A technician explains measurements whilst a scientist explains observations.

Alex Green's original paper

The following paper was submitted to numerous journals by Dr Green in 2002. I saw it on the internet a few years ago and it inspired my interest in this subject. I asked why it had not been published. The grounds for rejection were peculiar and showed that the editors had little understanding of relativity (my speciality) and no understanding that science progresses from empirical observation to (empirical) hypothesis to theory. Green refers to the fact that relativity is due to a 4D universe and that perception is empirically at least four dimensional so our experience might be expected if physics is right. My only gripe would be with the use of imaginary axes (a modern approach should use a metric tensor) but this is not unreasonable in an empirical hypothesis, and, of course, Minkowski did originally use imaginary axes. The paper is reproduced here with the author's permission.

A Testable, Geometrical Theory of Consciousness


Abstract - Descartes, Kant and others have given detailed empirical accounts of what it is like to be a conscious observer. Descartes described the observer as a non-extended entity (a geometric point) viewing things in an extended space. William James noted that our experience was extended in time as well as space. These descriptions can be combined to define conscious experience as things arranged in time and space that are at a point. This definition can be analysed using multidimensional geometry to produce a model where the contents of consciousness are 'folded' into a single place yet still in their original three dimensional positions. According to this model consciousness is brain activity, some of which derives from sense data. This brain activity is probably located in the thalamus although a more extensive field of activity cannot be ruled out. Any part of the brain that is conscious would be sensitive to mechanical deformation.

Key Words: Consciousness, thalamus, centromedian, intralaminar, relativity, multidimensional, quantum, deformation, localized.


It is frequently stated that conscious experience cannot be defined or described. Such statements are puzzling because philosophers of the western tradition have produced many descriptions of conscious experience that are consistent and generally in agreement with each other (Descartes 1641, Kant 1781, Green 2002).

Conscious experience was described by Descartes (1641) as the experience of things arranged in an extended space around a central, thinking observer who seems to occupy no space. Descartes also mentions that things in our experience can be assigned a duration and Kant elaborates upon this, pointing out that without representation in time the concepts of simultaneity and succession would be unknown to us.

These descriptions of conscious experience concur with our own experience. They can be summarised as an experience of things, including our bodies, smells, sounds, dreams etc. arranged around us in such a way that they are viewed and felt simultaneously at a point and extended in time and space.

Unfortunately this experience of consciousness contains numerous problems and paradoxes such as the problem of mental space, the problem of the experience of time, the problem of mental content and the problem of the "homunculus". These problems and paradoxes require explanation.

The problem of mental space is the paradox of how things which are evidently in our minds are seen as if they are separate from us. As an example, when you look at this page it seems separate from you but what are you actually seeing? The page makes an image on the retina that becomes activity in the brain; does this form some sort of electrical image in the brain and, if so, how can it be seen as if it is separate from the observer? Gregory (1966) describes this problem and qualifies it with the single sentence: "This is absurd." McGinn (1996) has reviewed the problem of mental space and concludes with the comment that consciousness "marks the place of a deep lack of knowledge about space, which is hard even to get into focus".

James (1890) described our conscious experience of time as "the short duration of which we are immediately and incessantly sensible". Le Poidevin (2000) summarises Gombrich's (1964) view of this as: "If the experienced present were only a durationless instant, then we could not understand a spoken sentence, because what would be presented to the senses at any point would only be a meaningless phoneme - indeed not even that, since any sound necessarily takes up time". Both James and Gombrich are describing a conscious experience that is extended through time, not as memories retrieved into the "durationless instant" but as a real extension in time that is similar to the way this text is extended in space.

The problem of content is linked to the problem of qualia. A typical quale is the experience of the colour "purple" (Tye (1997)). This experience can be prompted by light but also occurs in dreams and can be imagined. The nature of qualia is a mystery, are they brain activity and if so, how do nerve impulses become purple? Qualia, combined with extent and duration, compose things that are part of the content of consciousness.

The problem of the homunculus is closely related to the problems of space and time, if we observe the contents of our minds as if they are separate from us or historical then what is doing the observing? (cf: Ryle's "Ghost in the Machine" (Ryle 1949)) .

Any theory of consciousness would need to describe mental space, time and content even if it were concluded that the experiences of space, time or content were absurd, illusory or wrongly construed because most people believe that their experiences are events in space. Searle (1992) wrote that "conscious states are situated and they are experienced as situated" and further commented that "it is precisely the task of neurobiology to explain these and other questions about consciousness".

