The following is a copy of my material which was submitted to Science and to Nature in 1994 but not published. There has been little more change than the correction of a few typographical errors. It is not necessary to plough through all of this at this point, as my main narrative remains independent of it and there would be a considerable amount of duplication. I have included this for historical and biographic reasons. At the end of the article there is some useful bibliography. I have made use of some of the references. Now in October of the year 2000 I have made some further advances which are given in the main text.



It is generally accepted that information storage in the cerebral hemispheres is diffuse. A single neuron may have dendrites which have as many as 5,000 synapses so the information is widely dispersed. We know that in certain areas there is representation in topographic form, for instance the striate cortex, cutaneous tactile sensation, and the motor areas. It is difficult not to believe that our internal representation of the external world is not represented somewhere by a set of cells or synapses with some sort of point to point correspondence with what is out there. Nevertheless no very convincing theory as to how this information, once dispersed, could be brought together again has been presented so far. It is also difficult to see how the cerebral processing of concepts and ideas can take place without this. This the principal topic which this communication seeks to address.

In holography we have a photographic system which does something very similar, namely the dispersal of information into diffuse form and subsequent conversion back into topographic form, sometimes referred to here as "Discrete" form. Although the functioning of the brain is very far away from holography it is worth while comparing the two systems from the point of view of understanding how information is handled. Holographic models have been put forward by Longuet-Higgins (1968)1, Karl Pribram, P.T.Chopping (1968)2 , and others. As a starting point I take the view put forward in my own communication to Nature in 1968 (P.T.Chopping, "Holographic model of temporal recall".) which was developed further in neurobiology seminars (Unpublished Communications 19693). The basis of the idea was that the memory trace of an episode is laid down in the cerebral cortex in a distributed fashion in synapses, as an irregular pattern of inhibition and excitation. This is brought about by the interplay of the extensively branched dendrites from excitatory and inhibitory neurons located in the primary sensory cortex mediating vision, hearing, olfaction etc. or connected with these by interneurons. A Hebbian process causes memory to be written in as a result of areas of either increased or reduced function. The analogy with holography is based on the fact that in that system a single point on the object is represented as a distributed pattern on a photographic plate which is set up by the interplay of positive and negative values. In that case the parameter is electric field of positive or negative sign, whereas in the brain the parameter is positive or negative neural excitation. The wave properties of light are not invoked. The similarity of the two systems is in the way in which the record is written by the interplay of distributed positive and negative values which are mutually cancelable. Both systems may be expected to share the known properties of holograms such as the ability to store one record on top of another, independent recall by an associative memory, graceful degradation in the face of damage etc. It makes no difference what the parameters are.

In either system it is easy to see how the information becomes distributed but not so easy to see how this can be unraveled and brought back to some kind of "Discrete" or "Topographic" form, where there is a point to point correspondence with something recognizable. In the brain this is especially difficult as the signals have become so intertwined and mixed up. Indeed this is the problem which is central to all theories of brain function.

In the hologram, a single point on the object is represented on the photographic plate by grains of silver laid down in a series of concentric ellipses. This is brought about as the result of optical interference of coherent light between the divergent cone of rays from the point and a parallel beam from the laser. In holography the information on the hologram can be recovered by a process of wavefront reconstruction. In a system without lenses this is achieved by illuminating the plate with a laser beam coming in at exactly the same angle as that of the original reference beam. Each of the systems of ellipses, each of which represents an individual point, acts like a Fresnel zone plate and focuses the light, like a lens, back onto the original point thus reproducing it in its correct relative position. In some holographic arrangements this reconstruction can also be achieved in a feed forward system by the use of lenses. Applying this analogy to the brain, we have as the counterpart of an object point in holographic system, a single excited neuron (Or perhaps even just a single synapse), in a primary sense area such as the striate cortex. In this case there is a pattern of excitation and inhibition in the cerebral association cortex, representing the original neuron uniquely. It is quite irregular and not a neat collection of ellipses, because of the irregular nature of the dendritic branching. We have many such patterns stored one on top of another representing many individual neurons. What we are now looking for is a neural network which will do the same job as the wavefront reconstruction in holography. We are looking for a method of unraveling the distributed pattern and getting back to the original excited neuron. If we could send the information backwards along the same nerves by which they originally came this would do it. This would be very much like a wavefront reconstruction in a hologram. The nervous impulses would have to go antidromically, getting past junctions by meeting up with other pulses by exact timing. This idea does not appeal to neurobiologists and has had to be ruled out. There is a well established law of forward conduction. There are instances of antidromic conduction but this applies only on a very small scale. What we need is a feed forward network which will accomplish the same thing. I will refer to the network which constructs the distributed pattern as a "Scrambling" network and the one which does the reconstruction as a "Descrambling" network. It will be explained later how the "Unscrambling" network is set up. For now it is necessary to explain the purpose of the "Scrambling" and "Unscrambling" nets.

