D'Arcy Wentworth Thompson

http://www.archive.org/stream/onaristotleasbio00thomrich#page/n3/mode/2up On Aristotle as a biologist.
http://www.archive.org/stream/ongrowthform1917thom/ongrowthform1917thom_djvu.txt On Growth and Form.
== Thompson on natural selection ==
The physiological speculations we need not discuss : but, to 
take a single example from morphology, we begin to understand 
the possibility, and to comprehend the probable meaning, of the 
* Cf. Loeb, Science, May 14, 191.5, 
f Cf. Baumann u. Roos, Vorkommen von lod im Thierkorper, Zeitschr. fur 
Physiol. Chem. xxi, xxii, 1895, 6. 
% Le Neo- Vitalisme, Rev. Scientifique, Mars 1911, p. 22 (of reprint). 
§ La vie et la mort, p. 43, 1902. 
Ill] GEOWTH AND CATALYTIC ACTION 137 
all but sudden appearance on the earth of such exaggerated and 
almost monstrous forms as those of the great secondary reptiles 
and the great tertiary mammals*. We begin to see that it is in 
order to account, not for the appearance, but for the disappearance 
of such forms as these that natural selection must be invoked. 
And we then, I think, draw near to the conclusion that what is 
true of these is universally true, and that the great function of 
natural selection is not to originate, but to remove : donee ad 
inter itum genus id natura redegitf. 
The world of things living, like the world of things inanimate, 
grows of itself, and pursues its ceaseless course of creative evolution. 
It has room, wide but not unbounded, for variety of living form 
and structure, as these tend towards their seemingly endless, but 
yet strictly limited, possibilities of permutation and degree : it 
has room for the great and for the small, room for the weak and 
for the strong; Environment and circumstance do not always 
make a prison, wherein perforce the organism must either live 
or die ; for the ways of life may be changed, and many a refuge 
found, before the sentence of unfitness is pronounced and the 
penalty of extermination paid. But there comes a time when 
"variation," in form, dimensions, or other qualities of the organism, 
goes farther than is compatible with all the means at hand of 
health and welfare for the individual and the stock ; when, under 
the active and creative stimulus of forces from within and from 
without, the active and creative energies of growth pass the 
bounds of physical and physiological equilibrium : and so reach 
the limits which, as again Lucretius tells us, natural law has set 
between what may and what may not be, 
"et quid quaeque queant per foedera naturai 
quid porro nequeant." 
Then, at last, we are entitled to use the customary metaphor, 
and to see in natural selection an inexorable force, whose function 
* Cf. Dendy, Evolutionary Biology, 1912, p. 408; Brit. Ass. Report (Portsmouth), 
1911, p. 278. 
I Lucret. v, 877. "Lucretius nowhere seems to recognise the possibility of 
improvement or change of species by 'natural selection'; the animals remain as 
they were at the first, except that the weaker and more useless kinds have been 
crushed out. Hence he stands in marked contrast with modern evolutionists." 
Kelsey's note, ad loc. 
138 THE RATE OF GROWTH [cs. 
is not to create but to destroy, — to weed, to prune, to cut down 
and to cast into the fire*. 
===selection2===
* Even after we have so narrowed the scope and sphere of natural selection, 
it is still hard to understand ; for the causes of extinction are often wellnigh as hard 
to comprehend as are those of the origin of species. If we assert (as has been 
lightly done) that Smilodon perished owing to its gigantic tusks, that Teleosaurus 
was handicapped by its exaggerated snout, or Stegosaurus weighed down by its 
intolerable load of armour, we may be reminded of other kindred forms to show 
that similar conditions did not necessarily lead to extermination, or that rapid 
extinction ensued apart from any such visible or apparent disadvantages. Cf. 
Lucas, F. A., On Momentum in Variation, Amer. Nat. xh, p. 46, 1907. 
t See Professor T. H. Morgan's Regeneration (316 pp.), 1901 for a full account 
and copious bibliography. The early experiments on regeneration, by Vallisneri, 
Reaumur, Bonnet, Trembley, Baster, and others, are epitomised by HaUer, Elem. 
Physiologiae, vm, p. 156 seq. 
J Journ. Experim. Zool. vii, p. ,397, 1909. 
===selection3===
Histologically, the case is illustrated by a well-known pheno- 
menon in embryology. In the segmenting ovum, there is a 
tendency for the cells to be budded off in linear series ; and so 
they often remain, in rows side by side, at least for a considerable 
time and during the course of several consecutive cell divisions. 
Such an arrangement constitutes what the embryologists call the 
"radial type" of segmentation*. But in what is described as the 
"spiral type" of segmentation, it is stated that, as soon as the 
first horizontal furrow has divided the cells into an upper and 
a lower layer, those of "the upper layer are shifted in respect 
to the lower layer, by means of a rotation about the vertical 
axisf." It is, of course, evident that the whole process is 
merely that which is familiar to physicists as "close packing." 
