# Consciousness Studies/Geometrical phenomenalism

Contents
"If consciousness is in fact defined (and different) at every moment of time, it should also be related to points in space: the truly subjective observer system should be related to space-time points." from "Quantum Theory and Time Asymmetry", Zeh (1979).
It has been shown that conscious experience is a view of the output of the brain, it has no apparent function, it is seen from a point that is, itself, empty and it operates no processes. This bizarre description of consciousness should have been expected because if consciousness were simple it would have been explained centuries ago. In this chapter the description will be phrased in simple mathematical language and related to the inferred physical world so that it can be understood in terms of the neurophysiology of the brain.
The theory will describe experience as a virtual reality within the brain that spans both time and space. This virtual reality exists in the form of a set of vectors directed at an observation point which create a geometric form that we know as a 'view'. It will be proposed that our brains, like the rest of the universe (see Chapter 3), are arranged in at least 4 dimensions and it is the peculiar geometry of this four dimensional space-time that is responsible for the 'view'. It will be shown that nothing need move into the observation point within this 'view'. It will be proposed that most of the brain is dedicated to populating this small, conscious, volume of brain activity with a model of the world and self.
Part 1: Explaining the View
The first step in developing a hypothesis that incorporates consciousness is to describe the geometry of the 'view' described in chapter 1. The 'view' that is our experience consists of things arranged vertically and horizontally with an uncertain separation of things from the observation point. The observation point is a geometrical phenomenon that contains nothing and the things in the view occur simultaneously. The things in the view must be things in themselves, there cannot be a need for any other observer or further observation, this implies that a 4D coordinate system is required to describe them (see Chapter 3). The things in the view cannot have any separation from the point but also cannot be at the point in 3D. These constraints of simultaneity, four coordinate axes and zero separation from a point suggest that the position of any object in the view relative to the observation point might be described, using Pythagoras' theorem for intervals, as:
(1) 0 = x$^2$ + y$^2$ + z$^2$ – b$^2$
The equation describes a succession of three dimensional spherical surfaces that are separated from the observation point (origin) along the x,y,z and b axes but any point on the inside of any of these spheres is no distance at all from the origin. Things are 'out there' in the x,y,z directions but also no distance from the origin when the b direction is taken into account. The separation between things in the view depends upon the angular separation of the things at the observation point. There is both nothing and the whole view at the observation point in the same way as we observe the view at a point but can find nothing inside this point. This description is not a 'theory', it is simply a description of an aspect of conscious experience that uses mathematics.
Is it possible to go a step further and use the constraint of simultaneity to identify 'b' with a length of physical time, 'ct'? So that:
0 = x$^2$ + y$^2$ + z$^2$ – ct$^2$
This equation describes both binding and simultaneity. It has an identical form to the Minkowski Light Cone Equation (see Physics for Consciousness Studies) and either the equation is describing some non-physical space or it's use in this context is a reinterpretation of Relativity Theory (specifically, time might have imaginary coordinates, see below). This equation is a theory because there is no way to determine that b=ct, the identity is assumed from the similarity of the two equations and their field of application. If equation (1) were correct the 'view' would be a small volume or shell of brain activity, probably in the thalamus. The 'view' would be sensitive to mechanical distortion because x,y,z refer to actual positions within a volume of brain. The equation can be tested by cyclically deforming potential sites in the thalamus and observing the response of subjects. Bilateral deformation would be required and the expected response, if the deformation were severe, would probably be one of the following: absence seizure, akinetic mutism or delirium (see Note 1).
It has already been shown that bilateral electrical stimulation of the centromedian nuclei of the thalamus causes absence seizures (Velasco et al. (2000). It might also be expected that Transcranial Magnetic Stimulation could also be used to block ILN activity and so cause absence seizures. Administration of general anaesthetic by micropipette could be used to selectively deactivate areas of any nuclei that mediate consciousness and allow topographical analysis.
This hypothesis about the 'view' does not explain consciousness but it seems to account for the geometry of experience (perception, dreams, bodily sensation etc.).
Part 2: A Description of the Extended Present
The second step required for a theory of consciousness is to describe the "specious" or extended present.