Each of these problems will be analysed below and a theory proposed to incorporate them all.

Mental Space

Consider this page of text when viewed through one eye. Your sense of depth is slightly reduced compared with binocular vision but if you move closer to the page it is evident that you are closer because the page fills more of your field of view. As you might expect, the world appears as if a 'point eye' is viewing it. There is a spherical space arranged all around this 'point eye' and things are seen simultaneously. Observation from a point is also suggested by the way every point on the text seems to send a unique ray to your 'point eye' that is not smudged or obscured by rays coming from other parts of the text.

There is a problem with viewing from a point: according to the simple geometry and physics taught at school, something separated from an observation point cannot be observed unless another thing, such as a photon of light, or other information carrier, moves from it to the observation point. If this were the case then all the bits of information would pile up on top of each other at the point so that nothing could be seen distinctly. Clearly if we do observe from a point it must involve something more than simple geometry and physics.

What we seem to observe in mental space is a sphere of information that is viewed from a point with the paradox that the information would also need to be at the point to be viewed.

This description can be put in a simple mathematical form. Suppose the observation point is the origin of a co-ordinate system and x, y, z is the position of any bit of information on the inside of a sphere. The separation (h) of the bit of information from the viewing point is given by the three dimensional version of Pythagoras' theorem as:

h2 = x2 + y2 + z2

In three dimensions information can only be at the origin when x, y, and z are zero so that h is zero.

The analysis shows that in 3D information can either be on the inside of a sphere or jumbled up at a point, it cannot be in both places. Gregory (1966) realised this when he considered the observation of the retinal image and concluded that transferring information from place to place in the brain was an "absurd" way of explaining our conscious experience. The impossibility of a 3D point observation shows that such an observation is not three dimensional. Our observation exists so it must be something other than a 3D projection.

What is required to describe our actual experience is a geometrical formula where the original positions of the information are preserved but where the projection, h, is zero, in other words a description where the information is projected in 3D but also at a point. This can be described by introducing a new co-ordinate (f) at right angles to the other three so that:

(1) 0 = x2 + y2 + z2 - f2

The new co-ordinate would be measured in units of "imaginary" metres (the square root of minus one times metres) or would be composed of a conjugate such as minus f times plus f. The "imaginary" co-ordinate is at right angles to the x, y and z axes and when an object is displaced along this co-ordinate its projection from the origin can vary until it is zero. Equation (1) seems to be a credible description of mental space: (x2 + y2 + z2) represents the squared projection of information on the inside of a 3D sphere and the way the entire equation sums to zero describes how the information is also no distance from the observation point.

If we experience things so that their projection from the viewing point is zero then they would appear to be separated from each other by angles subtended at the viewing point rather than by actual 3D space. This is indeed how things appear to us, even things in dreams subtend angles at our mind's viewing point or 'mind's eye'. The mind's eye is not limited to vision, the positions of all sensations are related back to this observation point. Perhaps, in the spirit of science, before we ask what sees what the mind's eye sees, it would be productive to explore this empirical viewing point further.

Equation (1) is an empirical formula that describes experience, not an application of physical theory to experience, it does however have the same form as a well-known equation in physics called the "Minkowski Light Cone Equation" (Minkowski 1908). The "Minkowski Light Cone Equation" transformed Einstein's principle of relativity into a theory of a universe that is a space-time continuum where space and time are geometrically interdependent. This formulation of relativity is now the accepted form in physics and underpins the whole of special relativity, general relativity and much of quantum physics (cf: Dirac's relativistic version of the Schrodinger equation). The surface of the "Minkowski Light Cone" has the form:

(2) 0 = x2 + y2 + z2 - (ct) 2

where c is a constant that converts seconds to metres, t is the time difference between the origin and the time of an event and linearity is assumed (see Note 1). The constant "c", the factor for converting seconds into metres, is also known as the "speed of light" and is the maximum velocity. These zero length vectors are known as "null geodesics" and are simultaneously at the origin because they have no projection.