When a sensory pattern appears in the primary sensory cortex, involving two or more senses, vision and hearing for instance, in both areas it will be in "Topographic" form. In the striate we have an image and in the case of hearing we have a frequency spectrum. The information will be transmitted through the "Scrambling" networks to "Association" cortex. Here the two patterns will be combined with any other patterns in memory. This is "Associative" in nature and a new signal, representing the appropriate association which has been called out, will travel back through the "Descrambling" network to the primary sensory areas. When signals arrive back there, they will be translated back to "Topographic" form. The appropriate sensory pattern will give rise to a pictorial or auditory picture which enters consciousness. This pattern will now be sent back to the associative cortex, calling forth further associations and this process will continue to reverberate back and forth giving rise to a train of thought.

In order to see how the nets can be set up, we must now consider neural nets and some primitive organisms.



In the case of such organisms as Caenorhabtidis Elegans (A worm) and Aplysia (A water snail) the anatomy of the CNS appears to be almost completely specified genetically. In Caenorhabtidis the total number of cells is invariant and in Aplysia there is very little variation either in total cell number or in the arrangement of such features as the abdominal ganglion, which appears identical in all specimens. Such a creature's CNS can be regarded as a neural net with many properties in common with man made computer models of neural nets. It will have a repertoire of different sensory input combinations where the input pattern is in topographic form. These have to be mapped onto an appropriate set of output patterns, again in "Topographic" form. It would act like a "Look Up Table" as described by Churchland4. In between the input and the output the neural net carries this information in distributive form. This is what a trained neural net is normally able to do. A hardwired system works quite well because there is only a limited number of input and output patterns. (Outputs might be "Withdraw gill", "Retreat", "Feed", "Emit Ink" etc.) The arrangement is similar to a three layer neural net as is often in use in computers. There is an input and output layer and in between there is a hidden layer which does the computing. How is this hardwired system originally built up? Obviously it has been formed from a simpler system which has been gradually improved by "Evolution". In man made systems we start with a random network and improve it by having an "Instructor" or an algorithm which measures the amount of error in the "Input" "Output" Mapping. The network is run very many times and after each run certain elements are modified according to the amount and direction of the error. With Aplysia we can assume that the "Instructor" is evolution. Each run of its "Computer" corresponds to the life of a single Aplysia. Random mutations occur, some are beneficial and some are deleterious. A particular bunch of mutant genes in some individual in the species might carry a survival advantage. The Aplysiae with bad mutations simply die and we get a new line carrying the beneficial genes. A gradual improvement takes place which eventually culminates in a stable species which is well adapted to the environment, as Darwin envisaged. In higher organisms, such as mammals, the organism is much too complex for a hardwired system. There are not enough genes to specify all the connections. The genes will specify general anatomy such as the spinal cord and identifiable structures such as the superior colliculus and what bundle of fibers connects to what group of cells. We have to rely on a much more subtle plastic process for the specification of micro-connections. Learning is obviously important. We know for instance that the visual system fails to develop properly if the eyes remain closed and are not used. Plastic changes must also be occurring in utero. Some mammals such as the African Wildebeast have to be up and running from the first day of birth or they just will not survive. This implies a fully functioning brain and visual system within hours of when they hit the ground. It is necessary to postulate a self organizing process operating in foetal and early neonatal life. In the present context we are looking for a self organizing process for the formation of the descrambling network feeding back to the primary sensory areas.



