the outer lack of similarity between the physical structures and the soul-spiritual. The life of feeling does in fact belong directly to the rhythmic system in the same way as the life of mental representation belongs to the nervous system. The nerve-sense system, however, is a kind of external physical image of mental life, while the rhythmic system — what is accessible to external sense-empirical investigation — shows hardly any resemblance to what takes place in the soul as feeling. Just because this is so, external research never discovers that this similarity exists; it only reveals itself when we come to another kind of cognition than that of imagination. With this step, as I indicated yesterday, we approach a path of knowledge which was followed in a more primitive, or instinctive way in the practice of yoga in ancient India. Those who practiced the yoga system, (as already pointed out, to try to renew this yoga would be wrong, because it is not suited to the changed constitution of modern man) tried for short periods of time to replace the ordinary, normal, but largely unconscious respiratory process with a more consciously regulated respiration. They inhaled differently from the way we ordinarily do in our normal, unconscious breathing. The breath was then held, to bring to awareness of how long it was held and then it was exhaled in a particular manner. At best, such a method of breathing could give additional support to present spiritual life. In India, however, this process was done by those who wanted to reach the awe-inspiring Vedanta philosophy or the philosophical foundation of the Vedas. This is no longer possible todäy. In fact, it would contradict what the human constitution actually is today. Nevertheless, much can be learned from this way in which a rhythmic process is willfully made conscious by an alteration of normal breathing. What otherwise takes place quite naturally in the course of living is lifted into the domain of conscious will. Thus respiration — all that takes place in the human life-process during breathing — is carried out consciously. Because it is carried out consciously, the entire content of human consciousness changes. In breathing we draw what is in the environment into our own organization. In the kind of consciously structured breathing process I have described, something of a soul-spiritual nature is also drawn into the human organization. Now consider the following. When we contemplate the human organization as a whole, if we are not satisfied with abstraction but want to move on to reality, then we cannot really say: We are only what is within our skin. We have within us the respiratory process, it may be about to begin, or it may be proceeding with the transformation of oxygen and so on. But what is in us now was outside us before and it belonged to the world. And, what is in us now, when exhaled, will again belong to the world. As soon as we approach the rhythmic system, we do not find ourselves individualized organically in the same way as we picture ourself when we consider only what is not of an aeriform nature within our skin. When the human being becomes fully aware that he exchanges his aeriform organization quite rapidly — now the air is without, now it is within — he cannot help but appear to himself as a self-conscious finger would appear to itself, as a part of our organism. The finger could not say: I am independent — it could only feel part of the whole human organism. As a breathing organism, we must feel the same way. We are members of our cosmic surroundings precisely by virtue of the respiratory organism and the only reason we do not pay attention to the fact that we are a part of it is because we perform this rhythmical organizing activity naturally, almost unconsciously. When, on the other hand, this fact is raised to consciousness through the yoga process, one notices that, in fact, it is not just material air that is inhaled and combined with one's self, but along with the air something of a soul-spiritual nature is inhaled and assimilated. When exhaling, something of a soul-spiritual nature is returned to the outer world. One comes to know not only one's material connection with the cosmic surroundings; one also comes to know one's soul-spiritual connection with the cosmic surroundings. The entire rhythmic process is metamorphosed so that a soul-spiritual element can incorporate itself. Just as the cosmic environment integrates itself into the process of mental representation, so into the breathing process (which otherwise is an inner physical-organic process), something of a soul-spiritual nature is incorporated. In this way the transformed yoga breathing becomes a more pantheistically-tinged way of knowing, in which the separate entities are less individualized. Thus in the Indian, a different consciousness takes shape from the ordinary one. He experiences himself in another state of consciousness in which he is, as it were, surrendered to the world. At the same time, this has the effect of leading him into an objective relationship with his accustomed mental world as he moves down, as it were, with his consciousness into the respiratory-rhythmic system. Before this, his conscious life was in the nerve-sense system, in the form of the sum total of his mentally-viewed images. Now he experiences himself, precisely what he experiences he doesn't know, but as soon as it becomes objective it comes into inner view, and through this he learns to recognize the true nature of his accustomed image world. He now experiences himself one level lower, so to speak, in the rhythmic system. When we become acquainted with this inner process of experience, then we can understand in a new way what is breathing through the Vedas. The Vedanta philosophy is not only something that has taken a different form than it takes in the west; it grows out of something immediately experienced — from the experience that is simply given in a consciousness displaced into the breathing process. There is still a further experience when we descend into this respiratory process. Before I mention it, however, I would like to review more precisely what I indicated the day before yesterday. I said that the yoga-process is not for us any more, and the human constitution has advanced since then. In our age we are no longer capable of entering into the yoga process, simply because our intellectual organization is so strong today; because our mental images are so inwardly “hardened” — this is just meant figuratively — that we would send much more power into the respiratory system than did the Indian with his “softer” mental life. Today the human being would be inwardly numbed or he would disturb his rhythmic system in some other way if he proceeded as the Indian did in the yoga process. As I have pointed out — and as I will describe later in greater detail, we are in a position to advance from a further development of the memory faculty to a development of the process of forgetting. By entering into the depth of the forgetting process, we take hold of respiration from above, and can leave it as it is. We do not need to change it. The right way for modern man is to let it be. With an artificially enhanced forgetting, we shine down, as it were, into the respiratory system. We transfer our consciousness into this region. But now it is possible to do this in a more fully conscious way, with greater penetration of the will than the ancient Indian could use. In this way, we now have the possibility to recognize the rhythmic system in its association with human feeling life. When we gain the ability to retain a mental imaging capacity in this region, when it becomes possible for us to have inspired mental images, we no longer feel the need for the sense-perceptible structure to be similar to the soul structure — as is the case where the brain structure is similar to the connections between mental images. In fact, the external, sensory structure can be so different from the related soul element that it completely escapes the notice of conventional physiology, as in Theodor Ziehen's case. Looking at the world in a more spiritual way, looking at it purely spiritually, we find that in fact it is the feeling life that enables us to penetrate consciously into the rhythmic system. Thus we begin to see why in earlier times (the Indians, after all, are simply representative of what came from the earlier stages of human development), when human beings strove to go beyond an ordinary everyday understanding of the world, their path to knowledge led them down into the life of feeling. Cognition remained an activity of mental picturing, but it penetrated into the feeling life, it was suffused with feeling. Modern research only speaks of a coloration of feeling. What the yogi of old, and human beings in general in older cultures experienced, was a sinking down into the realm of feeling. Yet this was without the vagueness typical of this realm. The full clarity of conscious mental life remained, and yet not only was feeling not extinguished, but it appeared more intense than in ordinary everyday life, thereby suffusing everything that normally had a sober, prosaic character. At the same time the mental images, in going through a metamorphosis, a deepening, took on other forms. These transformed mental images were so suffused with feeling that the will was directly stimulated. What this human being of earlier times then did was something that we do today in a more abstract way, when we take something we are carrying in our soul and use it as a subject for drawing or painting. What was experienced in yoga in this way was so intense that the mere drawing or painting of it would not have been enough. It was an entirely natural step to transform it into an external symbolism embodied in external objects. Here you have the psychological origin of all that appeared in the form of rituals in ancient culture. To find the motive for these rituals, one must look at their inner nature. It was not out of some form of childishness, but out of his way of experiencing knowledge that the human being of old came to perform ritualistic ceremonies and to regard them as something real. For he knew that what he molded into his ritual was something inward put into outer form, something rooted in a cognition from which he was not estranged, but which connected him with reality. What he impressed into his ritual was what the world had first impressed into him. When he had reached this state of knowledge, he said to himself: Just as the physical breath from the surrounding cosmos lives within me, now the spiritual essence of the world lives in my transformed consciousness. And when I in turn make an outer structure, when I build into the objects and rituals what first formed itself in me out of the spiritual cosmos, I am performing an act that has a direct connection with the spiritual content of the cosmos. Thus for the human being of an ancient culture, the outward cultic objects stood before him symbolically in such a way that through them he felt again the original connection with the spiritual entities he had first experienced through ordinary knowledge. He knew that in the elements of the ritual something is concentrated in an outer visible form. This something does not exhaust itself in the outward expression I see before me, for the soul-spiritual powers that live in the cosmos are alive in the ritual while it takes place. What I am relating to you is what went on in the souls of those human beings who as a result of their inner experiences gave form to the rituals. One reaches a psychological understanding of such rituals when one is willing to accept the idea of inspired cognition. These things simply cannot be explained in the usual external way. One must enter deeply into man's being and must consider how the various functions of the entire human race developed in sequence — how, for instance, in a certain epoch particular rituals developed. The religious ceremonies of today are actually rernnants of something that took form in ancient times and then stood still afterward. This is why it is becoming so difficult for a person today to understand the reason for the religious ritual, for he feels it is no longer a justifiable way of relating to the outer world. Furthermore, we can see another aspect of how the soul works in the course of mankind's development. Deep knowledge, as I have described, underlies the creation of a ritual or the carrying out of a ritual. But humanity has developed further and another factor has entered in, which still lives more or less in the unconscious. What shows itself most clearly when we reach imaginative cognition is that the nervous system is formed out of our soul-spiritual powers. This too has developed in the course of human history. Particularly since the middle of the fifteenth century, humanity in all its various groups has developed in such a way that this instinctive incorporation of the soul-spiritual powers into the nervous system has become stronger than it was formerly. We simply have a stronger intellect today. This is obvious when one studies Plato and Aristotle. Our intellect is organized differently. In my Riddles of Philosophy I have demonstrated this from the history of philosophy itself. Our intellectual functioning is different. We simply overwork that element of the soul which has grown stronger in the course of human development. And this element which has grown stronger has also become more independent. The increasing independence of our intellect from the nervous system simply has not reached the attention of the philosophers — or of mankind in general. Because the human being has grown stronger on the inside, so to say — because he has penetrated his nervous system with a stronger organizing power from the soul-spiritual realm, he feels the need to make use of this intensified intellectual activity in the outer world. In ancient times, knowledge attained inwardly was used in the creation and the exercise of rituals; there was a striving to carry over what had been originally experienced inwardly as knowledge into what was performed outwardly. In the same way today, the longing arises to satisfy our stronger, more independent intellect in the outer world. The intellect wants a counterpart that corresponds to the ritual. What is the result of such a wish? Please accept the paradox, for psychologically it is so: Where inner experience is expelled, as it were; where the intellect alone wishes to arrange a procedure so that it can live in the object just as cosmic life was once intended to live in the “object” of the ritual: what results from this is the scientific device, serving the experiment. Experiment is the way the modern human being satisfies his now stronger intellect. Thereby he lives of the opposite pole from the time when man satisfied his relation to the cosmos through the cultic object and ritual ceremony. These are the two opposite poles. In an ancient culture of instinctive clairvoyance, the impulse was to give outer presence to inner cosmic experience in what could be called ritualistic exercise. Our intensified modern intellect, on the other hand, is such that it wishes to externalize itself in controlled movements that are devoid of all inwardness, in which nothing subjective lives — and yet the experiment is controlled just precisely through the subjective attainments of our intellect. It may seem strange to you that the same underlying impulse gives rise on the one hand to the ritual, and on the other to the experiment, but one can understand these polarities if one considers the human being as a whole. Starting with this as a foundation, we will continue our discussion tomorrow.

Anthroposophy and Science

Lecture V

https://rsarchive.org/Lectures/GA324/English/MP1991/19210321p01.html

Stuttgart

21 Mar 1921

GA324-5

In the lectures so far, I have spoken of the capacities for supersensory knowledge and I have named them Imagination and Inspiration. Today I would like to say something about acquiring these capacities. At the moment I can only mention a few details. In my book Knowledge of the Higher Worlds and Its Attainment , you will find this presented in greater depth. Today, however, I would point out what is important in the context I have chosen for the present lecture. I have indicated that what I call Imagination with regard to knowledge of the world is attained through a development modeled on the memory process, only on another level. The importance of the memory process is that it retains in picture form what the human being encounters in outer experience. Our first task will be to understand certain characteristics of the ordinary memory process, and then we must distill out what can be called pure memory in the true sense, also in ordinary life. One of the peculiarities of memory is that it tends to alter to a certain degree what has been experienced. Perhaps it is unnecessary to go into detail here, since most of you will be quite familiar with the fact that at times you can despair when you are relating something, and you hear from your own telling what has become of your experience by its passing through your memory. Even in ordinary life a certain self-education is necessary if we wish to come closer to pure memory, to the capacity to have these pictures ready at hand so that they faithfully render our experience. We can distinguish what happens with memory. On the one hand there is an activity of fantasy, quite justified, that goes on in an artistic direction. On the other hand there is a falsification of our experience. It should suffice for the moment to point out the difference between the fantasy tendency and the falsifying tendency, and that we must be able to experience this to maintain a healthy soul life. Certainly we must be aware of how memory is transformed by our fantasy, and how, when it is not subjected to such arbitrary action, when it is allowed to proceed according to a kind of natural similarity in the soul, it becomes increasingly faithful and true. In any case, both from the good tendency to artistic fantasy, as well as from the forces active in falsifying the memories — when we study it psychologically, we can recognize what is alive in the memory forces. And out of these forces, something can take form that is no longer just memory. For example, one can point to certain mystical teachings that are in fact essentially falsified memory images; and yet we can profit from studying 'such images that have taken the form of earnest mystical experience. What concerns us at this moment, however, is what I have already indicated, that we can attain a power of the soul which is alive in the memory which can be metamorphosed into something else. This must happen in such a way that the original power of memory is led in the direction of inner faithfulness and truth, and not toward falsification. As I have said, when we repeatedly evoke easily surveyable mental images, which we intentionally combine out of their separate elements and then view as a whole, just as easily as the mathematical images: when we call up such images, hold them in our consciousness and dwell upon them, not so that we are fascinated by them, but so that at each moment we continue to hold them through an inner act of will — then gradually we succeed in transforming the memory process into something different, something of which we were previously unaware. The details are contained in the book I named, and also in Occult Science, an Outline . If we continue long enough with such exercises (how long depends on the individual) and if we are in a position to expend sufficient soul energy on them, then we come to a point where we simply begin to experience pictures. The form of these pictures in the life of the soul is like that of memories. Gradually we win the capacity to live in such imaginations of our own making, although in their content they are not of our making. The exercise of this capacity results in imaginations rising up in the soul, and if we maintain a “mathematical” attitude of soul, we can make sure at any time whether we are being fooled by a suggestion or auto-suggestion, or are really living in that attitude of soul voluntarily. We begin to have mental images with the characteristic form of memory pictures but with a greater degree of intensity. Let me emphasize: at first these imaginations have the character of memory pictures. Only through inspiration do they become permeated with a more intense experience. At first they have the character of memory pictures, but of such a kind that we know their meaning does not relate to any experiences we have lived through externally since our birth. They do, however, express something just as pictorially as memory pictures express pictorially our personal experiences. They refer to something objective, yet we know that this objective something is not contained in the sphere which is surveyed by our memory. We are conscious that these imaginations contain a strong inner reality, yet at the same time we are aware that we are dealing with just images — just pictures of the reality. It is a matter of being able to distinguish these pictures from those of memory, in order that these imaginations remain pure, so that no foreign elements slip into them. I will describe the outer process, but of course in just a few lectures one cannot go into any great detail. We may form a mental picture of an outer experience and we can see how in a sense the outer experience passes over into our organism, and — expressed abstractly — it then leads a further existence there, and can be drawn forth again as a memory picture. We notice that there is a certain dependence between what lives in the memory and the physical condition of the human organism. The memory is really dependent on our human organism right into the physical condition. In a way we pass on what we have experienced to our organism. It is even possible to give a detailed account of the continuation of the various pictures of our experience in the human organism. But this would be an entire spiritual-scientific chapter in itself. For our memories to remain pure and true, no matter how much our organism may participate in what lives on in the memory process, this involvement may not add anything of real content. Once mental pictures of an experience have been formed, nothing further should flow into the content of the memories. If we are clear about this fact of memory life, we are then in a position to ascertain what it means when pictures appear in our consciousness that have the familiar character of memory pictures, but a content which does not relate to anything in our personal experience. In the process of experiencing imagination we realize the necessity of continually increasing the power of our soul. For what is it that we must really do? Normally our organism takes over the mental pictures we have formed from life and provides memory. Thereby the mental pictures do not just sink down into an abyss, if I may so express it, but are caught and held by our organism so that they can be reflected back again at any necessary moment. With imaginative pictures, this is just what should not be the case; we must be in a position to hold them through inner soul forces alone. Therefore it is necessary for us to acquire something that will make us stronger than we are ordinarily in receiving and retaining mental images. There are of course many ways to do this; I have described them in the books already named. I wish to mention just one of them. From what I now tell you, you will be able to see the relation between various demands of life which spring from anthroposophical spiritual science and their connection with the foundation of anthroposophical research. Whoever uses his intellect to spin all kinds of theories about what he confronts as phenomena in the world (which of course can be extraordinarily interesting at times) will hardly find the power for imaginative activity. In this respect, certain developments in the intellectual life of the present day seem specifically suited to suppress the imaginative force. If we go further than simply taking the outer phenomena of the mineral-physical realm and connecting them with one another through the power of our intellect; if we begin to search for things that are supposed to be concealed behind the visible phenomena, with which we can make mental constructions, we will actually destroy our imaginative capacity. Perhaps I may make a comparison. No doubt you have had some dealings with what could be called phenomenalism in the sense of a Goethean world view. In arranging experiments and observations, Goethe used the intellect differently from the way it is used in recent phases of modern thought. Goethe used the intellect as we use it in reading. When we read, we form a whole out of the individual letters. For instance, when we have a row of letters and succeed in inwardly grasping the whole, then we have solved a certain riddle posed by this row of individual letters. We would not think of saying: Here is a b , an r , an e , an a and a d — I will look at the b . As such, this isolated b tells me nothing in particular, so I have to penetrate further for what really lies behind the b . Then one could say: Behind this b there is concealed some mysterious “beyond,” a “beyond” that makes an impression on me and explains the b to me. Of course, I do not do this; I simply take a look at the succession of letters in front of me and out of them form a whole: I read bread. Goethe proceeds in the same way in regard to the individual phenomena of the outer world. For instance, he does not take some light phenomenon and begins to philosophize about it, wondering what states of vibration lie behind this phenomenon in some sort of “beyond.” He does not use his intellect to speculate what might be hiding behind the phenomenon; rather, he uses his intellect as we do when we “think” the letters together into a word. Similarly he uses the intellect solely as a medium in which phenomena are grouped — grouped in such a way that in their relation to one another they let themselves be “read.” So we can see that regarding the external physical-mineral phenomenological world, Goethe employs the intellect as what I would call a cosmic reading tool. He never speaks of a Kantian “thing in itself” that must be sought behind the phenomena, something Kant supposed existed there. And so Goethe comes to a true understanding of phenomena — of what might be called the “letters” in the mineral-physical world. He starts with the archetypal or “ Ur ”-phenomenon, and then proceeds to more complex phenomena which he seeks either in observation or in experiments which he contrives. He "reads" what is spread out in space and time, not looking behind the phenomena, but observing them in such a way that they cast light on one another, expressing themselves as a whole. His other use of the intellect is to arrange experimental situations that can be “read” — to arrange experimental situations and then see what is expressed by them. When we adopt such a way of viewing phenomena and make it more and more our own, proceeding even further than Goethe, we acquire a certain feeling of kinship with the phenomena. We experience a belonging-together with the phenomena. We enter into the phenomena with intensity, in contrast to the way the intellect is used to pierce through the phenomena and seek for all kinds of things behind them — things which fundamentally are only spun-out theories. Naturally, what I have just said is aimed only at this theoretical activity. We need to educate ourselves in phenomenology, to reach a “growing together with” the phenomena of the world around us. Next in importance is to acquire the ability to recall a fully detailed picture of the phenomena. In our present culture, most people's memories consist of verbal images. There comes a moment when we should not be dependent on verbal images: these only fill the memory so that the last memory connection is pushed up out of the subconscious into consciousness. We should progress toward a remembering that is really pictorial. We can remember, for instance, that as young rascals we were up to some prank or other — we can have a vivid picture of ourselves giving another fellow punches, taking him by the ear, cuffing him, and so on. When these pictures arise not just as faded memories, but in sharp outline, then we have strengthened the power we need to hold the imaginations firmly in our consciousness. We are related to these pictures in inner freedom just as we are to our ordinary memories. With this strengthened remembering, we grow increasingly interested in the outer world, and as a result the ultimate "living together with" all the various details of the outer world penetrates into our consciousness. Our memories take on the quality of being really objective, as any outer experience is, and we have the feeling that we could affectionately stroke them. Or one could say: These memory pictures become so lively that they could even make us angry. Please bear with me as I describe these things to you! It is the only thing I can do with our present language. Then comes the next step: we must practice again and again eliminating these imaginations so that we can dive down again and again into an empty consciousness. If we bring such pictures into our consciousness at will and then eliminate them again in a kind of inner rhythm — meditating, concentrating, creating images, and then freeing ourselves of them — this will quicken powerfully the feeling of inner freedom in us. In this way we develop a great inner mobility of soul — exactly the opposite of the condition prevailing in psychopaths of various kinds. It really: is the exact opposite, and those who parallel what I have just described here with any kind of psychopathic state show that they simply have no idea of what I am talking about. When we finally succeed in strengthening our forgetting — the activity which normally is a kind of involuntary activity — when now we control this activity with our will, we notice that what we knew before as an image of reality, as imagination, fills with content. This content shows us that what appears there in pictorial form is indeed reality, spiritual reality. At this point we have come to the edge of an abyss where, in a certain sense, spiritual reality shines across to us from the other side of existence. This spiritual reality is present in all physical sense reality. It is essential to develop a proper sense for the external world in order to have a correct relationship to these imaginations. Whoever wishes just to speculate about phenomena, to pierce them through, as it were, hoping to see what is behind them as some kind of ultimate reality — whoever does this, weakens his power to retain and deal with imaginations. When we have attained a life of inspiration — that is, experiencing the reality of the spiritual world just as ordinarily we experience the physical world through our external senses — then we can say: now I finally understand what the process of remembering means. Remembering means (I will make a kind of comparison) that the mental images we have gained from our experiences sink down into our organism and act there as a mirror. The pictures we form in our minds are retained by the organism, in contrast to a mirror which just has to reflect, give back again what is before it. Thus we have the possibility of transforming a strictly reflective process into a voluntary process — in other words, what we have entrusted to memory can be reflected back from the entire organism and particularly from the nervous system. Through this process, what has been taken up by the organism in the form of mental pictures is held in such a way that we too cannot see “behind the mirror.” Looking inward upon our memories, we must admit that having the faculty of memory prevents us from having an inner view of ourself. We cannot get into our interior any more than we can get behind the reflective surface of a mirror. Of course what I am telling you is expressed by way of comparisons, but these comparisons do portray the fact of the matter. We realize this when inspiration reveals these imaginations to us as pictures of a spiritual reality. At this moment the mirror falls away with regard to the imaginations. When this happens we have the possibility of true insight into ourselves, and our inner being appears to us for the first time in what is actually its spiritual aspect. But what do we really learn here? By reading such mystics as Saint Theresa or Mechtild of Magdeburg, beautiful images are evoked, and from a certain point of view this is justified. One can enter into a truly devotional mood before these images. For someone who begins to understand what I have just described to you, precisely this kind of mystical visions cease to be what they very often are for the nebulous types of mystic: When someone comes to real inner vision, not in an abnormal way (as is the case with such mystics) but by the development of his cognitive faculty as I have described it, then he learns not only to describe a momentary aspect as Mechtild of Magdeburg, Saint Theresa and others do, but he learns to recognize what the real interior of the human organization is. If one wants to have real knowledge and not mystical intoxication, one must strive toward the truth and put it in place of their mist-shrouded images. (Of course, this may seem prosaic to the nebulous mystic.) When this is accomplished, the mirror drops away and one gains a knowledge, an inner vision of the lungs, diaphragm, liver, and stomach. One learns to experience the human organization inwardly. It is clear that Mechtild of Magdeburg and Saint Theresa also viewed the interior, but in their case this happened through certain abnormal conditions and their vision of the human interior was shrouded in all manner of mists. What they describe is the fog which the true spiritual investigator penetrates. To a person who is incapable of accepting such things, it would naturally be a shock if, let's say hypothetically, a lofty chapter out of Mechtild were read and the spiritual researcher then told him: Yes, that is really what one sees when one comes to an inner vision of the liver or the kidneys. It is really so. For anyone who would rather it were otherwise, I can only say: That is the way it happens to be. On the other hand, for someone who has gained insight into the whole matter, this is for him the beginning of a true relation to the secrets of world existence. For now he learns the origin of what constitutes our human organization and at what depths they are to be recognized. He clearly recognizes how little we know of the human liver, the human kidneys, not to speak of other organs, when we merely cut open a corpse — or for that matter, when we cut open the living human organism in an operation — and get just the one-sided view of our organism. There is the possibility not just to understand the human organism from the external, material side, but to see and understand it from the inside. We then have spiritual entities in our consciousness, and such entities show us that a human being is not so isolated as we might think — not just shut up inside his skin. On the contrary! Just as the oxygen I have in me now was first outside and is now working within me, in the same way — though extended over a long period of time — what is now working in me as my inner organization (liver, kidneys, and so on) is formed out of the cosmos. It is connected with the cosmos. I must look toward the cosmos and how it is constituted if I want to understand what is living in the liver, kidneys, stomach, and so on; just as I must look toward the cosmos and the make-up of the air if I want to understand what the substance is that is now working in my lungs, that continues to work on in the blood stream. You see, in true spiritual research we are not limited to separate pictures of separate organs but we come to know the connections between the human organism and the whole cosmos. Not to be overlooked is the simple symbolic picture which we have already mentioned of the senses. We can in a way visualize our senses as “gulfs,” through which the outer world and its happenings flow into us. At the same time our senses continue inward as I have described them. Little by little we can see this activity from an inner point of view — the forming and molding activity that has worked on our nervous system since our birth. I have described the subjective experience of this activity as a life review, a life panorama, and we discover in the configuration of the nervous system an external pictorial form of what is really soul-spiritual. It can also be said that first we experience imaginations and then we see how these imaginations work in the formation of nerve substance. Of course this should not be taken in too broad a sense, since, as we know, nerve substance is also worked on before birth. I shall come back to this tomorrow. But essentially what I have said holds true. We can say: here is where the activity continues toward the inside; you can see exactly how it goes farther. It is the same activity, in a certain sense, that "engraves" itself into the nervous system. For the parts of the nervous system that are formed completely, this "engraving" activity can be seen streaming through the nerve paths. In childhood, however, for the parts that are still in the-process of being formed, this “engraving” acts as a real modeling force, a structuring proceeding out of imaginations. This leaves the rest of the human organism, about which we will speak shortly — what underlies the muscles, bones, and so on, also the physical basis of the nervous system — in fact, all of the organic tissue. At this point I should relate to you a certain experience I had; it will make this all a bit clearer. I spoke once before the Theosophical Society about a subject I called “anthroposophy.” I simply set forth at that time as much of this anthroposophy as had revealed itself to my spiritual research. There was a request for these lectures to be printed and I set about doing this. In the process of writing them down, they turned into something different. Not that anything that had first been said was changed, but it became necessary to add to what was said by way of further explanation. It was also necessary to state the facts more precisely. This task would require a whole year. Now came another opportunity. There was again a general meeting of the Society and there was a request that the lectures should be ready for sale. So they had to get finished. I sent the first signature (16 pages) of the book Anthroposophy to the printer. The printing was rapidly done and I thought I would be able to continue writing. I did continue writing but more and more it became necessary to explain things more accurately. So a whole number of pages were printed. Then it happened that one signature was only filled up to page thirteen or fourteen and I had to continue writing to fill up all sixteen pages. In the meantime I became aware that in order to get this matter done the way I wanted to would require a more accurate, detailed development of certain mental processes, a very specific working out of imaginative, of inspirational cognition and then to apply these modes of cognition to these anthroposophical issues. And so I had to take a negative step, I dropped the whole idea of writing on Anthroposophy. It is still lying there today as it lay then — many pages. 1 Published in German as Anthroposophie — Ein Fragment , Bibl. Nr. 45; English translation in preparation by Mercury Press. For my intention was to make further investigations. Thus I became thoroughly acquainted with what I want to describe to you now. I can only describe it schematically at this time, but it is a sum total of many inner experiences that are really a cognitive method of investigating the human being. It became increasingly clear to me that before one could finish the book called “ Anthroposophy ,” in the form intended at that time, one must have certain experiences of inner vision. One must first be able to take what one perceives as soul-spiritual activity working in the nervous system and carry it further inward, until one comes to the point where one sees the entire soul-spiritual activity — which one grasps in imagination and inspiration — crossing itself. This crossing point is really a line, in a vertical direction if looked at schematically. For certain phenomena the point lies farther up, for others farther down. In these lectures I can't describe this in detail, I just wanted to make a kind of cross section through the whole of it. Now because of this crossing, one is no longer free in exercising this activity. In fact, one was not altogether free before, as I have shown; now one is even less free. The whole situation undergoes a change. One is now being held strongly in an imaginative-inspired state. Expressed concretely, if one comes to an imagination of the eye by taking hold of visual sense-perception and the continuation into mental processes with imaginative-inspired cognition, then this activity proceeds inwardly and one comes to a kind of crossing, and with the activity first encompassing the eye another organ is encompassed, and that is the kidney. The same applies to the other organs. In each case, when one carries one's imaginative-inspired activity into the body, one finds various relatively complete organs — complete at least in their basic form from birth — and one comes to a real inner view of the human organism. This kind of research is very demanding; and as I was not obliged at that moment to finish the book, and had to give another lecture cycle, which also demanded research efforts, you can imagine that it was not easy to continue to work out the method which I had developed at that time — of course, it was quite a few years ago that this occurred. I mention this only to show you some of the difficulties — how one is continually held back by various demands. To continue in this, one must hold one's inner forces firmly together if one is to accomplish it. One must, in fact, repeatedly resolve to intensify one's thinking ability, the force of one's inner soul work — to strengthen it through love of external nature. Otherwise one simply cannot proceed. One goes consciously into oneself, but again and again one is thrown back, and instead of what I would call an inner view, one gets something not right. One must overcome the inward counterblow that develops. I wanted to tell you all this so that you could see that the spiritual investigator has moments when he must wrestle with certain problems of spiritual research. Unfortunately, in the years that followed the event I have just described to you, my time was so filled with everything imaginable, particularly in recent years, that the needful — indeed, indispensable — activity for finishing my Anthroposophy could not take place. You see, something that is inwardly understood, something we spoke of above rather abstractly, is in fact what is spun into an enveloping form of an organ, something quite concrete. If you picture this to yourselves, you will realize that such an insight into the human being can also build a bridge to practical activities. These activities must of course be founded on a vision of the human being and his relation to the world. I have already indicated in another connection how through developing imagination we gain knowledge not only of the sensory realm and its continuation into the nervous system, but also of the plant world. When we advance to inspiration, we become acquainted with the whole realm of forces that are at work in the animal world. At the same time we become aware of other things of which the animal world is only the outer expression. We now recognize the nature of the respiratory system, we can understand the external forms of the respiratory system through this relationship. The external form of the respiratory and circulatory system is not directly similar in its outer shape to its inner counterpart, as is the case with the outer form of the nervous system and the inner mental life. I showed this yesterday — how in the case of the nervous system two people, representing very different points of view, were able to draw similar pictures. In a parallel manner we become acquainted with the outer world and its kingdoms and the inner aspect of the human being. Tomorrow I will consider what this inwardly experienced knowledge adds to our insight into the nature of the human being and his relation to his environment. Naturally, a great deal is revealed to us about specific relationships between the human being and his environment. It is possible to perceive the nature of a specific human organ and its connection to what exists in the outer natural realm. Thereby we discover in a rational way the transition from a spiritualized physiology to a true therapy. What once was won through instinctive inner vision is now possible to be renewed. I have mentioned yoga, and I could name even older systems which made it possible to perceive in an instinctive, childlike way the connection between the human being and the world around him. Many of today's therapeutic measures come from this older time — perhaps in somewhat different form, but they are still among the most fruitful today. Only on this spiritual path can therapy be developed that is suited to meet the real needs of today. Through insight into the connection of the human organs with the cosmos, a medicine will be developed based an inner perceptions, not just external experiment. I set this before you just as an example of how spiritual science must fructify the various specialized branches of science. That this is needed is obvious when one looks at external research efforts, which have been very active and are magnificent in their own way — but which abound with questions. Take, for example, outer physiology or outer pathology: questions are everywhere. Whoever studies these things today and is fully awake will find the questions there — questions that beg for answers. In the last analysis, spiritual science recognizes there are great questions in outer life, and that they require answers. It does not overlook what is great and triumphant in the other sciences. At the same time, it wishes to study what questions result from this; it wishes to find a way to solutions to these questions in just as exact a manner as can be taught in the other sciences. In the end, the questions can be found (even for sense-bound empirical investigation) only through spiritual investigation. We will speak more about this tomorrow.

Anthroposophy and Science

Lecture VI

https://rsarchive.org/Lectures/GA324/English/MP1991/19210322p01.html

Stuttgart

22 Mar 1921

GA324-6

Unfortunately our time together is so short that I have only been able to deal with our theme in a broad way, just intimating its development. The intention was to present a few ideas that lie, one might say, at the entrance of an anthroposophical spiritual science. From what has been presented, you will surely feel that everything we have touched upon needs further elaboration. I have spoken of various ways of knowing that through inner soul work can follow as further steps from our everyday kind of knowing and from ordinary scientific cognition. I have already mentioned the first two of these further steps and called them imaginative cognition and inspired cognition. Yesterday I showed how, when imaginative and inspired cognition work together, and when we take account of a certain experience that I described yesterday as an inner crossing in the consciousness, a knowledge of the human being can arise in conjunction with a knowledge of the surrounding world. When this experience that we have in inspired-imaginative cognition is developed further, through certain exercises found in my books, something arises which has a similar name in ordinary life — that is, intuition. In ordinary life intuition refers to a kind of knowing that is not sharply delineated, to something more in the realm of feeling. This dimly experienced knowledge is not what the spiritual researcher means when he speaks of intuition and yet there are good reasons for thinking of the undeveloped, dim experiences of ordinary intuition as a kind of early stage of real intuition. Real intuition is a kind of knowing, a condition of the soul that is just as suffused with clarity of consciousness as is mathematical thinking. This intuition is reached through a continuation of what I have called exercises for the attainment of forgetting. These exercises must be continued in such a way that one really forgets oneself. When these exercises have been carried on in a precise and systematic way, then arises what the spiritual investigator calls intuition in the higher sense. This is the natural form of cognition into which inspired imaginations flow. Before I go on with my discussion, I would like to stress one thing, to avoid possible misunderstanding. I can easily imagine that someone might raise a certain objection to what I described at the end of yesterday's lecture. First let me assure you that the conscientious spiritual investigator is the first to make various objections for himself. This is inherent in the process of spiritual research. With every step one must be aware from what possible angle objections may come, and how they can be met. To be specific, someone could raise an objection about what I said yesterday concerning the experiencing of a “crossing” that arises in the process of looking within, embracing our own inner organization. It could be said: This is an illusion. The fact is that especially the spiritual investigator (as is meant here) is not allowed to be a dilettante in external science; he is sure to know a thing or two about the inner organization of the human being from conventional anatomy and physiology. One might suspect that the investigator yields to a sort of self-deception, taking what he knows of external science and incorporating this into his inner vision. The spiritual researcher fully reckons with the possibility of self-deception along his path. One can settle the objections that have been raised by noting that what is perceived in the human organism during this inner viewing is totally different from anything one could possibly get from external anatomy or physiology. This perception of the inner organization could really be called a perception of the spiritual aspect of the human interior. The only help ordinary anatomy and physiology can render is the establishment of something like a mathematical reference point — a reference point for what has been spiritually perceived in the soul by inner vision, a definite content of perception at this level of cognition. For example, when we spiritually perceive the inner nature of what corresponds to the lung, it will be easier to connect this with the lung if we are already familiar with it through outer anatomy and physiology than if we knew nothing of it. These two aspects — an inner vision of the lung, and what we know in an outer way through anatomy and physiology — are two completely different contents that must be reconciled later. At this level of cognition there is only a repetition of the kind of relationship that we experience between what is inwardly grasped in mathematical thinking and what is directly visible in the physical-mineral realm. The difference that exists between what we grasp inwardly in mathematical thought and what we find given in outer observation is very similar to the difference between what we grasp in inspired-imaginative activity and what we can learn through external research. Inner clarity of consciousness throughout is, of course, a basic requirement. When we rise from inspired imagination to intuition, we encounter a situation similar to the one we described at the beginning of these lectures. We said: The outer world and its phenomena enter into us through our senses as through “gulfs.” Mathematical lines and forms which we construct influence our perception of the outer forms of the world. So with respect to our bodily nature there is a jutting in, a really essential penetration of the outer world into our spatial-bodily condition. We have a similar experience when all that I have described comes into us through intuition. Through this experience we become aware of one thing particularly: that what has been experienced within the human being is inexplicable of itself — or perhaps better said, it is something essentially unfinished. When we come to know ourselves through intuition, as long as we remain within the experience of self-knowledge we are basically dissatisfied. In contrast to this, with inspired imagination, when we apply it to knowledge of the self we feel a certain satisfaction. We learn what the human rhythmic system really is. This is a difficult process of knowledge. It is a process that can really never be completed, because it leads into endless further developments. In this type of knowledge you are learning to know yourself in connection with the world, as I showed yesterday. One can arrive at concrete insights concerning the connection of the healthy organism with its cosmic environment also the connection of the ailing organism with the cosmic environment. In this way the very interior of the human being can be penetrated. At this point I would like to speak of something I described in the previous lecture course. 1 The Boundaries of Natural Science , Bibl.-Nr. 322, eight lectures, Dornach 1920, Anthroposophic Press. We are able to perceive through our inspired imagination how the human organism must relate itself to receiving something like a sense organ. It is, in fact, predisposed toward the sense organs. It opens itself outward so as to send a certain force system — if I may use such an expression — toward each separate sense. Beyond the interaction of the force system with our regular senses, one can discover abnormal cases of such tendencies arising in other places. A normal organization for the development of a sense can appear in a wrong place. Such a force system can be inserted into some organ not meant to be a sense organ, whose normal function is something else. The appearance of a metamorphosed force system in a place not right for it causes abnormalities in the human organism. A consequence of the particular abnormality just mentioned is the formation of a tumor where the displaced force system occurs. What we find here in the human organism is a more complex version of what Goethe in his teachings on metamorphosis always looked for, under simpler circumstances. We come to realize that a system of forces correctly associated with growth, when directed differently and in a metamorphosed form, can become the cause of illness. When inspired-imaginative cognition is directed to the whole matter of how man's sensory organization is related to the kingdoms of nature — to his whole environment — one discovers important relationships. These relationships lead us to remedies in our environment that can be used against pathological forms of forces. Now you may see the vistas that are opened up by what I have described. This is not just fantasizing into the blue — nor is it nebulous mysticism to evoke satisfaction in the soul. Either would be completely foreign to what is meant here by anthroposophically-oriented spiritual science. This spiritual science wishes to penetrate into the real nature of the world in a serious and exact manner. At the same time, it must be admitted that much of what can be achieved in this way is still in its infancy today. And yet a fair amount of what I presented last spring in the course for physicians and medical students (which I plan to continue shortly) on pathology and therapy, made — I believe — a favorable impression on the listeners. Its view of the essential being of nature and the world, of the inner relationships, gave rise to the impression that here is something that can fertilize and complement outer observation and experiment. The contemporary world should see that here is at least an attempt to find out what it is that is creating the questions of external science, when there is no sign of any possibility in the scientific field of finding satisfactory answers to the questions. As we advance along this path of knowledge (keeping always to what is spiritually real and concrete and avoiding abstraction), we have an experience on the other side of the human organization, of something similar to the "jutting" of the outer world into our sensory life. I said earlier that when we come to self-knowledge through intuition, it proves inevitably to be unfinished. We understand this now, for we see that here on the other side we have the reverse relationship to that of the sense organs. The senses are “gulfs” into which the outer world flows. On the other hand, we discover that the entire human being, becoming a sense organ in intuition, now reaches into the spiritual world. On the one hand, the outer world reaches into the human being; on the other, the human being reaches into the spiritual “outer world.” As I mentioned earlier in connection with the eye organization, the human being has a certain active relation to the depth dimension; with intuition he has (as long as he remains with intuition in the realm of self-knowledge) a certain relation to the vertical dimension. Thus something very similar to sense perception takes place, except that it is reversed. We find that through intuition the human being places himself with his entire being in the spiritual world. Just as through the senses the external sense world projects inward, through intuition one consciously places oneself in the spiritual world. In this conscious projection into the spiritual world through intuition, the human being has a similar feeling to the feeling he has toward the outer world through perception. The feeling of being in the spiritual world, a kind of dim feeling of standing within the spiritual world, in ordinary life we call intuition. But this intuition is suffused with bright clarity when the stage of cognition is striven for which I have described. Thus you can realize that perception is just one side of our human relation to the outer world. In perception we have something indefinite, something that first must be inwardly worked upon. As perception is worked upon by our intellect and we discover laws at work in this perception, there is at the same time something corresponding to this that initially has just as indefinite a relation to us as does perception. It must be penetrated by inner knowledge that has been achieved, in the same way that perceptions must be penetrated by mathematical thinking. In short, our ordinary experience must be penetrated by our inwardly achieved knowledge. In ordinary experience we call this kind of intuition belief or faith. Just as the human being faces the outer sense world and has the experience of perception, so, participating in a dim way in the spiritual world, he has the experience of belief. And just as perception can be illumined by the intellect or reason, so the content of this indefinite dim experience of belief can be illumined by our steadily increasing knowledge. This dim experience of faith becomes one of scientific knowledge just as perception attains scientific value through the addition of the intellect. You see how the things relate. What I am describing to you is truly a progression through inner spiritual work to transform the ordinary experience of faith into an experience of clear knowledge. When we rise into these regions, transforming faith into an experience of knowledge, we find this similar to the process of subjecting our perceptions to what has been worked out mathematically or logically. What is inherent here is not some artificial construction, it is a description of something a human being can experience — just as, for instance, one experiences what develops from early childhood when the intellect is not yet useable to a later time when the intellect and reason are in full use. There are other experiences bound up with these — for example, the following: The moment we advance to inspired cognition, we have already had what I have described as the life panorama, which extends back to early childhood and, at times, even to birth. With this we have gained an inner kind of perception. It is only with the attainment of inspired cognition, however, that a kind of enhanced faculty of forgetting comes about which I must characterize as a complete extinguishing of the surroundings that up to this point were given through sense perception. In other words, a state of consciousness arises in which our own inner life, indeed our inner life in time up to birth, becomes the object of our consciousness. At this time one has the subjective feeling that one is inwardly empty, that one is in the outer world with one's consciousness, not within one's body. When we have succeeded in reaching this enhanced forgetting whereby the outer sense-perceptible world is really extinguished for a moment, then something appears through this experience being combined with what is attained intuitively. I must describe this in the following way. We have already discussed imagination and we know it does in fact relate to reality, although at first it appears to have pictorial character. It relates to a reality, but at first we have only pictures in our consciousness. When we experience inspiration, we advance from the pictorial to the corresponding spiritual reality. When we reach the moment in which external sense perception is completely extinguished through inspiration, a new content appears for the first time. The content that appears corresponds to our existence before conception. We learn to look into our soul-spiritual being as it was before it took possession of a physical organism arising out of the stream of heredity. Thus this imagination fills itself with a real spiritual content that represents our pre-birth existence. Characterized in this way, this may still seem paradoxical to many people of our time. One can only indicate the exact point in the cognitive process where such a view of the human soul-spiritual self enters in, and where what we call the question of immortality takes on real meaning. At the same time we gain a more exact view of the other pole of the human organization. When we penetrate what we have at first only as intuitive belief and raise this to knowledge, the possibility arises to relate imaginations — although in another way than in the case just described — to the conditions after death. In short, we have a view of what one can call the eternal in man and I will only just mention the following. When intuition has developed further, to the point it is really capable of reaching, we develop our true “I” for the first time. And within the true “I” there appears to inner vision what in anthroposophical spiritual science is referred to as knowledge of repeated earth-lives. The knowledge that we were a soul-spiritual being before conception and that we will continue to be after death: this is really experienced in inspired imagination. The knowledge of repeated earth-lives is added to this only in intuition. When we have reached this area, we first begin to discover the full significance of waking up and falling asleep, and the condition of sleep as such. Through a deepening of the cognition related to the pole of perception, we discover the experience of falling asleep, which otherwise remains unconscious. At the other pole of intuitive thought, we discover the experience of waking up. Between these two is the experience of sleep, which I would like just to characterize as follows: when the human being falls asleep in ordinary consciousness, he is in a condition in which his consciousness is completely dimmed. This empty consciousness in which the human being lives between falling asleep and awakening, is a state which he cannot know from his own subjective point of view. The inspired-imaginative condition is very similar. In this condition the will impulses are silenced just as in sleep the senses are silenced. The subjective human activity is silent in both sleep and inspired imagination. The major difference is this: in sleep the consciousness is empty. In the condition of inspired imagination one's consciousness is filled; one's inner experiences are independent of sense perception and will impulses; in a certain sense one is awake while one is asleep. One has therefore the possibility of studying the life of sleep. I would like to return to something that I spoke of this morning in the history seminar. The historical problems we spoke of take on new meaning when seen in connection with the experiences we have just been speaking of. At one time or another you may have reflected upon such historians as Herodotus. He and others were really precursors of what we call history in the modern scientific sense. The way history is written today developed with the intellectual culture that finds special satisfaction in experiment. In other words, those who find special satisfaction in experiment also find satisfaction in the external aspect of history. This science of history proceeds empirically, and rightly so from its own point of view. It collects data, and from this data it pieces together a picture of the course of history. One can, however, object that this way of interpreting empirical data easily allows that history could have developed differently. As I put it this morning, one could hypothesize that Dante somehow died as a boy. We would then be faced with the possibility that what we experience as coming through Dante would be absent, at least it would be absent as manifested in the person of Dante. In the study of history one will meet with great difficulties in reaching true insight, unless one is satisfied with the ready-made scholarly harangues. Let us take another example. Historians set out to study the Reformation, using the available facts of external history. (We cannot go into detail here; you can research this yourself if you are interested.) For instance, if the monk Luther had died young, I would really like to know what would have been recorded as derived purely from the external historical method! Certainly something quite different from what is recorded today. Quite serious difficulties arise when one wants truly to characterize historical knowledge. One may say if one focuses on the philosophy of history, one can follow the observable outer events from the point of view of some abstract element of necessity, or one may want to find an element of purpose shaping the events as Strindberg did. The fact that the other reforms would not have been there either if Luther had died as a boy, would not affect this theoretical finding of purpose or necessity, in whatever might have taken place instead of the Reformation. If Luther had died, the other reformers would not have been there either. One must be very careful in coming to conclusions when one is working in the field of external historical observation. However, the course of human development reveals something quite different when it is observed from the level of knowledge that I have been describing to you. Let me give you a concrete example. One would see that there were certain forces at work in European civilization around the fourth century between the time of Constantine and Julian the Apostate. The outer aspect of this world would appear differently if records existed of a personality so impressive as, for instance, Dante. There really is a problem here, and I confess I am not finished with it yet but must pursue it a bit further. The problem is a most concrete one. I am not yet finished in that I cannot tell you whether important documents, important evidence concerning an important figure around the period of 340 or 350 A.D. somehow disappeared from the view of external history, or whether he died in his youth — or somehow perished in those turbulent, war-filled times. It is a fact, however, that one sees forces at work in this period that cannot be traced in external history today. These forces would only be accessible to external history through some stroke of luck, like the chance discovery of written documents in some monastery. It is beyond any doubt for the spiritual investigator, however, that these forces are active. The spiritual investigator can truly establish what otherwise would be seen as forces abstracted from outer circumstances. Now suppose we would wish to look back on the life of Dante and acquaint ourselves with him. We would try to make him come to life in our soul, really to try to know him inwardly. We would also familiarize ourselves with the forces active in the time of Dante. This is an external approach to knowledge. Naturally, the knowledge that the spiritual scientist gains of the Dantean period will look somewhat different from what can be found in external documents — for example, in the Divine Comedy . One could of course object that the spiritual scientist might confuse what he has learned through external perception with what he has obtained through inner vision. When, however, inner vision operates in such a way that we know beyond any doubt that in a particular age — as in this one just named — the outer events do not correspond to the inner happenings, we know that spiritual powers are really at work. Under these circumstances it is possible to present history as I did recently for a small circle, by looking exclusively at the forces seen inwardly. We come to the point where we have inwardly observed these forces; they penetrate us, they live within us. It would really be a miracle if, for instance, one could just fantasize about the forces at work in Julian the Apostate at the time in question. Those times can only be truly explored spiritually. The level of historical observation achieved here can be described as a direct viewing of the original spiritual forces that are active in the historical process. Thereby one receives a satisfactory explanation for precisely the parts of history where external facts are missing — because documents are missing, or men and women did not have a chance to live their lives out normally. In such cases what is viewed inwardly can help external history. Examples of the result of such inner knowledge, pointing to the forces behind historical events, are given in my little book, The Spiritual Guidance of Mankind . What is presented there must naturally be preceded by the inner vision of the missing aspects of external history, as I have mentioned. It is only at this point, assuming we intend to be inwardly responsible in our relation to knowledge, that we can feel justified in saying: It is possible simply on the foundation of sound human understanding to rise (as I have repeatedly described) to a level where such real forces are active. But, you may object, no one could speak of the beings I described in The Spiritual Guidance of Mankind who has not yet advanced to such vision. This is of course true; to speak with this degree of emphasis, one must have a certain level of cognition. But one may take something else into consideration. If we are honest in approaching the facts of history and if we are sufficiently schooled in philosophy to be aware of the riddles and doubts the usual study of history presents, we can still have an inner experience of a certain kind. This experience is similar to the one that the astronomer had when on the basis of certain gravitational forces he predicted the as-yet-unseen planet of Neptune. The discovery of the spiritual laws and essential nature of history is really a very similar process in the spiritual domain to the calculations employed by LeVerrier to predict the existence of Neptune. LeVerrier did not somehow piece together a scientific result as is done in external history — with a positive or skeptical slant, simply avoiding connections: he followed the facts according to their truth. He said to himself: Something must be at work here. This is similar to what the astronomer before him said concerning Uranus. Uranus doesn't follow the course which it ought to according to the forces I already know, so there must be something exercising an influence on these known forces. The conscientious investigator also recognizes certain forces at work. He sees the intervention of these forces much as someone who on finding a limestone or silica shell-form in a rock formation looks for the active forces. From the way the silica fossil looks, he surely does not say: This silica form has somehow crystallized out of its mineral surroundings. Rather he says: At one time this form was filled out with something; it was made by some kind of animal and one can have a mental picture of this animal. If some being were to arrive who had lived at the time the animal was alive in that shell, and he described the animal, such an eyewitness could be likened to the spiritual investigator. The finder of the shell bearing the imprint of the animal is not necessarily the one who uses his sound human understanding to deduce from the outer configuration what must have been there to form the shell. What the living facts were is something only the spiritual investigator can say. The person who is willing to bring a sound sense of logic, a logical view of facts, and healthy human understanding, can follow and inwardly test what the spiritual researcher tells him about the forms in front of him. It is not necessary to have a blind belief in the spiritual investigator. Naturally, the actual discovery of such things as are presented in The Spiritual Guidance of Mankind requires spiritual research. When the spiritual researcher has presented what he wishes to tell in terms of what he calls higher beings, he will also readily agree to be tested for this vision by those gathering outer facts. His attitude is this: I invite you to rap my knuckles if you discover anything whatever that contradicts the outer order of events predicted by my inner vision. Something similar appeared in our circle, in connection with interpretations of the gospels which had been worked out in a purely spiritual manner. It has also occurred in such cases as the one given this morning. I am busy with a variety of literature, yet to this day the author was unknown to me of the work Dr. Stein cited this morning giving the date of Christ's death. I have never seen it. Naturally, this is not the sort of evidence that one can accept objectively — I mention this only parenthetically. Nevertheless, such things have occurred within our circle. Verifications have appeared that must be accepted objectively. Through a living involvement in spiritual-scientific work, many of our friends have a real personal conviction; it does not rest on blind faith, but precisely on their experience of the life that goes on in spiritual science. This explains why those who have been involved in the activities of spiritual science for many years can speak in a different tone from those for whom spiritual science is just a theory. I believe we can show in the context of the evolution of humanity the connections between the state of science today and the state of knowledge today. Naturally, everything has earlier stages; scientific experimentation is no exception. Given this, however, the experimentation of the past, up to the most recent times, cannot help but seem primitive compared to what we have today. When our fully developed experiment is experienced inwardly, it really calls for something more. From what has been combined by the intellect in the actual activity of experimentation something is released in the soul. What is released requires spiritual knowledge to balance it. We have shifted our understanding from mere observation to experimentation. Something happens when we discover the real difference between what is experienced in mere observation and what is experienced in the activity of experimentation: the urge arises in us to rise to a higher level of self-knowledge from the ordinary kind. This higher knowledge is what I have recently been describing. These two things are related. The urge for a higher knowledge, which is natural to human beings striving for knowledge today, has developed quite naturally in the course of history out of an elementary interest in experimentation itself. The scientific data that we have gained in regard to outer nature are, in many respects, really related to questions. The important thing is that if the formulation of the questions is correct, then a correct answer is possible. What natural science has given us recently is really in large measure no more than a statement of questions for the spiritual researcher. Whether we look at recent astronomy or the views of modern chemistry, when we grasp what is in them, the question arises: how is what is described related to what goes on in the human being himself? Questions arise about man's relation to the world precisely through the scientific results that have come from our shifting from observation over to the experimental realm. So we can see that for someone who really experiences modern science and does not theorize about it, this science is full of spiritual-scientific questions. From the nature of these questions, there simply is no choice but to go to spiritual science for answers. In the year 1859 Darwin came to a conclusion of what he had studied so meticulously; but for someone who studies these results afterwards, in spite of what Darwin took to be scientific conclusions, they appear as questions. We are helped by the kind of experience we have in experimenting but at the same time we recognize the essentially independent nature of mathematics. When we seek for the realm in which mathematics is applicable, where it will result in an inner satisfying knowledge, then we see a merging of observation and of mathematical thinking, of the results of mathematical thinking, into an understanding of nature. But we may ask, what underlies what we experience in experiment; what is really happening when we feel the necessity for a form of knowledge that can even venture into historical knowledge? Where does this lead? We tend to look for connections everywhere for which the threads are simply not to be found in the material of contemporary science. Once we have grasped what it is that brings order into the connections between the facts, and in all spheres of knowledge — from the study of nature up to the study of history, we sense higher beings revealing themselves, purely soul-spiritual beings. If we come this far, then the door is open to a contemplation of an independent spiritual world. My honored guests! I know just how much these lectures must seem unsatisfying to you, due to their sketchy and aphoristic nature. But rather than lecture on a narrowly defined subject, I chose to give a wide overview, even though in the particulars it could not be filled in. My intention was that you might learn something of the procedures involved in spiritual-scientific knowledge as it is meant here. I hoped you would get a feeling for the aims toward which it aspires. It aims for the greatest possible exactness and not some sort of fanciful or dilettante activity. For even in mathematics, what makes it so exact is the fact that we have an inner experience of it. In the Platonic age it was known why the words “God geometrizes” were inscribed as a motto on the school; it was clear that all who entered would receive a training in geometry and mathematics. In a similar way modern science of the spirit knows that to attain its goal it must have inner mathematical clarity. I hope you have received the impression, particularly as regards its methods, that the orientation of spiritual science is worthwhile. Perhaps on reflection you may come to ask the question: Can this not indeed lead to a fructification of our other sciences — not to belittle them, but to raise them to their true value? If I have achieved this to some degree, aphoristic and in some ways insufficient as these lectures have been, then my intention have been fulfilled.

Anthroposophy and Science

Lecture VII

https://rsarchive.org/Lectures/GA324/English/MP1991/19210323a01.html

Stuttgart

23 Mar 1921

GA324-7

Now we have come to the end of our university courses. We have heard lectures from various individuals who have worked in our anthroposophical spiritual science for some time. We have also had a number of seminars which were intended to fill out what the lectures only sketched as a framework. In spite of the fact that all the participants in these lectures have worked hard, we must also consider the quality of the time spent together given the nature of such an event. All we were able to do was to let some light come in, as through individual windows in a building — that light which we believe is present in our anthroposophical spiritual science. Please consider what is contained in this room, the openings into which we are describing symbolically as windows of the spiritual-scientific movement. The contents of the room are various subjects that are just at their beginning; a richer work will exist ultimately. If you take this into account, you can understand why we could present only a small amount of what we might hope to give in such courses on similar occasions. With such an event we hoped to draw students from all directions, and to our joy they have in fact appeared in great numbers. It is very gratifying to us and meaningful for the movement. For first and foremost, we would like to show, no matter how sketchily, that a genuine scientific attitude prevails in the anthroposophical movement. No doubt there are other spiritual intentions at work also, but these will have to be shown in other ways. Above all, these lectures are meant to demonstrate at the very least the will to strive toward real scientific knowledge. However, considering present-day conditions, anyone who understands the situation must feel: If we speak of a scientific attitude, a scientific spirit that plays directly into the living conditions of the modern human being, then it must be able to prove itself in the social sphere. It is really necessary that the scientific spirit of our day shall give rise to ideas that can bring strength and healing into our social life. It is not enough today to have a scientific spirit that calls the human being into an existence estranged from life. We need a scientific spirit that will give us real health in our social life. The social situation confronts us full of riddles and urgent demands, even in a certain way threatening. If we have a feeling for these times, we can sense the need for real solutions — solutions that can be found only by those who grasp the social life with scientific understanding. We believe we are able to recognize this necessity from the most significant signs of this time. It is out of this recognition that our anthroposophical movement is artistically, scientifically and culturally conceived; this includes the building in Dornach called the Goetheanum, the Free University for Spiritual Science. Our wish is that out of a genuine scientific attitude these impulses can come to life in us and become really socially active. We have attempted in the very structure of our lectures and seminars to make possible a recognition of the truly scientific spirit to which we aspire in our anthroposophical movement. Attacks from various directions accuse us of sectarianism or the desire to found a religion, but they come from those who don't know us, or — in some cases — from a malicious desire to slander us. The scientific spirit cannot of course be seen in the factual content of what is presented. Whoever would exclude empirical content, whether physical or super-sensible, shows that he himself is not imbued with the scientific spirit. It can only be seen in the treatment of the facts, in the striving to follow a definite method. And the real test of its validity — whether its results originated from sensory or supersensory experience — is based on the nature of this striving. Do we strive toward the scientific spirit that rules in the recognized sciences? Is this striving demonstrated in our methodology, in our thinking with scientific accuracy? This is a justifiable question. It is also a worthwhile point of discussion inasmuch as this scientific spirit, as it prevails among us, is in need of improvement. One can determine whether our movement is scientific or not, not on the content we present but by how we proceed. Let it be shown in any instance that we have proceeded illogically, unscientifically, or in a dilettante fashion and — since we are serious about the correct development of our spiritual-scientific endeavors — we will make the necessary improvements without argument. We do not wish to deny this principle of progress in any way. So, enough about the underlying elements for discussing the scientific status of our endeavors. We have striven to prove in the social realm, in life itself, what results from our knowledge of the world. In our discussions we have tried to present what we believe to be the truth regarding knowledge of the human being and the world. In the seminars we showed how the Waldorf School movement arose out of the anthroposophical movement. The lively manner of teaching in the Waldorf schools raises the question whether what is found in spiritual science will also prove itself in the shaping of today's young people. We don't want to exhaust ourselves in fruitless theoretical discussion: we want to let reality itself test what we believe is the truth toward which we should strive. Goethe said, “What is fruitful, that alone is true.” Even those far removed from modern philosophical pragmatism or the “as if” school must have their truth proven by its fruitfulness. We can declare ourselves in full agreement with the Goethean principle that only what is fruitful yields proof of its truth before reality — particularly where social truths are concerned. If what flows livingly out of spiritual science can return again into life, and if life can show that the result of recognized truth, or supposed truth, can send a human being out into life with ability, vigor, sureness, and enthusiasm and strength for work, then this is a proof of the truth which has been striven for. At the same time we have attempted something else, but it is really still too much in its infancy to be outwardly demonstrated. In Der Kommende Tag , in Futura , we have put forth economic ideas which are intended to show that what is derived in a spiritual way, out of reality, also enables us to see the affairs of practical life in the right light. The time has not yet come when we can speak of these things becoming manifest, of fulfilling the conditions for a real proof. However, even in the economic realm, one may grant us the fact that we have not been afraid to extend something that was won purely in the spiritual out into practical life. This is actual testimony that we do not shy away from the tests of reality. How things develop in this region is perhaps not fully within our own will to determine. In such cases, even more than in the field of education, one is dependent on the practicalities of life, as well as how one is understood by the world and one's own circle. In this way, we try to take into account the signs of the times. We have recently seen in some of our lectures that these signs point directly to spiritual-scientific demands; they also confront us with great social questions. But above all we seek to take into account the inner soul needs of the human being. For someone who is familiar with one area, for example the natural sciences, it is very easy to believe that we are already in possession of an infallible scientific method. Ultimately, however, what arises as science can only be fruitful for the whole evolution of humanity if it joins human evolution in a way that sustains the life of man. With this essential condition in mind, I ask you: Isn't there something in today's universities or in similar circumstances that can cause the soul to come somewhat into error? One can, of course, enter a laboratory and work in the dissection room, believing that one is working with a correct method and that one has an overview of all factors involved, grasping them in accord with present conditions and the level of humanity's evolution. But for humanity's evolution something else is necessary. Something is necessary which perhaps occurs very rarely, and the significance of which is not properly appreciated. It would be necessary that someone who has worked seriously and conscientiously with scientific spirit in the chemistry lab, observatory, or clinic, could then step into a history or aesthetics classroom and hear something there that would live in inner conformity with what he had learned in his technical courses. Such unity is needed — for the simple reason that regardless to what degree individuals may specialize, ultimately the things achieved in separate disciplines must work together in the process of general human evolution, and must spring from a common source. We believe it is impossible today to experience a unity directly between, for instance, present historical pronouncements and the teachings of natural science. For this reason we strive toward what stands behind all scientific endeavors: the spiritual reality, the source that is common to them all. The aim of our striving is to come to know this spiritual reality. With our feeble powers we are striving to establish the validity of such knowledge of the spirit and its right to exist. In this lecture series and similar events, we have striven to show you what we are doing and how we do it, and we are grateful that you joined us. May I touch on one additional subject: A short time ago, a coworker of long standing in our movement spoke with me. He knew that for spiritual-scientific reasons I must speak about two Jesus children. Until recently he hadn't told me of his intentions to follow this matter up in a conscientious manner studying the external aspect. His recent conversation with me was after he had finished his investigations. He said that he had compared the gospels thoroughly with one another, and had discovered that they don't begin to make sense until they are regarded from this spiritual-scientific viewpoint. May research proceed thus in all realms! If it does, we know that our spiritual science will be able to stand fast. We do not fear the testing, no matter how detailed the examination may be. We have no fear of the request to verify. We only worry if someone opposes our viewpoint without proof, proof of all the individual details. The more carefully our spiritual research is tested, the more at ease we can be about it. This consciousness we bear deep within us. It is with such awareness that we have taken the responsibility of calling you all here, you who are striving to build a life of science and of scientific spirit. Today, my honored students, it is impossible to offer you the things of the outer world. In the places where this is done, our efforts are sometimes rejected in a surprising manner. Even so, your appearing here allows us to feel we are correct in saying that there are still souls among today's youth whose concern is the truth and striving toward the truth. Therefore we wish to say — I speak from the fullness of my heart, and I know I am also speaking for the coworkers of these courses we have truly enjoyed working with you. This is particularly gratifying because at the same time from other quarters attacks are raining down on us from ill-will, and we are called upon again and again to refute these attacks. We do as much as we can to make the refutations — as much as time permits. But really, the burden of proof lies with the one who makes an assertion; he should bring evidence of its truth. Otherwise, one could blithely throw assertions at anyone, leaving him to refute everything. I only wish to indicate how the opposition operates toward us, personally attacking us rather than attempting to understand our ideas by discussing matters seriously with us. What is most strongly held against us is that in one important area we have to insist upon setting ourselves against the well-intended strivings of the times. We cannot just go along with the general attitude to take what traditional science represents in the various fields and simply let it be carried in a popular way throughout the world. Rather, from our own knowledge we believe there is another need. Something must be brought into those quarters which consider themselves infallible these days. It is generally believed that such authority is held in those quarters that their ideas can be taken unaltered and be disseminated among the masses. We believe, however, that certain scientific elements still lacking must enter those quarters to fructify their scientific work. The fact that we do not merely want the scientific spirit disseminated from certain quarters into the wide world but also want to bring a different spirit into science — this, I believe, is why we are confronted by such frightful opposition. It would be good if these matters were considered in a calm and objective way. For we must not hide the fact that we are in serious need of the collaboration of wider circles, even though every one of us is convinced of the scientific value of our endeavors. What worries us most is that we have so few coworkers who can really stand their ground. This is why it means so much to us that you, the university youth, have been coming to us now for some time. We have faith in you young students. We believe that what we need can sprout out of your youthful energy. Therefore, my honored fellow students, we would particularly like to work together with you in our field, as far as time and conditions permit. It is with this spirit that we sought to permeate the work in these courses. Perhaps you can carry away with you the conviction that it has at least been our aspiration to work in this direction. I began today by comparing what we are offering to a closed room, opening out through windows to the surrounding world of spiritual science. Through these windows we have wanted to let fragments shine in of a world of knowledge, which we want to apply in a spiritual-scientific way. Now we are at the end of the course, and I wish to say a heartfelt “goodbye till we meet again” in similar circumstances. But I would still like to return to the comparison with which I began the course. It is not generally my habit to pay homage to fine phrases, even when they are time-honored; rather, I like to return to just a simple expression of truth. In our cultural literature, a high-sounding phrase is often quoted as being Goethe's dying words, “Light, more light!” Well, Goethe lay in a tiny room in a dark corner when he was dying, and the shutters on the opposite window were closed. From my knowledge of Goethe I have every reason to believe that in truth his words were simply: “Open the shutters!” Now that I have dealt with that lofty phrase of my beloved and revered Goethe in an heretical manner, I would like to use my version of it as we end our work. My honored students! As we feel ourselves together in the room whose windows open out to spiritual knowledge, windows through which we have sought in a fragmentary way to let in what we believe to be light, I call to you out of the spirit that led us to invite you here: I call out to you, “Open the shutters!”

Anthroposophy and Science

Lecture VIII

https://rsarchive.org/Lectures/GA324/English/MP1991/19210323p01.html

Stuttgart

23 Mar 1921

GA324-8

Because I will begin by discussing elementary aspects of the fourth dimension, what you hear today may disappoint you, but dealing with these issues in greater depth would require a thorough knowledge of the concepts of higher mathematics. I would first like to provide you with very general and elementary concepts. We must distinguish between the reality of four-dimensional space and the possibility of thinking about it. Four-dimensional space deals with a reality that goes far beyond ordinary sense-perceptible reality. When we enter that realm, we must transform our thinking and become familiar with the way in which mathematicians think. We must realize that at each step mathematicians take, they must account for its impact on their entire line of reasoning. When we concern ourselves with mathematics, however, we also must realize that even mathematicians cannot take a single step into four-dimensional reality. [They can arrive at conclusions only from what can and cannot be thought.]. The subjects we will deal with are initially simple but become more complicated as we approach the concept of the fourth dimension. We first must be clear about what we mean by dimensions. The best way to gain clarity is to check the dimensionality of various geometrical objects, which then will lead us to considerations that were first tackled in the nineteenth century by such great mathematicians as Bolyai, Gauss, and Riemann. [Note 01] The simplest geometrical object is the point. It has no size, — it can only be imagined. It fixes a location in space. It has a dimension which equals zero. The first dimension is given by a line. A straight line has one dimension, — length. When we move a line, which has no thickness, it leaves the first dimension and becomes a plane. A plane has two dimensions, — length and breadth. When we move a plane, it leaves these two dimensions. The result is a solid body with three dimensions — height, breadth, and depth (Figure 1). When you move a solid body (such as a cube) around in space, however, the result is still only a three-dimensional body. You cannot make it leave three-dimensional space by moving it. There are still a few more concepts we need to look at. Consider a straight line segment. It has two boundaries, two endpoints — point \(A\) and point \(B\) (Figure 2). Suppose we want to make point \(A\) and point \(B\) meet. To do this, we must bend the straight line segment. What happens then? It is impossible to make points \(A\) and \(B\) coincide if you stay within the [one-dimensional] straight line. To unite these two points, we must leave the straight line — that is, the first dimension — and enter the second dimension, the plane. When we make its endpoints coincide, the straight line segment becomes a closed curve, that is, in the simplest instance, a circle (Figure 3). A line segment can be transformed into a circle only by leaving the first dimension. You can duplicate this process with a rectangular surface, but only if you do not remain in two dimensions. To transform the rectangle into a cylinder or tube, you must enter the third dimension. This operation is performed in exactly the same way as the preceding one, in which we brought two points together by leaving the first dimension. In the case of a rectangle, which lies in a plane, we must move into the third dimension in order to make two of its boundaries coincide (Figure 4). Is it conceivable to carry out a similar operation with an object that already has three dimensions? Think of two congruent cubes as the boundaries of a three-dimensional rectangular solid. You can slide one of these cubes into the other. Now imagine that one cube is red on one side and blue on the opposite side. The only way to make this cube coincide with the other one, which is geometrically identical but whose red and blue sides are reversed, would be to turn one of the cubes around and then slide them together (Figure 5). Let's consider another three-dimensional object. You cannot put a left-handed glove onto your right hand. But if you imagine a pair of gloves, which are symmetrical mirror images of each other and then you consider the straight line segment with its endpoints \(A\) and \(B\), you can see how the gloves belong together. They form a single three-dimensional figure with a boundary, (the mirroring plane), in the middle. The same is true of the two symmetrical halves of a person's outer skin. [Note 02] How can two three-dimensional objects that are mirror images of each other be made to coincide? Only by leaving the third dimension, just as we left the first and second dimensions in the previous examples. A right- or left-handed glove can be pulled over the left or right hand, respectively, by going through four-dimensional space. [Note 03] In building up depth, the third dimension of perceived space, we pull the image from our right eye over the image from our left eye, that is, we fuse the two images. [Note 04] Now let's consider one of Zöllner's examples. [Note 05] Here we have a circle and, outside it, a point \(P\) (Figure 6). How can we bring point \(P\) into the circle without cutting the circumference? We cannot do this if we remain within the plane. Just as we need to leave the second dimension and enter the third in order to make the transition from a square to a cube, we must also leave the second dimension in this example. Similarly, in the case of a sphere, it is impossible to get to the interior without either piercing the sphere's surface or leaving the third dimension. [Note 06] These are conceptual possibilities, but they are of immediate practical significance to epistemology, especially with regard to the epistemological problem of the objectivity of the contents of perception. We first must understand clearly how we actually perceive. How do we acquire knowledge about objects through our senses? We see a color. Without eyes we would not perceive it. Physicists tell us that what is out there in space is not color but purely spatial movement patterns that enter the eye and are then picked up by the visual nerve and conveyed to the brain, where the perception of the color red, for example, comes about. Next, we may wonder whether the color red is present when sensation is not. We could not perceive red if we had no eyes or the sound of bells ringing if we had no ears. All of our sensations depend on movement patterns that are transformed by our psycho-physical apparatus. The issue becomes even more complicated, however, when we ask where that unique quality "red" is located — is it on the object we perceive, or is it a vibrational process? A set of movements that originates outside us enters the eye and continues into the brain itself. Wherever you look, you find vibrational processes and nerve processes, but not the color red. You also will not find it by studying the eye itself. It is neither outside us nor in the brain. Red exists only when we ourselves, as subjects, intercept these movements. Is it impossible then to talk about how red comes to meet the eye or C-sharp the ear? The questions are, what is an internal mental image of this sort, and where does it arise? These questions pervade all of nineteenth- century philosophy. Schopenhauer proposed the definition "The world is our mental image." [Note 07] But in this case, what is left for the external object? Just as a mental image of color can be "created" by movement, so, too, the perception of movement can come about within us as a result of something that is not moving. Suppose we glue twelve snapshots of a horse in motion to the inner surface of a cylinder equipped with twelve narrow slits between the images. When we look sideways at the turning cylinder, we get the impression that we are always seeing the same horse and that its feet are moving. [Note 08] Our bodily organization can induce the impression of movement when the object in question is really not moving at all. In this way, what we call movement dissolves into nothing. In that case, what is matter? If we strip matter of color, movement, shape, and all other qualities conveyed through sensory perception, nothing is left. If "subjective" sensations, such as color, sound, warmth, taste, and smell, which arise in the consciousness of individuals as a result of environmental stimuli, must be sought within ourselves, so, too, must the primary, "objective" sensations of shape and movement. The outer world vanishes completely. This state of affairs causes grave difficulties for epistemology. [Note 09] Assuming that all qualities of objects exist outside us, how do they enter us? Where is the point at which the outer is transformed into the inner? If we strip the outer world of all the contents of sensory perception, it no longer exists. Epistemology begins to look like Münchhausen trying to pull himself up by his bootstraps. [Note 10] To explain sensations that arise within us, we must assume that the outer world exists, but how do aspects of this outer world get inside us and appear in the form of mental images? This question needs to be formulated differently. Let's consider several analogies that are necessary for discovering the connection between the outer world and internal sensation. Let's go back to the straight line segment with its endpoints \(A\) and \(B\). To make these endpoints coincide, we must move beyond the first dimension and bend the line (Figure 7). Now imagine that we make the left endpoint \(A\) of this straight line segment coincide with the right endpoint \(B\) in such a way that they meet below the original line. We can then pass through the overlapping endpoints and return to our starting point. If the original line segment is short, the resulting circle is small, but if I bend ever longer line segments into circles, the point where their endpoints meet moves farther and farther away from the original line until it is infinitely distant. The curvature becomes increasingly slight, until finally the naked eye can no longer distinguish the circumference of the circle from the straight line (Figure 8). Similarly, when we walk on the Earth, it appears to be a straight, flat surface, though it is actually round. When we imagine the two halves of the straight line segment extended to infinity, the circle really does coincide with the straight line. [Note 11] Thus a straight line can be interpreted as a circle whose diameter is infinitely large. Now we can imagine that if we move ever farther along the straight line, we will eventually pass through infinity and come back from the other side. Instead of a geometric line, envision a situation that we can associate with reality. Let's imagine that point \(C\) becomes progressively cooler as it moves along the circumference of the circle and becomes increasingly distant from its starting point. When it passes the lower boundary \(A\), \(B\) and begins the return trip on the other side, the temperature starts to rise (Figure 9). Thus, on its return trip, point \(C\) encounters conditions that are opposite to the ones it encountered on the first half of its journey. The warming trend continues until the original temperature is reached. This process remains the same no matter how large the circle, — warmth initially decreases and then increases again. With regard to a line that stretches to infinity, the temperature decreases on one side and increases on the other. This is an example of how we bring life and movement into the world and begin to understand the world in a higher sense. Here we have two mutually dependent activities. As far as sensory observation is concerned, the process that moves to the right has nothing to do with the process that returns from the left, and yet the two are mutually dependent. [Note 12] Now let's relate the objects of the outer world to the cooling stage and our internal sensations to the warming stage. Although the outer world and our internal sensations are not linked directly by anything perceptible to the senses, they are interrelated and interdependent in the same way as the processes I just described. In support of their interrelationship, we also can apply the metaphor of seal and sealing wax. The seal leaves an exact impression, or copy, of itself in the sealing wax even though it does not remain in contact with the wax and there is no transfer of substance between them. The sealing wax retains a faithful impression of the seal. The connection between the outer world and our internal sensations is similar. Only the essential aspect is transmitted. One set of circumstances determines the other, but no transfer of substance occurs. [Note 13] Viewing the connection between the outer world and our own impressions in this way, we realize that geometric mirror images in space are like right- and left-handed gloves. To make them coincide directly with a continuous motion, we need the help of a new dimension of space. If the relationship between the outer world and an internal impression is analogous to the relationship between figures that are geometric mirror images, the outer world and the internal impression also can be made to coincide directly only by means of an additional dimension. To establish a connection between the outer world and internal impressions, we must pass through a fourth dimension where we are still in the third. Only there, where we are united with the outer world and inner impressions, can we discover their commonalties. We can imagine mirror images floating in a sea in which they can be made to coincide. Thus we arrive, though initially purely on the level of thinking, at something that is real but transcends three-dimensional space. To do this, we need to enliven our ideas of space. Oskar Simony attempted to use models to depict enlivened spatial formations. [Note 14] As we have seen, we can move step by step from considering zero dimension to imagining four-dimensional space. Four-dimensional space can be recognized most easily with the help of mirror-image figures or symmetrical relationships. Knotted curves and two-dimensional strips offer another method of studying the unique qualities of empirical, three-dimensional space as it relates to four-dimensional space. What do we mean by symmetrical relationships? When we interlink spatial figures, certain complications arise. These complications are unique to three-dimensional space, — they do not occur in four-dimensional space. [Note 15] Let's try a few practical thought exercises. When we cut along the middle of a cylindrical ring, we get two such rings. If we give a strip a 180° twist before gluing its ends, cutting it down the middle results in a single twisted ring that will not come apart. If we give the strip a 360° twist before gluing its ends, the ring falls apart into two twisted, interlocking rings when we cut it. And finally, if we give the strip a 720° twist, cutting it results in a knot. [Note 16] Anyone who thinks about natural processes knows that such twists occur in nature. In reality, all such twisted spatial formations possess specific forces. Take, for example, the movement of the Earth around the Sun and then the movement of the Moon around the Earth. We say that the Moon describes a circle around the Earth, but, if we look more closely, we realize that it actually describes a line that is twisted around the circle of the Earths orbit — that is, a spiral around a circle. And then we also have the Sun, which moves so quickly through space that the Moon makes an additional spiral movement around it. Thus, the force-lines extending through space are very complex. We must realize that we are dealing with complicated spatial concepts that we can understand only if we do not try to pin them down but instead allow them to remain fluid. Let's review what we discussed today. Zero dimension is the point, the first dimension is the line, the second dimension is the surface, and the third dimension is the solid body. How do these spatial concepts relate to one another? Imagine that you are a being who can move only along a straight line. What kind of spatial images do one-dimensional beings have? Such beings would be able to perceive only points, and not their own one-dimensionality, because when we attempt to draw something within a line, points are the only option. A two-dimensional being would be able to encounter lines and thus to distinguish one-dimensional beings. A three-dimensional being, such as a cube, would perceive two-dimensional beings. Human beings, however, can perceive three dimensions. If we draw the right conclusions, we must say that just as a one-dimensional being can perceive only points, a two-dimensional being only one dimension, and a three-dimensional being only two dimensions, a being that perceives three dimensions must be a four-dimensional being. Because we can delineate external beings in three dimensions and manipulate three-dimensional spaces, we must be four-dimensional beings. [Note 17] Just as a cube can perceive only two dimensions and not its own third dimension, it is also true that we human beings cannot perceive the fourth dimension in which we live. János (Johann) Bólyai (1802-1860), Hungarian mathematician. He studied the problem of parallel lines and, along with Carl Friedrich Gauss and Nikolai Ivanovich Lobachevsky , is considered one of the founders of hyperbolic non-Euclidean geometry. His paper on this subject, his only published work, appeared in 1832 as an appendix to the mathematics text written by his father, Farkas (Wolfyang) Bólyai (1775-1856). For more information on the two Bólyais, see Stäckel [1913]. Carl Friedrich Gauss (1777-1855), mathematician and physicist in Göttingen. One of the first to consider the problem of parallel lines, he concluded that explaining them required a non-Euclidean geometry. None of his work on this subject was published during his lifetime. See Reichardt [1976]. Bernhard Riemann (1826-1866), mathematician in Göttingen and the first to discover elliptical non-Euclidean geometry. His thesis on The Hypotheses Underlying Geometry developed differential geometry by generalized measurements in n-dimensional space. This supplied an incentive for research (then in its infancy) into higher-dimensional space. Riemann was the first to distinguish between limitlessness and infinity of space, — the former is an expression of spatial relationships, that is, of the general geometric structure (topology) of space, while the latter is a consequence of numerical relationships. This distinction led to the clear differentiation between topology and differential geometry. See Scholz [1980]. Immanuel Kant drew attention to this phenomenon in his Prolegomena [1783), §13: "What can be more similar, in all its parts, to my hand or my ear than its image in a mirror? And yet I cannot replace the original with what I see in the mirror, because if the original is a right hand, its mirror image is a left hand, and the image of a right ear is a left ear and can never take the place of its original. There are no intrinsic, rationally conceivable differences between them, and yet our senses teach us that they are indeed intrinsically different, because in spite of all apparent similarity and sameness, a left hand is not contained within the same boundaries as a right hand (that is, they are not congruent) and a glove that fits one hand cannot be worn on the other." See also Kant's Lebendige Kräfte ("Living Forces") [ 1746], §§9-11, and Gegenden im Raum (“Areas in Space") [1768], Kant took this phenomenon as proof that human beings are capable of grasping only sensory perceptions of objects — that is, their appearances — and not their intrinsic nature. For an analysis of Kant's view of space with regard to the dimension problem, see Zöllner, Wirkungen in die Ferne ("Distant Effects") [1878a], pp. 220-227. In its projection onto the plane, the figure rotated through space appears to lose a dimension as it passes through axis a and becomes parallel to the direction of projection. Note that the outlines of F and F' can be made to coincide through rotation within the plane (i.e., around points in the plane) only if they are broken into line segments that are then rotated around the corresponding points on axis \(a\). In an analogous operation, the two three-dimensional geometric figures \(F\) and \(F’\), which are mirror images joined by plane a, can be transformed into each other without breaking contact by means of the (three-dimensional) spatial orthogonal affinity with a as the plane of affinity (Figure 69). This transformation can be interpreted as an orthogonal projection (in three-dimensional space) of a four-dimensional Euclidean rotation around plane a . In this projection, the three-dimensional figure \(F\) seems to lose a dimension as it passes through the two-dimensional plane \(a\). If the outer surface of \(F\) is broken into appropriate sections, these sections can be rotated around the corresponding axes in a to form the outer surface of figure \(F’\). Basing his theories on this analogy between two- and three-dimensional mirror images, August Ferdinand Möbius was apparently the first mathematician to conceive of the possibility of a four-dimensional space in which three-dimensional mirror-image figures can be made to coincide without breaking contact (see Möbius's Barycentric Calculus [1827], §140, note). He rejected this idea as "impossible to think," however, and did not pursue it further. The fact that we have two eyes makes depth perception possible for us; see also Rudolf Steiner's answers to questions by A. Strakosch, March 11, 1920, reprinted in this volume. On the significance of independent activity in perceiving the dimension of depth, see the questions and answers of April 7, 1921 (GA 76, reprinted here), and Note 17 here. (Johann Karl) Friedrich Zöllner (1834-1882), astrophysicist in Leipzig, considered one of the founding fathers of astrophysics because of his fundamental experimental and theoretical contributions to photometry and spectroscopy. His theory on the structure of comets set the direction for all later investigations. His book On the Nature of Comets: Contributions to the History and Theory of Knowledge [1886], like almost all of his treatises, contains far-reaching philosophical and historical commentary as well as polemical critiques of his contemporaries' pursuit of science. In connection with his studies on the Principles of an Electrodynamic Theory of Matter [ 1876], On Distant Effects [1878a], and On the Nature of Comets [1886], Zöllner became familiar with contemporary studies of non-Euclidean and higher-dimensional geometry. By the early 1870s, he surmised that only curved space or a fourth dimension could explain certain phenomena of physics. Around 1875, the research of the chemist and physicist William Crookes (1832-1919) inspired Zöllner to study spiritualism. He developed the view that the existence of spiritualistic phenomena could be explained by assuming the existence of four-dimensional space and that these phenomena proved that four-dimensional space is a reality, not merely a conceptual possibility (Zöllner [1878a], pp. 273ff). A short time later, Zöllner began his own studies of spiritualistic phenomena (see [1878b], pp. 752ff; [1878c], pp. 330ff; and especially [1878c]). For an overview of Zöllner's spiritualistic experiments, see Luttenberger [1977], for a contemporary analysis of Zöllner, see Simony's Spiritualistic Manifestations [1884]. On spiritualism in general, see Hartmann's Spirit Hypothesis [1891] and Spiritualism [1898]. On the history of spiritualism from Rudolf Steiner's point of view, see his lectures of February 1 and May 30, 1904 (GA 52), and October 10-25, 1915 (GA 254). Zöllner conceived of Kant's "things as such" as real four-dimensional objects projected into our perceptual space as three-dimensional bodies. He found proof of this view in the existence of three-dimensional mirror-image figures, which, though mathematically congruent, cannot be made to coincide without breaking contact with each other [in three dimensions] (see Note 3): "In fact, space that can explain the world we see without contradictions must possess at least four dimensions, without which the actual existence of symmetrical figures can never be traced back to a [single] law."(Zöllner [1878a], p. 248). Zöllner saw Kant's ideas as a precursor to his own views (see Note 2). In the essay quoted, Zöllner describes some of the unique characteristics of the transition from the third to the fourth dimension. Both his theoretical considerations and his spiritualistic experiments are based on these characteristics. He begins with a discussion of knots in three-dimensional space and draws attention to the fact that they can be untied only if "portions of the string temporarily disappear from three-dimensional space as far as beings of the same dimensionality are concerned [see Note 15], The same thing would happen if, by means of a movement executed in the fourth dimension, a body were removed from within a completely enclosed three-dimensional space and relocated outside it. Thus it seems possible to nullify the law of the so-called impermeability of matter in three-dimensional space in a manner completely analogous to removing an object from within a closed curve contained in a plane by lifting the object over the boundary of the curve without touching it." (Zöllner [1878a], p. 276.) See also Note 6. A perpendicular can be dropped to any point on a two-dimensional surface. If a point \(P\) moves away from the surface along this perpendicular, it distances itself from all points on the surface without changing its vertical projection \(M\) on the surface in any way. If this point \(M\) is the midpoint \(M\) of a circle, as point \(P\) leaves the surface, it is always equidistant from any of the points on the periphery of the circle, though this distance is constantly increasing. If we let point \(P\) move out along the perpendicular until its distance from midpoint \(M\) of the circle is greater than the radius of the circle and then rotate the perpendicular until it coincides with the plane of the circle, point \(P\) will have moved out of the circle without cutting through its circumference. Analogously, a point P inside a sphere can move out of the interior of the sphere without piercing its surface as soon as we enlist the help of four-dimensional space. Any point in three-dimensional space can leave it and enter four-dimensional space along the straight line of a perpendicular without touching any point in the original space. If we remove the midpoint \(M\) of a sphere from three-dimensional space in this way, point \(M\) distances itself increasingly but equally from all points on the sphere's surface. As soon as the distance from the initial location \(M\) is greater than the radius of the sphere, the point has been removed from the sphere, and the operation can be made visible by rotating the straight line along which the point traveled back into three-dimensional space. Arthur Schopenhauer (1788-1869): "The world is my mental image': this is a truth that applies to any living, cognizant being." ( The World as Will and Mental Image , vol. I, §1 [1894], p. 29). Rudolf Steiner also uses this example in his book Intuitive Thinking as a Spiritual Path: A Philosophy of Freedom (GA 4), chapter VI, "The Human Individuality," p. 106. See also his lecture of January 14, 1921 (GA 323, p. 252). Rudolf Steiner discusses these difficulties in greater detail in Intuitive Thinking as a Spiritual Path — A Philosophy of Freedom (GA 4), chapter IV, "The World as Perception," and in his Introduction to Goethe's Natural Scientific Works (GA 1), chapter IX, "Goethe's Epistemology," and chapter XVI.2, 'The Archetypal Phenomenon." Rudolf Steiner also uses this comparison in his lecture of November 8, 1908 (GA 108), where he investigates more closely how sensation, perception, mental images, and concepts relate to each other. Strictly speaking, this statement about the transition from circle to straight line is valid only in Euclidean geometry. In projective geometry, the transitional circle coincides with both the tangent, which remains constant, and the infinitely distant straight line (see Locher [1937], chapter IV, especially pp. 69ff). Only when the Euclidean plane becomes a projective plane by incorporating the infinitely distant straight line is it possible to pass through infinity (see also Ziegler [1992], chapter III). This phenomenon is directly related to the geometric fact that it is impossible to pass through infinity without leaving the domain of Euclidean geometry (see Note 11). In other words, the point we imagine as moving in one direction is not transformed into the point we imagine as coming back from the other side. The two portions of the straight line that we can imagine in sensory terms are connected through infinity only by a lawfulness that we can conceive, — they are separated by their manifestation in points that we can visualize. Rudolf Steiner uses the metaphor of seal, sealing wax, and impression repeatedly in epistemological considerations about the relationship between the objective outer world and the consciousness of the cognizant individual. The decisive aspect of this metaphor is that in it, as in the psycho-physical domain, transmission of form is not bound to transmission of substance. See also Steiners essays Philosophy and Anthroposophy (GA 35) and Anthroposophy's Psychological Foundations and Epistemological Position (GA 35), p. 138. Oskar Simony (1852-1915), mathematician and scientist in Vienna, son of the geographer and alpine researcher Friedrich Simony (1812-1896) and professor at the Vienna College of Agriculture from 1880 to 1913. His mathematical studies focused on number theory and the empirical and experimental topology of knots and two-dimensional surfaces in three-dimensional space (see Muller [1931] and [1951]). Some of the models Steiner mentions are illustrated in Simony's treatises. Simony's early involvement with topology was inspired by his encounters with Zöllner's spiritualistic experiments (see Note 5). He felt compelled to study the spatial problems posed by the discovery of non-Euclidean and multidimensional geometry. His investigations expanded to include physiological and epistemological considerations (see Simony [1883], [1884], and [1886]). The importance of not confusing the empirical realm and the realm of mathematical ideas was clear to him. The conceptual possibility of four-dimensional space was not a problem to him as a mathematician, but he could not accept Zöllner's thesis that all objects in three-dimensional space are projections of four-dimensional objects that are not perceptible to the senses. His intention, however, was not to reject the existence of spiritualistic phenomena out of hand. On the contrary, he, like Zöllner, advocated exact scientific investigation of such phenomena. He also considered how the spiritualistic phenomena reported by Zöllner might be proved using the traditional methods of physics and physiology, or at least reconciled with these fields (Simony, Spiritualistic Manifestations [1884], He felt that it was important to demonstrate that explaining such phenomena did not require leaving three-dimensional, empirical space. He pointed out that Zöllner's hypothesis of the existence of four-dimensional space contradicted our ordinary experience of space, — If this hypothesis is correct, objects in the ordinary three-dimensional space of physics are shadow images that we can change at will without having direct access to their prototypes (Simony [1881b], §6, and [1884], pp. 20ff). As shown by the example of a shadow projected by a three-dimensional object onto a surface, however, no change in the shadow is possible without direct access to the object that casts it. Simony's topological experiments were intended to investigate the nature of three-dimensional, empirical space, as opposed to curved space or any other mathematically conceivable space: 'The phenomena investigated here, since they belong to the realm of our senses, [can] be incorporated only into an empirical geometry without being brought into connection with the theory of so-called higher manifolds. In addition, the course of development I chose also makes it clear why, in investigating various sections of the first and second type, I avoided using either analytical geometry or infinitesimal calculus in order to remain independent of any possible hypothesis about the nature of perceived space" ([1883], pp. 963ff). As a mathematician, Simony was especially interested in how knots develop in twisted ring-shaped surfaces and in unknotted cross-shaped closed surfaces. He demonstrated that such surfaces can be cut in ways that either do not destroy their closed character or produce knots, under appropriate circumstances (Simony [1880], [1881a], [1881b]. The simplest and most famous example of this type, a closed strip incorporating a 720° twist, is mentioned by Rudolf Steiner in this lecture. In four-dimensional space, there are no knots, — that is, every knot in a closed thread or strip can be untied simply by pulling, without cutting (opening) the thread or strip. Felix Klein (1845-1925) seems to have been the first mathematician to draw attention to this phenomenon in the early 1870s. According to an account by Zöllner [1878a], Klein spoke with him during a scientific conference on this subject shortly before publishing a treatise [1876] in which he discussed this theme in passing. Klein also reported on their meeting and expressed the opinion that it inspired Zöllner's thesis on the existence of four-dimensional space and its significance in explaining spiritualistic phenomena (Klein [1926], pp. 169ff). While Klein ([1876], p. 478) discusses the subject only in general terms, Hoppe [1879] uses an analytically formulated example to untie concretely a simple three-dimensional knot in four-dimensional space (see also Durège [1880] and Hoppe [1880]). In Distant Effects ([1878a], pp. 272-274), Zöllner demonstrates the dissolution of knots in four-dimensional space with the help of an analogy. He first considers the dissolution of a two-dimensional knot in a closed curve (Figure 70): Without cutting the curve, the crossing cannot be eliminated if we remain within the plane, but by rotating a section of the curve through three-dimensional space around a straight line lying in the plane, any crossing can be undone without cutting the curve. "If these considerations are transferred via analogy to a knot in three-dimensional space, it is easy to see that such a knot can be tied and untied only through operations in which the elements of the thread describe a doubly bent curve." Without being cut, this knot cannot be untied in three-dimensional space. "If, however, there were beings among us capable of carrying out fourdimensional movements of material objects, these beings would be able to tie and untie such knots much faster, by means of an operation fully analogous to untying the two-dimensional knot described above. [...] My observations on knot formation in a flexible thread in different dimensions of space were inspired by oral communications from Dr. Felix Klein, professor of mathematics in Munich. "Clearly, in the operations indicated here, portions of the thread must disappear temporarily from three-dimensional space, as far as beings of the same dimensionality are concerned" (Zöllner [1878a], pp. 273-276). Undoing a knot in three-dimensional space is indeed always possible if either self-crossing or passing through four-dimensional space is allowed, since the latter makes possible the results of self-crossing without the actual self-crossing (see Seifert/Threlfall [1934], p. 3 and p. 315). All we need to do is rotate a suitably shaped section of the curve in plane a around plane b through four-dimensional space (Figure 71). Giving a strip a 360° twist before joining its ends into a ring results in a surface that is the four-dimensional equivalent of a three-dimensional cylindrical ring (Figure 72). In other words, twists that are whole-number multiples of 360° can be undone in four-dimensional space (see later discussion). Simony was presumably aware of this phenomenon, though he does not mention it explicitly in his topological works, since he was primarily concerned with the unique qualities of empirical three-dimensional space. The equivalence of an untwisted cylindrical strip in three-dimensional space and a strip with a 360° twist in four-dimensional space results from the fact that both rings are characterized by two non-intersecting curved edges. In the second instance, these curved edges are twisted around each other, while in the first instance they are not. In four-dimensional space, the twisting can be undone without any overlapping, converting the twisted ring into an untwisted ring (see the transition from Figure 73 to 74). Note that this operation cannot be performed on the so-called Möbius strip, a cylindrical ring incorporating a 180° twist (Figure 75). This surface has only one edge curve, — even in four-dimensional space, it cannot be transformed into an untwisted ring in any way without cutting through the surface. (This phenomenon has to do with the fact that such a surface cannot be oriented, — see Seifert/Threlfall [1934], §2. The Möbius strip was first described by Möbius [1865], §11.) Geometrically speaking, (static) vision in a plane or in space can be interpreted as a central projection of objects in the plane or in space onto a surface. To a being in three-dimensional space with this type of vision, therefore, all objects would appear as if projected on a surface. This being has an indirect impression of the third dimension only if it is able to see dynamically; that is, if its visual apparatus includes two projection directions and the ability to accommodate them. If not, such a being would be able to conclude that the third dimension exists (as one-eyed people do on the basis of much experience and many opportunities for comparison) but would not be able to experience it. The very fact of three-dimensional dynamic vision in human beings is evidence of our "four-dimensional" nature, which we cannot perceive directly (i.e. by means of our senses), though we can conclude that it exists. On the basis of geometry and physics, Charles Howard Hinton (1853-1907) also concluded that human beings must be beings of four or more dimensions. "It can be argued that symmetry in any number of dimensions is the evidence of an action in a higher dimensionality. Thus considering living beings, there is evidence both in their structure, and in their different mode of activity, of a something coming in from without into the inorganic world." (Hinton, The Fourth Dimension [1904], p. 78).