The experience of a stable world involves not just a view but a view extended in time. This extension in time is not a trivial set of instantaneous, frozen models of the world but is a continuous set of events. We hear whole words and experience movements; we are not confined to an impossible instant. The important features of this time extension are that things are experienced extended in time at their location in mental space and that they are observed at a point. This was discussed in full in the section on "Time" in chapter 1. The empirical equation (1) can be extended by adding a displacement in another coordinate axis:
(2) 0 = x$^2$ + y$^2$ + z$^2$ - Δb$^2$ + Δe$^2$
Where Δe is a small displacement of an object in mental time; small displacements have been specified because the extended present is fairly short and may not be linearly related to the other variables. This equation applies to particular objects, once a sequence of events involving a given object has ended the events are no longer available i.e.: when a word is finished it is no longer in the extended present. This description is not a 'theory'. For a given spherical shell (x$^2$ + y$^2$ + z$^2$) is the radius, r, of the sphere relative to the observation point so:
0 = r$^2$ - Δb$^2$ + Δe$^2$
If r is small compared with Δb and Δe and constant:
Δb$^2$ ≈ Δe$^2$
These are empirical equations describing experience but they can be tentatively extended to describe physical space and time. If 'b' is substituted by physical time:
(cΔt)$^2$ = Δe$^2$
So Δt = Δe/c
And ΔT = Δt
Where T is mental time in seconds rather than metres and t is physical time in seconds. Our experience of time would be due to displacements in mental time, not physical time. In contrast, the physical time axis would be responsible for creating the geometric form of the view where things seem to be observed at a point because it has an opposite sign to the other axes. Equation (2) is a highly simplified description of the geometric form of the view; even a brief consideration of the possible configurations of a five dimensional space-time leads to endless possibilities such as Lorentz Transformations of axes and the disappearance of separation along the path taken by the observation point. Again, the identification of 'b' with 'ct' means that this is a theory.
The arrangements of objects in time seem 'timelike' because they are independent arrangements of things at a given place that do not obscure each other, a thing arranged in space in the immediate past does not overlie its arrangement in space now. Furthermore the observation point seems to be moving perpetually along the time axis so that the extended present attached to a past event is always lost to observation at the end of the event, or event sequence. This time extended configuration of data might provide the stability required for a reference model of the world and mind, or Reference State, in a small set of neurons.
This idea of experience as a form rather than a process is well known (cf: Bateson's (1979) "zigzag ladder of dialectic between form and process") and it is usually argued that experience can be neither a form nor a process. However, if experience is a form that includes the succession of events then it is a form that includes processes. At any instant there is a structured set of events stretching into the past and spread out in space that are part of the geometric form. The events are separated by angles through both space and time at the observation point. The future has not yet been selected so there are no defined events leading into the future. This provides an experience of moving forward into the future at any instant.
An important feature of this theory is that experience is not the observation point at an instant. Experience is both the successions of events extended in time and the observation point. In the equation
0 = x$^2$ + y$^2$ + z$^2$ - Δb$^2$ + Δe$^2$
experience is all those events that have coordinates (x,y,z,b,e), not those events that have coordinates (0,0,0,0,0). This means that experience is a set of events laid out in a framework that has remarkable properties. It has a 'negative' dimension (b) that allows places where separations in both time and space are zero. The framework has a geometrical duality where the same events are at a point at an instant and 'out there', spread out in the time and space of the brain.
Part 3: Control of Brain Activity by a Geometrical Form
If this description is correct the past state of a system at a point exists and might provide a preferred basis for the present instant. This is not too dissimilar to Zeh's (1979) suggestion that the conscious observer is a configuration of quantum states at a point (see Note 2). The problem confronting the theorist is how to connect the empirical equation for the positions of the objects in experience:
0 = x$^2$ + y$^2$ + z$^2$ - Δb$^2$ + Δe$^2$
With Zeh's equation for the superposition at a point observer:
|β>$_0$ = ∫d(ф$_1$(x$_0$))... d(ф$_ν$(x$_0$)) f({ф$_ν$(x$_0$)}) |{ф$_ν$(x$_0$)}>
and how to integrate a five dimensional geometry into the physical universe. It should be stressed that equation (2) is an empirical equation. It is the task of mathematicians and theoretical physicists to discover how such an equation could be compatible with modern science or to suggest an equation that is more appropriate.