When Minkowski derived the "light cone equation" he proposed that space and time are geometrically interrelated and that the universe is a four dimensional space-time. This is now the conventional view in physics. Hermann Weyl wrote that reality is a "four-dimensional continuum which is neither "time" nor "space". Only the consciousness that passes on in one portion of this world experiences the detached piece which comes to meet it and passes behind it, as history, that is, as a process that is going forward in time and takes place in space" (Weyl 1918). Almost every text on Special Relativity after Minkowski's formulation of space-time stresses the geometric interdependence of space and time but it is characteristic of Weyl's genius to note that the physical time which composes the fourth dimension is not the same as mental time.

Most students have difficulty conceptualising a physical time that interacts geometrically with the extension of a thing in space. They have a feeling that the simple length of things must be constant. In fact it is only the four dimensional extension of a thing that is constant (invariant) between inertial observers, other measurements such as length vary according to who observes them (see for instance Carroll 2001 or any advanced physics textbook). The fact that length measurements differ in the expected manner between inertial observers proves that the universe is at least four dimensional. This geometrical interaction of space and physical time is an integral part of Special Relativity and has been the bedrock of the ontology of physics for about a century.

The similarity between equations (1) and (2) is such that it would be surprising if they did not describe the same thing. Our empirical experience of viewing from a point and of seeing things simultaneously and projected is an experience of variables of an identical type and in an identical relationship to those described by Minkowski's equation. Given this identical type and relationship, it is not at all speculative to propose that Minkowski's equation describes some of the geometry of our experience.

Notice that Minkowski's equation (2) is insensitive to the sign of the coordinates and could describe a vector pointing into the future or a vector pointing into the past along the same path. It might, for instance, describe the path of an electromagnetic wave with the retarded wave travelling forwards in time and the advanced wave travelling backwards in time (See for example Cramer 1986).

Minkowski's equation (2) is a description of a sphere of things connected to the centre by null geodesics. Any tendency of a field or particle to perform an oscillation into the centre and back again along a null geodesic would appear as an alignment that favours such a motion, the motion itself being completed instantaneously at the position of the particle. Fields or particles possessing such an alignment would be extended along the zero length path that constitutes the null geodesic. Another way in which equations (1) and (2) could be interpreted is to propose that time can be calculated using imaginary numbers (cf: Hawking 1993) so that a real zero projection exists provided that no energy is transferred along it. The sphere of things would then be at a Euclidean geometric point in 4D.

That physical interpretations may exist is intriguing but in an empirical analysis of conscious experience it is sufficient to point out that null geodesics appear to have the same mathematical form and are composed of the same variables in the same relationships as the vectors that populate our conscious experience. It is the role of theoretical physicists to extend the analysis beyond this identification of conscious experience with the classical four dimensional observer that is embodied in physical theory and described by Minkowski's equation.

Minkowski's equation is a description of physical space-time and the standard neurobiological model of the mind is that it is produced by the brain as a combination of sense data and internal processes. This means that if Minkowski's equation is also a description of our mental space there must be clear physical correlates of mental space in the brain. The spherical shell of observed mental events would need to be represented in a smooth volume of brain activity. The x, y, z co-ordinates would be positions of activity relative to the observation point and the observation point itself would be at the geometric centre of such activity (the origin of the co-ordinate system). The convolutions of the cerebral cortex and cerebellum are unlikely locations for smooth volumes of activity. In view of this it is probable either that such a uniform volumes are physically located in the smooth, phylogenetically older parts of the brain or in some form of "field", like an electric, magnetic, quantum field etc. that is created by the whole, or part of, the brain.

The activity at the observation point itself would be the activity of all those parts of the brain that are zero distance from it in the direction of the null geodesics. This could be brain activity that occurred a few pico-seconds ago, depending upon the radius of the brain activity that is observed (this value is calculated from t = radius/c). The observation point would be in the future relative to the physical present.

If some part of the brain specialises in creating mental space then lesions in that part would abolish our mental space and, probably, our consciousness. The idea that consciousness might be localised in a small part of the brain has been current since Descartes' proposed the pineal body for this role. Bogen (1995) has proposed that consciousness may be localised in the Intralaminar Nuclei (ILN) of the thalamus because these are related to arousal and intimately connected to the cerebral cortex and because bilateral lesions of the ILN can abolish consciousness. Combining the model in equation (1) and Bogen's analysis of the site of consciousness leads to the proposition that mental space could be located in the ILN or in nuclei dependent upon them.

The Experience of Time

If someone is speaking we hear their words from the direction of their mouths, if we feel pressure or pain we feel it at a particular place in our bodies. In general, when we observe events they take place at the positions of the events in our mental space.