It is a very simple case of what Lord Kelvin used to call 
"a problem in tactics." It is a mere question of the rigidity 
of the system, of the freedom of movement on the part of 
its constituent cells, whether or at what stage this tendency 
to slip into the closest propinquity, or position of minimum 
potential, will be found to manifest itself. 
However the hexactinellid spicules be arranged (and this is 
* Se^, for instance, the figures of the segmenting egg of Synapta (after Selenka), 
in Korschelt and Heider's Vergleichende Entwicklutigsgescliichte (AUgem. Th., 3*<^ 
Lief.), p. 19, 1909. On the spiral type of segmentation as a secondary derivative, 
due to mechanical causes, of the "radial" type of segmentation, see E. B. Wilson, 
CeU-Uneage of Nereis, Journ. of Morphology, vi, p. 450, 1892. • 
•f Korschelt and Heider, p. 16. 
454 ON CONCRETIONS, SPICULES, ETC. [ch. 
not at all easy to determine) in relation to the tissues and chambers 
of the sponge, it is at least clear that, whether they be separate 
or be fused together (as often happens) in a composite skeleton, 
they effect a symmetrical partitioning of space according to the 
cubical system, in contrast to that closer packing which is repre- 
sented and effected by the tetrahedral system*. 
This question of the origin and causation of the forms of 
sponge-spicules, with which we have noAv briefly dealt, is all the 
more important and all the more interesting because it has been 
discussed time and again, from points of view which are charac- 
teristic of very different schools of thought in biology. Haeckel 
found in the form of the sponge-spicule a typical illustration of 
his theory of "bio-crystalhsation"' ; he considered that these 
" biocrystals " represented "something midway — ein Mittelding — 
between an inorganic crystal and an organic secretion"; that 
there was a "compromise between the crystallising efforts of the 
calcium carbonate and the formative activity of the fused cells 
of the syncytium"; and that the semi-crystalline secretions of 
calcium carbonate " were utihsed by natural selection as ' spicules ' 
for building up a skeleton, and afterwards, by the interaction of 
adaptation and heredity, became modified in form and differen- 
tiated in a vast variety of ways in the struggle for existence f." 
What Haeckel precisely signified by these words is not clear to me. 
F. E. Schultze. perceiving that identical forms of spicule were 
developed whether the material were crystalline or non-crystalline, 
abandoned all theories based upon crystallisation ; he simply saw 
in the form and arrangement of the spicules something which 
was "best fitted" for its purpose, that is to say for the support 
and strengthening of the porous walls of the sponge, and found 
clear evidence of "utiUty" in the specific structure of these 
skeletal elements. 
===selection4===
IX] OF THE SKELETON OF SPONGES 455 
Sollas and Dreyer, as we have seen, introduced in various 
ways the conception of physical causation, — as indeed Haeckel 
himself had done in regard to one particular^ when he supposed 
the position of the spicules to be due to the constant passage of 
the water-currents. Though even here, by the way, if I under- 
stand Haeckel aright, he was thinking not merely of a direct or im- 
mediate physical causation , but of one manifesting itself through 
the agency of natural selection *. Sollas laid stress upon the " path 
of least resistance"' as determining the direction of growth; 
while Dreyer dealt in greater detail with the various tensions 
and pressures to which the growing spicule was exposed, amid 
the alveolar or vesicular structure which was represented alike 
by the chambers of the sponge, by the reticulum of constituent 
cells, or by the minute structure of the intracellular protoplasm. 
But neither of these writers, so far as I can discover, was inclined 
to doubt for a moment the received canon of biology, which sees 
in such structures as these the characteristics of true organic 
species, and the indications of an hereditary affinity by which 
blood-relationship and the succession of evolutionary descent 
throughout geologic time can be ultimately deduced. 
===selection5===
NOTE: Come back to tautology in this section
Lastly, Minchin, in a well-known paper f, took sides with 
Schultze, and gave reasons for dissenting from such mechanical 
theories as those of Sollas and of Dreyer. For example, after 
pointing out that all protoplasm contains a number of "granules" 
or microsomes, contained in the alveolar framework and lodged 
at the nodes of the reticulum, he argued that these also ought to 
acquire a form such as the spicules possess, if it were the case that 
these latter owed their form to their very similar or identical 
position. "If vesicular tension cannot in any other instance cause 
the granules at the nodes to assume a tetraxon form, why should 
it do so for the sclerites ? " In all probability the answer to this 
question is not far to seek. If the force which the "mechanical" 
hypothesis has in view were simply that of mechanical pressure, 
* Op. cif. p. 483. " Die geordnete, oft so sehr regelmassige imd zierliche Zusam- 
mensetzung des Skeletsystems ist zum grossten Theile luimittelbares Product 
der Wasserstromung ; die characteristische Lagerung der Spicula ist von der 
constanten Richtung des Wasserstroms hervorgebracht ; zum kleinsten Theile ist 
sie die Folge von Anpassungen an untergeordnete aussere Existenzbedingungen." 
t Materials for a Monograph of the Ascones, Q. J. M. S. XL, pp. 469-587, 1898. 