The Fourth Dimension

First Lecture

https://rsarchive.org/Lectures/GA324a/English/AP2001/19050324p02.html

Berlin

24 Mar 1905

GA324a-1

Today I will discuss elementary aspects of the idea of multidimensional space, with particular reference to the thoughts of Charles Hinton, a very wise man. [Note 18] As you recall, last time we began by considering the zero dimension and moved on to multidimensional space. Let me briefly reiterate the ideas we developed about two- and three-dimensional space. What do we mean by a symmetrical relationship? How do I make two plane figures that are mirror images of each other, such as this red figure and this blue one, coincide? This is relatively easy to do with two half circles. I simply insert the red one into the blue one by rotating it (Figure 10). This is not so easy with the mirror-image symmetry below (Figure 11). No matter how I try to insert the red part into the blue part, I cannot make them coincide if I remain within the plane. There is a way to accomplish this, however, if we leave the board — that is, the second dimension — and use the third dimension, — in other words, if we lay the blue figure on top of the red by rotating it through space around the axis of reflection. The situation is similar with a pair of gloves. We cannot make the one coincide with the other without leaving three-dimensional space. We have to go through the fourth dimension. Last time I said that if we want to acquire an idea of the fourth dimension, we must allow relationships in space to remain fluid in order to produce circumstances similar to those present when we make the transition from the second to the third dimension. We created interlocking spatial figures from strips of paper and saw that interlocking brings about certain complications. This is not just a game, because such interlocking occurs everywhere in nature, especially in the intertwined motions of material objects. These motions include forces, so the forces also are intertwined. Take the Earth's movement around the Sun in connection with the Moon's movement around the Earth. The Moon describes a circle that winds around the Earth's orbit around the Sun, — that is, the Moon describes a spiral around a circle. Because of the Sun's own movement, however, the Moon makes an additional spiral around it, resulting in very complicated lines of force that extend throughout space. The relationships of the heavenly bodies resemble Simony's twisted strips of paper, which we looked at last time. We must realize, as I said earlier, that we are dealing with complicated spatial concepts that we can understand only if we do not allow them to become fixed. If we want to understand the nature of space, we will have to conceive of it as immobile, initially, but then allow it to become fluid again. It is like going all the way to zero, where we find the living essence of a point. Let's visualize again how the dimensions are built up. A point is zero dimensional, a line is one dimensional, a surface two dimensional, and a solid object is three dimensional. Thus, a cube has three dimensions: height, width, and depth. How do spatial figures of different dimensions relate to one another? Imagine being a straight line. You have only one dimension and can move only along a line. If such one-dimensional beings existed, what would their idea of space be? They would not be able to perceive their one-dimensionality. Wherever they went, they would be able to imagine only points, because points are all we can draw while remaining within a straight line. A two-dimensional being would encounter only lines, — that is, it would perceive only one-dimensional beings. A three-dimensional being, such as a cube, would perceive two-dimensional beings but not its own three dimensions. Human beings, however, can perceive their own three dimensions. If we draw the correct conclusion, we must realize that if a one-dimensional being can perceive only points, a two-dimensional being only straight lines, and a three-dimensional being only surfaces, a being who perceives three dimensions must be four dimensional. The fact that we can delineate external beings in three dimensions and manipulate three-dimensional spaces means that we ourselves must be four-dimensional. Just as a cube would be able to perceive only two dimensions and not its own third dimension, it is clear that we cannot perceive the fourth dimension in which we ourselves live. Thus you see that human beings must be four-dimensional beings. We float in the sea of the fourth dimension like ice in water. Let's return to our discussion of mirror images (Figure 11). This vertical line represents a cross-section formed by a mirror. The mirror reflects an image of the figure on the left side. The reflection process points beyond the second dimension into the third. In order to understand the direct, uninterrupted relationship of the mirror image to the original, we must assume that a third dimension exists in addition to the first and second. Now let's consider the relationship between external space and internal perception. A cube outside me appears as a perception inside me (Figure 12). My idea of the cube relates to the cube itself as a mirror image relates to the original. Our sensory apparatus develops a mental image of the cube. If we want to make this image coincide with the original cube, we must pass through the fourth dimension. Just as a two-dimensional mirroring process must pass through the third dimension, our sensory apparatus must be four-dimensional to be able to bring about a direct connection between a mental image and an outer object. [Note 19] If you were to visualize in two dimensions only, you would confront merely a dream image. You would have no idea that an actual object exists in the outer world. When we visualize an object, we spread our capacity for mental pictures directly over outer objects by means of four-dimensional space. In the astral state during earlier periods of human evolution, human beings were only dreamers. The only images arising in their consciousness were dream images. [Note 20] Later, humans made the transition from the astral state to physical space. Having said this, we have defined the transition from astral to physical, material existence in mathematical terms: before this transition, astral humans were three-dimensional beings, — therefore, they could not extend their two-dimensional mental images to the objective, three-dimensional, physical, material world. When human beings themselves became physical, material beings, they acquired the fourth dimension and therefore also could experience life in three dimensions. The unique structure of our sensory apparatus enables us to make our mental images coincide with outer objects. By relating our mental images to outer things, we pass through four-dimensional space, putting the mental image over the outer object. How would things look from the other side, if we could get inside them and see them from there? To do so, we would have to go through the fourth dimension. The astral world itself is not a world of four dimensions. Taken together with its reflection in the physical world, however, it is four-dimensional. When we are able to survey the astral and physical worlds simultaneously, we exist in four-dimensional space. The relationship of our physical world to the astral world is four-dimensional. We must learn to understand the difference between a point and a sphere. In reality, a point such as the one pictured here is not passive, but radiates light in all directions (Figure 13). What would the opposite of such a point be? Just as the opposite of a line running from left to right is a line running from right to left, a point radiating light also has an opposite. Imagine a gigantic sphere, an infinitely large sphere that radiates darkness inward from all sides (Figure 14). This sphere is the opposite of a point that radiates light. The true opposite of a light-radiating point is an infinite space that is not passively dark but actively floods space with darkness from all directions. The source of darkness and the source of light are opposites. We know that a straight line that vanishes into infinity returns to the same point from the other side. Similarly, when a point radiates light in all directions, the light returns from infinity as its opposite, as darkness. Now let's consider the opposite case. Take the point as a source of darkness. Its opposite is then a space that radiates light inward from all directions. As I explained in the previous lecture, a point moving on a line does not vanish into infinity, — it returns from the other side (Figure 15). Analogously, a point that expands or radiates does not vanish into infinity, — it returns from infinity as a sphere. The sphere is the opposite of the point. Space dwells within the point. The point is the opposite of space. What is the opposite of a cube? Nothing less than the totality of infinite space minus the part defined by the cube. We must imagine the total cube as infinite space plus its opposite. We cannot get by without polarities when we attempt to imagine the world in terms of dynamic forces. Only polarities give us access to the life inherent in objects. When occultists visualize a red cube, the rest of space is green, because red is the complementary color of green. Occultists do not have simple, self-contained mental images. Their mental images are alive rather than abstract and dead. Our mental images are dead, while the objects in the world are alive. When we dwell in our abstract mental images, we do not dwell in the objects themselves. When we imagine a star that radiates light, we must also imagine its opposite — that is, infinite space — in the appropriate complementary color. When we do such exercises, we can train our thinking and gain confidence in imagining dimensions. You know that a square is a two-dimensional area. A square composed of two red and two blue smaller squares (Figure 16) is a surface that radiates in different directions in different ways. The ability to radiate in different directions is a three-dimensional ability. Thus we have here the three dimensions of length, width, and radiant ability. What we did here with a surface also can be done with a cube. Just as the square above is composed of four sub-squares, we imagine a cube composed of eight sub-cubes (Figure 17). Initially, the cube has three dimensions: height, width, and depth. In addition, we must distinguish a specific light-radiating capacity within each sub-cube. The result is another dimension, radiant ability, which must be added to height, width, and depth. If every one of the eight sub-cubes has a different capacity to radiate, then, if I have just one cube with its one-sided capacity to radiate and I want to get a cube that radiates in all directions, I have to add another one in all directions, double it with its opposites — I have to compose it out of 16 cubes? [Note 21] Next time we meet, we will learn ways of imagining higher-dimensional space. Charles Howard Hinton (1853-1907), mathematician and author. Hinton was strongly influenced by his father, James Hinton (1822–1875), a surgeon who also wrote essays, including several on the art of thinking, or "thought-artistry,” in which he rejected any artificial restraints on thinking and experience due to religious, social, or legal regulation of behavior. Through his parents' contact with Mary Everest Boole (1832-1916), the widow of the logician and mathematician George Boole, (1815-1864) Hinton met the Booles' daughter, Mary Ellen, his future wife. Hinton studied mathematics at Oxford and taught at various institutions before leaving England for Japan in 1886. He lived in Japan until 1891 and then spent the rest of his life in the United States. Hinton's search for certainty provoked a severe crisis in 1875. He resorted to the idea that only the arrangement of objects in space could lead to absolutely certain knowledge. In his preoccupation with thought exercises and visualizations concerning the arrangement of a cube subdivided into smaller cubes, he attempted to free himself from all subjectively imposed limitations such as the concepts of "above" and "below" ("Casting Out the Self" [1886], pp. 205-229). In this process, he encountered the problem of mirror-image subdivisions of two cubes and wondered whether this phenomenon might not also prove to be subjectively determined. While investigating this question, he discovered a treatise by Friedrich Zöllner on four-dimensional space [1878e] in the Quarterly Journal of Science (edited by William Crookes). In this paper, Zöllner briefly presented his experiments and views on the reality of the fourth dimension. Crookes (a chemist and physicist) and Zöllner both belonged to the group of university-based researchers who were attempting, though with little success, to use scientific methods to approach spiritualism. Hinton spent the rest of his life studying the problem of the fourth dimension. His works concentrated on popularizing ideas about four-dimensional space and dealt especially with how to acquire the ability to visualize it. In this connection, Hinton studied the transition from the second to the third dimension in many different ways in order to create a solid foundation for depicting the fourth dimension in three-dimensional perceived space. In particular, he developed methodical exercises for acquiring a consistent view of three-dimensional space and for a time held the opinion that it was possible to acquire a non-sensory view of four-dimensional space in the same way (see A New Era of Thought [1900] and The Fourth Dimension [1904]). Hinton believed that the world included a material extension into the fourth dimension and attempted to prove this hypothesis through various experiments in psychology and physics. This view met with resistance both from materialists, who accepted the existence of only three spatial dimensions, and from spiritualists, who preferred to interpret the fourth dimension as purely spiritual in character (see Ballard [1980]). Hinton was a controversial writer who was avidly read and highly esteemed by the lay public, especially theosophists and avant-garde artists (see Henderson [1983] and [1988]). He was rejected or ignored in academic circles. See the corresponding explanations in the previous lecture See Rudolf Steiner, An Outline of Esoteric Science (GA 13), chapter IV: "Cosmic Evolution and the Human Being." A definitive reconstruction of what Steiner meant by this analogy is not possible, and there is nothing in Hinton's works that corresponds to this train of thought. Although Hinton also uses colors to illustrate the transition from the second to the third dimension and especially the transition from the third to the fourth, he uses them very differently. In his lecture of May 24, 1905, reprinted in this volume, Steiner gives a review of Hinton's thoughts on this subject. The geometric basis of the thoughts Steiner presents here is as follows: A line segment bisected in the middle can be developed into a square by allowing each half of the segment to form the shared side of two adjacent smaller squares. The result is a larger square divided into four smaller ones (Figure 16). A cube divided into eight smaller cubes can then be constructed by allowing each of the smaller squares to form the shared surface of two adjacent cubes (Figure 17). The corresponding four-dimensional figure, the four-dimensional cube, results when each of the eight sub-cubes of the three-dimensional cube is interpreted as the shared boundary between two four-dimensional cubes. The result is a four-dimensional cube divided into sixteen sub-cubes.

The Fourth Dimension

Second Lecture

https://rsarchive.org/Lectures/GA324a/English/AP2001/19050331p02.html

Berlin

31 Mar 1905

GA324a-2

Today I will continue with the difficult subject we have undertaken to explore. We will need to refer back to the topics I mentioned in the last two lectures. After that, I would like to develop a few basic concepts so that in the two final lectures we will be able to use Mr. Schouten's models to fully grasp both the details of the geometric relationships and theosophy's interesting practical perspectives. [Note 22] As you know, the reason we tried to envision the possibility of four-dimensional space was to gain at least some idea of the socalled astral realm and still higher forms of existence. I have already pointed out that entering the astral world is initially quite confusing for students of esotericism. Without making a closer study of theosophy and esoteric subjects, at least on a theoretical level, it is extremely difficult to form any idea of the very different nature of the objects and beings that we encounter in the so-called astral world. Let me briefly sketch this difference to show you how great it is. In the simplest example I mentioned, we have to learn to read all numbers in reverse. Esoteric students who are accustomed to reading numbers only as they are read here in the physical world will not be able to find their way through the labyrinth of the. astral realm. In the astral world, a number such as 467 must be read 764. You must become used to reading each number symmetrically, as its mirror image. This is the basic prerequisite. Applying this rule to spatial figures or numbers is easy enough, but it becomes more difficult when we begin to deal with relationships in time, which also must also be interpreted symmetrically — that is, later events come first and earlier events appear later. Thus, when you observe astral events, you must be able to read them backward, from the end to the beginning. I can only suggest the character of these phenomena, which can seem totally grotesque if you have no idea of what is going on. In the astral realm, the son is there first and then the father, — the egg is there first, and the chicken follows. In the physical world, the sequence is different — birth happens first, and birth means that something new emerges from something old. In the astral world, the reverse takes place. There, the old emerges from the new. In the astral realm, the fatherly or motherly element appears to engulf the son or daughter. Greek mythologies provide a lovely allegory. The three gods Uranus, Kronos, and Zeus symbolize the three worlds. Uranus represents the heavenly world, or devachan, Kronos the astral world, and Zeus the physical world. It is said of Kronos that he devoured his children. [Note 23] The issue becomes even more complex when we consider morality on the astral plane. Morality, too, appears in reverse form, or as its own mirror image. You can imagine how greatly explanations of events there differ from our habitual explanations in the physical world. Imagine, for example, that we see a wild animal approaching us in the astral realm, and it strangles us. That is how it appears to someone who is used to interpreting external events, but we cannot interpret this event as we would in the physical world. In reality, the wild animal is an internal quality, — an aspect of our own astral body is strangling us. The attacking strangler is a quality that is rooted in our own desires. If we have a vengeful thought, for example, the thought may appear in external form, tormenting us as the Angel of Death. In reality, everything in the astral world radiates from us. We must interpret everything that seems to approach us in the astral world as radiating outward from ourselves (Figure 18). It comes back to us on all sides as if from the periphery, from infinite space. In truth, however, we are confronting only what our own astral body has given off. We interpret the astral world correctly and discover its truth only when we are able to bring the periphery into the center, to construe the periphery as the central element. The astral world appears to bear down on you from all sides, but you must envision it as actually radiating outward from you in all directions. At this point I would like to make you aware of a concept that is very important in esoteric schooling. It appears, ghostlike, in many different works on occult research but seldom is it understood correctly. Once you have achieved a certain level of esoteric development, you must learn what your karma predisposes you to find in the astral world. What joys, sorrows, pain, and so forth can you expect to encounter? Correct theosophical thinking allows you to realize that in this day and age, your outer life and physical body are nothing more than the result, or intersection, of two streams that converge from opposite directions. Picture one stream coming from the past and one coming from the future. The result is two intermingling streams that join together at all these points (Figure 19). Imagine a red stream flowing from one direction and a blue stream flowing from the other. Now picture four different points where the streams join together. At each of these four points, the red and blue streams interact. This is an image of the interaction of four successive incarnations, — in each incarnation we encounter something coming from one direction and something coming from the other. You might say that one stream always travels toward you and that you bring the other stream along with you. Each human being is the confluence of two such streams. To gain an idea of this state of affairs, imagine in this way: As you sit here today, you have a certain sum of experiences. At the same time tomorrow, the sum of these events will be different. Now imagine that the experiences you will possess tomorrow are already there. Becoming aware of them would be like seeing a panorama of events coming toward you in space. Imagine that the stream coming toward you from the future is bringing you the experiences you will have between today and tomorrow. You are supported by the past as the future comes to meet you. At any point in time, two streams flow together to form your life. One stream flows from the future toward the present and the other from the present toward the future, and an interface occurs wherever they meet. Anything that still remains for us to experience in our life appears in the form of astral phenomena, which make a tremendous impression on us. Imagine that students of esotericism reach the point in their development when they are meant to see into the astral world. Their senses are opened, and they perceive all their future experiences until the end of this time period as outer phenomena surrounding them in the astral world. This sight makes a great impression on each student. An important level in esoteric schooling is reached when students experience an astral panorama of everything they have yet to encounter up to the middle of the sixth root race, which is how long our incarnations will last. The way is opened to them. Without exception, students of esotericism experience all the remaining outer phenomena they will encounter from the near future to the sixth root race. When you reach this threshold, a question arises: Do you want to experience all this in the shortest possible time? That is the issue for initiation candidates. As you consider this question, your entire future life appears to you in a single moment in the external panorama characteristic of astral vision. Some people will decide not to set out into the astral realm, while others will feel that they must enter. At this point in esoteric development, which is known as the threshold, or moment of decision, we experience ourselves along with everything we must still live through. This phenomenon, which is known as meeting the "guardian of the threshold," is nothing more than facing our own future life. Our own future lies beyond the threshold. Another unique quality of the world of astral phenomena is initially quite impenetrable if that world is revealed suddenly, through one of life's unforeseen events. When this happens, there is nothing more confusing than this terrible sight. It is good to know about it in case the astral world suddenly breaks in on you as the result of a pathological event, such as the loosening of the connection between the physical body and ether body or between the ether body and the astral body. Such events can reveal a view of the astral world to people who are quite unprepared for it. These people then report seeing apparitions that they cannot interpret because they do not know that they must read them in reverse. For instance, they do not know that a wild animal attacking them must be interpreted as a reflection of an internal quality. In kamaloka, a person's astral forces and passions appear in a great variety of animal forms. In kamaloka, recently disembodied individuals who still possess all their passions, drives, wishes, and desires are not a pretty sight. Such people, though they are no longer in possession of physical and etheric bodies, still retain all the astral elements that bind them to the physical world and that can be satisfied only through a physical body. Think of average, modern citizens who never amounted to much in their lives and made no particular effort to achieve religious development. They may not have rejected religion in theory, but in practice — that is, as far as their own feelings were concerned — they threw it out the window. It was not a vital element in their lives. What do such people's astral bodies contain? They contain nothing but urges that can be satisfied only through the physical organism, such as the desire to enjoy tasty food, for example. Satisfying this desire, however, would require taste buds. Or the individual in question may long for other pleasures that can be satisfied only by moving the physical body. Suppose that such urges persist, living on in the astral body after the physical body is gone. We find ourselves in this situation if we die without first undergoing astral cleansing and purification. We still have the urge to enjoy tasty food and so on, but such urges are impossible to satisfy. They cause terrible torment in kamaloka, where those who die without first purifying the astral body must lay their desires aside. The astral body is freed only when it learns to relinquish the desires and wishes that can no longer be satisfied. In the astral world, urges and passions take on animal shapes. As long as a human being is incarnated in a physical body, the shape of the astral body conforms more or less to the human physical body. When the material body is gone, however, the animal nature of urges, desires, and passions is revealed in the forms they assume. In the astral world, therefore, an individual is a reflection of his or her urges and passions. Because these astral beings can also make use of other bodies, it is dangerous to allow mediums to go into a trance without the presence of a clairvoyant who can ward off evil. In the physical world, the form of a lion expresses certain passions, while a tiger expresses other passions and a cat still others. It is interesting to realize that each animal form is the expression of a specific passion or urge. In the astral world, in kamaloka, we approximate the nature of animals through our passions. This fact is the source of a common misunderstanding with regard to the doctrine of transmigration of souls taught by Egyptian and Indian priests and teachers of wisdom. This doctrine, which teaches that we should live in ways that do not cause us to incarnate as animals, does not apply to physical life but only to higher life. It is intended only to encourage people to live their earthly lives in ways that will not require them to assume animal forms after death, in kamaloka. For example, someone who cultivates the character of a cat during earthly life appears in the form of a cat in kamaloka. To allow individuals to appear in human form in kamaloka is the goal of the doctrine of transmigration of souls. Scholars who fail to understand the true teachings have only an absurd idea of this doctrine. We saw that when we enter the astral realm of numbers, time, and morality, we are dealing with a complete mirror image of everything we customarily think and do here on the physical plane. We must acquire the habit of reading in reverse, a skill we will need when we enter the astral realm. Learning to read in reverse is easiest when we take up elementary mathematical ideas such as those suggested in the previous lecture. In the discussions that follow, we will become more and more familiar with these ideas. I would like to begin with a very simple one, namely, the idea of a square. Picture a square as you are accustomed to seeing it (Figure 20). I will draw each of its four sides in a different color. This is what a square looks like in the physical world. Now I will draw a square as it looks in devachan. It is impossible to draw this figure precisely, but I want to give you at least an idea of what a square would look like on the mental plane. The mental equivalent [of a square] is something approximating a cross (Figure 21). Its main features are two intersecting perpendicular axes — or, if you will, two lines that cross each other. The physical counterpart is constructed by drawing lines perpendicular to each of these axes. The physical counterpart of a mental square can best be imagined as a stoppage in two intersecting streams. Let's imagine these perpendicular axes as streams or forces working outward from their point of intersection, with counter tendencies working in from the opposite direction, from the outside inward (Figure 22). A square arises in the physical world when we imagine that these two types of streams or forces — one coming from within and one coming from outside — meet and hold each other at bay. Boundaries develop where a stoppage occurs in the streams of force. This image describes how everything on the mental plane relates to everything on the physical plane. You can construct the mental counterpart of any physical object in the same way. This square is only the simplest possible example. If, for any given physical object, you could construct a correlate that relates to that object in the same way that two intersecting perpendicular lines relate to a square, the result would be the image of the physical object in devachan, on the. mental level. With objects other than a square, this process is much more complicated, of course. Now instead of the square, imagine a cube. A cube is very similar to a square. A cube is a figure bounded by six squares. Mr. Schouten has made an extra model showing the six squares that delineate a cube. Instead of the four boundary lines in a square, imagine six surfaces forming the boundaries. Imagine that the boundary of the stopped forces consists of perpendicular surfaces instead of perpendicular lines and assume that you have three instead of two perpendicular axes. You have just defined a cube. At this point, you probably also can imagine a cube's correlate on the mental level. Again we have two figures that complement each other. A cube has three perpendicular axes and three different directions to its surfaces. We must imagine that stoppage occurs in these three surface directions (Figure 23). The three directions of the axes and the six surfaces, like the square's two axes (directions) and four lines, can be imagined only as opposites of a particular sort. Anyone who thinks about this subject at all must conclude that in order to imagine these figures, we must first arrive at a concept of opposites that contrast activity and counter-activity, or stoppage. This concept of opposites must enter into our considerations. The examples we used are simple, but by practicing with geometric concepts, we will learn how to construct the mental counterparts of more complicated objects properly, — this activity will show us the way to higher knowledge to a certain extent. You already can imagine the monumental complexity of trying to find the mental counterpart of some other figures. Far greater complications emerge. Just imagine thinking about a human form and its mental counterpart with all its different shapes and activity. You can conceive what a complicated mental structure this would be. My book Theosophy gives approximations of how mental counterparts would look. [Note 24] In the case of a cube, we have three extensions, or three axes. Two planes, one on each side, are perpendicular to each axis. At this point you need to understand clearly that each surface of a cube, like the human life I described earlier, comes about as the meeting of two streams. You can picture streams moving outward from the midpoint. Imagine one of these axial directions. Space streams outward from the midpoint in one direction and toward the midpoint from the other direction, from infinity. Now envision these streams in two different colors, one red and one blue. At the moment of their meeting, they flow together to create a surface. Thus, we can see the surface of a cube as the meeting of two opposing streams in a surface. This visualization gives us a living idea of the nature of a cube. A cube is a section of three interacting streams. When you think of the totality of their interaction, you are dealing with six directions rather than three: backward/forward, up/down, and right/left. There are actually six directions. The issue is complicated further by the existence of two types of streams, one moving outward from a point and another moving inward from infinity. This will give you a perspective on the practical applications of higher, theoretical theosophy. Any direction in space must be interpreted as two opposing streams, and any physical shape must be imagined as their result. Let's call these six streams, or directions, \(a\), \(b\), \(c\), \(d\), \(e\), and \(f\). If you could visualize these six directions — and next time we will talk about how to cultivate such mental images — and then eliminate the first and last, \(a\) and \(f\), four would remain. Please note that these remaining four are the ones you can perceive when you see only the astral world. I have attempted to provide you with some idea of the three ordinary dimensions and of three additional and opposite dimensions. Physical forms arise as a result of the opposing action of these dimensions. If you remove one dimension on the physical level and one on the mental level, however, you are left with the four dimensions that represent the astral world, which exists between the physical and mental worlds. The theosophical worldview must work with a higher geometry that transcends ordinary geometry. Ordinary geometrists describe a cube as delineated by six squares. We must conceive of a cube as the result of six interpenetrating streams — that is, as the result of a movement and its opposite or as the consequence of interacting opposing forces. I would still like to give you an example from the natural world of a concept that embodies such a pair of opposites and shows us one of the profound mysteries of the world's evolution. In his The Green Snake and the Beautiful Lily , Goethe speaks of the 'revealed mystery,' one of the truest and wisest phrases ever formulated. [Note 25] Let's compare a human being to a plant. This is not a game, though it looks like one. It points to a profound mystery. Which part of the plant is in the ground? It is the root. Up top, the plant develops stems, leaves, flowers, and fruit. The plant's 'head,' its root, is in the ground, and its organs of reproduction develop above ground, closer to the sun. This can be called the chaste method of reproduction. Picture the whole plant inverted, with its root becoming the human head. There you have the human being, — with the head above and the reproductive organs below, — as the inverse of a plant. The animal occupies the middle and represents an interface. The result of inverting a plant is a human being. Esotericists throughout the ages have used three lines to symbolize this phenomenon (Figure 24). One line symbolizes the plant, another represents the human being, and a third opposing line corresponds to the animal — three lines that together form a cross. The animal occupies the horizontal position — that is, it crosses what we humans have in common with plants. As you know, Plato speaks of a universal soul that is crucified on the body of the Earth, bound to the cross of the Earth. [Note 26] Strength is required to perceive this world, but those who already have the appropriate organs of perception will recognize what we see in the interrelationship of these three kingdoms. If you interpret the animal kingdom as emerging from an interface, you will discover the relationship between the plant and animal kingdoms and the animal and human kingdoms. The animal stands perpendicular to the direction of the two other kingdoms, which are complementary, interpenetrating streams. Each lower kingdom serves the next higher one as food. This fact sheds light on the difference between the human-plant relationship and the animal-human relationship. Human beings who eat animals develop a relationship to a condition of interfacing. The real activity consists in the meeting of opposing streams. In making this statement, I am initiating a train of thought that will reappear later in a strange and very different guise. In summary, we have seen that a square comes about when two axes are cut by lines. A cube comes about when three axes are cut by surfaces. Can you imagine four axes being cut by something? The cube is the boundary of the spatial figure that comes about when four axes are cut. A square forms the boundary of a three-dimensional cube. Next time we will see what figure results when a cube forms the boundary of a four-dimensional figure. What does it mean to imagine six streams and then eliminate two, and so on? The six streams must be imagined as two times three: three of them work from the center outward in the directions defined by the three axes, and the other three work in the opposite direction, coming from infinity. Thus, for each axial direction there are two types, — one going outward from the interior and the other moving inward from outside. If we call these two types positive and negative, plus and minus, the result is this: \(+a\)    \(-a\) \(+b\)    \(-b\) \(+c\)    \(-c\) To enter the astral realm we must eliminate one entire direction of inward and outward streams: \(+a \) and \(-a\), for example. Mr. Schouten . In all probability, Jan Arnoldus Schouten (1883–1971), a Dutch mathematician from Delft. In the archives of the Rudolf Steiner Nachlassverwaltung, there is a letter from Schouten to Steiner. The part that relates to this lecture reads: Delft December 1, 1905 Dear Dr. Steiner, Before leaving for home in July of this year, I stopped in to say goodbye to you, but unfortunately you had already left. Consequently, the models you needed for your lecture are still in your possession. Since I intend to give several lectures here on the fourth dimension, could you please send the models to me? These lectures are intended for several lodges, including the one in Delft, which was founded a short time ago. Sincerely yours, J. A. Schouten M. T. S. After studying electrical engineering at the technical college in Delft, Schouten practiced his profession for several years in Rotterdam and Berlin. In order to be able to understand the theory of special relativity, Schouten studied mathematics privately and wrote the book Grundlagen der Vektor- und AJfinoranalysis ('The Bases of Vector and Affine Analysis") [1914], which he submitted as his dissertation to the University of Delft. Shortly thereafter, he was named professor at Delft, where he remained until 1943. Schouten's book [1914], with a personal dedication by the author, was found in Rudolf Steiner's library. Schouten's mother, H. Schouten (1849–19??) was a member of the Theosophical Society and later of the Anthroposophical Society. To date, only one other indication of a connection between Schouten and Rudolf Steiner has been found, in a letter (also in the Steiner archives) to Rudolf Steiner from Schouten’s mother, dated March 4, 1913. This letter reads in part: I was very confident that my son, now that he intends to give up his membership in the Theosophical Society, would become a member of the Anthroposophical Society, but he says that for the moment he cannot do so with a clear conscience because he has not been able to keep up his theosophical studies. He told me that he makes a point of seriously studying everything he undertakes in life, and that because his own academic work is so demanding at the moment that he has almost no time to go out, he is temporarily unable to take up the study of theosophy again. The first draft of his paper has been sent to the Royal Academy. In addition to his private work, he is lecturing weekly on mathematics in Delft and on electricity in Rotterdam. In the week when you will be in the Hague, the Philosophical Society in Amsterdam has asked him to give a lecture on his concepts of non-material mathematics. Praise God, both he and his wife have absorbed the truths of reincarnation and karma. They would like to attend your public lectures, and my son also thought that some of his colleagues might attend if the subject appealed to them. I hope you and my son will find the opportunity to meet. Schouten's first paper in the Verslagen en Mededeelingen der Koninglijke Akademie van Wetenschappen appeared in 1917 in volume 26; a paper in the Verhandelingen der Koninglijke Akademie van Wetenschappen te Amersterdam appeared in 1918 in volume 12. Kronos (not to be confused with Chronos, or Time) is one of the sons of Uranus and Gaia. He married his sister Rhea, who gave birth to three daughters (Hestia, Demeter, and Hera) and two sons (Poseidon and Zeus). Kronos devoured all of them except Zeus, whom Rhea had entrusted to her mother, Gaia. (See Kèrenyi, Die Mythologie der Griechen ["The Mythology of the Greeks"] [1966], volume I, chapter I, sections 1 and 2.) See Rudolf Steiner's Theosophy . Johann von Wolfgang Goethe (1749–1832). Meanwhile the golden king said to the man with the lamp, "How many mysteries do you know?" 'Three," answered the old man. "Which is the most important?" 'The revealed one," answered the old man. Plato (427–347 BC). Timaeus 36b-37a. See also Rudolf Steiner's Christianity as Mystical Fact (GA 8), pp. 65 ff.

The Fourth Dimension

Third Lecture

https://rsarchive.org/Lectures/GA324a/English/AP2001/19050517p02.html

Berlin

17 May 1905

GA324a-3

In a recent lecture I attempted to develop a schematic idea of four-dimensional space, which would be very difficult to do without using an analogy of sorts. The problem that confronts us is how to indicate a four-dimensional figure here in three-dimensional space, which is the only type of space initially accessible to us. To link the unfamiliar element of four-dimensional space to something we know about, we must find ways to bring a four-dimensional object into three dimensions, just as we brought a three-dimensional object into two dimensions. I would like to use the method popularized by Mr. Hinton to demonstrate a solution to the problem of how to represent four-dimensional space in three dimensions. [Note 27] Let me begin by showing how three-dimensional space can be depicted in two dimensions. Our chalkboard here is a two-dimensional surface. Adding depth to its dimensions of height and width would give us a three-dimensional space. Now let's attempt to depict a three-dimensional figure here on the chalkboard. A cube is a three-dimensional figure because it has height, width, and depth. Let's try to bring a cube into two-dimensional space — that is, into a plane. We can take a cube and unfold it so that its six square sides are spread out in a plane (Figure 25). In two dimensions, therefore, the surfaces defining a cube can be imagined as forming a cross. These six squares form a cube again when I fold them up so that squares 1 and 3 are opposite each other. Squares 2 and 4 are also opposite each other, as are 5 and 6. This is a simple way of transferring a three-dimensional figure to a plane. We cannot use this method directly when we want to draw the fourth dimension in three-dimensional space. For that, we need a different analogy. We will need to use colors. I will color the edges of the six squares differently, so that opposite sets of squares are of the same colors. For squares 1 and 3, I will make one pair of edges red (dotted lines) and another blue (solid lines). I also will color all the horizontal edges of the other squares blue and all the verticals red (Figure 26). Look at these two squares, 1 and 3. Their two dimensions are represented by two colors, red and blue. For us, then, on the vertical board, where square 2 is flat against the board, red means height, and blue means depth. Having consistently used red for height and blue for depth, let's add green (dashed lines) for width, the third dimension, and complete our unfolded cube. Square 5 has blue and green sides, so square 6 must look the same. Now only squares 2 and 4 are left. When you imagine them unfolded, you find that their sides are red and green. Having visualized these colored edges, you realize that we have transformed the three dimensions into three colors. Instead of height, width, and depth, we now call them red (dotted), green (dashed), and blue (solid). These three colors replace and represent the three dimensions of space. Now imagine the whole cube folded up again. You can explain the addition of the third dimension by saying that the blue and red square has moved through green i.e., from left to right in Figure 26. Moving through green, or disappearing into the dimension of the third color, represents the transition through the third dimension. Imagine that a green fog tints the red-and-blue squares, so that both edges (red and blue) appear colored. The blue edge becomes blue-green and the red acquires a murky tint. Both edges reappear in their own color only where the green stops. I could do the same thing with squares 2 and 4 by allowing a red-and- green square to move through a blue space. You could do the same with the two blue-and-green squares, 5 and 6, moving one of them through red. In each case, the square disappears on one side, submerging into a different color that tints it until it emerges on the other side in its original coloration. Thus, the three colors positioned at right angles to each other are a symbolic representation of our cube. We simply have used colors for the three directions. To visualize the changes the cube's three pairs of surfaces undergo, we imagine them passing through green, red, and blue, respectively. Instead of these colored lines, imagine squares, and instead of empty space, picture squares everywhere. Then I can draw the entire figure in a still different way (Figure 27). The square through which the others pass is colored blue, and the two that pass through it — before and after they make the transition — are drawn flanking it. Here they are in red and green. In a second step, the blue-and-green squares pass through the red square, and, in a third step, the two red-and-blue squares pass through the green. Here you see a different way of flattening out a cube. Of the nine squares arranged here, only six — the upper and lower rows — form the boundaries of the cube itself (Figure 27). The other three squares in the middle row represent transitions, — they simply signify that the other two colors disappear into a third. Thus, with regard to the movement of transition, we must always take two dimensions at once, because each of these squares in the upper and lower rows is made up of two colors and disappears into the color that does not contain it. We make these squares disappear into the third color in order to reappear on the other side. The red-and-blue squares pass through green. The red-and-green squares have no blue sides, so they disappear into blue, while the green-and-blue squares pass through red. As you see, we can thus construct our cube out of two-dimensional — that is, bi-colored — squares that pass through a third dimension or color. [Note 28] The next obvious step is to imagine cubes in the place of squares and to visualize these cubes as being composed of squares of three colors (dimensions), just as we constructed our squares out of lines of two colors. The three colors correspond to the three dimensions of space. If we want to proceed just as we did with the squares, we must add a fourth color so that we can make each cube disappear through the color it lacks. We simply have four differently colored transition cubes — blue, white, green, and red — instead of three transition squares. Instead of squares passing through squares, we now have cubes passing through cubes. Mr. Schouten's models use such colored cubes. [Note 29] Just as we made one square pass through a second square, we must now make one cube pass through a second cube of the remaining color. Thus the white-red-and-green cube passes through a blue one. On one side, it submerges in the fourth color, — on the other side, it reappears in its original colors (Figure 28.1). Thus we have here one color or dimension that is bounded by two cubes whose surfaces are three different colors. Similarly, we must now make the green-blue-and-red cube pass through the white cube (Figure 28.2). The blue-red-and-white cube passes through the green one (Figure 28.3), and, in the last figure (Figure 28.4), the blue-green-and-white cube has to pass through a red dimension, — that is, each cube must disappear into the color it lacks and reappear on the other side in its original colors. These four cubes relate to each other in the same way as the three squares in our previous example. We needed six squares to delineate the boundaries of a cube. [Note 30] Similarly, we need eight cubes to form the boundaries of the analogous four-dimensional figure, the tessaract. [Note 31] In the case of a cube, we needed three accessory squares that simply signified disappearance through the remaining dimension. A tessaract requires a total of twelve cubes, which relate to one another in the same way as the nine squares in a plane. We have now done to a cube what we did with squares in the earlier example. Each time we chose a new color, we added a new dimension. We used colors to represent the four directions incorporated by a four-dimensional figure. Each of the cubes in this figure has three colors and passes through a fourth. The point in replacing dimensions with colors is that three dimensions as such cannot be incorporated into a two-dimensional plane. Using three colors makes this possible. We do the same thing with four dimensions when we use four colors to create an image in three-dimensional space. This is one way of introducing this otherwise complicated subject. Hinton used this method to solve the problem of how to represent four-dimensional figures in three dimensions. Next I would like to unfold the cube again and lay it down in the plane. I'll draw it on the board. For the moment, disregard the bottom square in Figure 25 and imagine that you can see in two dimensions only — that is, you can see only what you can encounter on the surface of the board. In this instance, we have placed five squares so that one square is in the middle. The interior area remains invisible (Figure 29). You can go all the way around the outside, but since you can see only in two dimensions, you will never see square 5. Now instead of taking five of the six square sides of a cube, let's do the same thing with seven of the eight cubes that form the boundaries of a tessaract, spreading our four-dimensional figure out in space. The placement of the seven cubes is analogous to that of the cube's surfaces laid down in a plane on the board, but now we have cubes instead of squares. The resulting three-dimensional figure is analogous in structure to the two-dimensional cross made of squares and is its equivalent in three-dimensional space. The seventh cube, like one of the squares, is invisible from all sides. It cannot be seen by any being capable only of three-dimensional sight (Figure 30). If we could fold up this figure, as we can do with the six unfolded squares in a cube, we could move from the third into the fourth dimension. Transitions indicated by colors show us how this process can be visualized. [Note 32] We have demonstrated at least how we humans can visualize four-dimensional space in spite of being able to perceive only three dimensions. At this point, since you also may wonder how we can gain an idea of real four-dimensional space, I would like to make you aware of the so-called alchemical mystery, because a true view of four-dimensional space is related to what the alchemists called transformation. [ First text variant: ] If we want to acquire a true view of four-dimensional space, we must do very specific exercises. First we must cultivate a very clear and profound vision — not a mental image — of what we call water. Such vision is difficult to achieve and requires lengthy meditation. We must immerse ourselves in the nature of water with great precision. We must creep inside the nature of water, so to speak. As a second exercise, we must create a vision of the nature of light. Although light is familiar to us, we know it only in the form in which we receive it from outside. By meditating, we acquire the inner counterpart of outer light. We know where and how light arises, — we ourselves become able to produce something like light. Through meditation, yogis or students of esotericism acquire the ability to produce light. When we truly meditate on pure concepts, when we allow these concepts to work on our souls during meditation or sense-free thinking, light arises out of the concepts. Our entire surroundings are revealed to us as streaming light. Esoteric students must "chemically combine" the vision of water that they have cultivated with their vision of light. Water fully imbued with light is what the alchemists called mercury. In the language of alchemy, water plus light equals mercury. In the alchemical tradition, however, mercury is not simply ordinary quicksilver. After we awaken our own ability to create light out of our own work with pure concepts, mercury comes about as the mingling of this light with our vision of water. We take possession of this light-imbued power of water, which is one of the elements of the astral world. The second element arises when we cultivate a vision of air, just as we previously cultivated a vision of water. Through a spiritual process, we extract the power of air. Then, by concentrating the power of feeling in certain ways, feeling kindles fire. When you chemically combine, as it were, the power of air with the fire kindled by feeling, the result is "fire-air." As you may know, this fireair is mentioned in Goethe's Faust. [Note 33] It requires the inner participation of the human being. One component is extracted from an existing element, the air, while we ourselves produce the other fire or warmth. Air plus fire yields what the alchemists called sulfur, or shining fire-air. The presence of this fire-air in a watery element is truly what is meant when the Bible says, "And the Spirit of God brooded upon the face of the waters." [Note 34] The third element comes about when we extract the power of the earth and combine it with the spiritual forces in sound. The result is what is called the Spirit of God. It also is called thunder. The active Spirit of God is thunder, earth plus sound. Thus, the Spirit of God hovered over astral substance. The biblical "waters' are not ordinary water but what we know as astral substance, which consists of four types of forces: — water, air, light, and fire. The sequence of these four forces is revealed to astral vision as the four dimensions of astral space. That is what they really are. Astral space looks very different from our world. Many supposedly astral phenomena are simply projections of aspects of the astral world into physical space. As you can see, astral substance is half-subjective, that is, passively given to the subject, and half water and air. Light and feeling (fire), on the other hand, are objective, that is, made to appear by the activity of the subject. Only one part of astral substance can be found outside, given to the subject in the environment. The other part must be added by subjective means, through personal activity. Conceptual and emotional forces allow us to extract the other aspect from what is given through active objectification. In the astral realm, therefore, we find subjective- objective substance. In devachan, we would find only a completely subjective element; there is no longer any objectivity at all that is simply given to the subject. In the astral realm, therefore, we find an element that must be created by human beings. Everything we do here is simply a symbolic representation of the higher worlds, or devachan. These worlds are real, as I have explained to you in these lectures. What lies within these higher worlds can be attained only by developing new possibilities for vision. Human beings must be active in order to reach these worlds. [ Second text variant: (Vetfelahn): ] If we want to acquire a true view of four-dimensional space, we must do very specific exercises. First, we must cultivate a clear and profound vision of water. Such vision cannot be achieved as a matter of course. We must immerse ourselves in the nature of water with great precision. We must creep inside water, so to speak. Second, we must create a vision of the nature of light. Although light is familiar to us, we know it only in the form in which we receive it from outside. By meditating, we acquire the inner counterpart of outer light. We learn where light comes from, so we ourselves become able to produce light. We can do this by truly allowing these concepts to work on our souls during meditation or sense-free thinking. Our entire surroundings are revealed to us as streaming light. Then we must "chemically combine" the mental image of water that we have cultivated with that of light. Water fully imbued with light is what the alchemists called mercury. In the language of alchemy, water plus light equals mercury. This alchemical mercury, however, is not simply ordinary quicksilver. We must first awaken our own ability to create mercury out of the concept of light. We then take possession of mercury, the light-imbued power of water, which is one element of the astral world. The second element arises when we cultivate a vivid mental image of air and then extract the power of air through a spiritual process, combining it with feeling inside us to kindle the concept of warmth, or fire. One element is extracted, while we ourselves produce the other. These two — air plus fire — yield what the alchemists called sulfur, or shining fire-air. The watery element is truly the substance referred to in the biblical statement 'The Spirit of God brooded upon the face of the waters." [Note 35] The third element is "Spirit-God," or earth combined with sound. It comes about when we extract the power of the earth and combine it with sound. The biblical "waters" are not ordinary water but what we know as astral substance, which consists of four types of forces: water, air, light, and fire. These four forces constitute the four dimensions of astral space. As you can see, astral substance is half subjective, — only one part of astral substance can be acquired from the environment. The other part is acquired through objectification from conceptual and emotional forces. In devachan, we would find only a completely subjective element, — there is no objectivity there. Everything we do here is simply a symbolic representation of the world of devachan. What lies within the higher worlds can be reached only by developing in ourselves new ways of perceiving. Human beings must be active in order to reach these worlds. In the course of his life, Hinton developed and popularized not one but many methods of representing four-dimensional space in three-dimensional perceived space. He was noted more for his popularization of the subject than for his mathematical originality. See the list of Hinton's works in the bibliography. Hinton employed several different color systems and distributions of color. He saw the two-dimensional representation of three-dimensional figures as preparation for the three-dimensional representation of four-dimensional figures (see A New Era of Thought [1900], part II, chapters I-IV and VII, and The Fourth Dimension [1904], chapters XI-XIII). Steiner seems to be referring to a very simplified version of one of Hinton's systems. It is not evident from the context of the lecture whether Steiner intended the colors to suggest specific attributes of the corresponding dimensions, but it seems unlikely. The various transcriptions of the lecture differ substantially at this point, presumably owing to different ways of adapting Steiner's use of color (especially white) on the dark board to white paper. These models were not found among Steiners belongings after his death. Presumably, they were returned to J. A. Schouten (see the letter to that effect in Note 1 of Lecture 3). A cube bounded by six surfaces can be created by moving a square with its four edges in three-dimensional space. The six surfaces consist of the initial and final cubes plus the four produced by the movement of the edges. This is immediately apparent in the parallel projection of this movement onto a plane — that is, into two-dimensional space (see Figure 88). Similarly, the movement of a cube with six surfaces in four-dimensional space creates a figure with eight cubes forming its boundaries-the initial and final cubes plus the six created through the movement of the sides-as is easily apparent from a parallel projection of the cube's movement into three-dimensional space (see Figure 90). Hinton seems to have coined the term tessaract for the four-dimensional figure analogous to the cube. The spelling tessarat also occurs in his works. Hinton's The Fourth Dimension [1904], chapter XII, contains almost the same reasoning and identical figures. Goethe, Faust , part I, scene 4, Faust's study, verses 2065ff: Mephistopheles: So now we simply spread the cloak That is to carry both of us through the air. But do not bring too large a bundle As you take this daring step. A little fire-air I shall create To lift us swiftly from the earth. Once lightened, we shall quickly rise, — Congratulations on your new career! Genesis 1:2. See Rudolf Steiner, Genesis :The Secrets of the Biblical Story of Creation (GA 122), especially the lecture of August 20, 1910. Ibid.

The Fourth Dimension

Fourth Lecture

https://rsarchive.org/Lectures/GA324a/English/AP2001/19050524p02.html

Berlin

24 May 1905

GA324a-4

Last time we attempted to visualize a four-dimensional spatial figure by reducing it to three dimensions. First we converted a three-dimensional figure into a two-dimensional one. We substituted colors for dimensions, constructing our image using three colors to represent the three dimensions of a cube. Then we unfolded the cube so that all of its surfaces lay in a plane, resulting in six squares whose differently colored edges represented the three dimensions in two-dimensional space. We then envisioned transferring each square of the cube's surface into the third dimension as moving the square through a colored fog and allowing it to reappear on the other side. We imagined all the surface squares moving through and being tinted by transition squares. Thus, we used colors to attempt to picture a three-dimensional cube in two dimensions. To represent squares in one dimension, we used two different colors for their edge pairs, — to represent a cube in two dimensions, we used three colors. Depicting a four-dimensional figure in three-dimensional space required a fourth color. Then we imagined a cube with three different surface colors as analogous to our square with two different edge colors. Each such cube moved through a cube of the fourth color, — that is, it disappeared into the fourth dimension or color. In accordance with Hinton's analogy, we made each boundary cube move through the new fourth color and reappear on the other side in its own original color. Now I would like to give you another analogy. We will begin once again by reducing three dimensions to two in preparation for reducing four dimensions to three. We must envision constructing our cube out of its six square sides, but instead of leaving all six squares attached when we spread them out, we will arrange them differently, as shown here (Figure 31). As you see, we have split the cube into two groups of three squares each. Both groups lie in the same plane. We must understand the location of each group when we reassemble the cube. To complete the cube, I must place one group above the other so that square 6 lies over square 5. Once square 5 is in position, I must fold squares 1 and 2 upward, while squares 3 and 4 must be folded downward (Figure 32). The corresponding pairs of line segments — that is, the ones of the same color (here, with the same number and weight of slashes as shown in Figure 31) — will then coincide. These lines that are spread out in two-dimensional space coincide when we make the transition to three-dimensional space. A square consists of four edges, a cube of six squares, and a four-dimensional figure of eight cubes. [Note 36] Hinton calls this four-dimensional figure a tessaract. Our task is not simply to put these eight cubes together into a single cube, but to do so by making each one pass through the fourth dimension. When I do to a tessaract what I just did to a cube, I must observe the same law. We must use the analogy of the relationship of a three-dimensional figure to its two-dimensional counterpart to discover the relationship of a four-dimensional figure to its three-dimensional counterpart. In the case of an unfolded cube, I had two groups of three squares. Similarly, unfolding a four-dimensional tessaract in three-dimensional space results in two groups of four cubes, which look like this (Figure 33). This eight-cube method is very ingenious. We must handle these four cubes in three-dimensional space exactly as we handled the squares in two-dimensional space. Look closely at what I have done here. Unfolding a cube so that it lies flat in two-dimensional space results in a grouping of six squares. Performing the corresponding operation on a tessaract results in a system of eight cubes (Figure 34). We have transferred our reflections on three-dimensional space to four-dimensional space. Folding up the squares and making their edges coincide in three-dimensional space corresponds to folding up the cubes and making their surfaces coincide in four-dimensional space. Laying the cube flat in two-dimensional space resulted in corresponding lines that coincided when we reconstructed the cube. Something similar happens to the surfaces of individual cubes in the tessaract. Laying out a tessaract in three-dimensional space results in corresponding surfaces that will later coincide. Thus, in a tessaract, the upper horizontal surface of cube 1 lies in the same plane as the front surface of cube 5 when we move into the fourth dimension. Similarly, the right surface of cube 1 coincides with the front surface of cube 4, the left square in cube 1 coincides with the front square in cube 3, and the lower square in cube 1 coincides with the front square in cube 6. Similar correspondences exist between the remaining surfaces. When the operation is completed, the cube that remains is cube 7, the interior cube that was surrounded by the other six. [Note 37] As you see, we are concerned once more with finding analogies between the third and fourth dimensions. As we saw in one of the illustrations from the last lecture (Figure 29), just as a fifth square surrounded by four others remains invisible to any being who can see only in two dimensions, the same applies to the seventh cube in this instance. It remains hidden from three-dimensional vision. In a tessaract, this seventh cube corresponds to an eighth cube, its counterpart in the fourth dimension. All of these analogies serve to prepare us for the fourth dimension, since nothing in our ordinary view of space forces us to add other dimensions to the three familiar ones. Following Hinton's example, we might also use colors here and think of cubes put together so that the corresponding colors coincide. Other than through such analogies, it is almost impossible to give any guidance in how to conceive of a four-dimensional figure. I would now like to talk about another way of representing four-dimensional bodies in three-dimensional space that may make it easier for you to understand what is actually at issue. Here we have an octahedron, which has eight triangular surfaces that meet in obtuse angles (Figure 35). Please imagine this figure and then follow this train of thought with me. You see, these edges are where two surfaces intersect. Two intersect at \(AB\), for example, and two at \(EB\). The only difference between an octahedron and a cube is the angle at which the surfaces intersect. Whenever surfaces intersect at right angles, as they do in a cube, the figure that is formed must be a cube. But when they intersect at an obtuse angle, as they do here, an octahedron is formed. By making the surfaces intersect at different angles, we construct different geometric figures. [Note 38] Next, envision a different way of making the surfaces of an octahedron intersect. Picture that one of these surfaces here, such as \(AEB\), is extended on all sides and that the lower surface, \(BCE\), and the surfaces \(ADF\) and \(EDC\), at the back of the figure, are similarly extended. These extended surfaces must also intersect. There is a two-fold symmetry at this line of reflection also called "half-turn symmetry." When these surfaces are extended, the other four original surfaces of the octahedron, \(ABF\), \(EBC\), \(EAD\), and \(DCF\), are eliminated. Out of eight original surfaces, four remain, and these four form a tetrahedron, which also can be called half an octahedron because it causes half of the surfaces of the octahedron to intersect. It is not half an octahedron in the sense of cutting the octahedron in half in the middle. When the other four surfaces of the octahedron are extended until they intersect, they also form a tetrahedron. The original octahedron is the intersection of these two tetrahedrons. In stereometry or geometric crystallography, what is called half a figure is the result of halving the number of surfaces rather than of dividing the original figure in two. This is very easy to visualize in the case of an octahedron. [Note 39] If you imagine a cubed halved in the same way, by making one surface intersect with another surface, you will always get a cube. Half of a cube is always another cube. There is an important conclusion to be drawn from this phenomenon, but first I would like to use another example. [Note 40] Here we have a rhombic dodecahedron (Figure 37). As you see, its surfaces meet at specific angles. Here we also have a system of four wires — I will call them axial wires — that run in different directions, that is, they are diagonals connecting specific opposite corners of the rhombic dodecahedron. These wires represent the system of axes in the rhombic dodecahedron, similar to the system of axes you can imagine in a cube. [Note 41] In a system of three perpendicular axes, a cube results when stoppage occurs in each of these axes, producing intersecting surfaces. Causing the axes to intersect at different angles results in different geometric solids. The axes of a rhombic dodecahedron, for example, intersect at angles that are not right angles. Halving a cube results in a cube. [Note 42] This is true only of a cube. When the number of surfaces in a rhombic dodecahedron is halved, a totally different geometric figure results. [Note 43] Now let's consider how an octahedron relates to a tetrahedron. Let me show you what I mean. The relationship is clearly apparent if we gradually transform a tetrahedron into an octahedron. For this purpose, let's take a tetrahedron and cut off its vertices, as shown here (Figure 38). We continue to cut off larger portions until the cut surfaces meet on the edges of the tetrahedron. The form that remains is an octahedron. By cutting off the vertices at the appropriate angle, we have transformed a spatial figure bounded by four planes into an eight-sided figure. What I have just done to a tetrahedron cannot be done to a cube. [Note 44] A cube is unique in that it is the counterpart of three-dimensional space. Imagine that all the space in the universe is structured by three axes that are perpendicular to each other. Inserting planes perpendicular to these three axes always produces a cube (Figure 39). Thus, whenever we use the term cube to mean a theoretical cube rather than a specific one, we are talking about the cube as the counterpart of three-dimensional space. Just as the tetrahedron can be shown to be the counterpart of an octahedron by extending half of the octahedrons sides until they intersect, an individual cube is also the counterpart of all of space. [Note 45] If you imagine all of space as positive, the cube is negative. The cube is the polar opposite of space in its entirety. The physical cube is the geometric figure that actually corresponds to all of space. Suppose that instead of a three-dimensional space bounded by two-dimensional planes, we have a space bounded by six spheres, which are three-dimensional figures. I start by defining a two-dimensional space with four intersecting circles, i.e., two-dimensional figures. Now imagine these circles growing bigger and bigger, — that is, the radius grows ever longer and the midpoint becomes increasingly distant. With time, the circles will be transformed into straight lines (Figure 40). Then, instead of four circles, we have four intersecting straight lines and a square. Now instead of circles, imagine six spheres, forming a mulberry- like shape (Figure 41). Picture the spheres growing ever larger, just as the circles did. Ultimately, these spheres will become the planes defining a cube, just as the circles became the lines defining a square. This cube is the result of six spheres that have become flat. The cube, therefore, is only a special instance of the intersection of six spheres, just as the square is simply a special instance of four intersecting circles. When you clearly realize that these six spheres flattening into planes correspond to the squares we used earlier to define a cube — that is, when you visualize a spherical figure being transformed into a flat one — the result is the simplest possible three-dimensional figure. A cube can be imagined as the result of flattening six intersecting spheres. We can say that a point on a circle must pass through the second dimension to get to another point on the circle. But if the circle has become so large that it forms a straight line, any point on the circle can get to any other point by moving only through the first dimension. Let's consider a square that is bounded by two-dimensional figures. As long as the four figures defining a square are circles, they are two-dimensional. Once they become straight lines, however, they are one-dimensional. The planes defining a cube develop out of three-dimensional figures (spheres) when one dimension is removed from each of the six spheres. These defining surfaces come about by being bent straight, through reducing their dimensions from three to two. They have sacrificed a dimension. They enter the second dimension by sacrificing the dimension of depth. Thus, we could say that each dimension of space comes about by sacrificing the next higher dimension. If we have a three-dimensional form with two-dimensional boundaries, and so reduce three-dimensional forms to two dimensions, you must conclude from this that, if we consider three-dimensional space, we have to think of each direction as the flattened version of an infinite circle. Then if we move in one direction, we would ultimately return to the same point from the opposite direction. Thus each ordinary dimension of space has come about through the loss of the next higher dimension. A triaxial system is inherent in our three-dimensional space. Each of its three perpendicular axes has sacrificed the next dimension to become straight. In this way, we achieve three-dimensional space by straightening each of its three axial directions. Reversing the process, each element of space also could be curved again, resulting in this train of thought: When you curve a one-dimensional figure, the resulting figure is two-dimensional. A curved two-dimensional figure becomes three-dimensional. And, finally, curving a three-dimensional figure produces a four-dimensional figure. Thus, four-dimensional space can be imagined as curved three-dimensional space. [Note 46] At this point, we can make the transition from the dead to the living. In this bending you can find spatial figures that reveal this transition from death to life. At the transition to three-dimensionality, we find a special instance of four-dimensional space, — it has become flat. To human consciousness, death is nothing more than bending three dimensions into four dimensions. With regard to the physical body taken by itself, the opposite is true: death is the flattening of four dimensions into three. See note 30 from the Fourth Lecture. The situation described here corresponds to Figure 76 in the case of a cube laid out in a plane: The location of square 6, directly "above" square 5, cannot be directly depicted in a plane. The upper edge of square 2, the lower edge of square 4, and the right and left edges of squares 3 and 1, respectively, must be seen as identical to the edges of square 6. Correspondingly, cubes 7 and 8 "coincide" and cannot be distinguished in three-dimensional space by any direct means. The upper and lower surfaces of cubes 5 and 6, respectively, the left and right surfaces of 3 and 4, respectively, and the front and back surfaces of 1 and 2, respectively, also constitute the surfaces of cube 8. Unfolding a cube makes it easier to note the coincidence between the edges of the sixth square and those of its neighboring squares (Figure 77). Figure 78 shows the corresponding situation in the case of a tessaract. The surfaces of the eighth cube must be seen as identical to the corresponding surfaces of neighboring cubes. In each of the five regular convex polyhedrons — cube, tetrahedron, octahedron, dodecahedron, and icosahedron — all the angles of surface intersection are equal. The angle of intersection is unique to each regular polyhedron. The surfaces of any regular polyhedron are polygons that are both similar and regular, — that is, all of their edges are of equal length, and all of their angles are equal. Thus, we simply need to investigate how many polygons can meet at one vertex in order to gain a complete overview of all possible regular polyhedrons. Let's begin with equilateral triangles (Figure 79). Two equilateral triangles cannot be joined together to form one vertex of a polyhedron. Three such triangles yield a tetrahedron, four form one vertex of an octahedron, and five form one vertex of an icosahedron. Six triangles lie flat in a plane and cannot form a vertex. Three regular rectangular solids (i.e., squares) form one vertex of a cube, while four lie flat in a plane. Three pentagons form one vertex of a dodecahedron, but four pentagons would overlap (Figure 80). Three hexagons lie flat in a plane, and three heptagons overlap. Thus, there cannot possibly be more than the five types of regular polyhedrons mentioned earlier. Rudolf Steiner refers here to a standard procedure in geometric crystallography. The seven classes of crystals are based on the symmetries of the seven possible crystallographic systems of axes. A symmetry group, which represents all of the symmetry elements of one class, is called a holohedry. The polyhedrons belonging to such symmetry groups are called holohedral shapes. They are simple polyhedrons that can be converted into each other through symmetrical operations that all belong to a single crystal system. Hemihedral forms are polyhedrons with half as many surfaces as the corresponding holohedral forms. Hemihedrons are derived from holohedrons through the extension of some of the surfaces of the holohedrons and the disappearances of others. The symmetry group of the hemihedrons is correspondingly reduced (subgroup of holohedries of index 2). In this sense, a tetrahedron is a hemihedral variation on an octahedron because it has half the number of surfaces. Crystallographers also have introduced tetardohedrons, polyhedrons with one-fourth the number of surfaces of the corresponding holohedral figures and a correspondingly reduced symmetry group (subgroup of holohedries of index 4). For more information, see Hochstetter/Bisching [1868], pp. 20ff; Schoute [1905], pp. 190ff; and Niggli [1924], pp. 70ff and 129ff. In a cube, any two intersecting surfaces meet in a right angle. No matter which surfaces we choose, extending them always will result in a figure with 90° angles of intersection. In a cube, however, reducing the number of surfaces no longer results in a closed polyhedron. "In this case, the axes of a cube are the three perpendicular directions that intersect in the cube's midpoint, — one pair of surfaces is perpendicular to each axis. These axes are also the axes of the three zones of a cube (Figure 81). A zone or zone association is a set of at least three surfaces that are parallel to the straight line of a zone axis. A rhombic dodecahedron is easy to construct with the help of a cube. First all six diagonal planes connecting opposite edges of the cube are constructed (Figure 82). Then the mirror images of the resulting six internal pyramids are constructed on the outside of the cube (Figure 83). The four "axes" mentioned in the lecture are the diagonals of the rhombic dodecahedron that coincide with the diagonals of the cube. These four axes are the four zone axes of the rhombic dodecahedron — that is, each of them is parallel to six surfaces of this figure. These four groups of six planes are called the zones of the rhombic dodecahedron. Because its vertices are not all similar, a rhombic dodecahedron is not a regular polyhedron. Three surfaces intersect in each of the vertices that emerge from the cube, while four surfaces intersect in each of the other vertices. The zone axes pass through the vertex points where three surfaces meet. Note that the "axes" described here represent a specific selection from the seven possible diagonals (straight line segments connecting opposite comer points). About the drawings: The rhombic dodecahedron, like the other geometric figures depicted here, is drawn in oblique parallel projection, which is best suited to freehand drawing on the board. This projection results in slight distortions of subsequent figures, which must be taken into account. In addition to the axes described in the previous note, a rhombic dodecahedron also has axes perpendicular to its surfaces. If a rhombic dodecahedron is held in place while its four zone axes are rotated 45° around the perpendicular axis of the underlying cube, the axes then intersect the midpoints of eight of the rhombic dodecahedrons surfaces. The figure formed by these surfaces is an octahedron consisting of the four pairs of surfaces that are perpendicular to the zone axes (rotated 45°) of the rhombic dodecahedron (Figure 85). Adding to these four axes the two horizontal axes (also rotated 45°) of the cube (see previous note) results in a system of six "axes"; each surface of the rhombic dodecahedron is perpendicular to one of them. Halving the number of surfaces of a cube does not produce any new surface angles. A rhombic dodecahedron can be "halved" in several different ways (Figures 86 and 87). When this operation produces a closed polyhedron, it is an oblique parallelepiped. This statement presupposes that the cuts in the tetrahedron or cube are made parallel to existing surfaces. Successively cutting off the vertices of a cube so that the cut surfaces are perpendicular to the cube's diagonals results first in a cube-octahedron and eventually in an octahedron. See also Steiner's lecture of March 31, 1905. No matter which three of the six planes defining a cube are selected, the result of extending them into space results in a "figure" that stretches to infinity. If the three surfaces we select are perpendicular to each other, the result is a geometric figure consisting of three perpendicular axes and the planes that connect them in pairs. Such a figure can be seen as representing three-dimensional Euclidean space and is also the geometric basis of every Euclidean or Cartesian coordinate system. Here and in the remainder of the lectures, Steiners presentation seems to have been substantially abridged, and, as a result, various perspectives overlap. To the series square-cube-tessaract, we can add another series of geometrical figures where the planes or faces of the figure are curved rather than straight or flat. We can call the figures of this second series curved squares, curved cubes, and curved tessaracts. In such a figure, the elements forming its edges or sides have the same number of dimensions as the total figure. The circle, the spherical surface (two-dimensional sphere), and the solid (three-dimensional) sphere are topologically equivalent to the rectilinear elements defining the boundaries of a square, a cube, and a tessaract respectively. The disc, ball, and four-dimensional ball are topologically equivalent to the square, the cube, and the tessaract respectively. On the other hand, suitable bending of a one-dimensional line segment results in a two-dimensional segment of a curve or — in a special instance — in a segment of a circle. Bending a disc produces a three-dimensional figure, a hollow hemisphere. Bending a solid sphere produces a four-dimensional figure (in a special instance, a section of a four-dimensional sphere). In this way, a circle can be constructed from two curved line segments whose ends are joined. Similarly, in three-dimensional space, a spherical surface can be constructed from two discs that are first curved and then joined at their edges. In four-dimensional space, a three-dimensional sphere results when two curved solid spheres are joined at their surfaces (two-dimensional spheres). This three-dimensional sphere relates to three-dimensional space as a ball (the surface of an ordinary sphere) relates to a plane. [Mathematician David Cooper comments: You are comparing filled-in figures rather than boundaries in both cases. A sphere (the boundary of a ball) is two-dimensional, so the two-dimensional sphere's volume means the (three-dimensional) ball.]

The Fourth Dimension

Fifth Lecture

https://rsarchive.org/Lectures/GA324a/English/AP2001/19050531p02.html

Berlin

31 May 1905

GA324a-5

Today I must conclude these lectures on the fourth dimension of space, though I actually would like to present a complicated system in greater detail, which would require demonstrating many more of Hinton's models. All I can do is refer you to his three thorough and insightful books. [Note 47] Of course, no one who is unwilling to use analogies such as those presented in the previous lectures will be able to acquire a mental image of four-dimensional space. A new way of developing thoughts is needed. Now I would like to develop a real image (parallel projection) of a tessaract. We saw that a square in two-dimensional space has four edges. Its counterpart in three dimensions is the cube, which has six square sides (Figure 42). The four-dimensional counterpart is the tessaract, which is bounded by eight cubes. Consequently, the projection of a tessaract into three-dimensional space consists of eight interpenetrating cubes. We saw how these eight cubes can coincide in three-dimensional space. I will now construct a different projection of a tessaract. [Note 48] Imagine holding a cube up to the light so that it casts a shadow on the board. We can then trace the shadow with chalk (Figure 43). As you see, the result is a hexagon. If you imagine the cube as transparent, you can see that in its projection onto a plane, the three front faces coincide with the three rear faces to form the hexagonal figure. To get a projection that we can apply to a tessaract, please imagine that the cube in front of you is positioned so that the front point \(A\) exactly covers the rear point \(C\). If you then eliminate the third dimension, the result is once again a hexagonal shadow. Let me draw this for you (Figure 44). When you imagine the cube in this position, you see only its three front faces, — the three other faces are concealed behind them. The faces of the cube appear foreshortened, and its angles no longer look like right angles. Seen from this perspective, the cube looks like a regular hexagon. Thus, we have created an image of a three-dimensional cube in two-dimensional space. Because this projection shortens the edges and alters the angles, we must imagine the six square faces of the cube as rhombuses. [Note 49] Now let's repeat the operation of projecting a three-dimensional cube onto a plane with a four-dimensional figure that we project into three-dimensional space. We will use parallel projection to depict a tessaract, a figure composed of eight cubes, in the third dimension. Performing this operation on a cube results in three visible and three invisible edges, — in reality, they jut into space and do not lie flat in the plane of projection. Now imagine a cube distorted into a rhombic parallelepiped. [Note 50] If you take eight such figures, you can assemble the structures defining a tessaract so that they interpenetrate and doubly coincide with the rhombic cubes in a rhombic dodecahedron (Figure 45). This figure has one more axis than a three-dimensional cube. Naturally, a four-dimensional figure has four axes. Even when its components interpenetrate, four axes remain. Thus, this projection contains eight interpenetrating cubes, shown as rhombic cubes. A rhombic dodecahedron is a symmetrical image or shadow of a tessaract projected into three-dimensional space. [Note 51] Although we have arrived at these relationships by analogy, the analogy is totally valid. Just as a cube can be projected onto a plane, — a tessaract also can be depicted by projecting it into three-dimensional space. The resulting projection is to the tessaract as the cube's shadow is to the cube. I believe this operation is readily understandable. I would like to link what we have just done to the wonderful image supplied by Plato and Schopenhauer in the metaphor of the cave. [Note 52] Plato asks us to imagine people chained in a cave so that they cannot turn their heads and can see only the rear wall. Behind them, other people carry various objects past the mouth of the cave. These people and objects are three dimensional, but the prisoners see only shadows cast on the wall. Everything in this room, for example, would appear only as two-dimensional shadow images on the opposite wall. Then Plato tells us that our situation in the world is similar. We are the people chained in the cave. Although we ourselves are four-dimensional, as is everything else, all that we see appears only in the form of images in three-dimensional space. [Note 53] According to Plato, we are dependent on seeing only the three-dimensional shadow images of things instead of their realities. I see my own hand only as a shadow image, — in reality, it is four-dimensional. We see only images of four-dimensional reality, images like that of the tessaract that I showed you. In ancient Greece, Plato attempted to explain that the bodies we know are actually four-dimensional and that we see only their shadow images in three-dimensional space. This statement is not completely arbitrary, as I will explain shortly. Initially, of course, we can say that it is mere speculation. How can we possibly imagine that there is any reality to these figures that appear on the wall? But now imagine yourselves sitting here in a row, unable to move. Suddenly, the shadows begin moving. You cannot possibly conclude that the images on the wall could move without leaving the second dimension. When an image moves on the wall, something must have caused movement of the actual object, which is not on the wall. Objects in three-dimensional space can move past each other, something their two-dimensional shadow images cannot do if you imagine them as impenetrable — that is, as consisting of substance. If we imagine these images to be substantial, they cannot move past each other without leaving the second dimension. As long as the images on the wall remain motionless, I have no reason to conclude that anything is happening away from the wall, outside the realm of two-dimensional shadow images. As soon as they begin to move, however, I am forced to investigate the source of the movement and to conclude that the change can originate only in a movement outside the wall, in a third dimension. Thus, the change in the images has informed us that there is a third dimension in addition to the second. Although a mere image possesses a certain reality and very specific attributes, it is essentially different from the real object. A mirror image, too, is undeniably a mere image. You see yourself in the mirror, but you are also present out here. Without the presence of a third element — that is, a being that moves — you cannot really know which one is you. The mirror image makes the same movements as the original, — it has no ability to move itself but is dependent on the real object, the being. In this way, we can distinguish between an image and a being by saying that only a being can produce change or movement out of itself. I realize that the shadow images on the wall cannot make themselves move, — therefore, they are not beings. I must transcend the images in order to discover the beings. Now apply this train of thought to the world in general. The world is three-dimensional, but if you consider it by itself, grasping it in thought, you will discover that it is essentially immobile. Even if you imagine it frozen at a certain point in time, however, the world is still three-dimensional. In reality, the world is not the same at any two points in time. It changes. Now imagine the absence of these different moments — what is, remains. If there were no time, the world would never change, but even without time or changes it would still be three-dimensional. Similarly, the images on the wall remain two dimensional, but the fact that they change suggests the existence of a third dimension. That the world is constantly changing but would remain three-dimensional even without change suggests that we need to look for the change in a fourth dimension. The reason for change, the cause of change, the activity of change, must be sought outside the third dimension. At this point you grasp the existence of the fourth dimension and the justification for Plato's metaphor. We can understand the entire three-dimensional world as the shadow projection of a four-dimensional world. The only question is how to grasp the reality of this fourth dimension. Of course, we must understand that it is impossible for the fourth dimension to enter the third directly. It cannot. The fourth dimension cannot simply fall into the third dimension. Now I would like to show you how to acquire a concept of transcending the third dimension. (In one of my earlier lectures here, I attempted to awaken a similar idea in you.) [Note 54] Imagine that we have a circle. If you picture this circle getting bigger and bigger, so that any specific segment becomes flatter and fatter, the diameter eventually becomes so large that the circle is transformed into a straight line. A line has only one dimension, but a circle has two. How do we get back into two dimensions? By bending the straight line to form a circle again. When you imagine curving a circular surface, it first becomes a bowl and eventually, if you continue to curve it, a sphere. A curved line acquires a second dimension and a curved plane a third. And if you could still make a cube curve, it would have to curve into the fourth dimension, and the result would be a spherical tessaract. [Note 55] A spherical surface can be considered a curved two-dimensional figure. In nature, the sphere appears in the form of the cell, the smallest living being. The boundaries of a cell are spherical. Here we have the difference between the living and the lifeless. Minerals in their crystalline form are always bounded by planes, by flat surfaces, while life is built up out of cells and bounded by spherical surfaces. Just as crystals are built up out of flattened spheres, or planes, life is built up out of cells, or abutting spheres. The difference between the living and the lifeless lies in the character of their boundaries. An octahedron is bounded by eight triangles. When we imagine its eight sides as spheres, the result is an eight-celled living thing. When you "curve" a cube, which is a three-dimensional figure, the result is a four-dimensional figure, the spherical tessaract. But if you curve all of space, the resulting figure relates to three-dimensional space as a sphere relates to a plane. [Note 56] As a three-dimensional object, a cube, like any crystal, is bounded by planes. The essence of a crystal is that it is constructed of flat boundary planes. The essence of life is that is constructed of curved surfaces, namely, cells, while a figure on a still higher level of existence would be bounded by four-dimensional structures. A three-dimensional figure is bounded by two-dimensional figures. A four-dimensional being — that is, a living thing — is bounded by three-dimensional beings, namely, spheres and cells. A five-dimensional being is bounded by four-dimensional beings, namely, spherical tessaracts. Thus, we see the need to move from three-dimensional beings to four-dimensional and then five-dimensional beings. What needs to happen with a four-dimensional being? [Note 57] A change must take place within the third dimension. In other words, when you hang pictures, which are two-dimensional, on the wall, they generally remain immobile. When you see two-dimensional images moving, you must conclude that the cause of the movement can lie only outside the surface of the wall — that is, that the third dimension of space prompts the change. When you find changes taking place within the third dimension, you must conclude that a fourth dimension has an effect on beings who experience changes within their three dimensions of space. We have not truly recognized a plant when we know it only in its three dimensions. Plants are constantly changing. Change is an essential aspect of plants, a token of a higher form of existence. A cube remains the same, — its form changes only when you break it. A plant changes shape by itself, which means that the change must be caused by some factor that exists outside the third dimension and is expressed in the fourth dimension. What is this factor? You see, if you draw this cube at different points in time, you will find that it always remains the same. But when you draw a plant and compare the original to your copy three weeks later, the original will have changed. Our analogy, therefore, is fully valid. Every living thing points to a higher element in which its true being dwells, and time is the expression of this higher element. Time is the symptomatic expression or manifestation of life (or the fourth dimension) in the three dimensions of physical space. In other words, all beings for whom time is intrinsically meaningful are images of four-dimensional beings. After three years or six years, this cube will still be the same. A lily seedling changes, however, because time has real meaning for it. What we see in the lily is merely the three-dimensional image of the four-dimensional lily being. Time is an image or projection of the fourth dimension, of organic life, into the three spatial dimensions of the physical world. To clarify how each successive dimension relates to the preceding one, please follow this line of thought: A cube has three dimensions. To imagine the third, you tell yourself that it is perpendicular to the second and that the second is perpendicular to the first. It is characteristic of the three dimensions that they are perpendicular to each other. We also can conceive of the third dimension as arising out of the next dimension, the fourth. Envision coloring the faces of a cube and manipulating the colors in a specific way, as Hinton did. The changes you induce correspond exactly to the change undergone by a three-dimensional being when it develops over time, thus passing into the fourth dimension. When you cut through a four-dimensional being at any point — that is, when you take away its fourth dimension — you destroy the being. Doing this to a plant is just like taking an impression of the plant and casting it in plaster. You hold it fast by destroying its fourth dimension, the time factor, and the result is a three-dimensional figure. When time, the fourth dimension, is critically important to any three-dimensional being, that being must be alive. And now we come to the fifth dimension. You might say that this dimension must have another boundary that is perpendicular to the fourth dimension. We saw that the relationship between the fourth dimension and the third is similar to the relationship between the third and second dimensions. It is more difficult to imagine the fifth dimension, but once again we can use an analogy to give us some idea about it. How does any dimension come about? When you draw a line, no further dimensions emerge as long as the line simply continues in the same direction. Another dimension is added only when you imagine two opposing directions or forces that meet and neutralize at a point. The new dimension arises only as an expression of the neutralization of forces. We must be able to see the new dimension as the addition of a line in which two streams of forces are neutralized. We can imagine the dimension as coming either from the right or from the left, as positive in the first instance and negative in the second. Thus I grasp each independent dimension as a polar stream of forces with both a positive and a negative component. The neutralization of the polar component forces is the new dimension. Taking this as our starting point, let's develop a mental image of the fifth dimension. We must first imagine positive and negative aspects of the fourth dimension, which we know is the expression of time. Let's picture a collision between two beings for whom time is meaningful. The result will have to be similar to the neutralization of opposing forces that we talked about earlier. When two four-dimensional beings connect, the result is their fifth dimension. The fifth dimension is the result or consequence of an exchange or neutralization of polar forces, in that two living things who influence each other produce something that they do not have in common either in the three ordinary dimensions of space or in the fourth dimension, in time. This new element has its boundaries outside these dimensions. It is what we call empathy or sensory activity, the capacity that informs one being about another. It is the recognition of the inner (soul-spiritual) aspect of another being. Without the addition of the higher, fifth dimension — that is, without entering the realm of sensory activity, — no being would ever be able to know about any aspects of another being that lie outside time and space. Of course, in this sense we understand sensory activity simply as the fifth dimension's projection or expression in the physical world. It would be too difficult to build up the sixth dimension in the same way, so for now I will simply tell you what it is. If we continued along the same line of thinking, we would find that the expression of the sixth dimension in the three-dimensional world is self-awareness. As three-dimensional beings, we humans share our image character with other three-dimensional beings. Plants possess an additional dimension, the fourth. For this reason, you will never discover the ultimate being of the plant in the three dimensions of space. You must ascend to a fourth dimension, to the astral sphere. If you want to understand a being that possesses sensory ability, you must ascend to the fifth dimension, lower devachan or the Rupa sphere, and to understand a being with self-awareness — namely, the human being — you must ascend to the sixth dimension, upper devachan or the Arupa sphere. The human beings we encounter at present are really six-dimensional beings. What we have called sensory ability (or empathy) and self-awareness are projections of the fifth and sixth dimensions, respectively, into ordinary three-dimensional space. Albeit unconsciously for the most part, human beings extend all the way into these spiritual spheres, — only there can their essential nature be recognized. As six-dimensional beings, we understand the higher worlds only when we attempt to relinquish the characteristic attributes of lower dimensions. I cannot do more than suggest why we believe the world to be merely three-dimensional. Our view is based on seeing the world as a reflection of higher factors. The most you can see in a mirror is a mirror image of yourself. In fact, the three dimensions of our physical space are reflections, material images of three higher, causal, creative dimensions. Thus, our material world has a polar spiritual counterpart in the group of the three next higher dimensions, that is, in the fourth, fifth, and sixth. Similarly, the fourth through sixth dimensions have their polar counterparts in still more distant spiritual worlds, in dimensions that remain a matter of conjecture for us. Consider water and water that has been allowed to freeze. In both cases, the substance is the same, but water and ice are very different in form. You can imagine a similar process taking place with regard to the three higher human dimensions. When you imagine human beings as purely spiritual beings, you must envision them as possessing only the three higher dimensions of self-awareness, feeling, and time and that these dimensions are reflected in the three ordinary dimensions in the physical world. When yogis (students of esotericism) want to ascend to knowledge of the higher worlds, they must gradually replace reflections with realities. For example, when they consider a plant, they must learn to replace the lower dimensions with the higher ones. Learning to disregard one of a plant's spatial dimensions and substitute the corresponding higher dimension — namely, time — enables them to understand a two-dimensional being that is moving. What must students of esotericism do to make this being correspond to reality rather than remaining a mere image? If they were simply to disregard the third dimension and add the fourth, the result would be something imaginary. The following thought will help us move toward an answer: By filming a living being, even though we subtract the third dimension from events that were originally three-dimensional, the succession of images adds the dimension of time. When we then add sensory ability to this animated image, we perform an operation similar to the one I described as curving a three-dimensional figure into the fourth dimension. The result of this operation is a four-dimensional figure whose dimensions include two of our spatial dimensions and two higher ones, namely, time and sensory ability. Such beings do indeed exist, and now that I have come to the real conclusion of our study of the dimensions, I would like to name them for you. Imagine two spatial dimensions — that is, a plane — and suppose that this plane is endowed with movement. Picture it curving to become a sensate being pushing a two-dimensional surface in front of it. Such a being is very dissimilar to and acts very differently from a three-dimensional being in our space. The surface being that we have constructed is completely open in one direction. It looks two-dimensional, — it comes toward you, and you cannot get around it. This being is a radiant being, — it is nothing other than openness in a particular direction. Through such a being, initiates then become familiar with other beings whom they describe as divine messengers approaching them in flames of fire. The description of Moses receiving the Ten Commandments on Mount Sinai shows simply that he was approached by such a being and could perceive its dimensions. [Note 58] This being, which resembled a human being minus the third dimension, was active in sensation and time. The abstract images in religious documents are more than mere outer symbols. They are mighty realities that we can learn about by taking possession of what we have been attempting to understand through analogies. The more diligently and energetically you ponder such analogies, the more eagerly you submerse yourself in them, the more they work on your spirit to release higher capacities. This applies, for example, to the explanation of the analogy between the relationship of a cube to a hexagon and that of a tessaract to a rhombic dodecahedron. The latter is the projection of a tessaract into the three-dimensional physical world. By visualizing these figures as if they possessed independent life — that is, by allowing a cube to grow out of its projection, the hexagon, and the tessaract to develop out of its projection, the rhombic dodecahedron — your lower mental body learns to grasp the beings I just described. When you not only have followed my suggestions but also have made this operation come alive as esoteric students do, in full waking consciousness, you will notice that four-dimensional figures begin to appear in your dreams. At that point, you no longer have far to go to be able to bring them into your waking consciousness. You then will be able to see the fourth dimension in every four-dimensional being. The astral sphere is the fourth dimension. Devachan up to Rupa is the fifth dimension. Devachan up to Arupa is the sixth dimension. [Note 59] These three worlds — physical, astral, and heavenly (devachan) — encompass six dimensions. The still higher worlds are the polar opposites of these dimensions. PresumabIy, this reference is to Hinton's books Scientific Romances [1886], A New Era of Thought [ 1900], and The Fourth Dimension [ 1904]. Strictly speaking, the depiction of a tessaract in the previous lecture (May 31, 1905) is not a projection but simply an unfolded view. In the present lecture, Steiner proceeds to construct an orthogonal parallel projection of a tessaract in three-dimensional space, taking one of its diagonals as the direction of projection. Considering the framework formed by the edges of a cube, an oblique parallel projection of the cube onto a plane generally consists of two parallel, non-coinciding cubes and the line segments connecting their corresponding corners (Figure 88: oblique parallel projections of a cube). If the diagonal AC is selected as the direction of projection, vertices A and C coincide, producing an oblique hexagon and its diagonals. The images of the six individual faces of the cube can be reconstructed from this hexagon by tracing all the possible parallelograms defined by the existing structure of lines. Each of these parallelograms overlaps with two others, and the hexagon's surface is covered twice by the faces of the cube. When the direction of projection is perpendicular to the plane of projection, the resulting image of a cube is a regular hexagon (Figure 89: orthogonal parallel projections of a cube). Note that the three diagonals of the hexagon also represent the three (zone) axes of the cube. The zone associations belonging to each of these axes — that is, the four faces of the cube that parallel it — appear as four parallelograms or rhombuses with one edge coinciding with the corresponding axis. ’“Earlier in this lecture, Steiner called a distorted or oblique square a "rhombus," which is a parallelogram with four equal sides. The corresponding solid figure, Steiner's "rhombic parallelepiped," is an oblique cube — i.e., a parallelepiped whose edges are all the same length. If we see the tessaract as the framework formed by its edges, the result of projecting the tessaract into three-dimensional space generally consists of two parallel, displaced oblique cubes and the line segments connecting their corresponding vertices (Figure 90: oblique parallel projections of a tessaract). When the direction of projection passes through the diagonal A'C, the endpoints A' and C coincide, resulting in a rhombic dodecahedron with four diagonals. In the first figure, it is easy to trace the images of the eight cubes defining the boundaries of a tessaract: they are all the possible parallelepipeds formed by the edges of the existing framework. These parallelepipeds include the original cube, the displaced cube, and the six parallelepipeds that share one face each with the original and displaced cubes. This situation does not change fundamentally when we make the transition to the rhombic dodecahedron, except that in this instance all of the "rhombic cubes" (parallelepipeds) interpenetrate in such a way that they fill the internal space of the rhombic dodecahedron exactly twice, with each parallelepiped including portions of three others. The four diagonals of the rhombic dodecahedron that appear in the projection of the tessaract are the zone axes of the rhombic dodecahedron's four associations of six faces each. Each such face association consists of all six surfaces that are parallel to a single zone axis. (Note that in a rhombic dodecahedron the axes pass through vertices rather than through the centers of faces, as in a cube.) These four axes, however, are also the projections of the tessaract's four perpendicular axes in four-dimensional space. A cube's three axes pass through the centers of its square sides. Analogously, a tessaract's axes pass through the middle of the cubes that form its sides. In parallel projection, the middle of a cube is transformed into the middle of the corresponding parallelepiped. As we can ascertain by studying all eight parallelepipeds in a rhombic dodecahedron, the four axes pass exactly through the middles of these parallelepipeds. A cube's four perpendicular axes are simultaneously the zone axes of its three face associations of four faces each. Similarly, a tessaract's four axes are also the zone axes of four cell associations of six cells each (cell equals the cube forming a side of the tessaract). In the rhombic dodecahedron, the cells belonging to each axis are easy to find: they are the six parallelepipeds with one edge coinciding with that axis. Plato, The Republic , book 7, 514a-518c. It has not yet been possible to ascertain where Schopenhauer used this metaphor. Zöllner drew attention to this interpretation of Plato’s cave metaphor in his essay Über Wirkungen in die Ferne [ 1878a], pp. 260ff. See the lecture of March 24, 1905. What Steiner seems to mean here by spherical tessaract is not a four-dimensional cube in the narrower sense but rather its topological equivalent, the three-dimensional sphere in four-dimensional space, which is produced by curving and attaching two solid three-dimensional spheres. See Note 11 , Lecture 5. See Note 9 above and Note 11, Lecture 5. The remaining text of this lecture incorporates fragments of transcripts quoted in Haase's essay [1916], which helped clarify the meaning. Exodus 19, — also Exodus 33 and 34. ln theosophical literature, the three upper regions of the land of spirit were called Arupa regions, in contrast to the four lower, or Rupa, regions. See the editor's note to Rudolf Steiner's Die Grundelemente der Esoterik ,'The Basic Elements of Esotericism" (GA 93a), p. 281 ff. On the seven regions of the land of spirit, see Rudolf Steiner, Theosophy (GA 9), 'The Country of Spirit Beings." On the problem of dimensionality in connection with the planes or regions of the spirit world, see also Rudolf Steiner's lecture of May 17, 1905, — his response to questions asked by A. Strakosch on March 11, 1920, — the questions and answers of April 7, 1921 (GA 76), and April 12, 1922 (GA 82); and the lectures of August 19, 29, 22, and 26, 1923 (GA 227).