When we hear someone say a word such as "hello" we hear the "h", "e", "l" and "o" sounds distributed through time. An entire period of about a second is available to us. This spread of a word through time is reminiscent of the extension of a line through space. As an example, the line "_______" occupies a length of a co-ordinate axis which is at right angles to your direction of observation and located on the page so that you see the line as an angle made at your observation point. In a similar way the temporal extension of a word seems to be arranged along a time axis that extends from the location of the person who said the word and makes an angle through time at your observation point.

Notice that the "h" of "hello" becomes increasingly historical the moment it has left the mouth, it seems that everything we experience is actually historical. There appears to be no such thing as an experience of "now".

Temporal extension seems to occupy no more than one or two seconds, beyond this interval we must use recall to insert a word or event back into our experience.

You, the observer of the word, seem to be at a point in both space and time. The point in space is the observation point and the point in time is assumed to be the present instant. In other words your experience of time consists of events in mental space that extend through time and which are observed at an observation point. The observation point is both a point in space and a "durationless instant", or point, in time whilst the observation is extended in time and space.

Newtonian physics and Euclidean geometry do not contain the appropriate tools for analysing the way our experience is extended in time. These archaic models of the world do not involve a continuously existing past. Fortunately, from the time of Riemann onwards tools have been available for dealing with things arranged in time as well as space.

As Hermann Weyl noted, the mental experience of time is not the same as physical time. Physical time subtracts from space, drawing events toward an observation point, whereas mental time is a direction where events are laid out for observation. Mental time seems to be a new direction where events can be arranged, a new co-ordinate axis. The relationship between mental time (T), physical time and space might be described mathematically because all of these are zero distance from the observation point when they are observable:

(3) 0 = dx2 + dy2 + dz2 + k2dT2 - c2dt2

Where T is mental time and k is a conversion factor from mental seconds to metres, a differential form is used because mental time spans a short interval. This equation describes how we seem to experience events laid out within a sphere of indeterminate radius yet observed at a point. The events extend through mental time at their positions in space yet the observation point is at the present instant. This equation might be dismissed as highly speculative but this is not the case. The equation is based on our empirical experience: we do indeed experience things extended in time and we do indeed experience these from the same point as our general experience. It is an empirical equation that describes the trans-temporal projection of experience and uses no other authority than the multidimensional version of Pythagoras' theorem.

Mental time (T) could be any direction (or resultant direction of further dimensions) where information can be ordered independently of the other dimensions (x, y, z and t). It would acquire a time-like character from the fact that physical position (x2+ y2+z2)1/2 is constant and small compared with physical time in metres (ct) for times in excess of a microsecond or so. At relatively long times (microseconds) after an event, mental time (kT) becomes dependent on physical time (ct) and any ordering of events in physical time will appear as a sequence of events in mental time. Notice that, to remain observable, an event would need to increase displacement in mental time as it is displaced in physical time, this might be accomplished by a movement of our observation point along the fifth dimension at nearly the speed of light.

Unlike equation (1), equation (3) does not correspond to a universally accepted physical reality although five dimensional space-times are currently at the forefront of physical theories of the cosmos and matter (Overduin and Wesson 1997, Sajko, Wesson and Liu 1999, Linde 1990-2002). Five dimensional space-time has long been a possible interpretation of General Relativity Theory and in the form given here is known as a "de Sitter universe", physical time is conventionally imaginary in such a universe. The physical correlates of equation (3) are clear: it would describe a sequence of activity inside of a sphere of brain tissue or a sequence of changes in some whole brain field (electric, quantum etc). This sequence of activity would have a zero-length projection from a central, five dimensional observation point.

Although words appear to extend in time for perhaps a second or so, change in visual content seems to extend in time for much briefer intervals. If you move a finger in front of this text the image of the underlying text appears to replace the image of the finger almost as soon as it has passed. In the case of vision it seems to be the static part of the visual field that extends through time in preference to changes in the visual field (although changes may have a small extension in time).

Given that it is the static part of the visual field that seems to persist in preference to changes it is possible that some of our sense of depth is encoded in mental time, each view at a particular depth being placed in conscious experience in time sequence. Such an effect would occur naturally as a result of focusing in and out when viewing a scene. (See Peters (2000) for a review of modern theories of depth perception.)

Our experience of time is central to our feeling of being conscious. If we experienced no more than a durationless instant we would experience nothing. Nothing happens in no time at all. Our conscious experience is an experience of the duration of things and it is because the "I" and the "am" of "I am" are both available that you "are".