456 ON CONCRETIONS, SPICULES, ETC. [ch. 
as between solid bodies, then indeed we should expect that any 
substances whatsoever, lying between the impinging spheres, 
would tend (unless they were infinitely hard) to assume the 
quadriradiate or "tetraxon" form; but this conclusion does not 
follow at all, in so far as it is to surface-energy that we ascribe the 
phenomenon. Here the specific nature of the substances involved 
makes all the difference. We cannot argue from one substance 
to another ; adsorptive attraction shews its effect on one and not 
on another; and we have not the least reason to be surprised if 
we find that the little granules of protoplasmic material, which 
as they lie bathed in the more fluid protoplasm have (presumably, 
and as their shape indicates) a strong surface-tension of their 
own, behave towards the adjacent vesicles in a very different 
fashion to the incipient aggregations of calcareous or siliceous 
matter in a colloid medium. "The ontogeny of the spicules," says 
Professor Minchin, "points clearly to their regular form being a 
phylogetiefic adaptation, ivhicJi has become fixed and handed on by 
heredity, appearing in the ontogeny as a prophetic adaptation.^ 
And again, " The forms of the spicules are the result of adaptation 
to the requirements of the sponge as a whole, produced by the 
action of natural selection upon variation in every direction^ It 
would scarcely be possible to illustrate more briefly and more 
cogently than by these few w^ords (or the similar words of Haeckel 
quoted on p. 454), the fundamental difference between the 
Darwinian conception of the causation and determination of 
Form, and that which is characteristic of the physical sciences. 
If I have dealt comparatively briefly with the inorganic 
skeleton of sponges, in spite of the obvious importance of this 
part of our subject from the physical or mechanical point of view, 
it has been owing to several reasons. In the first place, though 
the general trend of the phenomena is clear, it must be at once 
admitted that many points are obscure, and could only be discussed 
at the cost of a long argument. In the second place, the physical 
theory is (as I have shewn) in manifest conflict with the accounts 
given by various embryologists of the development of the spicules, 
and of the current biological theories which their descriptions 
embody; it is beyond our scope to deal with such descriptions 
IX] OF THE RADIOLARIAN SKELETON 457 
in detail. Lastly, we find ourselves able to illustrate the same 
physical principles with greater clearness and greater certitude in 
another group of animals, namely the Radiolaria. In our descrip- 
tion of the skeletons occurring within this group we shall by no 
means abandon the preliminary classification of microscopic 
skeletons which we have laid down ; but we shall have occasion 
to blend with it the consideration of certain other more or less 
correlated phenomena. 
===selection6===
Notes: Finally got a tautology in this section
■f The whole phenomenon is described by biologists as a "surprising exhibition 
of constructive and selective activity," and is ascribed, in varying phraseology, to 
intelligence, skill, purpose, psychical actiArity, or "microscopic mentality": that is 
to say, to Galen's rex^i-Kr) 0i'>ais, or " artistic creativeness " (cf. Brock's Galen, 1916, 
p. xxix). Ci. CaTY>en.teT, Mental Physiology, 1874, p. 41; Norman, Architectural 
achievements of Little Masons, etc., Ann. Mag. Nat. Hist. (5), i, p. 284, 1878; Heron- 
AUen, Contributions... to the Study of the Forammifera, Phil. Trans. (B), ccvi, 
pp. 227-279, 1915 ; Theory and Phenomena of Purpose and Intelligence exhibited by 
the Protozoa, as illustrated by selection and behaviour in the Foraminifera, Journ. R. 
Microscop. Sac. pp. 547-557, 1915; ibid., pp. 137-140, 1916. Prof. J. A. Thomson 
(New Statesman, Oct. 23, 1915) describes a certam little foraminifer, whose proto- 
plasmic body is overlaid by a crust of sponge-spicules, as "a psycho-physical 
individuality whose experiments in self-expression include a masterly treatment of 
sponge-spicides, and illustrate that organic skill which came before the dawn of Art." 
Sir Ray Lankester finds it "not difficult to conceive of the existence of a mechanism 
in the protoplasm of the Protozoa which selects and rejects building-material, and 
determines the shapes of the structures built, comparable to that mechanism which 
is assumed to exist in the nervous system of insects and other animals which 
'automatically' go through wonderfully elaborate series of complicated actions." 
And he agrees with "Darwin and others [who] have attributed the building up of 
these inherited mechanisms to the age-long action of Natural Selection, and the 
survival of those individuals possessing quaUties or 'tricks' of life-saving value," '''
J. R. Microsc. Soc. April, 1916, p. 136. 
===selection7===
Notes: In this section Thompson manages to get a glimpse of Popper unfalsifiability with ns
In certain Ammonites the septal outline is further compUcated 
in another way. Superposed upon the usual sinuous outline, with 
its "lobes" and "saddles," we have here a minutely ramified, or 
arborescent outline, in which all the branches terminate in wavy. 