The Fourth Dimension

Sixth Lecture

https://rsarchive.org/Lectures/GA324a/English/AP2001/19050607p02.html

Berlin

7 Jun 1905

GA324a-6

Our ordinary space has three dimensions — length, width, and height. A line has only one dimension, length. This blackboard is a plane, that is, it has two dimensions, length and width. A solid object encompasses three dimensions. How does a three-dimensional figure arise? Imagine a figure with no dimensionality at all, namely, the point. It has zero dimensions. When a point moves in a constant direction, a straight line, or one-dimensional figure, results. Now visualize the line moving. The result is a plane, which has length and width. And, finally, a moving plane describes a three-dimensional figure. We cannot continue this process, however. We cannot use movement to create a four-dimensional figure or a fourth dimension from a three-dimensional object. How can we use images to develop a concept of the fourth dimension? Some mathematicians and scientists — Zöllner, for example — have felt tempted to bring the spiritual world into harmony with our sense-perceptible world by assuming that the spiritual world exists in four-dimensional space. [Note 60] Imagine a circle, a completely closed figure lying in a plane. Suppose that someone asks us to move a coin into the circle from outside. We must either cross the circumference of the circle (Figure 46) or — if we are not allowed to touch the circumference — pick up the coin, lift it into space, and place it inside the circle, which requires leaving the second dimension and entering the third. To move a coin magically into a cube or a sphere, we must leave the third dimension and pass through the fourth. [Note 61] In this lifetime, I first began to grasp the nature of space when I began to study modern synthetic, projective geometry and understood the significance of transforming a circle into a line (Figure 47). The world is revealed in the soul's subtlest thoughts. [Note 62] Now let's imagine a circle. We can trace its circumference all the way around and return to our original starting point. Let's picture the circle growing bigger and bigger while a tangent line remains constant. Since the circle is growing increasingly flat, it will eventually become a straight line. When I trace these successively larger circles, I always go down on one side and come back up on the other before returning to my starting point. Ultimately, I move in one direction — let's say to the right — until I reach infinity. Thus, I must return from infinity on the other side, from the left, since the sequence of points in a straight line behaves just like a circle. So we see that space has no end, just as a straight line has no end, since its points are arranged just like those in a closed circle. Correspondingly, we must imagine the infinite expanse of space as self-contained, like the surface of a sphere. We have now depicted infinite space in terms of circles or spheres. This concept will help us conceive the reality of space. [Note 63] Instead of imagining ourselves proceeding mindlessly toward infinity and returning unchanged from the other direction, let's imagine that we carry a light. As seen from a constant point on the line, this light becomes ever weaker as we carry it away and ever stronger as we return with it from infinity. If we then picture the changes in the intensity of the light as positive and negative, we have positive on one side, where the light grows stronger, and negative on the other. We find these two poles, which are simply the opposite effects of space, in all effects in the natural world. This thought leads to the concept of space as possessing force, — the forces at work in space are simply manifestations of force itself. We will no longer doubt the possibility of discovering a force that works from within in three-dimensional space, and we will realize that all spatial phenomena are based on actual relationships in space. One such relationship is the intertwining of two dimensions. To make two closed rings interlock, you must open one of them in order to insert the other. I will now convince myself of the inherent manifoldness of space by twisting this figure, a rectangular strip of paper, twice — that is, I secure one end while rotating the other end 360°. I then hold the two ends together, securing the strip with pins. Cutting this twisted ring in half lengthwise results in two interlocking rings that cannot be separated without breaking one of them. Simply twisting the strip made it possible to perform an operation in three dimensions that can otherwise be carried out only by entering the fourth dimension. [Note 64] This is not just a game, — it is cosmic reality. Here we have the Sun, the Earth's orbit around the Sun, and the Moon's orbit around the Earth (Figure 48). Because the Earth moves around the Sun, the orbits of the Moon and Earth are just as intertwined (as our two rings of paper). In the course of Earth's evolution, the Moon broke away from the Earth. This separation occurred in the same way as the interlocking of our two rings of paper. When we look at space in this way, it becomes inherently alive. Next, consider a square. Imagine it moving through space until a cube has been described. The square's movement must be perpendicular to its original location. A cube consists of six squares that form its surface. To give you an overview of a cube, I can lay the six squares down beside each other in a plane (Figure 49). I can reconstruct the cube by folding these squares upward, moving them into the third dimension. The sixth cube lies on top. To form this cross-shaped figure, I broke the cube down into two dimensions. Unfolding a three-dimensional figure transforms it into a two-dimensional figure. As you see, the boundaries of a cube are squares. A three-dimensional cube is always bounded by two-dimensional squares. Let's look at a single square. It is two-dimensional and bounded by four one-dimensional line segments. I can lay these four line segments out in single dimension (Figure 50). The edges defining one of the square's dimensions are colored red solid lines, and the other dimension is colored blue dotted lines. Instead of saying length and width, I can talk about the red and blue dimensions. I can reconstruct a cube from six squares. That is, I go beyond the number four (the number of line segments forming the edges of a square) to the number six (the number of planes forming the sides of a cube). Taking this process one step further, I move from six to eight (the number of cubes forming the "sides" of a four-dimensional figure). I arrange the eight cubes to form the three-dimensional counterpart of the earlier figure, which consisted of six squares, in the two-dimensional plane (Figure 51). Now, imagine that I can turn this figure inside out, fold it up, and put it together so that the eighth cube closes off the entire figure. I use eight cubes to create a four-dimensional figure in four-dimensional space. Hinton calls this figure a tessaract. Its boundaries consist of eight cubes, just as the boundaries of an ordinary cube consist of six squares. Thus, a four-dimensional tessaract is bounded by eight three-dimensional cubes. Envision a being that can see only in two dimensions. When this being looks at the unfolded squares of a cube, it sees only squares 1, 2, 3, 4, and 6, but never square 5, the shaded square in the middle (Figure 52). Something similar is true when you yourself look at an unfolded four-dimensional object. Since you can see only three-dimensional objects, you can never see the hidden cube in the middle. Picture drawing a cube on the board like this, so that the outline of a regular hexagon appears. The rest of it is hidden behind. What you see is a shadow image of sorts, a projection of the three-dimensional cube into two-dimensional space (Figure 53). The cube's two-dimensional shadow image consists of rhombuses or equilateral parallelepipeds. If you imagine the cube made of wire, you can also see the rhombuses in the back. This projection shows six overlapping rhombuses. In this way, you can project the entire cube into two-dimensional space. Now imagine our tessaract in four-dimensional space. Projecting this figure into three-dimensional space must yield four oblique cubes (parallelepipeds) that do not interpenetrate. One of these rhombic oblique cubes would be drawn like this (Figure 54). Eight such oblique rhombic cubes, however, must interpenetrate in order to yield a complete three-dimensional image of a four-dimensional tessaract in three-dimensional space. We can depict the complete three-dimensional shadow of a tessaract with the help of eight suitably interpenetrating rhombic cubes. The resulting spatial figure is a rhombic dodecahedron with four diagonals (Figure 55). In our rhombic projection of a cube, three adjacent rhombuses coincide with the other three so that only three of the six surface cubes are visible. Similarly, in the rhombic dodecahedron projection of a tessaract, only four non-interpenetrating rhombic cubes are visible as the projections of the tessaract's eight boundary cubes, since four adjacent rhombic cubes completely cover the remaining four. [Note 65] Thus we can construct a tessaract's three-dimensional shadow, though not the four-dimensional object itself. Similarly, we our74 selves are shadows of four-dimensional beings. When we move from the physical to the astral plane, we must cultivate our capacity to form mental images. Picture a two-dimensional being repeatedly attempting to imagine vividly such a three-dimensional shadow image. Mentally constructing the relationship of the third dimension to the fourth fosters inner forces that will permit you to see into real, not mathematical, four-dimensional space. We will always remain powerless in the higher world if we do not develop faculties that permit us to see in the higher world here, in the world of ordinary consciousness. The eyes we use for seeing in the physical, sense-perceptible world develop when we are still in the womb. Similarly, we must develop supersensory organs when we are still in the womb of the Earth so that we can be born into the higher world as seers. The development of physical eyes in utero is an example that illuminates this process. A cube must be constructed by using the dimensions of length, width, and height. A tessaract must be constructed by using the same dimensions with the addition of a fourth. Because it grows, a plant breaks out of three-dimensional space. Any being that lives in time frees itself from the three ordinary dimensions. Time is the fourth dimension. It remains invisible within the three dimensions of ordinary space and can be perceived only with clairvoyant powers. A moving point creates a line, a moving line creates a plane, and a moving plane creates a three-dimensional figure. When three-dimensional space moves, the result is growth and development. There we have four-dimensional space, or time, projected into three-dimensional space as movement, growth, and development. You will find that our geometric thoughts on building up the three ordinary dimensions continue into real life. Time is perpendicular to the three dimensions and constitutes the fourth dimension. It grows. When time is enlivened within a being, sensory ability arises. When time is multiplied internally within a being so that self-movement takes place, the result is a sensate animal being. In reality, such a being has five dimensions, while a human being has six. We have four dimensions in the ether realm (astral plane), five dimensions in the astral realm (lower devachan), and six dimensions in upper devachan. Thus, the various manifestations of the spirit emerge in you. When devachan casts its shadow into astral space, the result is our astral body. When the astral realm casts its shadow into etheric space, the result is our ether body, and so on. [Note 66] The natural world dies when time moves in one direction and is re-enlivened when it moves in the other. The two points where these streams meet are birth and death. The future is constantly coming to meet us. If life moved in one direction only, nothing new would ever arise. Human beings also possess genius — that is, their future, their intuitions, streaming toward them. The past that has been worked on is the stream coming from the other side, — it determines the being as it has evolved up to the present time. See Steiner's lectures of March 24 and 31, 1905, and the relevant notes. See Note 6, (March 24, 1905). See Rudolf Steiner's autobiography, Autobiography — Chapters in the Course of my Life (GA 28), chapter III, p. 63, and his lecture of April 3, 1922, "Die Stellung der Anthroposophie in den Wissenschaften" in Damit der Mensch ganz Mensch werde: Die Bedeutung der Anthroposophie im Geistesleben der Gegenwart (GA 82). In this passage, Rudolf Steiner refers to the distant (or absolute) plane of Euclidean space, resulting in a projective space. A projective space is self-contained and has no limits or boundaries, meaning that we can travel to "infinity" in any direction and return from the other side. See also the explanation in his lecture of March 24, 1905 and the accompanying notes. See the explanations at the beginning of the preceding lecture (June 7, 1905) and the accompanying notes. The upper and lower devachen are heavenly realms through which the soul passes through after death. See Rudolf Steiner's Theosophy .

The Fourth Dimension

Four-Dimensional Space

https://rsarchive.org/Lectures/GA324a/English/AP2001/19051107p02.html

Berlin

7 Nov 1905

GA324a-7

Today's subject will present us with a variety of difficulties, and this lecture you requested must be seen as one in a series. A profound understanding of the subject, even on a merely formal level, requires previous mathematical knowledge. Grasping the reality of the subject, however, requires deeper insight into esotericism. We will be able to address this aspect only very superficially today, providing stimulus for further thought. It is very difficult to talk about higher dimensions at all, because in order to picture any dimensions beyond the ordinary three, we must enter abstract realms, where we fall into an abyss if our concepts are not very precisely and strictly formulated. This has been the fate of many people we know, both friends and foes. The concept of higher-dimensional space is not as foreign to mathematics as we generally believe. [Note 67] Mathematicians are already performing calculations involving higher-dimensional operations. Of course, mathematicians can speak about higher-dimensional space only to a very limited extent, — essentially, they can discuss only the possibility that it exists. Determining whether or not such space is real must be left to those who actually can see into it. Here we are dealing with pure concepts that, if precisely formulated, will truly clarify our concept of space. What is space? We usually say that space is all around us, that we walk around in space, and so on. To gain a clearer idea of space, we must accept a higher level of abstraction. We call the space we move around in three-dimensional. It extends upward and downward, to the right and to the left, and forward and backward. It has length, width, and height. When we look at objects, we see them as occupying three-dimensional space, that is, as possessing a certain length, width, and height. We must deal with the details of the concept of space, however, if we wish to achieve greater clarity. Let's look at the simplest solid shape, the cube, as the clearest example of length, width, and height. The length and width of a cube's lower surface are equal. When we raise this lower surface until its height above its original location is the same as its length or width, we get a cube, that is, a three-dimensional figure. When we examine the boundaries of a cube, we find that they consist of plane surfaces, which are bounded in turn by sides of equal length. A cube has six such plane surfaces. What is a plane surface? At this point, those incapable of very keen abstractions will begin to go astray. For example, it is impossible to cut off one of the boundaries of a wax cube in the form of a very thin layer of wax, because we would always get a layer with a certain thickness — that is, a solid object. We can never arrive at the boundary of the cube in this way. Its real boundary has only length and width, but no height — that is, no thickness. Thus, we arrive at a formula: a plane surface is one boundary of a three-dimensional figure and has one less dimension. Then what is the boundary of a plane surface such as a square? Again, the definition requires a high degree of abstraction. The boundary of a plane figure is a line, which has only one dimension, length. Width has been eliminated. What is the boundary of a line segment? It is a point, which has zero dimensions. Thus we always eliminate one dimension to find the boundary of a geometric figure. Let's follow the train of thought of many mathematicians, including Riemann, who has done exceptionally good work. [Note 68] Let's consider a point, which has zero dimensions, — a line, which has one, — a plane, which has two, — and a solid object, which has three. On a purely technical level, mathematicians ask whether it is possible to add a fourth dimension. If so, the boundary of a four-dimensional figure would have to be a three-dimensional figure, just as a plane is the boundary of a solid body, a line the boundary of a plane, and a point the boundary of a line segment. Of course, mathematicians can then proceed to consider figures with five, six, seven, or even ii dimensions, where h is a positive integer. At this point a certain lack of clarity enters in, when we say that a point has zero dimensions, a line one, a plane two, and a solid object three. We can make solid objects, such as cubes, out of any number of materials — wax, silver, gold, and so on. Their materials are different, but if we make them all the same size, each one occupies the same amount of space. If we then eliminate all the matter these cubes contain, we are left with only specific segments of space, the spatial images of the cubes. These segments of space are the same size for all the cubes, regardless of the material of which they were made, and they all have length, width, and height. We can imagine such cubical spaces extending to infinity, resulting in an infinite three-dimensional space. The material object is only a segment of this space. The next question is, Can we extend our conceptual considerations, which took space as their point of departure, to higher realities? For mathematicians, such considerations include only calculations involving numbers. Is this permissible? As I will now show you, using numbers to calculate the size of spaces results in great confusion. Why is this so? A single example will suffice. Imagine you have a square figure. This plane figure can be made broader and broader on both sides, until eventually we have a plane figure that extends to infinity between two lines (Figure 56) Because this plane figure is infinitely wide, its size is infinity (oo). Now suppose other people hear that the area between these two lines is infinitely large. Naturally, these people think of infinity. But if you mention infinity, they may get a totally incorrect idea of what you mean. Suppose I add another square to each of the existing ones, that is, a second row of infinitely many squares. The result is again infinity, but a different infinity that is exactly twice as great as the first (Figure 57). Consequently, \(∞ = 2\cdot∞\). In the same way, I could also arrive at \(∞ = 3\cdot∞\). In calculating with numbers, infinity can be used just as easily as any finite number. It is true in the first case that the space is infinite, but it is just as true in the latter instances that it is \(2\cdot∞\), \(3\cdot∞\), and so on. That's what happens when we calculate using numbers. You see, as long as the concept of infinite space is linked to a numerical reckoning, it makes it impossible to penetrate more deeply into higher realities. Numbers actually have no relationship to space. Like peas or any other objects, numbers are totally neutral with regard to space. As you know, numerical calculations in no way change the reality of the situation. If we have three peas, multiplication cannot change that fact, even if we multiply correctly. Calculating that \(3 \times 3 = 9\) will not produce nine peas. Merely thinking about something changes nothing in such cases, and numerical calculations are mere thinking. We are left with three peas, not nine, even if we performed the multiplication correctly. Similarly, although mathematicians perform calculations pertaining to two, three, four, or five dimensions, the space that confronts us is still three-dimensional. I'm sure you can experience the temptation of such mathematical considerations, but they prove only that it is possible to perform calculations concerning higher-dimensional space. Mathematics cannot prove that higher-dimensional space actually exists, — it cannot prove that the concept is valid in reality. We must be rigorously clear on this point. Let's consider some of the other very astute thoughts mathematicians have had on this subject. We human beings think, hear, feel, and so on in three-dimensional space. Let's imagine beings capable of perceiving only in two-dimensional space. Their bodily organization would force them to remain in a plane, so they would be unable to leave the second dimension. They would be able to move and perceive only to the right and left and forward and backward. They would have no idea of anything that exists above or below them. [Note 69] Our situation in three-dimensional space, however, may be similar. Our bodily organization may be so adapted to three dimensions that we cannot perceive the fourth dimension but can only deduce it, just as two-dimensional beings would have to deduce the existence of the third dimension. Mathematicians say that it is indeed possible to think of human beings as being limited in this particular way. Of course, it is certainly possible to say that even though this conclusion might be true, it might also simply be a misinterpretation. Here again, a more exact approach is required, though the issue is not as simple as the first example, where we tried to use numbers to understand the infinity of space. I will deliberately restrict myself to simple explanations today. The situation with this conclusion is not the same as with the first, purely technical arithmetical line of reasoning. In this instance, there is really something to take hold of. It is true enough that a being might exist who could perceive only objects that move in a plane. Such a being would be totally unaware of anything existing above or below. Imagine that a point within the plane becomes visible to the being. Of course, the point is visible only because it lies within the plane. As long as the point moves within the plane, it remains visible, but as soon as it moves out of the plane, it becomes invisible. It disappears as far as the plane-being is concerned. Now let's suppose that the point appears later somewhere else. It becomes visible again, disappears again, and so on. When the point moves out of the plane, the plane-being cannot follow it but may say, "In the meantime, the point is somewhere where I cannot see it." Let's slip into the mind of the plane-being and consider its two options. On the one hand, it might say, 'There is a third dimension, and that object disappeared into it and later reappeared.” Or it could also say, "Only stupid beings talk about a third dimension. The object simply disappeared, and each time it reappeared, it was created anew." In the latter case, we would have to say that the plane-being violates the laws of reason. If it does not want to assume that the object repeatedly disintegrates and is recreated, it must acknowledge that the object disappears into a space that plane-beings cannot see. When a comet disappears, it passes through four-dimensional space. [Note 70] Now we see what must be added in a mathematical consideration of this issue. We would have to find something in our field of observation that repeatedly appears and disappears. No clairvoyant abilities are needed. If the plane-being were clairvoyant, it would know from experience that there is a third dimension and would not have to deduce its existence. Something similar is true of human beings. Anyone who is not clairvoyant is forced to say, "I myself am restricted to three dimensions, but as soon as I observe something that disappears and reappears periodically, I am justified in saying that a fourth dimension is involved." Everything that has been said thus far is completely incontestable, and its confirmation is so simple that it is unlikely to occur to us in our modern state of blindness. The answer to the question, "Does something exist that repeatedly disappears and reappears?" is very easy. Just think of the pleasure that sometimes rises in you and then disappears again, so that no one who is not clairvoyant can still perceive it. Then the same feeling reappears because of some other event. In this case, you, like the plane-being, can behave in one of two ways. Either you can say that the feeling has disappeared into a space where you cannot follow it, or you can insist that the feeling vanishes and is created anew each time it reappears. It is true, however, that any thought that disappears into the unconscious is evidence of something that can disappear and then reappear. If this idea seems plausible to you, the next step is to attempt to formulate all the possible objections that could be raised from the materialistic viewpoint. I will mention the most pertinent objection now, — all the others are very easy to refute. People may claim to explain this phenomenon in purely materialistic terms. I want to give you an example of something that disappears and reappears in the context of material processes. Imagine a steam piston in action. As long as force is applied to the piston, we perceive its motion. Now suppose we counteract its motion with an identical piston working in the opposite direction. The movement stops and the machines are motionless. The movement disappears. Similarly, people might claim that the sensation of pleasure is nothing more than molecules moving in the brain. As long as the molecules are moving, I experience pleasure. Let's assume that some other factor causes an opposite movement of molecules. The pleasure disappears. Anyone who does not pursue this line of thought very far might indeed find it a very significant argument against the ideas presented earlier, but let's take a closer look at this objection. Just as the movement of a piston disappears as a result of an opposite movement, a feeling that is based on molecular movement is said to be eliminated by an opposing molecular movement. What happens when one piston movement counteracts another? Both the first and the second movement disappear. The second movement cannot eliminate the first without eliminating itself, too. The result is a total absence of movement, — no movement remains. Thus, no feeling that exists in my consciousness could ever eliminate another without also eliminating itself. The assumption that one feeling can eliminate another is therefore totally false. In that case, no feeling would be left, and a total absence of feeling would result. The most that can still be said is that the first feeling might drive the second into the subconscious. Having said this, however, we admit the existence of something that persists yet evades our direct observation. Today we have been speaking only about purely mathematical ideas, without considering clairvoyant perception at all. Now that we have admitted the possibility that a four-dimensional world exists, we may wonder whether we can observe a four-dimensional object without being clairvoyant. A projection of sorts allows us to do so. We can turn a plane figure until the shadow it casts is a line. Similarly, the shadow of a line can be a point, and the shadow image of a solid three-dimensional object is a two-dimensional plane figure. Thus, once we are convinced of the existence of a fourth dimension, it is only natural to say that three-dimensional figures are the shadow images of four-dimensional figures. This is one purely geometric way of imagining four-dimensional space. But there is also a different way of visualizing it with the help of geometry. Imagine a square, which has two dimensions. Now picture the four line segments that form its boundaries straightened out to form a single line. You have just straightened out the boundaries of a two-dimensional figure so that they lie in one dimension (Figure 58). Let's take this process one step further. Imagine a line segment. We proceed just as we did with the square, (removing one dimension) so that the boundaries of the figure fall in two points. We have just depicted the boundaries of a one-dimensional figure in zero dimensions. We can also unfold a cube, flattening it into six squares (Figure 59). We unfold the boundaries of a cube so that it lies in a plane. In this way, we can say that a line can be depicted as two points, a square as four line segments, and a cube as six squares. Note the sequence of numbers: two, four, six. Next we take eight cubes. Just as the previous examples consist of the unfolded boundaries of geometric figures, the eight cubes form the boundaries of a four-dimensional figure (Figure 60). Laying them out results in a double cross that represents the boundaries of a regular four-dimensional figure. Hinton calls this four-dimensional cube a tessaract. This exercise gives us a mental image of the boundaries of a tessaract. Our idea of this four-dimensional figure is comparable to the idea of a cube that two-dimensional beings can develop by flattening a cube's boundaries, that is, by unfolding them. The first mathematical studies of the problem of higher-dimensional space date from the middle of the nineteenth century. See the introduction to Manning's Geometry of Four Dimensions [1914], In the passages that follow, Rudolf Steiner bases himself on Riemann's studies on the geometry of n -dimensional manifolds. See Note 1, Lecture 1 (March 24, 1905). See also the following books, which were well-known and popular in their time: Abbott, Flatland [1884], Hinton, the chapter "A Plane World" in Scientific Romances [1886] (pp. 129-159), and Hinton, An Episode of Flatland [1907], See also Rudolf Steiner's lecture of April 10, 1912 (GA 136). We have not been able to confirm the assumption that this statement of Steiner's refers to Zöllner’s views on the subject. Zöllner's comet theory (see Zöllner [1886]) became the basis and point of departure for modern conventional comet theories, and there is no indication that Zöllner saw any connection between his comet theory and his spiritualistic ideas about four-dimensional space.

The Fourth Dimension

On Higher-Dimensional Space

https://rsarchive.org/Lectures/GA324a/English/AP2001/19081022p02.html

Berlin

22 Oct 1908

GA324a-8

In the original German publication the first question and answer is front 1904 in Berlin. [Note 1] There is no recorded question, only that it was asked by Mr. Schouten [Note 2] and the answer is simply a reply from Steiner that he would be giving a lecture shortly on the fourth dimension. A Question about the work of the “I." [Note 3] The "I" works on the astral body, the ether body, and the physical body. All human beings work on the astral body through moral self-education. But even when a person begins the process of initiation or esoteric schooling, much work remains to be done on the astral body. Initiation marks the beginning of more intensive work on the ether body through the cultivation of aesthetic taste and religion. Initiates work consciously on the ether body. In a certain respect, astral consciousness is four-dimensional. To give you an approximate idea of it, let me say that anything dead tends to remain within the three ordinary dimensions, while anything living constantly transcends them. Through its movement, any growing thing incorporates the fourth dimension within the three. If we move in a circle that is growing ever larger, we eventually arrive at a straight line (Figure 61). If we continue moving along this line, however, we will no longer be able to return to our starting point, because our space is three-dimensional. In astral space, which is closed off on all sides, we would return. In astral space, it is impossible to continue to infinity. [Note 4] Physical space is open to the fourth dimension. Height and width are two dimensions, and the third dimension is the lifting out and entering into the fourth dimension. [Note 5] A different geometry prevails in astral space. These comments were made after a lecture on Christianity (not yet published in the complete edition of Rudolf Steiner's works) to the Berlin branch. Jan Arnoldus Schoutan (1883-1971) See Note 1, Lecture 3 (May 17, 1905). This question suggests that the problem of the fourth dimension was topical even in Rudolf Steiner's immediate circle and that his lectures on the subject were meant above all to address related spiritual scientific questions. This question-and-answer session took place during the lecture cycle Vor dem Tore der Theosophie (GA 95). By space, Rudolf Steiner apparently means ordinary, perceived space that is defined by the laws of Euclidean geometry. In this type of space, infinity (or, when this space is embedded in projective space, the distant plane) is an impenetrable boundary. According to Steiner, the same does not apply to astral space, whose structure is related to that of projective space. In this type of space there is no boundary, no unattainable infinity. Projective space is self-contained, — we can set out in any direction from a fixed starting point and ultimately return to the same point. It has not been possible to reconstruct exactly what this sentence means. On the basis of the drawing that has been preserved (Figure 62), the sentence may be a fragment of an explanation with approximately the following contents: In the second dimension, a two-dimensional object within a circle cannot leave the circle without crossing the circumference. The object can easily be moved outside the circle, however, by enlisting the help of the third dimension. Similarly, an object located within a sphere in three-dimensional space cannot be removed without puncturing the sphere, except by passing through the fourth dimension. (See the explanations in the lecture of March 24, 1905, and the accompanying notes.)

The Fourth Dimension

Questions and Answers I

https://rsarchive.org/Lectures/GA324a/English/AP2001/19060902q01.html

Stuttgart

2 Sep 1906

GA324a-10

QUESTION: Since [Note 6] time had a beginning, it is obvious to assume that space also has limits. What is the reality of the situation? That's a very difficult question, because the faculties needed to understand the answer cannot be developed by most people of today. For now, you will have to simply take the answer at face value, but a time will come when it will be understood completely. The physical world's space with its three dimensions, as we human beings conceive of it, is a very illusory concept. We usually think that space either must reach to infinity or have boundaries where it is somehow boarded up and comes to an end. Kant put forward these two concepts of the infinity and the finiteness or limitedness of space and showed that there is something to be said for and against both of them. [Note 7] We cannot judge the issue so simply, however. Since all matter exists in space and all matter is a condensed part of spirit, it becomes evident that we can achieve clarity on the question of space only by ascending from the ordinary physical world to the astral world. Our non-clairvoyant mathematicians already have sensed the existence of a strange and related phenomenon. When we imagine a straight line, it seems to reach to infinity in both directions in our ordinary space. But when we follow the same line in astral space, we see that it is curved. When we move along it in one direction, we eventually return from the other side, as if we were moving around the circumference of a circle. [Note 8] As a circle becomes larger, the time needed to go around it grows longer. Ultimately, the circle becomes so huge that any given section seems almost like a straight line because there is so little difference between the circle's very slightly curved circumference and a straight line. On the physical plane, it is impossible to return from the other side as we would do on the astral plane. While the directions of space are straight in the physical world, space is curved in the astral world. When we enter the astral realm, we must deal with totally different spatial relationships. [Note 9] Consequently, we can say that space is not the illusory structure we think it to be but a self-contained sphere. And what appears to human beings as physical space is only an imprint or copy of self-contained space. [Note 10] Although we cannot say that space has limits where it is boarded up, we can say that space is self-contained, because we always return to our starting point. This question-and-answer session took place during the lecture cycle The Apocalypse of St. John (GA 104). Kant, Prolegomena to Any Future Metaphysics [1783], "Cosmological Ideas", §50- 53, — and Critique of Pure Reason [1787], "The Antinomies of Pure Reason, the First Conflict of Transcendental Ideas," §454ff. Kant shows that arguments can be presented both for and against the infinity of space. For him, the origin of this contradiction lies in the implicit assumption that space and its objects must be taken as absolute givens and as objective laws of things as they are (" von Dingen an sich "). If they were understood as what Kant says they are — namely, mere mental images (ways of looking at things, or phenomena) of things as they are — then the "conflict of ideas" dissolves. Rudolf Steiner's statements here are based on the discovery that Euclidean geometry is embedded in projective geometry. A Euclidean straight line disappears into infinity in both directions, and the right and left directions are separated by infinity (the distant point). A projective straight line has no such limits — with regard to the sequence of its points, it is closed like a circle. The text that has been preserved is insufficient to reconstruct whether Steiner attributes an actual geometric curve to astral space. In any case, a self-contained projective straight line is not curved. It is possible that Steiner simply wanted to point out the structural relationships on a projective straight line and how they behave on the circumference of a circle. Here, too, Steiner presumably uses the term sphere only to draw attention to the self-contained character of astral space in the sense of a projective space. In the topological sense, neither the projective plane of a two-dimensional sphere nor the projective space of a three-dimensional sphere is equivalent.

The Fourth Dimension

Questions and Answers II

https://rsarchive.org/Lectures/GA324a/English/AP2001/19080628q01.html

Nuremberg

28 Jun 1908

GA324a-11

QUESTION: Does the concept of three-dimensionality apply to the spiritual hierarchies, since toe speak of their "areas” of dominion? We [Note 11] can say that a human being's essence is realized in space. Space itself, however, from the esoteric perspective, must be seen as something produced as a result of creative activity. Its creation precedes the work and activity of the highest hierarchies, so we can presuppose the existence of space. We should not imagine the highest Trinity in spatial terms, however, because space is a creation of the Trinity. We must imagine spiritual beings without space, because space is a creation. The effects of the hierarchies within our world, however, have spatial limits, as do those of human beings. The other hierarchies move within space. QUESTION: Does time apply to spiritual processes? Certainly, but the highest spiritual processes in the human being lead to the concept that they run their course timelessly. The activities of the hierarchies are timeless. It is difficult to talk about how time came about because the concept of time is implicit in the words to come about. Instead, we would have to talk about the essence or being of time, which is not easy to discuss. No time would exist if all beings were at the same level of development. Time arises through the interaction between a number of higher beings and a number of lower beings. In timelessness, various levels of development are possible, but their interaction makes time possible. QUESTION: What is space? We must imagine the Trinity without space, because space is a creation of the Trinity. As such, space is a creation and belongs to our world. Space is significant only for beings that develop within earthly existence. Between birth and death human beings are cut off from the spirit in space and time in the same way that a worm lives beneath the Earth's surface. As for time, the highest states accessible to human beings are timeless. Because of the subtleties that come into play, it is not easy to speak about the concept of time coming into existence or about the essence or being of time. Time has had meaning only since the separation of the ancient Moon from the Sun. Everything external exists in space and everything internal runs its course in time. We are circumscribed by both space and time. There would be no time if all beings of the universe were at the same level of development. In timelessness, we can imagine evolutionary levels that are equivalent. The concept of time emerges when these levels begin to differ and to interact. Even the divinity evolves. As evolution continues, even the concept of evolution itself evolves. "This question-and-answer session and the following one took place during the lecture cycle The Spiritual Hierarchies and the Physical World (GA 110).

The Fourth Dimension

Questions and Answers III

https://rsarchive.org/Lectures/GA324a/English/AP2001/19090421q01.html

Düsseldorf

21 Apr 1909

GA324a-12

(The wording of the Question has not been preserved.) We are able to visualize three-dimensional space. An important theorem of the Platonic school is "God geometrizes." [Note 12] Basic geometric concepts awaken clairvoyant abilities. [Note 13] Positional geometry proves that the same point is everywhere on the circumference — the infinitely distant point on the right is the same as the starting point on the left. Thus, ultimately, the universe is a sphere, and we return to our starting point. [Note 14] Whenever I use geometric theorems, they turn into concepts at the borderline of normal conceptuality. [Note 15] Here, three-dimensional space returns us to our starting point. That is how in astral space, point A can work on point B without any connection between them. [Note 16] We introduce materialism into theosophy when we make the mistake of assuming that matter becomes increasingly less dense as we move toward the spirit. This kind of thinking does not lead to the spirit, but ideas about the connection between point A and point B allow us to visualize the fourth dimension. As an example, we can think of the narrow waist of the gall wasp (Figure 63). [Note 17] What if the physical connection in the middle were absent and the two parts moved around together, connected only by astral activity? Now extend this concept to many spheres of activity (Figure 64) in higher-dimensional space. "This statement cannot be found in Plato's works. It comes from the table conversations recounted by Plutarch that form one section of his Moralia. There, one participant in the conversations says, "God is constantly doing geometry — if this statement actually can be ascribed to Plato." Plutarch adds, This statement is nowhere to be found in Plato's writings, but there is sufficient evidence that it is his, and it is in harmony with his character" (Plutarch, Moralia, "Quaestiones convivales," book VIII, question 2; Stephanus 718c). l3See also Rudolf Steiner's essay "Mathematik und Okkultismus (1904) in Philosophic und Anthroposophie (GA 35). HSee the notes to the questions and answers of September 2, 1906, and June 28, 1908. The term positional geometry is an outdated name for synthetic projective geometry. ,5From the perspective of projective geometry, all theorems in Euclidean geometry having only to do with the position and arrangements of points, lines, and planes (and not with any measurements) are seen as special or borderline" instances of general projective theorems. l6Two points A and B of a projective straight line s separate the line into two segments (Figure 91), one of which includes the distant point of line s. In projective geometry, both segments are considered to connect points A and B. In Euclidean geometry, however, only the segment that does not include the distant point of the straight line g is considered a connection between A and B. ,7Gall wasp: Similar discussions about the possibility of individual parts of a whole affecting each other without being spatially connected also are found in Rudolf Steiners lectures of October 22, 1906, in Berlin (in GA 96) and March 22, 1922, in Dornach (in GA 222). None of the many subspecies of gall wasps described in the scientific literature match Rudolf Steiner's description, but a long, stem-like connection between the head and the abdomen occurs in several species of grave wasps, especially in the sand wasp subspecies. The note taker may have misheard the name of this insect.

The Fourth Dimension

Questions and Answers IV

https://rsarchive.org/Lectures/GA324a/English/AP2001/19090422q01.html

Düsseldorf

22 Apr 1909

GA324a-13

(The wording of the question has not been preserved.) Plants [Note 18] have four dimensions. In the direction of the fourth dimension, a force works from below upward, counteracting the force of gravity so that the sap can flow upward. This rising direction, in conjunction with the fact that the two horizontal directions are unimportant to the leaves, results in the spiral arrangement of the leaves. In plants, therefore, the downward direction, or the direction of gravity, is nullified by the fourth dimension. As a result, plants can move freely in one direction in space. Animals have five dimensions. Their fourth and fifth dimensions counteract two of the other dimensions. Because two dimensions are nullified in animals, animals can move freely in two directions. Human beings are six-dimensional beings. Dimensions four through six counteract the other three dimensions Consequently, three dimensions are nullified in humans. As a result, human beings possess three spatial dimensions and can move in three directions. [Note 19] Notes of a question-and answer-session during the lecture cycle Psychosophie," in Anthroposophie-Psychosophie-Pneuntatosophie (GA 115).

The Fourth Dimension

Questions and Answers V

https://rsarchive.org/Lectures/GA324a/English/AP2001/19101102q01.html

Berlin

2 Nov 1910

GA324a-14

QUESTION: What is electricity? Electricity [Note 20] is light in the sub-material state, light compressed to the greatest possible extent. We must also attribute inwardness to light, — light is itself at every point. Warmth can expand into space in three directions, but in the case of light we must speak of a fourth direction. It expands in four directions, with inwardness as the fourth. Notes of a question-and-answer session after the lecture to members entitled "Die Ätherisation des Blutes. Das Eingreifen des ätherischen Christus in die Erdenentwickelung" in Das esoterische Christentum und die geistige Führung der Menschheit (GA 130).

The Fourth Dimension

Questions and Answers VI

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Basel

1 Oct 1911

GA324a-15

QUESTION: Has spiritual science achieved anything with regard to the fourth and higher dimensions? It [Note 21] is not easy to make the answer to your question understandable. We human beings start from what we know from the physical, sense-perceptible world, where space has three dimensions. At least on a theoretical level, mathematicians formulate ideas about a fourth dimension and higher dimensions by analytically expanding their ideas on three-dimensional space through variables. At least in the context of mathematical thought, therefore, it is possible to speak of higher manifolds. [Note 22] For those familiar with these issues — that is, for those who put heart and soul into the question and also have the necessary mathematical knowledge— many things come to light. Let me mention Simony in Vienna as an example. [Note 23] Initially, higher dimensions exist only in ideas. Actually seeing them begins when we enter the spiritual world, where we are immediately forced to come to grips with more than three dimensions. There, any image presented to us — that is, anything that still possesses intrinsic characteristics of three-dimensionality — is nothing more than a reflection of our own soul processes. In the higher worlds, very different spatial relationships prevail, if indeed we still want to call them spatial relationships. The same is true with regard to time. There are always many people who argue, How can we be sure that all your claims are not based on hallucinations? Such people need to consider the situation with regard to time, because they disregard the fact that the field of spiritual science works with phenomena that are totally different from hallucinations. Your question provides an opportunity to supplement what 1 said in the lecture, because it is never possible to say everything, and today's lecture was very long. Let me still point out the changes that take place with regard to time and space when we enter the spiritual world. The return of the images that we have banished to Hades, as it were, makes sense only when approached in terms of higher dimensions. There, however, this is just as natural and self-evident as three-dimensionality is in the sense-perceptible world. That is why ordinary geometry is a poor match for the beings and events of the spiritual world. On behalf of mathematicians, it must be said that their speculations about the fourth dimension acquire real value when we enter the spiritual world. Usually, however, their conclusions about higher-dimensional space are only generalizations based on Euclidean three-dimensional perceived space rather than on reality, to which their conclusions do not fully correspond. We would need still better mathematics in order to perform calculations regarding the beings and events that spiritual researchers investigate. And yet the answer to your question is "yes." Correlations to a suprasensible world, and also mathematical ideas about infinity, become a reality, especially certain subjects from the fringes of mathematics. Here is an example that I myself experienced many years ago. I know that I had a sudden flash of insight into an extremely important attribute of astral space when 1 was studying modern synthetic projective geometry and analytical mechanics at the university. [Note 24] There is a relationship here to the concept that, on a straight line extending to infinity, the infinitely distant point on the left is identical to the infinitely distant point on the right. That a straight line, with regard to the arrangements of its points, is really a circle,- if we do not get winded and continue in a straight line long enough, we return from the other side. [Note 25] We may understand this, but we should not draw conclusions from it, since conclusions lead nowhere in spiritual research. Instead, allowing phenomena to work on us leads to knowledge of the supra-sensible world. It is important not to overestimate mathematics when dealing with the supra-sensible world. Mathematics is useful only on a purely formal level. It cannot possibly grasp the reality of the situation. Like spiritual science, however, mathematics can be understood by means of forces inherent in the soul itself and is equally true for everyone. That is what mathematics and spiritual science have in common. This question and answer session took place after a public lecture on "Wahrheiten der Geistesforschung," which was published in the periodical Mensch und Welt: Blätter für Anthroposophie , vol. 20, 1968, no. 5, pp.167—177. It has not yet been published in the complete edition (GA) of Rudolf Steiner's works. Here Rudolf Steiner refers again to Bernhard Riemann's studies, mentioned several times in the lectures. See Note 1, Lecture I. 0skar Simony (1852-1915). See Rudolf Steiner's lecture of March 24, 1905 (Lecture 1), and Note 14, Lecture I. See Rudolf Steiner, Autobiography (GA 28). See the answers to the preceding questions and the accompanying notes.

The Fourth Dimension

Questions and Answers VII

https://rsarchive.org/Lectures/GA324a/English/AP2001/19121125q01.html

Munich

25 Nov 1912

GA324a-16

QUESTION: Is the Golden Section based on occult laws? Because [Note 26] it is founded upon the effect of what exists in space, the Golden Section is indeed based on an occult law. Goethe said of this law that what is most hidden is most revealed and vice versa — namely, the law that is intimately related to our human constitution, the law of repetition and varied repetition. [Note 27] [Note 28] If you look at the Buddhas talks, for example, you find that the same content is always repeated with slight variations that must not be omitted, because the content is not the only important factor. [Note 29] The golden section is not simply a matter of repetition. We repeatedly discover the same proportion, since there are actually only three components. [Note 30] The self-contained character of a repetition, which, however, is not self-formed, is what makes the golden section so appealing to us. Notes of a question-and-answer session after a public lecture in Berlin in the House of Architects on "Lionardos geistige Grosse am Wendepunkt zur neueren Zeit" (GA 62). Goethe's Das Märchen . See Note 3, Lecture 3. For further discussion of the general occult law of repetition and varied repetition, see Rudolf Steiner's Outline of Esoteric Science (GA 13), chapter 4, "Cosmic Evolution and the Human Being." On the law of repetition as an elementary principle of the etheric realm, see, for example, Rudolf Steiner's lecture of October 21, 1908 (GA 107), where he illustrates this principle using the example of plant growth and points out the varied repetition in the ongoing process of leaf formation. The significance of repetitions in the Buddha's talks is also mentioned in lectures Rudolf Steiner gave on September 18, 1912 (GA 139), and on the afternoon of September 27, 1921 (included in GA 343). Fra Luca Pacioli (ca. 1445-1517), who was influenced by Piero della Francesca (1410–1492) and Leonardo da Vinci (1452—1519), wrote the paper Divina proportion (Venice, 1509) using drawings copied from his friend Leonardo. This paper was the first thorough study to focus on the mathematical and aesthetic characteristics of the Golden Section. The golden section ( sectio aurea ), also called "constant division," results from dividing a line segment into two parts in such a way that the ratio of the smaller portion to the larger is the same as that of the larger to the whole. When we continue to divide a line segment according to the golden section, the result is a sequence of line segments such that the proportion between any two adjacent sections is the golden section. This explains the term constant division . A further indication of the principle of repetition and varied repetition in the context of the golden section is the appearance of the proportion of the golden section in continued fractions. Furthermore, the approximation fractions of these fraction sequences are the quotients of successive members of the Fibonacci series 1, 1, 2, 3, 5, 8..., which play a major role in the arrangement of leaves in plants (phyllotaxis) (see Coxeter [1981], chapter 11).

The Fourth Dimension

Questions and Answers VIII

https://rsarchive.org/Lectures/GA324a/English/AP2001/19130213q01.html

Berlin

13 Feb 1913

GA324a-17

QUESTION: Do human beings between death and rebirth have the same perception of time as those incarnated in bodies? My [Note 31] lecture on March 19, 1914 on the human being between death and rebirth will supply more information on this subject. [Note 32] For today, let me just say that life after death means leaving the relationships of the sense-perceptible, physical world and entering totally different relationships of space and time. With the theory of relativity, we are beginning to develop different concepts of time. [Note 33] We can make the transition from the factors in the formula for movement into the circumstances of the spiritual world only when we use these factors in the form \(c = s/t\), because s and t as we know them belong to the sense-perceptible world, while \(c\) (or \(v\) for velocity) actually belongs to the domain of inner experience, even with regard to an inorganic object. Thus when we want to understand time in the spiritual world, we must first speak of the quantum of speed that the being in question has,- then, through comparison, we as outsiders can determine something about temporal relationships. Through a comparison of sorts, for example, we can discover that speed is three times as great in life in kamaloka. Such investigations give us an impression of the relationship between time in spiritual life and time in the life of the senses. In the spiritual world, different principles of time prevail. In comparison with those of the sense-perceptible world, these principles are internalized and variable. Because the time we experience there is dependent on inner developmental processes, it cannot be compared in clear mathematical terms with periods of time in the physical world. Questions and answers after the public lecture "Vom Tode,” held in Berlin in the House of Architects (published in GA 63). Rudolf Steiner's lecture of March 19, 1914, "Zwischen Tod und Wiedergeburt des Menschen" (published in GA 63). With regard to the remainder of this question-and-answer session, see also the questions and answers of March 7, 1920, and the accompanying notes.

The Fourth Dimension

Questions and Answers IX

https://rsarchive.org/Lectures/GA324a/English/AP2001/19131127q01.html

Berlin

27 Nov 1913

GA324a-18

(The wording of the Question has not been preserved.) Mathematics [Note 34] is an abstraction of the sum total of forces working in space. When we say that mathematical theorems are valid a priori , this statement is based on the fact that human beings exist within the same lines of force as other beings and that we are able to abstract this from everything not belonging to the pattern of space, etc. A handwritten note by Rudolf Steiner in response to a question asked by Georg Herberg. A facsimile of this note is included in the volume Geisteswissenschaftliche Impulse zur Entwickelung der Physik, Erster Naturwissenschaftlicber Kurs (GA 320), Dornach, 1987, p. 192. Georg Herberg (1876-1963), one of Germany's first Ph.D.s in engineering, was an independent engineering consultant in the field of heat and energy economy in Stuttgart from 1913 onward.

The Fourth Dimension

Questions and Answers X

https://rsarchive.org/Lectures/GA324a/English/AP2001/19190000q01.html

Stuttgart

1919

GA324a-19

FIRST QUESTION: Is the law of the absolute propagation of light correct? SECOND QUESTION: Is there any reality to the relativity of time assumed by Einstein? I assume that your first question deals with whether light in absolute space travels at a constant speed. [Note 35] As you know, we cannot really talk about the propagation of light in absolute space because absolute space does not exist. What basis do we actually have for talking about absolute space? You said, and rightly so, that you assume the propagation of light is infinitely great and that light derives its actual propagation from the resistance of the medium. Now I ask you, in your view is it altogether possible to speak of the speed of light in the same sense that we speak of the speed at which any other body travels? HERMANN VON BARAVALLE: Absolutely not. If we do not hypothetically equate light with any other body, we cannot measure its speed in the same way as that of any other body. Let's assume that an ordinary body, a material object, is flying through space at a certain speed. This object is at a specific place at a specific moment in time, and our entire method of measuring speed depends on considering the difference in the object's location from its point of departure at two different times. This method of measurement remains possible only if the moving material body completely leaves the points on the line in which it is moving. Let's assume that it does not leave these points but leaves traces behind. Applying this method of measurement immediately becomes impossible if the object moving through a given space does not leave that space but continues to occupy the line of movement, not because we cannot measure the differences but because the propelling speed constantly modifies the propelled object. I cannot apply my ordinary method of measurement when, instead of dealing with matter that leaves the space empty behind it, I am dealing with an entity that does not completely vacate the space but leaves traces behind. Thus, we cannot speak of a constant speed of light in the same sense that we speak of the speed of a material object, because we cannot formulate an equation based on differences in location, which, of course, provide a basis for calculating speed. Thus, when we are dealing with the propagation of light, we find ourselves compelled to speak only about the speed of the outer propagation of light. But if we speak about the speed of the propagation of light, we would be obliged to go back constantly to the source of the spreading light in order to measure its speed. In the case of the Sun, for example, we would be obliged to go back to the origin of the spreading light. We would have to begin measuring where the spread of light began, and we would have to assume hypothetically that the light continues to replicate indefinitely. This assumption is not justified, however, because the frontal plane in which the light is spreading, instead of always simply growing larger, becomes subject to a certain law of elasticity and reverses direction when it achieves a certain size. At that point we are no longer dealing simply with spreading light but with returning light, with light retracing the same path in reverse. On an ongoing basis, therefore, I am not dealing with a single location that I assume to exist in light-filled space — that is, with something that is spreading from one point to another — but with an encounter between two entities, one of which is coming from the center and the other from the periphery. Thus, I cannot avoid asking the fundamental question, are we really dealing with speeds in the ordinary sense when we consider the transmission of light? I don't know whether or not I have made myself understood. I am not dealing with speed of propagation in the ordinary sense, and when I take the step from ordinary speeds to speeds of light, I must find formulas based on formulas for elasticity. If I may use the image of material movement, such formulas must reflect how elastically related portions of space behave in a closed elastic system with a fixed sphere as its boundary. [Note 36] Therefore, I cannot use an ordinary formula when I shift to describing the behavior of light. For this reason I see a fundamental error in Einstein's work, namely, that he applies ordinary mechanical formulas — for that is what they are — to the spreading of light and assumes hypothetically that light can be measured in the same way as any material body flying through space. [Note 37] He does not take into account that spreading light does not consist of material cosmic particles speeding away. Light is an event in space that leaves a radiant trace behind, so that when I measure it (reference to drawing that has not been preserved), I cannot simply measure as if the object comes this far and leaves nothing behind. When light is transmitted, however, there is always a trace here, and I cannot say that it is transmitted at a specific speed. Only the frontal plane is transmitted. That is the main point. I am dealing with a specific entity in space that has been subsumed by the spreading element. And then I see a second error that has to do with the first, namely, that Einstein applies principles to the whole cosmos that actually apply to mechanical systems of points that approach each other, thus disregarding the fact that the cosmos as a whole system cannot be merely a summation of mechanical processes. For example, if the cosmos were an organism, we could not assume that its processes are mechanical. When a mechanical process takes place in my hand, it is not essentially determined merely by the closed, mechanical system because my entire body begins to react. Is it is acceptable to apply a formula for other movements to the movement of light, or is the reaction of the entire cosmos involved? A universe without light is even more difficult to imagine without the reaction of the entire universe, and this reaction works very differently from speeds in a closed, mechanical system. [Note 38] It seems to me that these are Einstein's two principal errors. I have studied his theory only briefly, and we all know that mathematical derivations can indeed coincide with empirical results. The fact that starlight that has passed the Sun, for example, coincides with theoretical predictions does not verify Einstein's theory once and for all. [Note 39] These two principal underlying factors are why Einstein's way of thinking is always so paradoxical and abstract. The situation here is somewhat similar to the example from Wilhelm Busch that you used earlier, where an arm is raised forcefully and you almost have the feeling that you are going to be slapped on the face. It's a bit like that when Einstein draws conclusions from what would happen if a clock sped away at the speed of light and then returned. [Note 40] I ask you, is there any reality to this notion? I absolutely cannot complete the thought, because I am forced to wonder what happens to the clock. If you are accustomed to restricting your thoughts to reality, you cannot carry thoughts such as this through to completion. [Note 41] The passages where Einstein presents such thoughts show that his conclusions are based on fundamental errors such as the one I just mentioned. That was my first comment. On the subject of time, we would need to begin basing our thoughts on elastic formulas rather than ordinary mechanical formulas. We would need to borrow from the theory of elasticity. By extension, any distribution or spreading that forms a frontal plane cannot be imagined as an entity that continues to spread out to infinity. It always reaches a certain sphere where it turns back in on itself. If we want to address the reality of the situation, we cannot say that the Sun radiates light that vanishes into infinity. That is never the case. There is always a boundary where the spreading force of elasticity is exhausted and turns back in on itself. There is no such thing as an infinite system that meets the criteria of spreading out and disappearing into nothingness. Any spreading entity reaches a boundary where it turns around, somewhat as if it were obeying the law that governs elastic bodies. When we speak of light, we are never dealing with something that continues to spread indefinitely in all directions. Instead, we always find a situation comparable to standing waves. That is where we must look for the formulas, not in ordinary mechanics. [Note 42] Then there is still the question of time itself. In fact, time does not go through all these transformations, does it? Here in the realm of mechanics time as such is not a reality. Take the very simplest formula, \(s = e \times t\). According to the ordinary law of multiplication, s must be essentially identical to \(c\), — otherwise the space \(s\) would be identical to the time, which is impossible. In this formula, I can think of space only as somehow mathematically identical to \(c\). We cannot multiply apples and pears, can we? We have to put one in terms of the other. In mathematical formulas, time can only be a number, which, however, does not mean that the reality of time is a number. We can write the formula like this only when we assume that we are dealing with an unnamed number. [Note 43] The formula \(c = s/t\) is a different matter. Here we have a space \(s\) of a certain size as it relates to the size of the number \(t\). The result is the speed c. This is the reality of the situation regardless of whether I imagine atoms, molecules, or matter that occupies a specific, perceivable amount of space. I must imagine that any thing I confront empirically has a specific speed. Any further conclusions are just abstractions. Time is something that I derive from the divisor and the distance traveled is something I derive from the dividend, but these are abstractions. The reality — and this applies only to mechanical systems — is the immanent speed of each body. For example, when physicists accept atomic theory for other reasons, they must not assume that atoms exist without immanent speed. Speed is a true reality. [Note 44] Thus we must say that we abstract time as such from events and processes. It is actually an abstraction from events. Only the speeds of what we encounter can be seen as realities. When we understand this completely, we can no longer avoid concluding that what I call time appears as a result of phenomena. It plays a collaborative role in phenomena, and we must not disregard it as a relative. [Note 45] The collaboration of this abstracted factor yields a specific real and fundamental concept of an organism's life span, for example. The life span of an organism cannot be measured externally, — its course is immanent. Any given organism has a specific, inherent life span that is integrated into and results from all the processes taking place in the organism. The same is true of an organism's size. It is intrinsic to the organism and is not to be measured in relationship to anything else. The fitting conclusion is that such concepts of life span and size are not valid in the same way that we ordinarily assume. Human beings are a specific size. Now let me hypothetically assume that very small human beings exist in our ordinary universe. For all other purposes, the size of human beings relative to other objects is not important. Their typical size is important to human beings, however, because this size is intrinsic. This point is important. Imagining that human beings can be arbitrarily larger or smaller is an offense against the entire universe. For example, certain scientific thinkers wonder what life would be like in a solar system that is infinitely large or small compared with ours. This question is nonsense. Both the sizes and the life spans of the real entities we encounter are matters of inner necessity. At this point I must state that any entity that can be considered a totality essentially carries its own time within it. I can look at a piece of an inorganic object independent of anything else, but I cannot do the same with a leaf because its continued existence depends on the tree. Thus, I must consider whether or not the entity I am observing is a totality, a whole, self-contained system. Any totality that I observe, however, incorporates time as an immanent factor. Consequently, I do not think much of the idea of an abstract time that exists outside objects and in addition to the time that is inherent in each object or event. Looking at time that is supposed to run from beginning to end is a bit like developing the abstract concept horse on the basis of individual horses. Individual horses exist in the external reality of space, but the concept requires something more. The same is true of time. Whether time is inherently changeable or not is essentially an empty question because each total system in its own immanent existence has its own time and its own speed. The speed of any inorganic or vital process points back to this immanent time. For this reason, instead of a theory of relativity that always assumes we can relate one axial coordinate system to another, I would prefer to establish a theory of absolutes to discover where total systems exist that can be addressed in the same way we address an organism as a totality. We cannot talk about the totality of the Silurian period in the Earth's evolution, for example, because the Silurian period must be united with other evolutionary periods to form a system that is a totality. It is equally impossible to speak about the human head as a totality, because the rest of the body belongs with it. We describe geologic periods independently of each other, as if that were the reality of the situation. It is not. One period is a reality only in connection with the entire evolution of the Earth, just as a living organism is a reality from which nothing can be removed. Instead of relating our processes to coordinate systems, it would be much more pertinent to relate them to their own inherent reality, so that we could see the whole systems, or totalities. At that point, we would have to return to a certain type of monadism. We would overcome the theory of relativity and arrive at a theory of absolutes. We would then truly see that Einstein's theory is the last expression of the striving for abstraction. Einstein functions in abstractions that sometimes become intolerable when his assumptions are applied to very elementary matters. For example, how does sound work when I myself am moving at the speed of sound? If I do that, of course I never hear real sounds, because the sound is traveling with me. To anyone who thinks in real terms, in terms of totalities, such a concept cannot be implemented, because any being that can hear would fall apart if it moved at the speed of sound. Such concepts are not rooted in observations of the real world. [Note 46] The same is true when I ask whether time is inherently changeable. Of course, it is impossible to confirm any changes in abstract or absolute time, which must be imagined a priori. When we talk about changes in time, however, we must grasp the reality of time, which we cannot do without considering how temporal processes are intrinsically linked to total systems that exist in the world. Questions and answers during the lecture cycle Geisteswissenschaftliche Impulse zur Entwickelung der Physik: Zweiter Naturwissenschaftlicher Kurs (GA 321). These questions were asked by Hermann von Baravalle (1898-1973), mathematics and physics teacher at the first Waldorf School in Stuttgart), after a lecture he gave on the theory of relativity (Stuttgart, March 7, 1920). To date, no transcript of Baravalle's lecture has been discovered. ’’The theory of elasticity was one of the The theory of elasticity was one of the theoretical aids used by nineteenth century physicists in formulating their various theories of optics, which all assumed the existence of a physical ether. Later, the electromagnetic theory of light, James Clark Maxwell (1831-1879), in conjunction with the negative outcome of the ether drift experiment (188iff) conducted by Albert Michelson (1852-1931) and Edward Morley (1838-1923), superseded the idea of a quasi-material ether but failed to eliminate it totally from the field of physics. (On the evolution of ether theories and their status in the late nineteenth and early twentieth centuries, see Whittaker [1951-1953]). In volume II of his lectures on theoretical physics [1944], §15, Arnold Sommerfeld (1868-1951) discusses an ether model based on a quasi-elastic body. This model originated in the investigations of James MacCullagh (1809-1847), for more information, see Klein [1926]. Sommerfeld shows that the equations for the movement of this body take the form of Maxwells electrodynamic equations for empty space. Friedrich Dustmann [1991] shows that this ether model meets many of the requirements for a theory of light that Steiner presents here and elsewhere. In addition, the basis of this quasi-elastic ether model is a specific anti-symmetrical tensor, which from the geometric perspective represents a linear complex, thus forming a bridge to the theory of hypercomplex numbers, which Steiner mentions in his response to a question by Strakosch on March 11,1920. (For more on this subject, see Gschwind [1991], especially section 8.5, and [1986], pp. 158-161). It is no longer possible to reconstruct whether Steiner was referring indirectly here to papers on the mechanical and elastic theory of light and was thinking of a suitable extension of or supplement to such theories from his own time. In any case, we must keep in mind that Steiner's suggestions for transforming or reformulating an ether theory for mathematics and physics must not be imagined solely in the context of a purely material and energetic phenomenology of light; see Steiner's responses to questions on March 31, 1920 (Blümel), and January 15, 1921, and the accompanying notes. From this perspective, Steiner's remarks here and in the passages that follow are not to be construed as criticizing the scientific foundations of Einstein's special theory of relativity but rather as calling for an appropriate expansion of the perspectives of physics through the methods and concepts of anthroposophical spiritual science (see also his lecture of January 6, 1923, in GA 326). Similar-sounding remarks of Steiner's on the elastic oscillation/return of light are to be found in his lecture of December 6, 1919 (GA 194), — in the teacher's" conference of September 25, 1919 (GA 300a), — and in the lecture of February 16, 1924 (GA 235). Similar statements on the behavior of energy are found in the questions and answers of November 12, 1917 (GA 73). Albert Einstein (1879-1955), physicist in Zurich, Berlin, and Princeton, — the founder of the special theory of relativity and the general theory of gravitation. The only passage in Steiner's written works that addresses the special theory of relativity is in The Riddles of Philosophy (GA 18), pp. 590-593. This passage is fundamentally important for assessing all of Steiner's comments on the theory of relativity in lectures and question-and-answer sessions. To clarify Steiner's primary view on the theory of relativity, this passage will be quoted here in its entirety: A new direction in thinking has been stimulated by Einstein's attempt to transform fundamental concepts of physics. Until now, physics accounted for the phenomena accessible to it by imagining them arranged in empty three-dimensional space and taking place in one-dimensional time. Thus space and time were assumed to exist outside and independent of objects and events, in fixed quantities. With regard to objects, we measured distances in space, — with regard to events, we measured durations in time. Distance and duration, according to this view of space and time, do not belong to the objects and events. This view now has been countered by the theory of relativity introduced by Einstein. From this perspective, the distance between two objects belongs to the objects themselves. A specific distance from another object is an attribute, a property just like any other property an object may possess. Interrelationships are inherent in objects, and outside these interrelationships there is no such thing as space. Assuming the independent existence of space makes it possible to conceive of a geometry for that space, a geometry that can be applied to the world of objects. This geometry arises in the world of pure thoughts, and objects must submit to it. We can say that relationships in the world must obey laws that were laid down in thought before actual objects were observed. The theory of relativity dethrones this geometry. Only objects exist, objects whose relationships can be described by means of geometry. Geometry becomes a part of physics. In that case, however, we can no longer say that the laws of geometry can be laid down before the objects are observed. No object has a location in space but only distances relative to other objects. A similar assumption is made about time. No event exists at a specific point in time, — it happens at a temporal distance from another event. Thus, spatial and temporal distances between interrelated objects are similar and flow together. Time becomes a fourth dimension that is similar to the three dimensions of space. An event happening to an object can be described only as taking place at a temporal and spatial distance from other events. An objects movement can be conceived of only as happening in relationship to other objects. This view alone is expected to supply faultless explanations of certain processes in physics, but assuming the existence of independent space and independent time leads to contradictory thoughts about these processes. When we consider that many thinkers have accepted only those aspects of the natural sciences that can be presented in mathematical terms, the theory of relativity contains nothing less than the nullification of any real science of nature, because the scientific aspect of mathematics was seen as lying in its ability to ascertain the laws of space and time independent of observations of nature. Now, in contrast, natural objects and natural processes are said to determine spatial and temporal relationships, — these objects and events are to provide the mathematics. The only certain factor is surrendered to uncertainty. According to this view, every thought of an essential reality that manifests its nature in existence is precluded. Everything is only in relation to something else. To the extent that we human beings look at ourselves in the context of natural objects and processes, we will not be able to escape the conclusions of this theory of relativity. If, however, our experience of ourselves as beings prevents us from losing ourselves in mere relativities as if in a state of soul paralysis, we will no longer be permitted to seek intrinsic beingness in the domain of nature but only above and beyond nature, in the kingdom of spirit. We will not escape the theory of relativity with regard to the physical world, but it will drive us into knowledge of the spirit. The significance of the theory of relativity lies in pointing out the need for spirit knowledge that is sought by spiritual means and independently of our observations of nature. That the theory of relativity forces us to think in this way establishes its value in the evolution of our worldview. For further discussion of the specific problems with regard to the theory of relativity addressed by this question-and-answer session, see linger [1967], chapter VIII, and Gschwind [1986] and the literature they list. See also the additions to this note in Beiträge zur Rudolf Steiner Gesamtausgabe , no. 114/115, Dornach, 1995. Rudolf Steiner spoke repeatedly about the theory of relativity and apparently did not distinguish clearly between the special theory of relativity and the general theory of gravitation, which Einstein also called the general theory of relativity. The following lectures and question-and-answer sessions (Q&A) discuss or mention the theory of relativity (RT). The list does not claim to be exhaustive. Rudolf Steiner spoke repeatedly about the theory of relativity and apparently did not distinguish clearly between the special theory of relativity and the general theory of gravitation, which Einstein also called the general theory of relativity. The following lectures and question-and-answer sessions (Q&A) discuss or mention the theory of relativity (RT). This passage makes it clear that Rudolf Steiners criticism of Einstein's thoughts does not have to do with their scientific foundation but rather with the fact that they have been applied to contexts and domains of life that are no longer solely attributable to physics as an inorganic science. The British astronomer and astrophysicist Arthur Eddington (1882-1944) undertook an experimental test of Einstein's prediction that light rays are influenced by gravitational fields (gravitational aberration). The test was to measure the change in apparent location of fixed stars close to the Sun during a solar eclipse. Two British expeditions (one to the western coast of Africa, the other to northern Brazil) were assigned to photograph the environs of the Sun during the solar eclipse of May 29, 1919, and compare them to the known locations of the stars. The result was published on November 6, 1919, and proclaimed as a triumph for Einsteins theory. The deviation at the edge of the Sun, as Einsteins theory predicted, was approximately 1.75 seconds of an arc. Questions immediately arose as to whether the accuracy of the results was sufficient to confirm Einstein's theory. Steiner's objection, however, may have less to do with the inaccuracy of his contemporaries' measuring techniques, which were later superseded as this experiment and others were repeated, than with a question of principle, namely, whether even very precise quantitative experimental confirmations of a theoretical mathematical model constitute an adequate guarantee that the model is true or corresponds to reality. In his commentary on Goethe's natural scientific works Geschichte der Farbenlehre, Enter Teil, Sechste Abteilung): Newtons Persönlichkeit , Steiner writes about this problem: "Mathematical judgments, like any others, are the results of certain presuppositions that must be assumed to be true. But in order to apply these presuppositions correctly to experience, the experience must correspond to the conclusions that result. We cannot draw the opposite conclusion, however. An empirical fact may correspond very well to mathematical conclusions that we have arrived at, and yet in reality the presuppositions that apply may not be those of mathematical scientific research. For example, the fact that the phenomena of interference and light refraction coincide with the conclusions of the wave theory of light does not mean that the latter must be true. It is completely wrong to assume that a hypothesis must be correct if empirical facts can be explained by it. The same effects may be due to different causes, and the justification for the presuppositions we accept must be proved directly, not in a roundabout way by using consequences to confirm them." ( Goethean Science , edited by Rudolf Steiner, volume 4, GAld.) See Einstein, The Principle of Relativity [1911]: The situation is most comical when we imagine causing this clock to fly off at a constant high speed (almost equal to c) and in a constant direction. After it has covered a great distance, we then give it an impulse in the opposite direction, so that it returns to the point where it was originally thrown out into space. We then discover that the hands have scarcely moved at all during its entire trip, whereas the hands of an identical clock, which remained motionless at the starting point for the entire time, have moved considerably. We must add that what is true of this clock, which we have introduced as a simple representative of all events in physics, also applies to any other self-contained physical system. For example, a living organism that we place in a box and subject to the same motion as the clock would be relatively unchanged on returning to its starting point after the flight, while a similar organism that remained in the same place would have made way for new generations a long time ago. For an organism moving at approximately the speed of light, the long traveling time would amount to only a moment. This is an irrefutable consequence of the underlying principles that experience imposes on us... The theory of relativity has several important conclusions for physics that must be mentioned here. We saw that according to the theory of relativity, a moving clock runs slower than an identical clock that is not moving. We will probably never be able to use a pocket watch to verify this statement, because the speeds that can be imparted to a watch are minuscule in comparison to the speed of light. Nature, however, does provide objects that are clock-like in character and that can be made to move extremely rapidly, namely, atoms that give off spectral lines. Through the use of an electrical field, these atoms can achieve speeds of several thousand kilometers (channel rays). According to the theory, it is to be expected that the influence of these atoms' movement on their frequency of oscillation is similar to what we deduced with regard to the moving clock. Clearly, Einstein does not hesitate to extend his theories, which are based purely on considerations belonging to the field of physics, to objects not belonging to that field alone. Thus he claims implicitly that the theory of relativity does not encompass simply systems belonging to the field of physics in the narrower sense but that the entire cosmos underlies his theory. This relatively indiscriminate view is the primary reason for Steiner's harsh objections to what he calls the abstractness and lack of reality of Einstein's thinking. That Einstein really chose not to recognize any significant difference between the different domains of reality is evident from a contemporary report by Rudolf Lämmel (1879-1971), a physicist and ardent popularizer of Einstein's theory of relativity. In his book Die Grundlagen der Relativitätstheorie [1921], Lämmel says: The strangest consequence of these new ideas of the theory of relativity is this: distances are shorter for observers at rest than for those who travel them. Similarly, elapsed time seems longer for an observer "at rest" than for one who is traveling with the clock ... Thus, if we send an expedition out into space today, traveling at half the speed of light, when the travelers return at the same speed after an 11 1/2 year absence, they will ascertain that they spent exactly ten years en route.... Thus the questions "How long is this distance?" and "How long is this duration" no longer can be answered in absolute terms but only with regard to specific observers, that is, relatively. This insight is no mere philosophical remark, but a mathematically confirmed relationship. In his Zurich lectures to the Physicalischen Gesellschaft (Society for Physics) and the Naturforschenden Gesellschaft (Society for Scientific Research), Einstein took up the above example of the duration of a space trip and concluded that under certain circumstances, the explorers might find on their return that their former contemporaries had aged considerably, while they themselves had been traveling for only a few years. This author objected to Einstein's claim and stated that the conclusion applied to units of measurement and to clocks, but not to living beings. Einstein, however, replied that ultimately all processes taking place in our blood, nerves, and so on, are periodic oscillations and therefore movements. Since the principle of relativity applies to all movements, the conclusion about unequal aging is admissible! ... (p. 84 f). For more on the debate about the theory of relativity during the first few decades of the twentieth century, see Hentschel's thorough study [1990], "The issue here later became known as the "paradox of the clocks" or "paradox of the twins." See the comparable passage in the questions and answers of October 15, 1920. See Note 36 on ether theory. See Steiners thorough explanation in his lecture of August 20, 1915 (GA 164). If the formula \(s = e \times t\) is interpreted as an equation of quantities: it is unavoidable to conclude that \(t\) is of a different dimension from \(s\) and \(c\). In any case, \(f\) is certainly not without dimension and that is not what Steiner meant, because the result would be meaningless in the dimensional calculus of physics. Steiner's intent is not to correct the dimensional calculus but rather to point out the problem of the reality of the quantities and calculations that appear in physics. In this sense, no reality can be attributed to the quantity \(t\), though in formulas it must appear to have a specific dimensionality. "Time" \(t\) is not a dimensionless factor but a factor with no reality — that is, a pure number with no reality. See the following comparable passages on speed as a reality: questions and answers of November 27, 1913, — lectures of August 20, 1915 (GA 164), December 6, 1919, December 27, 1919,and January 2, 1920 (GA 320), — questions and answers of October 15, 1920, — and the lecture of January 6, 1923 (GA 326). On this point, see Rudolf Steiner's Einleitungen zu Goethes Naturwissenschaftlichen Schriften ("Introductions to Goethe's Natural Scientific Writings") (GA 1), chapter XVI.2, "Das Urphänomen" ('The Archetypal Phenomenon"). Steiner is referring here to unprotected movement through the air, not to travel in airplanes or similar vehicles. See the comparable passages in his lectures of August 7, 1917 (GA 176), — September 25, 1919 (GA 300a), June 27, 1921 (GA 250f); June 28, 1921 (GA 205), — April 30, 1924 (GA 300c), — and July 20, 1924 (GA 310).

The Fourth Dimension

Questions and Answers XI

https://rsarchive.org/Lectures/GA324a/English/AP2001/19200307q01.html

Stuttgart

7 Mar 1920

GA324a-20

QUESTION: According to Einstein's theory, there is a tremendous amount of energy stored in one kilogram of matter. Is it possible to tap a new source of energy by breaking matter apart — that is, by spiritualising it? The [Note 47] issues you raise are not related directly to the part of Einstein's theory that we discussed today. [Note 48] It certainly would be possible to release energy through the fission of matter. The theoretical aspects present no particular difficulties. The only question is whether we have the technology to utilize this energy. Would we be able to put to use the gigantic forces that would be released? We would not, if they destroy the motor they are meant to run. We first would have to develop mechanical systems capable of harnessing this energy. From a purely theoretical perspective, releasing large amounts of radiant energy for use in a mechanical system requires a substance that can resist the energy. Releasing the energy is quite possible and much easier than utilizing it. QUESTION.- Would it be possible to eliminate matter altogether, so that only energy or radiation is left? [Note 49] In a certain respect, matter is eliminated as in what happens in vacuum tubes. Only a flow of electricity remains. Only speed remains and speed is the determining factor in the mathematical formulas that refer to this phenomena. [Note 50] The question is, Does the formula (E = mc2), in which energy and mass appear at the same time, sufficiently consider the fact that mass as such is different from energy? Or, when I write this formula, am I very abstractly separating two things that are actually one and the same? Is this formula justifiable? [Note 51] It is justifiable only for potential energy, in which case Einstein's formula (E = me2) is simply the old formula for potential energy in a new disguise. [Note 52] QUESTION: Can't we take \( p \times x\) as our starting point? [Note 53] A difficulty arises here simply because when I relate two members of one system of magnitude to something that belongs to another system — for example, if I relate the time it takes two people to do a certain job to a factor supplied by the Sun's setting — the process in the whole system (because it can truly be applied to all members of the system) very easily assumes the character of something that does not belong to any system but can stand on its own. You must not assume that an abstraction, such as a year, that is derived from the solar system is also valid in another system. For example, if you confirm how much a human heart changes in five years, you can then describe the condition of a person's heart as it was five years ago in comparison to what it is now. But by simply continuing the same arithmetical process, you also can ask what that person's heart was like a hundred and fifty years ago or what it will be like three hundred years from now. This is what astronomers do when they start from the present state of the Earth. They neatly calculate changes over periods of time that make as little sense with regard to present conditions on Earth as our calculations about the state of a human heart in three hundred years. We always forget that a conclusion that is valid with regard to the immanent time of a process ceases to have meaning when the process comes to an end. Thus I cannot transcend the organism as a currently living total system. The total system allows me to keep my concepts within the system, and I immediately violate the system when I step outside its bounds. The appearance of validity is evoked because we are accustomed to relating to systems of magnitude in the sense of total systems and then make absolutes out of factors that apply only within such systems of magnitude. Answers to questions raised by Georg Herberg during the lecture cycle Geisteswissenschaftliche Impulse zur Entwickelung der Physik: Zweiter Naturwissenschaftliche Kurs ('Spiritual Scientific Impulses for the Evolution of Physics: Second Scientific Course") (GA 321). The date of this question-and-answer session cannot be ascertained with certainty on the basis of documents in the Rudolf Steiner archives. It is unlikely that the questions date from March 13, 1920 — the time ascribed to them by Hans Schmidt in his book Das Vortragswerk Rudolf Steiners ('The Lectures of Rudolf Steiner"), Dornach, 1978, expanded second edition, p. 319 — because the theory of relativity was not mentioned in either Steiner's lecture on that date or Eugen Kolisko's lecture on "hypothesis-free chemistry" on the same day. Steiner's approach to the question suggests that it may belong to the previous question-and-answer session (March 7, 1920), which took place after Hermann von Baravalle's lecture on the theory of relativity. The word rotation in the transcript of the document seems meaningless in this context and has been replaced by radiation . Steiner is referring here to the phenomenon of electrical conductance in rarefied gases and, in particular, to cathode rays — that is, to streams of high-speed electrons emitted from the cathode of a vacuum tube. Steiner's remarks coincide with the standard thinking of physicists on the subject. The kinetic energy \(1/2mv^2 = eU\) that is imparted to the individual electrons (with the charge \(e\) by an electrical field of voltage \(U\) plays a determining role in all calculations related to cathode rays. Furthermore, the force \(K\) (Lorentz force) with which a charge e is deflected in a magnetic field \(B\) is a function of the speed \(v\). On the subject of cathode rays, see also Steiner's lecture of January 2, 1920 (GA 320). Einstein's formula \(E = mc^2\) establishes the proportionality of energy and inert matter. It is often called the most important result of the special theory of relativity. As is the case with other basic formulas in physics, there are no real proofs, but at best certain justifications (see below) of the formula \(E = mc^2\). Thus, this formula is seen as a postulate underlying relativistic physics. According to Einstein [1917], §15, where \(c\) is the speed of light, the kinetic energy of a body with a resting mass \(m\) moving at a speed \(v\) is If we develop the relativistic term \(E_{kin}\) for kinetic energy in a series, the result is If \(v ˂ ˂ c\) the term remaining in the non-relativistic borderline case \(v/c \rightarrow 0\) is \(mc^2 + 1/2mv^2\). Thus, the resting energy \(mc^2\) must be added to the ordinary kinetic energy \(1/2mv^2\) if non-relativistic mechanics is to result (as the borderline case \(v/c \rightarrow 0\) from relativistic mechanics. This changes nothing in non-relativistic mechanics, because \(mc^2\) is an unchangeable constant that influences only the conventionally determined null point on the energy scale. This passage in the transcript reads "...mass and energy are only a new disguise for the old formula, p.g. energy." It has not been possible to reconstruct the meaning of this formula, if indeed it was correctly recorded. What is intended here is probably the formula for the potential energy \(U\) of a body of mass \(m\) in the gravitational field. where \(g\) is the gravitational constant and \(z\) the \(z\)-coordinate. In fact, the thoughts presented in Note 40 show that \(E = mc^2\) plays the role of a potential energy of sorts (resting energy), though it is not directly significant for calculations in non-relativistic mechanics. If \(p\) is interpreted as force in the sense of potentia , the formula \(W = p \times s\) represents the work \(W\) of an unchanging force \(p\) over a distance of \(s\).

The Fourth Dimension

Questions and Answers XII

https://rsarchive.org/Lectures/GA324a/English/AP2001/19200307q02.html

Stuttgart

7 Mar 1920

GA324a-21

FIRST QUESTION: Does my attempt to define the hyper-imaginary through relationships of points on curved surfaces, or manifolds, correspond to reality? SECOND QUESTION: Is it possible to acquire an enlivened view of the realm of imaginary numbers, and do actual entities underlie this realm? THIRD QUESTION: Which aspects of modern mathematics, and which formal aspects in particular, need to be developed further along spiritual scientific lines? Let [Note 54] me begin with your second question. The answer is not easy to formulate because in order to do so, we must leave the realm of visualization to a very great extent. When I answered Dr. Muller's question several days ago, [Note 55] you saw that in order to provide a concrete correlate for a mathematical case, I had to turn to the transition from long bones to head bones, and yet the graphic example was still valid. [Note 56] At least in that case we were still able to visualize the objects and hence the transition from one to another. When we attempt to look at the domain of imaginary numbers as a spiritual reality, [Note 57] we find that we need to shift from positive to negative, as I recently demonstrated in these lectures on physics. [Note 58] This shift makes our ideas true to reality when we attempt to understand certain relationships between so-called ponderable matter and so-called imponderables. But even when we visualize very ordinary domains, we can see the need to transcend customary ways of illustrating them. Let me mention just one example. On a plane drawing of the ordinary spectrum, we can draw a straight line from red through green to violet. [Note 59] Such a drawing, however, does not symbolize all the relevant aspects, which are encompassed only when we draw a curve, more or less in this plane (reference to a drawing that has not been preserved), to symbolize the red. Then, to depict the violet, we go to the board and behind the board, so that the red, as seen from above, lies in front of the violet. I would have to move out of the plane for the red and back into it for the violet in order to characterize the violet as moving inward toward chemical activity and the red as moving outward toward warmth. [Note 60] Thus, I am forced to expand the straight line here and to see my ordinary drawing as a projection of what I actually ought to draw. To achieve clarity concerning certain phenomena of higher reality, it is not enough to shift from the positive material aspect to the negative. That is just as unsatisfactory as moving in a straight line from red through green to violet. When we move from the spatial realm to the non-spatial (as symbolized by positive and negative, respectively), we must shift to a higher form of spatial and non-spatial. This process is like moving along a spiral, instead of moving around a circle and returning to our starting point. Just as elsewhere two different types may be summed up in a union that contains both, we also can imagine the existence of something that is both spatial and non-spatial. We must seek this third element. In the domain of higher reality, if we describe physical reality as positive, we are obliged to describe the etheric realm, where we leave space and begin to enter spirit, as negative. [Note 61] When we take the step into the astral realm, however, space and negative space are no longer enough. We must turn to a third element that relates to positive and negative space in exactly the same way that imaginary numbers relate to positive and negative numbers in formal mathematics. And if we then take the step from the astral realm to the true being of the "I," we need a concept that is hyper-imaginary in relationship to the imaginary. For this reason, I have never been happy with academic antipathy to the concept of hyper-imaginary numbers, because this concept is truly needed when we ascend to the level of the "I" and cannot be omitted unless we want our mathematical formulations to leave the realm of reality. [Note 62] The issue is simply how to use the concept correctly in purely formal mathematics. Someone I met today discussed the problem of probability, a question that very clearly demonstrates the great difficulty of relating a mathematical procedure to reality. Insurance companies can calculate when a person is likely to die, and their figures are very accurate when applied to groups. It is impossible, however, to conclude from actuarial figures that any individual is going to die exactly in the year that is predicted. Consequently, these calculations lack reality. The results of calculations are often correct in a formal respect yet do not correspond to reality. We also might have to rectify the formal aspects of mathematics in some instances to accord with such results of hyper-empirical reality. For example, is it correct to state that \(a \times b = 0\) is true only when one of the factors is zero? When either \(a\) or \(b\) is equal to zero, their product certainly is zero. But is it possible for the product to equal zero when neither of the two factors is zero? Indeed, this might be possible if the reality of the situation forced us to turn to hyper-imaginary numbers, which are the correlates of hyper-empirical reality. [Note 63] We must indeed attempt to clarify the relationship of real to imaginary numbers and the relationship of hyper-imaginary numbers to imaginary and real numbers, but we also may have to modify the rules governing calculations. [Note 64] With regard to your first question, in the human being we can distinguish only what lies above a certain level and below a certain level. I explain this to almost everyone I think will be able to understand it. To anyone who looks at the wooden sculpture in Dornach of Christ in the center as the representative of humanity, with Ahriman and Lucifer on either side, I explain that we truly must imagine the human beings we encounter as existing in a state of balance. On one side is the suprasensible, on the other the subsensible. Each human being always represents only the state of balance between the suprasensible and the subsensible. Of course, the human being is a microcosm of sorts and as such is related to the macrocosm. Therefore, we must be able to express the connection between each detail of the human being and a corresponding phenomenon in the macrocosm. Let me illustrate it like this: If this is the plane of balance (reference to a drawing that has not been preserved) and I imagine the subsensible element in the human being as a closed curve and the suprasensible element, or what human beings have in their consciousness, as an open curve, the resulting form is knotted below and opens outward above. This also represents how the human being is incorporated into the macrocosm. This lower, knob-like area pulls us out of the macrocosm, while the open curve of this upper surface incorporates us into the macrocosm. Here is the approximate location of freely willed human decisions. Above the level of free will, human forces are allowed to move out into the macrocosm. Everything below this level encloses macrocosmic forces so that we can assume a specific form. Within the plane figures formed by this curve, let's note a series of data that I will call \(x\), representing the cosmic thoughts that we can survey. Here we have the cosmic forces that can be surveyed and here the cosmic movements. If I formulate a function involving these numbers up here, the result corresponds to what is down here in the human being. We need a function of factors \(x\), \(y\), and \(z\). When I attempt to find numbers that express this relationship, however, I cannot find them in the domain of the number system that is available on this plane. In order to connect the suprasensible and the subsensible human being, I must resort to equations containing numbers that belong to systems lying on curved surfaces. These surfaces can be more precisely defined as the surfaces lying on paraboloids of revolution, surfaces that emerge when cones rotate in such a way that each rotating point constantly changes speed. [Note 65] There are also more complicated rotational paraboloids whose points, instead of maintaining fixed relationships among each other, are able to change within the limits of certain laws. Thus, the surfaces that serve my purpose are enlivened rotational paraboloids. The relationship I am describing is extremely difficult. To date, certain individuals have imagined it, and the need for it has been discovered, but formal calculations will become possible only once esoteric or spiritual science is able to collaborate with mathematics. The path you have outlined for us today constitutes a beginning, a possible initial response to the challenge to discover what corresponds to the association of related functions that refer to number systems on the surfaces of two rotational paraboloids (one that is closed below and one that is open above) whose vertices meet in one point. As I have described, we would simply need to find the numbers lying on these surfaces, which do indeed correspond to a real situation. With regard to the future development of formal mathematics, I must admit that it seems that much remains to be done and that much is possible. My next comment may do formal mathematics an injustice, since I have been less able to keep up with it in recent years. It has been a long time since I was fully aware of what is going on in this field, and things may have changed. Before the turn of the century, however, I always had the feeling that the papers published in the field of formal mathematics were terribly unconcerned about whether their calculations and operations were actually possible at all, or whether they would need to be modified at a certain point in accordance with some real situation. For example, we can ask what happens when we multiply a one-dimensional manifold by a two-dimensional manifold. Although it is possible to answer such questions, we must nonetheless wonder whether an operation like this corresponds to any reality at all or even to anything we can imagine. In order to get somewhere, it may be necessary to define clearly the concept of "only calculable." As an example, a long time ago I attempted to prove the Pythagorean theorem in purely numerical terms, without resorting to visual aids. [Note 66] It will be important to formulate the purely arithmetical element so strictly that we do not unwittingly stray into geometry. When we calculate with numbers — as long as we stay with ordinary numbers — they are just numbers, and there is no need to talk about number systems in specific domains of space. When we talk about other numbers, however — imaginary numbers, complex numbers, hypercomplex numbers, hyper-imaginary numbers — we do have to talk about a higher domain of space. You have seen that this is possible, but we have to leave our ordinary space. That is why I feel that before purely formal mathematics sets up numbers that can only be symbolized — and in a certain sense, applying additional corresponding points to specific domains of space is symbolization — we must investigate how such higher numbers can be imagined without the help of geometry, [Note 67] that is, in the sense that I can represent a linear function through a series of numbers. We would have to answer the question of how to imagine the relationship of positive and negative numbers on a purely elementary level. Although I cannot provide a definitive answer, because I have not concerned myself with the subject and do not know enough about it, Gauss's solution — namely, to assume that the difference between positive and negative is purely conceptual — seems inadequate to me. [Note 68] Dühring's interpretation of negative numbers as nothing more than subtraction without the minuend seems equally inadequate. [Note 69] Dühring accounts for the imaginary number a/-1 in a similar way, but this number is nothing more than an attempt to perform an operation that cannot be carried out in reality, though the notation for it exists. [Note 70] If I have 3 and nothing I can subtract from it, 3 remains. The notation for the operation exists, but nothing changes. In Dühring's view, the differential quotient is only a notated operation that does not correspond to anything else. [Note 71] To me, Dühring's approach also seems one-sided, and the solution probably lies in the middle. We will get nowhere in formal mathematics, however, until these problems are solved. Questions posed by Enist Blümel (1884–1952) after his lecture "Über das Imaginäre und den Begriff des Unendlichen und Unmöglichen" ("On the Domain of the Imaginary and the Concepts of Infinity and Impossibility") on March 11, 1920. Blümel taught mathematics in the school of continuing education at the Goetheanum in Dornach and in the first Waldorf School in Stuttgart. To date, no transcript of his lecture has been found. Ernst Müller (1884–1954), mathematician, author, and Hebraic and cabalistic scholar, gave a lecture on "Methoden der Mathematik" ('The Methods of Mathematics") in Stuttgart on March 8, 1920. To date, neither a transcript of Müller's lecture nor a record of Steiner's answer to his question has been found. For further discussion of the metamorphosis of long bones into head bones, see also Steiner's lectures of September 1, 1919 (GA 293), — April 10, 1920 (GA 201); and January 1, 10, 11, 15, and 17, 1921 (GA 323). 0n the reality of imaginary numbers, see also Steiner's lectures of March 12, 1920 (GA 321), and January 18, 1921 (GA 323). ’’Lectures on physics: Rudolf Steiner, Geisteswissenschaftliche Impulse zur Entwickelung der Physik: Zweiter Naturwissenschaftlicher Kurs, Die Wärme auf der Grenze Positiver und Negativer Materialität ("Spiritual Scientific Impulses for the Evolution of Physics: Second Natural Scientific Course. Warmth on the Boundary Between Positive and Negative Matter") (GA 321). See especially the lectures of March 10 and 11, 1920. Compare the passage that follows with Steiner's lectures of March 12 and 14, 1920 (GA 321). A collection of materials on an experiment in bending the spectrum using a strong magnet can be found in Beiträge zur Rudolf Steiner Gesamtausgabe ("Articles on Rudolf Steiner's Complete Works"), vol. 95/96, 1987. A variant of the text reads "The red moves outward toward the position/situation/ Iayer," which makes no sense in either English or German. See Steiner's explanations of the ether and negative space in his lectures of January 8, 15, and 18, 1921 (GA 323); the question-and-answer session of April 7, 1921 (GA 76), the lectures of April 8 and 9, 1922 (GA 82), — and the questions and answers of April 12, 1922 (GA 82). In a lecture given on May 11, 1917 (GA 174b), Rudolf Steiner tells of a related personal experience during a class at the University of Vienna. According to Steiner's account, Leo Königsberger (1837–1921), a well-known mathematician of the day, rejected the concept of hypercomplex numbers because they would lead to zero factors (see Note 18). Just as complex numbers were slow to gain recognition, hyper-imaginary or hypercomplex numbers were only reluctantly accepted by mathematicians. The difference of opinion between adherents of the calculus of quaternions dating back to William Rowan Hamilton (1805–1865) and advocates of the vector analysis developed by Oliver Heaviside (1850–1925) and Josiah Gibbs (1839–1903) formed the background of the debate Rudolf Steiner alludes to here. Vector analysis initially gained the upper hand in practical applications because of the progress in theoretical physics that accompanied its development. At approximately the same time, however, the development of abstract algebra led to the discovery and classification of different systems of hypercomplex numbers. For more information on the above-mentioned debate, see Schouten [1914] (introduction) and Crowe [1967], On the history of the discovery and refinement of hypercomplex number systems, see Van der Waerden [1985], — on the mathematics of hypercomplex numbers, see Ebbinghaus et al. [1988], Part B. These and other generalized number systems have many applications in modern theoretical physics, — see Gschwind [1991] and the bibliography to his book. In his lecture of May 11, 1917 (GA 174b), Rudolf Steiner reports becoming aware of the mathematical problem of zero factors during a lecture by Leo Königsberger. Zero factors are generalized numbers whose product is zero, though the factors themselves are not equal to zero. Königsberger mentions this problem in the first lecture in his book Vorlesungen über die Theorie der elliptischen Funktionen ("Lectures on the Theory of Elliptical Functions") [1874], pp. 10-12, where he says of the existence of hypercomplex numbers, "Assuming that the validity of common rules of calculation for all arithmetic quantities remains a condition that must be met, if quantities of this sort can be incorporated into pure arithmetic, calculations that involve them and that are carried out according to the rules established for the numbers discussed earlier must lead to results that do not contradict the main propositions/theorems of arithmetic that have been discovered for real and complex imaginary numbers. Thus, according to the rules for multipart expressions, multiplying two numbers of the same type must yield a number of the same type, and the product cannot disappear unless one of the factors becomes zero." The passage that follows demonstrates concretely that the product of two such hypercomplex numbers can indeed disappear without one of the factors being zero, "which contradicts the basic rule for real numbers that a product of zero results only when one of the factors disappears." Later, Steiner received a copy of Oskar Simony's paper Über zwei universelle Verallgemeinerungen der algebraischen Grundoperationen ("On Two Universal Generalizations of Basic Algebraic Operations") [1885] with a personal dedication by the author. Simony discusses the problem of the existence of zero factors at the very beginning of this article, which is devoted to the concrete construction of two systems of hypercomplex numbers, one of which includes zero factors ([1885], §8). Additional material on this subject can be found in Beiträge zur Rudolf Steiner Gesamtausgabe ("Articles on Rudolf Steiner's Complete Works"), vol. 114/115, Dornach, 1995, p. 5. Schouten's work [1914], also with a personal dedication to Rudolf Steiner, includes an introduction to hypercomplex number systems (which Schouten calls associative systems), — zero factors are mentioned on p. 15. See Gschwind's investigations [1991] and list of references for further reading. The typed transcript reads "rotational parallelepopods," a term that does not exist in mathematics and that is probably due to an error in transcription. It seems unlikely from the context that the term "parallelopipeds" was intended. In all the transcripts the archives have received, the term "parallelepopods” is crossed out and replaced by "paraboloids" (in handwriting). Rotational paraboloids are surfaces that result from the rotation of a parabola around its axis of symmetry. This interpretation of the transcript presents the problem of how to relate such a surface to rotating cones. Without going into the problem in greater detail, Gschwind [1991] had good reasons for deciding on this wording and based important and fruitful conclusions on it. Specifically, he demonstrated a relationship between such surfaces and hypercomplex numbers. Exhaustive supplementary material can be found in Beiträge zur Rudolf Steiner Gesamtausgabe ("Articles on Rudolf Steiner's Complete Works"), vol. 114/115, Domach, 1995, pp. 5-7. Presumably Rudolf Steiner is referring here to the problem in number theory of finding whole numbers that can replace \(a\), \(b\), and \(c\) in the equation \(a^2 + b^2 = c^2\). Such numbers are known as Pythagorean triplets . Algorithms for finding all possible solutions to this equation — that is, all possible Pythagorean triplets have been known since antiquity. Rudolf Steiners call for establishing the foundations of arithmetic and algebra independent of geometry had already been taken up at the end of the nineteenth century, when the tendency to arithmeticize mathematics sometimes went so far that it threatened to displace geometry. It was one of the most important mathematical accomplishments of the early twentieth century, though initially it remained an internal issue in the field of mathematics. Some time elapsed before this development found its way into textbooks and the teaching of mathematics. Carl Friedrich Gauss (1777–1855), mathematician in Göttingen who explained negative numbers as simply the opposites of positive numbers. He presented his general views on the subject in his Theoria Residuorum Biquadraticorum [1831], pp. 175ff: "Positive and negative numbers can be applied only where the union of a quantity and its opposite eradicates that quantity. Precisely speaking, this prerequisite does not apply when substances (that is, objects that can be imagined as standing on their own) are involved but only in relationships between objects that are enumerated. It is postulated that these objects are arranged in a series, such as \(A\), \(B\), \(C\), \(D\), . . ., and that the relationship of \(A\) to \(B\) can be considered the same as that of \(B\) to \(C\), and so on. In this case, the concept of opposites means nothing more than reversing the members in a relationship, so that if the relationship between (or transition from) \(A\) to \(B\) is \(+1\), the relationship of \(B\) to \(A\) can be described as \(-1\). Inasmuch as such a series has no limits in either direction, each real whole number represents the relationship between a member that has been selected arbitrarily as the beginning and another specified member of the series." See also the discussion in Kowol [1990], pp. 88ff. Eugen Dühring (1833–1921), philosopher and author of books on political economy. See especially the book he coauthored with his son Ulrich [1884], which contains harsh criticism of Gauss' definition of negative numbers. According to the Dührings, the contrast or opposition that characterizes negative numbers results from unimplemented subtraction, which they view as the only essential aspect of negative numbers. See [1884], p. 16: "The incisive characteristic of an isolated negative number, however, is that it not only results from a numerical operation in which subtraction cannot be carried out but also points to an operation in which subtraction can be implemented. We must carefully distinguish between these two operations — or, if you will, these two parts of a general operation." For a comparison between Gauss' and Dühring's views on negative numbers, see Kowol [1990], p. 88 ff. On Dührings view of imaginary numbers, see E. and U. Dühring [1884], Chapters 2-4, and 13. A discussion of Dührings thoughts compared with other attempts to deal with this issue can be found in Kowol [1990], pp. 118ff. and 122ff. See E. and U. Dühring [1884], Chapters 4, 12, 14, and 15.