Mental Content

If mental time and space are accepted, mental content can only be things in this time and space. Even content such as emotions exists in mental time and space, being a mixture of sensations from the body and global changes in the texture and vividness of other mental content. Objects would be represented by the brain activity that outlines and fills the shape of the object and colours would be particular types or sequences of activity, as would other qualia such as sounds, sickness or intuitions.

The exact nature of the brain activity that generates content, whether it is electrical impulses, electrical fields (McFadden 2002), states of microtubules (Hammeroff and Penrose 1996) or quantum fields (Flanagan 2002) is not clear.

A completely representational model of mental content is being proposed but such a model is inevitable once mental space and time are identified with the real space and time of the brain.

The Homunculus

It was proposed above that the contents of mental time and space are brain activity observed at a point. But what observes this activity? We feel 'we' are at the point of observation but the equations given above suggest that only the observed brain activity is 'at' this point, being zero distance from it. In other words the observation is also the observer. This sounds bizarre but consider your analysis of the phrase "the observation is also the observer", you might think pictorially of a person looking out at something but where is that picture? It is in your mental space. Alternatively you may have an intuition that there must be something at the observation point that processes the observation, but where is that intuition? It might be a verbal thought in that part of mental space that represents your head.

The identification of the observer with the observation is also true of time. The extension of the mind in time allows the intuition of the question "am I conscious?" and of the answer "yes" to be embraced in the same trans-temporal experience in the same way as the sound "h" and the sound "o" are both part of the entire trans-temporal experience of the word "hello". This is not a speculation but an observed part of our everyday lives. Again the observation is extended, in this case extended in time, but the observation point is just a geometric phenomenon that we call the present instant.

Whatever 'we' might be we are to be found in our observation, in the content of our minds, in contrast the observation point itself is nothing more than a geometric phenomenon where this observation has zero projection in four or more dimensions.

This entire article is a description of mental geometry so it must be possible to communicate the geometrical form of being an observer to our material brain. A possible candidate for this communication is part of what is known as "attention". When we attend to something it is usually either because our unconscious brain has inserted a thought such as "find a doughnut" or because something unexpected occurs. In both these cases we are matching our perception to a template created by the unconscious brain. In the first case we are explicitly matching the form of the doughnut of our desires with the form of a "doughnut" derived from our senses and in the second we are matching the expected sequence of events with that which actually occurred.

It seems that the observation point/observation structure may communicate whether there is a match or mismatch between states of brain activity.

The ability of the conscious mind to match the current state of an observation to previous states has been proposed as a feature of quantum computation in the brain (Woolf and Hameroff, 2001). These authors propose that the state vector of the quantum computation is reduced by "Orchestrated Objective Reduction" (Orch OR) (Penrose 1989) to provide a defined output when superposed quantum states match.

An alternative form of state vector reduction could occur if quantum events are actually due to 5D waves such as those suggested by Sajko,Wesson and Liu 1999. Mental content would have a highly constrained position in five dimensions because, to remain observable, an event would need to increase displacement in the fifth dimension as physical time increases. This suggests that a five dimensional observation might achieve state vector reduction by selection of a particular state rather than by "collapsing" the state vector. Such a suggestion is highly speculative but might link a 5D theory of consciousness into the wider problem of the observer in quantum physics. The result of the quantum computation would be brain activity that would constitute an observation and also be capable of communicating with the unconscious brain.

A model of consciousness can now be proposed that does not require a homunculus and which can be described in terms of experience and brain activity. Our experience of consciousness consists of information that is arranged in space and time but has zero projection from a geometric point. There is nothing at this geometric observation point but the projected observation. Observations, including thoughts and emotions appear almost fully formed in this mental space and time, being inserted there by the unconscious part of our brains. Attention occurs within consciousness and it is this attention that communicates the conscious state to the unconscious part of the brain. Above all it is extension in time that imparts awareness because both an event and the analysis of the event are within an observation.

If the brain activity that is the mind is at a geometric point then our experience is entirely an experience of vectors pointing inwards and our knowledge of both space and time is the experience of these vectors and their angular separations. This might explain why everything has a "sidedness", why "bob" does not appear as "dod" or "bod" or just a jumble of points. Experience is the vectors emanating from the brain activity that represents a thing rather than the brain activity itself. Brain activity itself has no "sidedness", there is no reason to prefer one side of an EM field or one side of a synaptic field to another unless experience is a directed set of vectors emanating from the field.