The Reference State would provide an alternative preferred basis to that supplied by the aqueous medium of the brain. If the Reference State selected configurations of brain activity that generated actions it would change the world in general via these actions in the normal way. In quantum mechanical terms, the state vector of the world in general would be most influenced by the ambient environment but would contain contributions from the preferred basis of each conscious observer. It should be stressed that this idea is purely theoretical.
The existence of a Reference State in the brain could be investigated by examining brain activity in comatose subjects. If the brain activity in comatose subjects shows patterns that can be ascribed to quantum fluctuations in individual neurons or small groups of neurons but does not show these in conscious subjects the hypothesis would be supported. Bershadskii et al. (2003) may have recently observed such an effect in the "genetically depressive limbic brain" of the Flinders Sensitive Line of rats.
A New Empiricism: Geometrical Phenomenalism
The theory that conscious experience is a phenomenon, a geometric form that allows knowledge of a phenomenal world, will be called 'geometrical phenomenalism'. Geometrical Phenomenalism maintains that consciousness is a complex phenomenon that consists of a geometric form of the output of neural processing. It is largely an empirical theory.
The empirical part of the theory is fairly straightforward, it proposes that the paradox of consciousness is due to a mind that is brain activity spread out in space and time but also not separated from a point that is at the present instant. This is how the mind seems as our physical body looks around the world: our experience is brain activity but it seems to be viewed from a point eye within this activity. The theory explicitly describes as 'non-conscious' all activity that is not in the space and time of the mind. It differs from information systems theories because it describes conscious experience, not the non-conscious processes that load things into this experience.
Part 3 of the theory is not empirical. As such it is most open to criticism. Each part of the theory is independent of the other parts so Part 1 may be true even if Part 2 or Part3 are found to be false.
The Interpretation of Relativity and Quantum Theory
Geometrical Phenomenalism introduces a negative dimension (Weyl, 1918) which may correspond to physical time. Historians of Relativity Theory will immediately recognise this as the 'imaginary time' used in early, simplistic models of the theory (see chapter 2) and modern Relativity Theorists will, quite rightly, chuckle at such an archaic concept. There can be little doubt that 'real time' is needed to describe the motion of matter and energy. Energy flows into an observation point along one path in space-time and flows out from it along another, different path. These two paths are not distinguished by 'imaginary time' but are clearly different in real time. However, there is a major difference between our conscious experience and this conventional description of the universe: nothing flows into the observation point in conscious experience.
Is it possible that space and time have one geometry that applies to observation points in conscious experience and another geometry that applies to actual movements of energy from place to place? The answer to this is not only 'yes' but there is ample evidence that this occurs. Quantum physicists have long persisted in using the archaic form of Relativity in a disguise known as the Wick Rotation in Feynman Path Integrals. They use this embarrassing formalism because it works; it describes how all the possible positions of a particle that never actually occur affect the position of the particle that is observed. The problem confronting quantum physicists is quite similar to the problem confronting the empirical science of consciousness: what is the geometry of space-time where nothing actually moves?
Cosmologists have also incorporated imaginary time into descriptions of the universe as a whole and the current, empirical description of the geometry of the universe might be summarised as:
".. we see that, today, the qualitative behavior of our universe is that of a de Sitter universe except that the presence of matter has caused the universe to expand less than in the de Sitter case." Reid et al. (2002). A "de Sitter" universe is described by the metric: ds$^2$ = dx$^2$ + dy$^2$ + dz$^2$ – dt$^2$ + de$^2$ where t is conventionally imaginary (i.e.: square root of minus one multiplied by t). This is very similar to equation (2) above.
The use of 'imaginary time' may not be the only way to explain conscious observation. It is possible that real time might apply, perhaps by some 'virtual movement of photons back and forwards towards the centre of a volume of neural tissue.