A "Scrambling" network can in principle be represented by an algebraic matrix. For a rather simple treatment of a neural net as a series of simultaneous equations see Chopping P.T. 19692 and as a matrix see Churchland S.C. 19934, and also Chopping.P.T.19693. Each synapse can be regarded as a cell in an artificial neural net which operates by fixed rules such a multiplying factor, or "Weight", an arithmetic addition of positive and negative values, and a transfer function as is usual in computer generated neural nets. To be valid the processes being represented should be linear. In the biological context this will usually not be the case but we must ignore this difficulty for the moment. The problem of providing a "Descrambling" network is essentially similar to the mathematical operation of inverting the matrix. This can be done if the number of equations represented is equal to (Or greater than) the number of unknowns, even if the number of unknowns is very large. This means that we could in principle design a "Descrambling" network which does all of the needed multiplications and additions necessary solve the system of simultaneous equations and invert the matrix. The non-linearity objection has to be met by two arguments. First, there is no objection to some degree of transformation of the information so long as we get an answer in "Topographic" form. Secondly, in the context of neural nets, it is perfectly possible to perform operations using a network, for which there is no mathematically equivalent process, provided that you are satisfied with an approximate rather than an exact answer. A non-linear transfer function actually increases the power of a net.

With appropriate training an artificial neural net will achieve any desired input to output mapping operation to a good approximation. One prerequisite is that the data are sufficiently unique to specify the desired output. We would need some way of making an assessment of the amount of error in the output and an "Instructor" to apply back propagation of the error in order to make the necessary modifications, over a very large number of trials. In the biological situation the capability of the net is the same but the difficulty is in providing the "Instructor" to make the assessment and apply the corrections. In simple organisms such as Aplysia "Evolution" will do the job but in complex organisms such as mammals this has to be done by means of a learning or self organizing process. The following section deals with a possible way in which this could be accomplished.



The clue to explaining this is feedback. It is well known that there is extensive feedback at almost all levels of the CNS. There are many "Reentrant" connections. This has been remarked upon by Vernon Mountcastle and many other authors since. See Churchland P. S. and Sejnowski T. J.(1992)5. We must assume that the feedback connections are predominantly inhibitory, otherwise we would have an unstable system which would be in a continuous state of oscillation. There is a situation present where there are local areas of oscillation which become quickly quenched by the overall powerful negative feedback as soon as habituation has time to take effect. We may be in the borderland between "Order and "Chaos". It was noted at the Santa Fe institution that this is where "Complexity" arises. (See "Complexity" Waldrop M.M.6.) In our case we can be quite specific about the mechanism required to build up a descrambling network and as to how this is accomplished. What we need is a neural net which feeds back from a particular irregular pattern in the association cortex to the original cell in the sensory cortex which formed it. In the holographic analogy this corresponds to the way in which the ellipses converge back onto a single point. In the foetus and neonate the CNS is vastly overconnected. Many of the connections are numerous and random. We are looking particularly at the excitatory feedback fibers. Just the "Right" ones required to form our "Descrambling network" connect back in the appropriate way, from a particular pattern to a particular point in the sensory cortex. Those "Correct" connections are very numerous, enough to cause positive feedback and oscillations. During maturation of the CNS we get oscillatory circuits set up between many, many patterns and their appropriate points. The "Wrong" pathways are not numerous enough to set up oscillations and they have little effect. We therefore get vigorous activity in just the "Right" pathways. The repetitive signals due to feedback loop become written in by a Hebbian process. The wrong pathways do not get activated in an oscillatory fashion and therefore wither away. An inverting matrix becomes written in permanently.