This model also explains how our experience becomes a whole. Every vector in our experience has an angular relationship to every other vector as a result of the termination of all the vectors at the same point where they are a single entity.

It is the fact that all of our immediate experience is historical up to a limit of about 1 to 2 seconds coupled with our inexorable flight into the future that makes us aware. At any instant there are vectors pointing inwards from the entire second or so of extended present, as new vectors appear the oldest vectors are lost. Our minds become a continuous reappraisal by our unconscious brain of the current slice of extended present.


The model of the observer proposed above is an empirical model. It analyses the time and space that is evident in our experience using the multidimensional version of Pythagoras' theorem, the simplest tool available for such a task. The resulting 5D mathematical model is simple but describes our empirical experience of time and space. The model turns out to be very similar to the model of time and space that physicists use to describe the physical world. This would be expected if the mind is brain activity or part of the brain's activity.

The link between the geometry of our experience and the geometry of the physical world is most simply understood if physical time is a true geometrical entity. The geometrical nature of physical time is widely assumed in physics (Weyl 1918, Rietdijk 1966, Petkov 1988, Dowden 2001) and in practice physical time is integrated into the geometry of the world used in Special Relativity, General Relativity and Quantum Theory. It is largely non-physicists who regard the fourth dimension as something to do with "Star Trek" and not something that interacts with our everyday lives through phenomena as common as kinetic energy, magnetism and gravity.

It should be stressed that the geometrical theory does not depend on time as an "imaginary" dimension, the standard model in physics that uses "real" time also supports the theory and is also understood by physicists to be a dimension that interacts geometrically with space. In fact the geometrical theory could be interpreted as a simple mathematical description of conscious experience without noting that it has exact parallels in the physical world, however, if the world is, at least, 4 dimensional it would not be surprising if our brains reflected this in the form of a mind.

In the geometrical theory of consciousness the brain activity that gives rise to conscious experience could be a field of activity generated by a substantial portion of the brain or, more probably, activity in a small part of the brain that becomes a 'consciousness centre'. Brain activity would be arranged in at least five dimensions and would form a set of zero length vectors terminating at a point. This would allow things to be present on the inside of a sphere of indeterminate radius and positioned according to their angular separation. Brain activity would also be extended into a putative 5th co-ordinate axis along which the succession of arrangements of things that are experienced would be ordered. The observation point would be a geometrical phenomenon that would move continually along the diagonal between the fourth and fifth co-ordinate axes so providing the flow of time.

The conscious mind would be the five dimensional null geodesics at a point that would span a few millimetres of brain tissue and a second or so of time, the starting points of the vectors being a multidimensional matrix of brain activity.

It is the fact that we can experience events trans-temporally that results in awareness. The state of a matrix of conscious brain activity at one instant can become an input to the unconscious, processing parts of the brain. The unconscious brain can modify the matrix at a later instant in response to the input and the matrix as a whole can span both instants. As an example the unconscious brain might load the matrix with "am I conscious?", this would become an input to the unconscious brain which would then load the matrix with "yes". Both the question and the answer would be present trans-temporally in the matrix. Any immediate uncertainty about whether the reply had really been "yes" would be resolved by the evident presence of "yes" half a second away in the matrix, the unconscious brain would insert the intuition "definitely" to confirm this. If you ask yourself the questions and provide the answers you can experience this happening.

It is also proposed that the geometry of conscious experience would be the phenomenon that would resolve the state of a quantum processor that matches the patterns of brain activity to the patterns of the world. This means that the 'consciousness centre' would be part of a feedback loop that controls the state of the cerebral cortex. The thalamus is the most probable location for a 'consciousness centre' because it receives input from every part of the cerebral cortex by way of the corticothalamic tracts and is able to provide feedback to the entire cortex through the thalamocortical tracts. The "corticothalamic synapses on thalamic neurons largely outnumber afferent synapses" (Destexhe 2000) which suggests that the primary role of the thalamus is the integration of cortical activity. (The cerebral cortex itself is composed of specialised areas rather than areas that integrate all activity; see for instance Zeki & Bartel (1999).)