The Fourth Dimension

Questions and Answers XIII

https://rsarchive.org/Lectures/GA324a/English/AP2001/19200311q01.html

Dornach

11 Mar 1920

GA324a-22

FIRST QUESTION: The Question is, does such an understanding correspond to reality? Since what we did in simple geometry also would have to be possible in all domains of mathematics, could understanding mathematical objects as intermediary links between archetype and physical image perhaps serve as a foundation for the types of calculations needed to support the physics presented in this lecture? SECOND QUESTION: Might this be a path to the so-called hyper-empirical realm that we reach by controlling and enhancing our thinking? If I understand your first question correctly, you are asking whether we can approach the realm of mathematics as an intermediary stage between archetype and physical image. [Note 72] [Note 73] Let's look at the domains of mathematics from a purely spiritual and empirical perspective. What are the spatial and geometric domains of mathematics? Or were you thinking of arithmetic as well? Alexander STRAKOSCH: I was thinking of geometry. During this lecture series, I have already suggested parenthetically how we arrive at ordinary geometric figures. [Note 74] We do not discover them by abstracting from empirical ideas. Initially, mathematical and geometric figures are an intuition of sorts. They are derived from the will nature of the human being, so we can say that when we experience mathematical figures, it is always possible for us to be active and to relate to reality in the mathematical domain. Thus, such figures, even on an empirical level, already represent a type of intermediate state between external realities (which we can possess only in image form) and the direct contents of being (which we experience inwardly). A spiritually empirical perspective would show that when we understand geometry, we grasp an intermediate stage between archetype and physical image. However, there is something we must still do in order to verify this train of thought. If geometric and mathematical figures are indeed intermediate states between archetype and image, they must have a certain non-material ideal attribute that images do not have, though it only becomes so non-material in the sphere of images. An image also can be a combination, — it does not necessarily correspond to its archetype. Any mere image that we confront need not correspond to an archetype. But if we have an intermediate state that incorporates a certain amount of reality, we need to be able to discover a corresponding specific field of reality, and we cannot combine such domains arbitrarily. We can never combine archetypes in a living way, — we must seek them out in their own domains, where they are present as distinct experiences. Thus, in order to grasp this middle domain in the right way, what you called the domain of the perceived lawfulness of mathematical objects, we also must understand its construction as an intermediate state between absolute, fixed archetypes and a boundless number of images. That is, we would have to interpret all of mathematics, and especially geometry, as inherently mobile, as existing at least in latent form in all of reality. For example, we could not imagine a triangle as immobile but would have to visualize the full scope of the concept. What is a triangle? A triangle is an area bounded by straight lines, and the sum of its angles is 180°. We would have to imagine the lengths of its three sides as being infinitely variable, and our definition would yield an infinite number of triangles, or a triangle in flux. This way of looking at things would result in a fluid geometry. [Note 75] We would have to be able to prove that this fluid geometry has some significance for the natural kingdom — that it corresponds to an aspect of the law of crystallization, for example. So the answer to your question is yes, this view is indeed based on an idea that corresponds to reality, but a great deal remains to be done to make the entire concept clear. I must still touch on another subject that plays into all this. You see, in recent times people have made a habit of taking refuge in higher dimensions when they want to enter higher domains of reality. That was not always the case in the formalism that formed the basis of our conceptions of the occult. In earlier times, people said that while we must conceive of ordinary physical figures as three dimensional, figures belonging to astral space must be seen in the context of a two-dimensional plane. Note that I am now talking about the spheres or planes of existence, and therefore the term astral is used in a sense different from the one I used when talking with Mr. Blümel and describing the steps between the physical body and the "1." We must imagine the next level, the Rupa plane, as one-dimensional in scope, and when we imagine the Arupa plane, we arrive at a point. [Note 76] In this way we can say that as we move toward more spiritual ideas, the number of dimensions must decrease rather than increase. We are subject to this phenomenon when we move from above to below, as we do, for example, when we attempt the following train of thought. We can distinguish quite well among spirit, soul, and body. But what is the spiritual element in a human being walking around on Earth? We must say that this spiritual element is present in an extremely filtered form. We humans owe our abstract thinking to the spirit; it is the spiritual element in us. On its own, it tends to perceive only sense-perceptible objects and events, but the means of perceiving is spiritual. When we trace the spirituality of thinking down into the bodily element, we find that it has an expression in the human physical body, while the more comprehensive spiritual element has no such expression. Crudely speaking, one-third of the spiritual world in which we humans take part has an expression in the physical human body. Moving on to the soul, two-thirds of the spiritual world in which humans take part achieve expression in the physical human body. And when we move on to the physical body, three-thirds has achieved expression. As we move from above to below, we must imagine that in the progression from the archetype to its image, the archetype easily leaves aspects of its being behind, and this phenomenon provides the essential characteristic of our physical aspect. In contrast, as we move upward, we discover new elements that have not been incorporated into the image. As we move downward, however, what we encounter is not merely an image, — reality plays into it. It is not true that at night when the physical and ether bodies are lying in bed, the astral body and "I" simply pull out of the body and leave it empty. Higher forces enter the physical and ether bodies and enliven them while the astral body and "1" are gone. Similarly, an image contains elements that do not originate only in its archetype. These elements enter when the image becomes an image, when it belongs to the entity. Then the interesting question arises, How does a merely imaginatively combined image become a real image? That is when the other subject I mentioned enters in. Let me still comment that when we consider two dimensions, our initial train of thought leads directly to a second that can illuminate the first. All two-dimensional figures can be drawn in two dimensions, but figures that occupy three-dimensional space cannot. Suppose, however, that I begin to sketch a picture using colors instead of drawing in perspective or the like — that is, I copy colors, — I supply images of colors. Anyone will admit that I am then incorporating space directly into the plane to form the image. At this point I may ask, Does what expresses color in this image lie in any of the three dimensions of space? Is it possible to use colors to suggest something that can replace the three dimensions? Once we have an overview of the element of color, we can arrange colors in a specific way that creates an image of three-dimensionality in two dimensions. Anyone can see that all blues tend to recede, while reds and yellows advance. Thus, simply by supplying color, we express three dimensions. By using the intensive aspect of color to express the extensive aspect of three-dimensionality, we can compress three-dimensionality into two dimensions. By linking other thoughts to this train of thought, we arrive at fluid geometry. And we may indeed be able to expand geometry to incorporate considerations such as this: In mathematics, we can construct congruent triangles A and B, but could we not also discover an expanded mathematical connection between red and blue triangles drawn in a plane? Is it really permissible for me simply to draw the simple lines that form a red triangle in the same way that I draw a blue triangle? Would I not have to state expressly that when I draw a red triangle and a blue one in the same plane, the red one would have to be small just because it is to represent red, while the blue one would have to be large simply because it is blue? Now the question arises, Is it possible to incorporate an intensity factor into our geometry, so that we can perform calculations with intensities? This would reveal the full significance of how our right and left eyes work together. Stereoscopic vision depends on both eyes working together. In the domain of optics, this phenomenon is the same as grasping my left hand with the right. A being that could never touch one part of its body with another would be physically incapable of conceiving of the "I." This conception depends on being able to touch one part of my being with another. I can experience myself as an "I" in space only because of a phenomenon that is slightly hidden by ordinary empiricism, namely, the fact that my right and left vision crosses. This fact, though it does not encompass the reality of the "I," allows us to form a correct conception of the "I." Now imagine how our physical ability to conceive of the "I" would be affected if our eyes were strongly asymmetrical instead of more or less symmetrical. What if your left eye, for example, was significantly smaller than the right, making your left and right stereoscopic images very different? Your left eye would produce a smaller image that it would constantly attempt to enlarge, while your right eye would have to attempt the opposite, namely, to reduce the size of its image. These efforts would add an enlivened form of vision to your static stereoscopic vision. Real enlivened vision, however, must be achieved as soon as you even begin to approach imaginative perception. This perception results from constantly having to adapt asymmetrical elements to each other. The central figure in the Dornach sculpture had to be depicted as strongly asymmetrical in order to show that it is ascending to the spirit. It also suggests that every aspect of the human being — for example, our stereoscopic vision — is basically a state of balance that constantly deviates toward one or the other pole. We are human because we must continually create a state of balance between above and below, forward and back, and left and right. Question-and-answer session during the lecture cycle Geisteswissenschaftliche Impulse zur Entwickelung der Physik: Zweiter Naturwissenschaftlicher Kurs ("Spiritual Scientific Impulses for the Development of Physics: Second Scientific Course") (GA 321). Alexander Strakosch (1879-1958), railway engineer and teacher at the first Waldorf School in Stuttgart, asked these questions after giving a lecture on "Mathematical Figures as an Intermediate Link Between Archetype and Copy" in Stuttgart, March 11, 1920. To date no transcript of his lecture has been found. On the relationship between archetype and image in the context of mathematics, see also Rudolf Steiners essay on "Mathematics and Occultism" in Philosophy and Anthroposophy (GA 35). In the lecture of March 5, 1920 (GA 321). For further discussion of the evolution of geometric and mathematical views arising out of the will nature of the human being, see also Rudolf Steiner's lectures of January 3, 1920 (GA 320), — September 29, 1920 (GA 322), — March 16, 1921 (GA 324); and December 26, 1922 (GA 326). For a further discussion of fluid or mobile geometry, see also Rudolf Steiner's lecture of January 20, 1914 (GA 151). For more on the relationships between the planes or regions of the spiritual world and the higher dimensions, see also Rudolf Steiner's lectures of May 17 and June 7, 1905, — the question-and-answer sessions of April 7, 1921 (GA 76) and April 12, 1922 (GA 82), and the lectures of August 19, 20, 22, and 26, 1923 (GA 227). Ernst Blümel (1884–1952), mathematician and teacher. See Renatus Ziegler's Notizen zur Biographie des Mathematikers und Lehrers Ernst Blümel ("Notes on the Biography of Ernst Blümel, Mathematician and Teacher"), Dornach, 1995, in Arbeitshefte der Mathematisch-Astronomischen Sektion am Goetheanum , Kleine Reibe, Heft 1 ("Working Papers of the Section for Mathematics and Astronomy at the Goetheanum, Short Series, No. 1").

The Fourth Dimension

Questions and Answers XIV

https://rsarchive.org/Lectures/GA324a/English/AP2001/19200311q02.html

Dornach

11 Mar 1920

GA324a-23

QUESTION: How will anthroposophy affect the further evolution of chemistry? Assuming [Note 77] that we undertake the type of phenomenology described by Dr. Kolisko, this question is so all-encompassing that the answer can only be hinted at. First and foremost, we must realize that we would have to develop an appropriate phenomenology. Phenomenology is not simply an arbitrary assemblage of phenomena or experimental results. Real phenomenology is a systematization of phenomena, such as that attempted by Goethe in his theory of color. [Note 78] It derives the complicated from the simple, leading back to the foundations where the basic elements or phenomena appear. Of course, I am quite aware that some truly intelligent people will argue that a sophisticated presentation of the connection between qualitative phenomena and archetypal phenomena is not comparable to the way in which complicated geometric relationships are mathematically derived from axioms. This is because geometric relationships are systematized on the basis of intrinsic structure. We experience the further development of mathematics from these axioms as an inherently necessary continuation of the mathematical process, while, on the other hand, we must depend on observing a physical state of affairs when we systematize phenomena and archetypal phenomena. This argument, though it enjoys widespread support, is not valid and is simply the result of an incorrect epistemology, specifically, a confused mingling of the concept of experience with other concepts. This confusion results in part from failure to consider that human subjects shape their own experience. It is impossible to develop a concept of experience without imagining the connection of an object to a human subject. Suppose I confront a Goethean archetypal image. When I make it more complicated, the result is a derivative phenomenon, and I seem to depend on outer experience to support my conclusion. Is there any difference, in principle, between this subject-object relationship and what happens when I demonstrate mathematically that the sum of the three angles in a triangle is 180° or when I prove the Pythagorean theorem empirically? Is there really any difference? In fact, there is no difference, as became evident from studies by very gifted nineteenth- and twentieth-century mathematicians who realized that mathematics ultimately also rests on experience in the sense in which the so-called empirical sciences use the term. These mathematicians developed non-Euclidean geometries that initially merely supplemented Euclidean geometry. [Note 79] Theoretically, the geometric thought that the three angles of a triangle add up to 380° is indeed possible, though admittedly we must presuppose that space has a different rate of curvature. [Note 80] Our ordinary space has regular Euclidean measurements/ dimensions and a rate of curvature of zero. Simply by imagining that space curves more, that is, that its rate of curvature is greater than I, we arrive at statements such as: The sum of the three angles of a triangle is greater than 180°. Interesting experiments have been conducted in this field, such as those of Oskar Simony, who has studied the subject in greater detail. [Note 81] Such efforts show that from a certain perspective, it is already necessary to say that conclusions we state in mathematical or geometric theorems need empirical verification as much as any phenomenological conclusions. Question-and-answer session after Eugen Kolisko's lecture on "Anthroposophy and Chemistry" during the conference on "Anthroposophy and the Specialized Sciences" held at the Goetheanum in Dornach from March 21 to April 7, 1920. Eugen Kolisko (1893–1939) was a physician and taught at the first Waldorf School in Stuttgart. To date, no transcript of his lecture has been discovered. See the brief report on the conference in the journal Dreigliederung des sozialen Organismus ('The Threefolding of the Social Organism"), vol. 1, 1919/1920, no. 45. Goethe, Zur Farbenlehre ("On Color Theory") [1810] and Der Versuch als Vermittler von Objekt und Subject ('The Experiment as Mediator Between Object and Subject") [1823]. See Rudolf Steiner's Einleitungen zu Goethes Naturwissenschaftlichen Schriften ("Introduction to Goethe's Natural Scientific Works," GA 1), chapters X and XVI; Grundlinien einer Erkenntnistheorie der Goetheschen Weltanschauung ("Outline of an Epistemology of the Goethean Worldview," GA 2), chapter 15; and the chapter in Goethe's Weltanschauung ("Goethe's Worldview," GA 6) entitled Die Erscheinungen der Farbenwelt ('The Phenomena of the World of Color"). The discovery of non-Euclidean geometries showed that Euclidean geometry was not the only imaginable geometry. As a result, the question of which type of geometry applies to the space we experience became an epistemological problem for the sciences. For more on the impact of the discovery of non- Euclidean geometries, see also Rudolf Steiner's lectures of August 26, 1910 (GA 125); October 20, 1910 (GA 60); January 3, 1920 (GA 320),- March 27, 1920 (GA 73a),- January 1 and 7, 1921 (GA 323); and April 5, 1921 (GA 76). On the importance of the discovery of non-Euclidean geometry in the history of consciousness, see Ziegler [1987], On the history of this discovery, see Bonola/Liebmann [1919],- Klein [1926], chapter 4; and Reichardt [1976]. On the relationships of axioms, archetypal phenomena, and experience, see Ziegler [ 1992], chapters VII and VIII. In an elliptical geometry such as Riemann's (Riemann [1867]), the rate of curvature of measurement is greater than 1, and the sum of the angles of a triangle is always greater than 180°. In hyperbolic geometry , the rate of curvature of measurement is less than 1, and the sum of the angles of a triangle is always less than 180°. The relationship of spaces or manifolds with a constant curvature to non-Euclidean geometries was discovered by Eugenio Beltrami (1835–1900) and Bernhard Riemann (1826–1866). In contrast to Euclidean geometry (Pythagorean theorem), the measurement of such a space is determined by a function of the coordinates. In general, this function is no longer a sum of squares. On this subject, see Klein [1927], chapter 3C, and Scholz [1980], chapter III. See Simony [1888b], §5; [1883]; and [1886].

The Fourth Dimension

Questions and Answers XV

https://rsarchive.org/Lectures/GA324a/English/AP2001/19200330q01.html

Dornach

30 Mar 1920

GA324a-24

QUESTION: Ordinary mathematics encompasses the forms, surfaces, and lines of force of solids, liquids, and gases. How would you imagine a mathematics of the domains of warmth, chemistry, and life? First of all, the field of mathematics as such would need to be appropriately expanded if we want to describe higher realms in a way that is analogous — but no more than analogous — to mathematics. As you may know, the need to expand mathematics became evident already in the nineteenth century. [Note 82] Let me just mention a point I have discussed on other occasions — including yesterday, I believe. [Note 83] In the late nineteenth century, it became apparent that a non-Euclidean geometry was needed to supplement Euclidean geometry and to make it possible to carry out calculations involving higher dimensions. Mathematicians of that time were suggesting that mathematics needed to be expanded. [Note 84] In contrast, as long as we are considering ordinary, ponderable matter, there is no appropriate use for dimensions other than the three ordinary Euclidean dimensions. Mathematicians today, however, are so disinclined to explore appropriate views of the domains of warmth, chemical effects, and the elements of life that extending mathematical thinking into these areas is really very problematic. [Note 85] The views mathematicians propound today certainly do not create a counterbalance to the professed inability of physics to grasp the essential nature of matter. And to be consistent, physicists would have to admit that physics does not deal with the essential nature of light but only with what Goethe calls the image of light. Of course, sensible physicists will refuse to delve into the essential nature of things in the pursuit of their profession. Admittedly, the result is an unfortunate state of affairs: Physicists refuse to deal with the essential nature of things on any level. And those who concoct philosophies from the conventional, material views of physics not only refuse to inquire into the essential nature of things but even claim that it is impossible to do so. As a result, our view of the Earth today is very one-sided, because, in fact, physics is never simply a matter of geology but deals with the sum total of what such a specialized field can yield for general knowledge. Thus, we face the adverse consequences of the mechanistic, non-mathematical worldview that physics has developed over time. What Goethe meant when he said that we should not talk about the being or nature of light but rather should attempt to become familiar with the facts about it, with its deeds and sufferings — which yield a complete description of the nature of light — is by no means the same as refusing on principle to consider the question of the nature of light. Goethe's statement simply points out that true phenomenology (structured in the way we discussed here yesterday) [Note 86] ultimately does provide an image of the being in question. [Note 87] To the extent that physics is or intends to be real phenomenology, it does provide — at least with respect to mechanics — an image of the essential nature of phenomena. It can be said therefore that when we are not dealing with merely mechanical aspects of the phenomena of physics — that is, when we are dealing with fields other than mechanics — a mechanistic view hinders our ability to recognize the essential nature of things. To this extent, then, we do need to emphasize the radical difference between Goethe's intended phenomenology, which can be cultivated in Goetheanism, and any system whose principles rule out the possibility of approaching the true nature of things. This has nothing to do with the advantages of mechanistic methods for our urge to control nature. [Note 88] It is quite understandable that the field of technology and mechanics — which has produced the greatest triumphs of the last few centuries — and its mechanistic basis for understanding nature should satisfy our urge to control nature to a certain extent. But to what extent has this drive to understand and control nature fallen behind in other fields because they refused to press on toward the type of knowledge to which technology aspired? The difference between technology or mechanics and the fields of study beginning with physics and continuing through chemistry to biology is not that these higher fields deal only with qualitative properties or the like. The difference is simply that mechanics and mechanistic physiology are very elementary and easy-to-grasp aspects and have therefore managed to satisfy our desire for control at least to a certain extent. At this point, however, the question arises, How do we satisfy our urge to control when we move on to higher, less mechanistic fields? In the future, we will have to count on being at least somewhat able to dominate nature in ways that go beyond mere technology. Even in the technological field, we can very easily experience failures to understand and control nature. If someone builds a bridge without adequate knowledge of the laws of mechanics that apply to railways, the bridge eventually will collapse, carrying the train with it. We react immediately to inadequate control due to faulty information. The proof is not. always so easy, however, when control is based on more complicated domains that are derived not from mechanics but from the process of developing a phenomenology. It is fairly safe to say that a bridge that collapses when the third train crosses it must have been built by someone inadequately motivated to understand the mechanics involved. In the case of a physician whose patient dies, it is not so easy to confirm a similar connection between the practitioner's desire to understand and his or her control over nature. It is easier for us to say that an engineer designed a faulty bridge than that a doctor cured the disease but killed the patient. In short, we should be somewhat less hasty to emphasize the importance of our urge to control nature simply because our mechanistic view of nature has proved capable of satisfying this urge only in the domain of mechanistic technology. Other ways of looking at nature will be able to very differently satisfy our urge to control. Let me point again to something that I believe I mentioned yesterday from a different perspective. We can never bridge the gap between the mechanistic view of the world and the human being except by applying a true phenomenological approach. [Note 89] Goethe's color theory not only presents the physical and physiological phenomena of color but also makes the whole subject humanly relevant by exploring the sensory and moral effects of colors. [Note 90] In our spiritual scientific work, we can move from the effects of colors pointed out by Goethe to the broader subject of understanding the entire human being and then to the still broader subject of understanding all of nature. In some ways it may be beneficial to draw people's attention repeatedly to the fact that a large part of the decadence we experience today in Western culture is related to satisfying our urge to control only from the mechanistic perspective. In this regard, we have done very well. We not only have developed railways, telegraphs, and telephones, and even wireless and multiple telegraphy, but we also have paved over and destroyed large parts of this continent. Thoroughly satisfying our urge to control has led to destruction. Following the straight line of development that began with our purely technological urge to control has led to destruction. This destructive aspect will be eliminated completely when we replace our pathologically expanding mechanistic view of the phenomena of physics with a view that does not eradicate the specifics of physical phenomena simply by blanketing them in mechanistic ideas. We will move away from the mechanistic view, which admittedly has produced very good physiological explanations, to the specifics of the phenomena of physics. Our new view, which cannot be discussed down to its last consequences in one hour, also will lead to an expansion of mathematics that is based on reality. We must realize that in the past thirty to fifty years, confused mechanistic ideas have made possible all kinds of opinions about the so-called ether. After much effort, the physicist Planck, whom I mentioned earlier in a different context, arrived at this formulation: If we want to speak about the ether in physics at all, we cannot attribute any material properties to it. [Note 91] We must not imagine it in material terms. Planck forced physics to refrain from attributing material properties to the ether. The errors inherent in ideas and concepts about the ether are not due to having done too little mathematics or anything of that sort. They arose because proponents of the ether hypothesis were completely consumed by the trend that attempted to expand mathematics to cover the specifics of physics. Their mathematics was faulty because they behaved as if they were dealing with ponderable matter when they inserted numbers into formulas in which ether effects played a role. As soon as we realize that when we enter the domain of the ether, we can no longer insert ordinary numbers into mathematical formulas, we also will feel the need to look for a true extension of mathematics itself. There are only two points that need to be made in this regard. The physicist Planck says that if we want to talk about the ether in physics, we must at least refrain from attributing material properties to it. And Einstein's theory of relativity — or any other theory of relativity, for that matter — forces us to eliminate the ether completely. [Note 92] In reality, we need not eliminate it. I can give only a brief indication here, but the main point is simply that when we shift to the ether, we must insert negative numbers into the formulas of physics — that is, mathematical formulas that are applied to phenomena in physics. These numbers must be negative because when we move from positive matter through zero to the other side, as when we move from positive to negative numbers in formal physics, what we encounter in the ether is neither nothing (as Einstein believes) nor a pure negative (as Planck says) but something that we must imagine as possessing properties that are the opposite of the properties of matter just as negative numbers are the opposite of positive numbers. [Note 93] Although we may debate what negative numbers are, the purely mathematical extension of the number line into negative numbers becomes significant for reality even before we clearly understand the character of negative numbers. Of course, I am well aware of the significant mathematical debate in the nineteenth century between those who saw qualitative aspects in plus and minus signs and those who saw the minus sign only as a subtrahend lacking a negative minuend. [Note 94] This debate is not especially important, but it is important to note that when physics shifts from ponderable effects to etheric effects, it is forced to take the same route that we take in formal mathematics when we move from positive to negative numbers. We should check the results of the formulas when we decide to handle the numbers in this way. Much good work has been done in formal mathematics to justify the concept of formal imaginary numbers. In physics, too, we are obliged at a certain point to substitute imaginary numbers for positive and negative numbers. At this point, we begin to interact with numbers relevant to nature. I know that I have sketched all this very briefly and summed it up in only a few words, but I must make you aware of the possibilities. As we move from ponderable matter to the forces of life, we must insert negative numbers into our formulas to signify the inverse of the quantitative aspect of matter. And as soon as we transcend life, we must shift from negative numbers to imaginary numbers, which are not mere formal numbers but numbers with properties derived not from positive or negative matter but from the substantial aspect that is related, qualitatively and intrinsically, to both the etheric aspect or negative matter and the ponderable aspect or positive matter in the same way that the imaginary number line relates to the real number line of positive and negative numbers. Thus, there is indeed a connection between formal mathematics and certain domains of reality. It would be highly regrettable if attempts to make our ideas approximate reality or to immerse our ideas in reality were to fail because of the trivial notion that the offerings of truly rational, rather than merely mechanistic, physics and physiology would be less effective in satisfying the human urge to control nature. In fact, they would be more effective than applying the mechanistic worldview to the technology that we have glorified to such an extent. This mechanistic technology has certainly produced great results for humanity's cultural development. But people who constantly talk about the glorious progress of the natural sciences as a result of the conventional calculations of physics should keep in mind that other areas may have suffered as a result of turning our attention totally to the technological domain. To escape from the decadence brought on by our merely technical understanding and control of nature, we would do well to turn to a physiology and physics that, unlike our mechanical and mechanistic knowledge, cannot refuse to acknowledge the essential nature of things. You see, this mechanical domain can easily dismiss the essential nature of things precisely because this essential nature is available — spread out in space all around us. It is somewhat more difficult for the entire field of physics to progress in the way that the field of mechanics has progressed. This is the reason for all of this talk of refusing to acknowledge the essential nature of things. When physicists choose to think in purely mechanical terms, they can easily refuse to understand beings. There is no being behind the formulas that are used today to express mechanics in mathematical terms. Beings begin only when we no longer simply apply these formulas but delve into the essential nature of mathematics itself. I hope this addresses the question of how to extend the field of mathematics to cover imponderables. Questions and answers after Karl Stockmeyer's lecture on "Anthroposophy and Physics" during the conference on "Anthroposophy and the Specialized Sciences" held at the Goetheanum in Dornach from March 21 to April 7, 1920. Ernst August Karl Stockmeyer (1886–1963) was a teacher at the first Waldorf School in Stuttgart. To date, no transcript of his lecture has been discovered. See the brief report on the conference in the journal Dreigliederung des sozialen Organismus ('The Threefolding of the Social Organism"), vol. 1, 1919/1920, no. 45. See the questions and answers of March 30, 1920, and Steiner's lectures of March 27, 1920 (GA 73a), and January 3, 1920 (GA 320). Bernhard Riemann (1826–1866), whom Steiner mentions repeatedly, typifies this trend. See also Note 1, Lecture 1 (March 24, 1905) on Bolyai, Gauss, and Riemann. See the beginning of the question-and-answer session on March 11, 1920 (E. Bliimel's questions) and related notes. See the question-and-answer session of March 1, 1920. Goethe says at the very beginning of the Preface to his Zur Farbenlehre ("On Color Theory") [1810]: When the subject of color is addressed, the very natural question arises of whether light should be discussed first and foremost. The brief and honest response to this question is that so much has been said about light, and so often, that it seems questionable to repeat or add to what has been said. For, in fact, our attempts to express the essential nature of light are in vain. We become aware of the effects of a being, and a complete account of them probably does encompass its essential nature. Our efforts to describe a person's character are all in vain, but if we present all of his actions and deeds, a picture of his character will emerge. Colors are the deeds of light, its deeds and sufferings. In this sense, we can expect them to yield conclusions about light. Colors and light are related very precisely, but we must think of both of them as belonging to all of Nature, because through them Nature and Nature alone attempts to reveal itself to the sense of sight. The editors of the German version, noting that the context requires a meaning of “control" or "understanding," substituted the word Beherrschung (control), here and elsewhere in the lecture for Beharrung ) (perseverance), which appeared consistently in the typescript of the stenographic notes. See also Rudolf Steiner's lecture of March 30, 1920 (GA 312), and the question- and-answer session that took place on the same date. Goethe, Zur Farbenlehre ("On Color Theory") [1810], section 6, Sinnlich-sittliche Wirkung der Farbe ('The Sensory-Moral Effect of Color"), §758-920. Max Planck (1858–1947), theoretical physicist in Munich, Kiel, and Berlin. The hypothesis of a quasi-material ether that served as the medium for light processes and electrical phenomena had its roots in the thinking of Isaac Newton (1642–1727) and René Descartes (1596–1650). This qualitative type of ether made it possible to interpret processes whose more precise mechanisms were not yet understood. The chief characteristic of nineteenth-century ether hypotheses was quantifiability, which made it possible to incorporate such processes concretely into mathematical theories on the phenomena of physics. See also the beginning of the question-and-answer session of March 7, 1920, and the corresponding notes. The exact wording of Planck's formulation has not been found. Planck [1910] emphasizes, however, "I believe that I will not encounter any serious opposition among physicists when I summarize this position as follows: Presupposing that the simple Maxwell-Hertz differential equations are fully valid for electrodynamic processes in pure ether excludes the possibility of explaining them mechanically" (p. 37). Later he says, "similarly, it is certainly correct to state that the first step in discovering [Einstein's] principle of relativity coincides with the question of what relationships must exist between natural forces if it is impossible to ascribe any material properties to the light ether — that is, if light waves replicate through space without any connection to a material vehicle. In that case, of course, it would be impossible to define — let alone measure — the speed of a moving body with regard to the light ether. I need not emphasize that the mechanical view of nature is virtually incompatible with this view. Thus, anyone who sees this view as a postulate of the thinking of physics will never be comfortable with the theory of relativity. Those who are more flexible in their judgments, however, will first ask where this principle leads us" (p. 39). See the question-and-answer session of March 7, 1920, and the corresponding notes. Compare this and the following passages to the question-and-answer sessions of March 11, 1920 (Blümel), and January 15, 1921, and to the corresponding notes. ’’Comments about the debate surrounding the concept of negative numbers can be found at the end of the question-and-answer session of March 11,1920 (Blümel). See Kowol [1990], chapter IV.B.

The Fourth Dimension

Questions and Answers XVI

https://rsarchive.org/Lectures/GA324a/English/AP2001/19200331q01.html

Dornach

31 Mar 1920

GA324a-25

A question about Copernicus's third law. It is impossible to speak about Copernicus's third law in such a short time, [Note 95] so let me simply comment on its history. If you look at Copernicus's basic work, which severely shook the old Ptolemaic system and revolutionized our view of the heavenly bodies, you will find that it encompasses three laws. [Note 96] The first of these three laws speaks about Earth's annual movement around the Sun in an eccentric circle, the second about the Earth's rotation around its axis, and the third about the Earth's movement around the Sun in relationship to the seasons and precession. As astronomy progressed, it failed to consider this third Copernican law in its entirety. In fact, Copernicus's successors effectively eliminated it. That is all I can say about this law without doing extensive drawings, which would keep us here until midnight. On the basis of the phenomena available to him, Copernicus first calculated the daily changes caused by the Earth's circular movement around the Sun, disregarding the seasonal, yearly, and longer-term changes encompassed by his third law. He then concluded that if we consider the daily changes and those dependent on the Earth's circular movement around the Sun in the Earths position with regard to the other heavenly bodies, the result is a view of the Earth revolving around the Sun. This view is opposed by other phenomena such as the seasons and precession, which actually nullify the assumption that the Earth revolves around the Sun. For the sake of being able to quantify and calculate the interactions between the Earth and the other heavenly bodies, We make it easy for ourselves and disregard any changes that can be observed only over a year or over centuries, because these changes complicate the daily changes that depend on the Earth's circular movement around the Sun. Calculating the daily changes on the basis of the assumptions expressed by Copernicus in his first and second law results in the Earth's yearly revolution around the Sun. As Copernicus himself said, if we include the third law in our calculations, it counteracts the factor contained in the first law, which we calculated into the daily movement and which yields the Earths yearly movement, and almost eliminates any such yearly movement. [Note 97] In any case, the third Copernican law has been disregarded. People preferred the easy assumption that the Earth rotates around its axis in twenty-four hours, progressing all the while so as to move around the Sun in the course of one year. This solution was simple as long as we clung dogmatically to the Copernican assumption that the Sun does not move at all. We were forced to abandon this assumption a long time ago, however, and the third Copernican law had to be reinstated. [Note 98] I can summarize this subject only briefly — as I said, a detailed mathematical and geometric explanation would take hours — but if we take the third Copernican law seriously, it does not result in movement of the Earth around the Sun. The Sun moves, — it would outrun the Earth if the Earth simply revolved around the Sun. The Earth cannot revolve around the Sun because meanwhile theSJun would move away from it. In reality, the Sun moves on, and the Earth and the other planets follow it. We have a line like the thread of a screw, with the Sun at one point and the Earth at the other end. Our dual focus on the Earth and Sun and on their progressive, screw-like movement creates the illusion that the Earth is revolving around the Sun. [Note 99] The interesting point in all this is that Copernicus was more advanced than we are today. We have simply omitted his third law from astronomy's post-Copernican development. Our astronomy has been developed without this third law, which states that other phenomena negate the yearly movements around the Sun that we calculate for the Earth. To do full justice to Copernicus, this law must be reintroduced. [Note 100] This subject does not attract much interest, because if we were to apply a true phenomenological approach to astronomy, we would have to realize first and foremost that, as Dr. Vreede [Note 101] already mentioned, we are dealing with extremely complicated movements. And that the ordinary geometric constructions we use in attempting to describe these movements are suited only to descriptions of simple geometric processes. Because the heavenly bodies do not obey such simple processes, disturbances always appear, and we are forced to compensate by adding more hypotheses. [Note 102] When we get beyond such hypotheses, astronomy will look completely different. This will happen only when we progress to a form of natural science that truly includes the human being and observes phenomena within the human being. Taking these phenomena into account will allow us to develop a view of the events and processes of cosmic space. As Dr. linger also mentioned, [Note 103] the human being actually has been ousted from today's science, which disregards the human element. Ideas such as the theory of relativity, [Note 104] which certainly do not correspond to reality, are able to take hold only because modern science is so utterly estranged from reality that it deals with everything outside human beings but nothing that happens inside them. To think in ways that correspond to reality is a skill that humanity will have to relearn. If you have a stone lying here (reference to a drawing that has not been preserved), you can see it as leading an independent existence, at least to a certain extent. It all depends on your presuppositions. We can say that when we consider what we see within the boundaries of the stone, we develop a certain view of the stone. But now assume that instead of a stone, we are considering a rose that I have picked. It is not possible to ascribe reality to the rose in the same way that we ascribed reality to the stone within its boundaries, because a plucked rose cannot exist in isolation. It must develop in connection with something else. We are forced to say that while the stone within its described limits possesses a certain real existence, the rose does not, because it can exist only in association with its rootstock. If I separate it from its roots, the prerequisites for its existence are no longer present, and it cannot persist. We must relearn the skill of submerging our thinking in things and taking the things themselves into account. Only when we have reacquired this skill will we have a healthy form of astronomy, for example, as a matter of course. We will be spared the terrible abstraction of such ideas as the theory of relativity. Essentially, the theory of relativity is based on ideas that are not true realities. The ordinary formula \(s = v \times t\), (distance equals speed multiplied by time) is quite illuminating. When I am describing a reality, I can write only this: When we grasp a reality by means of abstraction, I can calculate everything that is in a real object. Because it is possible to grasp many different things on an abstract level, we can perform many different calculations while remaining within the abstract. We must not believe, however, that these abstractions are realities. In the inorganic world, only speeds are realities, and both time and space are mere abstractions. Thus when we begin to perform calculations involving time and space, we enter the domain of unreality, and once we begin thinking in unreal terms, we can no longer return to reality. These issues, therefore, are related to very significant shortcomings of our times. In recent times, humankind has disregarded the spirit completely while attempting to understand nature, and our souls have moved toward abstractions. In one sense, dealing with abstractions is extremely comfortable, because we do not need to learn to submerse ourselves in objects and events. It is easier to think in terms of space and time than to immerse ourselves in qualitative aspects or to realize that whatever we can think of as real in connection with something else, can therefore be thought about in real terms. (Editor's note: not abstractly.) You need not believe what I am about to say, but it is true nonetheless. It is torture for a person who has cultivated a capacity for thinking and a desire to understand reality to read Einstein's theory of relativity, because even though all the ideas Einstein presents are mathematically very consistent, they are literally unthinkable for someone with any sense of reality. It is impossible to pursue such thoughts to their conclusion. What does it mean and what kind of sense does it make when Einstein presents a whole complex of thoughts about someone who is sealed up in a box and journeys through space at high speed and returns to find a new generation of people and totally different circumstances? [Note 105] When we think about such a situation, of course we are thinking only in terms of space and time and disregarding the outer bodily nature of the person or object, which would be destroyed while undergoing the experiment. Although this objection may seem naive to fanatical thinkers on the subject of relativity, it inevitably comes into consideration with regard to reality. [Note 106] Anyone who has a sense for reality cannot see such thoughts through to the end. Suppose that we are traveling in a car, for example, and have a flat tire. Let's assume that it makes no difference whether I think that the car, with me in it, is speeding over the ground or that the car is standing still while the ground moves out from under me. If, in fact, it makes no difference, why should the ground suddenly go on strike because of a minor breakdown that concerns only the car? If it makes no difference how we conceive of this situation, the outcome should not be affected by the outer change. As I said before, although such objections are terribly naive as far as relativity theorists are concerned, they do reflect current realities. Anyone whose thinking is grounded in reality rather than in abstraction — even an abstraction that can sustain consistent thoughts — is forced to point out such issues. Fundamentally, therefore, we are living with a theoretical form of astronomy. A classic example is our disregard of the third Copernican law. We push it aside because it is uncomfortable. When we study it, we learn to feel uncomfortable about our customary calculations. What do we do? We apply the second Copernican law, but our calculations do not come out even, and noon falls in the wrong place. So we introduce the daily corrections known as Bessel's corrections. [Note 107] If we realize their full implications, however, we see the need to take the third Copernican law into account — that is, we begin to deal with realities. The point here is to acknowledge the principles behind such issues. The way we presently deal with such principles permits us to go astray in many different directions. Mr. Steffen did an excellent job of presenting three such tortuous paths in a specific field of knowledge. [Note 108] Such misleading paths are easy to encounter today, and they influence real life. We have trained ourselves to think in ways derived from a mathematics that lacks reality, and this type of thinking gradually has become almost a touchstone of genius. In fact, a sense of reality is sometimes much more helpful than genius, because if you have a sense of reality, you must abide by the realities of the situation. You must immerse yourself in objects and events and live with them. If you have no sense of reality, you can impose all sorts of abstractions onto space and time in the most ingenious way, simply by manipulating mathematical formulas and methods. You can rise to truly terrible levels of abstraction. These abstractions sometimes can be very seductive. I am thinking of modern set theory, which has been used as the basis for explaining infinity. Set theory dissolves number, the very principle of mathematics, because it no longer sees a number as an ordinary number but merely compares one arbitrary set with another, classifying individual entities with no regard to their qualities and sequence}. [Note 109] Set theory makes it possible to develop certain theories of infinity, but swimming in abstractions all the while. In concrete reality, it is impossible to perform such operations. It is important to note that we gradually have become accustomed to disregarding the need to immerse ourselves in reality. In this connection, spiritual science really needs to set the record straight. I am now going to present two opposites. This appears to have nothing to do with theory, but in truth it has a great deal to do with theory, because all of these matters deal with much more than a theory, which can be corrected if our thinking about it is sound. The real issue is the need to develop sound thinking, thinking that is not merely logical, because logic also applies to mathematics. We can incorporate logic into mathematics, and the result is a completely coherent structure that nonetheless need not apply to reality at all. By now we have reached the point of being able to show how things look to an undisciplined way of thinking that lacks any true sense of reality. Here you have on the one hand a book that attempts to summarize everything that modern science has to offer. Thousands and thousands of copies — seventy or eighty thousand, I believe — of this famous book have already been sold. It is Oswald Spengler's book The Decline of the West. [Note 110] As you know, this means that four or five times that number of people have read the book, so we know what a tremendous influence it has had on modern thought, simply because it emerged from modern thought, in a certain sense. The author of this book had the courage to formulate the ultimate consequences of modern thinking. In this book, Spengler looks at everything that astronomy, history, the natural sciences, and art have to offer, and we are forced to admit that he has amassed a huge body of evidence. Because Spengler really thinks in this way, he has the courage to draw the ultimate conclusions from the thinking of truly modern astronomers, botanists, art historians, and so on. As clearly as we can prove the second law of thermodynamics, [Note 111] for example, Spengler's book also proves that in the beginning of the third millennium, Western civilization will have degenerated into complete barbarity. We must admit that this book not only has shown us the decline of modern civilization but also has proved a future event as clearly as any scientific statement can be proved today. In terms of the methods of modern science, Spengler's proof of the decline of the West is certainly as good as any astronomical proof or the like and much better than any proof of the theory of relativity. His conclusions can be circumvented only by those who see factors that Spengler himself does not see, namely, by those who will provide completely new impulses for humanity from now on. Impulses that must be born out of the inmost core of the human being and that are invisible to any science based solely on contemporary thought. But what is Spengler's thinking like? Unlike the relativity theorists, Oswald Spengler thinks in categories that correspond to reality. Not everything he thinks fits together, however. The concepts he develops about astronomy, biology, art history, architecture, sculpture, and so on do not always mesh. They form a structure that I would like to compare to crystals that have grown together. They are all confused, and they destroy each other. If we maintain a sense of reality while reading Spengler's book, we find that his concepts are very full (reference to a drawing that has not been preserved). Oswald Spengler certainly knows how to think and develop concepts, but his concepts destroy each other. They blow each other up and cut each other apart. Nothing remains whole because one concept always negates another. We see terrible destructive actions when we apply a sense of reality to the development of Spengler's ideas. Spengler represents one pole in modern thought, the pole that constructs a unity out of concepts drawn from all different fields. The philosophers associated with this trend neatly define everything on such an abstract level that all of the concepts they derive from individual sciences can be gathered together and united into a system of sorts, in an attempt to come to a point. They fail to come to a point, however, but simply splinter and obliterate each other. Spengler is a much better philosopher of modern science than many other philosophers, whose concepts do not destroy each other because their formulators lack the courage to define them precisely enough. In their philosophies of science, these other philosophers are always confusing tiger claws with cat paws, as it were, resulting in comical constructs that are said to be the philosophical consequences of individual scientific investigations. If we consider these philosophers seriously, we see that Spengler is experienced in all the sciences and knowledgeable about anything scientific that can result from the customs of philosophy. The other pole is represented by a philosopher who is also popular, though not revered to the extent that Spengler is, namely, Count Hermann Keyserling. [Note 112] Keyserling differs from Oswald Spengler in that none of his concepts have any content. While Spengler's concepts are meaty, Keyserling's are empty. They never contradict each other because they are basically only empty husks of words. Keyserling's only thought, which is also an empty husk, is that the spirit must unite with the soul. [Note 113] Count Keyserling attacks anthroposophy vehemently. In the periodical Zukuiift, for example, he accused me of splitting the human being into various members — ether body, sentient body, sentient soul, and so on — while in fact the human being is a unity and functions as such. [Note 114] The thought that the spirit must unite with the soul seems fiendishly clever, but in fact it is no more clever than saying that a suit is a unity and should not be broken down into component parts, such as a vest, a pair of pants, boots, and so on. It's all a unity, so I should not have the tailor make the jacket and pants separately and then go to the cobbler for boots to match. Of course, all of these things form a unity on the human being who is wearing them. But it makes no sense to say that jacket and pants and probably the boots as well should be stitched together into a single article of clothing, even if Count Keyserling in his abstract idealism insists that they are a unity. This is the opposite pole. We have, on the one hand, Spengler with his concepts that destroy each other and on the other hand, we have Keyserling with his totally empty concepts. For anyone who has any sense of reality, it is a torment to read Spengler and to see all his concepts colliding with and crushing each other and forcing their way into each other. You really are compelled to experience all this, especially if you have any artistic sensibility. Spengler's book is a totally inartistic construct, but when you read Keyserling's book, you stop and gasp for breath after one page, because his concepts have no air in them. [Note 115] We want to form a thought, but there is nothing there, which makes it very easy for people to understand these concepts and feel comfortable with them. This is especially true if this impotent non-thinker also tells them that while there may be some truth to the facts that spiritual science confirms, he himself cannot corroborate them and therefore will not assume that they are true, since he is not one of those people who has intuitions, and so on and so forth. [Note 116] Of course, people lap up this kind of talk, especially if they themselves cannot supply the necessary proof. Especially today, such people much prefer a writer who admits to being unable to confirm the facts to one they have to struggle to keep up with. Keyserling's scribblings on art, in particular, are enough make your hair stand on end, but they are very popular. That is all I have to say on this subject. By now, you may have developed a sense for what it means when Goethe says, "Consider the What, but consider How more seriously. [Note 117] You can consider the What when you read Spengler, because he has a lot of What to offer. But Goethe knew that a worldview depends on how we see the whole in the coordination, organization, and inherent harmony of ideas. That is why we can say, referring to Spengler, consider the What. Spengler does consider the What as it should be considered, but he fails to consider the How at all. Above all else, Goethe challenges us to consider how ideas are arranged. With regard to Keyserling, we might say that he appears to possess the How — in fact, his work is teaming with How, but there is no What, no content. Question-and-answer session during a "conversation on spiritual science" in the context of the anthroposophical conference of September 26 to October 16, 1920, at the Goetheanum in Dornach. Rudolf Steiner's introductory lectures on Grenzen der Naturerkenntnis ('The Limits of Our Understanding of Nature") were held from September 27 to October 3, 1920, and appeared in GA 322. Many lectures by other participants were printed in Aenigmatisches aus Kunst und Wissenschaft ("Enigmatic Aspects of Art and Science"), vols. I and II, Stuttgart, Der Kommende Tag Verlag 1922 (available from the Goetheanum bookstore), or in Kultur und Erziehung ("Culture and Education"), Stuttgart, Der Kommende Tag Verlag, 1921 (available from the Goetheanum bookstore). See also the announcement of the conference, which includes a detailed program, in the periodical Dreigliederung des sozialen Organismus ('The Threefolding of the Social Organism"), vol.2, 1920/1921, no. 9. Reports on this conference by Alexander Strakosch and Gunther Wachsmuth appeared in the same periodical (nos. 15, 16, and 18). According to Ptolemy ( Claudius Ptolemeus , ca. 100—170 A.D.), the basic structure of the solar system was classically geocentric, with the resting Earth in its center. In his chief work, Almagest , Ptolemy uses a complicated construction of concentric circles to explain the details of planetary movements. (See Ptolemy [1962]; Ziegler [1976]; Teichmann [1983], chapter 3.2; Van der Waerden [1988, chapter XIX.) With regard to planetary orbits that result from combinations of circular movements, nothing essential is changed by shifting from the geocentric Ptolemaic system to the heliocentric Copernican system, except that the Sun and the Earth exchange places, which corresponds to a simple geometric transformation. Furthermore, both Ptolemy's and Copernicus's arguments are essentially kinematic (Steiner would have said "phoronomic") — that is, they do not take force relationships into account. See Vreede [1980], "Über das kopernikansiche System " ("On the Copernican System”), pp. 349-359: Teichmann [1983], chapter 3; and Neugebauer [1983], section 40. In his chief work De Revolutionibus Orbium Coelestium , 1543, volume 1, chapter 11, Nicolas Copernicus (1473–1543) separates the movement of the Earth into three components (see Copernicus [1879], pp. 28ff or [1990], pp. 139ff.). The first movement is the Earth's daily rotation around its axis, the second is its movement in an eccentric orbit around the Sun, and the third is its "movement in declination." Copernicus formulates it like this: Since so many important planetary phenomena testify that the Earth moves, we will describe this movement in general terms, inasmuch as it confirms the phenomena, like a hypothesis. We must assume that this movement is threefold: the first movement, which the Greeks called nychthemerinon, daily-nightly , is the actual circulation of day and night, which moves around the Earth's axis from west to east in the same way that we formerly believed the Earth to move in the opposite sense. This circulation defines the equinoctial circle or equator, which some call the circle of equal days in imitation of the Greeks, who called it isemerinos, of equal days . The second is the yearly movement of the center, the Earth and its satellite through the zodiac around the Sun from west to east — that is, in direct motion — between Venus and Mars. The result of this movement, as we said, is that the Sun itself seems to make a similar movement through the zodiac, so that when the Earth (the central point) is moving through Capricorn, Aquarius, and so forth, the Sun appears to be moving through Cancer, Leo, and so on. We must imagine that the slant of the equator and of the Earth's axis varies in relationship to the plane of the circle that passes through the center of the zodiac signs. If the slant were constant and only the midpoint (the Earth) moved no change in the length of days and nights would occur and we would have always either the summer solstice or the winter solstice or an equinox—in any case, an unchanging season. Thus, the third movement, or movement of declination, occurs in a yearly cycle but in the opposite direction from the movement of the midpoint (the Earth). As a result of these two almost equal but opposite movements, the Earth's axis, and thus also the equator—the greatest parallel circle—remain pointing to almost the same area of the heavens, as if they were immobile, while the Sun, because of the progressive movement of the Earth's center, seems to move through the oblique plane of the zodiac in a way that is no different from what it would do if the Earth were the center of the solar system, if we only remember that the Sun's distance from the Earth in the sphere of fixed stars has already exceeded our perceptive capacity (Copernicus [1879], p. 28ff). Rudolf Steiner seems to have reversed the order of the first two laws of Copernicus's De Revolutionibus . The above sequence, however, is the one Copernicus also uses in discussing the three movements of the Earth in De Hypothesibus Motuum Coelestium a se Constitute Commentariolus , also called simply Commentariolus , published in 1514. (See Copernicus [1948], pp. 12ff, or [1990], PP 9ff.) In the passages that follow, we have preserved Steiners sequence: l. The Earths annual movement around the Sun in an eccentric orbit 2. The Earths daily rotation around its axis 3. Movement in declination: the Earths axis describes a cone, moving in the opposite direction from its revolution around the Sun. In a geometric or kinematic sense, the first movement (if considered in isolation, disregarding the second and third movements) is the Earths revolution around the Sun. Note that the Earths axis does not remain parallel to itself — except in a special instance when the axis is parallel to the axis of rotation, which is not the case here. Instead, it describes a cone in relationship to the Earths midpoint. In other words, the intersection of the extension of the Earth's axis with a line perpendicular to the plane of the Earth's eccentric orbit around the Sun is a fixed point of this movement. If this movement existed in isolation, there would be no change of seasons, because the Earth's position in relationship to the Sun would always be the same. Consequently, Copernicus had to introduce another movement to account for the phenomenon of changing seasons, on the one hand, and precession (shifting of the vernal equinox), on the other. His "movement in declination," the third movement in Steiner's sequence, served this purpose. This movement consists of the yearly rotation of the Earth's axis in the opposite direction from its movement around the Sun. It negates the rotation of the Earth's access created by the second movement, and a slight excess accounts for precession. 97In 1783 at the latest, the fact that the Sun itself also moves was acknowledged when William Herschel (1738–1822) discovered its movement (called the apex movement ) in the direction of the constellation Hercules. (See Wolf [1891-1893], §292.) Rudolf Steiner often spoke of the spiral or screw-like movement of the Earth as it follows the movement of the Sun, — see the lectures of March 24 and 31, 1905, for example. Beginning with his lecture of September 1, 1906 (GA 95), he often links the third Copernican movement to his own description of the problem of the Sun and Earth's motion. From 1916 on, he adds the aspect of a progressive lemniscatic quality of movement. (For a general overview of this problem, see Vreede [1980], " Über das Kopernikanische System " ["On the Copernican System"], p. 349ff.) The following list includes most of the lectures and question-and-answer sessions (Q&A) in which Steiner discusses the problem of the Sun and Earth's motion, especially the third Copernican movement (Copernicus 3), Bessel's corrections (Bessel), and/or the problem of spiral or lemniscatic (∞) movements of the Sun and Earth. Especially important and thorough presentations include those of October 1, 1916 (GA 171); April 10, 1920 (GA 201); and January 2 and 17, 1921 (GA 323). Various attempts have been made to unite Rudolf Steiner's scattered indications into a consistent interpretation but to date, no view has successfully encompassed all of them. For some of the more significant efforts, see (in chronological order) Locher [1942], Hagemann [1966], Kaiser [1966], Schmidt [1966], Vetter [1967], Van Bemmelen [1967], Unger [1981], Bauer [1981, 1988], Hemming/Pinkall [1983], Hardorp [1983], Junge [1983], Rudnicki [1984], Adams [1989] (Chapter 4), and Vanscheidt [1992], The mechanical interpretation of the solar system that has been customary since Newtons time renders the assumption of a separate third Copernican movement "superfluous." That is, if the Earth is seen as an (almost) symmetrical top spinning in the Sun's gravitational field, then according to the law of the preservation of rotation, the direction L of the axis of rotation (Earth's axis) essentially remains fixed in space. This interpretation, derived from physics, of course, would have been foreign to Copernicus. Among his successors, only a very few authors lament the neglect of the third Copernican movement or even consider it a serious factor. On this subject, see C. L. Menzzer's informative note 36 on De Revoltitionibus, volume 1, chapter 11, "Bctveis von tier dreifachen Betvegung der Erde" ("Proof of the Threefold Movement of the Earth") (Copernicus [1879], appendix, p. 28-31). In this context, Rudolf Steiner's lecture of September 25, 1919 (GA 300a), also mentions the works of the poet and author Johannes Schlaf (1862—1941). See Schlaf [1914] and [1919]: both were found in Steiner's library, and the first contains a handwritten dedication by the author to Rudolf Steiner. Elisabeth Vreede (1879–1943), mathematician and astronomer and, from 1924 on, the first head of the Section for Mathematics and Astronomy of the School of Spiritual Science at the Goetheanum in Dornach. During this conference, Dr. Vreede gave two lectures (on October 1 3 and 14, 1920) on 'The Justification for, and Limits of, Mathematics in Astronomy" [1922], Vreede [1922], pp. 138ff and 160. Carl Unger (1878–1929), manufacturer, engineer, and philosopher. During this conference, he gave six lectures (October 11-16, 1920) on the subject of Rudolf Steiner's work [1921]. See also the report on these lectures by Willy Storrer in Linger [1921], especially sections III and IV. For more about the theory of relativity with regard to the passage that follows, see the question-and-answer session of March 7, 1920 and the corresponding notes and the question-and-answer sessions of March 31, 1920, and January 15, 1921. See the passage by Einstein quoted in Note 6 to the question-and-answer session of March 7, 1920. Steiner is referring here to a problem later known as the "paradox of the twins" or the "paradox of the clocks." Its interpretation, still controversial today, is related to the significance of the concept of time in physics, but more especially to the interpretation of a physical system's "own time" in the context of the theory of relativity. On this subject, see Gschwind [1986], for example, and the references listed there. According to Einstein [1917], §18, the special principle of relativity states that the universal natural laws of physics are formally identical for two systems of reference subject to uniform motion (inertial systems). Of course, this statement presupposes that inertial systems exist. Popular examples taken from elementary mechanics do not strictly satisfy most of the prerequisites, — hence, such examples fail to correspond to reality even from the perspective of physics. Thus, for example, the frame of reference "Earth" (like any rotating system) is an accelerated system, as is the frame of reference "car." Because it overcomes the resistance of friction, a uniformly moving car executes accelerated move* ment. Because of wear and tear, the car is not an unchanging system—the more so when it has a flat tire and its speed decreases. Similar considerations apply to the oft-cited example of the train and the railway embankment. The only examples of relativistic behavior that the field of physics considers realistic occur on the atomic or subatomic level, as Einstein [1917] also points out in his lecture. According to Steiner, however, the full reality of the realm of such phenomena cannot be grasped without extending physics in keeping with anthroposophical spiritual science (see the lectures of the first and second scientific courses, GA 320 and GA 321). Friedrich Wilhelm Bessel (1784–1846), astronomer, geodesist, and mathematician in Königsberg. Bessel made fundamental contributions to the techniques and technology of astronomical observation, including improvements in the instruments, systematic analysis of errors due to instruments and faulty observation, and thorough reduction of observations. Both instrumental errors and the influence of the Earth's atmosphere (refraction) must be eliminated when the location of a star is measured. Furthermore, for the sake of an objective standard that can be compared with other measurements, such locations must be calculated in terms of a common point in time, taking the effects of the observation point and the Earth's movement into account. Doing this requires an exact knowledge of precession, nutation (slight oscillation of the Earth's axis caused by the moon), and daily, yearly, and long-term aberration (caused by the ultimate/finite speed of light and apparent changes in the location of stars due to the Earth's movement). Bessel's analysis/utilization (reduction) of the positions of 3,222 stars obtained by James Bradley (1693—1762) of the Greenwich Observatory became a milestone in astronomical observation because it made precisely reliable star positions available for the first time. Bessel published his results in the books Fundamenta Astronomiae pro Anno 1755 Deducta ex Observationibus Viri Incomparabilis James Bradley in Specula Astrouomica Grenovicensi per Annas 1750-1762 Instituti (Königsberg [1818]) and Tabulae Regiomantanae Reductionum Observationum Astronomicum ab Anno 1750 usque ad Annum 1850 Computatae (Königsberg [1830]). Related studies by Bessel yielded improved methods of determining the independent movement of fixed stars and the first means of determining parallaxes of individual fixed stars. These parallaxes constituted the first astronomical proof of the yearly movement of the Earth (on this and other proofs of this movement, see Teichmann [1983], chapter 3.4). The so-called Bessel reduction formulas for star coordinates have to do with the yearly and long-term influences of precession and nutation. (For more on this subject, see Schmidt [1967]: Wolf [1890-1893], §609 and §613; and astronomical yearbooks such as The Astronomical Almanac , 198iff, p. §22 ff.) Albert Steffen (1884–1963), poet and, from 1924 on, the first head of the Section for Fine Arts/Arts and Letters of the School of Spiritual Science at the Goetheanum in Dornach. During this conference, Steffen gave two lectures (on October 14 and 15, 1920) on the subject of "Spiritual Science and Crisis in the Life of the Artist." Steffen published his own summary of these lectures in the collection Die Krisis im Leben des Kiiustlers ("Crisis in the Life of the Artist") [1922], See especially the essay of the same title in part II, pp. 3Iff. Set theory was founded almost single-handedly by the mathematician Georg Cantor (1845-1918). Cantor sent Rudolf Steiner a copy of his Lehre vom Transfiniten ("Theory of the Transfinite") [1890], complete with personal dedication and handwritten corrections. In a treatise dated 1884, Cantor gives this definition of a set: "In general I understand a "manifold" or "set" to be a group of multiple elements that can be thought of as a whole. It is the epitome of specific elements that can be lawfully united into a whole. I believe I have thus defined something related to the Platonic eidos, or idea ... (Cantor [1932], footnote to p. 204). Rudolf Steiner's remarks refer to Cantor's investigations of various levels of infinity. The basis for these studies is this definition, which Steiner paraphrases: "I understand the prime or cardinal number of a set \(S\) (which consists of distinct and conceptually separate elements \(s\), \(s’\), ... and is defined and delineated by them) to be the general or universal concept that we gain by abstracting from the set both the character of its elements and ail relationships of these elements either to each other or to other objects, and especially the order that may prevail among the elements, and reflect only on what is common to all sets that are equivalent to \(S\). I call two sets \(S\) and \(T\) equivalent , however, when each element of one can clearly be made to correspond to exactly one element of the other" (Cantor [1890], p. 23 ff. or [1932] p. 387). See also the essay entitled "Georg Cantor and Rudolf Steiner" ("Georg Cantor und Rudolf Steiner") in Beiträge Zur Rudolf Steiner Gesamtausgabe ("Articles on the Complete Edition of Rudolf Steiner's Work"), No. 114/115, Dornach, 1995. Oswald Spengler (1880–1936), originally a mathematician, later a writer. "Form and Actuality," the first volume of Spengler's principal work The Decline of the West, appeared in its first edition in 1918, and by 1920 had appeared in 32 printings. The second volume, "Perspectives of World History," which appeared in 1922, did not have as wide a readership. Decline of the West was first published in the U.S. in 1926—28. The second law of thermodynamics is based on the concept of entropy, which was first formulated by Rudolf Clausius (1822–1888). This concept states that entropy strives toward a maximum in any real thermodynamic process that takes place in a self-contained physical system. In the context of physics, proof of this law is possible only on the basis of other unprovable assumptions or postulates. For example, in the statistic kinetic gas theory dating back to James Clark Maxwell (1831–1879) and Ludwig Bolzmann (1844–1906) this second law takes the form of a provable theorem (Boltzmann's so-called H theorem) based on the hypothesis of complete molecular chaos. Count Hermann Keyserling (1880–1946), philosopher, author, and co-founder and scientific head of the "School of Wisdom" ( or "Society for Independent Philosophy") in Darmstadt. See his works, such as D as Reisetagebuch eines Philosophen ("A Philosopher's Travel Diary) [1919a], Der Weg der Vollendung: Des Grafen Hermann Keyserling philosophischen Schaffen ('The Path of Perfection: The Philosophical Activity of Count Hermann Keyserling") [ 1919b], and Philosophie als Kunst ("Philosophy as an Art") [1920], "’Keyserling, Philosophic als Kunst ("Philosophy as an Art") [1920], p. 293: The School of Wisdom must become a third element alongside the church (taking the word in the broadest possible nondenominational sense) and the university. Like each of these other elements, its intent is to shape the whole human being and spiritualize the human soul. In addition, however, it aspires to a synthesis between human soul life and the independent, fully conscious spirit, so that neither faith nor abstract knowledge is the final authority, but faith, knowledge, and life become one in a living, higher unity of consciousness crowned by the School of Wisdom, whose task would be to organically incorporate abstract academic knowledge into a living synthesis and to transform mere "knowing" into "being." Presumably Steiner is referring to the weekly magazine Die Zukunft ("The Future"), edited by Maximilian Harden (volumes 1-118, 1892-1922). To date, the essay by Hermann Keyserling that Steiner mentions has not been found. See also the discussions about Keyserling in the periodical Dreigliederung des sozialen Organismus (The Threefolding of the Social Organism"), volume 2, 1920/1921, nos. 20-25, especially the report by Ernst Uebli (1875–1959) on Rudolf Steiner's lecture of November 16, 1920, in nos. 21 and 22. Further comments about Keyserling can be found in Rudolf Steiners lecture of August 26, 1921, published in the periodical Gegenwart ("The Present"), volume 15, 1953-1954, no. 2, pp. 49-64. To date, the source of this statement by Keyserling has not been discovered. Goethe, Faust , Part II, Act 2, Scene 2, in the laboratory, verses 6989ff. Homunculus says to Wagner, who remains behind: Unfold the ancient parchments, As bidden, collect life's elements and join them carefully to each other, considering the What , but more the How . While I wander through a portion of the world, I will, no doubt, discover the dot upon the i.

The Fourth Dimension

Questions and Answers XVII

https://rsarchive.org/Lectures/GA324a/English/AP2001/19201015q01.html

Dornach

15 Oct 1920

GA324a-26

A Question about the need for the anthroposophical position on the Einstein problem. Why must we suddenly reverse the sign when we leave the realm of the tangible for the ether? Of course this also can be done without taking a specifically anthroposophical position, simply by studying the phenomena, [Note 118] as is done in many other scientific fields. (I illustrated an unbiased view of the phenomena of so-called heat theory in a course I gave to a small audience here a few months ago.) [Note 119] We then must attempt to express these phenomena in mathematical formulas. The peculiar feature of such formulas is that they are correct only when they correspond to processes we can observe, that is, when the results of the formulas correspond to, and can be verified by, reality. If you want to understand what happens when a gas contained under pressure is heated, it is artificial to apply the formulas worked out by Clausius and others, although it can be done. [Note 120] As is officially admitted today, however, that the facts do not correspond to the formulas. [Note 121] In connection with Einstein's theory, it is strange to note the experiments that have been conducted. These experiments were set up on the supposition that a certain theory was correct. Because the experiments did not confirm the theory, another theory, based exclusively on experiments that exist only in thought, was then developed. [Note 122] In contrast, if you attempt to deal with heat phenomena by simply inserting the relevant positive and negative signs into the formulas, depending on whether you are dealing with conductive or radiant heat, you will find that reality confirms the formulas. [Note 123] Admittedly, when we move on to other imponderables, simply changing the sign to negative is not enough, and we must include other considerations. We must imagine that forces in the tangible realm work radially, while those belonging to the etheric realm come from the periphery, have negative values, and work only within a circular area. Thus, when we move on to other imponderables, we must insert the corresponding values differently. We then will find that we arrive at formulas that are verified by actual phenomena. Anyone can take this approach, with or without becoming involved in anthroposophy. I would like to emphasize a different point here. You must not think that what I told you in these four lectures simply stems from my anthroposophical approach. I have told you these things because they are true. The so-called anthroposophical approach does not anticipate phenomena, — it results from them. It is simply the consequence of an appropriate overview. If we attempt to recognize and understand objects and events without bias, an anthroposophical approach can result. The prospects for what I have told you would be poor if we had to take a biased view as our starting point, but that is not the case. We must pursue the relevant phenomena on a strictly empirical basis. Although I still maintain that the anthroposophical approach can be the best approach, it is only the end result. After answering other Questions, Rudolf Steiner says in conclusion: I can emphasize repeatedly only that the anthroposophically oriented spiritual science that is developing here in Stuttgart is not a sectarian or amateurish movement. Although its forces are still weak, it is striving for real, authentic science. The more you test spiritual science, the more you will realize that it is a match for any scientific method of testing. The many misunderstandings to which spiritual science is subject today are not the results of a truly scientific approach. The opponents of spiritual science battle it not because they themselves are too scientific but because they are not scientific enough, as further investigation will show. [Note 124] In future, however, we must become more scientific rather than less so. Science must make real progress, — namely, it must lead us into the spiritual realm as accurately as it leads us into the material realm. Question-and-answer session at the conclusion of four lectures to an academic audience on the relationships between spiritual science and individual specialized fields of science. The four lectures in this cycle, Proben über die Beziebungen der Geisteswissenschaft zu den einzelnen Fachwissenschaften ("Attempts at Formulating the Connections of Spiritual Science to Individual Specialized Fields of Science ), were held in Stuttgart from January 11 to 15, 1921, and were first published in the following editions of the periodical Gegenwart ("The Present), vol. 14 (1952-1953): January 11, 1921, no. 2, pp. 49-67; January 12, 1921, no. 3, pp. 97-118; January 15, 1921, no. 4/5, pp. 145-167; January 14, 1921, no. 6, pp. 225-236, and no. 7, pp. 257-268; question-and-answer session of January 15, 1921, no. 8, pp. 305-317. These lectures will be published in GA 73a. See also the report on this conference by Eugen Kolisko (1893–1939) in the periodical Dreigliederung des sozialen Organismus ('The Threefolding of the Social Organism ), vol. 2, 1920-1921; no. 31, pp. 4-5; no. 32, p. 5; and no. 33, p. 4. Geisteswissenschaftliche Impulse zur Entwickelung der Physik: Zweiter Naturwissenschaftlicher Kurs. Wärmelehre ("Spiritual Scientific Impulses for the Further Development of Physics: Second Scientific Course. Heat Theory") (GA 321), Stuttgart, March 1 to 14, 1920. Rudolf Clausius (1822–1888), physicist in Berlin, Zurich, Wurzburg, and Bonn. Clausius, along with Ludwig Boltzmann (1844–1906) and James Clark Maxwell (1831–1879), is considered one of the founders of modern thermodynamics, which is based on kinetic gas theory and statistical mechanics. Clausius's book Die Mechanische Wärmetheorie ('The Mechanical Theory of Heat") includes his treatises on heat theory [1876-1891 ]. See also Rudolf Steiner's lectures of March 1 and 11,1920 (GA 321). The editors of Steiner's second scientific course (GA 321) point out that various authors expressed concern about efforts to explain thermodynamics on the basis of mechanics. (See the Note to p. 26 of the lecture of March 1, 1920, on pp. 222 ff.). We would like to add here that prior to the discovery of quantum mechanics and quantum statistics, it was not possible to reconcile completely various attempts to develop a mechanical model of the molecular structure of matter with experimental findings, especially those of spectroscopy. On this subject, see Harman [1982], chapters V and VI. The ether drift experiment conducted by Michelson and Morley beginning in 1881 was intended to determine the Earth's speed relative to the presumably stationary quasi-material ether of physics. The outcome of this extremely precise experiment was negative and raised questions about the validity of all theories of light and electricity that were based on the assumption of an absolutely stationary ether. A theoretical explanation of these findings was developed by Hendrik Antoon Lorentz (1853–1928) and George Francis Fitzgerald (1851–1901), working independently of each other. A short time later, Albert Einstein (1879–1955) derived the resulting formulas, such as Lorentz's contraction, from the basic assumptions of his special theory of relativity (the principle of relativity, the absolute constancy of the speed of light). Einstein used a series of experiments that exist only in thought to derive and illustrate his theory. 0n the formulas for conductive and radiant heat and on the explanations that follow here, see also Rudolf Steiner's lectures of March 12, 1920 (GA 321), and January 8, 1921 (GA 323). The relevant equations are discussed according to the methods of modern mathematics in Dustmann/Pinkall [1992], See, for example, the chapter in Rudolf Steiner's Riddles of the Soul (GA 21) entitled "Max Dessoir on Anthroposophy" and the discussions about Hermann Keyserling at the end of the previous question-and-answer session (October 15, 1920).

The Fourth Dimension

Questions and Answers XVIII

https://rsarchive.org/Lectures/GA324a/English/AP2001/19210115q01.html

Stuttgart

15 Jan 1921

GA324a-27

QUESTION: It has hem said that the three dimensions of space differ in structure. Where does this difference lie? This statement was never formulated like that [Note 125] — "The three dimensions of space differ in structure." You are probably referring to the following thought. First we have mathematical space, which we imagine — if indeed we imagine it with any precision at all — as consisting of three perpendicular dimensions or directions, which we define by means of a coordinate system on three perpendicular axes. When we consider this space from the usual mathematical perspective, we treat the three dimensions as if they were exactly the same. We make so little distinction between the dimensions of up and down, right and left, and forward and backward that we even can believe them to be interchangeable. In terms of merely mathematical space, it ultimately makes no difference whether we say that the plane of the \(y\)-axis, which is perpendicular to the plane formed by the \(x\)- and \(z\)-axes (which are also perpendicular to each other), is ''horizontal'' or "vertical." We are equally unconcerned about the boundedness of this type of space, which does not mean that we ordinarily get so far as to imagine it as limitless. We simply do not worry about its limits. We assume that from any point on the x-axis, for example, we can continue to move along the axis indefinitely, without ever reaching the end. During the nineteenth century, metageometry presented many ideas contrary to this Euclidean concept of space. [Note 126] Let me simply remind you, for example, how Riemann distinguished between the "limitlessness" of space and the "infinity" of space. [Note 127] From the perspective of purely conceptual thinking, too, there is no need to assume that limitlessness and infinity are identical. Take the outer surface of a sphere, for instance. When you draw on such a surface, you never encounter any spatial limit that prevents you from continuing your drawing. Eventually, of course, you will intersect your previous drawing, but as long as you remain on the sphere's surface, you will never encounter a boundary that forces you to stop. Thus, you can say that a sphere's surface is limitless with regard to your ability to draw on it. This does not mean, however, that anyone claims that such a surface is infinite. In this way, on a purely conceptual level, we can distinguish between limitlessness and infinity. Under specific mathematical conditions, this distinction also can be extended to space as a whole. If we imagine that we never will be hindered from extending an \(x\)- or \(y\)-axis by continuing to add segments to it, this property of space speaks for its limitlessness but not for its infinity. The fact that I can continue adding segments indefinitely does not mean that space is necessarily infinite. It might be simply limitless. We must distinguish between these two concepts. If space is limitless but not infinite, we can assume that it is inherently curved and returns to its starting point in some way, just as a spherical surface does. Certain ideas in modern metageometry depend on such assumptions. It is not easy to raise objections to these assumptions, because we cannot conclude that space is infinite from our experience of it. It equally well could be curved and finite. I cannot carry this train of thought to its conclusion, of course, without explaining almost all of recent metageometry. Treatises by Riemann, Gauss, and others are readily available, however, and will provide you with plenty of food for thought if you are interested in mathematical ideas of this sort. [Note 128] These are the purely mathematical arguments against the fixed, neutral space of Euclidean geometry. All of the arguments I have mentioned so far are based purely on the concept of limitlessness . Your question, however, is rooted elsewhere, in the idea that space — the space of our calculations and the space we encounter in analytical geometry, for example, when we are dealing with a coordinate system of three perpendicular axes — is an abstraction. And what is an abstraction? This question must be answered first. It is important to know whether we are restricted to an abstract idea of space. Is abstract space the only space we can talk about? To put it better, if this abstract concept of space is the only one we are justified in speaking of, only one objection is possible, and this one objection has been raised adequately by Riemann's geometry or other forms of metageometry. [Note 129] Kant's definitions of space, for example, rest soundly on a very abstract concept of space. His concept is initially unconcerned with limitlessness or infinity. In the course of the nineteenth century, this concept of space was shattered — also internally, with regard to its conceptual content — by mathematics. [Note 130] It is impossible to imagine applying Kant's definitions to a space that is limitless but not infinite. Much of what Kant presents later in his Critique of Pure Reason — his theory of paralogisms, for example — would begin to totter if we were forced to substitute the concept of a limitless, curved space. [Note 131] I know that this concept of curved space poses problems for our ordinary way of imagining things. But from the purely mathematical or geometric perspective, the only possible argument against the assumption that space is curved is that it forces us to move into a realm of pure abstraction that is initially quite remote from reality. Looking at the situation more closely, we discover that a curious circular argument exists in the derivations of modern metageometry, namely, that we arrive at them by taking as our starting point the ideas of Euclidean geometry, which is unconcerned with any limitations of space. We then move on to certain derivative ideas, such as those that apply to the surface of a sphere. On the basis of these derivatives and the forms that result, we can undertake certain transpositions and then make reinterpretations of space. Everything we say, however, presupposes Euclidean coordinate geometry. Under this presupposition, we get a specific rate of curvature. We arrive at the derivations. All this calculation presupposes Euclidean geometry. Here we come to a turning point, however. We use ideas such as the rate of curvature, which we developed only with the help of Euclidean geometry, to arrive at another idea that can lead to a new view and an interpretation of what we have gained from the curved forms. [Note 132] Essentially, we are functioning in a realm remote from reality by deriving abstractions from abstractions. This activity is justified only when an empirical reality forces us to align ourselves with the results of such abstractions. Thus the question is, Where does abstract space correspond to our experience? Space as such, as Euclid imagined it, is an abstraction. [Note 133] Where does its perceptible, empirical aspect lie? We must take our human experience of space as our starting point. We actually perceive only one dimension of space — namely, the dimension of depth — as a result of our own active experience. This active perception of depth is based on a process in our consciousness that we very frequently overlook. This active perception, however, is very different from the idea of a plane, of extension in two dimensions. When we look out into the world with both eyes, these two dimensions are not the result of our own soul activity. They are there as givens, while the third dimension comes about as a result of activity that usually does not become conscious. We need to work at recognizing depths, at knowing how distant an object is from us. We do not work out the extent of a plane, — direct perception provides us with that knowledge. We do, however, use both eyes to work out the dimension of depth. The way we experience depth lies very close to the boundary between the conscious and the unconscious. But when we learn to pay attention to such processes, we know that the never fully conscious activity of estimating depth — it is at most semiconscious or one-third conscious — more closely approximates a rational activity, an active soul process, than does seeing objects only in a plane. In this way, we actively acquire one dimension of three-dimensional space on behalf of our objective consciousness. And we are forced to say that our upright position contributes a quality to the dimension of depth — that is, forward and backward — that makes it non-interchangeable with any other dimension. The fact that we stand there actively experiencing this dimension makes it non-interchangeable with any other dimension. For the individual human being, the dimension of depth is not interchangeable with the other dimensions. It is also true that our perception of two-dimensionality — that is, of up and down and right and left, even when these two dimensions are in front of us — is associated with different parts of the brain. This perception is inherent in the sensory process of seeing, while the third dimension arises for us in parts of the brain located very close to the centers associated with rational activity. Thus, we see that even in terms of our experience, the third dimension arises in a way that is very different from the other two dimensions. When we rise to the level of imagination, however, we leave our experience of the third dimension behind and see in two dimensions. At this level, we must work to experience right and left, just as experiencing forward and backward in our ordinary consciousness requires work of which we are not fully aware. And, finally, when we rise to the level of inspiration, the same is true of the dimension of above and below. [Note 134] As far as our ordinary nerve-related perception is concerned, we must work to experience the third dimension. When we exclude the ordinary activity of this system, however, and turn directly to the rhythmic system, we experience the second dimension. In a certain respect, this is what happens when we rise to the level of Imagination. I have not expressed this very precisely, but it will do for now. And we experience the first dimension when we rise to the level of Inspiration — that is, to the third member of our human organization. What we encounter in abstract space proves to be exactly what it appears to be, because all of our mathematical accomplishments come from within ourselves. The mathematical consequence, threefold space, is something we derive from ourselves. When we move down through the levels of suprasensible perception, the result is not abstract space with three equivalent directions, but rather three different values for the three different dimensions of forward and backward, right and left, and above and below. These dimensions are not interchangeable. [Note 135] We can then conclude that we also need not imagine the three dimensions as having the same intensity, which is essentially how we imagine the \(x\)-, \(y\)-, and \(z\)-axes in Euclidean space. If we want to abide by the equations of analytical geometry, we must see the \(x\)-, \(y\)-, and \(z\)-axes as equivalent in intensity. If we make the \(x\)-axis larger, stretching it with a certain intensity as if it were elastic, the \(y\)- and \(z\)-axes must grow with the same intensity. In other words, when I apply a certain intensity to expanding one dimension, the force of expansion must be the same for all three axes, that is, all three dimensions of Euclidean space. That is why I would like to call this type of space "fixed space." Fixed space is an abstraction of real space, which is developed from within the human being, and the principle of equivalent intensity does not apply to real space. When we consider real space, we can no longer say that the intensity of expansion is the same for all three dimensions. Instead, it depends on human proportions, which are the result of spatial expansion intensities. For example, take they-axis, the up-down direction. We must imagine its expansion intensity as greater than that of the x-axis, which corresponds to the left-right direction. The formula that is an abstract expression of real space — we must be aware that this formula, too, is an abstraction — describes an ellipsoid with three axes. Suprasensible perception dwells within the three very different expansion possibilities of this triaxial space. Our physical body provides direct experience of the three axes, and such experience tells us that this space also expresses the relationships among the effects of the heavenly bodies within it. Visualizing space in this way, we must also consider that everything we think of as existing in the three-dimensional universe cannot be accounted for if the expansion intensity of the \(x\)-, \(y\)-, and \(z\)-axes is the same, as is the case in Euclidean space. We must imagine the universe with a configuration of its own, corresponding to an ellipsoid with three axes. The configuration of certain stars suggests that this idea is correct. For example, we usually say that our Milky Way galaxy is lens-shaped, and so on. We cannot possibly imagine it as a sphere. We must find a different way of imagining it if we want to accommodate the facts of physics. The way we treat space demonstrates how poorly modern thinking coincides with nature. In ancient times and cultures, the concept of fixed space did not occur to anyone. We cannot even say that the original Euclidean geometry incorporated a clear idea of fixed space with three equal expansion intensities and three perpendicular lines. It was only in fairly recent times, when abstraction became an essential attribute of our thinking and we began to apply calculations to Euclidean space, that the abstract concept of space emerged. [Note 136] The knowledge available to people in ancient times was very similar to what can be redeveloped now on the basis of suprasensible insights. As you see, concepts that we depend on heavily and take for granted today assume a high degree of importance only because they work in a sphere that is foreign to reality. The space we reckon with today is one such abstraction. It is far removed from anything real experience can teach us. We are often content with abstractions today. We harp on empiricism, but we refer very frequently to abstractions without even being aware of doing so. We believe that we are dealing with real things in the real world. You can see, however, how badly our ideas need correction in this respect. Spiritual researchers do not simply ask if every idea they encounter is logical. Riemann's concept of space is thoroughly logical, though in a certain respect it depends on Euclidean space. It cannot be thought through to its conclusion, however, because we approach it by means of highly abstract thinking, and in this process our thinking is turned upside down because of one of the conclusions we draw. [Note 137] Spiritual researchers do not simply ask whether an idea is logical. They also ask whether it corresponds to reality. For them, that is the decisive factor in accepting or rejecting an idea. They accept an idea only if it corresponds to reality. Correspondence to reality will apply as a criterion when we begin to deal appropriately with such ideas as the justification of the theory of relativity. In itself, this theory is as logical as it can possibly be, because it is understood purely in the domain of logical abstractions. Nothing can be more logical than the theory of relativity. The other question, however, is whether we can act on it. If you simply look at the analogies presented in support of this theory, you will discover that they are very foreign to reality. They are simply ideas being tossed around. The proponents of relativity theory tell us that these ideas are there only as symbols to help us visualize the issues. They are not merely symbols, however. Without them, the entire process would be left hanging in the air. [Note 138] This, then, is what I wanted to say in reference to your question. As you see, there is no easy answer to questions that touch on such domains. Questions and answers (disputation) during the second anthroposophical conference at the Goetheanum in Dornach, April 3 to 10, 1921. Rudolf Steiner's lectures on "Anthroposophy and the Specialized Sciences" appeared, along with the question-and-answer sessions (disputations), in Die befruchtende Wirkung der Anthroposophie auf die Fachwissenschaften ("Anthroposophy's Positive Effect on the Specialized Sciences") (CA 76). Reports by Willy Stokar on this conference can be found in the periodical Dreigliederung des sozialen Organismus ('The Threefolding of the Social Organism"), vol. 2, (1920-1921), nos. 42 and 43. Eugen Kolisko's reports were published in Die Drei ("The Three"), vol. 1 (1921-1922), pp. 471-478. See also the invitation to this conference and the detailed program in Dreigliederung des sozialen Organismus , vol. 2 (1920-1921), no. 36. Metageometry is an almost obsolete term encompassing various types of non- Euclidean geometry. In the second half of the nineteenth century, these non- Euclidean geometries included projective geometry, hyperbolic and elliptical geometry, the geometry of general curved spaces (Riemann's geometry), and the geometry of higher-dimensional spaces. Riemann: See Note 1, Lecture 1 (March 24, 1905). Gauss: See Note 1, Lecture 1 (March 24, 1905). Riemann’s metageometry" probably means either so-called elliptical geometry, which was first discovered and described by Riemann and is closely related to the geometry of a spherical surface, or the general theory — also based on Riemann's work — of curved spaces (manifolds with a Riemannian metric), of which elliptical geometry is only a special instance (space with a constant positive curve). Kant did not distinguish between the mathematical or geometric view of the concept of space and the laws of perceived space. He interpreted the latter as necessary, subject-based prerequisites of sense perception. "Space is a necessary idea a priori and underlies all external views." ( Critique of Pure Reason = CPR, B 38). 'The apodictic certainty of all geometric theorems is based on this necessity a priori , and the possibility of their construction a priori" (CPR, A 24). Thus, "Geometry is a science that determines the properties of space synthetically and yet a priori" (CPR, B 40). "For example, space has only three dimensions,- such statements, however, cannot constitute, and cannot be concluded on the basis of, empirical judgments" (CPR, B 41). "How can the mind encompass an outer view that precedes the objects themselves and in which the concept of the latter can be determined a priori? Apparently only to the extent that it is affected by objects only in the subject, as the latter's formal constitution...that is, only as the form of the outer sense altogether." (CPR, B 41) Thus, "Space is nothing other than simply the form of all manifestations of outer senses, that is, the subjective condition of sensory nature, which alone makes our outer perception possible" (CPR, B 42). Thus for Kant, the laws of perceived space coincide with geometric principles that can be thought. In Kant's time, ideas about non-Euclidean measurement and spaces with more than three dimensions had not yet appeared in mathematics. In particular, Kant lacked the clear distinction between topological and metric properties that dates back only to Riemann, so he saw no difference between the topological attribute of limitlessness and the metric attributes (that is, those pertaining to measured relationships) of infinity. Thus, in his explanations of the "antinomies of pure reason," where he proclaims the insolubility of certain problems that cannot be interpreted from his perspective, Kant says, 'The same is true of the dual answer to the question of the size of the cosmos, because if it is infinite and boundless, it is too big for all possible empirical concepts. If it is finite and limited, you are right to ask, What determines the limit?" (CPR, B 515). Kant's concept of space, which clings to three-dimensional Euclidean geometry, could no longer be reconciled with the various concepts of space that developed as mathematics continued to evolve. One of the first to point this out clearly from the perspectives of physics and physiology was Hermann von Helmholtz (1821–1894). On this subject, see Helmholtz's speech Die Thatsachen in tier Wahrnehmung ("Facts in Perception") [1878]. Kant's discussion of the paralogisms (deceptive or faulty conclusions) and antinomies of pure reason constitute the major portion of the second volume, Transcendental Dialectics of The Critique of Pure Reason [1787]. Kant intended his critique of the paralogisms of pure reason as a critique of the claims of the rational psychology of his day (including the problems of unchangeability, preexistence of the soul, etc.) rather than as a discussion of classic paralogisms. "A logical paralogism is the formal falsehood of a rational conclusion, regardless of its content. A transcendental paralogism, however, has a transcendental reason for coming to a formally false conclusion. In this way, a faulty conclusion of this sort has its reasons in the nature of human reason itself and carries an inevitable if not insoluble illusion with it" (CPR, B 399). As he does later in his discussion of the antinomies of pure reason, Kant also attempts here in his discussion of paralogisms to demonstrate that they "dissolve" only when his own view is applied, namely, that we can know only the manifestations of "things as such" and that while our reason can order these manifestations according to regulative principles (such as the perceived forms of space and time), no direct insight into the constitution of things as such is possible. The problem of space plays only a peripheral role in Kant's discussion of the paralogisms of pure reason, namely, in the fourth paralogism about the soul's relationship "to possible objects in space" (CPR, B 402). In contrast, Kant's view of space is of fundamental importance in his discussion of the system of cosmological ideas in the section on the antinomies of pure reason. Of course, three-dimensional Euclidean space was the historical point of departure and, initially, the foundation on which non-Euclidean concepts were developed in projective geometry and the geometries of curved and higher-dimensional space. To this extent, these new forms of space were derivative in nature; although they were not special instances of Euclidean space, they expanded the concept of space on the basis of fundamental Euclidean concepts. Steiner's reference to circular logic has to do with the fact that we achieve only an apparent generalization of the view of space as long as the relevant concepts depend essentially on a Euclidean point of departure. The further evolution of mathematics has shown that we can dispense with the Euclidean foundation, that the laws of space can be developed step by step without presupposing the development of any specifically Euclidean concepts. We begin with a topological manifold that is defined as coordinate-free, supplement it with metrical and, if needed, differential geometric structures, arriving at Euclidean geometry as a special instance of a three-dimensional metric manifold. Seen systematically, there is no longer any circular logic involved in this process. When Steiner answered this question, these issues had not been clarified finally, even among mathematicians. See also Rudolf Steiner's handwritten notes and the corresponding footnotes in no. 114/115 of Beiträge Zur Rudolf Steiner Gesamtausgabe ("Articles on Rudolf Steiner's Complete Works"), Dornach, 1995, p. 49. In any case, with regard to the structure of real space, mathematical concepts, which indicate only which spatial forms are possible, are indeed abstract and remote from reality in this sense, as long as their correspondence with reality has not been established. The concept of space that dates back to Euclid (ca. 320–260 B.C.) can be found in his comprehensive, thirteen-volume work Elements , especially in book XI and, to a lesser extent, in book I. This view of space focuses on the fundamentals of stereometry, that is, calculating the volumes of three-dimensional objects. On the relationship of Imagination, Inspiration, and Intuition to the dimensions of space, see Rudolf Steiner's lectures of August 19 and 26, 1923 (GA 227, pp. 39-41 and 161-163). See also his lectures of May 17, 1905 (GA 324a),- September 16, 1907 (GA 101, pp. 189ff.); January 15, 1921 (GA 323, pp. 274-283); April 8, 1922 (GA 82); June 24, 1922 (GA 213); and the question- and-answer session of April 12, 1922 (GA 82 and 324a). See also Rudolf Steiner's lectures of April 9 and 10, 1920 (GA 201); March 17, 1921 (GA 324); December 26 and 27, 1922, and January 1, 1923 (GA 326). In the section on Goethe's concept of space in Einleitungen zu Goethes Naturwissenschaftlichen Schriften ("Introductions to Goethe's Scientific Works," GA 1, pp. 288-295), Steiner also develops the idea that the three dimensions are not interchangeable, but from a totally different perspective. Essentially, Euclid's three-dimensional geometry is still stereometry, that is, the study of the geometric properties of three-dimensional objects. Right angles and the concept of the perpendicular play an important role in Euclidean geometry, but Euclid placed no particular emphasis on the cube or on the related system of three perpendicular axes. The implicit introduction of such axes as a reference system for the algebraic treatment of curves dates back to Pierre de Fermat (1601–1665) and René Descartes (1596–1650). Both of these mathematicians, however, often used oblique-angled axes, and in their work the coordinate system did not yet play a role as an independent structure that could be dissociated from the geometric object being discussed. Until the end of the eighteenth century, the same was true of developments in analytical geometry based on the work of these pioneers. The systematic application of two perpendicular or oblique directions as a reference system for coordinates and the discussion of algebraic curves occurs first in a treatise by Isaac Newton (1643–1727) entitled Enumeratio Linearum Tertii Ordinis (1676). Newton was also the first to use negative coordinates systematically and to draw curves in all four quadrants of the coordinate system. The analytical geometry of three-dimensional space and the corresponding use of a system of three perpendicular axes dates back to systematic studies of surfaces conducted by Leonhard Euler (1707–1783). Analytical geometry in the modern sense was definitively formulated in the late eighteenth and early nineteenth centuries by Gaspard Monge (1746–1818) and his pupil François Lacroix (1765–1843), who was one of the nineteenth century's most successful authors of mathematical textbooks. Previously, coordinate systems had been used primarily in connection with specific geometrical figures, but in the new analytical geometry, a preexisting coordinate system provided a framework for the study of geometric figures, their internal proportions, and their interrelationships. See the standard work on this subject by Boyer [1956], See the discussion of this problem in Note 8 above. See the question-and-answer session of March 7, 1920, and the corresponding notes, particularly Note 3.

The Fourth Dimension

Questions and Answers XIX

https://rsarchive.org/Lectures/GA324a/English/AP2001/19210407q01.html

Dornach

7 Apr 1921

GA324a-28

QUESTION: Are toe meant to understand that the Sun moves through space in a spiral and that the Earth also moves in a spiral as it follows the Sun and therefore does not revolve around the Sun? In a longer lecture series, [Note 139] it would be relatively easy to discuss these issues in more detail; I have referred to them only briefly here. It is almost impossible to explain their foundations in a few words. Let me begin to respond to your question by simply summarizing the results of spiritual scientific research. [Note 140] First of all, any conclusions we draw about (spatial) relationships in the universe on the basis of observation and from specific perspectives are always one-sided. The Ptolemaic solar system represented a one-sided view, and so do all other models of the solar system, including the Copernican model. Our conclusions about the relationships of moving objects are based on our specific vantage point, and these relationships are invariably supplemented or altered by movements that cannot be measured from that perspective. Having stated this cautious presupposition, I ask you to consider another spiritual scientific finding that will help us develop a view of the relationship of the Earth's movement to that of the Sun. We must imagine that the Sun moves through space on a curved path. If we trace this curve far enough, it proves to be a complicated spiral form. A simplified version looks like this (Figure 65a): The Earth moves along the same path, following the Sun. When you consider the Earth's possible locations in relationship to the Sun, you discover that when the Earth is here, an observer would have to look to the right to see the Sun. Now let me sketch another possible location (Figure 65b). The arrows indicate the direction of view. In the first instance, we saw the Sun by looking in one direction, and now we see it by looking in the opposite direction. As you will easily understand if you visualize this model correctly, the consequence of the Earth following the Sun is that we see the Sun first from one side, and then from the other, and the Earth appears to move around the Sun in a circular or elliptical orbit. The primary component of this movement, the fact that the Earth follows the Sun, is differentiated still further by certain other relationships that would take hours to explain. The truth of the matter, however, is that only our direction of view rotates. As I said, this summary represents the results of lengthy spiritual scientific investigations and is complicated even more when we take other relationships into account. We must realize that as we gain a better overview of the Sun's movements, the simple lines we use to describe the Copernican system to schoolchildren become increasingly complex, until ultimately they can no longer be drawn at all and fall out of the spatial realm altogether. [Note 141] This is what I wanted to say from the perspective of spiritual science. From the perspective of the history of the physical sciences, I would like to comment that what we find so striking today about the research results I outlined above is inherent in the Copernican view. Copernicus postulated three laws. The first states that the Earth rotates around its own axis,- the second, that the Earth revolves around the Sun,- and the third, that the Earth's movement around the Sun provides only a provisional explanation on the conceptual level. While in fact the Earth stands in a fixed relationship to the Sun. [Note 142] This third law proves that Copernicus was truly convinced that the second movement he describes, the Earth's revolution around the Sun, was merely a convention assumed for the convenience of certain calculations and that he did not intend to state it as fact. Today, we consistently disregard this third law and believe that the Copernican model of the solar system encompasses only the first two laws. If we were truly to study the entire Copernican view, however, we would quickly conclude that this [third law] is indeed necessary, simply on the basis of astronomical calculations. [Note 143] You see what often happens in the history of science. Questions and answers (open discussion) during the Summer Art Course at the Goetheanum, August 21 to 27, 1921. Rudolf Steiner's own summaries of his lectures during this conference were published in the Nachrichten der Rudolf Steiner-Nachlassverwaltung ("News from the Rudolf Steiner Archives"), no. 8, 1962, pp. 4-20. (Beginning with no. 29, 1970, the name of this publication was changed to Beitrage zur Rudolf Steiner Gesamtausgabe ["Articles on Rudolf Steiner's Complete Works''].) A detailed conference program was published in the journals Dreigliederung des sozialen Organismus ('The Threefolding of the Social Organism”), vol. 3, no. 5, and Das Goetheanum, vol. 1, 1921-1922, no. 1. Transcripts of the lectures were first published in the periodical Gegenwart ('The Present"). The introductory lecture of August 21, 1921, appeared in vol. 14, 1952-1953, no. 9/10, pp. 353-363; the lecture of August 23, 1921, in vol. 14, no. 11, pp. 417-428; the lecture of August 24, 1921, in vol. 15, 1953-1954, no. 1, pp. 4-19; and the lecture of August 26, 1921, in vol. 15, no. 2, pp. 44-63. Publication of this lecture series is planned for GA 73a. The question-and- answer session appears here in print for the first time. Compare this and the following passages to the question-and-answer session of October 15, 1920, and the relevant notes. See also Rudolf Steiner's lectures of May 2, 1920 (GA 201), and January 16, 1921 (GA 323). In this lecture, Rudolf Steiner lists these laws in the order given by Copernicus in chapter 11 of the first volume of his main work, De Revolutionibus Orbium Coelestinum . See also Notes 2 and 3 to the question-and-answer session of October 15, 1920. Presumably, Rudolf Steiner refers here to Bessel's reductions, which he mentions in the question-and-answer session of October 15, 1920.