It is now necessary to consider how the oscillations might stop. Many of the properties of neurons have been worked out in Aplysia, particularly by Kandel E.R.(1976)7. We can be sure that human neurons work in a very similar way at the cellular level. It is widely accepted that we get both facilitation and habituation in appropriate circumstances. Kandel has shown that in Aplysia we get habituation over a time scale of about from about ten seconds to three minutes. An individual synapse habituates to 30 percent. If we have to go through several synapses, this 30 percent is multiplied several times over. For three synapses the feedback could be reduced to three or four percent in ten seconds. We also expect a powerful general overall inhibition. This could be fairly slow. This, plus a reduction in the loop gain by a factor of thirty is more than enough to produce quenching. It is possible that during maturation oscillations go on for ten seconds or perhaps for several minutes. In the mature animal we suggest that quenching occurs more quickly. The unwanted "Wrong" feedback connections have disappeared by now. In man and probably in monkey we have a "Thought" time of a few tenths of a second but it is to be expected that the combined effects of habituation and negative feedback would be sufficient to quench the oscillations in a fraction of a second and the overall neural net would be quite stable. Oscillations could persist for a longer time during maturation. Oscillations have in fact been observed in the visual cortex. Oscillations are 40 - 60 Hz, Zeki S. 19938, fitting in well with the timescale for persistence of vision, persistence of a stable image during eye blink (0.1 + sec.) R.Hari et alia9 and the rate of the thought process. The length of time for a thought corresponds to the duration of a local oscillation. The time required for the persistence of a thought would also be expected to be of the same order of magnitude as the time taken for a stabilized retinal image to disappear. This is only a fraction of a second. It can be predicted that these oscillations must last longer in the immature animal. In Aplysia, facilitation lasts from three minutes to two hours and we would therefore expect a longer time scale for LTP and memory encryption. Presumably the timescale in man is similar. As a result of this we may expect permanent Hebbian changes in the long term, so that the connections are gradually written in as memory.

Feedback, causing localized areas of oscillation, writes in the "Unscrambling" network which is the inverse of the "Scrambling" net. It has also been shown how these networks could be working to produce an ongoing thought process. The holographic analogy shows how an associative memory works.



There is massive feedback at all higher levels of the brain and we must now consider how it could be working generally. Reentry is an important integrating principle which applies throughout. We would expect that the mechanism which has just been described to be present also, namely that during maturation wherever the output of a distributed pattern passes to another area, an "Unscrambling" network would be carved out. This happens because the "Correct" connections give maximal loop gain, oscillations occur and are quenched, the desired pathway is made permanent by Hebbian effects. Wherever the data permit of presentation in "Topographic" form, this will happen. Moreover the information automatically organizes itself to a "Topographic form" at the highest possible resolution. This is because this condition gives the maximum possible loop gain. At the next stage it becomes "Diffuse" again, and we go alternately from "Distributed" to "Topographic" and vice versa as cerebral processing progresses from one part of the brain to another. This is the way that the brain analyses data. At one level we have images. At the next we have sorting of data into categories. After that we have concepts. Semir Zeki has indicated that above the level of V1 we should not be thinking of any sort of a hierarchy but there are several parallel streams (Zeki S. 1993, "A Vision of the Brain"10.) For instance we have a two separate pathways for form, one of which carries color information. There is no super center to which all the lower areas report. He considers that conscious thought accompanies the simultaneous activity of many areas talking to one another, often in the form of parallel streams. There is a switching and control function which focuses attention on some particular aspect. It is becoming apparent from PET and MRI studies that the cortical areas relative to the conscious perception of a sensory experience or a thought experience are simultaneously activated along with a specific arousal network involving thalamic nuclei (Posner M.I.& Raichle M.E.(1994)11 "Images of Mind". These all play their part in giving rise to consciousness. At a lower level we have the reticular activating system which switches on the sensory systems when appropriate. We do have various areas of the brain talking to one another and it is being suggested here that signals go from "Topographic to "Distributed" and back to "Topographic" as we reach the next area. In some places we have images and as we progress we have information separated into categories and after that come concepts. It is apparent that the separation into categories is often anatomically distinct. The determination of what group of neurons is connected to what is probably genetic but the microconnections are determined by the process described here.

Obviously the hippocampus plays a very important part in making memory permanent and in relatively short term memory and it would need to be part of the loop for this. During dreaming we have one part of the cortex talking to another. Dreams are not remembered except for a very short time. The Hippocampus is active during REM sleep though with a different rythm. This failure to record may be due to the "Activating Network" being shut down.

The visual system warrants special examination. The phenomenon of hyperacuity would be due to the fact that the information organizes itself into "Topological" form to the greatest resolution that is possible from the data. Fine tuning could only be carried out using the eyes in post natal life. One would expect that the connections which result in the finest resolution would concentrate the feedback maximally through the narrowest channel and would give the highest loop gain. This would cause the oscillations to persist the longest, with maximal Hebbian effects. It is difficult not to believe that the phenomenon of hyperacuity entails a set of cells, or possibly synapses, which carry the "Discrete" information. It would be difficult to demonstrate this as these cells or synapses would be scattered about and embedded amongst other cells. Nevertheless it might be possible to show this with P.E.T. or M.R.I. We already know that there is a fairly good "Topographic" representation in the striate cortex. During the second and third month of neonatal life the infant learns eye fixation, presumably through the superior colliculus system. After that the retinal image becomes stable, independent of head movements and it the becomes possible for the "Discreteness" detector to start working. We need a little more stabilization than this. When we look at a scene and move our point of attention slightly the whole picture does not move. In pattern recognition we have managed to lose absolute position but have retained relative position. This requires some kind of a transformation and this will be considered shortly.