Fig. 307. Suture-line of a Tiiassic Ammonite (Pinacoccras). 
(From Zittel, after Hauer.) 
more or less circular arcs, — looking just Uke the 'landscape 
marble ' from the Bristol Rhaetic. We have no difficulty in 
recognising in this a surface-tension phenomenon. The figures 
are precisely such as we can imitate (for instance) by pouring a 
XI] CONCLUSION 585 
few drops of milk upon a greasy plate, or of oil upon an alkaline 
solution. 
We have very far from exhausted, we have perhaps little 
more than begun, the study of the logarithmic spiral and the 
associated curves which find exemplification in the multitudinous 
diversities of molluscan shells. But, with a closing word or two, 
we must now bring this chapter to an end. 
In the spiral shell we have a problem, or a phenomenon, of 
growth, immensely simplified by the fact that each successive 
increment is irrevocably fixed in regard to magnitude and position, 
instead of remaining in a state of flux and sharing in the further 
changes which the organism undergoes. In such a structure, then, 
we have certain primary phenomena of growth manifested in their 
original simplicity, undisturbed by secondary and conflicting 
phenomena. What actually grotvs is merely the lip of an orifice, 
w^here there is produced a ring of solid material, whose form we 
have treated of under the name of the generating curve ; and 
this generating curve grows in magnitude without alteration of 
its form. Besides its increase in areal magnitude, the growing 
curve has certain strictly limited degrees of freedom, which define 
its motions in space : that is to say, it has a vector motion at 
right angles to the axis of the shell ; and it has a sliding motion 
along that axis. And, though we may know nothing whatsoever 
about the actual velocities of any of these motions, we do know 
that they are so correlated together that their relative velocities 
remain constant, and accordingly the form and symmetry of the 
whole system remain in general unchanged. 
But there is a vast range of possibilities in regard to every 
one of these factors : the generating curve may be of various 
forms, and even when of simple form, such as an ellipse, its axes 
may be set at various angles to the system ; the plane also in 
which it lies may vary, almost indefinitely, in its angle relatively 
to that of any plane of reference in the system ; and in the several 
velocities of growth, of rotation and of translation, and therefore 
in the ratios between all these, we have again a vast range of 
possibihties. We have then a certain definite type, or group of 
forms, mathematically isomorphous, but presenting infinite diver- 
sities of outward appearance : which diversities, as Swammerdam 
586 THE LOGARITHMIC SPIRAL [ch. xi 
said, ex sola nascuntur diversitate gyrationum ; and which accord- 
ingly are seen to have their origin in differences of rate, or of 
magnitude, and so to be, essentially, neither more nor less than 
differences of degree. 
In nature, we find these forms presenting themselves with 
but little relation to the character of the creature by which they 
are produced. Spiral forms of certain particular kinds are common 
to Gastropods and to Cephalopods, and to diverse families of 
each; while outside the class of molluscs altogether, among the 
Foraminifera and among the worms (as in Spirorbis, Spirographs, 
and in the Dentalium-like shell of Ditrupa), we again meet with 
/similar and corresponding forms. 
Again, we find the same forms, or forms which (save for external 
ornament) are mathematically identical, repeating themselves in 
all periods of the world's geological history ; and, irrespective of 
climate or local conditions, we see them mixed up, one with 
another, in the depths and on the shores of every sea. It is hard 
indeed (to my mind) to see where Natural Selection necessarily 
enters in, or to admit that it has had any share whatsoever in the 
production of these varied conformations. Unless indeed we use 
the term Natural Selection in a sense so wide as to deprive it of 
any purely biological significance; and so recognise as a sort of 
natural selection whatsoever nexus of causes sufiices to differ- 
entiate between the likely and the unlikely, the scarce and the 
frequent, the easy and the hard : and leads accordingly, under 
the pecuUar conditions, limitations and restraints which we call 
"ordinary circumstances," one type of crystal, one form of cloud, 
one chemical compound, to be of frequent occurrence and another 
to be rare. 
===selection8===
notes: Fibonacci sequences in leaves and ns
is to vary, to make blind shots at constructions, or to 'mutate 
as it is now termed ; and the most suitable of these constructions 
will in the long run be isolated by the action of Natural Selection.' 
Finally, and this is the most concrete objection of all, the supposed 
isolation of the leaves, or their most complete "distribution to 
the action of the surrounding atmosphere" is manifestly very little 
affected by any conditions which are confined to the angle of 
azimuth. If we could imagine a case in which all the leaves of 
the stem, or all the scales of a fir-cone, were crushed down to one 
and the same level, into a simple ring or whorl of leaves, then 
indeed they would have their most equable distribution under 
the condition of the "ideal angle," that is to say of the "golden 
mean." But if it be (so to speak) Nature's object to set them 
further apart than they actually are, to give them freer exposure 
to the air than they actually have, then it is surely manifest that 
the simple way to do so is to elongate the axis, and to set the 
leaves further apart, lengthways on the stem. This has at once 
a far more potent effect than any nice manipulation of the "angle 
of divergence." For it is obvious that in i^(^ . sin 6) we have a 
greater range of variation by altering 6 than by altering 4>. We 
come then, without more ado, to the conclusion that the "Fibon- 
acci series," and its supposed usefulness, and the hypothesis of 
its introduction into plant-structure through natural selection, 
are all matters which deserve no place in the plain study ol 
botanical phenomena. As Sachs shrewdly recognised years ago. 
all such speculations as these hark back to a school of mystical 
idealism. 