The Fourth Dimension

Questions and Answers XX

https://rsarchive.org/Lectures/GA324a/English/AP2001/19210826q01.html

Dornach

26 Aug 1921

GA324a-29

Question about higher-dimensional space. We can say that the ordinary axial coordinate system describes three-dimensional space. Schematically speaking, we can proceed on the basis of certain algebraic assumptions and, on an abstract level, repeat the process that led us from a plane to three-dimensional space. The result is four-, five-, or \(n\)-dimensional space. We can even construct figures such as Hinton's tessaract. The tessaract, however, is not a real figure but simply the projection of a true tessaract into three-dimensional space. [Note 145] On a purely theoretical and abstract level, there is nothing wrong with such deductions. On a theoretical level, we also can move from three-dimensional space to the fourth dimension in time simply by using the formulas and calculations and taking into account the leap that we are making, because moving into time is different from moving from the first to the second to the third dimension. By refining this process, however, we can indeed make the transition to time. The result is an abstract four-dimensional space. We can remain on the abstract, purely intellectual level as long as we do not need to visualize what we are doing. When we attempt to do so, however, we are confronted with a problem of elasticity, whereas our purely abstract train of thoughts led to a regressus in infinitum . We also can imagine initially that a pendulum simply will continue to swing indefinitely, but in dynamics we have oscillations. That is the reality of the situation. When we rise to the level of imaginative perception, we cannot simply repeat the process indefinitely, assuming the existence of a fourth and subsequent dimensions. If we use the notation \(+ a\) for the first dimension, \(+ b\) for the second, and \(+ c\) for the third, we cannot, if we are describing real space, write the fourth dimension as \(+ d\). Instead, the reality of the situation forces us to write \(- c\). The fourth dimension simply nullifies the third, and only two remain. At the end of the process, therefore, we are left with two dimensions instead of four. Similarly, if we assume the existence of a fifth dimension, we must use the notation \(- b\) for it and \(- a\) for the sixth. That is, we come back to a point. [Note 146] Through the principle of elasticity, we have returned to the starting point. This phenomenon not only is present in Imagination — that is, as a subjective experiment — but also becomes a reality in the way I described the day before yesterday. [Note 147] As long as we are looking at the Earth's surface here and plant roots here (Figure 66a), we are dealing with a specific manifestation of gravity and remain within the ordinary dimensions of space. When we attempt to explain the shape of a flower, however, these ordinary dimensions no longer suffice. Instead of taking the intersection of the axes as our starting point, we must begin with infinite space, which is simply the counterpart of the point. Instead of moving centrifugally outward, we must move centripetally inward (Figure 66a). The result is a wavy surface. Instead of dissipating into the distance, pressure is exerted from outside, resulting in gliding and scraping movements. Such movements, which result from pressure, cannot be described correctly by taking the intersection of axes as the starting point for our coordinates. Instead, we must take an infinitely large sphere as the center of the coordinates, and the coordinates must all move toward the center. [Note 148] That is, as soon as we move into the etheric realm, we need to apply an axial coordinate system that is the opposite — also qualitatively speaking — of the ordinary coordinate system. Ordinary theories about the ether of physics err in not taking this difference into account, making it difficult to define the ether. It is sometimes seen as a fluid and sometimes as a gas. It is wrong to apply a coordinate system that radiates from a central point to the ether. As soon as we enter the ether, we must take a sphere and construct the whole system from the outside in, instead of the other way around. Such issues become interesting when they are traced mathematically and enter the domain of physics. Developing our theories, which begin to seem very realistic, would contribute a great deal to solving problems of limits. At present, however, such theories meet with very little understanding. For example, I once attempted to introduce this subject in a lecture to the mathematical society of a university. [Note 149] In this lecture, I said that if these are the asymptotes of a hyperbola and these its branches, we must imagine that the part on the right is dissipating, while the part on the left is becoming concentrated. That is, a complete reversal takes place (Figure 66b). Such considerations gradually lead us to a more concrete treatment of space, but this treatment finds little acceptance. Purely analytical mathematicians often are somewhat biased against synthetic geometry. Modern synthetic geometry, however, permits us to move away from purely formal mathematics and tackle empirical problems. As long as we apply only purely analytical geometry, we cannot approach the domain of reality. Analytical geometry allows us to establish only the endpoints of coordinates, their geometric locations, and so"on. When we restrict our constructions to lines and circles, we need the help of images and are forced to turn to visualization for help. What makes synthetic geometry so beneficial is that it allows us to leave behind the formal aspect of mathematics. It shows us how we must conceive of the mathematical element in nature. [Note 150] Question about the theory of relativity. The discussion about the theory of relativity is endless. [Note 151] This theory cannot be refuted from our vantage point as observers of cosmic events in three-dimensional space. That is, it is impossible to refute the theory of relativity on the basis of perceived space. As far as our perception is concerned, of course, it makes no difference whether a sphere flattens out or space as a whole expands inward in the direction of the sphere's flattening. Thus, as long as we are dealing with the perspective of three-dimensional space, Einstein's theory of relativity is absolutely correct. This theory appeared at the very moment in humanity's evolution and in the history of science when we first managed to think in purely spatial terms — that is, to take Euclidean space as our starting point for further thinking, whether in the sense of non-Euclidean spaces or in the sense of relativity theory. It is impossible to refute Einstein's theory in three-dimensional space. We can begin to discuss the possibility of refuting this theory only when we discover how to make the transition to the etheric realm — that is, the transition from the three-dimensional spatial body to the ether body. The ether body is centripetally, rather than centrifugally, formed. In your ether body, you dwell within the totality of space. For example, your inner perception of the distance between point A and point B is sometimes this and sometimes that (Figure 67a). Having recognized this phenomenon, you can say that one or the other of the points must have moved, in absolute terms, but to do that you yourself must stand within the totality of space. At this point, discussion becomes possible. For this reason, I am convinced that all of our discussions of current concepts about the theory of relativity must end in the question, "Well, how do you know that?" In contrast, as soon as we make the transition to inner perception — a domain where absolutes can be discovered — we are forced to realize that issues such as the theory of relativity show us that we have arrived at what Nietzsche calls the observers standpoint, of which the theory of relativity represents the most extreme version. For anyone who accepts this standpoint, the theory of relativity is simply a fact, and no arguments against it are possible. It can, however, be eliminated from practical considerations. A fanatical relativity theorist in Stuttgart once explained why it makes no difference whether we make a movement in one direction or the opposite direction. If I hold a matchbox in one hand and a match in the other, the result is the same whether I move the match past the box or the box past the match. Of course, in such cases the theory of relativity is absolutely correct, but I would have liked to shout out, "Please try again with the box nailed to the wall!" This in no way diminishes the validity of the theory of relativity. It simply shows that just as we can move from two-dimensional space into the dimension of depth, we can move into the spiritual element from any location in the world. Then and only then does the theory of relativity cease to be valid. That's why I said that discussions about the theory of relativity tend to go on ad infinitum, because it is irrefutable from the observer's standpoint. Any arguments against the theory can always be disputed. As an observer, you stand outside what you are observing; you must make a radical distinction between subject and object. As soon as you rise to higher levels of knowledge, subjectivity and objectivity cease. There is much more that could be said on this subject than can possibly be said in the context of a question-and- answer session, but I would like to submit one more idea as a stimulus to further thinking. As long as we remain in the beholder's world, in the world of space, relativity theory as such is irrefutable. On first escaping from this world, we enter worlds where we are not mere beholders but share the experience of the object, such as pain, for example. As soon as you learn to shift from mere relationships with other beings — and it is understandable enough that a theory of relativity is possible only within relationships — to the pain of shared inner experience, to use an example, it is no longer possible to speculate about whether this experience is relative. Thus, you cannot construct contradictions and then say that because a contradiction exists, the situation is not real. In life, contradictions are reality, because the beings that constitute life belong to different but intersecting spheres. As soon as you make the transition to reality, it is no longer permissible to say that any contradiction that exists must be resolved. If it is real, it cannot be resolved. My point here is that the theory of relativity is a natural development in the world of relationships. No arguments could be raised against this theory if the beholder's standpoint were the only possible perspective. As soon as we become involved in beings, however, and in pain and pleasure, the theory of relativity is no longer tenable. QUESTION: Dr. Steiner, what do you mean when you say that the physical body is a spatial body while the body of formative forces is a temporal body? The physical body is also active in time when it grows and declines. Yes, but your statement is based on imprecise thinking, if I may say so. To give it a more exact foundation, you first would have to analyze the concept of time. Consider this: In the reality we usually encounter, space and time intermingle. We can conceive of the physical body as spatial and the body of formative forces as temporal only when we separate space and time. In our usual objective knowledge, time is not present as a given. As you know, time is measured in terms of space, — that is, changes in spatial units are our means of knowing about what we call time. But now imagine a different way of measuring time. You no longer measure time in terms of space when you shift to a true experience of time, which people usually do unconsciously. Our thinking actually becomes conscious through imaginative cognition. You have a true experience of time, for example, if you examine your soul life on April 12, 1922, at 4:04 and however many seconds. You see a temporal cross-section of your soul life. Although you cannot say that this temporal section contains any particular spatial section, it includes all of your immediate earthly past. If you want to draw it schematically, and the stream of your experience flows from a to \(b\), you must draw the section \(AB\) (Figure 67b). Figure 67b You cannot avoid interposing your entire experience into this section, and yet there is a perspective in it. You can say that events lying further back in time are reproduced with less intensity than more recent events. All of these events, however, are present in the single section. As a result, the connections are different from what they are when you analyze time. We can raise time to the level of a mental image only when we refrain from analyzing it as we do in physics, according to methods of understanding space, and instead reflect on our soul life. As long as you have only abstract thoughts, however, your soul life remains stuck in the time body. It is important to be able to see this time body as an organism. As you know, when you have a digestive disturbance, for example, you may find that other parts of your spatial organism also are affected adversely. In the spatial organism, individual areas are spatially separate from each other, while in our time organism — in spite of the fact that we differentiate between later and earlier — different times are related organically. I sometimes use the following example. When some very old people talk to younger ones, especially to children, their words seem to bounce right off; they mean nothing to the children. This is not the case with other old people. When they talk to children, their words seem to flow straight into the children's souls. To find the origin of the power of old people to bless others, you sometimes have to go back to their early childhood. (We usually do not study matters such as this, because we very seldom look at the whole person. We do not focus our attention long enough to observe such things. The scope of our present powers of observation is inadequate. That is a task for anthroposophy.) If you go back far enough, you will find that those who possess an unusual spiritual power to bless others in their old age, whose words flow as blessings into young people, learned how to pray in their own childhood. Metaphorically speaking, we can say that the folded hands of childhood become the blessing hands of old age. [Note 152] Here you see a connection between a person's influence on others in old age and the pious sentiments and so on that were present in that person's early childhood. Earlier qualities and later ones are connected organically. There are an infinite number of such connections in each person, but we see them only when we understand the whole human being. Today our whole life is external to this reality. We think we are steeped in reality, but we deceive ourselves. In today's culture, we are abstractionists. We pay no attention to true reality and therefore disregard qualities such as those I mentioned. We also pay no attention to the fact that when we teach children, especially in the elementary grades, we must avoid giving them sharply defined concepts. The effect of such concepts on later life is similar to that of binding limbs and not allowing them to grow larger. What we communicate to children must be an organism, and it must be flexible. I hope that you are gradually becoming able to see what I mean by an organism. Of course, Imagination alone makes it possible to grasp this meaning completely. Nonetheless, it is possible to gain an idea of the nature of an organism simply by realizing that the temporal course of events in the life of a human being is related to the time organism rather than to the space organism. You see, time possesses an inherent reality, as you can infer from mathematics. I believe it was Ostwald — in any case, it was not an anthroposophist but simply someone who is not a materialist — who pointed out in a wonderful discussion of this subject that, unlike mechanical processes, organic processes that take place over time are not reversible. [Note 153] In fact, ordinary calculations always remain external to temporal processes and do not allow us to approach them. For example, if you insert negative numbers into a formula for calculating eclipses of the Moon, you get instances in the more distant past, but you do not move away with the things. You move only in the sphere of space. Thus, we develop a correct idea of the actual physical human body only when we are able to separate the temporal element from the spatial. This is fundamentally important with regard to human beings, because we cannot come to any understanding of human beings if we do not know that the temporal element in humans runs its course as an independent entity and that the spatial element is governed by the temporal or dynamic element. In machines, however, the temporal element is only a function of activity in space. That is the difference. In humans, the temporal element is a real entity, while in mechanical devices the temporal element is only a function of space. QUESTION: Einstein says that the time-space continuum is four-dimensional. If I understood correctly, you said that the fourth dimension becomes two dimensional because the fourth dimension is a negative third dimension. Should this be interpreted to mean that there is a connection between the imaginative world and Einsteins continuum? According to conventional scientific thinking, I would have to conclude that such a space is a plane. Consequently, the imaginative world would be a very specific plane in three-dimensional space. It would not have to be straight, and it would not have to remain in the same place, but it would have to be possible to confirm its presence at any given moment. My thoughts on this subject are probably not in line with anthroposophy, but I would like to know what anthroposophy has to say about it. With the exception of a few comments, your thoughts are quite in line with anthroposophy. I would like to add that it is absolutely correct that when we attempt to shift from the three dimensions to the fourth on a real rather than abstract level, we must use a negative sign to describe the fourth dimension. That is, the transition to the fourth dimension simply eliminates or cancels out the third, just as debt cancels out savings. There is no other way of imagining the situation. But if we simply hurry on abstractly, we come to the regressus in infinitum that assumes the existence of more and more dimensions. This, however, is an abstract way of continuing and is not based on actually looking at the situation. When we enter the imaginative world, we do indeed confront a plane world, to use an expression borrowed from geometry. We confront the world of the plane of time. One peculiar feature of this world is that it can no longer be referred back to the third dimension of space. This is difficult to understand, but you will find an analogous situation in synthetic geometry, which is forced to consider the boundary of three-dimensionality — if, in fact, we impose boundaries on the three-dimensional world — as a surface and as a plane surface rather than a spherical surface. That is, synthetic geometry assumes that three-dimensional space is bounded by a plane. When you reach the boundary of three-dimensionality, you find a plane whose limit, in turn, must be imagined as a straight line rather than a circle, and this straight line has one, rather than two, endpoints. [Note 154] At this juncture, your thinking and your perception cannot completely coincide, no matter how consistent it is to speak of a plane as the boundary of three-dimensional space, of a straight line as the boundary of a plane, and of a single infinitely distant point as the limit of a straight line. To synthetic geometry, these ideas are real. Synthetic geometry plays into the perception that develops in the imaginative world. But when we say that the imaginative world lies in a plane, we cannot refer this plane back to three-dimensional space by defining its coordinates. It is lifted out of three-dimensional space and is anywhere and everywhere. This is difficult to imagine because we are used to visualizing in three-dimensional space. The imaginative world, however, does not lie in three-dimensional space, and the definitions of three-dimensionality do not apply to it. We find another analogue for the imaginative world in art, when we practice painting on the basis of color. When we do so, we are working on a flat surface, or, if we work on a curved surface, its curve does not originate in the painting but in other circumstances. When we paint on a plane, our possibilities are not limited to drawn perspective, which is a relatively recent discovery, as you may know. Perspective appeared very late in the history of painting, only a few centuries ago. [Note 155] In addition to drawn perspective, however, we can utilize the perspective inherent in color. [Note 156] We have been using such principles in our painting in Dornach. On the basis of feeling and color, rather than thoughts, yellow appears to come toward us so strongly that it is almost aggressive. In contrast, when we use blue paint, the color recedes, yet both colors lie on the same surface. Thus, it is possible to express three-dimensional phenomena even though only a two-dimensional expanse is available to us. This is simply an example to help you visualize the situation, because the imaginative world is not the same as the world of painting. Although the ideas you expressed in your question are very true to anthroposophy, we cannot really say without qualification that the imaginative world has a connection to Einstein's continuum. Einstein's continuum is based on abstraction rather than perception. Its fourth dimension is constructed as an analogue to the other three dimensions, which is not acceptable when we move from objective cognition in space to real suprasensible cognition, which manifests first as Imagination and can be expressed in spatial terms only by allowing the third dimension to be cancelled out by its negative. What I am going to say next will seem very daring to some, — nonetheless, it is my experience. In reality, the situation looks like this: When you function in the objective world with healthy common sense, your orientation is derived only from the three dimensions of space. The first dimension is inherent in your own upright posture, the second in your left-right dimension, and the third in the focusing of your eyes. You do not dwell in these three dimensions when you are in the imaginative world. There, you dwell only in two dimensions. If I had to locate these dimensions in space, I would have to take a vertical section through the human being. In Imagination, we can speak only of the dimensions of up and down and right and left. When you move in the imaginative world, these are the only dimensions you carry with you. For this reason I cannot say that they relate to a coordinate system in space. I cannot define them in terms of Euclidean geometry. To our perception, however, they are real. It makes no sense to talk about three dimensions in the context of the imaginative world. We must realize that we are dealing with an experience of two-dimensionality, an experience we cannot have in the objective world. Two dimensions are a reality in the imaginative world, and a single dimension is a reality in the inspired world. All Inspirations move vertically, if indeed we want to assign them a location in space. Intuition is point-like, but it to cannot be referred to a coordinate system. In these higher realms, we cannot revert to Euclidean space. For more information on Hinton, see Note 1 to the lecture of March 31, 1905. On the tessaract, see the lecture of May 31, 1905, and the relevant notes. See Notes 10 and 11 and the corresponding passages in the question-and-answer session of April 7, 1921. See Rudolf Steiner's lectures of April 8, 9, and 10, 1922 See the similar passages at the end of Rudolf Steiners lecture of January 10, 1921 (GA 323, pp. 199-200) and at the beginning of the lecture of January 18, 1921 (GA 323, pp. 318-320). Presumably Rudolf Steiner refers here to the lecture he gave to the Mathematical Society in Basel during the winter semester of 1920-1921. For more about this lecture, see the essay Über einen mathematischen Vortrag Rudolf Steiners in Basel ("On a Mathematical Lecture by Rudolf Steiner in Basel") in B eiträge zur Rudolf Steiner Gesamtausgabe ("Articles on Rudolf Steiner's Complete Works"), no. 114/115, Dornach, 1995. See the parallel passages in the lectures of January 11, 1921 (published in Gegenwart ['The Present"], vol. 14, pp. 49-67, especially p. 65) and April 5, 1921 (GA 76). See the question-and-answer session of March 7, 1920, and the relevant notes. For more on this subject, see the lectures of October 28, 1909, and February 10, 1910, in Rudolf Steiner's Metamorphosen des Seelenlebens ('The Metamorphoses of Soul Life") and Pfade der Seelenerlebnisse ("The Paths of Soul Experience"), GA 58 and 59. Friedrich Wilhelm Ostwald (1853–1932), chemist, color theorist, and scientific philosopher. In his lecture Die Überwindung des wissenschaftlichen Materialismus ("Overcoming Scientific Materialism) of September 20, 1895, which included a plea for his own energetics-based worldview and consciously contrasted it to the mechanistic worldview of Emil du Bois-Reymond (1818–1896), Ostwald said: While efforts to interpret the familiar phenomena of physics in mechanical terms may seem in vain, having ultimately failed in every single serious attempt, the conclusion is unavoidable that success is even less likely with regard to the incomparably more complex phenomena of organic life. The same principled contradictions apply here, too, and the claim that all natural phenomena essentially can be traced back to mechanical phenomena cannot even be considered a usable working hypothesis,- it is a simple error. This error becomes most apparent when we confront the following fact. A feature of all mechanical equations is that they permit changing the sign of the unit of time. That is, theoretically perfect mechanical processes can run backward as well as forward. In a purely mechanical world, therefore, there would be no earlier and later as we know them in our world. A tree could revert to the seed stage, a butterfly could be transformed back into a caterpillar, and an elderly person into an adult. The mechanistic worldview cannot explain why this does not occur, and because of the above-mentioned feature of mechanical equations, no such explanation is possible. Thus, the non-reversibility of true natural phenomena proves the existence of processes that cannot be described by mechanical equations and pronounces judgment on scientific materialism ([1895], p. 20). Steiner means that a projective straight line must be visualized as having only one (rather than two) infinitely distant points. The founder of modern perspective was Filippo Brunelleschi (1377–1446), the architect and builder of the cupola of the cathedral in Florence. The new theory of perspective was first promoted by the architect and scholar Leon Battista Alberti (1401–1472) and the painter and mathematician Piero della Francesca (1416–1492). A work by Albrecht Dürer (1471–1528), Underweysung der messung mit dan zirckel und richtscheyt in linien, ebnen, und gantzen corporen ("Instruction in Measuring with Compass and Straightedge in Lines, Planes, and Solid Bodies," 1525) had a decisive influence on the cultural region north of the Alps. 0n color perspective, see Rudolf Steiner's lectures of June 2, 1923 (GA 291), and April 19, 1922 (GA 304, p. 208), and the question and answer session of March 11, 1920.

The Fourth Dimension

Questions and Answers XXI

https://rsarchive.org/Lectures/GA324a/English/AP2001/19220412q01.html

The Hague

12 Apr 1922

GA324a-30

DISCUSSION: As you will have gathered from the lecture, we must make a distinction between tactile space and visual space. This difference can stimulate us to move beyond considering mathematics on the one hand and the physical world on the other. As you may know from my lectures, [Note 157] it remains true that mathematics is a product of the human spirit or of the human being in general. And that as we move further into purely mathematical domains — that is, domains that are delineated in mathematical terms — we become less and less able to apprehend reality. [Note 158] You have all seen the difficulties that have arisen repeatedly in modern times when people have attempted to use mathematics to describe reality. For example, if you consider the transition from an infinitely large sphere to a plane, you scarcely will be able to reconcile this cornerstone of projective geometry with our ordinary ideas of reality, which are based on empirical interaction with the world around us. [Note 159] Consequently, our task — and many people with the appropriate educational background would have to work very hard at it — is to attempt to use mathematical ideas to apprehend reality in very concrete domains. [Note 160] At this point, I would like simply to present the problem. It can be solved successfully only if mathematicians really begin to work seriously on it. I have provided a theoretical explanation of tactile space. Now try to handle this space in a way that necessarily incorporates all of our earthly experience of touch — in fact, that is what we are dealing with. We must incorporate all of our tactile experience, including its inherent dimensionality, into our relationship to gravity. We are subject to gravity, and the various centripetal forces coming in different directions from the periphery make it possible to set up differential equations. With regard to tactile space, we must handle these equations in the same way that we handle equations for determined movements in analytical geometry and analytical mechanics. [Note 161] It then becomes possible to integrate these equations, which gives us specific integrals for what we experience in tactile space, whereas differentials always lead us out of reality. Integrating these differentials results in the diagrams I told you about the day before yesterday. [Note 162] If you want to return to their reality, you must do it as I indicated in that lecture. You must work with the integral equations in the domain of real touch. It will become evident that with regard to touch, the vertical dimension has a certain differentiation, so that the variable x in this equation must be preceded by a plus or minus sign. This makes it possible to set up integrals for our experiences of tactile space. Let me formulate it like this: The result would be integrals for our experiences of tactile space. Now let's move on and apply the same principle to visual space. Once again, we set up differential equations that we must handle in the same way that we handle equations for determined movements in analytical geometry and analytical mechanics. We will see that when we integrate, we get very similar integrals, but ones that must be thought of as negative (taking into account that the variable \(x\) was positive in the last instance). When we handle the integration in this way (I'll dispense with all the trimmings), we get a result that leads to other integrals: But when I subtract the two from each other, they almost cancel each other out and the result approaches zero. That is, when I integrate with regard to visual space, the result is integrals that cancel out those for tactile space. And the integrals for tactile space remind me very much — though they are more extensive — of all the formulas I need for circumstances and relationships that refer to analytical geometry or mechanics in general. The only difference is that gravitation must be included in the mechanical formulas. I get integrals for visual space that seem applicable if I simply can find the right way to express the spatial aspect of vision in mathematical terms. It is always the case that we begin with a trivial instance and set up constructions about vision and fail to note that we must count on inevitable vertical movement when we consider visual space. We must accept that vision is always forced to work in the opposite direction from gravitation. [Note 163] Taking this fact into account, it becomes possible to relate the integrals to mechanics on the one hand and optics on the other hand. In this way, we formulate mechanics, optics, and so on in usable integrals that encompass the reality of a situation. It is not quite true, however, that the difference between the integrals is zero. In actual fact, it is a differential, and instead of writing zero, I must write: If repeated searches for such integrals and the resulting differentials lead to differential equations corresponding to \(dx\), I then will see that when I take \(dx\) to be positive here and negative there, \(dx\) is an imaginary number in the mathematical sense. If I integrate the resulting differential equation, however, the result is astounding. You can experience it for yourselves if you solve the problem correctly. This step leads to acoustics, to acoustical formulas. Thus, you really have used mathematics to apprehend an intrinsic reality. You have learned that we must write mechanics down below on the vertical and vision up above on the vertical — since light is equal to negative gravitation — while hearing, in reality, takes place horizontally. When you set up these calculations, you not only will observe discrepancies — mathematics on the one hand and physics on the other — as a result of the LaGrange equations. [Note 164] But you also will see that the work that can be done on this basis in the realm of mathematics and physics is just as productive as the work 1 pointed to earlier in the domain of phylogenetics. [Note 165] Along these lines — by working things out, not through merely descriptive considerations — we discover the differences between modern natural science and anthroposophy. We will have to demonstrate that our calculations are firmly rooted in concrete realities. ,57Rudolf Steiner's additional comments during the lecture cycle Der Enstehungsmoment der Naturwissenschaft in der Weltgeschichte und ihre seitherige Entwickelung ('The Emergence of the Natural Sciences in World History and Their Subsequent Development"), GA 326. Comments on the discussion following a lecture by Ernst Blümel (1884–1952) on "Die vier Raumdimensionen im Lichte der Anthroposophie" ("The Four Dimensions of Space in the Light of Anthroposophy"). To date, no transcript of Blümel's lecture has been found. my lectures: The lectures given on December 26-28, 1922 (GA 326). On tactile and visual space, see Rudolf Steiner's lectures of March 17, 1921 (GA 324), and January 1, 1923 (GA 326). Rudolf Steiner points to the transition from a sphere to a plane or a circle to a straight line in many different places. See the parallel passages in this volume in the lecture of March 24, 1905, and in the questions and answers of September 2, 1906,; July 28, 1908; and November 25, 1912. For more about "apprehending reality" through projective geometry, see Rudolf Steiner's lectures of January 11, 1921 (published in Gegenwart ["The Present"], vol. 14, 1952, no. 2, pp. 49-67; planned for publication in GA 73a); April 5, 1921 (GA 76); and the question-and-answer session of April 12, 1922 (GA 324a and 82). Today inevitable movements are understood as movements possessing only one degree of movement, that is, movements that are so restricted that only one free parameter for movement exists. Presumably, however, what Steiner means here is the very general problem of movement subject to secondary conditions. The Newtonian formulation of mechanics proves unwieldy in calculating movements subject to secondary conditions. Furthermore, this formulation made it difficult to introduce standard, non-rectilinear coordinates for movement. The LaGrange equations , which are based on a principle of mechanical variation, offer elegant solutions to both problems. '“See Rudolf Steiner's lecture of December 27, 1922 (GA 326). On negative gravitation, see Rudolf Steiner's lectures of January 7 and 8, 1921 (GA 323). LaGrange equations: Joseph-Louis LaGrange (1736–1813), mathematician, physicist, and astronomer in Turin, Berlin, and Paris. The derivation, discussion, and application of the equations later named after LaGrange constitute the majority of his book Mécanique Analitique (Paris, 1788). On the LaGrange equations, see Note 159. , Phylogatetics: See Rudolf Steiner's lecture of December 28, 1922 (GA 326).

The Fourth Dimension

Questions and Answers XXII

https://rsarchive.org/Lectures/GA324a/English/AP2001/19221229q01.html

Dornach

29 Dec 1922

GA324a-31

Recent lectures given at the Goetheanum have laid repeated emphasis on the fact that the Spiritual Science cultivated here must work fruitfully upon the whole scientific mind of to-day and also upon the various branches of science. This is perhaps brought home to us most strongly of all when we realise the light that is shed by Spiritual Science upon the problems of history. And so far as the limits of two brief lectures allow, we will try to go into this matter. On many sides to-day it is being said that the science of history is facing a crisis. Not so very long ago, among certain circles in the days of the historian Ranke, it was held that history must be made into an ‘exact’ science — exact in the sense in which this expression is used in connection with ordinary scientific research. We often hear it said by those to whom ‘exact research’ implies the methods current in the domain of external science, that all historical writings are inevitably coloured by the nationality, temperament and other personal propensities of the historian, by the element of imagination working in the condensation of the details, by the depth of his intuitive faculty and the like. And as a matter of fact in the most recently written histories it is abundantly evident that the presentation of objective facts and events varies considerably according to the nationality of the historian, according to his power of synthesis, his imagination and other faculties. In a certain respect, Spiritual Science is well fitted to cultivate an objective outlook in the study of history. It is, of course, not to be denied that the measure of talent possessed by the historian himself will always play an important part. Nevertheless, in spite of what our opponents choose to say to the contrary, it is precisely in the study of history that a quality essentially characteristic of Spiritual Science comes into play. By its very nature Spiritual Science must begin with a development of the inner, subjective faculties in the being of man. Forces otherwise latent in the soul must be awakened and transformed into real faculties of investigation. The subjective realm, therefore, is necessarily the starting-point. But in spite of this, the subjective element is gradually overcome in the course of genuine spiritual research; depths are opened up in the soul in which the voice of objective truth, not that of subjective feeling, is speaking. It is the same in mathematics, when objective truths are proclaimed, in spite of the fact that they are discovered by subjective effort. From this point of view I want to speak to you of a chapter of history which cannot but be of the deepest interest to us in this modern age. I will choose from the wide field of history the more spiritual forms of thought which came to the fore in the nineteenth century, and speak about their origin in the light of Spiritual Science. To-day I propose to deal with the more exoteric aspect — if I may use this expression — and pass on in the next lecture more into the realm of the esoteric connections and deeper causes underlying the facts of the spiritual and mental life of humanity. As we look back to the nineteenth century — and the character of the first twenty years of the twentieth century is really very similar — the impression usually is that thought in the nineteenth century developed along an even, regular course. But those who go more deeply into the real facts discover that this was by no means the case. About the middle of the century a very radical change came about in the development of thought. The mode of thinking and outlook of men underwent a metamorphosis. People began to ask questions about the nature of the impulses underlying social life in the past and present. It is only possible to-day to indicate these things in a few characteristic strokes, but this we shall try to do. Leading minds in the first half of the nineteenth century were all characterised by certain spiritual and idealistic aspirations, in spite of the fact that they were the offspring of the kind of thought that had become habitual in the domain of natural science. These leading minds were still, to a certain extent, conscious of their dependence upon an inner guidance A few definite examples will show that this changes entirely in the second half of the century. In following up this particular line of development we shall not be able to concentrate upon those who were either scientists or artists in the narrower sense. We shall have to select typical representatives of scientific thought at that time who set themselves the task of clarifying the problems of the social life which had become more and more insistent in the course of the nineteenth century. More and more it was borne in upon eminent thinkers that the only way of approach to the problems of the social life was, on the one hand, to emphasise the importance of the results achieved by science and, on the other, to deal with the depression which had so obviously crept into the life and impulses of the soul. In the first half of the nineteenth century, we find a representative personality in Saint-Simon , a son, as it were, of the French Revolution, and who had thoroughly imbibed the scientific thought of his time. Saint-Simon was one whose mind, at the end of the eighteenth and beginning of the nineteenth centuries, may be taken as a typical example of the scientific thinking of the day. He was also deeply concerned with the social problem. He had experienced the aftermath of the French Revolution and had heard the cry for Liberty, Equality, Fraternity resounding from the depths of the human soul. But it had also been his lot to experience the disappointments suffered by Europe alter the Revolution. He witnessed the gradual emergence of what, later on, became the burning social question. And if we study the whole temper and outlook of Saint-Simon's mind, it is clear that he was a firm believer in the fact that knowledge can ultimately lead to ideas which will be fruitful for the social life, provided always that these ideas are in inner harmony with the demands of the times. He was convinced that study, understanding and enthusiasm for the tasks of social life would lead to the discovery of something which could be communicated to men, and that they would respond to knowledge born of enthusiasm for the betterment of social life and presented to them in a form suited to the conditions of the age. Betterment and progress — so thought Saint-Simon — will come about in the social life of Europe through the co-operation of individuals who have both understanding and strength of will. Saint-Simon was imbued with the firm belief that it is possible to convince human beings when one's own mind has grasped the truth and is capable of presenting it to others in the proper scientific form. And so he tries to base all his work upon the spiritual and mental conceptions of his day. He looks back to times which, in his opinion, had already fulfilled their mission; he thinks of the power once possessed by the nobles and the military class, and says to himself: In earlier times the nobles and the military class had their purpose and function. The nobles provided military forces for the protection of those who desired to devote their energies to the so-called arts of peace. But — thought Saint-Simon — in earlier times the priesthood too was a factor of great significance. For long ages the instruction and education of the people were in the hands of the priesthood and the priests were the bearers of the spiritual life. But this state of things has long since passed away. The nobles and the military class, nay even the priesthood, have lost their raison dêtre . And on the other hand, an entirely new line of activity has established itself in civilised life. Saint-Simon was well aware of all that the development of industry and industrial science meant in the evolution of humanity. He said to himself: This industrial development will in its turn give rise to a kind of thinking that has already been adopted by natural science, is employed in physics, chemistry, biology, and will inevitably spread to the other sciences. In astronomy, chemistry, physics and physiology we find evidences of the kind of thinking that is current in the modern age. But it is also essential to inaugurate a science of man, in other words, psychology and sociology. The principles of physics must be introduced into political science and then it will be possible to work and act effectively in the domain of social life. What is needed — so said Saint-Simon — is a kind of ‘political physics,’ and he set out to build up a science of social life and action that should be in line with the principles of chemistry, physics and physiology. Saint-Simon considered that this kind of thinking was evitable because of the overwhelming importance which industrial life was beginning to assume in his day, and he was convinced that no further progress would be possible in industry if it remained under the old conditions of subordination to the military class and to the priesthood. At the same time Saint-Simon indicated that all these changes were to be regarded as phases. The priests and the nobility had had their function to perform in days gone by and the same significance was, he said, now vested in the scholars and the industrialists. Although in former times a spiritual conception of life was thoroughly justified, the kind of thought that is fitting in the modern age, said Saint-Simon, is of a different character. But something always remains over from earlier times. Saint-Simon's rejection of the older, sacerdotal culture was due to his intense preoccupation with the industrialist mode of thinking that had come to the fore in his day. He spoke of the old sacerdotal culture as a system of abstract metaphysics, whereas the quest of the new age, even in the sphere of politics, must be for philosophy concerned as directly with concrete facts as industrial life is concerned with the facts of the external world. The old sacerdotal culture, he said, simply remains as a system of metaphysical traditions, devoid of real life, and it is this element that is found above all in the new form of jurisprudence and in what has crept into political life through jurisprudence. To Saint-Simon, jurisprudence, and the concepts on which it was based, were remnants and shadows of the time when sacerdotalism and militarism had a real function to perform in the life of the people. The views of a man like Saint-Simon are born of the scientific mode of thinking which had become so widespread in the eighteenth century, and even before that time. It is a mode of thinking which directs all inner activity in man to the external world of material facts. Saint-Simon's attitude, however, was influenced by yet another factor, namely, the demand for individual freedom which was at that time arising from the very depths of man's being. On the one side we find the urge to discover natural law everywhere and to admit nothing as being ‘scientific’ which does not fall into line with this natural law. — And on the other side there is the insistent demand for individual freedom: Man must be his own matter and be able in freedom to find a place in the world that is consistent with the dignity of manhood. These two demands are, as a matter of fact, in diametrical opposition to one another. And if we study the structure of the life of thought in the nineteenth century, we realise that the mind of Saint-Simon and others like him was faced continually with these great problems: How can I reconcile natural law — to which man too must, after all, be subject — with the demand for human freedom, for freedom of the individuality. In the French Revolution a materialistic view of the universe had been mingled with the inner demand for individual freedom. And it was the voice of the French Revolution, sounding over into the nineteenth century, which led men like Saint-Simon to this bitter conflict in the realm of knowledge. — The laws established by natural science hold good and are universal in their application. They obtain also in the being of man, but he will not admit it because within this body of scientific law he cannot find his freedom as an individual. And so at the beginning of the nineteenth century, men like Saint-Simon stood as it were without ground under their feet before two irreconcilable principles. In trying to solve the problems of social life it was a question, on the one side, of keeping faith with science and, on the other, of discovering a form of social life wherein the freedom of true manhood is preserved and maintained. Saint-Simon tried hard in every direction to find ideas for the institutions of industrial life and of human life in general which might bring him satisfaction. But again and again he was baffled by the incompatibility of these two demands of his age. The conflict, moreover, did not only make itself manifest in individual minds. Over the whole of the thought-life and its offspring, namely, the political and economic life of the beginning, of the nineteenth century, there loomed the shadow of this conflict. On the one side men yearn for unshakable law and, on the other, demand individual freedom. The problem was to discover a form of social life in which, firstly, law should be as supreme as in the world of nature and which, secondly, should offer man the possibility of individual freedom. The shrewdest minds of the age — and Saint-Simon was certainly one — were not able to find ideas capable of practical application in social life. And so Saint-Simon prescribes a social system directed by science and in line with scientific habits of thought. — But the demand for individual freedom finds no fulfilment. A cardinal demand had thus obtruded itself in the life of the times, and is reflected in many a mental conflict. Men like Goethe, not knowing where to turn and yet seeking for a reconciliation of these two opposing principles, find themselves condemned to a life of inner loneliness. At the beginning of the nineteenth century there is a feeling of despair in face of the fact that human thinking, in spite of every effort, is incapable along these lines of discovering a practicable form of the social organism. And the consequence of this is that minds of another character altogether begin to make a stir — minds not fundamentally under the influence of scientific thought nor desirous of applying the abstract demands of the French Revolution but who aim at establishing some permanent principle in the social life of a Europe shaken by the Revolution and the deeds of Napoleon. And support is forthcoming for a man like de Maistre who points back to conditions as they were in the early centuries of Christendom in Europe. De Maistre, born in the South of France, issued his call to the French Nation in the nineties of the eighteenth century, wrote his striking work on the Pope and also his Soirées de St. Petersbourg . He is the most universal mind among the reactionaries in the first half of the nineteenth century — a shrewd and ingenious thinker. He calls the attention of those who are willing to listen to the chaos that must gradually ensue if men prove incapable of evolving ideas upon which a social order may be built up. From this point of view he criticises with considerable acrimony those whom he considers responsible for the chaos in modern thought, among them, Locke, and he lays it down as an irrefutable principle that no social order worthy of the name can arise unless the civilisation of Europe is imbued once again with the old Catholic spirit of the early centuries of Christendom. We must be absolutely objective in our study here and try to put ourselves in the place of a man like de Maistre and of those who even to-day still think more or less as he did. We must be able to see with the eyes of one who is convinced that no true social science can be born of modern scientific thought and that if no spiritual impulse can find its way into the social organism, chaos must become more and more widespread. It is, of course, true that neither de Maistre himself nor those who listened to his impassioned words perceived the reality of a new spiritual impulse. De Maistre pointed back to olden times, when the building of social order had actually been within the capacity of men. In the world of scientific thought to-day his voice has to all intents and purposes died away, but on the surface only. Those who perceive what is really happening below the surface of civilised life, who realise how traditional religions are stretching out their tentacles once again and trying desperately to ‘modernise’ know how strongly the attitude of men like de Maistre is influencing ever-widening circles of reactionary thought. And if no counterbalance is created this influence will play a more and more decisive Part in our declining civilisation. An objective study of de Maistre makes it abundantly evident that there is in him no single trace of a new spirit but that he is simply an ingenious and shrewd interpreter of the ideas of Roman Catholicism. He has worked out the principles of a social system which would, in his opinion, be capable of calling forth from chaos a possible (although for the modern age not desirable) social order, directed by ecclesiasticism. A strange situation has arisen at this point in the life of modern thought. In a certain sense, another man who is also a typical representative of modern thinking came strongly under the influence of de Maistre. He gave an entirely different turn to the ideas of de Maistre but we must not forget that the actual content of a thought is one thing and the mode of thinking another, and it may be said with truth that the reactionary principles of de Maistre appear, like an illegitimate child of modern culture, in an unexpected place. Not from the point of view of content but from that of the whole configuration of thought, Auguste Comte , sometimes called the ‘father of modern society,’ is a true disciple of de Maistre for whom, moreover, he had considerable admiration. On the one side, Comte is a disciple of Saint-Simon, on the other, of de Maistre. This will not readily be perceived by those who concentrate on the actual content of the thoughts instead of upon the whole trend and bent of the mental life. Comte speaks of three phases in the evolution of humanity. — There is, firstly, the ancient, mythological period — the theological stage — when supremacy was vested in the priesthood. This, in his view, was superseded by the metaphysical phase, when men elaborated systematic thoughts relating to things super-physical. This stage too has passed away. The transition must now be made to a kind of political physics, in line with the idea of Saint-Simon. Science of given facts — this alone is worthy of the name of science. But there must be an ascent from physics, chemistry, biology, to sociology, and thus, following the same methods, to a kind of political physics. Comte outlines a form of society directed by positive thinking, that is to say, by thought based entirely upon the material facts of the external world. In this social structure there is, naturally, not a single trace of Catholic credulity to be found. But in the way in which Comte builds up his system, the way in which he substitutes the authority of the senses for the super-sensible authority of the Church, putting humanity in the place of God, declaring that it is the individual who acts but humanity who guides — all this is simply another way of saying: Man thinks and God guides. All this goes to show that the essentially Catholic, reactionary thought of de Maistre is working in the positive philosophy of Auguste Comte which is directed entirely to the things of the material world. Catholic thought is being promulgated in this sociology. And yet we must admit that there was an idealistic tendency too in the thought of Auguste Comte. He believes, provided always that his thought is in conformity with the spirit of the age, that he can discover in the social structure something that will be a blessing to man; he believes, furthermore, that this can be brought home to men and that a beneficial and desirable form of social life may thus be achieved. Implicit in every thinker during the first half of the nineteenth century there is a certain confidence in ideas that can be born in the mind of man and then communicated to others. There is a certain confident belief that if only men can be convinced of the truth of an idea, deeds of benefit to human life will spring from a will that is guided by intelligence. This attitude of confidence expresses itself in many different ways and is apparent in all the thinkers of the first half of the nineteenth century. Their individual views are, of course, partly influenced by nationality and partly by other factors, but this attitude is none the less universal. Consider for a moment how men like Saint-Simon, Comte or Quételet conceive of the social order. They work entirely with the intellect and reasoning faculty, systematising, never departing from the principles of mathematical calculation, building up statistics and orderly systems with a certain elegance and grace. And then think of a man like Herbert Spencer in England during the first half of the nineteenth century. Herbert Spencer is absolutely typical of the English outlook. He does not systematise like Saint-Simon and Comte, nor does he work with statistics. Economic and industrial thinking, the way in which the problems of industrial life are interlinked — all these things which he has learnt from the others, he then proceeds to build up into a social science. On the basis of scientific and economic thinking Herbert Spencer evolves a kind of ‘super-organism’. He himself does not use this expression but many other thinkers adopted it, and indeed it became a habit in the nineteenth century to place the prefix ‘super’ before anything of which they were unable to form a concrete idea. This may be quite harmless in the realm of lyrical thought, but when it becomes a question of raising the concrete to a higher level simply by using the prefix ‘super’ — as was usual at one time — then one is stumbling about in a realm of confused thoughts and ideas. In spite of this habit, however, eminent minds in the first half of the nineteenth century were all possessed of a certain confidence that the power of the spirit would ultimately lead them to the right path. In the second half of the nineteenth century there is a complete change. From many points of view, Karl Marx may be regarded as an outstanding figure of this period. He too, in his own way, tries to give to the social life a lead based upon modern scientific thought. But the attitude of Karl Marx is very different from that of Saint-Simon, of Auguste Comte, of Herbert Spencer. Karl Marx has really given up the belief that it is possible to convince others of something that is true and capable of being put into practice, once the conviction has been aroused. Saint-Simon, Comte, Herbert Spencer, Buckle and many others in the first half of the nineteenth century had this inner belief, but in the second half of the century it was not, could not be there. Marx is the most radical example, but speaking quite generally this trust in the spirit was simply non-existent. So far as Karl Marx is concerned, he does not believe that it is possible to convince men by teaching. He thinks of the masses of the proletariat and says to himself: These men have instincts which express themselves as class instincts. If I gather together those in whom these class instincts are living, if I organise them and work with what is expressing itself in these class instincts, then I can do something with them, I can lead them in such a way that the inauguration of a new age is possible. Saint-Simon and Comte are like priests who have been transported into the conditions of the modern age. They at least believe that conviction can be aroused in the hearts of men, and this was actually the case in the first fifty years of the nineteenth century. Karl Marx, however, sets to work like a strategist, or a General who never gives a thought to the factor of conviction but simply sets out to organise the masses. And there is really no difference between drilling soldiers and then the masses in order to prepare them for the field of battle, and marshalling the class instincts that already exist in human beings. And so we find the old sacerdotal methods in men like Saint-Simon, Auguste Comte, Herbert Spencer, and militaristic methods in men like Karl Marx who being out-and-out strategists have given up the belief that men can be convinced and through their conviction bring about a desirable state of affairs. Such thinkers say to themselves: I must take those whom I can organise just as they are, for it is not possible to convince human beings. I will organise their class instincts and that will achieve the desired result. A very radical change had come about in the course of the nineteenth century and anyone who studies this change deeply enough will realise that it takes place with considerable rapidity and is, moreover, apparent in another sphere as well. The natural scientific mode of thinking came to the fore in the modern age, during the first half of the nineteenth century. We have only to think of men like Fichte, Schelling, Hegel. In their days, men still had faith in the spirit and believed that the spirit would help them to fathom the world of nature; they believed that nature was in some way directed by the spirit. But later on, just as faith in the creative spirit was lost in the domain of sociological thinking, so too was faith lost in the sphere of the knowledge of nature. Men placed reliance alone upon observation and experiment, and confidence in the creative spirit died away entirely. The spirit, they said, is capable only of recording the results of observation and experiment. And then, when this attitude creeps into the realm of social science, the scientific mode of observation is applied, as in Darwinism, in the study of the evolution of man. Benjamin Kidd, Huxley, Russell, Wallace and others in the second half of the nineteenth century are typical representatives of this kind of thinking The spirit is materialised and identified with external things both in the realm of social life and in the realm of knowledge. It is strange how in the nineteenth century the human mind is beset by a kind of inner agnosticism, how it gradually loses faith even in itself. There was a radical increase of this agnosticism in the middle of the nineteenth century. Those who observe the way in which thoughts are expressed — and when it is a matter of discovering historical connections this is far more important than the actual content of the thoughts — will realise that these voices of the nineteenth century were the offspring of a tendency that was already beginning to make itself felt in the eighteenth century. It is possible, too, to follow the line of development back into the seventeenth, sixteenth and fifteenth centuries. We shall not there find direct evidence of the urge that became so insistent in the nineteenth century to unfold a new conception of the social order, in spite of a realisation that the goal was impossible of achievement, but we shall find nevertheless that the change which took place in men's thinking in the middle of the nineteenth century had been gradually working up to a climax since the fifteenth century. We find too, as we follow the development of thought back to the time of the fifteenth century, that concepts and ideas are invariably intelligible to us as thinkers living in the nineteenth and twentieth centuries. But this is no longer the case as soon as we get back to the time preceding the fifteenth century and towards the Middle Ages. I could tell you of many ideas and views which would prove to you the difference of outlook in these earlier centuries, but I will give one example only. — Anyone who genuinely tries to understand writings which deal with the world of nature, dating from the time preceding the fifteenth century, will find that he must approach them with an attitude of mind quite different from that which he will naturally bring to bear upon literature of the eighteenth or nineteenth centuries. Before the fifteenth century, all the writings on the subject of nature indicate quite clearly that anyone who experiments with processes of nature must be filled with a certain inner reverence. Experiments with mineral substances, for instance, must only be carried out in a mood that finds favour in the eyes of certain Divine Beings. Experiments with the processes of nature must be accompanied by a moral attitude of soul — so it was said. But just think of what would happen to-day if it were demanded of someone working to produce a chemical reaction in a laboratory, that his soul must first be suffused with a mood of piety! The idea would be ridiculed. Nevertheless, before the fifteenth century, and more strongly so in earlier times, it was quite natural that this demand should be made of those who were in any way working with the processes of nature. It was the aim of a man like de Maistre to bring to life again in the modern age, concepts that had really lost the vital meaning once attaching to them, and above all he tried to bring home the difference between the concepts of sin and of crime . According to de Maistre, the men of his day — he is speaking of the beginning of the nineteenth century — had no insight into the difference between sin and crime. The two concepts had become practically synonymous. And above all there was no understanding of the meaning of ‘original sin.’ Let me now try to describe the idea men had of original sin before the days of the fifteenth century. Modern thought is altogether unfitted to grasp the real meaning of original sin, but some measure of understanding at least must be present in studying the development of thought through the centuries. We must here turn to fundamental conceptions resulting from spiritual investigation. For it is only by independent research that we can understand the character of a mental outlook quite different from our own. When we peruse books on the subject we are simply reading so many words and we are dishonest with ourselves if we imagine that the words convey any real meaning. Enlightened minds before the fifteenth century would have set no store by such definitions of original sin as are given by modern theology. In those days — and I repeat that these things can only be discovered nowadays by Spiritual Science — it was said: The human being, from the time of his birth, from the time he draws his first breath, until his death, passes through certain processes and phases in his inner life. These inner processes are not the same as those at work in the world of nature outside the human being. It is, as a matter of fact, a form of modern superstition to believe that all the processes at work in the being of man can also be found in the animal. This is mere superstition, because the laws of the animal organisation are different from those of the human organism. From birth until death the organism of the human being is permeated by forces of soul. And when we understand the nature of the laws and forces at work in the human organism, we know that they are not to be found in outer nature. In outer nature, however, there is something that corresponds in a certain sense with the laws at work during the period of embryonic development, from the time of conception until birth. The processes at work in the being of man between birth and death are not to be explained in the light of the processes of outer nature. Nevertheless, if it is rightly applied, the knowledge gleaned from a study of external nature enables us to understand the processes at work during the embryonic period of the life of a human being. It is not easy for the modern mind to grasp this idea, but my object in speaking of it is to give an example of how Spiritual Science can throw light upon conceptions of earlier times. Not of course with clear consciousness, but out of dim feeling, a man engaged in the investigation of nature before the fifteenth century said to himself: Outer nature lies there before me, but the laws of this outer nature work only in the processes of my physical body as it was before birth. In this sense there is something in the inner being of man that is openly manifest in outer nature. But the evolution of the human being must not be subject to the laws and processes of external nature. Man would be an evil being if he grew as the plant grows, unfolding its blossom in the outer world of space. Such were the views of an earlier time. It was said that man falls into sin when he gives himself over to the forces by which his development in the mother's womb was promoted, for these forces work as do the forces of nature outside the human being. In nature outside the human being, these forces are working in their proper sphere. But if, after birth, man gives himself over to the forces of nature, if he does not make his being fit to become part of a world of super-sensible law — then he falls into sin. This thought leads one to the concept of original sin, to the idea of the mingling of the natural with the moral world order. Processes which belong to outer nature are woven, as it were, into the moral world order and the outcome is the birth of a concept like that of ‘original sin’ which was an altogether scientific concept before the days of the fifteenth century. De Maistre wanted to bring this concept of original sin again to the fore, to make a connecting link between natural science and the moral world. In the nineteenth century, however, the only possible way of preserving this concept of original sin was to bring about an even more radical separation of religion and scientific knowledge. And so we find great emphasis being laid upon the cleft between faith and knowledge. In earlier times no such cleft existed. It begins to appear a few hundreds of years before the fifteenth century but becomes more and more decisive as the centuries pass, until, in the nineteenth century, religion says: Let science carry out its own methods of exact research. We on our side have no desire to use these methods. We will ensure for ourselves a realm where we need simply faith and personal conviction — not scientific knowledge. Knowledge was relegated to science and religion set out to secure the realm of faith because the powers of the human soul were not strong enough to combine the two. And so, in the opinion of de Maistre, the concept of crime alone, no longer that of sin in its original meaning, conveyed any meaning to the modern mind, for the concept of sin could only have meaning when men understood the interplay between the natural and moral worlds. This example shows us that the concepts and ideas of men in the time immediately preceding the fifteenth century were quite different from ours. Going backwards from the fifteenth century, we come to a lengthy period generally referred to as the dark Middle Ages, during which we find no such progress in the realm of thought as is apparent from the fifteenth century onwards. The development of thought that has taken place since the days of Galileo and Copernicus, leading up to the achievements of the nineteenth century, bear witness to unbroken progress, but in the time preceding the fifteenth century we cannot speak of progress in this sense at all. We can go back century alter century, through the twelfth, eleventh, tenth, ninth, eighth, seventh and sixth centuries, and we find quite a different state of things. We see the gradual spread of Christianity, but no trace of progressive evolution in the world of thought such as begins in the fifteenth century and in the middle of the nineteenth century undergoes the radical change of which we have spoken. We come finally to a most significant point in the spiritual life of Europe, namely, the fourth century A.D. Gradually it dawns upon us that it is possible to follow stage by stage the progressive development beginning in the middle of the fifteenth century with Nicolas Cusanus, expressing itself in the thought of men like Galileo and Copernicus and ultimately leading on to the radical turning-point in the nineteenth century, but that things are not at all the same in earlier centuries. We find there a more stationary condition of the world of thought and then, suddenly, in the fourth century of our era, everything changes. This century is a period of the greatest significance in European thought and civilisation. Its significance will be brought home to us all the more when we realise that events after the turning-point in the fifteenth century, for example, the movements known as the Renaissance and the Reformation, denote a kind of return to conditions as they were in the fourth century of the Christian era. This is the decisive time in the process of the decline of the Roman Empire. The headway made by Christianity was such that Constantine had been obliged to proclaim religious freedom for the Christians and to place Christianity on an equal footing with the old pagan forms of religion. We see, too, a final attempt being made by Julian the Apostate to reinculcate into the civilised humanity of Europe the views and conceptions of ancient Paganism. The death of Julian the Apostate, in the year 363, marks the passing of one who strove with might and main to restore to the civilised peoples of Europe impulses that had reigned supreme for centuries, had been absorbed by Christianity but in the fourth century were approaching their final phase of decline. In this century too we find the onslaught of those forces by which the Roman Empire was ultimately superseded. Europe begins to be astir with the activities of the Goths and the Vandals. In the year A.D. 378 there takes place the momentous battle of Hadrianople. The Goths make their way into the Eastern Roman Empire. The blood of the so-called barbarians is set up in opposition to the dying culture of antiquity in the South of Europe. The history of this fourth century of our era is truly remarkable. We see how the culture of Greece, with its belief in the Gods and its philosophy, is little by little lift ed away from its hinges and disappears as an influence, and how the remnants of its thought pass over to the Roman Catholic Church. Direction of the whole of the spiritual and mental life falls into the hands of the priests; spirituality in its universal, cosmic aspect vanishes, until, brought to light once again by the Renaissance, it works an so strongly that when Goethe had completed his early training and produced his first works, he yearned with all his heart and soul for ancient European-Asiatic culture. What, then, is the state of things in the age immediately following the fourth century A.D. ? Education and culture had vanished into the cities, and the peasantry, together with the landowning population in Southern Europe, fused with the peoples who were pressing downward from the North. The next stage is the gradual fading away of that spiritual life which, originating in the ancient East, had appeared in another garb in the culture of Greece and Rome. These impulses die down and vanish, and there remain the peasantry, the landowning populace and the element with which they have now fused, living in the peoples who were coming down from the North into the Graeco-Roman world. Then, in the following centuries, we find the Roman priesthood spreading Christianity among this peasant people who practically constituted the whole population. The work of the priesthood is carried on quite independently of the Greek elements which gradually fade out, having no possibilities for the future. The old communal life is superseded by a system of commerce akin to that prevailing among the barbarians of the North. Spiritual life in the real sense makes no headway. The impulses of an earlier spirituality which had been taken over and remoulded by the priesthood, are inculcated into the uneducated peasant population of Europe; and not until these impulses have been inculcated does the blood now flowing in the veins of the people of Europe work in the direction of awakening the spirit which becomes manifest for the first time in the fifteenth century. In the fourth century A.D. we find many typical representatives of the forces and impulses working at such a momentous point of time in the evolution of humanity. The significance of this century is at once apparent when we think of the following dates. — In the year 333, religious tolerance is proclaimed by the Emperor Constantine; in the year 363, with the murder of Julian the Apostate, the last hope of a restoration of ancient thought and outlook falls to the ground; Hadrianople is conquered by the Goths in the year 378. In the year 400, Augustine writes his Confessions , bringing as it were to a kind of culmination the inner struggles in the life of soul through which it was the destiny of European civilisation to pass. Living in the midst of the fading culture of antiquity, a man like Augustine experienced the death of the Eastern view of the world. He experienced it in Manichæism, of which, as a young man, he had been an ardent adherent; he experienced it too in Neoplatonism. And it was only after inner struggles of unspeakable bitterness, having wrestled with the teachings of Mani, of Neoplatonism and even with Greek scepticism, that he finally found his way to the thought and outlook of Roman Catholic Christianity. Augustine writes these Confessions in the year A.D. 400, as it were on tables of stone. Augustine is a typical representative of the life of thought as it was in the fourth century A.D. He was imbued with Manichæan conceptions but in an age when the ancient Eastern wisdom had been romanised and dogmatised to such an extent that no fundamental under standing of Manichæan teaching was possible. What, then, is the essence of Manichæism? The teachings that have come down to us in the form of tradition do not, nor can they ever make it really intelligible to us. The only hope of understanding Manichæism is to bring the light of Spiritual Science to bear upon it. Oriental thought had already fallen into decadence but in the teachings of Mani we find a note that is both familiar and full of significance. The Manichæans strove to attain a living knowledge of the interplay between the spiritual and the material worlds. The aim of those who adhered to the teachings of Mani was to perceive the Spiritual in all things material. In the light itself they sought to find both wisdom and goodness. No cleft must divide Spirit from nature. The two must be realised as one. Later on, this conception came to be known by the name of dualism. Spirit and nature — once experienced as a living unity — were separated, nor could they be reunited. This attitude of mind made a deep impression upon the young Augustine, but it led him out of his depth; the mind of his time was no longer capable of rising to ideas which had been accessible to an older, more instinctive form of cognition, but which humanity had now outgrown. An inner, tragic struggle is waged in the soul of Augustine. With might and main he struggles to find truth, to discover the immediate reality of divine forces in cloud and mountain, in plant and animal, in all existence. But he finally takes refuge in the Neoplatonic philosophy which plainly shows that it has no insight into the interpenetration of Spirit and matter and, in spite of its greatness and inspiration, does no more than reach out towards abstract, nebulous Spirit. While Augustine is gradually resigning hope of understanding a spirit-filled world of nature, while he is even passing through the phase of despising the world of sense and idolising the abstract spirituality of Neoplatonism, he is led, by a profoundly significant occurrence, to his Catholic view of life. We must realise the importance of this world-historic event. Ancient culture is still alive in Augustine's environment, but it is already decadent, has passed into its period of decline. He struggles bitterly, but to no purpose, with the last remnants of this culture surviving in Manichæism and Neoplatonism. His mind is steeped in what this wisdom, even in its decadence, has to offer, and, to begin with, he cannot accept Christianity. He stands there, an eminent rhetorician and Neoplatonist, but torn with gnawing doubt. And what happens? Just when he has reached the point of doubting truth itself, of losing his bearings altogether along the tortuous paths of the decadent learning of antiquity in the fourth century of our era, when innumerable questions are hurtling through his mind, he thinks he hears the voice of a child calling to him from the next garden: ‘Take and read! Take and read!’ And he turns to the New Testament, to the Epistles of St. Paul, and is led through the voice of the child to Roman Catholicism. The mind of Augustine is laden with the oriental wisdom which had now become decadent in the West. He is a typical representative of this learning and then, suddenly, through the voice of a child, he becomes the paramount influence in subsequent centuries. No actual break occurs until the fifteenth century and it may truly be said that the ultimate outcome of this break appears as the change that took place in the life of thought in the middle of the nineteenth century. And so, in this fourth century of our era, we find the human mind involved in the complicated network of Western culture but also in an element which constitutes the starting-point of a new impulse. It is an impulse that mingles with what has come over from the East and from the seemingly barbarian peoples by whom Roman civilisation was gradually superseded, but whose instructors, after they had mingled with the peasantry and the landowning classes, were the priests of the Roman Church. In the depths, however, there is something else at work. Out of the raw, unpolished soul of these peoples there emerges an element of lofty, archaic spirituality. There could be no more striking example of this than the bock that has remained as a memorial of the ancient Goths — Wulfila's translation of the Bible. We must try to unfold a sensitive understanding of the language used in this translation of the Bible. The Lord's Prayer, to take one example, is built up, fragment by fragment, out of the confusion of thought of which Augustine was so typical a representative. Wulfila's translation of the Bible is the offspring of an archaic form of thought, of Arian Christianity as opposed to the Athanasian Christianity of Augustine. Perhaps more strongly than anywhere else, we can feel in Wulfila's translation of the Bible how deeply the pagan thought of antiquity is permeated with Arian Christianity. Something that is pregnant with inner life echoes down to us from these barbarian peoples and their culture, to which the civilisation of ancient Rome was giving place. The Lord's Prayer rendered by Wulfila, is as follows: Atta unsar thu in himinam, Veihnai namo thein; Quimai thiudinassus theins. Vairthai vilja theins, sve in himina, jah ana aerthai. Hlaif unsarana thana sinteinan, gif uns himma daga. Jah aflet uns, thatei skulans sijaima, svasve jah veis afletam thaim skulam unsaraim. Jah ni briggais uns in fraistubnjai, ak lausei uns af thamma ubilin. Unte theina ist thiu dangardi, jah mahts, jah vulthus in aivius. Amen. Atta unsar thu in himinam, veihnai namo thein; Quimai thiudinassus theins. Vairthai vilja theins, sve in himina, jah ana aerthai. — The words of this wonderful prayer cannot really be translated literally into our modern language, but they may be rendered thus: We feel Thee above in the Spirit-Heights, All Father of men. May Thy Name be hallowed. May Thy Kingdom come to us. May Thy Will be supreme, on the Earth even as it is in Heaven. We must be able to feel what these words express. Men were aware of the existence of a primordial Being, of the All-sustaining Father of humanity in the heights of spiritual existence. They pictured Him with their faculties of ancient clairvoyance as the invisible, super-sensible King who rules His Kingdom as no earthly King. Among the Goths this Being was venerated as King and their veneration was proclaimed in the words : Atta unsar thu in himinam. This primordial Being was venerated in His three aspects: May Thy Name be hallowed. ‘Name’ — as a study of Sanscrit will show — implied the outer manifestation or revelation of the Being, as a man reveals himself in his body. ‘Kingdom’ was the supreme Power: Veihnai namo thein; Quimai thiudinassus theins, Vairthai vilja theins, sve in himina, jah ana aerthai. ‘Will’ indicated the Spirit shining through the Power and the Name. — Thus as they gazed upwards, men beheld the Spirit of the super-sensible worlds in His three-fold aspect. To this Spirit they paid veneration in the words: Jah ana aerthai. Hlaif unsarana thana sinteinan, gif uns himma daga. So may it be on Earth. Even as Thy Name, the form in which Thou art outwardly manifest, shall be holy, so may that which in us becomes outwardly manifest and must daily be renewed, be radiant with spiritual light. We must try to understand the meaning of the Gothic word Hlaif , from which Leib ( Leib =body) is derived. In saying the words, ‘Give us this day our daily bread,’ we have no feeling for what the word Hlaif denoted here: — Even as Thy ‘Name’ denotes thy body, so too may our body be spiritualised, subsisting as it does through the food which it receives and transmutes. The prayer speaks then of the ‘Kingdom’ that is to reign supreme from the super-sensible worlds, and so leads on to the social order among men. In this super-sensible ‘Kingdom’ men are not debtors one of another. The word debt among the Goths means debt in the moral as well as in the physical, social life. And so the prayer passes from the ‘Name’ to the ‘Kingdom’, from the bodily manifestation in the Spirit, to the ‘Kingdom’. And then from the outer, physical nature of the body to the element of soul in the social life and thence to the Spiritual.— Jah aflet uns, thatei skulans sijaima, svasve jah veis afletam thaim skulam unsaraim. — May we not succumb to those forces which, proceeding from the body, lead the Spirit into darkness; deliver us from the evils by which the Spirit is cast into darkness. Jah ni briggais uns in fraistubnjai, ak lausei uns af thamma ubilin. — Deliver us from the evils arising when the Spirit sinks too deeply into the bodily nature. Thus the second part of the prayer declares that the order reigning in the spiritual heights must be implicit in the social life upon Earth. And this is confirmed in the words : We will recognise this spiritual Order upon Earth. Unte theina ist thiu dangardi, jah mahts, jah vulthus in aivius. Amen. — All-Father, whose Name betokens the out er manifestation of the Spirit, whose Kingdom we will recognise, whose Will shall reign: May earthly nature too be full of Thee, and our body daily renewed through earthly nourishment. In our social life may we not be debtors one of another, but live as equals. May we stand firm in spirit and in body, and may the trinity in the social life of Earth be linked with the super-earthly Trinity. For the Supersensible shall reign, shall be Emperor and King. The Supersensible — not the material, not the personal — shall reign. Unte theina ist thiu dangardi, jah mahts, jah vulthus in avius. Amen. — For on Earth there is no thing, no being over which the rulership is not Thine. — Thine is the Power and the Light and the Glory, and the all-supreme Love between men in the social life. The Trinity in the super-sensible world is thus to penetrate into and find expression in the social order of the Material world. And again, at the end, there is the confirmation: Yea, verily, we desire that this threefold order shall reign in the social life as it reigns with Thee in the heights: For Thine is the Kingdom, the Power and the revealed Glory. — Theina ist thiu dangardi, jah mahts, jah vulthus in aivius. Amen. Such was the impulse living among the Goths. It mingled with those peasant peoples whose mental life is regarded by history as being almost negligible. But this impulse unfolded with increasing rapidity as we reach the time of the nineteenth century. It finally came to a climax and led on then to the fundamental change in thought and outlook of which we have heard in this lecture. Such are the connections. — I have given only one example of how, without in any way distorting the facts, but rather drawing the real threads that bind them together, we can realise in history the existence of law higher than natural law can ever be. I wanted, in the first place, to describe the facts from the exoteric point of view. Later on we will consider their esoteric connections, for this will show us how events have shaped themselves in this period which stretches from the fourth century A.D. to our own age, and how the impulses of this epoch live within us still. We shall realise then that an understanding of these connections is essential to the attainment of true insight for our work and thought at the present time.

European Spiritual Life in the 19th Century

The Development of Thought from the 4th to the 19th Century I

https://rsarchive.org/Lectures/GA325/English/PAV1933/19210515p01.html

Dornach

15 May 1921

GA325-1

I have tried to show how about the middle of last century a radical transformation took place in spiritual life, and how moreover the peculiar configuration of the nineteenth century thought and the spiritual life in general that underwent this transformation can be traced back to another crucial turning point in the west which we have to look for in the fourth century A.D. Now it might at first sight appear as if we were trying to show too close a connection between two periods that are so very widely separated in point of time. But this very thought will serve to call attention to certain interconnections in the history of humanity. To-day we will begin where we left off yesterday, with the downfall of ancient culture and of the Roman empire. We drew attention to a distinguishing feature of that time. We placed before our souls two representative personalities; one of them was Augustine, who grew entirely out of the South-West; and we compared them with another personality, that of the Gothic translator of the Bible, Wulfila, and with the spiritual stream out of which Wulfila sprang. We have to be quite clear that Augustine was altogether the child of the conditions which had developed in the south-western parts of the European-African civilization of the day. At that time men who sought a higher culture only found it through contact with the philosophy, literature, art and science which had for a long time been pursued in a certain upper level of society. We even have to think of Greek culture as the possession of an upper class which relegated its more menial work to slaves. And still less can we think of Roman culture without widespread slavery. The life of this culture depended upon its possessors being remote from the thought and feeling prevailing in the masses. But one must not think that there was therefore no spiritual life in the masses. There was an exceptionally strong spiritual life among them. This was of course derived more from the native stock left behind at an earlier stage of evolution than that of the upper class, but it was nevertheless a spiritual life. History knows very little about it, but it was very like what was carried into the southern parts of Europe by the barbarian tribes, forced to migrate by the forward pressure of the Asiatic hordes. We must try to form a concrete idea of it. Take, for instance, the people who over-ran the Roman Empire — the Goths, the Vandals, the Lombards, the Herules. Before the migrations had begun, thus before the fourth century A.D. which is for us such an important turning-point, these men had spiritual life away in the East which culminated in a certain religious insight, in certain religious ideas, which pervaded everything; and the effects of these experiences influenced every aspect of daily life. Before the migrations began these people have had a long period of settled life. It was while they were thus settled that they first experienced the southern oriental peoples, from whom the Indian, Persian and succeeding cultures sprang, had experienced at a much earlier time; they experienced what we can call a religion which was closely connected with the blood relationships of the people. It is only through spiritual science that this can be observed, but it is also echoed in the sagas and myths I lived in these peoples. What they worshipped were the ancestors of certain families. But these ancestors first began to be worshiped long after they had passed away, and this worship was in no way based upon abstract ideas, but upon what was instinctively experienced as dreamlike clairvoyant ideas, if I can use the expression without causing misunderstanding. For there were certain ideas which arose in quite another way from the way our ideas of to-day are formed. When we have ideas nowadays our soul life comes into play more or less independently of our bodily constitution. We no longer feel the seething of the body. These people had a certain intensive inward sense that in what took place in their bodies all sorts of cosmic mysteries were active. For it is not only in the chemical retorts that cosmic processes work according to law, but in the human body also. And just as to-day, by means of the processes which take place in their retorts chemists seek with their abstract reason to understand the laws of the universe, so these men too tried through what they had experienced inwardly, through their own organism, whose inner processes they felt, to penetrate into the mysteries of the cosmos. It was entirely an inner experience that was still closely bound up with ideas arising in the body. And out of these ideas which were called forth by what we might describe as the inward seething of the organism, there developed the pictorial imaginations which these men connected with their ancestors. It was their ancestors whose voices they heard for centuries in these dream formations. Ancestors were the rulers of people living in quite small communities, in village tribal communities. These tribes had still this kind of ancestor-worship, which had its life in dreamlike ideas, when they pressed forward from the east of Europe towards the west. And if we look back to the teachers and the priests of these peoples we find that they were advanced spirits whose foremost task was to interpret what the individual saw in his dream-pictures, albeit dream-pictures which he experienced in his awake consciousness. They were interpreters of what the individual experienced. And now the migrations began. During the period of the migrations it was their greatest spiritual consolation that they had this inner clairvoyant life which was interpreted by their priests. This spiritual life was reflected in sagas which have been handed down, notably in the Slav world, and in these sagas you will find confirmation of what I have just briefly outlined. Now shortly after the end of the fourth century these tribes settled down again. Some of them were absorbed into the peoples who had already for a long time inhabited the southern peninsulas, that is to say they were absorbed into the lower classes of these peoples, for their upper classes had been swept away in the time of Augustine. The Goths were among the tribes absorbed in this way, but mainly those Goths who peopled the countries of middle and western Europe; those who settled in the northern regions of southern Europe maintained their own existence and acquired a permanent home there. Thus we see that after the fourth century the possession of a fixed dwelling place becomes an essential characteristic of these peoples. And now the whole spiritual life begins to change. It is most remarkable what a radical change now takes place in the spiritual life of these people through their peculiar talent. They were gifted not only with special racial dispositions, but with a much greater freshness as a folk for experiencing spiritual reality in dreams; something which in the southern regions had long since been transformed into other forms of spiritual life. But now they have become settled, and through their peculiar endowment a new kind of spiritual life developed in them. What in earlier times had expressed itself in ancestor-worship, had conjured before the soul the picture of the revered forefather, now attached itself to the place. Wherever there was some special grove, some mountain which contained let us say, special treasures of metal, wherever there was a place from which one could watch storms and so on, there, with a depth of feeling left to them from their old ancestor-imaginations and dreams, men felt something holy to be connected with the place. And the gods that used to be ancestral became gods of place. Religious perceptions lost their time a character and took on a spatial character. Those who had been previously the interpreters of dreams, the interpreters of inner soul-experience, now became the guardians what one might call the signs c — the peculiar reflection of the sun in this or that waterfall or other feature of nature, the phenomena of the cloud-drifts in certain valleys and so on — these are now the objects of interpretation, something which then became transformed into the system of Runes cultivated in certain places, where twigs were plucked from trees and thrown down, and the signs read from the special forms into which the twigs fell. Religion underwent a metamorphosis into a religion of space. The entire spiritual life became attached to the place . Thus these tribes became more and more susceptible to the influence which the Roman Catholic Church, since it had become the state church in the fourth century, had been accustomed to exercise over the southern peoples, that is to say over the lower classes which had been left behind after the upper classes have been swept away. And what was it that the church had done? In these southern regions the period of transition from the time conception to the spatial conception of the world was long since past, and something of extraordinary importance always happens in a period of transition from a time outlook to a spatial outlook, a certain living experience passes over into an experience through symbol and cult. This had already taken place for the lower classes of the people in the southern regions. So long as men continue to live in their time-conceptions, the priests, those who in the sense of ancient times we can call learned men, our interpreters of a corresponding life of the soul. They were engaged in explaining what man experience. They were able to do that because men lived in small village communities, and the interpreter, who was in fact the leader of the whole spiritual life, could address himself to the individual, or to a small group. When the transition takes place from the time-outlook to the space-outlook, then this living element is more or less suppressed. The priest can no longer refer to what the individual has experienced. He can no longer treat of what the individual tells them and explain to him what he has experienced. What is something living is thus transformed into something bound to a place. And thus ritual gradually arises, the pictorial expression of what in earlier times was a direct experience of the super-sensible world. And at this point development begins again, so to say, from the other side. The human being now sees the symbol, he interprets the symbol. What the Roman Catholic Church built up as cult was built up with exact knowledge of this world-historic course of human evolution. The transition from the ancient celebration of the Last Supper into the sacrifice of the Mass arose, in that the living Last Supper became the symbolic rite. Into this sacrifice of the Mass, it is true, flowed primeval holy mystery usages which had been handed down in the lower classes of the people. These practices were now permeated with the new conceptions Christianity brought. They became, so to say, christianised. The lower classes of the Roman people provided good material for such a birth of ritual, which was now to reveal the super-sensible world in symbol. And as the northern tribes had also made the transition to a spiritual life associated with place, this ritual could also be implanted among them, for they began to meet it with understanding. This is the bases of one of the streams which start in the fourth century A.D. The other stream must be characterised differently. I have described how the ancient ancestor-worship lived on, rolling over from the east upon the declining Roman Empire. In the “Our Father” of Wulfila we see that in these nomadic peoples Christianity was absorbed into the ancestral cults and the cults connected with locality. And that constitutes the essence of Arian Christianity. The dogmatic conflict in the background is not so important. The important thing for this Arian Christianity, which traveled with the Goths and the other German tribes from the East towards the West by a path which did not lead through Rome, is that in it Christianity becomes steeped in a living spiritual life which has not yet reached the stage of ritual, that is closely related to the dream experience, to the clairvoyant experience, if you will not misunderstand the expression. On the other hand the Christianity that Augustine experienced had passed through the culture of the upper classes of the southern peoples, and had to encounter all sorts of oriental cults and religious ideas, which flowed together in a great city of Rome. The heathen Augustine had grown up amidst these religious ideas and had turned from them towards Christianity in the way I have described. He stands within a spiritual stream which was experienced by the individual in quite a different way from the stream I have already mentioned. The latter arose out of the most elemental forces of the folk-soul life. What Augustine experienced was something which had risen into the upper class through many filtrations. And this was now taken over and preserved by the Roman Catholic clergy. Moreover its content is far less important for the progress of history than the whole configuration of soul that constituted first Greco-Roman culture and then, through the adoption of Christianity, the culture of the Catholic clergy. It is essential to see this culture as it was at that time and as it then lived on through the centuries. Our present-day educational system is something which remains over from the real culture of that time. After one had mastered the first elements of knowledge, which we should to-day call primary education, one entered what was called the grammar class. In the grammar classes one was taught structure of speech; one learned how to use speech properly in accordance with the usages established by the poets and the writers. Then one assimilated all other knowledge that was not kept secret, for even at that time quite a lot of knowledge was kept secret by certain mystery schools. What was not kept secret was imparted through grammar, but through the medium of speech. And if anyone reached a higher stage of culture, as for example Augustine, then he passed on from the study of grammar to the study of rhetoric. There the object was to train the pupil above all in the appropriate use of symbol, how to form his sentences rightly, particularly how to lead his sentences to a certain climax. This was what the people who aspired to culture had to practice. One must be able to sense what such a training develops in a human being. Through this purely grammatical and rhetorical kind of education he is brought into a certain connection with the surface of his nature, he is within what sounds through his mouth far more than is under the influence of thought. He pays much more attention to the structure of speech and to the connection of thought. And that was the primary characteristic of this ancient culture, that it was not concerned with the inner soul experience, but with structure, the form of speech, with the pleasure it gives. In short, the man became externalised by this culture. And in the fourth century, at that time Augustine was a student, as we should say to-day, we can see clearly this process of externalization, this living in the turn of words, in the form of expression. Grammar and rhetoric were the things that students had to learn. And there was good reason for this. For what we to-day call intelligent thought did not at that time exist. It is a mere superstition very commonly to be found in history to suppose that men have always thought in the way they think today. The entire thought of the Greek epoch right up to the fourth century A.D. was quite different. I have gone into this to a certain extent in my Riddles of Philosophy . Thought was not hatched out of inner soul activity, as is the case to-day, but thought came to the human being of itself like a dream. Particularly was this the case in the East, and the Oriental spiritual life which had animated Greece and still animated Rome was not won through thinking, it came, even when it was thought, as dream pictures come. And the oriental and south-european scholars only differed from those of the north in that the pictures that came to the northerners at first stimulated ideas of their ancestors, and later were associated with particular localities and became more or less ritualistic. The ideas that were formed in Asia, in southern Europe, already had the character of thought, but they were not thoughts won by inner soul activity, inner intelligence, they were inwardly revealed thoughts. One experienced what one called knowledge and elaborated for oneself only the word, the sentence, the discourse. There is no logical activity. Logic arose through Aristotle, when Greece was already decadent. And what lived in beauty of speech, in rhetoric, was essentially Roman culture, and became the culture of Catholic Christianity. This habit of living not in oneself but in an external element expresses itself in the education that was given, and one can see how in this respect Augustine was a representative of his time. The correspondence between Jerome and Augustine is illuminating in this respect. It shows how differently these people conducted an argument in the fourth or beginning of the fifth century from the way we should do so to-day. When we discuss things to-day we have a feeling that we make use of a certain activity of thought. When these people discussed, one of them would have the feeling — “Well, I have formed my own view about a certain point, but perhaps my organism does not give me the right view. I will hear what the other man has to say; perhaps something else will emerge from his organism.” These men were within a much more real element of inner experience. This difference is seen also in Augustine's attitude in condemning heretics of various sorts. We see people deriving from the life of the common people, people like the priests of Donatism, like Pelagius and some others, specially coming to the fore. These people, although they believe themselves to be entirely Christian, stress the point that man's relation to justice, to sin, must come from the man himself. And thus we see a whole series of people one after the other who cannot believe that it has any sense to baptize children and thereby to bring about forgiveness of sins. We see objections made against the Christianity issuing from Rome, we see how Pelagianism wins adherents, and how Augustine, as a true representative of the Catholic element, attacks it. He rejected a conception of sin connected with human subjectivity. He rejects the view that a relation to the spiritual world or to Christ can come from an individual human impulse. Hence he works to bring about gradually the passing over of the Church into the external institution. The important question is not what is in the child, but what the Church as external ordnance bestows upon it. The point is not that baptism signifies something for the soul's experience, but that there exists an external ordnance of the Church which is fulfilled in baptism. The value of the human soul living in the body matters less than that the universal spirit that lives in the sacrament, so to say an astral sacrament, should be poured out over mankind. The individual plays no part, but the important thing is the web of abstract dogmas and ideas which is spread over humanity. To Augustine it seems particularly dangerous to believe that the human being should first be prepared to receive baptism, for it is not a question of what the human being inwardly wills, but it is a question of admitting into the Kingdom of God which has objective existence. And that is essentially the setting in which Athanasian Christianity lived, in contrast to the other background that originated in the north-east, in which a certain popular element lived. But the Church understood how to clothe the abstract element in the ritualistic form which again arose from below. It was this that made it possible for the Church to spread in this European element, from which the ancient culture had vanished. And above all it attains this expansion through the exclusion of the wide masses of the people from the essential substance of religious culture. It is a matter of tremendous significance that in the centuries which follow this substance is propagated in the Latin language. And from the fourth century A.D. onward Christianity is propagated in the Latin tongue. It is as it were a stream flowing over the heads of men. That goes on right up to the fifteenth century. For what history usually relates is only the outer form of what went on in the souls of men. Christianity was kept secret by those who taught at right up to the eleventh and twelfth centuries, in a far deeper sense than the ancient Mysteries were kept secret. For only the outer ritual penetrated the masses. And what was transmitted, which at the same time laid claim to all science coming from the ancient culture and clothed it in the Latin tongue, this was the Church, something which hovered above the essential evolution of humanity. And the centuries between the fourth and the fourteenth stand under the sign of these two parallel streams. The external history books, even the histories of the mind, only give the traditional description of what leaks out into greater publicity from the Latin ecclesiastical stream. Hence from present-day historical literature we get no idea of what took place among the wide masses of the people. What took place among the masses was something like this. At first there were only village communities; in the colonization of the whole of middle, western and even of southern Europe the towns played a very small part. The most significant life developed in small village communities; such towns as did exist were really only large villages; in these large village communities there was the Catholic Church, way over the heads of men, but through the ritual working suggestively upon them; however, these men who only saw the symbolic rite, who participated in the cult, who watched something which they could not understand, did nevertheless develop a spiritual life of their own. The very rich spiritual life developed throughout Europe at that time, a spiritual life which stood first and foremost under the influence of human nature itself. It was something quite apart from their participation in the spread of Catholic doctrine. For to associate everything with the personality of Boniface, for instance, is to place things a false light. What went on in these village communities was an inner soul life through which echoed the omens of the divinity or spirituality associated with the place. Everywhere people saw intimations from one or other of these. They developed a magical life. Everywhere human beings had premonitions, and told their fellows about them. These premonitions expressed themselves in sagas, in mysterious hints as to what one or another had experienced spiritually in the course of his work. But something very remarkable permeated this remains of an ancient prophetic and clairvoyant dream-life, which continued to flourish in the village communities whilst Catholic doctrine passed over their heads, and one can see that everywhere in Europe the organization of the human being was involved in this characteristic spiritual life. Something was at work which indicated a quite special disposition of soul in two respects. When people told of their weightiest premonitions, their most significant dreams (these were always associated with places), when they describe their half-waking, half-sleeping experiences, these dreams are always connected either with events, with questions which were asked them from out of the spiritual world, or with tasks which were imposed upon them, with matters in which their skill played a part. From the whole character of these stories, which were still to be found among the common people in the nineteenth century, one sees that when men began to ponder and to dream and to build up their legendary sagas in their mythologies, of the three members of the human being it was not so much the nerve-system — which is more connected with the outer world — but the rhythmic system which was active; and in that the rhythmic system was drawn forth out of the organism it showed itself in clairvoyant dreams which passed by word of mouth from one to another, and in this way the villagers shared with one another fear and joy, happiness and beauty. In all this there was always an element of delicate questioning which came from the spiritual world. People had to solve riddles half in dreams, had to carry out skillful actions, had to overcome something or other. It was always something of the riddle in this dream life. That is the physiological basis of the widespread spiritual experience of these men who lived in village communities. Into this, of course, penetrated the deeds of Charlemagne of which history tells you; but those are only surface experiences, though they do of course enter deeply into individual destiny. They are not the main thing. The important thing is what takes place in the village communities, and there, side by side with the economic life, a spiritual life developed such as I have described. And this spiritual life goes on right into the ninth, tenth, and eleventh centuries. Of course, something of what has developed in the heads of men in the upper strata of society gradually trickles down into the lower strata, and the ghostly and magical character of the stories men recount gets charmingly mixed with the Christ and His deeds, and what comes from the human being himself is sometimes overlaid with what comes from the Bible or the Gospel. But then we see that it is primarily into social thinking that the Christian element is received. We see it in ‘Der Heliand’ and other poems which arose out of Christianity but always we see something spiritual brought to the people, who meet it with a spirituality of their own. When we come to the tenth and eleventh centuries we see a change in the external life. Even earlier, but at this time more markedly so, we see life centering itself in the towns. That life of picture-like waking dreams which I have described to you is altogether bound up with the soil. As, therefore, in the ninth, tenth, eleventh and twelfth centuries the whole country became covered with larger towns, in these towns another kind of thinking began to develop. Men living in towns had a different kind of thought. They were cut off from the places in which their local cults had developed, their attention was more directed towards what was human. But the human element which developed of the towns was still under the influence of this earlier state of mind, for some of the people who settled in the towns came from the villages and they with very special spiritual endowment made their own contribution. What they brought with them was an inner personal life which was an echo of what was experienced in the country, but which now manifested itself in a more abstract form. These men were cut off from nature, they no longer participated in the life of nature, and although they still have forms of thought derived from nature, they already began to develop the kind of thinking which was gradually directed towards intelligence. In the towns of the eleventh, twelfth and thirteenth centuries there developed the first trace of that intelligence which we see arise in the fifteenth century among the leading European peoples. Because life in the towns was more abstract, the abstract ecclesiastical element, clothed in the Latin tongue, became mixed up with what sprang directly out of the people. Thus we see how this Latin element developed in the towns in a more and more abstract form. Then we see the great outburst of people from below upwards in various countries. There is a great to-do when Dante, assisted by his teacher, makes his way up into the world of culture. But even that is only one instance of many similar outbursts which happened because of the peculiar manner in which the Latin culture came up against the popular element in the towns. We must not forget that still other streams entered into what was taking place at that time. It is of course true that the main streams of spiritual life, which so to say carried the others, was the one that continued the spiritual tradition in which Augustine had lived; that controlled everything and finally not only gave the towns the bishops, who controlled the spiritual life, if somewhat abstractly and over the heads of the people, but also, little by little, because it took over everything from the constitution of the Roman empire, ended by giving the civil government also, and built up the alliance between Church and State which in the eleventh and twelfth centuries was very close. We see other events light up in this stream, we see crusades arise, which I need not describe to you, because I want to lay the greatest stress upon the things that external history places in a false light; and too little importance is attached to other currents that were present. First of all there is the commercial traffic which had in fact always existed in Europe between the Danube basin and the East. There was constant trading in both directions particularly in the middle of the middle ages. In this way oriental ideas in an advanced stage of decadence were brought over into Europe. And someone who had probably never been in the east himself but had only traded with men from the east, brought to the householder not only spices, but spiritual life, a spiritual life tinged with Orientalism. This traffic went on throughout the whole of Europe. It had less influence on Latin culture, far more on the wide masses of people who understood no Latin. In the towns and in the surrounding villages there was a living intercourse with the east which was not merely a matter of listening to tales of adventure that which deeply influenced spiritual life. And if you want to understand figures such as Jacob Boehme, who came later, Paracelsus and many others, then you must bear in mind that they sprang from people who had developed without any understanding of the Latin culture which passed over their heads, but who were in a certain way steeped in Orientalism. All that developed as popular alchemy, astrology, fortune telling, had developed out of the union of what I described above as the inner experience of the riddle, told in waking dreams, with what came over from the east as decadent oriental life. Nor within the Latin culture have the will to think been able to make any headway. The logic of Aristotle had appeared, as it were, like a meteor. We see that even Augustine was little influenced by this logic. By the fourth century interest had been withdrawn from Greece, and later the Emperor Justinian had closed the School of Philosophy at Athens. This led to the condemnation for heresy of Origen, who had brought with him into Christianity much of oriental culture, of the earlier spiritual life. And the Greek philosophers were driven out. The teaching that they had from Aristotle was driven into Asia. The Greek philosophers founded centre in Asia, and carried on the Academy of Gondishapur, which had for its main objective the permeation of the old decadent oriental spiritual culture with Aristotelianism, its transformation into an entirely new form. It was the Academy of Gondishapur wherein a logical form of thought developed with giant strides, that saved Aristotelianism. Aristotelianism was not transmitted through Christianity, it came into Latin-ecclesiastical life by way of Africa, Spain and the west of Europe. And thus we see how Gondishapur, this philosophic form of Arabism, which does contain a living world-conception, although it is quite abstract, brings its influence to bear upon the current which we have already described as passing over the heads of men. I have described to you both these streams, the one at work above, in the heads of men, the other in their hearts. They work together and it is very significant that the ancient culture was transmitted in a dying language. Of course there then flows into all this what came through the Renaissance. But I cannot describe everything to-day. I want to point out some of the main things which are of special interest to us. The two currents existed side-by-side right on into the fifteenth century. Then something happened of extraordinary importance. The thought of antiquity, inspired thought which was half vision, became gradually clothed in abstract forms of speech, and became Christian philosophy, Christian spiritual life, the Scholastic philosophy, out of which the modern university system developed. In this grammatical-rhetorical atmosphere not thought, but the garment of thought, Romanism lived on. But in the popular stream thinking was born, evoked through subjective activity — for the first time in human evolution. Out of this ghostly-magical element of presentiment, mingled with Orientalism, which above all had its life in the interpretation of natural phenomena, active thinking was born. And this birth of thought out of the dreamlike mystical element took place somewhere about the fifteenth century. But up to that time the system of Roman law, clothed in Latin form, gathers strength side by side with the Roman priesthood. This current over the heads of men had been able to spread everywhere in a most systematic way first in the villages, then in the towns, and now in the new age which dawned in the fifteenth century it joined forces with that other current which now arose. In the towns people were proud of their individualism, of their freedom. One can see this in the portraits painted at that time. But the village communities were shut off from all this. Then the medieval princes rose to power. And those who outside in the villages gradually came to be in opposition to the towns, found in the princes their leaders. And it was from the country, from the villages that the impulse came which drew the towns into the wider administrative structure, into which then came Roman law. There arose the modern state, made up of the country parishes; thus the country conquered the towns again, and became itself permeated by what came out of the Latin element has Roman law. Thus the latter had now become so strong that what was stirring among the common people could find no further outlet; what in the times of unrest, as they were called, had expressed itself among the Russian peasants in the Hussite movement, in Wycliffism, in the Bohemian Brotherhood, such movements could no longer happen; the only thing that could find expression was what merged with the Roman-administrative element. Thus we see that the folk-element which had won for itself the reality of thought, which held its own in opposition to the Roman-Latin element, remained to begin with a faint glow under the surface. There is a cleavage in the spiritual life. Out of the Latin element develops Nominalism, for which universal concepts are merely names. Just as this was an inevitable development from grammar and rhetoric, so, where there still remained a spark of the folk-element, as was the case with Albertus Magnus and Thomas Aquinas, there developed Realism, which experienced thought and expression of something real. But at first Nominalism had the victory. All that happened in the historical evolution of humanity is in a sense necessary, and we see that the abstract element becomes all the stronger because it is carried by the dead Latin language right up to the fifteenth and sixteenth centuries, and is then fructified by thought, has to reckon with the birth of thought, but clothes thought in abstractions. And the fifteenth, sixteenth, seventeenth, and eighteenth centuries are primarily under the influence of thought born from out of the ancient Gothic Germanic way of life, clothed however in Roman formulae, in grammatical, rhetorical formulae. But now that they have been fructified by thought, these formulae can be called logical formulae. That now becomes inward human thinking. Now one could think thoughts, but the thoughts had no content. All the old world-conceptions contained, together with the inward experience, at the same time cosmic mysteries. So that thought still had content right up to the fourth century A.D. Then came the time which as it were bore the future in its womb, the time in which rhetoric, grammar and dialectic developed further and further in a dead language. Then that was fructified by the force of thought which came from below, and men acquired mastery over that, but in itself it had no content. There was a dim perception of Realism but a belief in Nominalism, and with the aid of Nominalism next came the conquest of nature. Thought as inner soul life brought no content with it. This content had to be sought from without. Thus we see how from the fifteenth to the nineteenth century the conquest of natural law was the achievement of a thinking that was empty of all content, but was born as a capacity out of all that Europe had brought forth as her own. In the middle of the nineteenth century men began to be aware “With your thought you are conquering natural law, you are conquering the external world, but thought itself is making no progress.” And men gradually got into the way of eliminating from their thought everything that did not come from outside. They found their life in religious faith which was supposed to have nothing to do with scientific knowledge, because their thinking has become void of content and had to fill itself only with external facts and natural entities. The content of faith was to be protected because it had to do with the super-sensible. But because this empty thinking had no content, it could apply itself to the sense-perceptible. But this faith in which man lived could only fill itself with old traditions, with the content of the oriental culture of the past, which still lived on. It was the same with art. If one looks back to earlier times, one finds art closely associated with religion, and religious ideas find their expression in works of art. One sees how their ideas about the Gods find expression in the Greek dramatists or the Greek sculptors. Art is something within the whole structure of the spiritual life. But by the time of the Renaissance Art begins to be taken more externally. Indeed in the nineteenth century we see more and more how men are happy to be offered a pure phantasy in art, something which they need not accept as a reality, something which has nothing to do with reality. And such men as Goethe are like modern hermits. Goethe says “He to whom nature begins to unveil her open secrets feels an irresistible longing for her worthiest interpreter, art.” Art, says Goethe, is a revelation of nature's secret laws, laws which would never be revealed without her. And it is worthy of note that Goethe has a way of turning to the past, different from that of other men, — he speaks therein for a content, in the age of empty intellect, filled only with the impression of the external world of the senses. He yearns toward Greece. And when in Rome he finds still something of what Greek art has fashioned out of the depths of its philosophy, he writes “That is necessity, that is God.” Art unveiled for him the spirituality of the world which he was trying to experience. But more and more men have a obscure ill-defined feeling “This thinking of ours is all right for the external world, but it is not suited to attain to an inner spiritual content.” And thus we see the second half of the nineteenth century run its course. As I remarked yesterday, the winds of the first half of the nineteenth century, such as Hegel, Saint-Simon or even Spencer, still believed that they could reach a philosophy, even a social philosophy, out of their inner soul experiences. In the second half of the nineteenth century men thought that no longer. But something of what had given birth to thought out of the unconscious was still at work. Why was it that in the portentous dreams of village populations over the whole of Europe right up to the twelfth century there was always something of this riddle-solving element, this cleverness which expresses itself in all sorts of cunning? It was because thought, reflection, the work of thinking, was born. The foundation of thought was laid. And now we see how in the second half of the nineteenth century there is utter despair. Everywhere we find statements as to the boundaries of knowledge. And with the same rigidity and dogmatism with which once the scholastics had said that reason could not rise to the super-sensible, du Bois-Reymond, for example, said that scientific investigation could not penetrate to the consciousness of matter. I mean that previously the barrier had been set up in relation to this super-sensible; now it referred to what was supposed to hide behind the senses. But in all manner of other spheres we see the same phenomena emerge. Ranke the historian of the second half of the nineteenth century is very typical in this respect. According to him history has to investigate the external events, even of the time in which Christianity begins to spread; one has to pay attention to what is taking place in the world around one politically and socially and culturally. What however has taken place through Christ in the course of human evolution — that Ranke assigns to the original world (Urwelt), not in the temporal sense, but to the world behind what can be investigated. We have seen that the scientist du Bois-Reymond says ‘ignorabimus’ as regards matter and consciousness. Natural Science can go pretty far; but what is there where matter lurks, what is there where consciousness arises, there du Bois-Reymond formulates his seven universal riddles; they are he pronounces his ‘ignorabimus!’ And Leopold von Ranke, the historian who works in the same spirit says “Upon all the wealth of existing documents historical investigations can pour its light; but behind what is at work as external historical fact there are events which seem to be primeval.” Everything which thus lies at the base of history he calls the ‘Urwelt’, just as does du Bois-Reymond the world lying beyond the limits of natural science. Within that sphere lie the Christian mysteries, the religious mysteries of all peoples. There the historian says ‘ignorabimus’. ‘Ignorabimus’ alike from scientist and historian; that is the mood of the entire spiritual life of the second half of the nineteenth century. Wherever you meet the spiritual life, in Wagnerian music, in the cult of Nietzsche, everywhere this mood is to be found. The former is driven to take refuge in certain musical dreams, the latter suffers through what is taking place in the world of ‘ignorabimus’. Agnosticism becomes fashionable, becomes politics, shapes the state. And anyone who wishes to do anything positive but relies not on any kind of gnosticism, but upon agnosticism. The strategy of Marxism builds upon what lies in the instincts, not upon something which it wants to bring forth of super-earthly nature. We see how everywhere spirituality is driven back, how agnosticism becomes the formative reality. It is thus that we have to understand modern spiritual life. We shall only understand it aright if we follow its origin from the fourth century A.D. , if we know that in it Nominalism is living, the purely legalistic and logical; and thought has been born in the way I have described. This thought, however, is still only so far born as to be able to make use of formalism, of empty thinking. It slumbers in the depths of civilised humanity. It must be brought out into the open. We learn how really to study history, if we illuminate with the light of spiritual investigation what has hovered over us since the fourth century. Then we can know what is above. And certainly thought has become fruitful and natural science because it has been fructified by thought born out of human nature in the way I have described. But now in the time of poverty, in the time of need, mankind needs to remember that thought which to begin with could only fructify formalism — empty thought that receives knowledge of nature from outside — has exhausted itself in natural scientific agnosticism, must strengthened itself, must become ripe for vision, must raise itself into the super-sensible world. This thought is there, it has already played a part in natural scientific knowledge, but its essential force still lies deep beneath the consciousness of human evolution. That we must recognize as a historical fact, then we shall develop trust in the inner force of spirituality, then we shall establish a spiritual science, not out of vague mysticism, but out of clarity of thought. And the thoughts of such a spiritual science will pass over into action, they will be able to work into the human social and other institutions. We are constantly saying that history should be our teacher. It cannot be our teacher by putting before us what is past and over, but by making it capable of discovering the new in the depths of existence. What goes forth from this place goes forth in search of such a new vision. And it can find its justification not only in the inculcation of spiritual scientific method, but also by a right treatment of history.