Binocular vision could be regarded as a special case of hyperacuity, using an extra dimension to obtain even finer resolution. In this case there is probably not enough information in a Julesz dot stereogram (Julesz B. 197112) to specify a 3D image (or 2 1/2 D of Barlow 198213) and the neural net cannot construct it. However, given the right amount of ocular vergence, the information becomes sufficient and after many experimental scans the net solves it. This would have to take place during the early neonatal months when the infant is exploring eye fixation etc. Redundant feedback connections are got rid of and effective ones are reinforced. During adult life a few scans are sufficient for the correct vergence to be found and the 3D image springs to life.

Color vision can also be regarded as another form of hyperacuity. The wavelength resolution provided by the three receptors in the cones is extremely poor and overlapping and the information is already smeared into distributed form both by chromatic aberration and lateral inhibition in the retina. Nevertheless the original signals do specify the reflectance of the object and a neural net should therefore, with appropriate training, be able to extract this. We know that the specification is there because it is a fact that we can actually see. It is within the power of an artificial neural net to transform the information in any desired way, given specifying data and appropriate training. The biological net should also be able to do this. This is achieved by the built in "Discreteness" detector already described and it does so for the most constant, and frequent parameter, which is reflectance, rather than just color. Reflectance wavelenth and form could be considered to come together in the infratemporal cortex being analyzed by a neural net involving this area along with the LGN, V1 and V4. The chromatic aberration is focused out by the "Discreteness" detector and is never seen. Again we must assume that during training in infancy we get a higher loop gain from reflectance rather than from color per se. Seki considers that the essential to integration is that all the relevant areas should be simultaneously activated. Zeki.S (1993)14.

As the retina is functionally part of the brain we should expect the same mechanisms to be present right down to this level. It is possible that reentrant fibers do go down as far as the retinal ganglion cells during foetal life, disappearing later and that the processes described here still apply. This would be worth investigating in the goldfish, given its remarkable powers of regeneration following severance of the optic nerve. We do know that reentrant fibers do go down to the LGN.

We now need to consider the analysis of form. The highest element in the subsidiary chain which is clearly identifiable is the hypercomplex cell. Fatigue experiments show that grid detectors are present also. End stopped cortical cells could be regarded as curvature detectors. Above this we seem to be going straight to a fully synthesized image. We need to examine the proposition that a neural net solves the problem from this level all in one go. Mathematically, for pattern recognition and for stabilized viewing, we require a transformation which is able to form an image which is independent of both absolute position and size. The positional information can be eliminated by a Fourier transform which would require a system of grid detectors of many orientations and spatial frequencies. These grids would completely specify the original picture. The positional information would be embodied in the grids with the lowest spatial frequencies. To get rid of this, the widest grids are simply omitted from the system. (Chopping 19693). Barlowe (Barlowe 198211,) considers that there is a Fourier transform but that it is local rather than global and this makes sense. (For a piecewise transform, see Glezer, 198515) A local log polar frequency analysis has been described by Cavanagh P.(1985)16 which deals with positional, size and orientational invariance. This whole question needs to be reexamined in the light of the recently developed "Wavelet" theory which is beginning to supplant Fourier analysis in many communication problems. (See Ingrid Daubechies, 199217) It is also necessary to examine the question of fractal image compression,(Michael Barnsley 199318,) as the brain may making use of both these methods of economizing on data. We do not necessarily have to solve the exact mathematical problem because neural nets do not need any such theories. All that is necessary is that the data specify the answer and a neural net, with appropriate training, will find it. It would appear that the striate cortex plus the LGN contain the necessary specification (It is a fact that we actually do see). The candidate area for integration of form is the infratemporal cortex. This analysis would seem to be within the capability of an artificial or biological neural net, The "Instructor" is supplied by the "Discrete Form" analyzer described above. Poggio has shown that with artificial nets mimicking the primate visual system, feature detectors similar to oriented line detectors do arise incidentally to the operation and can be identified. Poggio, Poggio T. (1990)11 The presence of "Grid detectors" has also been demonstrated by fatigue experiments in humans. It has been shown that exposure to a grid of one spatial frequency causes fatigue for that grid but not for others of different width.