===selection9===
In more recent times, other theories, based upon the principles 
of Natural Selection, have been current and very generally accepted, 
to account for these diversities of form. The pointed, conical 
egg of the guillemot is generally supposed to be an adaptation, 
* Cf. Lapierre, in Buffon's Histoire Naturelle, ed. Sonnini, 1800. 
t Eier 4er Vogel Deutschlands, 1818-28 (cit. des Murs, p. 36). 
t Traite d'Oologie, 1860, 
§ Lafresnaye, F. de, Comparaison des cBufs des Oiseaux avec leurs squelettes, 
comme seul moven de reconnaitre la cause de leurs differentes formes, Bev. ZooL, 
1845, pp. lSO-187, 239-244. 
II a. Des Murs, p. 67: "EUe devait encore penser au moment ou ce germe 
aurait besoin de I'espace necessaire a son accroissement, a, ce moment ou...il devra 
remplir exactement I'intervalle circonscrit par sa fragile prison, etc." 
^ Thienemann, F. A. L., Syst. Darstellung der Fortpflanzung der Vogel Europas, 
Leipzig, 1825-38. 
654 ON THE SHAPES OF EGGS [ch. 
advantageous to the species in the circumstances under which 
the egg is laid ; the pointed egg is less apt than a spherical one to 
roll off the narrow ledge of rock on which this bird is said to lay 
its sohtary egg, and the more pointed the egg, so much the fitter 
and UkeUer is it to survive. The fact that the plover or the 
sandpiper, breeding in very different situations, lay eggs that are 
also conical, ehcits another explanation, to the effect that here 
the conical form permits the many large eggs to be packed closely 
under the mother bird * . Whatever truth there be in these apparent 
adaptations to existing circumstances, it is only by a very hasty 
logic that we can accept them as a vera causa, or adequate 
explanation of the facts ; and it is obvious that, in the bird's egg, 
we have an admirable case for the direct investigation of the 
mechanical or physical significance of its formf. 
===selection10===
To buttress the theory of natural selection the same instances 
of "adaptation" (and many more) are used, which in an earher 
but not distant age testified to the wisdom of the Creator and 
revealed to simple piety the high purpose of God. In the words 
of a certain learned theologian J, "The free use of final causes to 
explain what seems obscure was temptingly easy.... Hence the 
finahst was often the man who made a liberal use of the ignava 
ratio, or lazy argument: when you failed to explain a thing by 
the ordinary process of causahty, you could "explain" it by 
reference to some purpose of nature or of its Creator. This method 
lent itself with dangerous facihty to the well-meant endeavours 
of the older theologians to expound and emphasise the beneficence 
of the divine purpose." Mutatis mutandis, the passage carries 
its plain message to the uaturahst. 
The fate of such arguments or illustrations is always the same. 
They attract and captivate for awhile; they go to the building 
of a creed, which contemporary orthodoxy defends under its 
severest penalties : but the time comes when they lose their 
fascination, they somehow cease to satisfy and to convince, their 
foundations are discovered to be insecure, and in the end no man 
troubles to controvert them. 
But of a very different order from all such "adaptations" as 
these, are those very perfect adaptations of form which, for 
instance, fit a fish for swimming or a bird for flight. Here we are 
* Nature, l, p. 572; li, pp. 33, 57, 533, 1894-95. 
f They are "wonderfully fitted for 'vanishment' against the flushed, rich- 
coloured skies of early morning and evening.... their chief feeding-times"; and 
"look like a real sunset or dawn, repeated on the opposite side of the heavens, — 
either east or west as the case may be": Thayer, Concealing -coloration in the 
Animal Kingdom, New York, 1909, pp. 154-155. This hypothesis, like the rest, 
is not free from difficulty. Twilight is apt to be short in the homes of the flamingo : 
and moreover. Mr Abel Chapman, who watched them on the Guadalquivir, tells 
us that they feed by day. 
% Principal Galloway, Philosophy of Religion, p. 344, 1914. 