The Physical Nature of the Site of Conscious Experience
Any site for conscious experience would be a small, nearly spherical, shell or volume of neurons that is highly interconnected with the cortex and the rest of the brain. It would be physically and functionally close to sensory input paths to obtain reference data from the senses. It would be large enough to represent all the content of experience. The optic nerve contains about a million fibres so a total of about one million data points might be needed. Data could be held at the level of individual synapses. There might be over 100000 synapses per mm$^3$ (over 1000 per neuron) in a nucleus which means that a nucleus of 2 mmin radius (about 3 million synapses) might support a sufficient density of data points to be a consciousness centre.
It is probable that there would be at least four such centres with two archaic centres below the cerebellum and two below the cerebrum. Only one would be dominant. The requirement that only one nucleus is dominant means that it would need to be well connected to both hemispheres of the cerebrum.
The best candidate for such a centre for conscious experience is one of the centromedian nuclei of the thalamus although this is not the only possibility.
Qualia
Objects in experience consist of qualia such as colours, sounds etc. The field of qualia that is experience could be any field of neural activity in the ILN although it could be limited, for example, to an electromagnetic field (McFadden 2002) or a 'spin' field (Hu 2002).
The Problem of Knowledge
Imagine something for no time at all. It cannot be done. Say a word like 'at'. Could you know the 'a' if it lasted for no time? Knowing involves two factors, classification and continuity. It was pointed out in chapter 1 that knowledge of sorts remains even when there is nothing to classify, such as when meditating so that there is only dark or light. There seems to be no difference between the experience called 'knowledge' and the experience called 'continuity' in these circumstances. Continuity is experiencing your experience of experiencing without the need for recursion (i.e.: without the need for cycling things around from one moment to the next).
An experience of an experience suggests that each instant of observation is available to succeeding instants. This is quite possible if five coordinate axes are permitted along with zero length vectors because things can be arranged in an enormous number of different ways. This flexibility makes it possible for an extended experience in the past to be a subset of present extended experience.
Having read this section many readers may be thinking 'Ah, but how do I know what things mean? If I see a tree why do I know its a tree?'. The answer to this is that your non-conscious brain has most of the details of 'tree' classified and logged. You do not know these details consciously, you just know that such details exist, a state called 'familiarity'. The continuity of the sensation of familiarity attached to the tree and the body ('gut feeling') is 'knowing you know' the tree.
Depth Perception
Geometrical Phenomenalism does not include any direct experience of depth. The separation of the observation point from the things in experience is indeterminate which is why we see the stars on the ceiling of a planetarium or on the screens of virtual reality goggles as incredibly distant from us. Although depth is indeterminate we still feel as if our chests are below our heads and our feet are below our chests, how is this done?
If you shut your eyes and swing an arm the path of the hand is experienced in a shadowy way. This shadowy progress of the hand does not have a common English term to describe it but we can all experience it. (Technically it might be called kinaesthesia or motion somaesthesis). If uniform swings are used it can seem as if the moving hand has two components, the actual moving hand and copy that follows it a split second later. If the hand is moved from the head to the knee the path of the hand occurs as a shadowy arc stretching through the extended present. This raises the possibility that our experience of depth within and around our bodies is actually an experience of time. For instance, when we experience our feet being below our chest we are actually experiencing an imaginary movement of the hand or a movement of the focussing muscles in the eyes or a succession of sensations first from the chest then from the feet etc. The space occupied by the body then becomes an 'action space' with separations defined by the timing of movements and sensations.
Binocular depth perception is different from the sense of bodily extension. When we look at the medium and far distance through either one or both eyes the view is almost identical. If we focus on objects that are close to us the more distant object become blurred; the act of focussing separates the world into a shell of things that are in focus and other things that are blurred. If we focus past a nearby object the nearby object splits into two images, one blurred and solid and the other blurred and transparent. All of these effects combined with the change in the relative size of objects with distance provide cues for judging distance. At no time do we have a clear view of things arranged in depth in the same way as we have a clear view of things arranged vertically and horizontally. We do, however have a sense of where we could reach out and touch things, which suggests that imaginary motion somaesthesis may create an experience of depth. If the non-conscious brain is providing models of motion to augment the experience of depth then this may be one of many possible explanations for how the accuracy of depth judgement decreases with distance (see for instance Cutting & Vishton 1995).