European Spiritual Life in the 19th Century

The Development of Thought from the 4th to the 19th Century II

https://rsarchive.org/Lectures/GA325/English/PAV1933/19210516p01.html

Dornach

16 May 1921

GA325-2

In these lectures I should like to bring forward some details about the connections existing between the spiritual life of nations and their destiny in history. Natural Science is an especially important element in our civilization to-day because of the constitution of our present day souls, and I shall therefore select from the many different points of view from which the theme can be treated, the scientific element, and show that the entire historical development of nations is the deep basis for our present day inclination towards the scientific view. It will be necessary first to give an introduction and treat the theme itself on the basis of to-day's observations. If we turn our attention to the historical development of nations — and for the moment we will remain within what is historic — we will see that by the side of external political and economic destinies, spiritual endow¬ments, acquisition and accomplishments are forced upon us. You know that to-day two modes of thought oppose each other strongly. I have pointed out these opposing tendencies of thought in an earlier lecture held here in Stuttgart. First there exists the view proceeding more from the Ideal, the supporters of which are of the opinion that a spiritual basis, merely in the form of an abstract idea, prevails in the evolution of a nation. Accord¬ing to this view external events are produced from out of such a spiritual basis. One can say that ideas prevail in history which express themselves from epoch to epoch, but usually one is not clear regarding the shadowy relation between the real spiritual basis and the sequence of ideas which are brought to expression in the course of history. The other view, which at present exercises great sway, considers that all spiritual phenomena, including Morals, Rights, Science, Art, Religion, etc., are simply a result of material events, or rather, as a great portion of mankind would say to-day, of the economic life. It is thought, in this case, that certain dim forces which are not investi¬gated further, have brought about this or that economic system or method of co-operation in the time sequence of history ; and so, through purely material economic processes, what men regard as Ideas, Morals, Rights, etc., have arisen. One can produce if desired convincing reasons for the one view as well as for the other. Both are capable of proof in the sense in which ' proofs' are often spoken of to-day. Whether a proof is regarded as decisive for the one or the other view depends on the way one is placed in the world with reference to one's ordinary interests or what one has experienced in life through mode of philosophic thought. Everything in this Wundt characterization is built up, is constructed. Some observations are made about the way in which modern uncivilized tribes show their way of thinking through their language. The hypothesis is continued and the primaeval population of the world is shown to have been like these primitive tribes which have remained in this earlier condition, only perhaps more decadent. From the ideas found here one can see how they have arisen. They are not gained from experience, but their originator who built them up uses the modern concepts of Causality, Cognition, Natural Causes, etc., and then he reflects how these would appear in more primitive conditions. Then he proceeds to carry over to primitive races what he has thus constructed. There is but little possibility to-day for looking into the soul of another human being. There is absolutely nothing in Wundt's exposition of which one can say, one can recognize that it has arisen from insight into the soul conditions, even those of primitive races to-day. The renowned Wundt merely revolves about his own ideas which he simplifies and applies to the human creatures he is studying. Because nothing correct exists to-day connecting primaeval races and the races with developed outlook upon the world, we see these things placed historically side by side without regard to the fact that it is, one might say, logically offensive to find highly developed views of the world supported by wonderful intuitions of the Hindus and Chinese placed immediately after such a description of primitive man as given by Wundt. What is so lacking to-day is this power of penetrating feelingly into other modes of thought. We go back with what we are accustomed to think in the 19th or 20th centuries to the 15th and 16th centuries and then to the middle ages. We do not feel allied to them and cannot understand them and so we say they were dark ages and that human civilization came to a certain pause. Then we go back to Greece and here one feels the necessity for close contact while retaining the same ideas one holds regarding the ordinary life of culture to-day. At best, men of fine feeling, like Hermann Grimm, speak differently. He has emphasized the fact that, with our modern ideas, we can only go as far back as the Romans. Generally speaking, we can understand them, we can grasp with modern ideas what transpires with the Romans. If we go back however to the Greeks we see that already Pericles, Alcibiades, even Socrates or Plato, Aeschylus or Sophocles are shadowy beside our modern understanding; there is something foreign about them, if we approach them with modern ideas. They speak to us as if from another world. They speak to us as if history itself starts with them as a fairy-tale world. Hermann Grimm has spoken in this way of facts. But one must add something if we proceed from another point of view, from the view existing in the world through the spirit of Natural Science (this was not the view of Hermann Grimm.) One cannot go back in thought even to the Romans so as to make them appear really objectively before us. Grimm, who did not have an education in Natural Science but only received what existed as a continuation from the Roman epoch into modern times, is still able to enter into, the spirit of Roman times but not into the Greek. And if the concepts of Rights of the State which are copied from Rome were not known to us, if we possessed nothing of that singular feeling for Art which arose again in the Renaissance and into which Grimm entered deeply, but if instead of all this we lived in purely scientific ideas we should be as little at home in the Roman world or even in the medieval world as Grimm felt himself at home in the Greek world. This is one point that must be added, and the other is that Grimm paid no attention either to the World of the East. With his whole observation of the world he only traces back as far as the Greeks. Consequently he does not attain to what he would have attained according to his own suppositions if he had applied himself to, let us say, the Vedas, to Vedantic philosophy. He would then have said: If the Greeks meet us as shadows, those men whose special conditions have found expression in the Vedas, in Vedanta, meet us not even as shadows but as voices from out of a quite different world, a world which does not resemble ours even in its shadow-images. But this is only valid if we have so taken up the present mode of thought and condition of spirit that we are able to understand these as soul content. Quite different is it if we adopt the methods which to-day are alone purposeful. Because of a certain entanglement in natural-scientific education, we are to-day imprisoned in a system of ideas which appear to be almost absolute. It is only through Spiritual science that one can to-day enter with one's feelings and one's life into past epochs of time. From the standpoint of Spiritual science the single epochs of human evolution appear absolutely different from each other; indeed, it is only in Spiritual Science that the possibility arises of entering into the spirit of what men in past epochs of historical development possessed as soul-constitution. How does this possibility arise? It is possible in the following way. I have often explained in lectures that Spiritual Science rests on a definite development of our soul powers. The cognition which we apply in Natural Science and in ordinary life and which in recent times we have carried over into History and into Social Science and even into the science of Religion, I have called in my books 'Objective Cognition.' This is namely what every human being who belongs to our modern civilized life is aware of. We observe the external world through the senses and combine sense impressions through the medium of the intellect. We thereby gain serviceable rules for life, a certain survey over life or over the laws of nature. In this consists what one calls objective cognition. As characteristic of this we acquire a clear distinction between ourselves and the surrounding world. Ignoring for the moment the different theories of knowledge, the different psychological and physiological hypotheses, we know that we face sense-perception as an Ego. Through the intellect, in which we clearly know ourselves to be active, we gain a kind of synthesis of what is given through the senses. We thus distinguish active, intellectual activity from passive perception. We feel ourselves as an Ego in the environment which reveals itself through sense experience. In other words, man distinguishes himself as a thinking, feeling and willing being from the environment which imparts itself to him through sense revelation. But I have continually pointed out that beyond this method of cognition other methods can be developed and I have shown in my books How to Attain Knowledge of the Higher Worlds and Occult Science how such methods are attained. The first steps for such cognition — whether one calls it 'higher' or something else does not matter — is Imaginative Cognition. This is distinguished chiefly from objective cognition by its working, not with abstract ideas, but with pictures which are as pregnant and as evident as ordinarily perceived images but which are not transformed into abstract thoughts. In our rela-tion to these pictures, as I have often emphasized, we produce and dominate them just as one does mathematical ideas. The method of raising oneself to Imaginative Cognition has a quite definite effect on the constitution of the soul. But this result — and I say this with emphasis — lasts only during the time given to Imaginative Cognition. For when the spiritual investigator finds himself once again in ordinary life he makes use of ordinary knowledge, or objective cognition, like anyone else. He is then in the same disposition of soul as another man who is not a spiritual investigator. During spiritual investigation, within that condition of looking into the spiritual world, the investigator is actually in his imaginative world. But there imaginations are not dreams, they are experienced with as much presence of mind as are mathematical ideas. With regard to this presence of mind the condition of soul is not changed during imaginative experiences, but with regard to ordinary working experience in the world it is changed. During imaginative experience the feeling is at first that of being one with all that runs its course in our own soul life in time apart from space. Space does not come into question here, only time. I have already explained how, with this entry into imaginative representations, our experiences since birth or since some definite time later stand before us as a tableau arranged in time, a time picture made perceptible. This is difficult for the ordinary intellect to conceive because we are dealing with a picture which is not spatial but must be thought of only in time in which, however, simultaneity is an inherent factor. In ordinary consciousness one has always to do with the single moment. From this one looks back into the past. During this moment the world is seen surrounding us in space and we see ourselves existing in a definite epoch in time distinct from this surrounding world. In Imaginative Cognition this is different. Here there is no sense in saying: I am living in the definite moment now; for when I behold this picture of life I flow with my life, I am just as much in the time of 10 or 20 years ago as in the present. To a certain degree the Ego is absorbed in the state of 'becoming' which is here perceived. One is united with this perception in time to the state of 'becoming.' It is as if the Ego which usually is experienced in the present moment is spread out over the past. As you can imagine, a transformation of the whole soul life is thus involved during the moments of such experiences. We have to deal with a world of pictures in which we are living. We feel ourselves to a certain extent to be a picture among pictures. Whoever understands this in the right frame of mind will no longer talk foolishly about the spiritual investigator being subject to some kind of suggestion or hypnosis; for he himself is absolutely clear about the picture and the character of his experience; clear that he is a picture among pictures. But just because of this he knows also that the pictures in his consciousness are just like other ordinary representations, they are copies of a reality; images which he does not yet perceive as reality but the pictures of which he beholds inwardly. One is in the condition of suggestion or hypnosis only if one has pictures and believes them to be realities like the realities perceptible through the senses. As soon as we are clear regarding the character of our experiences in consciousness, then it is simply a question of an inner possession of the same faculties that one uses in mathematics. The essential thing that I want especially to emphasize to-day is this merging into what is objective-temporal, into this 'becoming' so that one no longer clings to the 'Now' in time but feels alive in the stream of happenings. The next stage obtained through exercises, which I have also described in the books named, is that of Inspiration. This is distinguished from the Imagination stage by the picture element almost vanishing. One must first have the pictures in order to obtain correct ideas of Spiritual Science, but one must also be able to extinguish them from consciousness, one must obliterate them arbitrarily. And then the possibility comes for a holding back of something and what is held back is actually a revelation from the spiritual world. In my books named above I speak of inspired ideas of the spiritual world. But even with such experiences one has not yet attained the spiritual world. At first one had pictures, now one has the revelation to a certain extent of the spiritual world, but one stands independent and facing it, recognizing its reality in that one stands outside it. To-day I should like to consider especially the soul condition when, from out of one's own will, such Inspiration is evolved. The ordinary objective world is then renounced, one knows then what it means to have outside one's body a revelation of the spiritual world. In other words, we can now float in unison not only with time, but with all that is spiritually objective, external to man; we no longer feel the distinction between cosmic existence and Ego existence in the way pertaining to objective cognition, but we experience the Ego and in the Ego the Cosmos in its concrete variety and multiplicity. It is fundamentally the same, at this stage of knowledge whether I say 'I am in the world' or 'The world is in me.' Ordinary methods of expression cease to have validity. Prepositions such as 'in' or 'outside' can only be used when one connects them with another condition. One feels poured out in the whole world not only in the 'becoming' but in everything that appears anew in consciousness as spiritual. One no longer feels this 'outside you' and 'in you.' This is the soul condition which holds us during Inspiration. It is not as if the Ego were submerged, not as if the outpouring of the Ego were identical with a suppression of the Ego, but the Ego in all its activity feels that it has become one with the concrete, manifold varied world it now experiences. We know ourselves apart from our ideas, our feelings and our will impulses in spite of the fact that these are one with ourselves. So also through Inspiration we feel the manifold nature of the world in spite of knowing that we are really merged together with this world. In the present epoch of human evolution, these stages of cognition must be evoked by such energies as I have described in my books How to Attain Knowledge of the Higher Worlds and in the second part of my Occult Science. They have to be reached consciously. But we can distinguish what constitutes the feeling of the soul in these conditions from what we con-sciously evoke there as content. One can distinguish how one feels in the state of Imagination and Inspiration from what one gains there by working and from what one finally apprehends there. I do not want to indicate this soul condition through abstract considerations; I would like to describe it concretely. You see, when Goethe learnt to know Herder he, together with Herder, buried himself deep in the work of Spinoza. Whoever knows anything of Herder's biography knows to what an enthusiastic degree Herder admired Spinoza. But if one reads again such a work by Herder as, for instance his 'God,' in which he records his feelings regarding Spinoza's works, one must realize that Herder speaks about Spinoza, from out of Spinoza, but quite differently from Spinoza the philosopher himself. In one point Herder is similar to Spinoza and that is in the soul condition from which he reads Spinoza. Herder's soul was very similar to the soul condition from which Spinoza's Ethics, for example, were written. This condition passed over to Herder and, in a certain way, passed over also to Goethe while he plunged into the study of Spinoza with Herder. But while Herder had a certain satisfaction in this soul condition, Goethe had none. Goethe felt deeply that passing over into the object, that merging together of the Ego into the outer world, so magnificently alluded-to by Spinoza when he speaks in absolute passionless contemplation, as if the Cosmic ALL itself spoke, as if he would forget himself and as if his words were merely the means through which the Cosmos itself were speaking. Goethe could experience what can thus be experienced in objectivity, and in this connexion he felt just as Herder felt: but he was not satisfied. He still felt a longing for something else and it seemed to him that in spite of the depth of feeling acquired, Spinoza's philosophy cannot by any means fill the whole of man's needs. Fundamentally, what Goethe felt in this way towards Spinoza is but another 'nuance' of his feeling towards the northern world. The civilization accessible at Weimar dissatisfied him, and, you know how he was driven south, to Italy through this feeling. In Italy he at first saw only what the Italians created on the basis of Greek art, but something like a reconstruction of the Greek spirit and method in Art arose in his soul. One can feel deeply what is characteristic of Goethe at this period if one reads what he wrote to his Weimar friends while standing before those works of art which called up before his soul the creative art faculty of the Greeks. 'There is Necessity, there is God' (with reference to Herder's work' God' inspired by Spinoza). Goethe did not find in Spinoza that Necessity he wanted: he found it in what was presented to his soul during his Italian journey. Out of what fashioned itself then there arose in him the possibility of developing his own special outlook on Nature. One knows how he brought to expression his longing for an exposition of Nature in abstract, lyrical words in a 'Prose-Hymn,' before he travelled south. And one sees how what was poured out in abstract lyrical form in this prose hymn 'Nature' became in Italy concrete perception. How for example, the plant nature appeared before his soul as supersensible perceptible pictures and how he then discovered the 'primal plant archetype' among the manifold plant forms. This archetype is an ideal-real form which can only be seen spiritually, but in this spirit form it is real, lying at the base of all individual plants. We can see how from now on the object of his search is to bring before his soul those archetypes for all nature which are one and many. We can see how his knowledge rests on the transforming pictures, from the single plant's leaf-sequence on to the blossom and the fruit. He wishes to hold fast in pictures what is in process of becoming. From Spinoza's ethics which he read with Herder there streamed something that seemed invisible, resounding from out of another world, a world in which man can immerse himself with his feelings if he attains a passionless contemplation. But with Spinoza this was not perceptible. The longing for vision lived in Goethe's soul and this longing was fulfilled in a certain way when he was stimulated by those pictures appearing like resurrected art creations of the Greeks. And it was also satisfied when he was able to conjure pictorially before his soul the primal archetypes of Nature. What was it that Goethe thus experienced in sequences? It was that soul feeling — not soul content, not that which one can investigate — but the soul feeling which, on the one hand is Inspiration and on the other hand is Imagination. Neither Goethe nor Herder had the possibility in their time of looking into the spiritual world as can be done to-day through spiritual Science, but as a premonition of this spiritual science the feeling prevalent in them was the feeling which appears in special strength and intensity in Inspiration and Imagination. Herder and Goethe felt themselves in the mood of Inspiration while they read Spinoza and Goethe felt himself in the mood of Imagination when lie formulated an outlook on nature through the Italian works of Art. Out of this Inspiration mood of Spinoza Goethe experienced the longing for the Imaginative mood. What he discovered as the archetype of plant and animal, this was not yet real Imagination, for Goethe did not possess the method of acquiring real imagination. What he possessed was the mood for Imagination. He could kindle the mood in himself, not because lie strove towards real, pure imaginations freely created inwardly, but because he experienced in himself sensible supersensible pictures stimulated by what plants, animals and what the cloud world express. He could find himself in the mood which accompanies Imagination just as in reading Spinoza he found himself in the mood of Inspiration. He recognized the soul condition in which man experiences what he utters in such a way that he uses words so as to allow the secrets of the Cosmos to be uttered, to a certain extent, by the Cosmos itself. Whoever has really felt the transition in the soul which can take place through reading Spinoza's Ethics as a mathematical treatise, becoming immersed in the ideas as mathematical ideas so as to rise to the Scientia Intuitiva which speaks in Spinoza as consciously as though the world were using him as its mouthpiece, — any one who has felt thus will realize what Goethe and Herder felt in Spinoza. How the one, Herder, was satisfied and how the other lived with longing more in a mood of Inspiration. And we can say that a certain soul mood proceeds from what spiritual scientific investigation offers to-day as methods to attain Imagination and Inspiration. We can follow historically how Goethe, without having Inspiration or Imagination, tends towards these moods. Now if we go further we can regard Spinoza more exactly. When we study him historically (not as is often done to-day by the historians of philosophy) one is led from Spinoza to know who stimulated him. These were the adherents of Arabism, living in the South-west of Europe, adherents to the Arab-Semitic outlook on the world. He who understands such things will be able to experience once again that which flowed from the Kabbalah into the ideas of Spinoza. One is then led further back beyond Arabism to the East and one learns to know what comes forth in Spinoza is the conception of an ancient view of the world. In the old Eastern world what appears is the same as in Spinoza only not in intellectual form but as ancient Eastern inspiration. This inspiration was not acquired as ours is to-day, but it existed among certain oriental races as a natural gift and went through an especially profound development there. If we go back to the Egypt from which Moses created his views, to the sources from whence the Greeks created, we find that what came to Egypt from the Asiatic east is developed to a very high degree. The Egyptians before the 8th pre-Christian century lived instinctively in their environment so that they felt themselves one with it, so that what they discerned of their environment they experienced in inner contemplation. Now let us turn to the Imagination, to what Goethe longed for when he felt the mood of Inspiration. At first he recognized this to a certain degree in the art of Greece. He sensed in vision what Herder felt in concepts, in the world of perceptions as these appeared contemplatively with Spinoza. And what Goethe realized he deepened into a view of outer Nature so that later on he could utter, from out of his spirit, this deep saying: 'He to whom Nature reveals her manifest secret, yearns for Art, Nature's worthiest interpreter.' In Art, Goethe saw through to the basis of Imagination, and by relying on evolution in Nature he sought that soul mood which a man enters if he become one with this evolution. This conquest of oneself, together with maintaining oneself in Imagination, was revealed to Goethe through the art of the Greeks, and he sought it not only in Art but as the basis for a view of Nature. And if we follow on to further consequences this special element which Goethe thus developed, we attain in a fully conscious manner Imaginative Perception. If we follow this method of Goethe back to its origins, as we follow Spinoza's method, we are led to the Greeks, and from them further East. From the Greeks we come back to that view of the world which existed in the development of the so-called Chaldees, who again created from out of the Persian world and out of the entire Asiatic world. And just as we look back through the soul mood of Spinoza to ancient Egypt, so we look through the Goethe-Greek view of Art to that view of evolution which obtained in ancient Chaldea. One can follow, even into the details, this opposition of Chaldea and Egypt in Goethe and Spinoza. We can thus go back in feeling to earlier epochs of time if we do not entangle ourselves in what alone is regarded to-day as absolutely correct and exact. If we attempt to press forward to other kinds of ideas, to Imagination, to Inspiration, if we know the moods of soul pertaining to Imagination and Inspiration, then we can go back in cognition to earlier epochs. Whoever reads Spinoza today merely with the intellect which has been so strongly developed with us, and as if everything previous were fundamentally but childish ideas, he cannot feel how in Spinoza there lived as a mood what was productive intuitively and creatively as the highest blossom in ancient Egyptian civilized life. He cannot feel how the soul mood of the ancient Chaldeans lived on in that which ensouled Goethe as he uttered the words: 'There is Necessity. There is God,' or 'He to whom Nature reveals her manifest secret yearns for Art, Nature's worthiest interpreter.' Whoever bases himself merely on the abstract thought content of to-day, does not come back to the earlier historical epochs. Therefore there results for him that abyss to which I pointed at the beginning of this lecture. Only he can come into ancient epochs of humanity who immerses himself in this basic mood as it appears in Spinoza and Goethe. No Egyptian Myth, least of all the Osiris-Isis Myth, can be really experienced in its import if one does not base oneself in this mood. People may be ever so clever and give ever so many allegorical, symbolical interpretations. This is not the point. It is a question of feeling with one's entire being what was felt in ancient times. One may think this or that about ancient ideas, one may choose clever or foolish symbols, it is not a question of choice but of experiencing a basic mood. Through this we can come to what lived in an earlier epoch. One cannot find what existed in ancient Chaldea by the present means of investigating, but only by being able really to immerse oneself in the mood of Imagination which actually appeared to a certain extent with the Chaldeans as a view of the world. They lived in a 'becoming.' One understands what contrasts existed between the Chaldeans and Egyptians, for instance, as contemporary races. Trade relation went from Chaldea to Egypt and from Egypt to Chaldea. Their culture was so fashioned that they could write letters to each other. Everything consti-tuting external life stood in regulated interchange. Their inner soul constitution was however quite different. An Imaginative element lived with the Chaldeans, an Inspirational one with the Egyptians. There was, with the Chaldeans, an external perception, such as reappeared, intensified, in Goethe. With the Egyptians, from what proceeded out of inner being, the soul, there was that which later on appeared at a higher stage from out of the inner being of Spinoza. One can follow this into minute details. I will give an instance and one will see how such details are to be understood on the basis of these general moods. The Chaldeans had fundamentally a highly developed astronomy. They developed it by means of cleverly devised instruments, but above all by a quite definite kind of perception which was an instinctive Imagination. They came thereby to divide the course of time into Day and Night so that each was regarded as 12 hours long. But how did they divide the days and nights? They made the long summer day into 12 hours and they also made the short summer night into 12 hours. In winter they similarly divided the short day into 12 hours and the long night also into 12 hours, so that the winter hours by day were short and the summer day hours were long. Thus with the Chaldeans the hours in the different seasons had quite different lengths of time. This means that the Chaldeans so lived in the sense of 'becoming' that they carried this 'becoming' into Time. When they lived in the outer world in summer they could not let the hours run as they let them run in winter. In summer the course of time, the 'becoming' was drawn out. This "becoming was inwardly moveable, not rigid as it is with us. Time was elastic with them. How was it with the Egyptians? The Egyptians reckoned 365 days to the year. Through this they were obliged to add supplementary days at definite times, but they could not decide to depart in any way from their 365 days to the year. In reality the year is longer than 365 days, but this length remained immoveable with them up to the third pre-Christian century, and thereby the perceptible outer world got beyond their control. Through this the Festivals changed. For instance, a festival of early autumn became a festival of late autumn, and so on. Thus the Egyptians so lived into the course of time that they had a conception of time which was not applicable to outer perception. Here we see an important contrast. The Chaldeans lived so intensely in the externally perceptible that they made time elastic. The Egyptians made time so rigid, experiencing what lives subjectively from within, that they could not even correct it through intercalary days in order to make the feasts of the year harmonize with the seasons; and so they let the external festivals fall on the wrong months while the whole external world thus became unsteady. They did not find themselves in the outer world, they remained in their own inner being. That is the mood of Inspiration which we must have in order to come to real cognition. The Egyptians had it as instinctive Inspiration. As a man knowing the higher worlds one should be as mobile on the one hand as the Chaldeans and on the other hand be able to enter deeply to inner being as the Egyptians could. A rigid system of time was the basis of their whole life, even of their social and historical life. This contrast between the mood of naïve Inspiration and naïve Imagination thus comes to expression in History. Goethe, as a complete being, re-experienced the experience of Spinoza as a continuation of Orientalism and Egypt. Goethe experienced his longing for a complete adaptation to the external world from out of his inner feeling where everything is invisible, from whence a man looks out into the world and does not recognize things because he judges them according to what the inner being offers, so that the things are beyond his control. While Goethe felt the mood of Egypt, he sought to experience in himself the mood of Chaldea, as that of the other pole. If a man re-create out of his own nature historical moods, one can then see the threads extend from a newer over to an earlier epoch, and one hopes to reunite the different epochs of time through this observation. This now is essential, that one does not merely designate from documents what happened in this or that epoch, but that one learns as a complete human being to immerse oneself in these epochs, in what was felt and inwardly experienced by men and by races in the different epochs, in what mood of soul they existed. Their external fate was the result of this inner experience, of this peculiar soul constitution. This is the way that will lead us above such ideas as 'Does the egg come first or the hen?' and can lead us into the deeper regions of reality. It is the way which shows us how each time we observe the reality we must press forward beyond what is given by external objective cognition. And if it is often emphasized that one must learn from history about our activities to-day and in the future, then attention must be directed to the manner in which we should learn. We should so learn that what we experienced with our soils in past epochs should become living. The abyss of which I have spoken is bridged through this consideration. We are able to look hack into the metamorphosis of the soul constitution of men during the different epochs of time, and ardour and thoughtfulness will flow into our present soul constitution, so that we find the necessary thoughtfulness to build those ideas which are needed for the healing of the social relationships of to-day. But the necessary ardour must be kindled to have the force to attain full consciousness and to express in ideas that Imagination and Inspiration which formerly were developed instinctively.

Natural Science and the Historical Development of Humanity

Natural Science and the Historical Development of Humanity I

https://rsarchive.org/Lectures/GA325/English/UNK1924/19210521p01.html

Stuttgart

21 May 1921

GA325-3

If we wish to be convinced of what, in the newer sense of the word, Natural Science signifies, we must look back to the sources of our present civilization. As can be seen even front the ordinary historical and scientific observation, these sources must be thought of as lying very far back in time, it is only if one keeps in mind the evolution of man and the gradual appearance of his special powers in more recent times that one can set-how these powers arose front the depths of the human soul, powers which lead to the present observation of nature and the affiliation of this to technique and to life. There is a certain difficulty in placing more recent historical epochs in their essence before anyone who is wedded to the present day Science. In the previous lecture we attempted by way of introduction to proceed from the present — a present be it understood to which Herder and Goethe belong and to investigate certain streams which lead back to ancient times. We have seen how one of these two streams which existed so characteristically in Goethe led its hack to the Egyptian point of view, the other to the Chaldean. We went back to pre-Christian times and emphasized characteristic distinctions between the soul mood of the Chaldean people living in further Asia which can be traced back to about the beginning of the third pre-Christian millennium and that of Egypt, which can be studied still further back even in external history. We have seen how a view existed among the Chaldeans belonging more to the external world in which the human mind so lost itself in the external world that even time became elastic. This soul mood made it necessary to regard the day hours in summer longer than in winter, whereas with the Egyptians the division of the year throughout the centuries was held rigidly by a method of calculating and not from any grasp of external events. They reckoned 365 days to the year and went on in stages of 365 days, not noticing that in reality they were no longer in harmony with the course of the year as it ran in the sense world externally. While they reckoned the year shorter than it is they encountered contradictions with what is really perceived in the outer world. This shows a significant distinction in the soul moods of two people who were connected with each other through trade relations and by spiritual intercourse, people who stood near to each other outwardly. One can only value such a distinction correctly by entering deeply into the origins of human civilization. This is rendered increasingly difficult because the civilizations which have developed one after the other in time exist to-day side by side in space arrested at different phases of evolution. If to-day the European or the American who wishes to emerge from his materialism to more spiritual ideas about the human being, if he turn to the present Indian civilization, he finds within this a highly developed spirituality, a mysticism penetrated by acute intellectual concepts. He finds within its philosophy absolutely nothing of what he has learnt to know as the natural scientific view of Western or American civilization. If he feel a longing to experience something concerning humanity, something which modern science cannot give him, and if he do not allow himself to take into consideration what a newer spiritual science can give concerning man, then he will seek to absorb himself in the spiritual view of modern India or at least of what has been preserved from an epoch that is relatively not very ancient. Whoever is armed with spiritual science, however, and approaches this Indian view of the world will find that from what exists in it to-day or what has been preserved historically from a more or less far distant past, there is expressed something which is no longer quite apparent but which seems to be a kind of lower stratum, as something springing up from dark depths. This plays even into the language and especially into the ideas and images. It must be conceived as something which has undergone many transformations before it has reached its present form. What exists in modern India has only received its form in most recent times but it carries elements in itself which are primaeval, which have required thousands of years in order to be what they have become. If we turn to other civilizations, the Western Asiatic or the Chinese for instance, we find that something similar is the case; but we have the feeling that we need not go back so far in order to understand the present as we have to do in India. And if we observe Egyptian life as it transpired since about the beginning of the third pre-Christian millennium, we have the feeling that what is contained historically in documents is such that we are obliged to immerse ourselves into most ancient times, as we attempted to do, for example, in the last lecture. But we also find that the old has been preserved there with a kind of purity so that its fundamental depth is apparent even in later times, whereas in India it must be sought in the outset of its development. In a similar way this is the case with the Greek and with our own civilization which, as we shall see, begins about the fifteenth century. The matter so appears that for a penetrating view, primeval elements have continued but are hardly noticeable to ordinary observation. We will now see how the ancient elements within European and American civilizations are to be discussed. One might say that the natural scientific element which has entered recent civilization appears to have so thoroughly cleared away what was old that this old element can only be substantiated by definite methods. It is however still there. There exist side by side on earth civilizations of different ages. One must go far back in time in order to understand modern Indian civilization, not so far back to understand the civilizations and literature of Western Asia, still less far back for the Egyptian and again still less to understand the Greco-Roman culture. One can remain almost entirely in the present in seeking to understand modern European and American civilization. What has developed consecutively in the course of time stands side by side for us now and what stands side by side thus is in reality of varying ages, at least so far as regards external appearances. The temporal is mingled with the spacial and one must first find from a modern standpoint the methods which show from what present day civilizations one can go back into ancient times and from which one can find access to these old times by difficult and devious paths. Now as you know, the observation of natural science, the so-called anthropological or geological observation, joins on to what history furnishes and we saw in the last lecture how superficially this is often done. We are led back into very early European times by superficial anthropological investigation. Of course there is less said about the people of Asia but as regards European evolution we are led back into ancient epochs. You know that geology, enriched by modern anthropology and history, says that, concerning certain trustworthy artistic remains which have been found in caves in Spain and France, very ancient races of Europe date back thousands of years; that in these extraordinary paintings revealed by the cave explorations we are told how in ancient times men must have lived in Europe in a certain degree of civilization even before that significant event spoken of by anthropology and geology as the European ice-age within which a great part of the European continent was covered with ice and thus made uninhabitable. Such regions as those in which the cave explorations of Southern France and Spain have been undertaken, must have been oases. Amid the wide ice fields men must have dwelt: a relatively rich nature must have existed and a civilization have evolved. Thus are we led back even to-day into very ancient times of European life. And here, what external investigation can furnish joins on to what Spiritual Science has to say. Spiritual Science can indeed only proceed from what the developed soul powers of man can fathom, what can result from imagination and inspiration; it can speak of what can be consciously per-ceived inwardly. One can say in referring to what external history can investigate: Spiritual Science can in reality only fathom more or less the spiritual part of evolution, least of all that which has occurred in external nature. However, through spiritual investigation one can go back to those epochs which have seen man and his environment in quite different relations to those of the European ice-age. It will be the task of these lectures to go back to those ancient times when man lived under quite different relationships and in quite different regions of the earth than later; but a feeling ought to be evoked regarding how justified it is to point to a supersensible cognition which traces back the history of human evolution into early times. If anyone whose soul life, deepened through the view and feeling gained from spiritual science, approaches what outer history gives, he can have experience of the evolutionary path of civilized man. One can admit from the point of view of external anthropology and geology and history, that if one goes back ten to fifteen thousand years one finds quite another kind of life than that of modern civilized Europe. One can admit that in this epoch, during the last ten to fifteen thousand years, the evolution of European, Asiatic and eventually also of ancient American humanity takes place. But what lies in documents must be illumined in a special manner by spiritual science. One must of course say that out of such considerations as I discussed by way of introduction, if one has acquired the possibility of going back from the present into earlier soul-moods one can then perceive correctly that which exists side by side. In relation to antiquity, attention must be given first of all to the region of India. What is still there to-day as an extraordinary acute method of interpreting the world leads back to the times of the mighty Indian philosophy in which the Vedas had birth. But even if we let the Vedas, the Vedanta philosophy, the Yoga philosophy of India affect us we feel that in order to understand what, in its after effects, still exists beside us on Earth, we feel that we must go back into very early times indeed. If we compare it with, for example, our European method of thinking logically or with the Greek method of building up thoughts, we then find that the European culture of to-day, when compared with the Indian, appears like a descendant, like a grandchild, a child living beside his father and contemporary with him. Indian culture stands there reflecting very early times, but it has become old. In its old age condition one can still fathom what was revealed in ancient times as the highest spirituality, but one only sees it in decadence, in its old age. One sees it as one can see in the child certain early conditions of its father but these are changed because the conditions are experienced in a later date. Think of a man, for example, who was a child in the ninetieth year of the nineteenth century and then turn from him to his father or grandfather. The grandfather was a child in the fortieth or fiftieth year of the nineteenth century but he went through childhood in different conditions to those of the ninetieth year. The child of the latter time knows quite different things to what his grandfather knew with his naïve childhood in the fortieth year. If one acquire this kind of insight into the development of peoples, the present European civilization or even that of Greece appears, so far as we can penetrate into them, as if born late compared with what was born earlier in India or what to-day we find ancient in it. If we can sense this India which has grown old, which was already old at the time of the Vedas and Vedanta philosophy, if we can penetrate this in our mood of soul trained through spiritual science in order to see the earlier from out of the later just as one sees the childhood in a man who has become old, then we can arrive at a perception of primaeval India. But then we must realize that this primaeval India was without doubt a civilization fundamentally different from our own. It must have been absolutely permeated by the spirit and have comprehended man in a special, spiritual way. And if one observes the manifold character of what we find in India, the Veda poems with their imagery which remains however in a fluidic element, the acute Vedanta philosophy, the fervent Yoga philosophy, one must say that in the course of time civilization must have mingled with civilization there; that once upon a time a primaeval civilization of a thoroughly spiritual kind must have existed there. Then something less spiritual was drawn over this, something which found its expression in the Vedas. What appears in the fervent Yoga philosophy was then founded. It was impossible that all these could have arisen out of one race. Different peoples with different capacities have intermingled. The one brought the teachings of Yoga, the other the Veda poems. These peoples already found a primeval India which they absorbed and from which they took what was ripe and old and had withered in man. The incoming race came with fresh blood; they fashioned that which men in decadence could develop no further. And so it went on. In this way the present condition gradually arose and one is not far wrong in comparing this primaeval Indian culture with those remnants which exist in the regions where modern civilization has developed. We can compare with the men of primaeval India those who painted the extraordinary pictures in the west of Europe, the lines of which make such a deep impression on us. When we look at these pictures, if we can lose ourselves in what the human soul experienced while producing these pictures, we must say: certainly, something very primitive is contained here, often something like that which modern precocious children paint; but yet there is something else. We see from these pictures how men lived with a love for outer nature and we see that these pictures were painted from out of deep inner impulses. We see that they were painted by men who did not first analyse with the eye so as to decide how they should draw lines or place colours but who fashioned and painted from out of their inner experience what was deeply rooted in their love. If one compares this with what was founded in the civilization of primeval India, one finds a relationship. In Western Europe the development is primitive and it remains primitive; over in Southern Asia it evolves further and further because it is continually fructified by other races and it develops right on to the Vedanta philosophy. If I had brought these facts forward, as I have often done, in a spiritual scientific way you would then see that one can approach the matter concretely but quite differently. I now present them as they appear to the spiritual scientist when he takes external documents into consideration. But one cannot approach these matters, as customary to-day, with crude ideas acquired from a crude natural scientific observation. Our ideas must be pliable and plastic, as you will see from the considerations I will now place before you. Naturally one cannot show the connection between the cave civilization of Western Europe and the Indian as one proves the similarity of triangles, but the certainty we attain is not little if we only penetrate these things and if we adopt that soul-mood to which attention has been drawn. He who deepens his soul life — from this point of view in the wonderful ideas of the Vedanta philosophy, sees these transformed into an abstract spirit in the draughtsmanship of those paintings in the caves of Spain and Southern France. It does not appear striking, therefore, even from external investigation, that spiritual science explains how a common primaeval race, which must be sought for in the eighth pre-Christian millennium, gradually spread over the inhabitable regions of Europe, Africa and Asia and developed according to the different relationships of life. This ancient civilization within which man lived united to outer nature, showed itself in its most gifted form in ancient India. Here was revealed what comes to expression otherwise in a primitive way only. There was developed also farther that which has astounded people, for instance in the culture of Crete. This arose in the east of Europe. In India it developed as the primaeval Indian culture, and progressed further and further, remaining capable of life even in its old age. It passed through its blossom in that epoch when the Vedas, the Vedanta philosophy and other philosophical methods of thought arose. A great many things intermingled in this India which developed at different times but which are there to-day side by side. If we attend particularly to primeval Indian civilization we must say that everything points to a humanity with a soul mood into which we cannot enter through external means. I have said that one can press forward to Imaginative Cognition. If one does this consciously one gets an idea of what such men experienced, not consciously yet but instinctively like the ancient Chaldeans or the later Egyptians. Their mood of soul was absolutely different from that of modern men. Through this advance in Imaginative Cognition man himself becomes a picture; he blends with this picture and thus lives into the 'becoming' (das Werden) of the world. Thus did the Chaldeans for example, live in the 'becoming.' But on the other hand one learns to know also when to rise to Inspiration, how to overcome the separation between the inwardly subjective and the outwardly objective; to feel at one with the cosmic all, to so feel one's being in the Cosmos that one can say: What announces itself through me is the voice, the speech of the Cosmos itself. I only give myself to it in order to be an organ in the Cosmos and to let the world reveal itself through me. We can reach this state consciously in Inspiration. The Egyptian lived in it instinctively in a late stage. This leads us back to times from out of which a relatively good document obtains in Chinese civilization. What is usually described as such is a late product, but just as in India ancient stages, child stages reveal themselves so are revealed in China primaeval stages of civilization. We can feel how an instinctive Inspiration lives in the Chinese civilization. Through spiritual science we obtain to-day a conscious Inspiration, in China it was more or less instinctive; which means that its results exist as a background in what is imparted to-day in Chinese literature. We are led back to a view of man which presents him as a member of the entire Cosmos. Just as we speak to-day of a three-fold man, the head man, the member man, and the rhythmic man, and fathom his being in its full depths through Inspiration, in the same way the ancestors of the Chinese civilization once lived in an inspired knowledge of something similar. This however did not relate itself to man because man was only a member of the entire Cosmos but it related itself directly to the Cosmos. Just as we feel conscious of our head, the Chinese felt what he called 'Yang.' If we wish to contemplate our head especially we cannot look at it, we can at most see the tip of our nose if we turn our eyes that way. As we can see the surface portions of our organism when we regard ourselves outwardly but are only conscious of our head to a certain extent in our mind, in the same way the Chinese was conscious of something which he called Yang. And by this Yang he conceived what was to be found above, what spread itself out spiritually; the heavenly, the shining, the producing, the active, the giving. And he did not distinguish himself from what he knew as his head, from this Yang. Again, as we distinguish man from his environment when we feel the 'member-man' placing us in activity and connecting us with our environment, similarly the Chinese speak of 'Yin,' and in this he points to what is dark, what is earthy, receptive, and so on. We say to-day that in our limb and digestive system we take up external substances, uniting these through this system with our own being, and we take up the senses-thought element through our head organization, but between these two stands everything which maintains rhythm of breath; the rhythm of blood brings this about. As we feel and cognize man, in the same way the Chinese once saw the whole Cosmos: above the creative, illumining, heavenly; below the earthy, dark, receptive; and the equilibrium between the two, that which forms a rhythm between heaven and earth, that he felt when the clouds appeared in the sky, when the rain fell and when it evaporated, when the plants grew out of the earth towards the heavens. In all this he felt the rhythm of above and below and he called this 'Tao.' Thus he had a view of that with which he grew. It presented itself to him in this three-fold way. But he did not distinguish himself from all this. This view meets us transformed in Western Asia. What is transmitted to us as a primaeval civilization from the region of Persia, what shows itself in China, this must have once undergone a quite different development, metamorphosed into what is given as the opposition between Ahura Mazdao and Ahriman; Ahura Mazdao the illuminating, radiating God of Light and the dark, gloomy Ahriman, between whom the world is represented as running its course. The early Indian could not yet distinguish the higher from the lower, heaven from earth, and this is the difference between what was early Indian and what in China was metamorphosed entirely and can be found as the basis for many civilizations in further Asia that I have named the early Persian in my book Occult Science. As yet no difference was spoken about between what was subjective and inward in men and what was outward and objective. In the outer world no distinction was made between what is light spiritually and what inclines to be more bodily dark, while in later times, in the early Persian epoch, the two were distinguished from each other. The interchange of activity between the two was thought of as being brought about through Tao or through some rhythmic equilibrium. What is it that now took place? Why did men forsake the old standpoint so that they could no longer distinguish the spiritually light from the physically dark and for what reason did they go over to the conception of so opposite an idea as that of polarity or duality? When we realize what is to be found in documents and when we let the feeling which lies in these documents and in their tradition act upon our souls, we come to the knowledge that in those olden times men played little part in the outer world. They lived mostly, from our own correct point of view, on a high spiritual plane, but on the other hand also, in animal innocence. For everything that they experienced in relation to the universe was instinctive. Later on this was thought of as being the out-breathing of Brahma. All this was only possible to men who did not take part and work actively in outer nature, but who entered into nature, one might say, as does an animal, as a bird that takes what nature offers for nourishment without first working for it; fetching it merely by flight. These men therefore lived in full harmony with all the kingdoms of nature and extended their love over them all. When with full human understanding we place ourselves within all existence we realize directly that what was love of animals and plants in the Indian-oriental view of life has arisen out of the great all-love' that does not harm any being and therefore has not yet attained to the fully awakened human consciousness in which men lived in later days. They lived in an atmosphere of spirituality which was instinctive but was higher than that of the Greeks or of the spirituality of today. They lived blameless in nature: they did not kill, they even regarded the plants on which they lived in such a way that they did not sow them but took only those that grew wild. In such a way one looks back upon the peopling of the southern Asiatic regions thousands of centuries ago. Later there awoke in men the consciousness of the radical difference between the higher and lower, a consciousness of the spiritual which man cannot alter, which is above the physical upon which he can work and to which he can devote himself. About the beginning of the 6th or 5th millennium B.C. a change takes place — one can trace it in decadent remnants — in which what surrounded men and what they could alter is looked upon differently and as something over which they could exercise lordship. They begin to tame animals, they make domestic animals out of wild animals, and they become agriculturists. From the 7th or 6th millennium B.C. is the time of great radical change when men begin to work upon Nature and thus distinguish Nature from that which is radiant and shines upon what they could affect and what can gain form through humanity. But it is not only men that can give form to things: men can make instruments, a primitive axe was the instrument that preceded the plough — probably it was woman who first pursued agriculture — they ploughed the ground by hand, and sowed. But just as man saw that the earth could gain form through him he saw also that it was not through him that in spring the earth is decked out with plants and that in autumn the plants disappear. And therefore as the earth can acquire form through man, form also comes from what illumines him from out of surrounding space, and he comes to the distinguishing of light and darkness, spirit and matter. All this developed in such a way that men first learnt to distinguish themselves from the outer world through labouring on the land and being agriculturists and through breeding cattle. We can see in later Persian culture how everything depended on agriculture. We can see the connexion of this with what is expressed in the Avesta and we can recognize the progress from the early Indian civilization. But this develops in such a way that man does not as yet know himself as a Self. Humanity identifies itself with the external world. Men on the whole are entirely instinctively inspirational and they pass from instinctive inspiration to an understanding of the soul life which in after times, in the beginning of the third millennium, appears as the Chaldean imaginative civilization of which we can say that men have progressed so far that they not only distinguish the higher from the lower but that they occupy themselves with the stars; that they invent instruments, water-timepieces, etc. If however we study the Chaldeans we will find everywhere how strongly mankind lives in the outer world and that it is difficult for an inner life to be acquired. In Egypt we see something different. We see the Chaldean arising later than the Egyptian. We can follow the Egyptian back to the time in which we can also set the early Persian civilization with its metamorphosing of the Chinese culture, to the time when the higher and the lower were differentiated. But we can see, just in the beginning of the third millennium B.C., a mighty and radical change within the culture of Egypt. Just as we saw a similar radical change when taming animals and agriculture began, so do we see in the third millennium a still more extensive change. We come upon it in this way. We see how in Egypt the building of pyramids developed in a later period. We can also follow Egyptian culture historically to-day further back than the pyramids. These begin in the third millennium. Egyptian civilization reaches back to the time of Menes before this century. The mighty pyramids were not built then. At the same time that the pyramids were built we see something arising in Egypt which points in a conspicuous way to the fact that the Egyptians experienced intensely an inward development of consciousness. In order to build these pyramids powerful instruments must without doubt have existed. Such instruments could have only arisen through some kind of metal work and this working with metals implies a certain knowledge of the inner nature of metal . We see what was later named chemical knowledge arising in a primitive form with the Egyptians, in other words, we see how men began to make their inner nature strongly active and how they did not yet know that this inner nature was there. How mankind became aware of this inner nature and its strength can best be recognized by us when we examine from a definite point of view the highly developed Egyptian art of healing. It is quite different from our own medical science. For the illnesses existing in Egypt there were specialists, eye specialists in particular. The healers there made use of the so called Temple sleep. The sick were brought to the Temple and put into a kind of sleep during which they entered a sort of dream condition. What they then remembered was studied in its pictorial characteristics by priests who were versed in such things. These priests found out what taught them pathology through the inner dramatic course of the dreams, through the character of the pictures, whether they were dark on light or dark following light and so on. From another side they discovered indications for remedies in the particular configuration of the dreams. Through observation of what men experienced inwardly and what in dream pictures presented itself to the inner sight, the inward bodily condition of human beings was studied in Egypt. We see this occurring parallel with what was developing in Chaldea. There men lived more in an external outlook. They invented instruments, their wonderful water clocks for instance evolved from the pictorial character of their souls. They were so immersed in the pictorial element that they looked upon time as transmutable pictures. This picture making element was like an outward one in which they lived. With the Egyptian this element was grasped inwardly, it was so taken that they studied it in dream form. We see here an epoch when men did not feel themselves merely as members of the universe but in which they raised themselves out of the world and individualized themselves in these two ways in the Chaldean and the Egyptian. And we see an evolution in the arising of the pictorial observation of instinctive imagination. In a twofold way this meets us, the one in Chaldea, the other in Egypt. And in the beginning of the building of the pyramid, which in its measurements and geometric relations rests on a perception of proportions in the development of man, on the development of inner forces and on the experiencing of these forces, we see a third epoch of culture in which instinctive imagination gives a definite tint to the evolution of man. And we see how in this time the social conditions became the natural result of what arose as soul conditions. If we study the social conditions of primeval India we will find that men lived in peace together. We see in primaeval Persia how a warlike element existed, since there it was that men took up the fight with Nature, and we see how this warlike instinct went over into their imagination. And since they were possessed inwardly, since this instinctive inward possession of men in relation to themselves can only be what is emotional and of the will, those impulses for power showed themselves in the grotesque and great pyramids which are resting places for the dead and at the same time serve as testimonies of the outer power of those who ruled. We see how consciousness of power wells up but also how other folk mix with them bringing new blood into what existed as imaginative, instinctive, in the social conditions also. We see how such stock come more from out of central Asia and mix with the others. What they bring belongs to what is a feeling of 'themselves-now-men,' distinct from their environment. In Egypt there arose in a definite period what made the Egyptian realize himself as a godlike human being: he felt his self-consciousness so strongly that he looked upon all other people as barbarians and as human only those people who could live in inner pictures. One can see thus arising an intensified value of self-consciousness which runs parallel with an event belonging to this spiritual condition. If we study the laws of Hammurabi we find that the horse is not yet included among the domesticated animals. It came into civilized life, however, very soon after. Hammurabi speaks of the ass and the ox and soon after his time the horse is named in documents the 'mountain ass.' It was so called because it was brought over from the mountainous East. Races that had penetrated into Chaldea brought the horse with them and with this a war-like element appeared. We see the war-like element, born in olden times, developed further when the horse is tamed and added to the other tamed animals. This also is connected with a certain condition of the soul. One can say that up to this period man had not mounted a horse and strengthened his individuality to a certain extent through fettering the horse to his own movement. The point of development in which he now was awake expressed itself as the pictorial perception of the Chaldean and as the inner dreamlike life of the Egyptian. In this way the external relations of human evolution are intimately connected with the metamorphosis of the soul in the succeeding epochs: on one side the building of the pyramids, on the other the taming of the horse. Regarded externally they express the third epoch of culture, the Chaldean-Egyptian; and these are intimately connected with the arising of the instinctive-imaginative life. The highly developed civilisation of Egypt at the period in which the pyramids were built expressed itself in a dreamlike imagination. It came to a close relatively early. We see the first dawn at the beginning of the third millennium. After it had begun to decline its soul mood lived on in Asia, progressing through Western Asia, Asia Minor and over to the European continent. It is clearly perceptible in what comes over from Asia Minor from the older Greek civilization and is still perceptible in the Homeric poems and in their outlook on the world. But in the approach to these Homeric poems we come upon a radical transformation. What lies at their base as a world outlook shows imaginative ideas throughout and also the perception of man which is pictorial. In order to understand Homer's own peculiar method, one must see plastically with the inner eye of the soul when, apart from the fact that he speaks in pictures that can be seen outwardly of an Achilles or a Hector, he points out the pictorial element, as for example, 'the quick footed Achilles, Hector the hero with the waving crest.' In the whole nature of Homer we see something that is Chaldean. This becomes different as the Greek civilisation develops which we find with Aeschylus and Sophocles and in the Greek sculpture. We can distinguish this from what is older because we realise how strong was the impulse in Greece to understand man in his own actual human nature. If we look at the Chaldeans we see how the plastic perception appeared there in images and we see it especially in one of those races which were near to the Chaldeans locally, the Sumerians. We see how this race tends like the Egyptian towards the outward aspect of humanity. We find among the Greeks in drama and also where drama is led over into the domain of sculpture, how man is to be understood in his outward aspect. This was strongly felt by the man of the third epoch in his expression of deep, instinctive forces. This happened in Egypt during the building of the pyramids when, in their structure, men allowed their forces to grow into gigantic proportions; and in certain races of Asia who lived in an especially warlike way and placed themselves on horseback and felt themselves one with the horse. The Greek then proceeded to say: 'I do not require external means, all human forces lie within my skin.' And he fashioned plastically those forms of men, perfect in themselves, which take everything into themselves which a previous epoch had to seek through an external embodiment. This entire immersion of oneself, this entire living in what is human and this seeking for the sublime in man, this we find expressed in the Greek spirit. And we meet it later in another form in Rome if we call to mind the passing through the Forum of the Emperor or some other figures in the Roman toga. We can see even to-day how in a much more abstract way than in Greece there was this fashioning of men with the highest forces felt within their bodies. In the sixth pre-Christian century a new epoch begins; the Homeric age being still earlier. This age which now begins develops especially strong and powerful in Greece where it increases in splendour for about four centuries and then meets with a downfall. Then Christianity arises. When the Greek had his Zeus statue before him he still felt something fully living there, but when the Roman regarded his statues he saw fundamentally only an abstract idea. This abstraction be came more and more pronounced and even in the fourth post-Christian century when the Senators entered the Roman Senate Hall each one threw a grain of incense into the glowing flame which burned in front of the statue of Victory, before he took his seat as Senator. We see how that which was felt in Greece as the fulness of life in the statues of Zeus, Athene and Apollo is still felt in the statue though in a merely abstract thought form, which was however real. There was still something like the magic weaving of divine forces themselves in the Zeus and Athene statues. We then see how the Christian Emperor Constantine had this statue removed out of the Senate Hall because he thought it had lost all meaning in the sight of Christianity. And we see how Julian the Apostate once again absorbs himself in the fully human view of the fourth epoch, bringing back again the statue of Victory to the Senate Hall; how he causes the ancient ceremonies to be enacted again by the Senators but how he can no more renew the old and how he succumbs as a consequence. For the arrow which struck him down was the arrow of a murderer hired by his enemies. And out of all this the epoch develops which I shall have to characterize further, the epoch in which men occupy themselves with inner spirituality, with intellectuality, with the power of understanding. This develops in its own special way through the Middle Ages where the intellect was thought about as we find it in Scholasticism where men fought over Nominalism and Realism. In the 15th century a quite different spirit leads over to the age of Natural Science. In the beginning this spirit was specially strongly developed in Galileo and Copernicus who brought about the great progress in human consciousness which might be called 'interiorization' as compared with Greek consciousness. It may be so called in spite of having developed during the 18th century into that materialism which in the 19th century revealed so much with regard to external nature. To-day we stand at a great turning point. I do not want to bring forward epoch fantasies like those of Spengler but I wish to say something different. In the beginning of the Egyptian age we see the first stage of human understanding arising, how the age of the pyramids began and how this stage was announced through other symptoms. We see how the next stage begins in the eighth pre-Christian century, how it develops in Greece and in Rome in the soul mood which understands 'man as man,' how this age comes to an end and the 'interiorization' of the intellect begins in the fifteenth century. Thus we look back upon three great turning points: the point where the Egyptian-Chaldean epoch begins, we see how the Greek-Latin period begins and we see how that age arose which inaugurated Natural Science. In this last something again is introduced as was the case with the pyramids, something representing the special penetration of human evolution with what is new. The Romans could not uphold what was to the Greeks full of life; they could only carry out that abstraction and intellectuality which died in the lifeless Latin language. We must take heed of all this to-day because we have more consciousness than the Greeks. And from out of our consciousness we must take heed that we prevent from within that destruction which came upon Greece and which stands as a fearful example before us. We must learn from history in such a way that it will not happen to us as it has happened to men who were weak because they depended upon what was outward. We must conquer what could not be conquered in earlier ages. And when it is said that one must learn from history, we must do this in such a way that we steel ourselves and become attentive to what ancient times can teach us so that we not only learn to avoid those mistakes made by individuals but also what should be named the necessary omissions in human evolution. What threatens to come upon humanity today as it happened in the past must be overcome. We have got to transcend a great crisis. And we can only understand the nature of this present crisis if we understand it in the light of a deep comprehension of human evolution. Together with this we will understand how a spiritual Science arises from out of Natural Science. This can only be understood through being able to grasp it from out of the entire spirit of human evolution.

Natural Science and the Historical Development of Humanity

Natural Science and the Historical Development of Humanity II

https://rsarchive.org/Lectures/GA325/English/UNK1924/19210522p01.html

Stuttgart

22 May 1921

GA325-4

My dear friends! You have come together this Christmas, some of you from distant places, to work in the Goetheanum on some matters in the field of spiritual science. At the outset of our considerations I would like to extend to you — especially the friends who have come from afar — our heartiest Christmas greetings. What I myself, occupied as I am with the most manifold tasks, will be able to offer you at this particular time can only be indications in one or another direction. Such indications as will be offered in my lectures, and in those of others, will, we hope, result in a harmony of feeling and thinking among those gathered together here in the Goetheanum. It is also my hope that those friends who are associated with the Goetheanum and more or less permanently residing here will warmly welcome those who have come from elsewhere. Through our working, thinking and feeling together, there will develop what must be the very soul of all endeavors at the Goetheanum; namely, our perceiving and working out of the spiritual life and essence of the world. If this ideal increasingly becomes a reality, if the efforts of individuals interested in the anthroposophical world conception flow together in true social cooperation, in mutual give and take, then there will emerge what is intended to emerge at the Goetheanum. In this spirit, I extend the heartiest welcome to those friends who have come here from afar as well as to those residing more permanently in Dornach. The indication that I shall try to give in this lecture course will not at first sight appear to be related to the thought and feeling of Christmas, yet inwardly, I believe, they are so related. In all that is to be achieved at the Goetheanum, we are striving toward the birth of something new, toward knowledge of the spirit, toward a feeling consecrated to the spirit, toward a will sustained by the spirit. This is in a sense the birth of a super-sensible spiritual element and, in a very real way, symbolizes the Christmas thought, the birth of that spiritual Being who produced a renewal of all human evolution upon earth. Therefore, our present studies are, after all, imbued with the character of a Christmas study. Our aim in these lectures is to establish the moment in history when the scientific mode of thinking entered mankind's development. This does not conflict with what I have just said. If you remember what I described many years ago in my book Mysticism at the Dawn of the Modern Age , 1 Rudolf Steiner, Mysticism at the Dawn of the Modern Age (Blauvelt, NY: Steinerbooks, 1960) (formerly published as Eleven European Mystics ). you will perceive my conviction that beneath the external trappings of scientific conceptions one can see the first beginnings of a new spirituality. My opinion, based on objective study, is that the scientific path taken by modern humanity was, if rightly understood, not erroneous but entirely proper. Moreover, if regarded in the right way, it bears within itself the seed of a new perception and a new spiritual activity of will. It is from this point of view that I would like to give these lectures. They will not aim at any kind of opposition to science. The aim and intent is instead to discover the seeds of spiritual life in the highly productive modern methods of scientific research. On many occasions I have pointed this out in various way. In lectures given at various times on various areas of natural scientific thinking, 2 These include the three natural scientific courses held in Stuttgart: First First Scientific Lecture Course: Light Course (Forest Row, England: Steiner Schools Fellowship, 1977); Second Scientific Lecture Course: Warmth Course (Spring Valley, NY: Mercury Press, 1981); and Das Verhältnis der verschiedenen naturwissenschaftlichen Gebiete sur Astronomie . (Dornach, Switzerland: Rudolf Steiner Verlag). The relationship between natural science and spiritual science is dealt with in The Boundaries of Natural Science (Spring Valley, NY, Anthroposophic Press, 1983). I have given details of the path that I want to characterize in broader outline during the present lectures. If we want to acquaint ourselves with the real meaning of scientific research in recent times and the mode of thinking that can and does underlie it, we must go back several centuries into the past. The essence of scientific thinking is easily misunderstood, if we look only at the immediate present. The actual nature of scientific research cannot be understood unless its development is traced through several centuries. We must go back to a point in time that I have often described as very significant in modern evolution; namely, the fourteenth and fifteenth centuries. At that time, an altogether different form of thinking, which was still active through the Middle Ages, was supplanted by the dawn of the present-day mode of thought. As we look back into this dawn of the modern age, in which many memories of the past were still alive, we encounter a man in whom we can see, as it were, the whole transition from an earlier to a later form of thinking. He is Cardinal Nicholas Cusanus, 3 Nicholas Cusanus (Nicholas of Cusa), 1401–1464. Lawyer, churchman, philosopher, mathematician. Ordained priest between 1436–1440, Cardinal 1448. Bishop of Brixen, 1450. cf. chapter on Cusanus in Mysticism at the Dawn of the Modern Age . (Nicholas of Cusa) a renowned churchman and one of the greatest thinkers of all time. He was born in 1401, the son of a boatman and vinegrower in the Rhine country of Western Germany, and died in 1464, a persecuted ecclesiastic. 4 Nicholas Cusanus was made Cardinal and named Bishop of Brixen in rapid succession. Though a stranger to Brixen he was named Bishop there directly by the Pope. This led to a protracted conflict with his diocese, during which the latter gathered behind the Duke of Tirol. Cusa was ambushed by the Duke, imprisoned, and forced into accepting a demeaning agreement. The Duke was excommunicated by the Pope and attacked by the Swiss Confederation. However, he was supported by German Counts and remained intransigent. Cusa died before the Emperor could resolve the conflict. The battles around him did not rob Cusa of his peace of mind, and he developed his philosophic, mathematical and theological insights, writing fifteen of his works during the time in Brixen. Though he may have understood himself quite well, Cusanus was a person who is in some respects extremely difficult for a modern student to comprehend. Cusanus received his early education in the community that has been called “The Brethren of the Common Life.” 5 Brethren of Common Life (also of Good Will ): Founded by Gerhart Groote around 1376. Brother-houses in Holland, Northern Germany, Italy and Portugal. Brought into the Catholic Church in the Fifteenth Century. Their schools taught under the strict observance of dogma. There he absorbed his earliest impressions, which were of a peculiar kind. It is clear that Nicholas already possessed a certain amount of ambition as a boy, but this was tempered by an extraordinary gift for comprehending the needs of the social life of his time. In the community of the Brethren of the Common Life, persons were gathered together who were dissatisfied with the church institutions and with the monastic and religious orders that, though within the church, were to some degree in opposition to it. In a manner of speaking, the Brethren of the Common Life were mystical revolutionaries. They wanted to attain what they regarded as their ideal purely by intensification of a life spent in peace and human brotherhood. They rejected any rulership based on power, such as was found in a most objectionable form in the official church at that time. They did not want to become estranged from the world as were members of monastic orders. They stressed physical cleanliness; they insisted that each one should faithfully and diligently perform his duty in external life and in his profession. They did not want to withdraw from the world. In a life devoted to genuine work they only wanted to withdraw from time to time into the depths of their souls. Alongside the external reality of life, which they acknowledged fully in a practical sense, they wanted to discover the depths and inwardness of religious and spiritual feeling. Theirs was a community that above all else cultivated human qualities in an atmosphere where a certain intimacy with God and contemplation of the spirit might abide. It was in this community — at Deventer in Holland — that Cusanus was educated. The majority of the members were people who, in rather narrow circles, fulfilled their duties, and sought in their quiet chambers for God and the spiritual world. Cusanus, on the other hand, was by nature disposed to be active in outer life and, through the strength of will springing from his knowledge, to involve himself in organizing social life. Thus Cusanus soon felt impelled to leave the intimacy of life in the brotherhood and enter the outer world. At first, he accomplished this by studying jurisprudence. It must be borne in mind, however, that at that time — the early Fifteenth Century — the various sciences were less specialized and had many more points of contact than was the case later on. So for a while Cusanus practiced law. His was an era, however, in which chaotic factors extended into all spheres of social life. He therefore soon wearied of his law practice and had himself ordained a priest of the Roman Catholic Church. He always put his whole heart into whatever he did, and so he now became a true priest of the Papal church. He worked in this capacity in the various clerical posts assigned to him, and he was particularly active at the Council of Basle (1431–1449). 6 Council of Basel : 1431–1449. Called by Pope Martin V on July 23, 1431, the year of his death. This was the last of four reformatory councils with the aim of ending the division in the Church. There came a new rift in the Church. There he headed a minority whose ultimate aim it was to uphold the absolute power of the Holy See. 7 In 1437. This summarizes a long process: Cusanus entered the Council 1432 with the task from the Archdiocese of Trier to defend their Archbishop, whom they had chosen against the will of the Pope. Through the treatise De Concordantia Catholica (On Catholic Unity) which he distributed among the Council and which contained an exceptional survey of the decisions of the Councils and Decrees of the Church, he offered the advice welcome by the majority that the Common Council was beyond the Pope. Thus, he immediately became an important figure in the Council. Later, the Council majority and the history writings accused Cusanus of having changed his conviction. But Cusanus' deep understanding was ignored, which was rooted in his attitude and which comes to expression in the following words: “When a decision is made unanimously, then one can believe that it came from the Holy Spirit. It lies not in men's power to meet somewhere, and although they are so different from each other, they are able to come to a harmonious decision. It is God's work.” (From J.M. Duex, Der Deutsche Cardinal Nicolaus Von Cusa , Regensburg 1874, Bd. 2, s. 262, which has translated some of the most important of the De Concordantia Catholica . Cusanus must have experienced at the Council that his description of the meaning of a Council was not taken with interest, and he must have faced a decision that is mentioned in the lecture. The majority, consisting for the most part of bishops and cardinals from the West, were striving after a more democratic form, so to speak, of church administration. The pope, they thought, should be subordinated to the councils. This led to a schism in the Council. Those who followed Cusanus moved the seat of the Council to the South; the others remained in Basle and set up an anti-pope. 8 Pope Eugene 4th was put down and Duke Amadeus of Savoy was set up as Pope Felix 5th in 1439. His resignation in 1449 caused the disbandment of the Council. Cusanus remained firm in his defense of an absolute papacy. With a little insight it is easy to imagine the feelings that impelled Cusanus to take this stand. He must have felt that whatever emerged from a majority could at best lead only to a somewhat sublimated form of the same chaos already existing in his day. What he wanted was a firm hand that would bring about law and order, though he did want firmness permeated with insight. When he was sent to Middle Europe later on, he made good this desire by upholding consolidation of the Papal church. 9 From 1439–1448 Cusanus acted on the order of the Pope as “Hercules of the Eugenians” as an opponent called him. He went to worldly and churchly princes as well as to the “Reichstag,” and he tried to overcome the neutrality of the Germans about the split of churches, with complete success. He was therefore, as a matter of course, destined to become a cardinal of the Papal church of that time. As I said earlier, Nicholas probably understood himself quite well, but a latter-day observer finds him hard to understand. This becomes particularly evident when we see this defender of absolute papal power traveling from place to place and — if the words he then spoke are taken at face value — fanatically upholding the papistical Christianity of the West against the impending danger of a Turkish invasion. 10 At the meetings of the princes, 1454, in Nuremberg, Regensburg, and Frankfurt after the invasion of Constantinople by the Turkish, Cusanus tried to motivate the princes to a crusade. After J. Hunnyadis' victory over the Turkish Army in front of Belgrade in 1456 Cusanus organized, at the same day he received the message, a festival of thanksgiving, and he spoke the following words: “Because the lower man can only enjoy life animal-like and physical, Satan who wants to destroy the Gospels in a fine way, intended the appearance of Muhammad who knows the Gospel and the Bible, to let him give the Gospel and Bible an animal-like, sensual meaning. In this way Satan taught Muhammad knowledge to let go forth the head of Malignity, the son of Ruin, and to be an enemy of the cross of Christ.” (From a sermon, “ Landaus Invocalo Dominum ,” partly translated by J.M. Duex A.A.O.S. 165). Further sermons against the Turks are known from October 28, and November 5 of the same year. (E. Varisteenberge, Le Cardinal Nicolas De Cues , Paris 1920, S. 231 F, and index of sermons s. 480), but this sermon seems to be available only in Latin. Cusanus himself announced his appointment as Cardinal with a short autobiographical note in which is written: Nicolas was made Cardinal secretly by Pope Eugene ( Hist. Jahrbuch der Goerrers Gesellschaft 16.S.549). On the one hand, Cusanus (who in all likelihood had already been made a cardinal by that time) spoke in flaming words against the infidels. In vehement terms he summoned Europe to unite in resistance to the Turkish threat from Asia. On the other hand, if we study a book that Cusanus probably composed 11 De Pace Fidei ( On the Peace of the Faiths ), written in September 1453. “The horrible days of Constantinople ... had caused a deep feeling of sadness in the breast of a man who once had wandered through this region, and caused him to sink into deep contemplation, and he had a vision. In this sublime state, he particularly thinks about the differences of the religions of the world, and the possibility of their harmony. This harmony is, in his opinion, a basic condition for religious peace.” (Introduction to De Pace Fidei : Nach Duex A.A.O.S. 405). in the very midst of his inflammatory campaigns against the Turks, we find something strange. In the first place, Cusanus preaches in the most rousing manner against the imminent danger posed by the Turks, inciting all good men to defend themselves against this peril and thus save European civilization. But then Cusanus sits down at his desk and writes a treatise on how Christians and Jews, pagans and Moslems — provided they are rightly understood — can be brought to peaceful cooperation, to the worship and recognition of the one universal God; how in Christians, Jews, Moslems and heathens there dwells a common element that need only be discovered to create peace among mankind. Thus the most conciliatory sentiments in regard to religions and denominations flow from this man's quiet private chamber, while he publicly calls for war in the most fanatical words. This is what makes it hard to understand a man like Nicholas Cusanus. Only real insight that age can make him comprehensible but he must be viewed in the context of the inner spiritual development of his time. No criticism is intended. We only want to see the external side of this man, with the furious activity that I have described, and then to see what was living in his soul. We simply want to place the two aspects side by side. We can best observe what took place in Cusanus's mind if we study the mood he was in while returning from a mission to Constantinople 12 Cusanus left Basel in May 1437 together with other representatives of the minority and traveled for the minority with the legation of the Pope to Constantinople to accompany the Greek Emperor and the heads of the Eastern Church to the Union Council in Ferrara. They arrived in February 1438 in Italy. on the behalf of the Holy See. His task was to work for the reconciliation of the Western and Eastern churches. On his return voyage, when he was on the ship and looking at the stars, there arose in him the fundamental thought, the basic feeling, incorporated in the book that he published in 1440 under the title De Docta Ignorantia (On Learned Ignorance ). 13 De Docta Ignorantia ( The Learned Ignorance ). Three books finished in February 1440. What is the mood of this book? Cardinal Cusanus had, of course, long since absorbed all the spiritual knowledge current in the Middle Ages. He was well versed also in what the medieval schools of Neo-Platonism and Neo-Aristotelianism had attained. He was also quite familiar with the way Thomas Aquinas had spoken of the spiritual worlds as though it were the most normal thing for human concepts to rise from sense perception to spirit perception. In addition to his mastery of medieval theology, he had a thorough knowledge of the mathematical conceptions accessible to men of that time. He was an exceptionally good mathematician. His soul, therefore, was filled on the one side with the desire to rise through theological concepts to the world of spirit that reveals itself to man as the divine and, on the other side, with all the inner discipline, rigor and confidence that come to a man who immerses himself in mathematics. Thus he was both a fervent and an accurate thinker. When he was crossing the sea from Constantinople to the West and looking up at the starlit sky, his twofold soul mood characterized above revolved itself in the following feeling. Thenceforth, Cusanus conceived the deity as something lying outside human knowledge. He told himself: “We can live here on earth with our knowledge, with our concepts and thoughts. By means of these we can take hold of what surrounds us in the kingdom of nature. But these concepts grow ever more lame when we direct our gaze upward to what reveals itself as the divine.” In Scholasticism, arising from quite another viewpoint, a gap had opened up between knowledge and revelation. 14 See Rudolf Steiner, The Redemption of Thinking . (Spring Valley, NY: Anthroposophic Press, 1983). This gap now became the deepest problem of Cusanus's soul, the most intimate concern of the heart. Repeatedly he sent through this course of reasoning, repeatedly he saw how thinking extends itself over everything surrounding man in nature; how it then tries to raise itself above this realm to the divinity of thoughts; and how, there, it becomes ever more tenuous until it finally completely dissipates into nothingness as it realizes that the divine lies beyond that void into which thinking has dissipated. Only if a man has developed (apart form this life in thought) sufficient fervent love to be capable of continuing further on this path that his though has traversed, only if love gains the lead over thought, then this love can attain the realm into which knowledge gained only by thinking cannot reach. It therefore became a matter of deep concern for Cusanus to designate the actual divine realm as the dimension before which human thought grows lame and human knowledge is dispersed into nothingness. This was his docta ignorantia , his learned ignorance. Nicholas Cusanus felt that when erudition, knowledge, assumes in the noblest sense a state of renouncing itself at the instant when it thinks to attain the spirit, then it achieves its highest form, it becomes docta ignorantia . It was in this mood that Cusanus published his De Docta Ignorantia in 1440. Let us leave Cusanus for the moment, and look into the lonely cell of a medieval mystic who preceded Cusanus. To the extent that this man has significance for spiritual science, I described him in my book on mysticism. He is Meister Eckhart, 15 Meister Eckhart: Hochheim by Gotha about 1260–before 1328, Cologne. Dominican, schoolmaster, German mystic. Preached in leading posts in orders and churches; taught in Paris, Strasbourg, Cologne. Main work: Opus Tripartius . Based on Scholasticism and writings of Dionysius the Areopagite. Copies of his sermons partly went around without his control. Meister Eckhart died, accused as heretic, during the trial. See chapter, “Meister Eckhart,” in Rudolf Steiner's Mysticism at the Dawn of the Modern Age . a man who was declared a heretic by the official church. There are many ways to study the writings of Meister Eckhart and one can delight in the fervor of his mysticism. It is perhaps most profoundly touching if, through repeated study, the reader comes upon a fundamental mood of Eckhart's soul. I would like to describe it as follows. Though living earlier than Cusanus, Meister Eckhart too was imbued through and through with what medieval Christian theology sought as an ascent to the divine, to the spiritual world. When we study Meister Eckhart's writings, we can recognize Thomistic shades of thought in many of his lines. But each time Meister Eckhart's soul tries to rise from theological thinking to the actual spiritual world (with which it feels united,) it ends By saying to itself that with all this thinking and theology it cannot penetrate to its innermost essence, to the divine inner spark. It tells itself: This thinking, this theology, these ideas, give me fragments of something here, there, everywhere. But none of these are anything like the spiritual divine spark in my own inner being. Therefore, I am excluded from all thoughts, feelings, and memories that fill my soul, from all knowledge of the world that I can absorb up to the highest level. I am excluded from it all, even though I am seeking the deepest nature of my own being. I am in nothingness when I seek this essence of myself. I have searched and searched. I traveled many paths, and they brought me many ideas and feelings, and on these paths I found much. I searched for my “I,” but before ever I found it, I fell into “nothingness” in this search for the “I,” although all the kingdoms of nature urged me to the search. So, in his search for the self, Meister Eckhart felt that he had fallen into nothingness. This feeling evoked in this medieval mystic words that profoundly touch the heart and soul. They can be paraphrased thus: “I submerge myself in God's nothingness, and am eternally, through nothingness, through nothing, an I; through nothing, I become an I. In all eternity, I must etch the I from the ‘nothingness’ of God.” 16 These lines cannot be made clear and simple because the German text plays at length on the words Nicht and Ich . These are powerful words. Why did this urge for “nothing,” for finding that I in nothingness, resound in the innermost chamber of this mystic's heart, when he wanted to pass from seeking the world to seeking the I? Why? If we go back into earlier times, we find that in former ages it was possible, when the soul turned its gaze inward into itself, to behold the spirit shining forth within. This was still a heritage of primeval pneumatology, of which we shall speak later on. When Thomas Aquinas, for example, peered into the soul, he found within the soul a weaving, living spiritual element. Thomas Aquinas 17 Thomas Aquinas: Castle Roccasecca in the Neopolitan region, about 1225–1274 Cloister Fossanuova. Dominican, scholar, churchman. In Cologne, student and friend of Albertus Magnus. Advocated the spiritual reality of general concepts. He directed the theological school in Rome from 1261–1267. There the studies of the Dominican; from 1268 onwards he is teaching in Naples and France. See Rudolf Steiner, The Redemption of Thinking and Riddles of Philosophy (Spring Valley, NY: Anthroposophic Press, 1973). and his predecessors sought the essential ego not in the soul itself but in the spiritual dwelling in the soul. They looked through the soul into the spirit, and in the spirit they found their God-given I. And they said, or could have said: I penetrate into my inmost soul, gaze into the spirit, and in the spirit I find the I. — In the meantime, however, in humanity's forward development toward the realm of freedom, men had lost the ability to find the spirit when they looked inward into themselves. An earlier figure such as John Scotus Erigena (810–880) would not have spoken as did Meister Eckhart. He would have said: I gaze into my being. When I have traversed all the paths that led me through the kingdoms of the outer world, then I discover the spirit in my inmost soul. Thereby, I find the “I” weaving and living in the soul. I sink myself as spirit into the Divine and discover “I.” It was, alas, human destiny that the path that was still accessible to mankind in earlier centuries was no longer open in Meister Eckhart's time. Exploring along the same avenues as John Scotus Erigena or even Thomas Aquinas, Meister Eckhart could not sink himself into God-the-Spirit, but only into the “nothingness” of the Divine, and from this “nothing” he had to take hold of the I. This shows that mankind could no longer see the spirit in inner vision. Meister Eckhart brought the I out of the naught through the deep fervor of his heart. His successor, Nicholas Cusanus, 18 Nicholas Copernicus: Thorn 1473–1543 Frauenburg. Humanist, mathematician, astronomer, physician, lawyer. No publications during his life, with the exception of a translation. Finished his work on the heliocentric planetary system around 1507. Copernicus was already on his deathbed when his De Revolutionibus Orbium Coelestium was published. He dedicated it to Pope Paul III. His friend and publisher introduced it as a purely hypothetical, special scientific method of calculation. It thus slipped past the censor, until the third edition was banned in 1616/17. Not until 1822 was it accepted by the Catholic Church, cf. Rudolf Steiner, The Spiritual Guidance of Man . (Spring Valley, NY: Anthroposophic Press, 1983). admits with complete candor: All thoughts and ideas that lead us in our exploration of the world become lame, become as nothing, when we would venture into the realm of spirit. The soul has lost the power to find the spirit realm in its inner being. So Cusanus says to himself: When I experience everything that theology can give me, I am led into this naught of human thinking. I must unite myself with what dwells in this nothingness in order to at least gain in the docta ignorantia the experience of the spirit. — Then, however, such knowledge, such perception, cannot be expressed in words. Man is rendered dumb when he has reached the point at which he can experience the spirit only through the docta ignorantia . Thus Cusanus is the man who in his own personal development experiences the end of medieval theology and is driven to the docta ignorantia . He is, however, at the same time a skillful mathematician. He has the disciplined thinking that derives from the pursuit of mathematics. But he shies away, as it were, from applying his mathematical skills to the docta ignorantia . He approaches the docta ignorantia with all kinds of mathematical symbols and formulas, but he does this timidly, diffidently. He is always conscious of the fact that these are symbols derived from mathematics. He says to himself: Mathematics is the last remnant left to me from ancient knowledge. I cannot doubt its reliability as I can doubt that of theology, because I actually experience its reliability when I apprehend mathematics with my mind. — At the same time, his disappointment with theology is so great he dares not apply his mathematical skills in the field of the docta ignorantia except in the form of symbols. This is the end of one epoch in human thinking. In his inner mood of soul, Cusanus was almost as much of a mathematician as was Descartes later on, but he dared not try to grasp with mathematics what appeared to him in the manner he described in his Docta Ignorantia He felt as though the spirit realm had withdrawn from mankind, had vanished increasingly into the distance, and was unattainable with human knowledge. Man must become ignorant in the innermost sense in order to unite himself in love with this realm of the spirit. This mood pervades Cusanus's Docta Ignorantia published in 1440. In the development of Western civilization, men had once believed that they confronted the spirit-realm in close perspective. But then, this spirit realm became more and more remote from those men who observed it, and finally it vanished. The book of 1440 was a frank admission that the ordinary human comprehension of that time could no longer reach the remote perspectives into which the spirit realm has withdrawn. Mathematics, the most reliable of the sciences, dared to approach only with symbolic formulas what was no longer beheld by the soul. It was as though this spirit realm, receding further and further in perspective, had disappeared from European civilization. But from the opposite direction, another realm was coming increasingly into view. This was the realm of the sense world, which European civilization was beginning to observe and like. In 1440, Nicholas Cusanus applied mathematical thinking and mathematical knowledge to the vanishing spirit realm only by a timid use of symbols; but now Nicholas Copernicus boldly and firmly applied them to the outer sense world. In 1440 the Docta Ignorantia appeared with the admission that even with mathematics one can no longer behold the spirit realm. We must conceive the spirit realm as so far removed from human perception that even mathematics can approach it only with halting symbols; this is what Nicholas Cusanus said in 1440. “Conceive of mathematics as so powerful and reliable that it can force the sense world into mathematical formulas that are scientifically understandable.” This is what Nicholas Copernicus said to European civilization in 1543. In 1543 Copernicus published his De Revolutionibus Orbium Coelestium (On the Revolutions of the Celestial Bodies ,) where the universe was depicted so boldly and rudely that it had to surrender itself to mathematical treatment. One century lies between the two. During this century Western science was born. Earlier, it had been in an embryonic state. Whoever wants to understand what led to the birth of Western science, must understand this century that lies between the Docta Ignorantia and the De Revolutionibus Orbium Coelestium . Even today, if we are to understand the true meaning of science, we must study the fructifications that occurred at that time in human soul life and the renunciations it had to experience. We must go back this far in time. If we want to have the right scientific attitude, we must begin there, and we must also briefly consider the embryonic state preceding Nicholas Cusanus. Only then can we really comprehend what science can accomplish for mankind and see how new spiritual life can blossom forth from it.

The Origins of Natural Science

Lecture I

https://rsarchive.org/Lectures/GA326/English/AP1985/19221224p01.html

Dornach

24 Dec 1922

GA326-1

The view of history forming the basis of these lectures may be called symptomatological What takes place in the depths of human evolution sends out waves, and these waves are the symptoms that we will try to describe and interpret. In any serious study of history, this must be the case. The processes and events occurring at any given time in the depths of evolution are so manifold and so significant that we can never do more than hint at what is going on the depths. This we do by describing the waves that are flung up. They are symptoms of what is actually taking place. I mention this because, in order to characterize the birth of the scientific form of thinking and research I described two men, Meister Eckhart and Nicholas Cusanus, in my last lecture. What can be historically observed in the soul and appearance of such men I consider to be symptoms of what goes on in the depths of general human development; this is why I give such descriptions. There are in any given case only a couple of images cast up to the surface that we can intercept by looking into one or another soul. Yet, by doing this, we can describe the basic nature of successive time periods. When I described Cusanus yesterday, my intention was to suggest how all that happened in the early fifteenth century in mankind's spiritual development, which was pressing forward to the scientific method of perception, is symptomatically revealed in his soul. Neither the knowledge that the mind can gather through the study of theology nor the precise perceptions of mathematics can lead any longer to a grasp of the spiritual world. The wealth of human knowledge, its concepts and ideas, come to a halt before that realm. The fact that one can do no more than write a “docta ignorantia” in the face of the spiritual world comes to expression in Cusanus in a remarkable way. He could go no further with the form of knowledge that, up to his time, was prevalent in human development. As I pointed out, this soul mood was already present in Meister Eckhart. He was well versed in medieval theological knowledge. With it, he attempted to look into this own soul and to find therein the way to the divine spiritual foundations. Meister Eckhart arrived at a soul mood that I illustrated with one his sentences. He said — and he made many similar statements — “I sink myself into the naught of the divine, and out of nothing become an I in eternity.” He felt himself arriving at nothingness with traditional knowledge. Out of this nothingness, after the ancient wisdom's loss of all persuasive power he had to produce out of his own soul the assurance of his own I, and he did it by this statement. Looking into this matter more closely, we see how a man like Meister Eckhart points to an older knowledge that has come down to him through the course of evolution. It is knowledge that still gave man something of which he could say: This lives in me, it is something divine in me, it is something. But now, in Meister Eckhart's own time, the most profound thinkers had been reduced to the admission: When I seek this something here or there, all knowledge of this something does not suffice to bring me certainty of my own being. I must proceed from the Something to the Nothing and then, in an act of creation, kindle to life the consciousness of self out of naught. Now, I want to place another man over against these two. This other man lived 2,000 years earlier and for his time he was as characteristic as Cusanus (who followed in Meister Eckhart's footsteps) was for the fifteenth century. This backward glance into ancient times is necessary so that we can better understand the quest for knowledge that surfaced in the Fifteenth Century from the depths of the human soul. The man whom I want to speak about today is not mentioned in any history book or historical document, for these do not go back as far as the Eighth Century B.C. Yet, we can only gain information concerning the origin of science if, through spiritual science, through purely spiritual observation, we go farther back than external historical documents can take us. The man I have in mind lived about 2,000 years prior to the present period (the starting point of which I have assigned to the first half of the fifteenth century.) This man of pre-Christian times was accepted into a so-called mystery school of Southeastern Europe. There he heard everything that the teachers of the mysteries could communicate to their pupils concerning spiritual wisdom, truths concerning the spiritual beings that lived and still live in the cosmos. But the wisdom that this man received from his teachers was already more or less traditional. It was a recollection of far older visions, a recapitulation of what wise men of a much more ancient age had beheld when they directed their clairvoyant sight into the cosmic spaces whence the motions and constellations of the stars had spoken to them. To the sages of old, the universe was not the machine, the mechanical contraption that it is for men of today when they look out into space to the wise men of ancient times. The cosmic spaces were like living beings, permeating everything with spirit and speaking to them in cosmic language. They experienced themselves within the spirit of world being. They felt how this, in which they lived and moved, spoke to them, how they could direct their questions concerning the riddles of the universe to the universe itself and how, out of the widths of space, the cosmic phenomena replied to them. This is how they experienced what we, in a weak and abstract way, call “spirit” in our language. Spirit was experienced as the element that is everywhere and can be perceived from anywhere. Men perceived things that even the Greeks no longer beheld with the eye of the soul, things that had faded into a nothingness for the Greeks. This nothingness of the Greeks, which had been filled with living content for the earliest wise men of the Post-Atlantean age, 19 Post-Atlantean Age: cf. Rudolf Steiner, An Outline Of Occult Science (Spring Valley, NY: Anthroposophic Press, 1984). was named by means of words customary for that time. Translated into our language, though weakened and abstract, those words would signify “spirit.” What later became the unknown, the hidden god, was called spirit in those ages when he was known. This is the first thing to know about those ancient times. The second thing to know is that when a man looked with his soul and spirit vision into himself, he beheld his soul. He experienced it as originating from the spirit that later on became the unknown god. The experience of the ancient sage was such that he designated the human soul with a term that would translate in our language into “spirit messenger” or simply “messenger.” If we put into a diagram what was actually seen in those earliest times, we can say: The spirit was considered the world-embracing element, apart from which there was nothing and by which everything was permeated. This spirit, which was directly perceptible in its archetypal form, was sought and found in the human soul, inasmuch as the latter recognized itself as the messenger of this spirit. Thus the soul was referred to as the “messenger.” If we put into a diagram what was actually seen in those earliest times, we can say: The spirit was considered the world-embracing element, apart from which there was nothing and by which everything was permeated. This spirit, which was directly perceptible in its archetypal form, was sought and found in the human soul, inasmuch as the latter recognized itself as the messenger of this spirit. Thus the soul was referred to as the “messenger.” A third aspect was external nature with all that today is called the world of physical matter, of bodies. I said above that apart from spirit there was nothing, because spirit was perceived by direct vision everywhere in its archetypal form. It was seen in the soul, which realized the spirit's message in its own life. But the spirit was likewise recognized in what we call nature today, the world of corporeal things. Even his bodily world was looked upon as an image of the spirit. In those ancient times, people did not have the conceptions that we have today of the physical world. Wherever they looked, at whatever thing or form of nature, they beheld an image of the spirit, because they were still capable of seeing the spirit, a fragment of nature. Inasmuch as all other phenomena of nature were images of the spirit, the body of man too was an image of the spirit. So when this ancient man looked at himself, he recognized himself as a threefold being. In the first place, the spirit lived in him as in one of its many mansions. Man knew himself as spirit. Secondly, man experienced himself within the world as a messenger of this spirit, hence as a soul being. Thirdly, man experienced his corporeality; and by means of this body he felt himself to be an image of the spirit. 20 A literal translation of the transcript would read: “As body; and as body, as an image of the spirit.” Hence, when man looked upon his own being, he perceived himself as a threefold entity of spirit, soul, and body: as spirit in his archetypal form; as soul, the messenger of god; as body, the image of the spirit. This ancient wisdom contained no contradiction between body and soul or between nature and spirit; because one knew: Spirit is in man in its archetypal form; the soul is none other than the message transmitted by spirit; the body is the image of spirit. Likewise, no contract was felt between man and surrounding nature because one bore an image of spirit in one's own body, and the same was true of every body in external nature. Hence, an inner kinship was experienced between one's own body and those in outer nature, and nature was not felt to be different from oneself. Man felt himself at one with the whole world. He could feel this because he could behold the archetype of spirit and because the cosmic expanses spoke to him. In consequence of the universe speaking to man, science simply could not exist. Just as we today cannot build a science of external nature out of what lives in our memory, ancient man could not develop one because, whether he looked into himself or outward at nature, he beheld the same image of spirit. No contrast existed between man himself and nature, and there was none between soul and body. The correspondence of soul and body was such that, in a manner of speaking, the body was only the vessel, the artistic reproduction, of the spiritual archetype, while the soul was the mediating messenger between the two. Everything as in a state of intimate union. There could be no question of comprehending anything. We grasp and comprehend what is outside our own life. Anything that we carry within ourselves is directly experienced and need not be first comprehended. Prior to Roman and Greek times, this wisdom born of direct perception still lived in the mysteries. The man I referred to above heard about his wisdom, but he realized that the teachers in his mystery school were speaking to him only out of a tradition preserved from earlier ages. He no longer heard anything original, anything gained by listening to the secrets of the cosmos. This man undertook long journeys and visited other mystery centers, but it was the same wherever he went. Already in the Eight Century B.C., only traditions of the ancient wisdom were preserved everywhere. The pupils learned them from the teachers, but the teachers could no longer see them, at least not in the vividness of ancient times. But this man whom I have in mind had an unappeasable urge for certainty and knowledge. From the communications passed on to him, he gathered that once upon a time men had indeed been able to hear the harmony of the spheres from which resounded the Logos that was identical with the spiritual archetype of all things. Now, however, it was all tradition. Just as 2,000 years later Meister Eckhart, working out the traditions of his age, withdrew into his quiet monastic cell in search of the inner power source of soul and self, and at length came to say, “I sink myself into the nothingness of God, and experience in eternity, in naught, the ‘I’,” — just so, the lonely disciple of the late mysteries said to himself: “I listen to the silent universe and fetch 21 I listen to the silent universe: cf. Rudolf Steiner, Truth-Wrought Words . (Spring Valley, NY: Anthroposophic Press, 1979). the Logos-bearing soul out of the silence. I love the Logos because the Logos brings tidings of an unknown god.” This was an ancient parallel to the admission of Meister Eckhart. Just as the latter immersed himself into the naught of the divine that Medieval theology had proclaimed to him and, out of this void, brought out the “I,” so that ancient sage listened to a dumb and silent world; for he could no longer hear what traditional wisdom taught him. The spirit-saturated soul had one drawn the ancient wisdom from the universe. This had not turned silent, but still he had a Logos-bearing soul. And he loved the Logos even though it was no longer the godhead of former ages, but only an image of the divine. In other words, already then, the spirit had vanished from the soul's sight. Just as Meister Eckhart later had to seek the “I” in nothingness, so at that time the soul had to be sought in the dispirited world. Indeed, in former times the souls had the inner firmness needed to say to themselves: In the inward perception of the spirit indwelling me, I myself am something divine. But now, for direct perception, the spirit no longer inhabited the soul. No longer did the soul experience itself as the spirit's messenger, for one must know something in order to be its messenger. Now, the soul only felt itself as the bearer of the Logos, the spirit image; though this spirit image was vivid in the soul. It expressed itself in the love for this god who thus still lived in his image in the soul. But the soul no longer felt like the messenger, only the carrier, of an image of the divine spirit. One can say that a different form of knowledge arose when man looked into his inner being. The soul declined from messenger to bearer. Soul: Bearer Body: Force Since the living spirit had been lost to human perception, the body no longer appeared as the image of spirit. To recognize it as such an image, one would have had to perceive the archetype. Therefore, for this later age, the body changed into something that I would like to call “force.” The concept of force emerged. The body was pictured as a complex of forces, no longer as a reproduction, an image, that bore within itself the essence of what it reproduced. The human body became a force which no longer bore the substance of the source from which it originated. Not only the human body, but in all of nature, too, forces had to be pictured everywhere. Whereas formerly, nature in all its aspects had been an image of spirit, now it had become forces flowing out of the spirit. This, however, implied that nature began to be something more or less foreign to man. One could say that the soul had lost something since it no longer contained direct spirit awareness. Speaking crudely, I would have to say that the soul had inwardly become more tenuous, while the body, the external corporeal world, had gained in robustness. Earlier, as an image, it still possessed some resemblance to the spirit. Now it became permeated by the element of force. The complex of forces is more robust than the image in which the spiritual element is still recognizable. Hence, again speaking crudely, the corporeal world became denser while the soul became more tenuous. This is what arose in the consciousness of the men among whom lived the ancient wise man mentioned above, who listened to the silent universe and from its silence, derived the awareness that at least his soul was a Logos-bearer. Now, a contrast that had not existed before arose between the soul, grown more tenuous, and the increased density of the corporeal world. Earlier, the unity of spirit had been perceived in all things. Now, there arose the contrast between body and soul, man and nature. Now appeared a chasm between body and soul that had not been present at all prior to the time of this old sage. Man now felt himself divided as well from nature, something that also had not been the case in the ancient times. This contrast is the central trait of all thinking in the span of time between the old sage I have mentioned and Nicholas Cusanus. Men now struggle to comprehend the connection between, on one hand, the soul, that lacks spirit reality, and on the other hand, the body that has become dense, has turned into force, into a complex of forces. And men struggle to feel and experience the relationship between man and nature. But everywhere, nature is force. In that time, no conception at all existed as yet of what we call today “the laws of nature.” People did not think in terms of natural laws; everywhere and in everything they felt the forces of nature. When a man looked into his own being, he did not experience a soul that — as was the case later one — bore within itself a dim will, an almost equally dim feeling, and an abstract thinking. Instead, he experienced the soul as the bearer of the living Logos, something that was not abstract and dead, but a divine living image of God. We must be able to picture this contrast, which remained acute until the eleventh or Twelfth century. It was quite different from the contrasts that we feel today. If we cannot vividly grasp this contrast, which was experienced by everyone in that earlier epoch, we make the same mistake as all those historians of philosophy who regard the old Greek thinker Democritus 22 Democritus: c. 460–360 B.C. From his numerous writings about philosophy, mathematics, physics, medicine, psychology, and technology, only some fragments and an index remain. The remark mentioned is a report from Aristotle, Metaphysics 1:4: “That is why they (Leucippus and Democritus) say that the non-existent exists just as much as the existent, just as emptiness is just as good as fullness, and they posit these as material causes.” of the fifth century B.C. as an atomist in the modern sense, because he spoke of “atoms.” The words suggest a resemblance, but no real resemblance exists. There is great difference between modern-day atomists and Democritus. His utterances were based on the awareness of the contrast described above between man and nature, soul and body. His atoms were complexes of force and as such were contrasted with space, something a modern atomist cannot do in that manner. How could the modern atomist say what Democritus said: “Existence is not more than nothingness, fullness is not more than emptiness?” It implies that Democritus assumed empty space to possess an affinity with atom-filled space. This has meaning only within a consciousness that as yet has no idea of the modern concept of body. Therefore, it cannot speak of the atoms of a body, but only of centers of force, which, in that case, have an inner relationship to what surrounds man externally. Today's atomist cannot equate emptiness with fullness. If Democritus had viewed emptiness the way we do today, he could not have equated it with the state of being. He could do so because in this emptiness he sought the soul that was the bearer of the Logos. And though he conceived his Logos in a form of necessity, it was the Greek form of necessity, not our modern physical necessity. If we are to comprehend what goes on today, we must be able to look in the right way into the nuances of ideas and feelings of former times. There came the time, described in the last lecture, of Meister Eckhart and Nicholas Cusanus, when even awareness of the Logos indwelling the soul was lost. The ancient sage, in listening to the universe, only had to mourn the silence, but Meister Eckhart and Cusanus found the naught and had to seek the I out of nothingness. Only now, at this point, does the modern era of thinking begin. The soul now no longer contains the living Logos. Instead, when it looks into itself, it finds ideas and concepts, which finally lead to abstractions. The soul has become even more tenuous. A third phase begins. Once upon a time, in the first phase, the soul experienced the spirit's archetype within itself. It saw itself as the messenger of spirit. In the second phase, the soul inwardly experienced the living image of God in the Logos, it became the bearer of the Logos. Now, in the third phase, the soul becomes, as it were, a vessel for ideas and concepts. These may have the certainty of mathematics, but they are only ideas and concepts. The soul experiences itself at its most tenuous, if I may put it so. Again the corporeal world increases in robustness. This is the third way in which man experiences himself. He cannot as yet give up his soul element completely, but he experiences it as the vessel for the realm of ideas. He experiences his body, on the other hand, not only as a force but as a spatial body. Soul: Realm of Ideas Body: Spatial Corporeality The body has become still more robust. Man now denies the spirit altogether. Here we come to the “body” that Hobbes, Bacon, 23 Francis Bacon: (also Francis Bacon of Verulam), London 1561–1626 Highgate. Lawyer, doctor, politician, diplomat, essayist, philosopher and humanist. The leading English government liberal, successful during 1603–1621. In these years his main work was developed. The philosophy of his age he found stuck in hopeless experiments to solve insolvable problems with Aristotelian logic. The only source of sure knowledge and abilities for him was natural science. He saw a renewal of the spiritual and economic life in this science. Principal works: Novum Organum (an inductive logic contradicting that of Aristotle (the old Organum ); De Dignitate et Augmentis Scientiarum; a Critical Encyclopedia of all Science; Sylva Sylvarum: Preliminary Announcement of Procedure and Method (this remained in preparation). His literary success was astonishing, and it greatly furthered the materialistic world view. cf. Riddles of Philosophy . and Locke spoke of. Here, we meet “body” at its densest. The soul no longer feels a kinship to it, only an abstract connection that gets worse in the course of time. In place of the earlier concrete contrast of soul and body, man and nature, another contrast arises that leads further and further into abstraction. The soul that formerly appeared to itself as something concrete — because it experienced in itself the Logos-image of the divine — gradually transforms itself to a mere vessel of ideas. Whereas before, in the ancient spiritual age, it had felt akin to everything, it now sees itself as subject and regards everything else as object, feeling no further kinship with anything. The earlier contrast of soul and body, man and nature, increasingly became the merely theoretical epistemological contrast between the subject that is within a person and the object without. Nature changed into the object of knowledge. It is not surprising that out of its own needs knowledge henceforth strove for the “purely objective.” But what is this purely objective? It is no longer what nature was to the Greeks. The objective is external corporeality in which no spirit is any longer perceived. It is nature devoid of spirit, to be comprehended from without by the subject. Precisely because man had lost the connection with nature, he now sought a science of nature from outside. Here, we have once again reached the point where I concluded yesterday. Cusanus looked upon what should have been the divine world to him and declared that man with his knowledge must stop short before it and, if he must write about the divine world, he must write a docta ignorantia . And only faintly, in symbols taken from mathematics, did Cusanus want to retain something of what appeared thus to him as the spiritual realms. About a hundred years after the Docta Ignorantia appeared in 1440, the De Revolutionibus Orbium Coelestium appeared in 1543. one century later, Copernicus, with his mathematical mind, took hold of the other side, the external side of what Cusanus could not fully grasp, not even symbolically, with mathematics. Today, we see how in fact the application of this mathematical mind to nature becomes possible the moment that nature vanishes from man's immediate experience. This can be traced even in the history of language since “Nature” refers to something that is related to “being born,” whereas what we consider as nature today is only the corporeal world in which everything is dead. I mean that it is dead for us since, of course, nature contains life and spirit. But it has become lifeless for us and the most certain of conceptual systems, namely, the mathematical, is regarded as the best way to grasp it. Thus we have before us a development that proceeds with inward regularity. In the first epoch, man beheld god and world, but god in the world and the world in god: the one-ness, unity. In the second epoch, man in fact beheld soul and body, man and nature; the soul as bearer of the living Logos, the bearer of what is not born and does not die; nature as what is born and dies. In the third phase man has ascended to the abstract contrast of subject (himself) and object ( the external world.) The object is something so robust that man no longer even attempts to throw light on it with concepts. It is experienced as something alien to man, something that is examined from outside with mathematics although mathematics cannot penetrate into the inner essence. For this reason, Cusanus applied mathematics only symbolically, and timidly at that. The striving to develop science must therefore be pictured as emerging from earlier faculties of mankind. A time had to come when this science would appear. It had to develop the way it did. We can follow this if we focus clearly on the three phases of development that I have just described. We see how the first phase extends to the Eighth Century B.C. to the ancient sage of Southern Europe whom I have described today. The second extends from him to Nicholas Cusanus. We find ourselves in the third phase now. The first is pneumatological, directed to the spirit in its primeval form. The second is mystical, taking the world in the broadest sense possible. The third is mathematical. Considering the significant characteristics, therefore, we trace the first phase — ancient pneumatology — as far as the ancient Southern wise man. Magical mysticism extends from there to Meister Eckhart and Nicholas Cusanus. The age of mathematizing natural science proceeds from Cusanus into our own time and continues further. More on this tomorrow.