XVI] THE PROBLEM OF ADAPTATION 673 
far above the region of mere hypothesis, for we have to deal with 
questions of mechanical efficiency where statical and dynamical 
considerations can be applied and established in detail. The 
naval architect learns a great part of his lesson from the investi- 
gation of the stream-lines of a fish ; and the mathematical study 
of the stream-lines of a bird, and of the principles underlying the 
areas and curvatures of its wings and tail, has helped to lay the 
very foundations of the modern science of aeronautics. When, 
after attempting to comprehend the exquisite adaptation of the 
swallow or the albatross to the navigation of the air, we try to 
pass beyond the empirical study and contemplation of such 
perfection of mechanical fitness, and to ask how such fitness came 
to be, then indeed we may be excused if we stand wrapt in wonder- 
ment, and if our minds be occupied and even satisfied with the 
conception of a final cause. And yet all the while, with no loss 
of wonderment nor lack of reverence, do we find ourselves con- 
strained to believe that somehow or other, in dynamical principles 
and natural law, there lie hidden the steps and stages of physical 
causation by which the material structure was so shapen to its 
ends*. 
But the problems associated with these phenomena are 
difficult at every stage, even long before we approach to the 
unsolved secrets of causation ; and for my part I readily confess 
that I lack the requisite knowledge for even an elementary 
discussion of the form of a fish or of a bird. But in the form of 
a bone we have a problem of the same kind and order, so far 
simplified and particularised that we may to some extent deal 
with it, and may possibly even find, in our partial comprehension 
of it, a partial clue to the principles of causation underlying this 
whole class of problems. 
===Irreducible Complexity===
notes: Highlight Thompson seemingly first glimpse of Behe's IC or Irreducible Functionality concept
NOTES: Thompson called it composite integrity
In various ways our structural problem is beset by "limiting 
conditions." Not only must rigidity be associated with flexibility, 
but also stability must be ensured in various positions and 
attitudes ; and the primary function of support or weight-carrying 
must be combined with the provision of points (Vappui for the 
muscles concerned in locomotion. We cannot hope to arrive at 
a numerical or quantitative solution of this complicate problem, 
but we have found it possible to trace it out in part towards a 
qualitative solution. And speaking broadly we may certainly 
say that in each case the problem has been solved by nature 
herself, very much as she solves the difficult problems of minimal 
areas in a system of soap-bubbles; so that each animal is fitted 
with a backbone adapted to his own individual needs, or (in 
other words) corresponding exactly to the mean resultant of the 
stresses to which as a mechanical system it is exposed. 
Throughout this short discussion of the principles of con- 
struction, limited to one part of the skeleton, we see the same 
general principles at work which we recognise in the plan and 
construction of an individual bone. That is to say, we see a 
tendency for material to be laid down just in the lines of stress, 
and so as to evade thereby the distortions and disruptions due to 
shear. In these phenomena there lies a definite law of growth, 
712 ON FORM AND MECHANICAL EFFICIENCY [ch. 
whatever its ultimate expression or explanation may come to be. 
Let us not press either argument or hypothesis too far: but be 
content to see that skeletal form, as brought about by growth, 
is to a very large extent determined by mechanical considerations, 
and tends to manifest itself as a diagram, or reflected image, of 
mechanical stress. If we fail, owing to the immense complexity 
of the case, to unravel all the mathematical principles involved 
in the construction of the skeleton, we yet gain something, and 
not a little, by applying this method to the familiar objects of our 
anatomical study: obvia conspicimus, nubem pellente mathesi*. 
Before we leave this subject of mechanical adaptation, let us 
dwell once more for a moment upon the considerations which 
arise from our conception of a field of force, or field of stress, in 
which tension and compression (for instance) are inevitably 
combined, and are met by the materials naturally fitted to resist 
them. It has been remarked over and over again how harmoni- 
ously the whole organism hangs together, and how throughout 
its fabric one part is related and fitted to another in strictly 
functional correlation. But this conception, though never denied, 
is sometimes apt to be forgotten in the course of that process of 
more and more minute analysis by which, for simplicity's sake, 
we seek to unravel the intricacies of a complex organism. 
We tend, as we analyse a thing into its parts or into its 
properties, to magnify these, to exaggerate their apparent 
independence, and to hide from ourselves (at least for a time) the 
essential integrity and individuality of the composite whole. We 
divide the body into its organs, the skeleton into its bones, as 
in very much the same fashion we make a subjective analysis of 
the mind, according to the teachings of psychology, into component 
factors: but we know very well that judgment and knowledge, 
courage or gentleness, love or fear, have no separate existence, 
but are somehow mere manifestations, or imaginary co-efficients, 
of a most complex integral. And likewise, as biologists, we may 
go so far as to say that even the bones themselves are only in a 
limited and even a deceptive sense, separate and individual 
things. The skeleton begins as a continuum, and a continuum it 
remains all life long. The things that link bone with bone, 
* The motto was Macquorn Rankine's. 
XVI] ON THE SKELETON AS A WHOLE 713 
cartilage, ligaments, membranes, are fashioned out of the same 
primordial tissue, and come into being -pari jmssu, with the bones 
themselves. The entire fabric has its soft parts and its hard, its 
rigid and its flexible parts ; but until we disrupt and dismember 
its bony, gristly and fibrous parts, one from another, it exists 
simply as a "skeleton," as one integral and individual whole. 