The general thesis being presented here is that the mammalian CNS operates neural nets in similar way to man made neural nets and that the "Instructor" is a "Topographic Form" analyzer. This is based on reentrant nerves and oscillatory circuits, which develop spontaneously during maturation of the CNS. This may be important for other vertebrates besides mammals. It might be worth while looking for oscillations in other vertebrates for instance in the chicken's egg. It seems probable that any creature which is able to construct an elaborate internal image of the world, requires this mechanism. This would apply to all organisms with good vision and especially color vision, and this would extend to the goldfish and probably to all vertebrates. It is likely to play an important part in the echo location system of the dolphin and in fish with an electric sensory modality such as the shark. One would expect reentrant nerves in all these species but probably not in insects and most invertebrates.



A theory of cerebral integration in mammals is presented in which the essential features are as follows:-

During maturation of the CNS, oscillations occur because of feedback in reentrant nerve fibers. These reinforce many connections by a Hebbian process. Many others disappear. Those which are reinforced are "Correct" for the formation of a "Topographic Form" analyzer, because they result in the greatest loop gain and the longest persistence of oscillations. Oscillations are quenched by the combined effects of habituation and an overall negative feedback. The whole process is self organizing. This is explained by an analogy with holography.

This analyzer is formed whenever one area of the brain connects to another. Wherever a group of fibers carries information in distributed form it is converted to topographic form at the next location.



Barlowe H.B. and Mollon "The Senses,"1982 p 150 Cambridge University Press13

Barnsley M.F. and Hurd L.P. 1993, "Fractal Image Compression" A.K. Peters Ltd18

Cavanagh P. "Local log polar frequency analysis in the striate cortex as a basis for size and orientation invariance." "Models of the Visual cortex" 1985 David Rose & Vernon G. Dobson. John Wiley and Sons16

Chopping P.T. Nature "Holographic model of temporal recall", Vol 217, No 5130, pp 781-782, Feb 24, 19682

Chopping P.T. 1969, Unpublished communications, - Seminars, Stanford, Harvard, & M.I.T.3

Churchland P. S. and Sejnowski T.J. 1992 - "The Computational Brain" pp 764

Churchland P.S. and Sejnowski T.J. 1992 - "The Computational Brain" pp 23, 31, 286, 317, M.I.T. Press5

Daubechies I. 1992, "Ten Lectures On Wavelets", Society For Industrial And Applied Mathematics. Philadelphia P.A.17

Glezer V.D. 1985, "Spatial and Spatial characteristics of receptive fields of the visual cortex and piecewise Fourier analysis." "Models of the Visual Cortex" Edited by Rose D. & Dobson V.G. - John Wiley and Sons15

Hari R., Salmelln R.,Tissari S.O.,Kajola M., Virsu V., Nature, Vol.367, Jan 13 p 121, (1994)9

Julesz B. 1971 - In "Seeing", Frisby J.P. pp 80,81, 1979 Oxford University Press12.

Kandel E.R. "Cellular Basis of Behaviour", pp 480, 542. (1976)7

Longuet-Higgins H.C. Nature, Vol 217, p 104, 19681.

Poggio T (1990), "How The Brain Works" Cold Springs Harbour Symposium.11

Posner M.I.& Raichle M.E. pp 154 - 179 "Images of Mind", Scientific American Library, HPHLP New York. (1994)11

Waldrop M.M. "Complexity" p 334, Simon & Schuster6.

Zeki S. "A Vision Of The Brain", p 351, Blackwell Scientific, (1993)8.

Zeki S. "A Vision Of The Brain", p 356, Blackwell Scientific (1993)9

Zeki S. "A Vision of the Brain", p189, Blackwell Scientific (1993)10

Zeki S. "A Vision Of The Brain", pp 295-298), Blackwell Scientific, (1993)14