The Origins of Natural Science

Lecture II

https://rsarchive.org/Lectures/GA326/English/AP1985/19221225p01.html

Dornach

25 Dec 1922

GA326-2

In the last two lectures I tried to indicate the point in time when the scientific outlook and manner of thinking, such as we know it today, arose in the course of time. It was pointed out yesterday that the whole character of this scientific thinking, emerging at the beginning most clearly in Copernicus’ conception of astronomy, depends on the way in which mathematical thinking was gradually related to the reality of the external world. The development of science in modern times has been greatly affected by a change — one might almost say a revolutionary change — in human perception in regard to mathematical thinking itself. We are much inclined nowadays to ascribe permanent and absolute validity to our own manner of thinking. Nobody notices how much matters have changed. We take a certain position today in regard to mathematics and to the relationship of mathematics to reality. We assume that this is the way it has to be and that this is the correct relationship. There are debates about it from time to time, but within certain limits this is regarded as the true relationship. We forget that in a none too distant past mankind felt differently concerning mathematics. We need only recall what happened soon after the point in time that I characterized as the most important in modern spiritual life, the point when Nicholas Cusanus presented his dissertation to the world. Shortly after this, not only did Copernicus try to explain the movements of the solar system with mathematically oriented thinking of the kind to which we are accustomed today, but philosophers such as Descartes and Spinoza 24 Spinoza, Benedictus: Amsterdam 1632–1677. The Hague. Philosopher, mathematician, had Humanistic and Talmudistic training. By vocation, optician and politician. His main work Ethics with the characteristic full title Ethica Ordine Geometrica Demonstrata ( Ethic Represented by Geometric Method ) could only be published by his friends after his death. See Mysticism at the Dawn of the Modern Age and Riddles of Philosophy . began to apply this mathematical thought to the whole physical and spiritual universe. Even in such a book as his Ethics , the philosopher Spinoza placed great value on presenting his philosophical principles and postulates, if not in mathematical formulae — for actual calculations play no special part — yet in such a manner that the whole form of drawing conclusions, of deducing the later rules from earlier ones, is based on the mathematical pattern. By and by it appeared self-evident to the men of that time that in mathematics they had the right model for the attainment of inward certainty. Hence they felt that if they could express the world in thoughts arranged in the same clear-cut architectural order as in a mathematical or geometrical system, they would thereby achieve something that would have to correspond to reality. If the character of scientific thinking is to be correctly understood, it must be through the special way in which man relates to mathematics and mathematics relates to reality. Mathematics had gradually become what I would term a self-sufficient inward capacity for thinking. What do I mean by that? The mathematics existing in the age of Descartes 25 René Descartes: Lat., Renatus Cartenius, Le Haye (Tourraine) 1598–1650 Stockholm. Mathematician, physicist, philosopher. Educated by the Jesuits in La Fleche, he first became a soldier and was part of some campaigns but turned away from outer life to enter into the loneliness of a striver for knowledge, living first in Paris and then for a long time in Holland. He died in Stockholm, having been called there by Queen Christine. For him, doubt of tradition, but also of all sense perception, was the starting point of his philosophy and he found in self-consciousness the security of all being (“ Cogito ergo Sum ”). He developed the method of analytical geometry and gave an explanation of the rainbow. Main works: Essays , 1637, in it “ Discours de la Methode and Dioptiric ,” “ Meditationes de Prima Philosophia ,” 1641; “ Passions de L'Ame ,” 1650. See Riddles of Philosophy . and Copernicus can certainly be described more or less in the same terms as apply today. Take a modern mathematician, for example, who teaches geometry, and who uses his analytical formulas and geometrical concepts in order to comprehend some physical process. As a geometrician, this mathematician starts from the concepts of Euclidean geometry, the three-dimensional space (or merely dimensional space, if he thinks of non-Euclidean geometry.) 26 Non-Euclidian geometry is a prime example of “the self-contained inner ability to think.” C. Friedrich Gauss (1777–1855) discovered first that one can think more than only a geometric system. Because nobody understood this, he decided not to publish his results and to withdraw from the fruitless quarrel. Independently of Gauss in 1828 N.I. Lobatschewskij and in 1829 J. Boljai first published their solutions to the same problem. Rudolf Steiner often spoke about the meaning of this achievement, as in Wege und Ziele des geistigen Menschen in the lecture “ Der Heutige Stand der Philosophie und Wissenschaft ,” (Dornach, Switzerland: Rudolf Steiner Verlag, 1973; GA Bibl. Nr. 125). See also: Georg Unger, Physic am Scheidewege (Dornach: 1948), pages 19–28, and Vom Bielden Physikalischer Begriffe , Vol. 3 (Stuttgart: 1967), pages 31–32 and 193–194. In three-dimensional space he distinguishes three mutually perpendicular directions that are otherwise identical. Space, I would say, is a self-sufficient form that is simply placed before one's consciousness in the manner described above without questions being raised such as: Where does this form come from? Or, Where do we get our whole geometrical system? In view of the increasing superficiality of psychological thinking, it was only natural that man could no longer penetrate to those inner depths of soul where geometrical thought has its base. Man takes his ordinary consciousness for granted and fills this consciousness with mathematics that has been thought-out but not experienced. As an example of what is thought-out but not experienced, let us consider the three perpendicular dimensions of Euclidean space. Man would have never thought of these if he had not experienced a threefold orientation within himself. One orientation that man experiences in himself is from front to back. We need only recall how, from the external modern anatomical and physiological point of view, the intake and excretion of food, as well as other processes in the human organism, take place from front to back. The orientation of these specific processes differs from the one that prevails when, for example, I do something with my right arm and make a corresponding move with my left arm. Here, the processes are oriented left and right. Finally, in regard to the last orientation, man grows into it during earthly life. In the beginning he crawls on all fours and only gradually, stands upright, so that this last orientation flows within him from above downward and up from below. As matters stand today, these three orientations in man are regarded very superficially. These processes — front to back, right to left or left to right, and above to below — are not inwardly experienced so much as viewed from outside. If it were possible to go back into earlier ages with true psychological insight, one would perceive that these three orientations were inward experiences for the men of that time. Today our thoughts and feelings are still halfway acknowledged as inward experiences, but he man of a bygone age had a real inner experience, for example, of the front-to-back orientation. He had not yet lost awareness of the decrease in intensity of taste sensations from front to back in the oral cavity. The qualitative experience that taste was strong on the tip of the tongue, then grew fainter and fainter as it receded from front to back, until it disappeared entirely, was once a real and concrete experience. The orientation from front to back was felt in such qualitative experiences. Our inner life is no longer as intense as it once was. Therefore, today, we no longer have experiences such as this. Likewise man today no longer has a vivid feeling for the alignment of his axis of vision in order to focus on a given point by shifting the right axis over the left. Nor does he have a full concrete awareness of what happens when, in the orientation of right-left, he relates his right arm and hand to the left arm and hand. Even less does he have a feeling that would enable him to say: The thought illuminates my head and, moving in the direction from above to below, it strikes into my heart. Such a feeling, such an experience, has been lost to man along with the loss of all inwardness of world experience. But it did once exist. Man did once experience the three perpendicular orientation of space within himself. And these three spatial orientations — right-left, front-back, and above-below — are the basis of the three-dimensional framework of space, which is only the abstraction of the immediate inner experience described above. So what can we say when we look back at the geometry of earlier times? We can put it like this: It was obvious to a man in those ages that merely because of his being human the geometrical elements revealed themselves in his own life. By extending his own above-below, right-left, and front-back orientations, he grasped the world out of his own being. Try to sense the tremendous difference between this mathematical feeling bound to human experience, and the bare, bleak mathematical space layout of analytical geometry, which establishes a point somewhere in abstract space, draws three coordinating axes at right angles to each other and thus isolates this thought-out space scheme from all living experience. But man has in fact torn this thought-out spatial diagram out of his own inner life. So, if we are to understand the origin of the later mathematical way of thinking that was taken over by science, if we are to correctly comprehend its self-sufficient presentation of structures, we must trace it back to the self-experienced mathematics of a bygone age. Mathematics in former times was something completely different. What was once present in a sort of dream-like experience of three-dimensionality and then became abstracted, exists today completely in the unconscious. As a matter of fact, man even now produced mathematics from his own three-dimensionality. But the way in which he derives this outline of space from his experiences of inward orientation is completely unconscious. None of this rises into consciousness except the finished spatial diagram. The same is true of all completed mathematical structures. They have all been severed from their roots. I chose the example of the space scheme, but I could just as well mention any other mathematical category taken from algebra or arithmetic. They are nothing but schemata drawn from immediate human experience and raised into abstraction. Going back a few centuries, perhaps to the fourteenth century, and observing how people conceived of things mathematical, we find that in regard to numbers they still had an echo of inward feelings. In an age in which numbers had already become an abstract ads they are today, people would have been unable to find the names for numbers. The words designating numbers are often wonderfully characteristic. Just think of the word “two.” (zwei) It clearly expresses a real process, as when we say entzweien , “to cleave in twain.” Even more, it is related to zweifeln , “to doubt.” It is not mere imitation of an external process when the number two, zwei , is described by the word Entzweien , which indicates the disuniting, the splitting, of something formerly a whole. It is in fact something that is inwardly experienced and only then made into a scheme. It is brought up from within, just as the abstract three-dimensional space-scheme is drawn up from inside the mind. We arrive back at an age of rich spiritual vitality that still existed in the first centuries of Christianity, as can be demonstrated by the fact that mathematics, mathesis, and mysticism were considered to be almost one and the same. Mysticism, mathesis, and mathematics are one, though only in a certain connection. For a mystic of the first Christian centuries, mysticism was something that one experienced more inwardly in the soul. Mathematics was the mysticism that one experienced more outwardly with the body; for example, geometry with the body's orientations to front-and-back, right-and-left, and up-and-down. One could say that actual mysticism was soul mysticism and that mathematics, mathesis, was mysticism of the corporeality. Hence, proper mysticism was inwardly experienced in what is generally understood by this term; whereas mathesis, the other mysticism, as experienced by means of an inner experience of the body, as yet not lost. As a matter of fact, in regard to mathematics and the mathematical method Descartes and Spinoza still had completely different feelings from what we have today. Immerse yourself in these thinkers, not superficially as in the practice today when one always wants to discover in the thinkers of old the modern concepts that have been drilled into our heads, but unselfishly, putting yourself mentally in their place. You will find that even Spinoza still retained something of a mystical attitude toward the mathematical method. The philosophy of Spinoza differs from mysticism only in one respect. A mystic like Meister Eckhart or Johannes Tauler 27 Johannes Tauler: About 1300–1361 Strasbourg. Preacher and pastor, Dominican, mystic, student of Meister Eckhart. Sermons and writings in German by W. Lehmann, 1923; see also Mysticism at the Dawn of the Modern Age , the chapter “Friendship with God.” attempts to experience the cosmic secrets more in the depths of feeling. Equally inwardly, Spinoza constructs the mysteries of the universe along mathematical, methodical lines, not specifically geometrical lines, but lines experienced mentally by mathematical methods. In regard to soul configuration and mood, there is no basic difference between the experience of Meister Eckhart's mystical method and Spinoza's mathematical one. Anyone how makes such a distinction does not really understand how Spinoza experienced his Ethics, for example, in a truly mathematical-mystical way. His philosophy still reflects the time when mathematics, mathesis, and mysticism were felt as one and the same experience in the soul. Now, you will perhaps recall how, in my book The Case for Anthroposophy , 28 Rudolf Steiner, The Case for Anthroposophy (London: Rudolf Steiner Press, 1970). I tried to explain the human organization in a way corresponding to modern thinking. I divided the human organization — meaning the physical one — into the nerve-sense system, the rhythmic system, and the metabolic-limb system. I need not point out to you that I did not divide man into separate members placed side by side in space, although certain academic persons have accused 29 In a reply to two lectures, which Walter Johannes Stein and Eugen Kolisko gave to defend two articles on “Anthroposophy as Science” in the Goettingen newspaper, Hugo Fuchs, Professor of Anatomy, spoke sarcastically of a human being with head, breast, and belly system. (From a report of the newspaper Die Dreigliederung des Sozialen Organismus , August 1920, No. 5). me of such a caricature. I made it clear that these three systems interpenetrate each other. The nerve-sense system is called the “head system” because it is centered mainly in the head, but it spreads out into the whole body. The breathing and blood rhythms of the chest system naturally extend into the head organization, and so on. The division is functional, not local. An inward grasp of this threefold membering will give you true insight into the human being. Let us now focus on this division for a certain purpose. To begin with, let us look at the third member of the human organization, that of digestion (metabolism) and the limbs. Concentrating on the most striking aspect of this member, we see that man accomplishes the activities of external life by connecting his limbs with his inner experiences. I have characterized some of these, particularly the inward orientation experience of the three directions of space. In his external movements, in finding his orientation in the world, man's limb system achieves inward orientation in the three directions. In walking, we place ourselves in a certain manner into the experience of above-below. In much that we do with our hands or arms, we bring ourselves into the orientation of right-and-left. To the extent that speech is a movement of the aeriform in man, we even fit ourselves into direction of front-and-back, back-and-front, when we speak. Hence, in moving about in the world, we place our inward orientation into the outer world. Let us look at the true process, rather than the merely illusionary one, in a specific mathematical case. It is an illusionary process, taking place purely in abstract schemes of thought, when I find somewhere in the universe a process in space, and I approach it as an analytical mathematician in such a way that I draw or imagine the three coordinate axes of the usual spatial system and arrange this external process into Descartes’ purely artificial space scheme. This is what occurs above, in the realm of thought schemes, through the nerve-sense system. One would not achieve a relationship to such a process in space if it were not for what one does with one's limbs, with one's whole body, if it were not for inserting oneself into the whole world in accordance with the inward orientation of above-below, right-left, and front-back. When I walk forward, I know that on one hand I place myself in the vertical direction in order to remain upright. I am also aware that in walking I adjust my direction to the back-to-front orientation, and when I swim and use my arms, I orient myself in right and left. I do not understand all this if I apply Descartes’ space scheme, the abstract scheme of the coordinate axes. What gives me the impression of reality in dealing with matters of space is found only when I say to myself: Up in the head, in the nerve system, an illusory image arises of something that occurs deep down in the subconscious. Here, where man cannot reach with his ordinary consciousness, something takes place between his limb system and the universe. The whole of mathematics, of geometry, is brought up out of our limb system of movement. We would not have geometry if we did not place ourselves into the world according to inward orientation. In truth, we geometrize when we lift what occurs in the subconscious into the illusory of the thought scheme. This is the reason why it appears so abstractly independent to us. But his is something that this only come about in recent times. In the age in which mathesis, mathematics, was still felt to be something close to mysticism, the mathematical relationship to all things was also viewed as something human. Where is the human factor if I imagine an abstract point somewhere in space crossed by three perpendicular directions and then apply this scheme to a process perceived in actual space? It is completely divorced from man, something quite inhuman. This non-human element, which has appeared in recent times in mathematical thinking, was once human. But when was it human? The actual date has already been indicated, but the inner aspect is still to be described. When was it human? It was human when man did not only experience in his movements and his inward orientation in space that he stepped forward from behind and moved in such a way that he was aware of his vertical as well as the horizontal direction, but when he also felt the blood's inward activity in all such moving about, in all such inner geometry. There is always blood activity when I move forward. Think of the blood activity present when, as an infant, I lifted myself up from the horizontal to an upright position! Behind man's movements, behind his experience of the world by virtue of movements, (which can also be, and at one time was, an inward experience) there stands the experience of the blood. Every movement, small or large, that I experience as I perform it contains its corresponding blood experience. Today blood is to us the red fluid that seeps out when we prick our skin. We can also convince ourselves intellectually of its existence. But in the age when mathematics, mathesis, was still connected with mysticism, when in a dreamy way the experience of movement was inwardly connected with that of blood, man was inwardly aware of the blood. It was one thing to follow the flow of blood through the lungs and quite another to follow it through the head. Man followed the flow of the blood in lifting his knee or his foot, and he inwardly felt and experienced himself through and through in his blood. The blood has one tinge when I raise my foot, another when I place it firmly on the ground. When I lounge around and doze lazily, the blood's nuance differs from the one it has when I let thoughts shoot through my head. The whole person can take on a different form when, in addition to the experience of movement, he has that of the blood. Try to picture vividly what I mean. Imagine that you are walking slowly, one step at a time; you begin to walk faster; you start to run, to turn yourself, to dance around. Suppose that you were doing all this, not with today's abstract consciousness, but with inward awareness: You would have a different blood experience at each stage, with the slow walking, then the increase in speed, the running, the turning, the dancing. A different nuance would be noted in each case. If you tried to draw this inner experience of movement, you would perhaps have to sketch it like this (white line.) But for each position in which you found yourself during this experience of movement, you would draw a corresponding inward blood experience (red, blue, yellow — see Figure 2) Of the first experience, that of movement, you would say that you have it in common with external space, because you are constantly changing your position. The second experience, which I have marked by means of the different colors, is a time experience, a sequence of inner intense experiences. In fact, if you run in a triangle, you can have one inner experience of the blood. You will have a different one if you run in a square. What is outwardly quantitative and geometric, is inwardly intensely qualitative in the experience of the blood. It is surprising, very surprising, to discover that ancient mathematics spoke quite differently about the triangle and the square. Modern nebulous mystics describe great mysteries, but there is no great mystery here. It is only what a person would have experienced inwardly in the blood when he walked the outline of a triangle or a square, not to mention the blood experience corresponding to the pentagram. In the blood the whole of geometry becomes qualitative inward experience. We arrive back at a time when one could truly say, as Mephistopheles does in Goethe's Faust , “Blood is a very special fluid.” 30 From Goethe's Faust , Part I, the scene in the Student Room with Faust and Mephisto. See Rudolf Steiner, The Occult Significance of the Blood (London: Rudolf Steiner Press, 1967). This is because, inwardly experienced, the blood absorbs all geometrical forms and makes of them intense inner experiences. Thereby man learns to know himself as well. He learns to know what it means to experience a triangle, a square, a pentagram; he becomes acquainted with the projection of geometry on the blood and its experiences. This was once mysticism. Not only was mathematics, mathesis, closely related to mysticism, it was in fact the external side of movement, of the limbs, while the inward side was the blood experience. For the mystic of bygone times all of mathematics transformed itself out of a sum of spatial formations into what is experienced in the blood, into an intensely mystical rhythmic inner experience. We can say that once upon a time man possessed a knowledge that he experienced, that he was an integral part of; and that at the point in time that I have mentioned, he lost this oneness of self with the world, this participation in the cosmic mysteries. He tore mathematics loose from his inner being. No longer did he have the experience of movement; instead, he mathematically constructed the relationships of movement outside. He no longer had the blood experience; the blood and its rhythm became something quite foreign to him. Imagine what this implies: Man tears mathematics free from his body and it becomes something abstract. He loses his understanding of the blood experience. Mathematics no longer goes inward. Picture this as a soul mood that arose at a specific time. Earlier, the soul had a different mood than later. Formerly, it sought the connection between blood experience and experience of movement; later, it completely separated them. It no longer related the mathematical and geometrical experience to its own movement. It lost the blood experience. Think of this as real history, as something that occurs in the changing moods of evolution. Verily, a man who lived in the earlier age, when mathesis was still mysticism, put his whole soul into the universe. He measured the cosmos against himself. He lived in astronomy. Modern man inserts his system of coordinates into the universe and keeps himself out of it. Earlier, man sensed a blood experience with each geometrical figure. Modern man feels no blood experience; he loses the relationship to his own heart, where the blood experiences are centered. Is it imaginable that in the seventh or eighth century, when the soul still felt movement as a mathematical experience and blood as a mystical experience, anybody would have founded a Copernican astronomy with a system of coordinates simply inserted into the universe and totally divorced from man? No, this became possible only when a specific soul constitution arose in evolution. And after that something else became possible as well. The inward blood awareness was lost. Now the time had come to discover the movements of the blood externally through physiology and anatomy. Hence you have this change in evolution: On one hand Copernican astronomy, on the other the discovery of the circulation of the blood by Harvey, 31 William Harvey, 1578–1658, physiologist, Professor of Anatomy, London, discoverer of the main bloodstream: De Motu Cordis et Sanguinis (1628). a contemporary of Bacon and Hobbes. A world view gained by abstract mathematics cannot produce anything like the ancient Ptolemaic theory, which was essentially bound up with man and the living mathematics he experienced within himself. Now, one experiences an abstract system of coordinates starting with an arbitrary zero point. No longer do we have the inward blood experience; instead, we discover the physical circulation of the blood with the heart in the center. The birth of science thus placed itself into the whole context of evolution in both its conscious and unconscious processes. Only in this way, out of the truly human element, can one understand what actually happened, what had to happen in recent times for science — so self-evident today — to come into being in the first place. Only thus could it even occur to anybody to conduct such investigations as led, for example, to Harvey's discovery of the circulation of the blood. We shall continue with this tomorrow.

The Origins of Natural Science

Lecture III

https://rsarchive.org/Lectures/GA326/English/AP1985/19221226p01.html

Dornach

26 Dec 1922

GA326-3

In the last lecture, I spoke of a former view of life from which the modern scientific view has evolved. It still combined the qualitative with the form-related or geometrical elements of mathematics, the qualitative with the quantitative. One can therefore look back at a world conception in which the triangle or another geometrical form was an inner experience no matter whether the form referred to the surface of a given body or to its path of movement. Geometrical and arithmetical forms were intensely qualitative inner experiences. For example, a triangle and a square were each conceived as emerging from a specific inward experience. This conception could change into a different one only when men lost their awareness that everything quantitative — including mathematics — is originally experienced by man in direct connection with the universe. It changed when the point was reached where the quantitative was severed from what man experiences. We can determine this moment of separation precisely. It occurred when all concepts of space that included man himself were replaced by the schematic view of space that is customary today, according to which, from an arbitrary starting point, the three coordinates are drawn. The kind of mathematics prevalent today, by means of which man wants to dominate the so-called phenomena of nature, arose in this form only after it had been separated from the human element. Expressing it more graphically, I would say in a former age man perceived mathematics as something that he experienced within himself together with his god or gods, whereby the god ordered the world. It came as no surprise therefore to discover this mathematical order in the world. In contrast to this, to impose an arbitrary space outline or some other mathematical formula on natural phenomena — even if such abstract mathematical concepts can be identified with significant aspects in these so-called natural phenomena — is a procedure that cannot be firmly related to human experiences. Hence, it cannot be really understood and is at most simply assumed to be a fact. Therefore in reality it cannot be an object of any perception. The most that can be said of such an imposition of mathematics on natural phenomena is that what has first been mathematically thought out is then found to fit the phenomena of nature. But why this is so can no longer be discovered within this particular world perception. Think back to the other worldview that I have previously described to you, when all corporeality was regarded as image of the spirit. One looking at a body found in it the image of spirit. One then looked back on oneself, on what — in union with one's own divine nature — one experienced as mathematics through one's own bodily constitution. As a work of art is not something obscure but is recognized as the image of the artist's ideas, so one found in corporeal nature the mathematical images of what one had experienced with one's own divine nature. The bodies of external nature were images of the divine spiritual. The instant that mathematics is separated from man and is regarded only as an attribute of bodies that are no longer seen as a reflection of spirit, in that instant agnosticism creeps into knowledge. Take a concrete example, the first phenomenon that confronts us after the birth of scientific thinking, the Copernican system. It is not my intention today or in any of these lectures to defend either the Ptolemaic or the Copernican system. I am not advocating either one. I am only speaking of the historical fact that the Copernican system has replaced the Ptolemaic. What I say today does not imply that I favor the old Ptolemaic system over the Copernican. But this must be said as a matter of history. Imagine yourself back in the age when man experienced his own orientation in space: above-below, right-left, front-back. He could experience this only in connection with the earth. He could, for example, experience the vertical orientation in himself only in relation to the direction of gravity. He experienced the other two in connection with the four compass points according to which the earth itself is oriented. All this he experienced together with the earth as he felt himself standing firmly on it. He thought of himself not just as a being that begins with the head and ends a the sole of the feet. Rather, he felt himself penetrated by the force of gravity, which had something to do with his being but did not cease at the soles of his feet. Hence, feeling himself within the nature of the gravitational force, man felt himself one with the earth. For his concrete experience, the starting point of his cosmology was thus given by the earth. Therefore he felt he Ptolemaic system to be justified. Only when man severed himself from mathematics, only then was it possible also to sever mathematics from the earth and to found an astronomical system with its center in the sun. Man had to lose the old experience-within-himself before he could accept a system with its center outside the earth. The rise of the Copernican system is therefore intimately bound up with the transformation of civilized mankind's soul mood. The origin of modern scientific thinking cannot be separated from the general mental and soul condition, but must be viewed in context with it. It is only natural that statements like this are considered absurd by our contemporaries, who believe in the present world view far more fervently than the sectarians of olden days believed in their dogmas. But to give the scientific mode of thinking its proper value, it must be seen as arising inevitably out of human nature and evolution. In the course of these lectures, we shall see that by doing this we are actually assigning far greater value to science than do the modern agnostics. Thus the Copernican world conception came into being, the projection of the cosmic center from the earth to the sun. Fundamentally, the whole cosmic thought edifice of Giordano Bruno, 32 Giordano Bruno: Nola 1548–1600 Rome. Dominican, 1563–1576, a great traveler. Main works developed at the English court at the time of Elizabeth I. After he returned to Italy he was imprisoned because of heretical teachings, and was burned in Rome after 8 years in prison. See Riddles of Philosophy , and The Spiritual Guidance of Man , by Rudolf Steiner. who was born in 1548 and burned at the stake in Rome in 1600, was already contained in the Copernican world view. It is often said that Giordano Bruno glorifies the modern view of nature, glorifies Copernicanism. One must have deep insight into the inner necessity with which this new cosmology arose if one is to have any feeling at all for the manner and tone in which Giordano Bruno speaks and writes. Then one sees that Giordano Bruno does not sound like the followers of the new view or like the stragglers of the old view. He really does not speak about the cosmos mathematically so much as lyrically. There is something musical in the way Giordano Bruno describes the modern conception of nature. Why is that? The reason is that Giordano Bruno, though he was rooted with his whole soul in a bygone world perception, told himself with his outward intellect: The way things have turned out in history, we cannot but accept the Copernican world picture. He understood the absolute necessity that had been brought about by evolution. This Copernican world view, however, was not something he had worked out for himself. It was something given to him, and which he found appropriate for his contemporaries. Belonging as he did to an older world conception, he could not help but experience inwardly what he had to perceive and accept as knowledge. He still had the faculty of inner experience, but he did not have scientific forms for it. Therefore although he described them so wonderfully, he did not follow the Copernican directions of thought in the manner of Copernicus, Galileo, Kepler, or Newton. 33 Isaac Newton, Sir: Woolsthorpe, Lincolnshire 1642–1727 Kensington, London. Born as a dwarf-like child. Grew up on a farm and went to village and small town schools until 1661. After he was accepted at the University he was of medium talent until his “flaming” as a genius physicist, astronomer, mathematician 1663–1664. Professor in Cambridge 1669–1701, member of the Royal Society London 1662 and from 1703 until his death, its President. Main work: Law of Gravitation, Mathematically Adapted to the Law of Motion from Kepler , developed 1666, published 1687 in Philosophiae Naturalis Principa Mathematica. The idea of an infinitesimal mathematics came from Newton in 1663; three years later he had developed his differential mathematics. His Optics , 1704, put forth the division of light in color as well as emission theory. Later Newton lost all interest in physics, mathematics, and also in the destiny and consequences of his works. He turned towards chemical and alchemical experiments and studies of their old traditions. In his old age he was interested in religious-speculative studies. Before his death he compared his life with a day, in which a child is playing with sand and mussels and is not aware anymore of the cosmos at his back. Literature: J.W.N. Sullivan, Isaac Newton 1642–1727 (London 1938). Instead, he tried to experience the cosmos in the old way, the way that was suitable when the world cosmos was experienced within one's being. But in order to do this, mathematics would have had to be also mysticism, inward experience, in the way I described yesterday. This it could not be for Giordano Bruno. The time for it was past. Hence, his attempt to enter the new cosmology through living experience became an experience, not of knowledge but of poetry, or at least partially so. This fact lends Giordano's works their special coloring. The atom is still a monad; in his writings, it is still something alive. The sum of cosmic laws retains a soul quality, but not because he experienced the soul in all the smallest details as did the ancient mystics, and not because he experienced the mathematical laws of the cosmos as the intentions of the spirit. No, it was because he roused himself to wonder at this new cosmology and to glorify it poetically in a pseudo-scientific form. Giordano Bruno is truly something like a connecting link between two world conceptions, the present one and the ancient one that lasted into the fifteenth century. Man today can form scarcely any idea of the latter. All cosmic aspects were then still experienced by man, who did not yet differentiate between the subject within himself and the cosmic object outside. The two were still as one; man did not speak of the three dimensions in space, sundered from the orientation within his own body and appearing as above-below, right-left, and forward-backward. Copernicus tried to grasp astronomy with abstract mathematical ideas. On the other hand, Newton shows mathematics completely on its own. Here I do not mean single mathematical deductions, but mathematical thinking in general, entirely divorced from human experience. This sounds somewhat radical and objections could certainly be made to what I am thus describing in broad outlines, but this does not alter the essential facts. Newton is pretty much the first to approach the phenomena of nature with abstract mathematical thinking. Hence, as a kind of successor to Copernicus, Newton becomes the real founder of modern scientific thinking. It is interesting to see in Newton's time and in the age that followed how civilized humanity is at pains to come to terms with the immense transformation in soul configuration that occurred as the old mathematical-mystical view gave way to the new mathematical-scientific style. The thinkers of the time find it difficult to come to terms with this revolutionary change. It becomes all the more evident when we look into the details, the specific problems with which some of these people wrestled. See how Newton, for instance, presents his system by trying to relate it to the mathematics that has been severed from man. We find that he postulates time, place, space, and motion. He says in effect in his Principa : I need not define place, time, space, and motion because everybody understands them. 34 In Newton's second edition of his Philosophiae Naturalis Principa Mathematica of 1713 the definition is “But I do not define, because it is well known to all of us.” Everybody knows what time is, what space, place, and motion are, hence these concepts, taken from common experience, can be used in my mathematical explanation of the universe. People are not always fully conscious of what they say. In life, it actually happens seldom that a person fully penetrates everything he says with his consciousness. This is true even among the greatest thinkers. Thus Newton really does not know why he takes place, time, space, and motion as his starting points and feels no need to explain or define them, whereas in all subsequent deductions he is at pains to explain and define everything. Why does he do this? The reasons is that in regard to place, time, motion, and space all cleverness and thinking avail us nothing. No matter how much we think about these concepts, we grow no wiser than we were to begin with. Their nature is such that we experience them simply through our common human nature and must take them as they come. A successor of Newton's, Bishop Berkeley, 35 George Berkeley: Desert Castle, Thomastown, Ireland 1685–1753 Oxford. English philosopher and Anglican missionary, Bishop from 1734. Main works: Treatise Concerning the Principle of Human Knowledge , 1710; Alciphron , about ethics and free thinkers, 1732; Siris , concerning metaphysical questions. See: Riddles of Philosophy . Berkeley said: “One has to do it in such a way”: e.g., as in Paragraph 113 of Principles of Human Knowledge. In the writing De Motu ( From Motion ) is written in Paragraph 43: “Motion, even though perceived clearly by the senses, was darkened, but not because of its own being, but far more through commentaries by learned philosophers.” took particular notice of this point. He was involved in philosophy more than Newton was, but Berkeley illustrates the conflicts taking place during the emergence of scientific thinking. In other respects, as we shall presently hear, he was not satisfied with Newton, but he was especially struck by the way that Newton took these concepts as his basis without any explanation, that he merely said: I start out from place, time, space, and motion; I do not define them; I take them as premises for my mathematical and scientific reflections. Berkeley agrees that one must do this. One must take these concepts in the way they are understood by the simplest person, because there they are always clear. They become unclear not in outward experience, but in the heads of metaphysicians and philosophers. Berkeley feels that when these four concepts are found in life, they are clear; but they are always obscure when found in the heads of thinkers. It is indeed true that all thinking about these concepts is of no avail. One feels this. Therefore, Newton is only beginning to juggle mathematically when he uses these concepts to explain the world. He is juggling with ideas. This is not meant in a derogatory way; I only want to describe Newton's abilities in a telling manner. One of the concepts thus utilized by Newton is that of space. He manipulates the idea of space as perceived by the man in the street. Still, a vestige of living experience is contained therein. If, on the other hand, one pictures space in terms of Cartesian mathematics, without harboring any illusions, it makes one's brain reel. There is something undefinable about this space, with its arbitrary center of coordinates. One can, for example, speculate brilliantly (and fruitlessly) about whether Descartes’ space if finite or infinite. Ordinary awareness of space that is still connected with the human element really is not at all concerned with finiteness or infinity. It is after all quite without interest to a living world conception whether space can be pictured as finite or infinite. Therefore one can say that Newton takes the trivial idea of space just as he finds it, but then he begins to mathematize. But, due to the particular quality of thinking in his age, he already has the abstracted mathematics and geometry, and therefore he penetrates spatial phenomena and processes of nature with abstract mathematics. Thereby he sunders the natural phenomena from man. In fact, in Newton's physics we meet for the first time ideas of nature that have been completely divorced from man. Nowhere in earlier times were conceptions of nature so torn away from man as they are in Newtonian physics. Going back to a thinker of the fourth or fifth century A.D. — though people of that period can hardly be called “thinkers,” because their inner life was far more alive than the mere life in thoughts — we would find that he held the view: “I live; I experience space along with my God, and orient myself in space up-and-down, right-left, and forward-backward, but I dwell in space together with my God. He outlines the directions and I experience them.” So it was for a thinker of the third or fourth century A.D. and even later; indeed, it only became different in the fourteenth century. Thinking geometrically about space, man did not merely draw a triangle but was conscious of the fact that, while he did this, God dwelled within him and drew along with him. His experience was qualitative; he drew the qualitative reality that God Himself had placed within him. Everywhere in the outer world, whenever mathematics was observed, the intentions of God were also observed. By Newton's time mathematics has become abstracted. Man has forgotten that originally he received mathematics as an inspiration from God. And in this utterly abstract form, Newton now applies mathematics to the study of space. As he writes his Principia, he simply applies this abstracted mathematics, this idea of space (which he does not define,) because he has a dim feeling that nothing will be gained by trying to define it. He takes the trivial idea of space and applies his abstract mathematics to it, thus severing it from any inward experiences. This is how he speaks of the principles of nature. Later on, interestingly enough, Newton goes somewhat deeper. This is easy to see if one is familiar with his works. Newton becomes ill at ease, as it were, when he contemplates his own view of space. He is not quite comfortable with this space, torn as it is out of man and estranged completely from the spirit. So he defines it after all, saying that space is the sensorium of God. It is most interesting that at the starting point of modern science the very person who was the first to completely mathematize and separate space from man, eventually defines space as God's sensorium, 36 In the work Optice by Newton, which is the Latin translation of his Optics (1704), published by Samuel Clarke in 1706 and approved with additions made by Newton, the formula appears only at the end of the book at the so-called 28th Problem: “If these questions are answered in the right way, could we then not ascertain the phenomenon that there is a being, unbodily, intelligent, which can perceive the endless universe as it were with its sense organs, and which seems to look into the innermost and is surrounding it with its all-embracing presence, while that in us that is usually feeling and thinking are only handed-down pictures in which we then perceive and observe our organs?” This thought seems not only to be Newton's, but was also presented in a similar way by Henry More, the Platonist from Cambridge who was a friend of Newton. a sort of brain or sense organ of God. Newton had torn nature asunder into space and man-who-experiences-space. Having done this, he feels inwardly uneasy when he views this abstract space, which man had formerly experienced in union with his god. Formerly, man had said to himself: What my human sensorium experiences in space, I experience together with my god. Newton becomes uneasy, now that he has torn space away form the human sensorium. He has thereby torn himself away from his permeation with the divine-spiritual. Space, with all is mathematics, was not something external. So, in later life, Newton addresses it as God's sensorium, though to begin with he had torn the whole apart, thus leaving space devoid of Spirit and God. But enough feeling remained in Newton that he could not leave this externalized space devoid of God. So he deified it again. Scientifically, man tore himself loose from his god, and thus from the spirit; but outwardly he again postulated the same spirit. What happened here explains why a man like Goethe found it impossible 37 For his polemic concerning Newton's color theory, see Rudolf Steiner, Goethe the Scientist (New York: Anthroposophic Press, 1950), especially the Introduction, “Goethe, Newton and the Physicists”; see also the forthcoming book, Heinrich O. Proskauer, The Rediscovery of Color (Spring Valley, NY: Anthroposophic Press). to go along with Newton on any point. Goethe's Theory of Color is one particularly characteristic point. This whole procedure of first casting out the spirit, separating it from man, was foreign to Goethe's nature. Goethe always had the feeling that man has to experience everything, even what is related to the cosmos. Even in regard to the three dimensions Goethe felt that the cosmos was only a continuation of what man had inwardly experienced. Therefore Goethe was by nature Newton's adversary. Now let us return to Berkeley, who was somewhat younger than Newton, but still belonged to the period of conflict that accompanied the rise of the scientific way of thinking. Berkeley had no quarrel with Newton's accepting the trivial ideas of place, space, time, and motion. But he was not happy with this whole science that was emerging, and particularly not with its interpretations of natural phenomena. It was evident to him that when nature is utterly severed from man it cannot be experienced at all, and that man is deceiving himself when he imagines that he is experiencing it. Therefore, Berkeley declared that bodies forming the external basis for sense perceptions do not really exist. Reality is spiritual through and through. The universe, as it appears to us — even where it appears in a bodily form — is but the manifestation of an all-pervading spirit. In Berkeley, these ideas appear pretty much as mere assertions, for he no longer had any trace of the old mysticism and even less of the ancient pneumatology. Except for his religious dogma, he really had no ground at all for his assertion of such all-pervading spirituality. But assert it he did, and so vigorously that all corporeality become for him no more than a revelation of the spirit. Hence it was impossible for Berkeley to say: I behold a color and there is vibrating movement back of it that I cannot see — which is what modern science justifiably states. Instead, Berkeley said: I cannot hypothetically assume that there is anything possessing any corporeal property such as vibratory movement. The basis of the physical world of phenomena must be spiritually conceived. Something spiritual is behind a color perception as its cause, which I experience in myself when I know myself as spirit. Thus Berkeley is a spiritualist in the sense in which this term is used in German philosophy. For dogmatic reasons, but with a certain justification, Berkeley makes innumerable objections against the assumption that nature can be comprehended by mathematics that has been abstracted from direct experience. Since to Berkeley the whole cosmos was spiritual, he also viewed mathematics as having been formed together with the spirit of the cosmos. He held that we do in fact experience the intentions of the cosmic spirit insofar as they have mathematical forms, for that we cannot apply mathematical concepts in an external manner to corporeal objects. In accordance with this point of view, Berkeley opposed what mathematics had become for both Newton and Leibnitz, 38 Leibnitz: Leipzig 1646–1716 Hanover. Philologist, mathematician, physicist, lawyer, statesman, priest. Mostly living at princely courts, traveling a lot. Discoverer of the Infinitesimal Calculus 1686, independently of Newton. namely differential and integral calculus. Please, do not misunderstand me. Today's lecture must be fashioned in such a way that it cannot but provoke many objections in one who holds to the views prevailing today. But these objections will fade away during the ensuring lectures, if one is willing to keep an open mind. Today, however, I want to present the themes that will occupy us in a rather radical form. Berkeley became an opponent of the whole infinitesimal calculus 39 In his writing The Analyst ( The Analyst , 1734, included in the book Writings about the Origin of Mathematics and Physics ) the Table of Contents is in the form of 50 theses. No. 7, for example, is as follows: “Objections against the Secrets of Belief Which are Made Unfairly by Those who Admit Them in Science;” or No. 13: “The Rule for the Flux of Potency is Achieved through Unfair Reasoning;” and No. 22: “With the Help of a Double Mistake Analysts Come to their Truth, but not to Science, in which They do not even Know How They Came to Their Own Conclusions.” From the Polemic Dispute , which follows The Analyst , an example is: “No big name on this earth will ever cause me to take unclear things for clear ones. They think of one as if it were a crime to think one could see further than Sir Isaac Newton, even above him. I am convinced though that they speak for the feelings of many others. But there are also some ... who think and feel it unfair to copy some great man's shortcomings, and who see no crime in wanting to see further than Sir Isaac Newton, but further than the whole of mankind.” to the extent that it was then known. He opposed what was beyond experience. In this regard, Berkeley's feeling for things was often more sensitive than his thoughts. He felt how, to the quantities that the mind could conceive, the emergence of infinitesimal calculus added other quantities; namely, the differentials, which attain definition only in the differential coefficient. Differentials must be conceived in such a way that they always elude our thinking, as it were. Our thinking refuses to completely permeate them. Berkeley regarded this as a loss of reality, since knowledge for him was only what could be experienced. Therefore he could not approve of mathematical ideas that produced the indetermination of the differentials. What are we really doing when we seek differential equations for natural phenomena? We are pointing to something that eludes our possible experience. I realize, of course, that many of you cannot quite follow me on these points, but I cannot here expound the whole nature of infinitesimal calculus. I only want to draw attention to some aspects that will contribute to our study of the birth of modern science. Modern science set out to master the natural phenomena by means of a mathematics detached from man, a mathematics no longer inwardly experienced. By adopting this abstract mathematical view and these concepts divorced from man, science arrived at a point where it could examine only the inanimate. Having taken mathematics out of the sphere of live experience, one can only apply it to what is dead. Therefore, owing to this mathematical approach, modern science is directed exclusively to the sphere of death. In the universe, death manifests itself in disintegration, in atomization, in reduction to microscopic parts — putting it simply, in a crumbling into dust. This is the direction taken by the present-day scientific attitude. With a mathematics detached from all living experience, it takes hold of everything in the cosmos that turns to dust, that atomizes. From this moment onward it becomes possible to dissipate mathematics itself into differentials. We actually kill all living forms of thought, if we try to penetrate them with any kind of differential equation, with any differential line of thought. To differentiate is to kill; to integrate is to piece the dead together again in some kind of framework, to fit the differentials together again into a whole. But they do not thereby become alive again, after having been annihilated. One ends up with dead specters, not with anything living. This is how the whole perspective of what was opening up through infinitesimal calculus appeared to Berkeley. Had he expressed himself concretely, he might well have said: First you kill the whole world by differentiating it; then you fit its differentials together again in integrals, but you no longer have a world, only a copy, an illusion. With regard to its content, every integral is really an illusion, and Berkeley already felt this to be so. Therefore, differentiation really implies annihilation, while integration is the gathering up of bones and dust, so that the earlier forms of the slain beings can be pieced together again. But this does not bring them back to life; they remain no more than dead replicas. One can say that Berkeley's sentiments were untimely. This they certainly were, for the new way of approach had to come. Anyone who would have said that infinitesimal calculus should never have been developed would have been called not a scientific thinker but a fool. On the other hand, one must realize that at the outset of this whole stream of development, feelings such as Berkeley's were understandable. He shuddered at what he thought would come from a infinitesimal study of nature and had to do with the process of birth but a study of all dying aspects in nature. Formerly this had not been observed, nor had there been any interest in it. In earlier times, the coming-into-being, the germinating, had been studied; now, one looked at all that was fading and crumbling into dust. Man's conception was heading toward atomism, whereas previously it had tended toward the continuous, lasting aspects of things. Since life cannot exist without death and all living things must die, we must look at and understand all that is dead in the world. A science of the inanimate, the dead, had to arise. It was absolutely necessary. The time that we are speaking about was the age in which mankind was ready for such a science. But we must visualize how this went against the grain of somebody who, like Berkeley, still lived completely in the old view. The after-effects of what came into being then are still very much with us today. We have witnessed the triumphs of just those scientific labors that made Berkeley shudder. Until they were somewhat modified through the modern theory of relativity, 40 Prepared by Mach and Lorentz, developed by Einstein, Special Theory of Relativity 1905, Common Theory of Relativity 1916. Made it necessary to revise Newton's Mechanics with the help of non-Euclidean Geometry. See also Riddles of Philosophy and Georg Unger, Von Bidden, Physicalischer Begriffe , Part 3 (Stuttgart: 1967), pages 100–122. Newton's theories reigned supreme, Goethe's revolt against them made no impression. For a true comprehension of what went on we must go back to Newton's time and see the shuddering of thinkers who still had a vivid recollection of earlier views and how they clung to feelings that resembled the former ones. Giordano Bruno shrank from studying the dead nature that was now to be the object of study. He could not view it as dead in a purely mathematical manner of thought, so he animated the atoms into monads and imbued his mathematical thinking with poetry in order to retain it in a personal sphere. Newton at first proceeded from a purely mathematical standpoint, but then he wavered and defined space (which he has first completely divorced from man through his external mathematics) as God's sensorium. Berkeley in his turn rejected the new direction of thinking altogether and with it the whole trend towards the infinitesimal. Today, however, we are surrounded and overwhelmed by the world view that Giordano Bruno tried to turn into poetry, that Newton felt uncomfortable about, and that Berkeley completely rejected. Do we take what Newton said — that space is a sensorium of God — seriously when we think in the accepted scientific sense today? People today like to regard as great thinkers those men who have said something or other that they approve. But if the great men also said something that they do not approve, they feel very superior and think: Unfortunately, on this point he wasn’t as enlightened as I am. Thus many people consider Lessing 41 Lessing, Gottfried Ephraim: Kamenz/Lausitz 1729–1781 Brunswick. Dramatist, essayist, critic. Opens a new epoch in German literature and an. His last writing, “The Education of the Human Race,” (1780) finds it necessary to postulate reincarnation for the sake of the development of the human race. See Riddles of Philosophy . a man of great genius but make an exception for what he did toward the end of his life, when he became convinced that we go through repeated earth lives. Just because we must in the present age come to terms with the ideas that have arisen, we must go back to their origin. Since mathematics has once and for all been detached from man, and since nature has been taken hold of by this abstract mathematics that has gradually isolated us from the whole of nature, we must now somehow manage to find ourselves in this nature. For we will not attain a coherent spiritual knowledge until we once again have found the spirit in nature. Just as it is a matter of course that every living man will sooner or later die, so it was a matter of course that sooner or later in the course of time a conception of death had to emerge from the former life-imbued world view. Things that can only be learned from a corpse cannot be learned by a person who is unwilling to examine the corpse. Therefore certain mysteries of the world can be comprehended only if the modern scientific way of thinking is taken seriously. Let me close with a somewhat personal remark. 42 The reason was a controversy in the magazine Die Drei of 1921–1922, pages 1107 and 1114, as well as in the following years publication (see pages 172–330 about the reality of atoms). See Rudolf Steiner's First Scientific Lecture Course: Light Course (Forest Row, England: Steiner Schools Fellowship, 1977). The scientific world view must be taken seriously, and for this reason I was never an opponent of it; on the contrary, I regarded it as something that of necessity belongs to our time. Often I had to speak out against something that a scientist, or so-called scientist, had made of the things that were discovered by unprejudiced investigation of the sphere of death. It was the misinterpretation of such scientific discoveries that I opposed. On this occasion let me state emphatically that I do not wish to be regarded as in any way an opponent of the scientific approach. I would consider it detrimental to all our anthroposophical endeavors if a false opposition were to arise between what anthroposophy seeks by way of spiritual research and what science seeks — and must of necessity seek in its field — out of the modern attitude. I say this expressly, my dear friends, because a healthy discussion concerning the relationship between anthroposophy and science must come to pass within our movement. Anything that goes wrong in this respect can only do grave harm to anthroposophy and should be avoided. I mention this here because recently, in preparing these lectures, I read in the anthroposophical periodical Die Drei that atomism was being studied in a way in which no progress can be made. Therefore, I want to make it clear that I consider all these polemics in Die Drei about atomism as something that only serves to stultify the relations between anthroposophy and science.

The Origins of Natural Science

Lecture IV

https://rsarchive.org/Lectures/GA326/English/AP1985/19221227p01.html

Dornach

27 Dec 1922

GA326-4

The isolation of man's ideas (especially his mathematical ideas) from his direct experience has proved to be the outstanding feature of the spiritual development leading to modern scientific thinking. Let us place this process once more before our mind's eye. We were able to look back into ages past, when what man had to acquire as knowledge of the world was experienced in communion with the world. During those epochs, man inwardly did not experience his threefold orientation — up-down, left-right, front-back — in such a manner that he attributed it solely to himself. Instead, he felt himself within the universal whole; hence, his own orientations were to him synonymous with the three dimensions of space. What he pictured of knowledge to himself, he experienced jointly with the world. Therefore, with no uncertainty in his mind, he knew how to apply his concepts, his ideas, to the world. This uncertainty has only arisen along with the more recent civilization. We see it slowly finding its way into the whole of modern thought and we see science developing under this condition of uncertainty. This state of affairs must be clearly recognized. A few examples can illustrate what we are dealing with . Take a thinker like John Locke, who lived from the seventeenth into the eighteenth century. His writings show what an up-to-date thinker of his age had to say concerning the scientific world perception. John Locke 43 John Locke: Wrington by Bristol 1632–1704 Oates, Essex. Theologian, philosopher, and physician. Because raised Protestant and Puritan, he was persecuted in England and had to flee to Holland until after the English Revolution of 1689. From 1675–1689 Locke worked with many interruptions at his main work. An Essay Concerning Human Understanding , 1690. Originally he had planned a critical presentation of the already recognized teaching of primary and secondary sense characteristics, but then it grew to a perception theory or world view. His Essay was published 4 times in his lifetime. See Riddles of Philosophy , The Philosophy of Freedom , trans. Michael Wilson (Spring Valley, NY: Anthroposophic Press, 1964) and “Cardinal Nicolas of Cusa” in Mysticism at the Dawn of the Modern Age . divided everything that man perceives in his physical environment into two aspects. He divided the characteristic features of bodies into primary and secondary qualities. Primary qualities were those that he could only attribute to the objects themselves, such as shape, position, and motion. Secondary qualities in his view were those that did not actually belong to the external corporeal things but were an effect that these objects had upon man. Examples are color, sound, and warmth. Locke stated it thus: “When I hear a sound, outside of me there is vibrating air. In a drawing, I can picture these vibrations in the air that emanate from a sound-aroused body and continue on into my ear. The shape that the waves, as they are called, possess in the vibrating air can be pictured by means of spatial forms. I can visualize their course in time — all this, belonging to the primary qualities, certainly exists in the external world, but it is silent, it is soundless. The quality of sound, a secondary quality, only arises when the vibration of the air strikes my ear, and with it arises that peculiar inner experience that I carry within me as sound. It is the same with color, which is now lumped together with light. There must be something out there in the world that is somehow of a corporeal nature and somehow possesses shape and movement. This exercises an effect on my eye and thus becomes my experience of light or color. It is the same with the other things that present themselves to my senses. The whole corporeal world must be viewed like this; we must distinguish between the primary qualities in it, which are objective, and the secondary qualities, which are subjective and are the effects of the primary qualities upon us.” Simply put, one could say with Locke that the external world outside of man is form, position, and movement, whereas all that makes up the content of the sense world exists in truth somehow inside us. The actual content of color as a human experience is nowhere in the environment, it lives in me. The actual content of sound is nowhere to be found outside, it lives in me. The same is true of my experience of warmth or cold. In former ages, when what had become the content of knowledge was experienced jointly with the world, one could not possibly have had this view because, as I have said, a man experienced mathematics by participating in his own bodily orientation and placing this orientation into his own movement. He experienced this, however, in communion with the world. Therefore, his own experience was sufficient reason for assuming the objectivity of position, place, and movement. Also, though in another portion of his inner life, man again had this communion with the world in regard to color, tone, and so forth. Just as the concept of movement was gained through the experience of his own movement, so the concept of color was gained through a corresponding internal experience in the blood, and this experience was then connected with whatever is warmth, color, sound, and so forth in the surrounding world. Certainly, in earlier times, man distinguished position, location, movement, and time-sequence from color, sound, and warmth, but these were distinguished as being different kinds of experiences that were undergone jointly with different kinds of existence in the objective world. Now, in the scientific age, the determination of place, movement, position, and form ceased to be inward self-experience. Instead, they were regarded as mere hypotheses that were caused by some external reality. When the shape of a cannon is imagined, one can hardly say: This form of the cannon is actually somehow within me. Therefore its identification was directed outward and the imagined form of the cannon was related to something objective. One could not very well admit that a musket-ball was actually flying within one's brain; therefore, the hypothetically thought-out movements were attributed to something objective. On the other hand, what one saw in the flying musket-ball, the flash by which one perceived it and the sound by which one heart it, were pushed into one's own human nature, since no other place could be found for them. Man no longer knew how he experienced them jointly with the objects; therefore, he associated them with his own being. It actually took quite some time before those who thought along the lines of the scientific age perceived the impossibility of this arrangement. What had in fact taken place? The secondary qualities, sound, color, and warmth experience, had become, as it were, fair game in the world and, in regard to human knowledge, had to take refuge in man. But before too long, nobody had any idea of how they lived there. The experience, the self-experience, was no longer there. There was no connection with external nature, because it was not experienced anymore. Therefore these experiences were pushed into one's self. So far as knowledge was concerned, they had, as it were, disappeared inside man. Vaguely it was thought that an ether vibration out in space translated itself into form and movement, and this had an effect on the eye, and then worked on the optic nerve, and finally somehow entered the brain. Our thoughts were a means of looking around inside for whatever it was that, as an effect of the primary qualities, supposedly expressed itself in man as secondary qualities. It took a long time, as I said, before a handful of people firmly pointed out the oddity of these ideas. There is something extraordinary in what the Austrian philosopher Richard Wahle 44 Richard Wahle: 1857–1935, Vienna, Professor of Philosophy. Only valued perceptions, imaginations, and feelings, but rejected all philosophy hitherto written as theories of cognition. The “Ego” is for him “a summary of surface-like, physiologically accompanied pieces of consciousness, which are brought into being by invisible forces.” Some writings: The Whole of Philosophy and Its End , 1894; About the Mechanism of the Spiritual Life , 1906; The Tragic Comedy of Wisdom , 1915; Development of Characters , 1928; Basics of a New Psychiatry , 1931. wrote in his Mechanism of Thinking , though he himself did not realize the full implications of his sentence: “ Nihil est in cerebro, quod non est in nervis .” (“There is nothing in the brain that is not in the nerves.” It may not be possible with the means available today to examine the nerves in every conceivable way, but even if we could we would not find sound, color, or warmth experience in them. Therefore, they must not be in the brain either. Actually, one has to admit now that they simply disappear insofar as knowledge is concerned. One examines the relationship of man to the world. Form, position, place, time, etc. are beheld as objective. Sound, warmth, experience and color vanish; they elude one. 45 See Rudolf Steiner, The Philosophy of Freedom , Chapter 4. Finally, in the Eighteenth Century, this led Kant 46 Immanuel Kant: 1724–1804. Lived in Koenigsberg, which he seldom left. Philosopher, scientist, mathematician. Professor in Koenigsberg 1770–1794. Critique of Pure Reason , 1781. Its popular edition Dissertation on Any Future Metaphysics, 1783, his ethic Critique of Practical Reason , 1788, aesthetic and natural theology is handled in Critique of Judgment , 1790. He wrote the first mechanical cosmology 1755. It was taken up and changed by Laplace (1796) and known as the Kant-LaPlace Theory. Rudolf Steiner's exposition on Kant's theory is found in Truth and Knowledge , The Philosophy of Freedom , and An Autobiography , ed. Paul M. Alien, 2nd ed. (Blauvelt, NY: Steinerbooks, Garber Communications, 1980). E.g. in Critique of Pure Reason, “Transcendental Aesthetic, Common Remarks”: “We wanted to say that all our opinions are nothing but the conception of the appearance; that the things we look at are not actually what we take them for, nor is their relation constituted as they appear to us, and that if we would suspend our subject or even our subjective constitution of our senses as a whole, the whole constitution, all relationships of objects in space and time, even time and space itself would disappear. They would only exist in us, not as phenomena in themselves.” to say that even the space and time qualities of things cannot somehow be outside and beyond man. But there had to be some relationship between man and the world. After all, such a relationship cannot be denied if we are to have any idea of how man exists together with the world. Yet, the common experience of man's space and time relationships with the world simply did not exist anymore. Hence arose the Kantian idea: If man is to apply mathematics, for example, to the world, then it is his doing that he himself makes the world into something mathematical. He impresses the whole mathematical system upon the “things in themselves,” which themselves remain utterly unknown. — In the Nineteenth Century science chewed on this problem interminably. The basic nature of man's relation to cognition is simply this: uncertainty has entered into his relationship with the world. He does not know how to recognize in the world what he is experiencing. This uncertainty slowly crept into all of modern thinking. We see it entering bit by bit into the spiritual life of recent times. It is interesting to place a recent example side by side with Locke's thinking. August Weismann, 47 August Weismann, Frankfurt A.M. 1834–1914 Freiburg. Biologist, genetic scientist. Theory of polarity between cells (soma) and seed plasma. Determinants as heredity carriers. Writing: Studies on the Descent Theory. a biologist of the Nineteenth Century, conceived the thought: in any living organism, the interplay of the organs (in lower organisms, the interaction of the parts) must be regarded as the essential thing. This leads to comprehension of how the organism lives. But in examining the organism itself, in understanding it through the interrelationship of its parts, we find no equivalent for the fact that the organism must die. If one only observes the organism, so Weismann said, one finds nothing that will explain death. In the living organism, there is absolutely nothing that leads to the idea that the organism must die. For Weismann, the only thing that demonstrates that an organism must die is the existence of a corpse. This means that the concept of death is not gained from the living organism. No feature, no characteristic, found in it indicates that dying is a part of the organism. It is only when the event occurs, when we find a corpse in the place of the living organism, that we know the organism possesses the ability to die. But, says Weismann, there is a class of organisms where corpses are never found. These are the unicellular organisms. They only divide themselves so there are no corpses. The propagation of such beings looks like this: One divides into two; each of these divides into two again, and so on. There is never a corpse. Weismann therefore concludes that the unicellular beings are immortal. This is the immortality of unicellular beings that was famous in nineteenth-century biology. Why were these organisms considered immortal? Because they never produce any corpses, and because we cannot entertain the concept of death in the organic realm as long as there are no corpses. Where there is no corpse, there is no room for the concept of death. Hence, living beings that produce no corpses are immortal. This example shows how far man has removed himself in modern times from any connection between the world and his thinking, his inner experiences. His concept of an organism is no longer such that the fact of its death can be perceived from it. This can only be deduced from the existence of something like a corpse. Certainly, if a living organism is only viewed from outside, if one cannot experience what is in it, then indeed one cannot find death in the organism and an external sign is necessary. But this only proves that in his thinking man feels himself separated from the things around him. From the uncertainty that has entered all thinking concerning the corporeal world, from this divorce between our thoughts and our experience, let us turn back to the time when self-experience still existed. Not only did the inwardly experienced concept exist alongside the externally excogitated concept of a triangle, square, or pentagram, but there were also inwardly experienced concepts of blossoming and fading, of birth and death. This inner experience of birth and death had its gradations. When a child was seen to grow more and more animated, when its face began to express its soul, when one really entered into this growing process of the child, this could be seen as a continuation of the process of birth, albeit a less pronounced and intensive one. There were degrees in the experience of birth. When a man began to show wrinkles and grey hair and grow feeble, this was seen as a first mild degree of dying. Death itself was only the sum total of many less pronounced death experiences, if I may use such a paradox. The concepts of blossoming and decaying, of being born and dying, were inwardly alive. These concepts were experienced in communion with the corporeal world. No line was drawn between man's self-experience and the events in nature. Without a coastline, as it were, the inner land of man merged into the ocean of the universe. Owing to this form of experience, man lived himself into the world itself. Therefore, the thinkers of earlier ages, whose ideas no longer receive proper attention from science, had to form quite different ideas concerning something like what Weismann called the “immortality of unicellular beings.” What sort of concept would an ancient thinker have formed had he had a microscope and known something about the division of unicellular organisms? He would have said: First I have the unicellular being; it divides itself into two. Somewhat imprecisely, he might have said: It atomizes itself, it divides itself; for a certain length of time, the two parts are indivisible; then they divide again. As soon as division or atomization begins, death enters in. He would not have derived death from the corpse but from atomization, from the division into parts. His train of thought would have been somewhat as follows: A being that is capable of life, that is in the process of growth, is not atomized; and when the tendency to atomization appears, the being dies. In the case of unicellular beings, he would simply have thought that the two organisms cast off by the first unicellular being were for the moment dead, but would be, so to speak, revived immediately, and so forth. With atomization, with the process of splitting, he would have linked the thought of death. If he had known about unicellular beings and had seen one split into two, he would not have thought that two new ones had come into being. On the contrary, he would have said that out of the living monad, two atoms have originated. Further, he would have said that wherever there is life, wherever one observes life, one is not dealing with atoms. But if they are found in a living being, then a proportionate part of the being is dead. Where atoms are found, there is death, there is something inorganic. This is how matters would have been judged in a former age based on living inner knowledge of the world. All this is not clearly described in our histories of philosophy, although the discerning reader can have little doubt of it. The reason is that the thought-forms of this older philosophy are totally unlike today's thinking. Therefore anyone writing history nowadays is apt to put his own modern concepts into the minds of earlier thinkers. 48 Goethe's recital from Faust I, Act 1, Scene 2, “Night,” Gothic Room, Wagner and Faust: “My friend, the time of past Is a book with seven seals. What you call the Spirit of Time Is fundamentally the Gentleman's own spirit, In which the times reflect themselves.” But this is impermissible even with a man as recent as Spinoza. In his book on what he justifiably calls ethics, Spinoza follows a mathematical method but it is not mathematics in the modern sense. He expounds his philosophy in a mathematical style, joining idea to idea as a mathematician would. He still retains something of the former qualitative experience of quantitative mathematical concepts. Hence, even in contemplating the qualitative aspect of man's inner life, we can say that his style is mathematical. Today with our current concepts, it would be sheer nonsense to apply a mathematical style to psychology, let alone ethics. If we want to understand modern thinking, we must continually recall this uncertainty, contrasting it to the certainty that existed in the past but is no longer suited to our modern outlook. In the present phase of scientific thinking, we have come to the point where this uncertainty is not only recognized but theoretical justifications have been offered for it. And example is a lecture given by the French thinker Henri Poincaré 49 Henry Poincaré: Nancy 1854–1912 Paris. Author of the popular philosophical writings Science and Hypothesis (1902), The Value of Science (1905), Science and Method (1909), and Last Thoughts (1912). The lecture in question was held by Poincaré shortly before his death in a lecture cycle Conferences de Foi et de Vie printed in Le Materialisme Actuel with M.M. Bergson, H. Poincaré, Ch. Gide, Ch. Wagner, Firm Roz, De Witt-Guizotfriedel, Gaston Rion. (Paris: 1918), page 53. in 1912 on current ideas relating to matter. He speaks of the existing controversy or debate concerning the nature of matter; whether it should be thought of as being continuous or discrete; in other words, whether one should conceive of matter as substantial essence that fills space and is nowhere really differentiated in itself, or whether substance, matter, is to be thought of as atomistic, signifying more or less empty space containing within it minute particles that by virtue of their particular interconnections form into atoms, molecules, and so forth. Aside from what I might call a few decorative embellishments intended to justify scientific uncertainty, Poincaré's lecture comes down to this: Research and science pass through various periods. In one epoch, phenomena appear that cause the thinker to picture matter in a continuous form, making it convenient to conceive of matter this way and to focus on what shows up as continuity in the sense data. In a different period the findings point more toward the concept of matter being diffused into atoms, which are pictured as being fused together again; i.e. matter is not continuous but discrete and atomistic. Poincaré is of the opinion that always, depending on the direction that research findings take, there will be periods when thinking favors either continuity or atomism. He even speaks of an oscillation between the two in the course of scientific development. It will always be like this, he says, because the human mind has a tendency to formulate theories concerning natural phenomena in the most convenient way possible. If continuity prevails for a time, we get tired of it. (These are not Poincaré's exact words, but they are close to what he really intends.) Almost unconsciously, as it were, the human mind then comes upon other scientific findings and begins to think atomistically. It is like breathing where exhalation follows inhalation. Thus there is a constant oscillation between continuity and atomism. This merely results from a need of the human mind and according to Poincaré, says nothing about the things themselves. Whether we adopt continuity or atomism determines nothing about things themselves. It is only our attempt to come to terms with the external corporeal world. It is hardly surprising that uncertainty should result from an age which no longer finds self-experience in harmony with what goes on in the world but regards it only as something occurring inside man. If you no longer experience a living connection with the world, you cannot experience continuity or atomism. You can only force your preconceived notions of continuity or atomism on the natural phenomena. This gradually leads to the suspicion that we formulate our theories according to our changing needs. Just as we must breath in and out, so we must, supposedly, think first continuistically for a while, then atomistically for a while. If we always thought in the same way, we would not be able to catch a breath of mental air. Thus our fatal uncertainty is confirmed and justified. Theories begin to look like arbitrary whims. We no longer live in any real connection with the world. We merely think of various ways in which we might live with the world, depending on our own subjective needs. What would the old way of thought have said in such a case? It would have said: In an age when the leading thinkers think continuistically, they are thinking mainly of life. In one in which they think atomistically, they are thinking primarily of death, of inorganic nature, and they view even the organic in inorganic terms. This is no longer unjustified arbitrariness. This rests on an objective relationship to things. Naturally, I can take turns in dealing with the animate and the inanimate. I can say that the very nature of the animate requires that I conceive of it continuistically, whereas the nature of the inanimate requires that I think of it atomistically. But I cannot say that this is only due to the arbitrary nature of the human mind. On the contrary, it corresponds to an objective relating of oneself to the world. For such perception, the subjective aspect is really disregarded, because one recognizes the animate in nature in continual form and the inanimate in discrete form. And if one really has to oscillate between the two forms of thought, this can be turned in an objective direction by saying that one approach is suited to the living and the other is suited to the dead. But there is no justification for making everything subjective as Poincaré does. Nor is the subjective valid for the way of perception that belonged to earlier times. The gist of this is that in the phase of scientific thinking immediately preceding our own, there was a turn away from the animate to the inanimate; i.e., from continuity to atomism. This was entirely justified, if rightly understood. But, if we hope to objectively and truly find ourselves in the world, we must find a way out of the dead world of atomism, no matter how impressive it is as a theory. We must get back to our own nature and comprehend ourselves as living beings. Up to now, scientific development has tended in the direction of the inanimate, the atomistic. When, in the first part of the Nineteenth Century, this whole dreadful cell theory of Schleiden 50 Mathias Jakob Schleiden: Hamburg 1804–1881 Frankfurt A.M. Lawyer, physician, and, mainly, biologist. Developed a cell formation theory in Contributions to Phylogenesis (1838). and Schwann 51 Theodor Schwann: Neuss 1810–1882 Cologne, biologist. Founded the cell theory with his Microscopic Examinations of the Harmony in Structure and Growth of Animals and Plants (1839). made its appearance, it did not lead to continuity but to atomism. What is more, the scientific world scarcely admitted this, nor has it to this day realized that it should admit it since atomism harmonizes with the whole scientific methodology. We were not aware that by conceiving the organism as divided up into cells, we actually atomized it in our minds, which in fact signifies killing it. The truth of the matter is that any real idea of organisms has been lost to the atomistic approach. This is what we can learn if we compare Goethe's views on organics with those of Schleiden or the later botanists. In Goethe we find living ideas that he actually experiences. The cell is alive, so the others are really dealing with something organic, but the way they think is just as though the cells were not alive but atoms. Of course, empirical research does not always follow everything to its logical conclusion, and this cannot be done in the case of the organic world. Our comprehension of the organic world is not much aided by the actual observations resulting from the cell theory. The non-atomistic somehow finds its way in, since we have to admit that the cells are alive. But it is typical of many of today's scientific discussions that the issues become confused and there is no real clarity of thought.

The Origins of Natural Science

Lecture V

https://rsarchive.org/Lectures/GA326/English/AP1985/19221228p01.html

Dornach

28 Dec 1922

GA326-5

In my last lecture, I said that one root of the scientific world conception lay in the fact that John Locke and other thinkers of like mind distinguished between the primary and secondary qualities of things in the surrounding world. Locke called primary everything that pertains to shape, to geometrical and numerical characteristics, to motion and to size. From these he distinguished what he called the secondary qualities, such as color, sound, and warmth. He assigned the primary qualities to the things themselves, assuming that spatial corporeal things actually existed and possessed properties such as form, motion and geometrical qualities; and he further assumed that all secondary qualities such as color, sound, etc. are only effects on the human being. Only the primary qualities are supposed to be in the external things. Something out there has size, form and motion, but is dark, silent and cold. This produces some sort of effect that expresses itself in man's experiences of sound, color and warmth. I have also pointed out how, in this scientific age, space became an abstraction in relation to the dimensions. Man was no longer aware that the three dimensions — up-down, right-left, front-back — were concretely experienced within himself. In the scientific age, he no longer took this reality of the three dimensions into consideration. AS far as he was concerned, they arose in total abstraction. He no longer sought the intersecting point of the three dimensions where it is in fact experienced; namely, within man's own being. Instead, he looked for it somewhere in external space, wherever it might be. Thenceforth, this space framework of the three dimensions had an independent existence, but only an abstract thought-out one. This empty thought was no longer experienced as belonging to the external world as well as to man; whereas an earlier age experienced the three spatial dimensions in such a way that man knew he was experiencing them not only in himself but together with the nature of physical corporeality. The dimensions of space had, as it were, already been abstracted and ejected from man. They had acquired a quite abstract, inanimate character. Man had forgotten that he experiences the dimensions of space in his own being together with the external world; and the same applied to everything concerned with geometry, number, weight, etc. He no longer knew that in order to experience them in their full living reality, he had to look into his own inner being. A man like John Locke transferred the primary qualities — which are of like kind with the three dimensions of space, the latter being a sort of form or shape — into the external world only because the connection of these qualities with man's inner being was no longer known. The others, the secondary qualities, which were actually experienced qualitatively (as color, tone, warmth, smell or taste,) now were viewed as merely the effects of the things upon man, as inward experiences. But I have pointed out that inside the physical man as well as inside the etheric man these secondary qualities can no longer be found, so that they became free-floating in a certain respect. They were no longer sought in the outer world; they were relocated into man's inner being. It was felt that so long as man did not listen to the world, did not look at it, did not direct his sense of warmth to it, the world was silent. It had primary qualities, vibrations that were formed in a certain way, but no sound; it had processes of some kind in the ether, but no color; it had some sort of processes in ponderable matter (matter that has weight) — but it had no quality of warmth. As to these experienced qualities, the scientific age was really saying that it did not know what to do with them. It did not want to look for them in the world, admitting that it was powerless to do so. They were sought for within man, but only because nobody had any better ideas. To a certain extent science investigates man's inner nature, but it does not (and perhaps cannot) go very far with this, hence it really does not take into consideration that these secondary qualities cannot be found in this inner nature. Therefore it has no pigeonhole for them. Why is this so? Let us recall that if we really want to focus correctly on something that is related to form, space, geometry or arithmetic, we have to turn our attention to the inward life-filled activity whereby we build up the spatial element within our own organism, as we do with above-below, back-front, left-right. Therefore, we must say that if we want to discover the nature of geometry and space, if we want to get to the essence of Locke's primary qualities of corporeal things, we must look within ourselves. Otherwise, we only attain to abstractions. In the case of the secondary qualities such as sound, color, warmth, smell and taste, man has to remember that his ego and astral body normally dwell within his physical and etheric bodies but during sleep they can also be outside the physical and etheric bodies. Just as man experiences the primary qualities, such as the three dimensions, not outside but within himself during full wakefulness, so, when he succeeds (whether through instinct or through spiritual-scientific training) in really inwardly experiencing what is to be found outside the physical and etheric bodies from the moment of falling asleep to waking up, he knows that he is really experiencing the true essence of sound, color, smell, taste, and warmth in the external world outside his own body. When, during the waking condition, man is only within himself, he cannot experience anything but picture-images of the true realities of tone, color, warmth, smell and taste. But these images correspond to soul-spirit realities, not physical-etheric ones. In spite of the fact that what we experience as sound seems to be connected with certain forms of air vibrations, just as color is connected with certain processes in the colorless external world, it still has to be recognized that both are pictures, not of anything corporeal, but of the soul-spirit element contained in the external world. We must be able to tell ourselves: When we experience a sound, a color, a degree of warmth, we experience an image of them. But we experience them as reality, when we are outside our physical body. We can portray the facts in a drawing as follows: Man experiences the primary qualities within himself when fully awake, and projects them as images into the outer world. If he only knows them in the outer world, he has the primary qualities only in images (arrow in sketch). These images are the mathematical geometrical, and arithmetical qualities of things. It is different in the case of the secondary qualities. (The horizontal lines stand for the physical and etheric body of man, the red shaded area for the soul-spirit aspect, the ego and astral body.) Man experiences them outside his physical and etheric body, 53 One can find the basic reality explained in the chapter “Sleep and Death” in An Outline Of Occult Science and in Knowledge of the Higher Worlds and Its Attainment (Spring Valley, NY: Anthroposophic Press, 1983). and projects only the images into himself. Because the scientific age no longer saw through this, mathematical forms and numbers became something that man looked for abstractly in the outer world. The secondary qualities became something that man looked for only in himself. But because they are only images in himself, man lost them altogether as realities. As few isolated thinkers, who still retained traditions of earlier views concerning the outer world, struggled to form conceptions that were truer to reality than those that, in the course of the scientific age, gradually emerged as the official views. Aside from Paracelsus, 54 Paracelsus, Theophrastus von Hohenheim: Einsiedein, Kanton Schwytz 1493–1541 Salzburg, Md. Ferrara, Professor in Basel. Accomplished physician, scientist, and philosopher. Wrote about chemistry, medical science, biology, astronomy, astrology, alchemy, and theology. The myths about Paracelsus as goldmaker, magician, or charlatan were made up after his death and distorted the picture of his character. Most complete work published by Karl Sudhoff (fourteen volumes). See Riddles of Philosophy . there was, for example, van Helmont, 55 Helmont, Johann Baptist van: Brussels 1577–1644. Physician and iatrochemist. He managed the differentiation and separation of gases (hydrogen, carbon). He coined the name “gas” for the airy state. who was well aware that man's spiritual element is active when color, tone, and so forth are experienced. During the waking state, however, the spiritual is active only with the aid of the physical body. Hence it produces only an image of what is really contained in sound or color. This leads to a false description of external reality; namely, that purely mathematical-mechanistic form of motion for what is supposed to be experienced as secondary qualities in man's inner being, whereas, in accordance with their reality, their true nature, they can only be experienced outside the body. We should not be told that if we wish to comprehend the true nature of sound, for example, we ought to conduct physical experiments as to what happens in the air that carries us to the sound that we hear. Instead, we should be told that if we want to acquaint ourselves with the true nature of sound, we have to form an idea of how we really experience sound outside our physical and etheric bodies. But these are thoughts that never occurred to the men of the scientific age. They had no inclination to consider the totality of human nature, the true being of man. Therefore they did not find either mathematics or the primary qualities in this unknown human nature; and they did not find the secondary qualities in the external world, because they did not know that man belongs to it also. I do not say that one has to be clairvoyant in order to gain the right insight into these matters, although a clairvoyant approach would certainly produce more penetrating perceptions in this area. But I do say that a healthy and open mind would lead one to place the primary qualities, everything mathematical-mechanical, into man's inner being, and to place the secondary qualities into the outer world. The thinkers no longer understand human nature. They did not know how man's corporeality is filled with spirit, or how this spirit, when it is awake in a person, must forget itself and devote itself to the body if it is to comprehend mathematics. Nor was it known that this same spirituality must take complete hold of itself and live independently of the body, outside the body, in order to come to the secondary qualities. Concerning all these matters, I say that clairvoyant perception can give greater insight, but it is not indispensable. A healthy and open mind can feel that mathematics belongs inside, while sound, color, etc. are something external. In my notes on Goethe's scientific works 56 See Steiner, Goethe the Scientist . Especially see Chapters 7, 8, 9, 10, 11, 12, 15. in the 1880's, I set forth what healthy feeling can do in this direction. I never mentioned clairvoyant knowledge, but I did show to what extent man can acknowledge the reality of color, tone, etc. without any clairvoyant perception. This has not yet been understood. The scientific age is still too deeply entangled in Locke's manner of thinking. I set it forth again, in philosophic terms, in 1911 at the Philosophic Congress in Bologna. 57 Lecture of April 8, 1911, at the 9th International Philosophical Congress, “The Psychological Foundations of Anthroposophy,” in Rudolf Steiner, Esoteric Development , Spring Valley, NY: 1982), pp. 25–55. And again it was not understood. I tried to show how man's soul — spirit organization does indeed indwell and permeate the physical and etheric body during the waking state, but still remains inwardly independent. If one senses this inward independence of the soul and spirit, then on also has a feeling for what the soul and spirit have experienced during sleep about the reality of green and yellow, G and C-sharp, warm and cold, sour or sweet. But the scientific age was unwilling to go into a true knowledge of man. This description of the primary and secondary qualities shows quite clearly how man got away from the correct feeling about himself and his connection to the world. The same thing comes out in other connections. Failing to grasp how the mathematical with its three-dimensional character dwells in man, the thinkers likewise could not understand man's spirituality. They would have had to see how man is in a position to comprehend right-left by means of the symmetrical movements of his arms and hands and other symmetrical movements. Through sensing the course taken, for example, by his food, he can experience front-back. He experiences up-down as he coordinates himself in this direction in his earliest years. If we discern this, we see how man inwardly unfolds the activity that produces the three dimensions of space. Let me point out also that the animal does not have the vertical direction in the same way as man does, since its main axis is horizontal, which is what man can experience as front-back. The abstract space framework could no longer produce anything other than mathematical, mechanistic, abstract relationships in inorganic nature. It could not develop an inward awareness of space in the animal or in man. Thus no correct opinion could be reached in this scientific age concerning the question: How does man relate to the animal, the animal to man? What distinguishes them from one another? It was still dimly felt that there was a difference between the two, hence one looked for the distinguishing features. But nothing could be found in either man or animal that was decisive and consistent. Here is a famous example: It was asserted that man's upper jawbone, in which the upper teeth are located, was in one piece, whereas in the animal, the front teeth were located in a separate one, the inter-maxillary bone, with the actual upper jawbone on either side of them. Man, it was thought, did not possess this inter-maxillary bone. Since one could no longer find the relationship of man to animal by inner soul-spirit means, one looked for it in such external features and said that the animal had an inter-maxillary bone and man did not. Goethe could not put into words what I have said today concerning primary and secondary qualities. But he had a healthy feeling about all these matters. He knew instinctively that the difference between man and animals must lie in the human form as a whole, not in any single feature. This is why Goethe opposed the idea that the inter-maxillary bone is missing in man. As a young man, he wrote an important article suggesting that there is an inter-maxillary bone in man as well as in the animal. He was able to prove this by showing that in the embryo the inter-maxillary bone is still clearly evident in man although in early childhood this bone fuses with the upper jaw, whereas it remains separate in the animal. Goethe did all this out of a certain instinct, and this instinct led him to say that one must not seek the difference between man and animal in details of this kind; instead, it must be sought for in the whole relation of man's form, soul, and spirit to the world. By opposing the naturalists who held that man lacks the inter-maxillary bone Goethe brought man close to the animal. But he did this in order to bring out the true difference as regards man's essential nature. Goethe's approach out of instinctive knowledge put him in opposition to the views of orthodox science, and this opposition has remained to this day. This is why Goethe really found no successors in the scientific world. On the contrary, as a consequence of all that had developed since the Fifteenth Century in the scientific field, in the Nineteenth Century the tendency grew stronger to approximate man to the animal. The search for a difference in external details diminished with the increasing effort to equate man as nearly as possible with the animal. This tendency is reflected in what arose later on as the Darwinian idea of evolution. This found followers, while Goethe's conception did not. Some have treated Goethe as a kind of Darwinist, because all they see in him is that, through his work on the inter-maxillary bone, 58 See Steiner, Goethe the Scientist . he brought man nearer to the animal. But they fail to realize that he did this because he wanted to point out (he himself did not say so in so many words, but it is implicit in his work) that the difference between man and animal cannot be found in these external details. Since one no longer knew anything about man, one searched for man's traits in the animal. The conclusion was that the animal traits are simply a little more developed in man. As time went by, there was no longer any inkling that even in regard to space man had a completely different position. Basically, all views of evolution that originated during the scientific age were formulated without any true knowledge of man. One did not know what to make of man, so he was simply represented as the culmination of the animal series. It was a though one said: Here are the animals; they build up to a final degree of perfection, a perfect animal; and this perfect animal is man. My dear friends, I want to draw your attention to how matters have proceeded with a certain inner consistency in the various branches of scientific thinking since its first beginnings in the Fifteenth Century; how we picture our relation to the world on the basis of physics, of physiology, by saying: Out there is a silent and colorless world. It affects us. We fashion the colors and sounds in ourselves as experiences of the effects of the outer world. At the same time we believe that the three dimensions of space exist outside of us in the external world. We do this, because we have lost the ability to comprehend man as a whole. We do this because our theories of animal and man do not penetrate the true nature of man. Therefore, in spite of its great achievements we can say that science owes its greatness to the fact that it has completely missed the essential nature of man. We were not really aware of the extent to which science was missing this. A few especially enthusiastic materialistic thinkers in the Nineteenth Century asserted that man cannot rightly lay claim to anything like soul and spirit because what appears as soul and spirit is only the effect of something taking place outside us in time and space. Such enthusiasts describe how light works on us; how something etheric (according to their theory) works into us through vibrations along our nerves; how the external air also continues on in breathing, etc. Summing it all up, they said that man is dependent on every rise and fall of temperature, on any malformation of his nervous system, etc. Their conclusion was that man is a creature pitifully dependent on every draft or change of pressure. Anyone who reads such descriptions with an open mind will notice that, instead of dealing with the true nature of man, they are describing something that turns man into a nervous wreck. The right reply to such descriptions is that a man so dependent on every little draft of air is not a normal person but a neurasthenic. But they spoke of this neurasthenic as if he were typical. They left out his real nature, recognizing only what might make him into a neurasthenic. Through the peculiar character of this kind of thinking about nature, all understanding was gradually lost. This is what Goethe revolted against, though he was unable to express his insights in clearly formulated sentences. Matters such as these must be seen as part of the great change in scientific thinking since the Fifteenth Century. Then they will throw light on what is essential in this development. I would like to put it like this: Goethe in his youth took a keen interest in what science had produced in its various domains. He studied it, he let it stimulate him, but he never agreed with everything that confronted him, because in all of it he sensed that man was left out of consideration. He had an intense feeling for man as a whole. This is why he revolted in a variety of areas against the scientific views that he saw around him. It is important to see this scientific development since the Fifteenth Century against the background of Goethe's world conception. Proceeding from a strictly historical standpoint, one can clearly perceive how the real being of man is missing in the scientific approach, missing in the physical sciences as well as in the biological. This is a description of the scientific view, not a criticism. Let us assume that somebody says: “Here I have water. I cannot use it in this state. I separate the oxygen from hydrogen, because I need the hydrogen.” He then proceeds to do so. If I then say what he has done, this is not criticism of his conduct. I have no business to tell him he is doing something wrong and should leave the water alone. Nor is it criticism, when I saw that since the Fifteenth Century science has taken the world of living beings and separated from it the true nature of man, discarding it and retaining what this age required. It then led this dehumanized science to the triumphs that have been achieved. It is not a criticism if something like this is said; it is only a description. The scientist of modern times needed a dehumanized nature, just as chemist needs deoxygenized hydrogen and therefore has to split water into its two components. The point is to understand that we must not constantly fall into the error of looking to science for an understanding of man.