A bridge was once upon a time a loose heap of pillars and rods 
and rivets of steel. But the identity of these is lost, just as if 
they were fused into a solid mass, when once the bridge is built; 
their separate functions are only to be recognised and analysed 
in so far as we can analyse the stresses, the tensions and the 
pressures, which affect this part of the structure or that; and 
these forces are not themselves separate entities, but are the 
resultants of an analysis of the whole field of force. Moreover 
when the bridge is broken it is no* longer a bridge, and all its 
strength is gone. So is it precisely with the skeleton. In it is 
reflected a field of force : and keeping pace, as it were, in action 
and interaction with this field of force, the whole skeleton and 
every part thereof, down to the minute intrinsic structure of the 
bones themselves, is related in form and in position to the lines 
of force, to the resistances it has to encounter; for by one of 
the mysteries of biology, resistance begets resistance, and where 
pressure falls there growth springs up in strength to meet it. 
And, pursuing the same train of thought, we see that all this is 
true not of the skeleton alone but of the whole fabric of the body. 
Muscle and bone, for instance, are inseparably associated and 
connected ; they are moulded one with another ; they come into 
being together, and act and react together*. We may study 
them apart, but it is as a concession to our weakness and to the 
narrow outlook of our minds. We see, dimly perhaps, but yet 
with all the assurance of conviction, that between muscle and 
bone there can be no change in the one but it is correlated with 
changes in the other; that through and through they are linked 
in indissoluble association ; that they are only separate entities 
* John Hunter was seldom wrong ; but I cannot believe that he was right when 
he said (Scientific Works, ed. Owen, i, p. 371), "The bones, in a mechanical view, 
appear to be the first that are to be considered. We can study their shape, 
connections, number, uses, etc., without considering any other part of the body.^' 
714 ON FORM AND MECHANICAL EFFICIENCY [ch. 
in this limited and subordinate sense, that they are parts of a 
whole which, when it loses its composite integrity, ceases to 
exist. 
The biologist, as well as the philosopher, learns to recognise 
that the whole is not merely the sum of its parts. It is this, and 
much more than this. For it is not a bundle of parts but an 
organisation of parts, of parts in their mutual arrangement, 
fitting one with another, in what Aristotle calls "a single and 
indivisible principle of unity" ; and this is no merely metaphysical 
conception, but is in biology the fundamental truth which lies at 
the basis of Geoffroy's (or Goethe's) law of "compensation," or 
"balancement of growth." 
Nevertheless Darwin found no difficulty in believing that 
"natural selection will tend in the long run to reduce any part 
of the organisation, as soon as, through changed habits, it becomes 
superfluous : without by any means causing some other part to 
be largely developed in a corresponding degree. And conversely, 
that natural selection may perfectly well succeed in largely deve- 
loping an organ without requiring as a necessary compensation 
the reduction of some adjoining part*." This view has been 
developed into a doctrine of the "independence of single char- 
acters" (not to be confused with the germinal "unit characters" 
of Mendelism), especially by the palaeontologists. Thus Osborn 
asserts a "principle of hereditary correlation," combined with a 
" principle of hereditary separability whereby the body is a colony, 
a mosaic, of single individual and separable charactersf-" 
I cannot think that there is more than a small element of truth 
in this doctrine. As Kant said, "die Ursache der Art der Existenz 
bei jedem Theile eines lebenden Korpers ist im Ganzen enthalten..'^ 
And, according to the trend or aspect of our thought, we may 
look upon the co-ordinated parts, now as related and fitted to the 
end or function of the whole, and now as related to or resulting 
from the physical causes inherent in the entire system of forces 
to which the whole has been exposed, and under whose influence 
it has come into being J. 
* Origin of Species, 6th ed. p. 118. 
t Atner. Naturalist, April, 1915, p. 198, etc. Cf. infra, p. 727. 
J Driesch sees in "Entelechy" that something which differentiates the whole
XVI] THE PROBLEM OF PHYLOGENY 715 
It would seem to me that the mechanical principles and 
phenomena which we have dealt with in this chapter are of no small 
importance to the morphologist, all the more when he is inclined 
to direct his study of the skeleton exclusively to the problem of 
phylogeny; and especially when, according to the methods of 
modern comparative morphology, he is apt to take the skeleton 
to pieces, and to draw from the comparison of a series of scapulae, 
humeri, or individual vertebrae, conclusions as to the descent 
and relationship of the animals to which they belong. 
It would, I dare say, be a gross exaggeration to see in every 
bone nothing more than a resultant of immediate and direct 
physical or mechanical conditions ; for to do so would be t® deny 
the existence, in this connection, of a principle of heredity. And 
though I have tried throughout this book to lay emphasis on the 
direct action of causes other than heredity, in short to circum- 
scribe the employment of the latter as a working hypothesis in 
morphology, there can still be no question whatsoever but that 
heredity is a vastly important as well as a mysterious thing; it 
is one of the great factors in biology, however we may attempt to 
figure to ourselves, or howsoever we may fail even to imagine, 
its underlying physical explanation. But I maintain that it is 
no less an exaggeration if we tend to neglect these direct physical 
and mechanical modes of causation altogether, and to see in the 
characters of a bone merely the results of variation and of heredity, 
and to trust, in consequence, to those characters as a sure and 
certain and unquestioned guide to affinity and phylogeny. 