Philosophical Implications of the Theory and Free Will
The most important philosophical implication is that time exists. The mind should be considered as a trans-temporal entity occupying a length of time with an extended present that is accessible now. Another feature of the model is that the brain itself might, occasionally, become the source of a branch-point in the quantum multiverse. The theory is also compatible with philosophical systems that deny the physical world and science because it considers science to be a consistent system of things that are compatible with observation. The physical world can be accepted or rejected without invalidating the theory. It is, of course, also compatible with ordinary natural philosophy.
The theory may also have implications for the philosophical problem of "free will". A vast amount has been written about "free will" and the current state of the arguments is summarised in Timothy O'Connor's entry in the <A HREF="http://www.seop.leeds.ac.uk/entries/freewill/">Stanford Encyclopedia of Philosophy</A>. The aspect of "free will" that is of most interest when discussing consciousness is whether there can be "conscious free will". We are certainly conscious of the decisions made by the non-conscious brain but are there any types of decision that are due to consciousness itself?
If the theory of consciousness proposed above is correct our 'reference state of mind' will have a marked effect on decision taking. This state will select processes that are consistent with it from a myriad of possible processes. The 'reference state of mind' itself will depend on the history of the individual's previous selections and exposure to the world at large. It will also depend upon the type of state of mind that the individual is seeking. It is unique to the individual (cf: the "no cloning" objection of quantum physics) and consists of a combination of all the things in conscious experience from emotions through pains in the back to attitudes. In the sense that our 'reference state of mind' may be unique, impossible to measure and equally difficult to predict it may be said to be a basis for "free will". But can we navigate to a new 'reference state of mind', can we choose the basis of our choices?
The Self
The space and time of the mind contains sense data from the world, sense data from the body and output from neural processes such as those that generate imaginary speech, daydreams, dreams etc.. 'I' am the body nearest to the observation point and this has a speech processor that calls this body and itself 'me'. My body has an array of sensory processes, especially splanchnic sensations, motor controls, and modelling activities, including imaginary speech that are not found in the part of the mind that is not correlated with the body. This collection in the mind of body, thoughts, feelings and actions I call my 'self'. Most parts of 'self', such as the body, skills etc. are not themselves conscious. Only the mind is conscious and this contains things correlated with both the world and the 'self'.
Notes
Note 1: Schiff and Plum (2003) categorise the following states that can occur after destruction of the Intra Laminar nuclei as aroused but not aware or possibly not aware: persistent vegetative states, absence seizures, akinetic mutism, and severe delirium. In the absence of consciousness there is a profound lack of purposeful activity.
Note 2: Zeh's derivation of the quantum point observer.
Zeh postulates that the universe contains an observer that is a local system that can be specified as an orthonormal basis of states ф$_i$, the rest of the universe is a basis of states ψ$_k$, the global state of the universe is given by: Σ$_{ik}$ ф$_i$ψ$_k$. If a result, l is observed the new state would be a product state: ф$_l$ψ$_l$ where ф and ψ in this case refer only to the ensemble of probabilities of the new state. If space-time at a given moment, t, is divided into two regions, I$_1$ being the observer and I$_2$ the rest then any state vector |ф$_ν$(x)> is given by the direct product |ф$_ν$(x)$_1$>|ф$_ν$(x)$_2$>. It is possible to use this to derive the state vector of a given state (l) in terms of the space-time of the observer:
|β>$_1$ = ∫$_1$ D ф$_ν$(x) ψ$_l$[ф$_ν$(x), t]|ф$_ν$ (x)>$_1$
This specifies a set of product states that can be distinguished by the index, l. The integration only occurs over the space-time region of the observer and consciousness could branch into any of the product states. This means that at each point there is a different state. What is the state at a single point? This is derived from the previous equation with x set to x$_0$:
|β>$_0$ = ∫ d(ф$_1$(x$_0$))... d(ф$_ν$(x$_0$)) f({ф$_ν$(x$_0$)}) |{ф$_ν$(x$_0$)}>
So each point has a superposition of vectors.
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