The Origins of Natural Science

Lecture VI

https://rsarchive.org/Lectures/GA326/English/AP1985/19230101p01.html

Dornach

1 Jan 1923

GA326-6

Continuing with yesterday's considerations concerning the inability of the scientific world conception to grasp the nature of man, we can say that in all domains of science something is missing that is also absent in the mathematical-mechanistic sphere. This sphere has been divorced from man, as if man were absent from the mathematical experience. This line of thought results in a tendency to also separate other processes in the world from man. This in its turn produces an inability to create a real bridge between man and world. I shall discuss another consequence of this inability later on. Let us focus first of all on the basic reason why science has developed in this way. It was because we lost the power to experience inwardly something that is spoken of in Anthroposophy today and that in former times was perceived by a sort of instinctive clairvoyance. Scientific perception has lost the ability to see into man and grasp how he is composed of different elements. Let us recall the anthroposophical idea that man is composed of four members — the physical body, the etheric body, the astral body and the I-organization. I need not go into detail about this formation, since you can find it all in my book Theosophy . 59 Rudolf Steiner, Theosophy (Spring Valley, NY: Anthroposophic Press, 1971), pp. 1–39. When we observe the physical body and consider the possibility of inward experiencing one's physical body — we should begin by asking: What do we experience in regard to it? We experience what I have frequently spoken about recently; namely, the right-left, up-down, and front-back directions. We experience motion, the change of place of one's own body. To some extent at least, we also experience weight in various degrees. But weight is experienced in a highly modified form. When these things were still experienced within our various members, we reflected on them a good deal; but in the scientific age, no one gives them any thought. Facts that are of monumental importance for a world comprehension are completely ignored. Take the following fact. Assume that you have to carry a person who weighs as much as you do. Imagine that you carry this person a certain distance. You will consciously experience his weight. Of course, as you walk this distance, you are carrying yourself as well. But you do not experience this in the same way. You carry your own weight through space, but you do not experience this. Awareness of one's own weight is something quite different. In old age, we are apt to say that we feel the weight of our limbs. To some extent this is connected with weight, because old age entails a certain disintegration of the organism. This in turn tears the individual members out of the inward experience and makes them independent — atomizes them, as it were — and in atomization they fall a prey to gravity. But we do not actually feel this at any given moment of our life, so this statement that we feel the weight of our limbs is really only a figure of speech. A more exact science might show that it is not purely figurative, but be that as it may, the experience of our weight does not impinge strongly on our consciousness. This shows that we have an inherent need to obliterate certain effects that are unquestionably working within us. We obliterate them by means of opposite effects (“opposite” in the sense brought out by the analogy between man and the course of the year in my recent morning lectures. 60 Rudolf Steiner, Man and the World of Stars: The Spiritual Communion of Mankind (New York: Anthroposophic Press, 1963), pp. 141–172. Nevertheless, whether we are dealing with processes that can be experienced relatively clearly, such as the three dimensions or motion, or with less obvious ones such as those connected with weight, they are all processes that can be experienced in the physical body. What was thus experienced in former times has since been completely divorced from man. This is most evident in the case of mathematics. The reason it is less obvious in other experiences of the physical body is that the corresponding processes in the body, such as weight or gravity, are completely extinguished for today's form of consciousness. These processes, however, were not always completely obliterated. Under the influence of the mood prevailing under the scientific world conception, people today no longer have any idea of how different man's inner awareness was in the past. True, he did not consciously carry his weight through space in former times. Instead, he had the feeling that along with this weight, there was a counterweight. When he learned something, as was the case with the neophytes in the mysteries, he learned to perceive how, while he always carried his own weight in and with himself, the counter-effect is constantly active in light. It can really be said that man felt that he had to thank the spiritual element indwelling the light for counteracting, within him, the soul-spirit element activity in gravity. In short, we can show in many ways that in older times there was no feeling that anything was completely divorced from man. Within himself, man experienced the processes and events as they occurred in nature. When he observed the fall of a stone, for example, in external nature (an event physically separated from him) he experienced the essence of movement. He experienced this by comparing it with what such a movement would be like in himself. When he saw a falling stone, he experienced something like this: “If I wanted to move in the same way, I would have to acquire a certain speed, and in a falling stone the speed differs from what I observe, for instance, in a slowly crawling creature.” He experienced the speed of the falling stone by applying his experience of movement to the observation of the falling stone. The processes of the external world that we study in physics today were in fact also viewed objectively by the man of former times, but he gained his knowledge with the aid of his own experiences in order to rediscover in the external world the processes going on within himself. Until the beginning of the Fifteenth Century, all the conceptions of physics were pervaded by something of which one can say that it brought even the physical activities of objects close to the inner life of man. Man experienced them in unison with nature. But with the onset of the Fifteenth Century begins the divorce of the observation of such processes from man. Along with it came the severance of mathematics, a way of thinking which from then on was combined with all science. The inner experience in the physical body was totally lost. What can be termed the inner physics of man was lost. External physics was divorced from man, along with mathematics. The progress thereby achieved consisted in the objectifying of the physical. What is physical can be looked at in two ways. Staying with the example of the falling stone, it can be traced with external vision. It can also be brought together with the experience of the speed that would have to be achieved if one wanted to run as fast as the stone falls. This produces comprehension that goes through the whole man, not one related only to visual perception. To see what happened to the older world view at the dawn of the Fifteenth Century, let us look at a man in whom the transition can be observed particularly well; namely, Galileo. 61 Galileo Galilei: Pisa 1564–1642 Arcetri by Florence. Discovered isochromism in pendulum, hydrostatic scales, laws of free fall, law of inertia. Numerous astronomical inventions with self-constructed telescope. An Inquisition trial resulted in a banning of the Copernican world system. See Riddles of Philosophy , The Spiritual Guidance of Man , and Laurenz Muellner's speech, “ Die Bedeutung Galilei's fuer die Philosophie ,” Vienna 1894. (Reprinted in Anthroposophie , 1933/34:29). His Sermons de Motu Gravium ( About the Effects of Gravity ) contain the results of his investigations in Pisa. They first only circulated in manuscript copies; first edition: 1854. The final version is in the Discorsi e Dimenstrazioni Mathematiche Intomo a Due Nuove Scieme , published 1638 in Leyden. Also see L. Muellner's speech. Galileo is in a sense the discoverer of the laws governing falling objects. Galileo's main aim was to determine the distance traveled in the first second by a falling body. The older world view placed the visual observation of the falling stone side by side with the inward experience of the speed needed to run at an equal pace. The inner experience was placed alongside that of the falling stone. Galileo also observed the falling stone, but he did not compare it with the inward experience. Instead, he measured the distance traveled by the stone in the first second of its fall. Since the stone falls with increasing speed, Galileo also measured the following segments of its path. He did not align this with any inward experience, but with an externally measured process that had nothing to do with man, a process that was completely divorced from man. Thus, in perception and knowledge, the physical was so completely removed from man that he was not aware that he had the physical inside him as well. At that time, around the beginning of the Seventeenth Century, a number of thinkers who wanted to be progressive began to revolt against Aristotle, 62 Such opponents were Bacon, Bruno, Galilei. See Riddles of Philosophy and the speech of L. Muellner, p. 103. who throughout the Middle Ages had been considered the preeminent authority on science. If Aristotle's explanations of the falling stone (misunderstood in most cases today) are looked at soberly, we notice that when something is beheld in the world outside, he always points out how it would be if man himself were to undergo the same process. For him, it is not a matter of determining a given speed by measuring it, but to think of speed in such a way that it can be related to some human experience. Naturally, if you say you must achieve a particular speed, you feel that something alive, something filled with vigor, will be needed for you to do this. You feel a certain inner impetus, and the last thing you would assume is that something is pulling you in the direction you were heading. You would think that you were pushing, not that you were being pulled. This is why the force of attraction, gravity, begins to mean something only in the Seventeenth Century. Man's idea about nature began to change radically; not just the law of falling bodies, but all the ideas of physics. Another example is the law of inertia, it is generally called. The very name reveals its origin within man. (There is a play on words here. The German term for inertia, Trägheit , really means laziness.) Inertia is something that can be inwardly felt but what has become of the law of inertia in physics under the influence of “Galileoism?” the physicist says: A body, or rather a point, on which no external influence is exercises, which is left to itself, moves through space with uniform velocity. This means that throughout all time-spans it travels the same distance in each second. If no external influence interferes, and the body has achieved a given speed per second, it travels the same distance in each succeeding second. It is inert. Lacking an external influence, it continues on and on without change. All the physicist does is measure the distance per second, and a body is called inert if the velocity remains constant. There was a time when one felt differently about this and asked: How is a moving body, traveling a constant distance per second, experienced? It could be experienced by remaining on one and the same condition without ever changing one's behavior. At most, this could only be an ideal for man. He can attain this ideal of inertia only to a very small degree. But if you look at what is called inertia in ordinary life, you see that it is pretty much like doing the same thing every second of your life. From the Fifteenth Century on, the whole orientation of the human mind was led to such a point that we can fairly say that man forgot his own inward experience. This happens first with the inner experience of the physical organism — man forgets it. What Galileo thought out and applied to matters close to man, such as the law of inertia, was not applied in a wide context. And it was indeed merely thought out, even if Galileo was dealing with things that can be observed in nature. We know how, by placing the sun in the center instead of the earth, and by letting the planets move in circles around the sun, and by calculating the position of a given planetary body in the heavens, Copernicus produced a new cosmic system in a physical sense. This was the picture that Copernicus drew of our planetary, our solar system. And it was a picture that certainly can be drawn. Yet, this picture did not make a radical turn toward the mathematical attitude that completely divorces the external world from man. Anyone reading Copernicus's text gets the impression that Copernicus still felt the following. In the complicated lines, by means of which the earlier astronomy tried to grasp the solar system, it not only summed up the optical locations of the planets; it also had a feeling for what would be experienced if one stood amid these movements of the planets. In former ages people had a very clear idea of the epicycles the planets were thought to describe. In all this there was still a certain amount of human feeling. Just as you can understand the position of, let us say, an arm when you are painting a picture of a person because you can feel what it is like to be in such a position, so there was something alive in tracing the movement described by a planet around its fixed star. Indeed, even in Kepler's 63 Johannes Kepler: Weil der Stadt (Wuerttemberg) 1571–1630 Regensburg. Mathematician, physicist, astronomer, discoverer of the astronomical telescope. Astronomer and mathematician to three emperors. Persecuted as a Protestant. Totally exhausted through his life misery, he died prematurely at the “Reichstag” at Regensburg, where he hoped to secure his subsistence. To calculate his three laws of the motion of the planets he used the observation data of Tycho Brahe, whose follower he was at the court of Prague. On the other hand, the Copernican planetary system was the starting point for the finding of the three laws of the planets. Kepler was the first who tried to interpret the motion of the planetary orbit and moved the center of force to the sun. See The Spiritual Guidance of Man and, about the three planetary laws Das Verhaeltnis der Verschiedenen Naturwissenschaftlichen Gebiete zur Astronomie (Dornach: Rudolf Steiner Verlag, 1981), GA Bibl. Nr. 323. case — perhaps especially in his case — there is still something of a human element in his calculating the orbits described by the planets. Now Newton applies Galileo's abstracted principle to the heavenly bodies, adopting something like the Copernican view and conceiving things somewhat as follows: A central body, let us say a sun, attracts a planet in such a way that this force of attraction decreases in proportion to the square of the distance. It becomes smaller and smaller in proportion to the square, but increases in proportion to the mass of the bodies. If the attracting body has a greater mass, the force of attraction is porportionately greater. If the distance is greater, the force of attraction decreases, but always in such a way that if the distance is twice as great, the attraction is four times less; if it is three times as great, nine times less, and so forth. Pure measuring is instilled into the picture, which, again, is conceived as completely abstracted from man. This was not yet so with Copernicus and Kepler but with Newton, a so-called “objective” something is excogitated and there is no longer any experience, it is all mere excogitation. Lines are drawn in the direction in which one looks and forces are, as it were, imagined into them, since what one sees is not force; the force has to be dreamed up. Naturally, one says “thought up” as long as one believes in the whole business; but when one no longer has faith in it, one says, “dreamed up.” Thus we can say that through Newton the whole abstracted physical mode of conception becomes generalized so far that is applied to the whole universe. In short, the aim is to completely forget all experience within man's physical body; to objectify what was formerly pictured as closely related to the experience of the physical body; to view it in outer space independent of the physical corporeality, although this space had first been torn out of the body experience; and to find ways to speak of space without even thinking about the human being. Through separation from the physical body, through separation of nature's phenomena from man's experience in the physical body, modern physics arises. It comes into existence along with this separation of certain processes of nature from self-experience within the physical human body (yellow in sketch). Self experience is forgotten (red in Fig. 1) By permeating all external phenomena with abstract mathematics, this kind of physics could not longer understand man. What had been separated from man could not be reconnected. In short, there emerges a total inability to bring science back to man. In physical respects you do not notice this quite so much; but you do notice it if you ask: What about man's self-experience in the etheric body, in this subtle organism? Man experiences quite a bit in it. But this was separated from man even earlier and more radically. This abstraction, however, was not as successful as in physics. Let us go back to a scientist of the first Christian centuries, the physician Galen. 64 Galen: Pergamon, Asia Minor 129 A.D.–199 Rome. Physician and philosopher. Studies in Pergamon and travel for study to Corinth, Smyrna, and Alexandria. Personal physician of Emperor Marcus Aurelius. His one hundred and fifty medical texts with fifteen commentaries were the basis for future medicine and pharmacology. One hundred twenty-five texts concerning philosophy, mathematics, and jurisprudence. Looking at what lived in external nature and following the traditions of his time, Galen distinguished four elements — earth, water, air and fire (we would say warmth.) We see these if we look at nature. But, looking inward and focusing on the self-experience of the etheric body, 65 Rudolf Steiner, A Road to Self Knowledge: The Threshold of the Spiritual World (London: Rudolf Steiner Press, 1975), pp. 19–27,100–106. one asks: How do I experience these elements, the solid, the watery, the airy and the fiery in myself? Then, in those times the answer was: I experience them with my etheric body. One experienced it as inwardly felt movements of the fluids; the earth as “black gall,” the watery as “phlegm,” the airy as “pneuma” (what is taken in through the breathing process,) and warmth as “blood.” In the fluids, in what circulates in the human organism, the same thing was experienced as what was observed externally. Just as the movement of the falling stone was accompanied by an experience in the physical body, so the elements were experienced in inward processes. The metabolic process, where (so it was thought) gall, phlegm, and blood work into each other, was felt as the inner experience of one's own body, but a form of inward experience to which corresponded the external processes occurring between air, water, fire and earth. Warmth -Blood -Ego Organization Air -Pneuma -Astral Body Water -Phlegm -Etheric Body -Chemistry Earth -Black Gall -Physical body -Physics Here, however, we did not succeed in completely forgetting all inner life and still satisfying external observation. In the case of a falling body, one could measure something; for example, the distance traveled in the first second. One arrived at a “law of inertia” by thinking of moving points that do not alter their condition of movement but maintain their speed. By attempting to eject from the inward experience something that the ancients strongly felt to be a specific inner experience; namely, the four elements, one was able to forget the inner content but one could not find in the external world any measuring system. Therefore the attempt to objectify what related to these matters, as was done in physics, remained basically unsuccessful to this day. Chemistry could have become a science that would rank alongside physics, if it had been possible to take as much of the etheric body into the external world as was accomplished in the physical body. In chemistry, however, unlike physics, we speak to this day of something rather undefined and vague, when referring to its laws. 66 This is confirmed in chemical textbooks. They speak of chemistry as “a primarily empirical science.” In its laws one cannot come to mathematically definite values but to approximate numbers, whose limits are defined in tabular form. Therefore authors of chemical subject books need to add limiting explanations, such as “usually is valid,” or “generally one can say.” Chemical laws are mostly derived from physical laws, as for instance in the main theses of thermodynamics. It is thought unscientific to think otherwise than mechanically. Literature: H. Remy, Lehrbuch der Anorganischen Chemie , 7th ed., 2 vols. (Leipzig: 1954), Volume I, pages 14–23, 37, 50, 71–73. What was done with physics in regard to the physical body was in fact the aim of chemistry in regard to the etheric body. Chemistry states that if substances combine chemically, and in doing so can completely alter their properties, something is naturally happening. But if one wants to go beyond this conception, which is certainly the simplest and most convenient, one really does not know much about this process. Water consists of hydrogen and oxygen; the two must be conceived as mixed together in the water somehow but no inwardly experiencable concept can be formed of this. It is commonly explained in a very external way: hydrogen consists of atoms (or molecules if you will) and so does oxygen. These intermingle, collide, and cling to one another, and so forth. This means that, although the inner experience was forgotten, one did not find oneself in the same position as in physics, where one could measure (and increasingly physics became a matter of measuring, counting and weighing.) Instead, one could only hypothesize the inner process. In a certain respect, it has remained this way in chemistry to this day, because what is pictured as the inner nature of chemical processes is basically only something read into them by thought. Chemistry will attain the level of physics only when with full insight into these matters, we can again relate chemistry with man, though not, of course, with the direct experience possessed by the old instinctive clairvoyance. We will only succeed in this when we gain enough insight into physics to be able to consolidate our isolated fragments of knowledge into a world conception and bring our thoughts concerning the individual phenomena into connection with man. What happens on one side, when we forget all inner experience and concentrate on measuring externals (thus remaining stuck in the so-called “objective”) takes its revenge on the other side. It is easy enough to say that inertia is expressed by the movement of a point that travels the same distance in each succeeding second. But there is no such point. This uniform movement occurs nowhere in the domain of human observation. A moving object is always part of some relationship, and its velocity is hampered here or there. In short, what could be described as inert mass, 67 See Georg Unger, Vom Bilden Physicalischer Begriffe , Volume 1, pages 41–49 and 57. or could be reduced to the law of inertia, does not exist. If we speak of movement and cannot return to the living inner accompanying experience of it, if we cannot relate the velocity of a falling body to the way we ourselves would experience this movement, then we must indeed say that we are entirely outside the movement and must orient ourselves by the external world. If I observe a moving body (see Fig. 7) and if these are its successive positions, I must somehow perceive that this body moves. If behind it there is a stationary wall, I follow the direction of movements and tell myself that the body moves on in that direction. But what is necessary in addition is that from my own position (dark circle) I guide this observation, in other words, become aware of an inward experience. If I completely leave out the human being and orient myself only out there, then, regardless of whether the object moves or remains stationary, while the wall moves, the result will be the same. I shall no longer be able to distinguish whether the body moves in one or the wall behind it in the opposite direction. I can basically make all the calculations under either one or the other assumption. I lose the ability to understand a movement inwardly if I do not partake of it with my own experience. This applies, if I may say so, to many other aspects of physics. Having excluded the participating experience, I am prevented from building any kind of bridge to the objective process. If I myself am running, I certainly cannot claim that it is a matter of indifference whether I run or the ground beneath me moves in the opposite direction. But if I am watching another person moving over a given area, it makes no difference for merely external observation whether he is running or the ground beneath him is moving in the opposite direction. Our present age has actually reached the point, where we experience, if I may put it this way, the world spirit's revenge for our making everything physical abstract. Newton was still quite certain that he could assume absolute movements, but now we can see numerous scientists trying to establish the fact that movement, the knowledge of movement, has been lost along with the inner experience of it. Such is the essence of the Theory of Relativity, 68 See Footnote 40. which is trying to pull the ground from under Newtonism. This theory of relativity is a natural historical result. It cannot help but exist today. We will not progress beyond it if we remain with those ideas that have been completely separated from the human element. If we want to understand rest or motion, we must partake in the experience. If we do not do this, then even rest and motion are only relative to one another.

The Origins of Natural Science

Lecture VII

https://rsarchive.org/Lectures/GA326/English/AP1985/19230102p01.html

Dornach

2 Jan 1923

GA326-7

I have tried to show how various domains of scientific thought originated in modern times. Now I will try to throw light from a certain standpoint on what was actually happening in the development of these scientific concepts. Then we shall better understand what these concepts signify in the whole evolutionary process of mankind. We must clearly understand that the phenomena of external culture are inwardly permeated by a kind of pulse beat that originates from deeper insights. Such insights need not always be ones that are commonly taught, but still they are at the bottom of the development. Now, I would only like to say that we can better understand what we are dealing with in this direction if we include in our considerations what in certain epochs was practiced as initiation science, a science of the deeper foundations of life and history. We know that the farther we go back in history, 69 Steiner, The Boundaries of Natural Science , pp. 59–87. Chapters 5 and 6, as well as 7 and 8. the more we discover an instinctive spiritual knowledge, an instinctive clairvoyant perception of what goes on behind the scenes. Moreover, we know that it is possible in our time to attain to a deeper knowledge, because since the last third of the Nineteenth Century, after the high tide of materialistic concepts and feelings, simply through the relationship of the spiritual world to the physical, the possibility arose to draw spiritual knowledge once again directly from the super-sensible world. Since the last third of the Nineteenth Century, it has been possible to deepen human knowledge to the point where it can behold the foundations of what takes place in the external processes of nature. So we can say that an ancient instinctive initiation science made way for an exoteric civilization in which little was felt of any direct spirit knowledge, but now it is fully conscious rather than instinctive. We stand at the beginning of this development of a new spirit knowledge. It will unfold further in the future. If we have a certain insight into what man regarded as knowledge during the age of the old instinctive science of initiation, we can discover that until the beginning of the Fourteenth Century, opinions prevailed in the civilized world that cannot be directly compared with any of our modern conceptions about nature. They were ideas of quite a different kind. Still less can they be compared with what today's science calls psychology. There too, we would have to say that it is of quite a different kind. The soul and spirit of man as well as the physical realm of nature were grasped in concepts and ideas that today are understood only by men who specifically study initiation science. The whole manner of thinking and feeling was quite different in former times. If we examine the ancient initiation science, we find that, in spite of the fragmentary ways in which it has been handed down, it had profound insights, deep conceptions, concerning man and his relation to the world. People today do not greatly esteem a work like De Divisione Naturae (Concerning the Division of Nature) by John Scotus Erigena 70 Johannes Scotus Erigena: also Eriugena, Ireland 810–877 France. Pre-Scholastic philosopher, theologian with extensive comprehension of language. Came from Britain to France. Led the Emperor's Academy in Paris 845–877. Finished his translation of Dionysius the Areopagite in 858. His main work was De Divisione Naturae ( Division of Nature ), 867. He taught out of a Platonic comprehension. He stood up for the introduction of the hierarchical order in the worldly administration of the church. See also Mysticism at the Dawn of the Modern Age . in the Ninth Century. They do not bother with it because such a work is not regarded as an historical document since it comes from a time when men thought differently from the way they think today, so differently that we can no longer understand such a book. When ordinary philosophers describe such topics in their historical writings, one is offered mere empty words. Scholars no longer enter into the fundamental spirit of a work such as that of John Scotus Erigena on the division of nature, where even the term nature signifies something other than in modern science. If, with the insight of spiritual science, we do enter into the spirit of such a text, we must come to the following rather odd conclusion: This Scotus Erigena developed ideas that give the impression of extraordinary penetration into the essence of the world, but he presented these ideas in an inadequate and ineffective form. At the risk of speaking disrespectfully of a work that is after all very valuable, one has to say that Erigena himself no longer fully understood what he was writing about. One can see that in his description. Even for him, though not to the same extent as with modern historians of philosophy, the words that he had gleaned from tradition were more or less words only, and he could no longer enter into their deeper meaning. Reading his works, we find ourselves increasingly obliged to go farther back in history. Erigena's writings lead us directly back to those of the so-called pseudo-Dionysius the Areopagite. 71 The copy in Greek originated in the fifteenth century. Dionysius was a member of the Areopag in Athens and a student of the Apostle Paul (Acts 17:34). The setting up of the 3 times 3 hierarchies by Dionysius was adapted as dogma by the Catholic church. His writings in Latin translation were taken up enthusiastically, and were still taken as authentic in the seventeenth century. See Riddles of Philosophy , The Redemption of Thinking , Die Ursprungsimpulse der Geisteswissenschaft (Dornach: Rudolf Steiner Verlag, 1974), GA Bibl. Nr. 96, and Otto Willmann, Geschichte des Idealismus , Volume II, paragraph 59. I will now leave aside the historical problem of when Dionysius lived, and so forth. But again from Dionysius the Areopagite one is led still farther back. To continue the search one must be equipped with spiritual science. But finally, going back to the second and third millennia before Christ, one comes upon very deep insights that have been lost to mankind. Only as a faint echo are they present in writings such as those of Erigena. Even if we go no further back than the Scholastics, we can find, hidden under their pedantic style, profound ideas concerning the way in which man apprehends the outer world, and how there lives the super-sensible on one side and on the other side the sense perceptible, and so on. If we take the stream of tradition founded on Aristotle who, in his logical but pedantic way, had in turn gathered together the ancient knowledge that had been handed down to him, we find the same thing — deep insights that were well understood in ancient times and survived feebly into the Middle Ages, being repeated in the successive epochs, and were always less and less understood. That is the characteristic process. At last in the Thirteenth or Fourteenth Century, the understanding disappears almost entirely, and a new spirit emerges, the spirit of Copernicus and Galileo, which I have described in the previous lectures. In all studies, such as those I have just outlines, it is found that this ancient knowledge is handed down through the ages until the Fourteenth Century, though less and less understood. This ancient knowledge amounted essentially to an inner experience of what goes on in man himself. The explanations of the last few lectures should make this comprehensible: It is the experiencing of the mathematical-mechanical element in human movement, the experiencing of a certain chemical principle, as we would say today, in the circulation of man's bodily fluids, which are permeated by the etheric body. Hence, we can even look at the table that I put on the blackboard yesterday from an historical standpoint. If we look at the being of man with our initiation science today, we have the physical body, the etheric body, the astral body (the inner life of the soul,) and the ego organization. As I pointed out yesterday, there existed (arising out of the ancient initiation science) an inner experience of the physical body, an inward experience of movement, an inner experience of the dimensionality of space, as well as experiences of other physical and mechanical processes. We can call this inner experience the experiencing of physics in man. But this experience of physics in man is at the same time the cognition of the very laws of physics and mechanics. There was a physics of man directed toward the physical body. It would not have occurred to anyone in those times to search for physics other than through the experience in man. Now, in the age of Galileo and Copernicus, together with the mathematics that was thenceforth applied in physics, what was inwardly experienced is cast out of man and grasped abstractly. It can be said that physics sunders itself from man, whereas formerly it was contained in man himself. Something similar was experienced with the fluid processes, the bodily fluids of the human organism. These too were inwardly experienced. Yesterday I referred to the Galen who, in the first Christian centuries, described the following fluids in man: black gall, blood, phlegm, and the ordinary means of the intermingling of these fluids by the way they influence each other. Galen did not arrive at these statements by anything resembling today's physiological methods. They were based mainly on inward experiences. For Galen too these were largely a tradition, but what he thus took from tradition we once experienced inwardly in the fluid part of the human organism, which in turn was permeated by the etheric body. For this reason, in the beginning of my Riddles of Philosophy , 72 See Steiner, Riddles of Philosophy . I did not describe the Greek philosophers in the customary way. Read any ordinary history of philosophy and you will find this subject presented more or less as follows: Thales 73 Thales of Milet: About 650–560 B.C. pondered on the origin of our sense world and sought for it in water. Heraclitus looked for it in fire. Others looked for it in air. Still others in solid matter, for example in something like atoms. It is amazing that this can be recounted without questions being raised. People today do not notice that it basically defies explanation why Thales happened to designate water while Heraclitus 74 Heraclitus of Ephesus: About 550–480 B.C. chose fire as the source of all things. Read my book Riddles of Philosophy , and you will see that the viewpoint of Thales, expressed in the sentence “All things have originated from water,” is based on an inner experience. He inwardly felt the activity of what in his day was termed the watery element. He sensed that the basis of the external process in nature was related to this inner activity; thus he described the external out of inner experiences. It was the same with Heraclitus who, as we would say today, was of a different temperament. Thales, as a phlegmatic, was sensitive to the inward “water” or “phlegm.” Therefore he described the world from the phlegmatic's viewpoint: everything has come from water. Heraclitus, as a choleric, experienced the inner “fire.” He described the world the way he experienced it. Besides them, there were other thinkers, who are no longer mentioned by external tradition, who knew still more concerning these matters. Their knowledge was handed down and still existed as tradition in the first Christian centuries; hence Galen could speak of the four components of man's inner fluidic system. What was then known concerning the inner fluids, namely, how these four fluids — yellow gall, black gall, blood, and phlegm — influence and mix with one another really amounts to an inner human chemistry, though it is of course considered childish today. No other form of chemistry existed in those days. The external phenomena that today belong to the field of chemistry were then evaluated according to these inward experiences. We can therefore speak of an inner chemistry based on experiences of the fluid man who is permeated by the ether body. Chemistry was tied to man in former ages. Later it emerged, as did mathematics and physics, and became external chemistry (see Figure 1.) Try to imagine how the physics and chemistry of ancient times were felt by men. They were experienced as something that was, as it were, a part of themselves, not as something that is mere description of an external nature and its processes. The main point was: it was experienced physics, experienced chemistry. In those ages when men felt external nature in their physical and etheric bodies, the contents of the astral body and the ego organization were also experienced differently than in later times. Today was have a psychology, but it is only an inventory of abstractions, though no one admits this. You will find in it thinking, feeling, willing, as well as memory, imagination, and so forth, but treated as mere abstractions. This gradually arose from what was still considered as one's own soul contents. One had cast out chemistry and physics; thinking, feeling and willing were retained. But what was left eventually became so diluted that it turned into no more than an inventory of lifeless empty abstractions, and it can be readily proved that this is so. Take, for example, the people who still spoke of thinking or willing as late as the Fifteenth or Sixteenth Century. 75 See also the personalities spoken of in Mysticism at the Dawn of the Modern Age . If you study the older texts on these subjects you will see that people expressed themselves concerning these matters in a concrete way. You have the feeling, when such a person speaks about thinking, that he speaks as if this thinking were actually a series of inner processes within him, as if the thoughts were colliding with each other or supporting each other. This is still an experiencing of thoughts. It is not yet as abstract a matter as it became later on. During and towards the end of the Nineteenth Century, it was an easy thing for the philosophers to deny all reality to these abstractions. They saw thoughts as inner mirror pictures, as was done in an especially brilliant way by Richard Wahle, who declared that the ego, thinking, feeling, and willing were only illusions. Instead of abstractions, the inner soul contents become illusions. In the age when man felt that his walking was a process that took place simultaneously in him and the world, and when he still sensed the circulating fluids within him, he knew, for instance, that when he moved about in the heat of the sun (when external influences were present) that the blood and phlegm circulated differently in him than was the case in winter. Such a man experienced the blood and phlegm circulation within himself, but he experienced it together with the sunshine or the lack thereof. And just as he experienced physical and chemical aspects in union with the outside world, so he also experienced thinking, feeling, and willing together with the world. He did not think they were occurring only within himself as was done in later ages when they gradually evaporated into complete abstractions. Instead he experienced what occurred in him in thinking, feeling, and willing, or in the circulation of the fluids as part of the realm of the astral, the soul being of man, which in that age was the subject of a psychology. Psychology now became tightly tied to man. With the dawn of the scientific age, man drove physics and chemistry out into the external world; psychology, on the other hand, he drove into himself. This process can be traced in Francis Bacon and John Locke. All that is experienced of the external world, such as tone, color, and warmth, is pressed into man's interior. This process is even more pronounced in regard to the ego organization. This gradually became a very meager experience. The way man looked into himself, the ego became by degrees something like a mere point. For that reason it became easy to philosophers to dispute its very existence. Not ego consciousness, but the experience of the ego was for men of former ages something rich in content and fully real. This ego experience expressed itself in something that was a loftier science than psychology, a science that can be called pneumatology. In later times this was also pressed into the interior and thinned out into our present quite diluted ego feeling. When man had the inward experience of his physical body, he had the experience of physics; simultaneously, he experienced what corresponds in outer nature to the processes in his physical body. It is similar in the case of the etheric body. Not only the etheric, was experienced inwardly, but also the physical fluid system, which is controlled by the etheric. Now, what is inwardly experienced when man perceives the psychological, the processes of his astral body? The “air man” — if I may put it this way — is inwardly experienced. We are not only solid organic formations, not only fluids or water formations, we are always gaseous-airy as well. We breathe in the air and breathe it out again. We experienced the substance of psychology in intimate union with the inner assimilation of air. This is why psychology was more concrete. When the living experience of air (which can also be outwardly traced) was cast out of the thought contents, these thought contents became increasingly abstract, became mere thought. Just think how an old Indian philosopher strove in his exercises to become conscious of the fact that in the breathing process something akin to the thought process was taking place. He regulated his breathing process in order to progress his thinking. He knew that thinking, feeling and willing are not as flimsy as we today make them out to be. He knew that through breathing they were related to both outer and inner nature, hence with air. As we can say that man expelled the physical and chemical aspects from his organization, we can also say that he sucked in the psychological aspect, but in doing so he rejected the external element, the air-breath experience. He withdrew his own being from the physical and chemical elements and merely observed the outer world with physics and chemistry; whereas he squeezed external nature (air) out of the psychological. Likewise, he squeezed the warmth element out of the pneumatological realm, thus reducing it to the rarity of the ego. If I call the physical and etheric bodies, the “lower man,” and call the astral body and ego-organization the “upper man,” I can say that in the transition from an older epoch to the scientific age, man lost the inner physical and chemical experience, and came to grasp external nature only with his concepts of physics and chemistry. In psychology and pneumatology, on the other hand, man developed conceptions from which he eliminated outer nature and came to experience only so much of nature as remained in his concepts. In psychology, this was enough so that he at least still had words for what went on in his soul. As to the ego, however, this was so little that pneumatology (partially because theological dogmatism had prepared this development) completely faded out. It shrank down to the mere dot of the ego. All this took the place of what had been experienced as a unity, when men of old said: We have four elements, earth, water, air and fire. Earth we experience in ourselves when we experience the physical body. Water we experience in ourselves when we experience the etheric body as the agent that moves, mixes, and separates the fluids. Air is experienced when the astral body is experienced in thinking, feeling, and willing, because these three are experienced as surging with the inner breathing process. Finally, warmth, or fire as it was then called, was experienced in the sensation of the ego. So we may say that the modern scientific view developed by way of a transformation of man's whole relation to himself. If you follow historical evolution with these insights, you will find what I told you earlier — that in each new epoch we see new descriptions of the old traditions, but these are always less and less understood. The worlds of men like Paracelsus, van Helmont, or Jacob Boehme, 76 Jacob Boehme: Altseidenberg, Goerlitz 1575–1624 Goerlitz. Mystic. His profession was shoemaker. First writing Aurora , 1612. Further writings from 1619 onwards, despite the prohibition. See Riddles of Philosophy . bear witness to such ancient traditions. One who has insight into these matters gets the impression that in Jacob Boehme's case a very simple man is speaking out of sources that would lead too far today to discuss. He is difficult to comprehend because of his clumsiness. But Jacob Boehme shows profound insight in his awkward descriptions, insights that have been handed down through the generations. What was the situation of a person like Jacob Boehme? Giordano Bruno, his contemporary, stood among the most advanced men of his time, whereas we see in Jacob Boehme's case that he obviously read all kinds of books that are naturally forgotten today. These were full of rubbish. But Boehme was able to find a meaning in them. Awkwardly and with great difficulty Boehme presents the primeval wisdom that he had gleaned from his still more awkward and inadequate sources. His inward enlightenment enabled him to return to an earlier stage. If we now look at the Fifteenth, Sixteenth, and especially the Seventeenth and Eighteenth centuries, and if we leave aside isolated people like Paracelsus and Boehme (who appear like monuments to a bygone age,) and if we look at the exoteric stream of human development in the light of initiation science, we gain the impression that nobody knows anything at all anymore about the deeper foundations of things. Physics and chemistry have been eliminated from man, and alchemy has become the subject of derision. Of course, people were justified in scoffing at it, because what still remained of the ancient traditions in medieval alchemy could well be made fun of. All that is left is psychology, which has become confined to man's inner being, and a very meager pneumatology. People have broken with everything that was formerly known of human nature., On one hand, they experience what has been separated from man; and on the other, what has been chaotically relegated into his interior. And in all our search for knowledge, we see what I have just described. In the Seventeenth Century, a theory arose that remains quite unintelligible if considered by itself, although if it is viewed in the context of history it becomes comprehensible. The theory was that those processes in the human body that have to do with the intake of food, are based on a kind of fermentation. The foods man eats are permeated with saliva and then with digestive fluids such as those in the pancreas, and thus various degrees of fermentation processes, as they were called, are achieved. If one looks at these ideas from today's viewpoint (which naturally will also be outgrown in the future) one can only make fun of them. But if we enter into these ideas and examine them closely, we discover the source of these apparently foolish ideas. The ancient traditions, which in a man like Galen were based on inward experiences and were thus well justified, were now on the verge of extinction. At the same time, what was to become external objective chemistry was only in its beginnings. Men had lost the inner knowledge, and the external had not yet developed. Therefore, they found themselves able to speak about digestion only in quite feeble neo-chemical terms, such as the vague idea of fermentation. Such men were the late followers of Galen's teachings. They still felt that in order to comprehend man, one must start from the movements of man's fluids, his fluid nature. But at the same time, they were beginning to view chemical aspects only by means of the external processes. Therefore they seized the idea of fermentation, which could be observed externally, and applied it to man. Man had become an empty bag because he no longer experienced anything within himself. What had grown to be external science was poured into this bag. In the Seventeenth Century, of course, there was not much science to pour. People had the vague idea about fermentation and similar processes, and these were rashly applied to man. Thus arose the so-called iatrochemical school 77 Iatrochemistry: Name from the Greek “Iatro,” physician. Work with homeopathic remedies in continuation of Paracelsus' (1493–1541) method of healing, in the beginning with retention of his opinion about sulfur, mercury, and salt. The Iatrochemical School was established during Paracelsus' last years of life. It degenerated in the middle of the seventeenth century. In its place stepped Robert Boyle's chemistry (1627–1691), for which iatrochemistry had done good preparation. J.B. van Helmont (1577–1644) was one of the main contributors to Iatrochemical literature. of medicine. In considering these iatrochemists, we must realize that they still had some inkling of the ancient doctrine of fluids, which was based on inner experience. Others, who were more or less contemporaries of the iatrochemists, no longer had any such inkling, so they began to view man the way he appears to us today when we open an anatomy book. In such books we find descriptions of the bones, the stomach, the liver, etc. and we are apt to get the impression that this is all there is to know about man and that he consists of more or less solid organs with sharply defined contours. Of course, from a certain aspect, they do exist. But the solid aspect — the earth element, to use the ancient terminology — comprises at most one tenth of man's organization. It is more accurate to say that man is a column of fluids. The mistake is not in what is actually said, but in the whole method of presentation. It is gradually forgotten that man is a column of fluids in which the clearly contoured organs swim. Laymen see the pictures and have the impression that this is all they need to understand the body. But this is misleading. It is only one tenth of man. The remainder ought to be described by drawing a continuous stream of fluids (see Figure 2) interacting in the most manifold ways in the stomach, liver and so forth. Quite erroneous conceptions arise as to how man's organism actually functions, because only the sharply outlined organs are observed. This is why in the Nineteenth Century, people were astonished to see that if one drinks a glass of water, it appears to completely penetrate the body and be assimilated by his organs. But when a second or third glass of water is consumed, it no longer gives the impression that it is digested in the same manner. These matters were noticed but could no longer be explained, because a completely false view was held concerning the fluid organization of man. Here etheric body is the driving agent that mixes or separates the fluids, and brings about the processes of organic chemistry in man. In the Seventeenth Century, people really began to totally ignore this “fluid man” and to focus only on the solidly contoured parts. In this realm of clearly outlined parts, everything takes place in a mechanical way. One part pushes another; the other moves; things get pumped; it all works like suction or pressure pumps. The body is viewed from a mechanical standpoint, as existing only through the interplay of solidly contoured organs. Out of the iatrochemical theory or alongside it, there arose iatromechanics and even iatromathematics. 78 Iatromechanics and Iatromathematics. In the sixteenth and seventeenth centuries the proponents of these teachings were nearly all university professors, while iatrochemistry was represented by a union of practicing physicians. But that was true only in the Romantic countries and England. In Italy the main universities were Padua, Pisa, and Rome. There the teachings were rejected on philosophic grounds, because they were based on experience. Germany, where both branches worked hand in hand, was an exception and in a special position. Naturally, people began to think that the heart is really a pump that mechanically pumps the blood through the body, because they no longer knew that our inner fluids have their own life and therefore move on their own. They never dreamed that the heart is only a sense organ that checks on the circulation of the fluids in its own way. The whole matter was inverted. One no longer saw the movement and inner vitality of the fluids, or the etheric body active therein. The heart became a mechanical apparatus and has remained so to this day for the majority of physiologists and medical men. The iatrochemists still had some faint knowledge concerning the etheric body. There was full awareness of it in what Galen described. In van Helmont or Paracelsus there was still an inkling of the etheric body, more than survived in the official iatrochemists who conducted the schools of that time. In the iatromechanists no trace whatsoever remained of this ether body; all conception of it had vanished into tin air. Man was seen only as a physical body, and that only to the extent that he consists of solid parts. These were now dealt with by means of physics, which had in the meantime also been cast out of the human being. Physics was now applied externally to man, whom one no longer understood. Man had been turned into an empty bag, and physics had been established in an abstract manner. Now this same physics was reapplied to man. Thus one no longer had the living being of man, only an empty bag stuffed with theories. It is still this way today. What modern physiology or anatomy tells us of man is not man at all, it is physics that was cast out of man and is now changed around to be fitted back into man. The more intimately we study this development, the better we see destiny at work. The iatrochemists had a shadowy consciousness of the etheric body, the iatromechanists had none. Then came a man by the name of Stahl 79 Georg Ernst Stahl: Ansbach 1650–1734, Berlin. Physician and chemist, Professor of Medicine. Exponent of Animism and Vitalism and the hypothesis of the “life forces” in his major work Theoria Medico Vera , 1707. who, considering his time, was an unusually clever man. He had studied iatrochemistry, but the concepts of the “inner fermentation processes” seemed inadequate to him because they only transplanted externalized chemistry back into the human bag. With the iatromechanists he was still more dissatisfied because they only placed external mechanical physics back into the empty bag. No knowledge, no tradition existed concerning the etheric body as the driving force of the moving fluids. It was not possible to gain information about it. So what did Stahl do? He invented something, because there was nothing left in tradition. He told himself: the physical and chemical processes that go on in the human body cannot be based on the physics and chemistry that are discovered in the external world. But he had nothing else to put into man Therefore he invented what he called the “life force,” the “vital force,” With it he founded the dynamic school. Stahl was gifted with a certain instinct. He felt the lack of something that he needed; so he invented this “vital force.” The Nineteenth Century had great difficulty in getting rid of this concept. It was really only an invention, but it was very hard to rid science of this “life force.” Great efforts were made to find something that would fit into this empty bag that was man. This is why men came to think of the world of machines. They knew how a machine moves and responds. So the machine was stuffed into the empty bag in the form of L'homme machine by La Mettrie. 80 Offray de la Mettrie: Malo 1709–1751 Berlin. Physician and writer. Main work is L'Homme Machine , published in Leyden 1748. Man is a machine. The materialism, or rather the mechanics, of the Eighteenth Century, such as we see in Holbach's Systeme de la nature , 81 Baron Dietrich von Hollenbach: Heidesheim, Rheinpfalz 1723–1789 Paris. His main work Systeme de la Nature ou des Lois du Monde Physique et du Monde Moral appeared 1770 under the pseudonym Mira-baud . He only recognized mobile, material atoms, even in regard to thinking, and he based morals on self love. which Goethe so detested in his youth, reflects the total inability to grasp the being of man with the ideas that prevailed at that time in outer nature. The whole Nineteenth Century suffered from the inability to take hold of man himself. But there was a strong desire somehow or other to work out a conception of man. This led to the idea of picturing him s a more highly evolved animal. Of course, the animal was not really understood either, since physics, chemistry, and psychology, all in the old sense, are needed for this purpose even if pneumatology is unnecessary. But nobody realized that all this is also required in order to understand the animal. One had to start somewhere, so in the Eighteenth Century man was compared to the machine and in the Nineteenth Century he was traced back to the beast. All this is quite understandable from the historical standpoint. It makes good sense considering the whole course of human evolution. It was, after all, this ignorance concerning the being of man that produced our modern opinions about man. The development towards freedom, for example, would never have occurred had the ancient experience of physics, chemistry, psychology, and pneumatology survived. Man had to lose himself as an elemental being in order to find himself as a free being. He could only do this by withdrawing from himself for a while and paying no attention to himself any longer. Instead, he occupied himself with the external world, and if he wanted theories concerning his own nature, he applied to himself what was well suited for a comprehension of the outer world. During this interim, when man took the time to develop something like the feeling of freedom, he worked out the concepts of science; these concepts that are, in a manner of speaking, so robust that they can grasp outer nature. Unfortunately, however, they are too coarse for the being of man, since people do not go to the trouble of refining these ideas to the point where they ca also grasp the nature of man. Thus modern science arose, which is well applicable to nature and has achieved great triumphs. But it is useless when it comes to the essential being of man. You can see that I am not criticizing science. I am only describing it. Man attains his consciousness of freedom only because he is no longer burdened with the insights that he carried within himself and that weighed him down. The experience of freedom came about when man constructed a science that in its robustness was only suited to outer nature. Since it does not offer the whole picture and is not applicable to man's being, this science can naturally be criticized in turn. It is most useful in physics; in chemistry, weak points begin to show up; and psychology becomes completely abstract. Nevertheless, mankind had to pass through an age that took its course in this way in order to attain to an individually modulated moral conception of the world and to the consciousness of freedom. We cannot understand the origin of science if we look at it only from one side. It must be regarded as a phenomenon parallel to the consciousness of freedom that is arising during the same period, along with all the moral and religious implications connected with this awareness. This is why people like Hobbes 82 Thomas Hobbes: Malmesbury 1588–1679 Hardwicke. English natural philosopher and humanist. Opera Philosophica , 1688. All phenomena in nature and humanity, even the psychological ones, are result of mobility of bodies. The social processes are traced back to mechanical processes. The leading force in this process is the egoism of the single human being. The state which is “crushing everything underfoot,” he called “Leviathan” and said: “The natural social condition is the war of all against all.” and Bacon, who were establishing the ideas of science, found it impossible to connect man to the spirit and soul of the universe. In Hobbes' case, the result was that, on the one hand, he cultivated the germinal scientific concepts in the most radical way, while, on the other hand, he cast all spiritual elements out of social life and decreed “the war of all against all.” He recognized no binding principle that might flow into social life from a super-sensible source, and therefore he was able, though in a somewhat caricatured form, to discuss the consciousness of freedom in a theoretical way for the first time. The evolution of mankind does not proceed in a straight line. We must study the various streams that run side by side. Only then can we understand the significance of man's historical development.

The Origins of Natural Science

Lecture VIII

https://rsarchive.org/Lectures/GA326/English/AP1985/19230103p01.html

Dornach

3 Jan 1923

GA326-8

It is in the nature of the case that the subject of a lecture course like this one is inexhaustible. Matters could be elaborated and looked at more thoroughly. But since, unfortunately, we must come to an end, we have to be content with given guidelines and indication. Today, therefore, I shall only supplement the scanty outlines and hints already discussed to that in a certain sense the picture will be rounded out. Proceeding once again from the being of man as viewed by spiritual science, we must say that we member man into physical body, etheric or formative forces body, astral body (which essentially represents the soul life) and ego. Let us be clear that properly speaking the physical body resides only in the small part of the human organization that we can describe as solid and sharply defined. On the other hand, all that pertains to liquid or fluid forms is taken hold of by the etheric body in such a way that it is in a constant process of blending, separating, combining, and dissolving. It is in perpetual flux. Then there are the gaseous, aeriform elements, such as are active in oxygen and other gases. In these, the astral body is at work. Finally, the ego organization is active in everything that has to do with warmth. What I have just outlined cannot, however, be reduced to a diagram. We must clearly understand, for instance, that because the formative forces body pulsates through all fluid and liquid elements of the body, it also sweeps along the solid substances. Everything in the human organization is in close interaction, in constant interplay. We must always be aware of that. But now let us also remember that this human organization has been experienced in different ways in the course of evolution. This was one of the main themes of these lectures. What is described today as the subject matter of external physics or mechanics, was originally attained through an inward experience of the physical body. Our present-day physics contains statements that originated because there once existed an internally experienced physics of the physical body. As I have explained a number of times, this inward physics was divorced from man and now continues to function merely as a science that observes outer nature. During the decline of the medieval alchemy the same thing happened with what lives inwardly in man by virtue of the etheric body. The work of this body in the fluids was once experienced, but now it is only dimly perceptible in the fantastic, alchemistic formulas that we find in ancient writings. Originally this was intelligent science, but inwardly experienced within the etheric. In a way, this is still in the process of being divorced from man, because as yet we really do not have a fully developed chemistry. We have many chemical processes in the world that we seek to understand, but only in a physical and mechanical way. In the beginning man experienced all this inwardly by means of his organization, but in the course of time he cast it all out of himself. In this process of casting out all our science developed, from astronomy to the meager beginnings of modern chemistry. On the other hand, thinking, feeling and willing, the subject matter of abstract psychology (which today is no longer considered real) was in former times actually not experienced inside man. Man felt himself at one with the external world outside his own being, when he experienced the soul life. Thus what was corporeal was once experienced inwardly, whereas the soul element was experienced by leaving one's being and communing with the outer world. Psychology was once the science of that aspect of the world that affects man in such a way that he appears to himself as a soul being. Physics and chemistry were cast out of man, whereas psychology and pneumatology (which I shall discuss directly) were stuffed into him and lost their reality. They turned into subjective perceptions with which nothing could be done. What was experienced together with the cosmos through the astral body (which leaves us in sleep) has become the subject of psychology. What man experienced as spirit in union with the universe was pneumatology. Today, as I have already pointed out, this has shrunk down to the idea of the ego or to a mere feeling. Therefore we now have as science of external nature what was once inner experience, while our science of man's inner nature is what was once external experience. Now we must call to mind what is needed, on the one hand for physics and chemistry, and on the other for psychology and pneumatology, in order to develop them further in a conscious way, since man today finds himself in the age of the development of the consciousness soul. Take physics, for example, which in recent times has become mostly abstract and mechanical. From all that I have said you will have seen that the scientific age has increasingly felt impelled to restrict itself to the externally observed mechanics of space. Long ago, man accompanied motion by means of inward experience and judged it according to what he felt within as movement. Observing a falling stone, he experienced its inner impulse of movement in his own inner human nature, in his physical body. This experience, after the great casting out, led to the measuring of the rate of fall per second. In our attitude toward nature, the idea prevails that what is observed is what is real. What can be observed in the outer world? It is motion, change of position. 83 See Drawings, pages 92, 95 and compare with the ones on page 125. As a rule, we let velocity vanish neatly in a differential coefficient. But it is motion that we observe, and we express velocity as movement per second, hence by means of space. This means, however, that with our conscious experience, we are entirely outside the object. We are not involved in it in any way when we merely watch its motion, meaning its change of position in space. We can do that only if we find ways and means to inwardly take hold of the spatial, physical object by an extending of the same method with which we separated from it in the first place. Instead of the mere movement, the bare change of position, we have to view the velocity in the objects as their characteristic element. Then we can know what a particular object is like inwardly, because we find velocity also within ourselves when we look back upon ourselves. This is what is necessary. The trend of scientific development in regard to the outer physical world must be extended in the direction of proceeding from mere observation of motion to a feeling for the velocity possessed by a given object. We must advance from motion to velocity. That is how we enter into reality. Reality is not taken hold of if all we see is that a body changes its position in space. But if we know that the body possesses an inner velocity-impulse, then we have something that lies in the nature of the body. We assert nothing about a body if we merely indicate its change of position, but we do state something about it when we say that it contains within itself the impulse for its own velocity. This then is a property of it, something that belongs to its nature. You can understand this by a simple illustration. If you watch a moving person, you know nothing about him. But if you know that he has a strong urge to move quickly, you do know something about him. Likewise, you know something about him, when you know that he has a reason for moving slowly. We must be able to take hold of something that has significance within a given body. It matters little whether or not modern physics speaks, for example, of atoms; what matters is that when it does speak of them it regards them as velocity charges. That is what counts. Now the question is: how do we arrive at such a perception? We can discuss the best in the case of physics, since today's chemistry has advanced too little. We have to become clear about what we actually do when, in our thinking, we cast inwardly experienced mechanics and physics into external space. That is what we are doing when we say: The nature of what is out there in space is of no concern to me; I observe only what can be measured and expressed in mechanical formulas, and I leave aside everything that is not mechanical. Where does this lead us? It leads us to the same process in knowledge that a human being goes through when he dies. When he dies, life goes out of him, the dead organism remains. When I begin to think mechanistically, life goes out of my knowledge. I then have a science of dead matter. We must be absolutely clear that we are setting up a science of dead matter so long as the mechanical and physical aspect is the sole object of our study of nature. You must be aware that you are focusing on what is dead. You must be able to say to yourself: The great thing about science is that it has tacitly resolved that, unlike the ancient alchemists who still saw in outer nature a remnant of life, it will observe what is dead I minerals, plants, and animals. Science will study only what is dead in them, because it utilizes only ideas and concepts suitable for what is dead. Therefore, our physics is dead by its nature. Science will stand on a solid basis only when it fully realizes that its mode of thinking can take hold only of the dead. The same is true of chemistry, but I cannot go into that today because of the lack of time. When we look only at motion and lose sight of velocity, we are erecting a physics that is dead, the end-product of living things is then our concern, and the end-product is death. Hence, when we look at nature with the eyes of modern mechanics and physics, we must realize that we are looking at a corpse. Nature was not always like this. It was different at one time. If I look at a corpse, it would be foolish to believe that it was always in this condition. The fact that I realize that it is a corpse proves to me that once it was a living organism. The moment you realize that modern mechanics and physics lead you to view nature in this way, you will see that nature is now a corpse so far as physics is concerned. We are studying a corpse. Can we attain to something living, or at least an approach to it? The corpse is the final condition of something living. Where is the beginning condition? Well, my dear friends, there is no way to rediscover velocity by observing motion. You may stare at differential coefficients as long as you will but you will not find it. Instead, you must turn back to man. Whereas formerly he experienced himself from within, you must now study him from without through his physical organism, and you must understand that in man — and especially in his physical and etheric organizations — the beginning of a living condition must be sought. No satisfactory form of physics and chemistry will be attained save through a genuine science of man. But I expressly call attention to the fact that such a genuine anthropology will not be reached by approaching man with the methods of present-day physics and chemistry. That would only carry death back into man and make his body (his lower organization) even more dead than before. You must study what is living in man, and not revert to the method of physics and chemistry. What is needed are the methods that can be found through spiritual-scientific research. Briefly stated, spiritual-scientific research will meet the historic requirements of natural science. This historic requirement can be put in the following words: Science has reached the point of observing what is corpse-like in nature. Anthroposophical spiritual science must discover in addition to this the beginning of a living condition. This has been preserved in man. In former periods of evolution it was also externally perceptible. At one time, the processes of nature were totally different. Today, we walk around on the corpses of what existed in the beginning. But in the two lower bodies of man, the beginning condition has been preserved. There we can discover all that once existed, right back to the Saturn condition. An historical approach leads beyond the present state of science. It is quite clear why this is so. We are in the midst of a period of development. If, as is so frequently the case, we consider today's manner of thinking to be the most advanced and do not realize that the real course of events was very different, then we are looking at history the wrong way. As an example, a twenty-five year old person need not only be observed in the light of the twenty-five years that he has been alive, — one must also observe the element in him that makes it possible for him to live on. That is one point. Movement: Velocity : Dead Aspect (Final Condition of Being) Phenomenon: Being : Semblance (Initial Condition of Being) The other point is that our psychology has become very thin, while pneumatology has nearly reached the vanishing point. Again, we must know how far it has gone with these two sciences in the present age. If one speaks today of blue or red, of C-sharp or G, or of qualities of warmth, he will say that they are subjective sensations. That is the popular attitude; But what is a mere subjective sensation? It is a “phenomenon.” Just as we observe only motions in outer nature, we study only the phenomenon in psychology and pneumatology. And just as velocity is missing from motion in our external observation, the essential thing — the living essence — is missing from our observation of the inner soul life. Because we only study phenomena and no longer experience the living essence, we never get beyond mere semblance. The way thinking, feeling and willing are experienced today, they are mere semblance. Modern epistemologists have the man who wants to lift himself up by his own pigtail, or like the man in a railroad car who pushes against the wall without realizing that he cannot move the carriage in this way. This is how modern epistemologists look. They talk and talk, but there is no vitality in their talk because they are locked into the mere semblance. I have tried to put a certain end to this talk. The first time was in my Philosophy of Freedom , 84 See footnote 45. where I demonstrated how this semblance, inherent in pure thinking, becomes the impulse of freedom when inwardly grasped by man in thinking. If something other than semblance were contained in our subjective experience, we could never be free. But if this semblance can be raised to pure thinking, one can be free, because what is not real being cannot determine us, whereas real being would do so. This was my first effort. My second effort was at the Philosophical Congress in Bologna, when I analyzed the matter psychologically. I attempted to show that our sensations and thoughts are in fact outward experiences, rather than inward ones, and that this insight can be attained by careful observation. These indications will have to be understood. Then, we shall realize that we must rediscover being in semblance, just as we must rediscover velocity in movement. Then, we will understand what this inwardly experienced semblance really is. It will reveal itself as the initial state of being. Man experiences this semblance; experiences himself as semblance and as such lives his way into semblance and thus transforms it into the seed of future worlds. I have often pointed out that from our ethics, our morals, born of the physical world of semblance, future physical worlds will arise, just as from today's seed the plant will grow. 85 See Rudolf Steiner, The Karma of Vocation (Spring Valley, NY: Anthroposophic Press, 1984). We are dealing with the nascent state of being. In order to have a proper natural science, we must realize that psychology and pneumatology must understand what they observe as nascent states of being. Only then will they throw light on those matters that natural science wants to illuminate. But what is this “nascent” or “initial state?” Now this nascent state is in the outer world, not within. It is what I see when I behold the green tapestry of plants, the world of colors — red, green and blue — and the sounds that are out there. What are these fleeting formations that modern-day physics, physiology and psychology regard only as subjective? They are the elements from which the worlds of the future create themselves. Red is not engendered by matter in the eye or the brain, red is the first, semblance-like, seed of future worlds. If you know this, you will also want to know something about what will correspond in these future worlds to the corpse-like element. It will not be what we found earlier in our physics and chemistry, it will be the corpse of the future. We shall recognize what will be the corpse of the future, the future element of death, if we discover it already today in the higher organization of man, where astral body and ego are active. By experiencing the final condition there in reference to the initial one, we at last gain a proper comprehension of the nervous system and the brain insofar as they are dead, not alive. In a certain sense, they can be more dead than a corpse, inasmuch as they transcend the absolute point of death — especially in the case of the nervous system — and become “more dead than dead.” But this very fact makes the nervous system and the brain bearers of the so-called spiritual element — because the dead element dwells in them, the final state not yet even reached by outer nature — because they even surpass this final state. In order to find psychology and pneumatology in the outer world, we shall have to discover how the inanimate, the dead, dwells in the human organism; namely, in the head organization and in part of the rhythmic organization, mainly that of breathing. We must look at our head and say of it that it is constantly dying. If it were alive, the growing, sprouting living matter could not think. But because it gives up life and constantly dies, the soul-spiritual thoughts, endowed with being, have the opportunity to spread out over what is dead as new living, radiant semblance. You see, here lie the great tasks that, by means of the historical manner of observation result quite simply from natural science. If we don't take hold of them, we move like ghosts through the present development of science, and not with the consciousness that an epoch that has begun must find a way to continue. You can imagine that much of this is contained implicitly in what science has discovered. Scientific literature offers such indications everywhere. But people cannot yet distinguish clearly; they like what is chaotic. They don't care clearly to contemplate physics and chemistry on one hand, and psychology and pneumatology on the other, because then they would have to consider seriously the inner and outer aspects. They prefer to vacillate in the murky waters between physics and chemistry. Due to this, a bastard science has arisen that has become the darling of natural research and even philosophy; namely, physiology. As soon as the real facts are discovered, physiology will fall apart into psychology on the one hand — a psychology that is also a perception of the world — and on the other, into chemistry, meaning a chemistry that is also a knowledge of man. When these two are attained, this in-between science, physiology, will vanish. Because today you have a morass in which you can find everything, and because by juggling a bit to the left or the right, it is possible to find a bit of a soul or a corporeal element, people do quite well. The physiology of today is what above all must disappear as the last remnant of former conceptions that have become muddled. The reason physiological concepts are so abstruse is that they contain soul and corporeal elements that are no longer distinguished, thus they can play around with words and even juggle the facts. One who aims for clear insight must realize that physiology amounts in the end to fibbing with words and facts. Until we admit this, we can't take the history of natural science seriously. Science does not proceed only from undetermined past ages to our time, it continues on from the present. History can only be understood, if one comprehends the further course of things, not in a superstitious, prophetic sense but by beginning now to do the right thing. And infinitely much needs to be set right, particularly in the domain of science. Natural science has grown tall; it is like a nice teenager, who at the moment is going through his years of unpolished adolescence, and whose guidance must be continued so that he will become mature. Science will mature, if murky areas like physiology disappear, and physics and pneumatology arise again in the way outlined above. They will come into being, if the anthroposophical way of thinking is applied in earnest to science. This will be the case, when people feel that they are learning something, when somebody speaks to them of a real physics, a real chemistry, a real psychology and pneumatology; when they no longer have the urge to comprehend everything concerning the world and the human being through bastardized chaotic sciences like physiology. Then, the development of human knowledge will once again stand on a sound basis. Naturally, therapy is particularly affected and suffers under present-day physiology. You can well imagine this, because it works with all manner of things that elude one's grasp, when one begins to think clearly. We cannot confront the great challenges of our time with a few anthroposophical catchwords and phrases. It also does not suffice to dabble with physiology on the borderline between psychology and chemistry. The only way to proceed is to apply the methods of spiritual-scientific anthroposophy to physics and chemistry. If you are lazy — forgive me for this harsh expression, I don't mean it in such a radical sense in this case — you say: These matters can only be correctly judged, if one is clairvoyant. Therefore I will wait until I am clairvoyant. I won't venture to criticize physics and chemistry or even physiology. My dear friends, you need not have insights that surpass ordinary perception in order to know that a corpse is dead and that it must have originated in life. Neither do you need to be clairvoyant in order to analyze properly the true facts of today's physics and chemistry, and to refer them back to their underlying living element, once your attention is directed to the fact that this living element is to be found by studying the “lower man.” There you will have the supplement you need for chemistry and physics. Make the attempt, for once, really to study the mechanism of human movement. 86 Literature: Adolf Fink has studied the mechanism of human movement and the heat produced by muscular work, and published in 1857, 1869, and 1882 Gesammelte Schriften , (1903–06 in German). Instead of constantly drawing axis of coordinates and putting the movements into them apart from man; instead of multiplying differential coefficients and integrals, make a serious attempt to study the mechanics of movement in man. As they were once experienced from within, so do you now study them from without. Then you will have what you need, to add to your outer observation of nature, in physics and chemistry. In outer nature, those who proclaim atomism will always put you in the wrong. They even work themselves up to the very spiritual statement that when one speaks about matter in the sense of a modern physicist, matter is no longer material. The physicists, themselves are saying it; 87 In the beginning of the century Rudolf Steiner pointed to the speech of the philosopher and Prime Minister A.J. Balfour of August 17, 1904, in front of the British Association, immediately after it was held; see Rudolf Steiner, Lucifer Gnosis (Dornach: Rudolf Steiner Verlag, 1969), GA Bibl. No. 34, p. 467. Often Steiner also mentioned the lecture of Max Planck of 1910: “ Die Stellung der Neueren Physic zur Mechanischen Weltanshaung ” in Max Planck, Physikalische Abhandlungen und Vorträge (Brunswick, Germany, 1958), Vol. 3, pp. 30–46. our very opponents are saying it. In this case they are right, and if we in our replies to them stop short at the half-truths — that is to say, at the final conditions of being — we shall never be equal to that which issues from them. Here lie the tasks of the specialists, here lie the tasks of those who have the requisite preliminary training, in one or another branch of science. Then we shall not establish a physicized or chemicized Anthroposophy, but a true anthroposophical chemistry, anthroposophical physics. Then we shall not establish a new medicine as a mere variation on the old, but a true anthroposophical medicine. The tasks are at hand. They are outlined in all directions. Just as the simple heart can receive the observations that are scattered everywhere in our lectures or lecture cycles, and that give spiritual sustenance, so too the need is to take up on every hand the hints that can lead us to the much-needed progress in the several domains of science. In the future, it will not suffice if man and nature do not again become one. What physics and chemistry study in nature as the final state of being, must be supplemented by the state of being in “lower man” belonging to the realm of physics and chemistry — in man who is dependent on the physical and etheric bodies. It is important that this be sought. It is not important to single out as essential the valences of the structural formulas or the periodic law in chemistry, because these are but schemata. While they are quite useful as tools for counting and calculations, what matters is the following realization. If the chemical processes are externally observed, the chemical laws are not within them. They are contained in the origin of chemical processes. Hence, they are found only, if, with diligent effort, one tries to seek in the human being for the processes that occur in his circulation, in the activity of his fluids, through the actions of the etheric body. The explanation of the chemical processes in nature lies in the processes of the etheric body. These in turn are represented in the play of fluids in the human organism and are accessible to precise study. Anthroposophy poses a serious challenge in this direction. This is why we have founded research institutes 88 In 1920 a research institute was founded in Stuttgart for physics and chemistry, with a biological branch through the joint stock company “ Der Kommende Tag .” A few years later it was transferred to Dornach. The first works from the Institute were published in Der Kommende Tag: Scientific Research Institute News . It contains Heft I (1921), “ Milzfunktion und Blaettchen Frage ” von L. Kolisko; Heft II (1923), “ Der Villardsche Versuch ” von Dr. Rer. Nat. R.E. Maier; Heft III (1923): “ Physiologischer und Physicalischer Nachweis Kleinster Entitaeten ” von L. Kolisko. Later works appeared in the volumes Gaea Sophia, Jahrbuch der Wissenschaftlichen Sektion der Freien Hochschule fuer Geisteswissenschaft am Goetheanum , Volume I (1926), etc. in which serious, intensive work must begin. Then the methods gained from anthroposophy can be properly nurtured. This is also the main point of our medical therapy; namely, that the old, confused physiology finally be replaced with a real chemistry and psychology. Without this one can never assert anything about the processes of illness and healing in human nature, because every course of illness is simply an abnormal psychological process, and each healing process is an abnormal chemical process. Only to the extent that we know how to influence the chemical process of healing and how to grasp the psychological course of illness will we attain to genuine pathology and therapy. This will emerge from the anthroposophical manner of observation. If one does not want to recognize this potential in anthroposophy, then one only wants something a bit out of the ordinary and is unwilling to get to work in earnest. Actually, everything that I have sketched here is only a description of how the work should proceed, because a genuine psychology and chemistry come into being through work. All the prerequisites for this work already exist, because very man facts can be found in scientific literature that researchers have accidentally discovered but don't understand. Those of us who work in the spirit of anthroposophy should take up these facts and contribute something to their full comprehension. Take as an example what I emphasized yesterday 89 From this scientific discussion of January 5 no known copy exists. in speaking to a smaller group of people. The essential point about the spleen is that it is really an excretory organ. The spleen itself is in turn an excretion of the functions in the etheric body. Countless facts are available in medical literature that need only be utilize — and that is the point: they should be utilized — then the facts will be brought together and what is needed will result. A single person might accomplish this if a human life spanned six hundred years. But by that time, other tasks would confront him and his accomplishments would long since be outmoded. These things must be attained through cooperation, through people working together. So this is the second task — we must see to it that this becomes possible. I believe that these tasks of the Anthroposophical Society will emerge most clearly and urgently from a truly realistic study of the history of natural science in recent times. This history shows us at every turn that something great and wonderful has arisen through modern science. In earlier times, the truly inanimate dead aspects could never be discerned, hence, nothing could be made of them. In those times inward semblance could never really be observed; therefore, it couldn't be brought to life by human effort, and hence, one couldn't arrive at freedom. Today, we confront a grandiose world, which became possible only because natural science studies the dead aspects. This is the world of technology. Its special character can be discerned from the fact that the word “technique” is taken from the Greek. There, it still signifies “art,” implying that art reveals, where technology still contains spirit. Today, technology only utilizes spirit in the sense of the abstract, spirit-devoid thoughts. Technology could be achieved only by attaining a proper knowledge of what is dead. Once in the course of humanity's evolution it was necessary to concentrate upon the dead; it thus entered into the realm of technology. Today, man stands in the midst of this realm of technology that surrounds him on all sides. He looks out on it and realizes that here at last is a sphere in which there is no spirit in the proper sense. In regard to the spiritual element, it is important that in all areas of technology human beings experience this inner feeling, almost akin to one of pain over the death of a person. If feeling and sensation can be developed in knowledge, then such a feeling will arise, somewhat like the sensation one experiences when a person is dying and one sees the living organism turn into a corpse. Alongside the abstract indifferent cold knowledge, such a feeling will arise through the true realization that technology is the processing of the inanimate, the dead. This feeling will become the most powerful impetus to seek the spirit in new directions. I could well imagine the following view of the future: Man looks out over the chimneys, the factories, the telephones — everything that technology has produced in wondrous ways in the most recent times. He stands atop this purely mechanical world, the grave of all things spiritual, and he calls out longingly into the universe — and his yearning will be fulfilled. Just as the dead stone yields the living fiery spark if handled correctly, so from our dead technology will emerge the living spirit, if human beings have the right feelings about what technology is. On the other hand, one need only understand clearly what pure thinking is; namely the semblance from which can be brought forth the most powerful moral impulses — those individual moral impulses that I have described in my Philosophy of Freedom . Then, in a new way, man will face the feeling that was once confronted by Nicholas Cusanus and Meister Eckhart. They said: When I life myself beyond everything that I am ordinarily accustomed to observe, I come to “nothingness” with all that I have learned. But in this “nothingness” there arises for me the “I.” If man really penetrates to pure thinking, then he finds in it the nothingness that turns into the I and from which emerges the whole wealth of ethical actions, that will create new worlds. I can imagine a person who first lets all knowledge of the preset, as inaugurated by natural science, impress itself on him and then (centuries after Meister Eckhart and Nicholas Cusanus) turns his gaze inward and with today's mode of thinking arrives at the nothingness of his inner life. In it, he discovers that the spirit really speaks to him. I can imagine that these two images merge. On the one hand, man goes to the place where barren technology has left the spirit behind. There he calls out into cosmic expanses for the spirit. On the other hand, he stops, thinks and looks within himself. And here, out of his inner being, he receives the divine answer to the call he sent out into the distances of the universe. When we learn, through a new, anthroposophically imbued natural science, to let the calls of infinite longing for the spirit, sent out into the world, resound in our inner being, then this will be the right starting point. Here, through an “anthroposophized” inner perception, we will find the answer to the yearning call for the spirit, desperately sounded out into the universe. I did not want to describe the development of natural science in recent times in a merely documentary fashion. Rather, I wanted to show you the standpoint of a human being, who comprehends this natural-scientific development and, in a difficult moment of humanity's evolution, knows the right things to say to himself in regard to the progress of mankind. ˂˂ Previous Table of Contents Movement: Velocity : Dead Aspect (Final Condition of Being) Phenomenon: Being : Semblance (Initial Condition of Being) The other point is that our psychology has become very thin, while pneumatology has nearly reached the vanishing point. Again, we must know how far it has gone with these two sciences in the present age. If one speaks today of blue or red, of C-sharp or G, or of qualities of warmth, he will say that they are subjective sensations. That is the popular attitude; But what is a mere subjective sensation? It is a “phenomenon.” Just as we observe only motions in outer nature, we study only the phenomenon in psychology and pneumatology. And just as velocity is missing from motion in our external observation, the essential thing — the living essence — is missing from our observation of the inner soul life. Because we only study phenomena and no longer experience the living essence, we never get beyond mere semblance. The way thinking, feeling and willing are experienced today, they are mere semblance. Modern epistemologists have the man who wants to lift himself up by his own pigtail, or like the man in a railroad car who pushes against the wall without realizing that he cannot move the carriage in this way. This is how modern epistemologists look. They talk and talk, but there is no vitality in their talk because they are locked into the mere semblance. I have tried to put a certain end to this talk. The first time was in my Philosophy of Freedom , 84 See footnote 45. where I demonstrated how this semblance, inherent in pure thinking, becomes the impulse of freedom when inwardly grasped by man in thinking. If something other than semblance were contained in our subjective experience, we could never be free. But if this semblance can be raised to pure thinking, one can be free, because what is not real being cannot determine us, whereas real being would do so. This was my first effort. My second effort was at the Philosophical Congress in Bologna, when I analyzed the matter psychologically. I attempted to show that our sensations and thoughts are in fact outward experiences, rather than inward ones, and that this insight can be attained by careful observation. These indications will have to be understood. Then, we shall realize that we must rediscover being in semblance, just as we must rediscover velocity in movement. Then, we will understand what this inwardly experienced semblance really is. It will reveal itself as the initial state of being. Man experiences this semblance; experiences himself as semblance and as such lives his way into semblance and thus transforms it into the seed of future worlds. I have often pointed out that from our ethics, our morals, born of the physical world of semblance, future physical worlds will arise, just as from today's seed the plant will grow. 85 See Rudolf Steiner, The Karma of Vocation (Spring Valley, NY: Anthroposophic Press, 1984). We are dealing with the nascent state of being. In order to have a proper natural science, we must realize that psychology and pneumatology must understand what they observe as nascent states of being. Only then will they throw light on those matters that natural science wants to illuminate. But what is this “nascent” or “initial state?” Now this nascent state is in the outer world, not within. It is what I see when I behold the green tapestry of plants, the world of colors — red, green and blue — and the sounds that are out there. What are these fleeting formations that modern-day physics, physiology and psychology regard only as subjective? They are the elements from which the worlds of the future create themselves. Red is not engendered by matter in the eye or the brain, red is the first, semblance-like, seed of future worlds. If you know this, you will also want to know something about what will correspond in these future worlds to the corpse-like element. It will not be what we found earlier in our physics and chemistry, it will be the corpse of the future. We shall recognize what will be the corpse of the future, the future element of death, if we discover it already today in the higher organization of man, where astral body and ego are active. By experiencing the final condition there in reference to the initial one, we at last gain a proper comprehension of the nervous system and the brain insofar as they are dead, not alive. In a certain sense, they can be more dead than a corpse, inasmuch as they transcend the absolute point of death — especially in the case of the nervous system — and become “more dead than dead.” But this very fact makes the nervous system and the brain bearers of the so-called spiritual element — because the dead element dwells in them, the final state not yet even reached by outer nature — because they even surpass this final state. In order to find psychology and pneumatology in the outer world, we shall have to discover how the inanimate, the dead, dwells in the human organism; namely, in the head organization and in part of the rhythmic organization, mainly that of breathing. We must look at our head and say of it that it is constantly dying. If it were alive, the growing, sprouting living matter could not think. But because it gives up life and constantly dies, the soul-spiritual thoughts, endowed with being, have the opportunity to spread out over what is dead as new living, radiant semblance. You see, here lie the great tasks that, by means of the historical manner of observation result quite simply from natural science. If we don't take hold of them, we move like ghosts through the present development of science, and not with the consciousness that an epoch that has begun must find a way to continue. You can imagine that much of this is contained implicitly in what science has discovered. Scientific literature offers such indications everywhere. But people cannot yet distinguish clearly; they like what is chaotic. They don't care clearly to contemplate physics and chemistry on one hand, and psychology and pneumatology on the other, because then they would have to consider seriously the inner and outer aspects. They prefer to vacillate in the murky waters between physics and chemistry. Due to this, a bastard science has arisen that has become the darling of natural research and even philosophy; namely, physiology. As soon as the real facts are discovered, physiology will fall apart into psychology on the one hand — a psychology that is also a perception of the world — and on the other, into chemistry, meaning a chemistry that is also a knowledge of man. When these two are attained, this in-between science, physiology, will vanish. Because today you have a morass in which you can find everything, and because by juggling a bit to the left or the right, it is possible to find a bit of a soul or a corporeal element, people do quite well. The physiology of today is what above all must disappear as the last remnant of former conceptions that have become muddled. The reason physiological concepts are so abstruse is that they contain soul and corporeal elements that are no longer distinguished, thus they can play around with words and even juggle the facts. One who aims for clear insight must realize that physiology amounts in the end to fibbing with words and facts. Until we admit this, we can't take the history of natural science seriously. Science does not proceed only from undetermined past ages to our time, it continues on from the present. History can only be understood, if one comprehends the further course of things, not in a superstitious, prophetic sense but by beginning now to do the right thing. And infinitely much needs to be set right, particularly in the domain of science. Natural science has grown tall; it is like a nice teenager, who at the moment is going through his years of unpolished adolescence, and whose guidance must be continued so that he will become mature. Science will mature, if murky areas like physiology disappear, and physics and pneumatology arise again in the way outlined above. They will come into being, if the anthroposophical way of thinking is applied in earnest to science. This will be the case, when people feel that they are learning something, when somebody speaks to them of a real physics, a real chemistry, a real psychology and pneumatology; when they no longer have the urge to comprehend everything concerning the world and the human being through bastardized chaotic sciences like physiology. Then, the development of human knowledge will once again stand on a sound basis. Naturally, therapy is particularly affected and suffers under present-day physiology. You can well imagine this, because it works with all manner of things that elude one's grasp, when one begins to think clearly. We cannot confront the great challenges of our time with a few anthroposophical catchwords and phrases. It also does not suffice to dabble with physiology on the borderline between psychology and chemistry. The only way to proceed is to apply the methods of spiritual-scientific anthroposophy to physics and chemistry. If you are lazy — forgive me for this harsh expression, I don't mean it in such a radical sense in this case — you say: These matters can only be correctly judged, if one is clairvoyant. Therefore I will wait until I am clairvoyant. I won't venture to criticize physics and chemistry or even physiology. My dear friends, you need not have insights that surpass ordinary perception in order to know that a corpse is dead and that it must have originated in life. Neither do you need to be clairvoyant in order to analyze properly the true facts of today's physics and chemistry, and to refer them back to their underlying living element, once your attention is directed to the fact that this living element is to be found by studying the “lower man.” There you will have the supplement you need for chemistry and physics. Make the attempt, for once, really to study the mechanism of human movement. 86 Literature: Adolf Fink has studied the mechanism of human movement and the heat produced by muscular work, and published in 1857, 1869, and 1882 Gesammelte Schriften , (1903–06 in German). Instead of constantly drawing axis of coordinates and putting the movements into them apart from man; instead of multiplying differential coefficients and integrals, make a serious attempt to study the mechanics of movement in man. As they were once experienced from within, so do you now study them from without. Then you will have what you need, to add to your outer observation of nature, in physics and chemistry. In outer nature, those who proclaim atomism will always put you in the wrong. They even work themselves up to the very spiritual statement that when one speaks about matter in the sense of a modern physicist, matter is no longer material. The physicists, themselves are saying it; 87 In the beginning of the century Rudolf Steiner pointed to the speech of the philosopher and Prime Minister A.J. Balfour of August 17, 1904, in front of the British Association, immediately after it was held; see Rudolf Steiner, Lucifer Gnosis (Dornach: Rudolf Steiner Verlag, 1969), GA Bibl. No. 34, p. 467. Often Steiner also mentioned the lecture of Max Planck of 1910: “ Die Stellung der Neueren Physic zur Mechanischen Weltanshaung ” in Max Planck, Physikalische Abhandlungen und Vorträge (Brunswick, Germany, 1958), Vol. 3, pp. 30–46. our very opponents are saying it. In this case they are right, and if we in our replies to them stop short at the half-truths — that is to say, at the final conditions of being — we shall never be equal to that which issues from them. Here lie the tasks of the specialists, here lie the tasks of those who have the requisite preliminary training, in one or another branch of science. Then we shall not establish a physicized or chemicized Anthroposophy, but a true anthroposophical chemistry, anthroposophical physics. Then we shall not establish a new medicine as a mere variation on the old, but a true anthroposophical medicine. The tasks are at hand. They are outlined in all directions. Just as the simple heart can receive the observations that are scattered everywhere in our lectures or lecture cycles, and that give spiritual sustenance, so too the need is to take up on every hand the hints that can lead us to the much-needed progress in the several domains of science. In the future, it will not suffice if man and nature do not again become one. What physics and chemistry study in nature as the final state of being, must be supplemented by the state of being in “lower man” belonging to the realm of physics and chemistry — in man who is dependent on the physical and etheric bodies. It is important that this be sought. It is not important to single out as essential the valences of the structural formulas or the periodic law in chemistry, because these are but schemata. While they are quite useful as tools for counting and calculations, what matters is the following realization. If the chemical processes are externally observed, the chemical laws are not within them. They are contained in the origin of chemical processes. Hence, they are found only, if, with diligent effort, one tries to seek in the human being for the processes that occur in his circulation, in the activity of his fluids, through the actions of the etheric body. The explanation of the chemical processes in nature lies in the processes of the etheric body. These in turn are represented in the play of fluids in the human organism and are accessible to precise study. Anthroposophy poses a serious challenge in this direction. This is why we have founded research institutes 88 In 1920 a research institute was founded in Stuttgart for physics and chemistry, with a biological branch through the joint stock company “ Der Kommende Tag .” A few years later it was transferred to Dornach. The first works from the Institute were published in Der Kommende Tag: Scientific Research Institute News . It contains Heft I (1921), “ Milzfunktion und Blaettchen Frage ” von L. Kolisko; Heft II (1923), “ Der Villardsche Versuch ” von Dr. Rer. Nat. R.E. Maier; Heft III (1923): “ Physiologischer und Physicalischer Nachweis Kleinster Entitaeten ” von L. Kolisko. Later works appeared in the volumes Gaea Sophia, Jahrbuch der Wissenschaftlichen Sektion der Freien Hochschule fuer Geisteswissenschaft am Goetheanum , Volume I (1926), etc. in which serious, intensive work must begin. Then the methods gained from anthroposophy can be properly nurtured. This is also the main point of our medical therapy; namely, that the old, confused physiology finally be replaced with a real chemistry and psychology. Without this one can never assert anything about the processes of illness and healing in human nature, because every course of illness is simply an abnormal psychological process, and each healing process is an abnormal chemical process. Only to the extent that we know how to influence the chemical process of healing and how to grasp the psychological course of illness will we attain to genuine pathology and therapy. This will emerge from the anthroposophical manner of observation. If one does not want to recognize this potential in anthroposophy, then one only wants something a bit out of the ordinary and is unwilling to get to work in earnest. Actually, everything that I have sketched here is only a description of how the work should proceed, because a genuine psychology and chemistry come into being through work. All the prerequisites for this work already exist, because very man facts can be found in scientific literature that researchers have accidentally discovered but don't understand. Those of us who work in the spirit of anthroposophy should take up these facts and contribute something to their full comprehension. Take as an example what I emphasized yesterday 89 From this scientific discussion of January 5 no known copy exists. in speaking to a smaller group of people. The essential point about the spleen is that it is really an excretory organ. The spleen itself is in turn an excretion of the functions in the etheric body. Countless facts are available in medical literature that need only be utilize — and that is the point: they should be utilized — then the facts will be brought together and what is needed will result. A single person might accomplish this if a human life spanned six hundred years. But by that time, other tasks would confront him and his accomplishments would long since be outmoded. These things must be attained through cooperation, through people working together. So this is the second task — we must see to it that this becomes possible. I believe that these tasks of the Anthroposophical Society will emerge most clearly and urgently from a truly realistic study of the history of natural science in recent times. This history shows us at every turn that something great and wonderful has arisen through modern science. In earlier times, the truly inanimate dead aspects could never be discerned, hence, nothing could be made of them. In those times inward semblance could never really be observed; therefore, it couldn't be brought to life by human effort, and hence, one couldn't arrive at freedom. Today, we confront a grandiose world, which became possible only because natural science studies the dead aspects. This is the world of technology. Its special character can be discerned from the fact that the word “technique” is taken from the Greek. There, it still signifies “art,” implying that art reveals, where technology still contains spirit. Today, technology only utilizes spirit in the sense of the abstract, spirit-devoid thoughts. Technology could be achieved only by attaining a proper knowledge of what is dead. Once in the course of humanity's evolution it was necessary to concentrate upon the dead; it thus entered into the realm of technology. Today, man stands in the midst of this realm of technology that surrounds him on all sides. He looks out on it and realizes that here at last is a sphere in which there is no spirit in the proper sense. In regard to the spiritual element, it is important that in all areas of technology human beings experience this inner feeling, almost akin to one of pain over the death of a person. If feeling and sensation can be developed in knowledge, then such a feeling will arise, somewhat like the sensation one experiences when a person is dying and one sees the living organism turn into a corpse. Alongside the abstract indifferent cold knowledge, such a feeling will arise through the true realization that technology is the processing of the inanimate, the dead. This feeling will become the most powerful impetus to seek the spirit in new directions. I could well imagine the following view of the future: Man looks out over the chimneys, the factories, the telephones — everything that technology has produced in wondrous ways in the most recent times. He stands atop this purely mechanical world, the grave of all things spiritual, and he calls out longingly into the universe — and his yearning will be fulfilled. Just as the dead stone yields the living fiery spark if handled correctly, so from our dead technology will emerge the living spirit, if human beings have the right feelings about what technology is. On the other hand, one need only understand clearly what pure thinking is; namely the semblance from which can be brought forth the most powerful moral impulses — those individual moral impulses that I have described in my Philosophy of Freedom . Then, in a new way, man will face the feeling that was once confronted by Nicholas Cusanus and Meister Eckhart. They said: When I life myself beyond everything that I am ordinarily accustomed to observe, I come to “nothingness” with all that I have learned. But in this “nothingness” there arises for me the “I.” If man really penetrates to pure thinking, then he finds in it the nothingness that turns into the I and from which emerges the whole wealth of ethical actions, that will create new worlds. I can imagine a person who first lets all knowledge of the preset, as inaugurated by natural science, impress itself on him and then (centuries after Meister Eckhart and Nicholas Cusanus) turns his gaze inward and with today's mode of thinking arrives at the nothingness of his inner life. In it, he discovers that the spirit really speaks to him. I can imagine that these two images merge. On the one hand, man goes to the place where barren technology has left the spirit behind. There he calls out into cosmic expanses for the spirit. On the other hand, he stops, thinks and looks within himself. And here, out of his inner being, he receives the divine answer to the call he sent out into the distances of the universe. When we learn, through a new, anthroposophically imbued natural science, to let the calls of infinite longing for the spirit, sent out into the world, resound in our inner being, then this will be the right starting point. Here, through an “anthroposophized” inner perception, we will find the answer to the yearning call for the spirit, desperately sounded out into the universe. I did not want to describe the development of natural science in recent times in a merely documentary fashion. Rather, I wanted to show you the standpoint of a human being, who comprehends this natural-scientific development and, in a difficult moment of humanity's evolution, knows the right things to say to himself in regard to the progress of mankind.

The Origins of Natural Science

Lecture IX

https://rsarchive.org/Lectures/GA326/English/AP1985/19230106p01.html

Dornach

6 Jan 1923

GA326-9

(from the 2nd German Edition, abridged). NOTE BY EDITOR: The following pages are notes of collective conversations with Dr. Steiner on various occasions. After the more or less harmful effects of mineral fertilisers had been referred to, Dr. Steiner said on one occasion: In view of the obvious increase in output which people today seem to, think necessary, this kind of fertiliser might perhaps not be dispensed with. But the harmful effects upon man and animal will not fail to ensue. Some of these effects will appear only after several generations have passed. Remedies, therefore, have to be found in time. Such remedies are e.g. the leaves of fruit trees. It can be recommended, therefore, to plant fruit trees around arable land. In another discussion, Dr. Steiner spoke of the value of horn meal (ground horns and claws of cattle) as a fertiliser. He said that horn meal was one of the very best fertilisers if mixed with farmyard manure. The horn meal should not be sharply baked; the fresh horn meal is better because of its higher content of hydrogen. Hydrogen, Dr. Steiner said, is more important for its effect on the soil even than nitrogen. The Science of today has not yet discovered the importance of hydrogen for plant growth. (Taken from a conversation between Dr. Steiner and Dr. chem. Streicher) Dr. Streicher complained that modern agriculture confined itself to replacing in the soil the nitrogen, phosphoric acid and potassium, just as Liebig had suggested decades ago. Great danger arises from the nitrogen being compounded with very strong acids, which cause acidity of the soil and in case of drought in summer may become disastrous. DR. STEINER: Actually, the only healthy fertilizer is cattle, manure. This should be our starting point. In addition to this a principle has to be found whereby a healthy nitrogen content of the soil may be brought about. I cannot yet tell how this can be done; it ought to be a principle which causes the earthworms and similar animals to “work the soil through.” Besides this, certain weeds have to be discovered which should be planted in the neighbourhood of the field. It is, for example, important to plant sainfoin on rye and wheat fields — at least along the edge. This influence actually exists. You have to test rationally [“rational” is often used by Dr. Steiner in the sense of Goethe, as opposite to mere empiricism.] by experiment the fact that it is good to have horse radish planted along the edge of potato fields, and corn flowers grown among corn and to have the poppies destroyed. It is such things as these which have to be considered in studying the whole problem of fertilizers. Otherwise you arrive at abstract principles and confine yourselves to the mere neutralisation of the acidity of the soil. This would kill step by step the fertility of the soil; it would make it “deaf” (taub). Neither should one fall into the other extreme and use only plant manure. This is without doubt unfavourable to plant growth. The only ideal fertilizer is cattle manure. Besides this much depends on plant association, e.g. leguminous plants, especially sainfoin. And care should be taken to place all herbaceous plants in a dry soil, whereas cereals need a moist soil. But importance certainly attaches to the personal human relation of the sower to the seed (paradoxical as this may seem to the modern chemist and biologist). If you observe carefully you will find a different effect produced by the way in which the sower proceeds, whether he simply takes the seed from out of the sack and flings it down, or whether he is accustomed to shake it a little in his hand and to strew it gently on the ground. These differences are of importance for the problem of manuring and it would be good to discuss them with interested farmers for they have experience in the things which are beginning to be lost in modern agriculture. I would advise you to examine old agricultural calendars to find hints on the problem of manuring. They contain ideas which sound strange but which could be formulated in chemical terms. [DR. STREICHER here mentioned that the critical situation of the farmer has been aggravated by the infectious diseases which decimated the livestock last year, and by the shortage of food.] DR. STEINER: Scientists should have the courage to point out where the principal harm is done. Stable feeding, which has been unduly praised in late years, has no doubt some connection with cattle tuberculosis as well as with the fact that the yield of milk is increased for a time and so on. The state of health, however, declines of course in the subsequent generations. And it is certain that the dung which the farmer's wife gathers in her basket or collects with a shovel from the meadow is better than the dung produced in stable-feeding. Moreover, the animal should be prevented from taking in the breath of its neighbour while feeding. This is harmful. In walking across the pastures, you will see that the animals graze at some distance from each other, because they do not want to have the breath of the neighbour near themselves. It may also happen that an animal gets some little sores and if the breath of another animal touches this wound it will undoubtedly be a cause of disease. [DR. STREICHER indicated that there are tendencies in modern agriculture to feed livestock directly on urea and to avoid the “indirect” way of feeding them on plants; the urea is gained from synthetic nitrogen. People think that the farding bag (rumen) of the cow contains certain bacteria which decompose the urea and builds it up into albumen. If these experiments are adopted in practice by farmers, the deterioration of the livestock may be intensified.] DR. STEINER: With experiments of this kind no true results can be attained. We have to realise that in the sphere of vitality there is always present the law of inertia, if I might call it so. The effects may not manifest themselves in this or the following, but certainly they will do so in the third generation. The workings of the vital force will meantime veil the result. If such experiments deal only with one generation, you get quite a wrong impression. In the third generation one will have effects which have their cause in the feeding of the grand-parent animals, but science will seek for the causes elsewhere. Vitality cannot be broken down at once, but only in the course of generations. DR. STREICHER mentioned experiments of the English botanist Bottomley who succeeded in producing in peat moss a certain bacterial life., which results in decomposing the humus substance to other unknown substances, which have a stimulating effect upon plant growth. He calls them `Auximones’ and puts them on the same level as biologists do vitamins. DR. STEINER: If these substances are used to stimulate the growth of plants destined for human food, no ill results may appear in those who eat this food. But their children will perhaps be born with hydrocephalus. The procedure shows that the plants will become hypertrophied and if they serve as food, the nerve life of the succeeding generations deteriorates. One has to realise that certain effects upon the life process do not manifest themselves until the succeeding or even the third generation. Research has to be extended as far as this. DR. STREICHER said that experiments of a scientist in Freiburg have shown that organic compounds of quicksilver have an extraordinarily stimulating effect upon vegetable growth« People hope that in this way vegetables can be produced in a very short time. The plants exhibit signs of hypertrophy. Dr. STEINER: In this case one should find out whether the children of those who consume them become impotent. All this has to be considered. Experiments must not be carried out in too restricted a sphere, because the vital process is something which goes on in “Time,” and only in course of years does it degenerate in its inherent forces. Further Indications on Agriculture given by Rudolf Steiner. DR. STEINER in answer to a question by Herr Stegemann.: In sowing oats one should take care that the soil is dry; the same applies to potatoes and root crops. [Wheat and rye on the other hand should be sown in moist soil.] As marginal plants for cereals, Dr. Steiner named deadnettle and sainfoin; they should be planted at a distance of 4½ to 5½ yards. Turnips and potatoes can be surrounded by horseradish; this need only be planted at the four corners of the field and must be removed every year. Animal pests, Dr. Steiner said, will vanish gradually with the cultivation of new kinds of plants. To combat wireworms, Dr. Steiner recommended the exposure of rain water to the waning moon for a fortnight. The water must be poured on the places where the wireworms occur and must moisten the ground as deep as the worms go. In order to prevent the degeneration of the potato, he recommended that seed potatoes be cut into small pieces with one eye only in each. This process should be repeated the following year. To a question by Count von Keyserlingk: As a remedy against rust, the field can be surrounded with a border of stinging nettles. Manure heaps should be carried out to the field and remain there until they are wanted. Dr. Steiner recommended that an orchard on peaty ground be treated with Kali Magnesia. On looking at the flower garden at Whitsuntide, 1924, Dr. Steiner said: “The flowers do not seem to be quite happy here| there is too much iron in the soil.” On coming to the roses, which were not flowering well and were suffering from mildew, he recommended that very finely distributed lead should be added to the soil. When he was questioned about the enormous number of cow horns that would surely be necessary for treating the 30,000 acres at Koberwitz, Dr. Steiner gave the astonishing reply that when all measures were fully applied, as few as 150 cow horns would suffice. When asked about sainfoin, his instructions were to use about 2 lbs. for sowing with one acre of corn. To combat snails and slugs, Dr. Steiner recommended that a solution of 3-in-100 seed of conifers should be sprayed. This is understood to mean: obtain the sap of these seeds by pressure, dilute it in the proportion of 3:1000 of water and spray this on to the plant beds. Dr. Steiner encouraged such an experiment. Similar experiments should be made elsewhere. On a walk through the fields at Arlesheim and Dornach, Dr. Steiner told those who were with him that to increase the vigour of Preparation 500 for use upon meadows .and fields with fruit trees the following should be done: Take some fruit and a handful of leaves of the fruit trees in question and boil them in ¼ gallon of water so as to form a kind of infusion, then add this “fruit tea” when the content of the cow horn is stirred in the pail. In order to strengthen diseased and weak fruit trees a 4-irich deep trench can be made around the stem at a distance corresponding to the crown of the tree and into this a considerable quantity of the diluted and stirred cow horn preparation (Nr. 500) can be poured. Referring to the silica preparation (Nr. 501), Dr. Steiner said that it might even suffice to take a lump of quartz the size of a. bean and knead it with moist soil from the ground on which the preparation later on is to be sprayed; this mixture to be filled into the horn. If little pieces of it are diluted and stirred with water, this will hold sufficient silica-radiation. Marginal plants for vegetables in the garden: sainfoin, dandelion and horseradish. Concerning plant diseases, Dr. Steiner said that plants actually cannot be ill because the etheric principle is always healthy. When troubles appear, they show that the environment of the plants, and especially the soil, is out of order. Thus the soil has to be treated, not the plant. As an example, he recommended the strengthening of aged trees by taking fresh soil from the roots of blackthorn (Prunus spinosa) and birch and spreading that around the roots of the trees. One can make the weed-destroyer (pepper) more effective by burning the root-stock together with the seeds of the weed in question. (Report by Ehrenfried Pfeiffer) Some years before the war, when asked about the use of human faeces, Dr. Steiner gave a warning against the use of them because the circle from man to plant and from the (manured) plant back to man is too short. The way should lead from man to plant, from plant to animal, from animal to plant and then back again to man. Peat moss as a means of soil improvement was more than once rejected by Rudolf Steiner. It is, he said, neither suitable as manure nor for improving the physical condition of the soil. We ought to add humus again' and again in every form instead: as compost, leaf mould, etc. To a question concerning mineral manure (cf. page 39, 47 of this lecture course) Dr. Steiner replied: If one is compelled to use it, one has always to mix it up with liquid or solid stable manure. The use of liquid matter from the closet he strongly objected to; neither should this be poured on fresh compost “even if the soil is not to be used for four years, it will still contain what is harmful.” Under trees infested with Woolly Aphis, nasturtium (Tropaeolum) should be planted in a circle.

The Agriculture Course (1938)

Introductory Lecture

https://rsarchive.org/Lectures/GA327/English/RSPC1938/AG1938_appendix.html

Dornach

20 Jun 1924

GA327-1