Comparative anatomy has its physiological side, which filled 
men's minds in John Hunter's day, and in Owen's day ; it has its 
from the sum of its parts in the case of the organism: "The organism, we know, 
is a system the single constituents of which are inorganic in themselves ; only the 
whole constituted by them in their typical order or arrangement owes its specificity 
to 'Entelechy'" {Gifford LerAures, p. 2"?9, 1908): and I think it could be shewn 
that many other philosophers have said precisely the same thing. So far as the 
argument goes, I fail to see how this Entelechy is shewn to be peculiarly or 
specifically related to the living organism. The conception that the whole is 
ahvays somethini^ very different from its parts is a very ancient doctrine. The 
reader will perhaps remember how, in another vein, the theme is treated by Martinus 
Seriblerus: "In every Jack there is a meat-roasting Quality, which neither resides 
in the fly, nor in the weight, nor in any particular wheel of the Jack, but is the 
result of the whole composition; etc., etc." 
716 ON FOKM AND MECHANICAL EFFICIENCY [ch. 
classificatory and phylogenetic aspect, which has all but filled 
men's minds during the last couple of generations; and we can 
lose sight of neither aspect without risk of error and misconception. 
It is certain that the question of phylogeny, always difficult, 
becomes especially so in cases where a great change of physical 
or mechanical conditions has come about, and where accordingly 
the physical and physiological factors in connection with change 
of form are bound to be large. To discuss these questions at 
length would be to enter on a discussion of Lamarck's philosophy 
of biology, and of many other things besides. But let us take 
one single illustration. 
The affinities of the whales constitute, as will be readily 
admitted, a very hard problem in phylogenetic classification. 
We know now that the extinct Zeuglodons are related to the 
old Creodont carnivores, and thereby (though distantly) to the 
seals ; and it is supposed, but it is by no means so certain, that 
in turn they are to be considered as representing, or as allied to, 
the ancestors of the modern toothed whales*. The proof of any 
such a contention becomes, to my mind, extraordinarily difiicult 
and complicated ; and the arguments commonly used in such cases 
may be said (in Bacon's phrase) to allure, rather than to extort 
assent. Though the Zeuglodonts were aquatic animals, we do not 
know, and we have no right to suppose or to assume, that they 
swam after the fashion of a whale (any more than the seal does), 
that they dived like a whale, and leaped like a whale. But the fact 
that the whale does these things, and the way in which he does 
them, is reflected in many parts of his skeleton — perhaps more 
or less in all: so much so that the lines of stress which these 
actions impose are the very plan and working-diagram of great 
part of his structure. That the Zeuglodon has a scapula like that 
of a whale is to my mind no necessary argument that he is akin 
by blood-relationship to a whale : that his dorsal vertebrae are 
very different from a whale's is no conclusive argument that 
* "There can be no doubt that Fraas is correct in regarding this type (Procetus) 
as an annectant form between the Zeuglodonts and the Creodonta, but, although 
the origin of the Zeuglodonts is thus made clear, it still seems to be by no means 
so certain as that author believes, that they may not themselves be the ancestral 
forms of the Odontoceti"; Andrews, Tertiary Vertebrata of the Fayum, 1906, 
p. 235.
===selection12===
Notes: 
If, in the evolution of a fish, for instance, it be the case that 
its several and constituent parts — head, body, and tail, or this 
fin and that fin — represent so many independent variants, then 
our co-ordinate system will at once become too complex to be 
intelligible; we shall be making not one comparison but several 
* Historia Animalium i, 1. 
XVII] THE COMPARISON OF RELATED FORMS 727 
separate comparisons, and our general method will be found 
inapplicable. Now precisely this independent variability of parts 
and organs — here, there, and everywhere within the organism 
— would appear to be implicit in our ordinary accepted notions 
regarding variation; and, unless I am greatly mistaken, it is 
precisely on such a conception of the easy, frequent, and normal 
independent variability of parts that our conception of the process 
of natural selection is fundamentally based. For the morphologist, 
when comparing one organism with another, describes the 
differences between them point by point, and "character" by 
"character*." If he is from time to time constrained to admit 
the existence of "correlation" between characters (as a hundred 
years ago Cuvier first showed the way), yet all the while he 
recognises this fact of correlation somewhat vaguely, as a pheno- 
menon due to causes which, except in rare instances, he can hardly 
hope to trace ; and he falls readily into the habit of thinking and 
talking of evolution as though it had proceeded on the lines of his 
own descriptions, point by point, and character by characterf. '''
===selection13===
Natural selection 4, 58, 137, 456, 586, 
609, 651, 653
Category:TauTology