The size of a brain nucleus that might support conscious experience would depend on the density of information required. The optic nerve contains about a million fibres so a total of at least one million information points might be needed. The geometrical theory of consciousness presented here would allow the integration of information throughout the volume of a solid nucleus in the brain and would permit information to be held at the level of individual synapses. There might be over 100000 synapses per mm3 (over 1000 per neuron) in a nucleus which means that a nucleus of 2 mm in radius (about 3 million synapses) might support a sufficient density of information to be a consciousness centre. Even the smallest thalamic nucleus could be a potential candidate for a consciousness centre but as Bogen (1995) has pointed out, the ILN are particularly good candidates.

The observation that destruction of both sets of ILN causes irreversible coma, that electrical stimulation of the centromedian nuclei of the ILN causes absence seizures, that the thalamus and ILN are intimately connected to the output and input of the cortex and the many other arguments proposed by Bogen (1995) all suggest that the ILN could be a location for the experience of consciousness. The geometrical model of consciousness proposed here provides a description of how a small nucleus in the brain could contain this experience of consciousness and supports Bogen's hypothesis.

If there are localised centres for consciousness and if the geometric model of consciousness is correct then any physical manipulation that significantly deforms the centre should cause definite effects such as seizures, absence seizures, pre-epileptic auras or loss of consciousness. The effects could be monitored behaviourally or with an EEG. The design of an experiment to test this prediction might be difficult because of the effects of mechanical distortion on blood flow, the possibility of mechanisms that compensate for distortion and the difficulty of producing deformation in a solid nucleus. Bilateral symmetry and the possible existence of mechanisms that compensate for distortion means that a bilateral vibrating stimulus might be most effective.

Deforming putative centres for consciousness would test whether the geometry of the mind can affect brain activity. Such deformations may not have been tried in conscious patients because of the known danger of irreversible coma should the ILN be damaged. If bilateral deformation were to have no effect then the proposed feedback mechanism would not exist and, according to the geometrical theory, consciousness would be epiphenomenal, simply displaying brain activity.

Direct electrical stimulation of the consciousness centre should have perceptible effects. Extracellular stimulation might cause pre-epileptic auras, absence seizures, or other suspension of consciousness, intracellular or synaptic stimulation might cause localised qualia. Velasco et al (2000) have discovered that 3Hz stimulation of the Centromedian Nucleus of the Thalamus (part of the ILN) causes absence seizures.

The proposed centre would contain a representation of the contents of mental space that would be laid out as an exact mapping of the experience of the contents. This representation would be physiological rather than anatomical because mental space can contain visual images, dreams, sounds, feelings etc. In-vivo recording in the centre in a subject attending to a visual scene or cutaneous sensation should demonstrate neural activity that is positioned retino-topically or somato-topically.

Bilateral symmetry means that if consciousness is localised then there would be two centres for consciousness. In the case of the ILN, the centromedian nucleus of one side can be removed without severe adverse effects but bilateral damage causes coma, death, delirium and a range of other defects depending upon the severity of the lesions (Schiff & Plum 1999). This shows that, if there are two centres for consciousness within the ILN, then either can provide full functionality. The geometric model of consciousness would require that one side of the brain would be dominant but there could be two consciousness centres, the non-dominant acting as a substitute if the dominant centre were destroyed.

Although much emphasis has been placed on the ILN and especially the centromedian nucleus it is possible that any centre for consciousness would be in nuclei dependent upon these or even that consciousness exists in a field that extends over a volume of brain.

Although this article is concerned with neurophysiology and neurology, the geometrical model of consciousness may be regarded as direct observational evidence that the universe may conform to a geometry that is similar to that proposed by de Sitter.


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(1) Note that equation (1) can also be written as 0 = f2 - x2 - y2 - z2 and equation(2) as 0 = (ct)2 - x2 - y2 - z2 where x, y, z are the "imaginary" lengths. All variables in the equation are small displacements and the space-time is assumed to be linear. A more exact differential formulation that takes non-linearity into account is:

0 = df2 - dx2 - dy2 - dz2


  1. Looking over some of my old exchanges in the now defunct PSYCHE-D, I found this exchange with Alex Green. I know you are impressed with her ideas so this might interest you (I am AT; AG is Alex Green)):

    Alex Green


    The experiments you described in your last post provide a further, fascinating insight into this aspect of brain activity and I found your report on the triangle illusion most interesting.

    You seem to be suggesting that the brain is a modelling device and are proposing some mechanisms for this modelling. Modelling of the world is a natural design feature for any system that must deal with a changing environment. In the case of automated machines sensor readings are usually stored in buffers so that a new reading is not required whenever a control system needs a value. In fact it is probably a rule that all complex interfaces with the environment use stored versions of sensor data, not raw data itself.

    Your work seems to offer clear evidence that a stage of perceptual modelling is data storage in a special form of buffer. Other evidence for buffering comes from the everyday fact that the perceptual field remains stable despite saccades of the eyes. Our experience is a model aligned with vestibular input, not raw retinal data. This becomes clear when vestibular input is compromised such as after rotating the entire body a few times - the entire contents of the perceptual field continue to rotate when the body stops rotating.

    There can be little doubt that the brain is a modelling device that creates the content of conscious experience, whether this content is perceptions, illusions, imagination, dreams or hallucinations. Once created the content becomes part of a phenomenon that endows it with a space-time geometry so that things appear arranged in space at an instant and separate from a viewing point that contains nothing. The model uses the same space-time whether it contains dreams, imaginations or perceptions which is why hallucinations can appear real.

    In other words Descartes' "sensus communis" seems to exist but it has not yet been found in the brain. The key to locating the "sensus communis" lies in the homunculus argument: if conscious experience is due to data flow then there would need to be a homunculus to see it therefore it is not entirely due to data flow....

    Why do so many philosophers and others incorrectly use the Homunculus argument to reject the idea that conscious experience occurs in the brain? Perhaps they, like Descartes, track sense data into the brain but, unlike Descartes, they have an absolute belief in Galilean space and time. If nothing but things in Galilean space-time exist then there can be nothing outside it and so the 'chain of relations' or 'chain of cause and effect' must be pursued clear through the brain and back out into the world. This analysis is not credible at any level, it still requires a homunculus even if the content of consciousness is the sensory world itself, it proposes no direct physical substrate for the contents of consciousness, it disregards the overwhelming body of evidence that experience is brain activity, it relies on Galilean physics which is an ontological fiction and lastly it answers nothing about the nature of conscious experience such as dreams and our inner life. It may, however,
    explain much about behaviour.

    ..Is there an alternative to this kind of neurocognitive modeling that seems more promising as a way to advance our theoretical understanding of mind-brain? Any thoughts?

    I agree with you. Understanding how the brain models the world at a physical level may eventually not only be of value in fields as diverse as teaching and criminology but will clarify exactly which parts of brain activity form the field that is conscious experience.

    Best Wishes

    Alex Green

  2. Hi Arnold, thanks for this quote. I like the statement:

    "if conscious experience is due to data flow then there would need to be a homunculus to see it therefore it is not entirely due to data flow...."

    Yep, there is some other physics going on in the brain. I think I agree with Alex that there could be a small volume in the thalamus that hosts the arrangement of events that is conscious experience. If the ILN hosts consciousness it will be a very difficult place to investigate. If we use TMS and stick a magnet in the back of the nasal cavity we might turn consciousness off..but it could be argued that the ARAS was compromised.

  3. TMS is like a reversible excision of a volume of brain tissue. The problem remains, as in the many animal experiments involving localized extirpation of brain tissue, that we don't know what brain functions might be impaired in addition to the target function. As you say, ARAS might very well be impaired when ILN is disabled. If we were able to actually observe the neuronal structure and dynamic characteristics of selected parts of the brain and compare them with the structure and dynamics of our theoretical model of retinoid space we might be able to clinch the brain mechanism of consciousness. Since we can't do this with our current technology, it seems to me that the validity of the retinoid model of C can only be established by its success in explaining and predicting relevant phenomena. Isn't this also the case in particle physics where the particles as such are not directly observed, but their existence is "proven" by their theoretically predicted effects, as in the recent evidence for the Higgs boson?

  4. This is an excellent paper. No doubt it just went over the reviewers heads.

    The following paper comes to similar conclusions regarding the geometry of space and consciousness, though a profoundly different understanding of qualia.


    Imaginary axes are used here as well - more intuitive for non-mathematicians. Would be nice to see this model put on a rigorous mathematical footing... (any takers?)

    Philip Carter

    1. The first part of the paper was interesting. How would you explain the constancy of the retinotopic representation of the world in the occipital cortex despite saccadic suppression ? If perceptual "filling in" produces an electrical "image" in the cortex corresponding to the intercalated content how is this experienced - surely the experience is based on cortical activity?