Novel Symmetry, Self-Similarity(Fractal) & Recursivity decomposition of the structures and processes of Brain and Mind leads to several key unifying insights.

 

Abstract

 

Brain and Mind science is characterized by dizzying complexity and a myriad diversity of facts and findings. We demonstrate that through the systematic application of the inter-related and fundamental concepts of symmetry, self-similarity and recursivity; we can show that the complexity of the brain reduces to a small number invariant organizational patterns and processes. These hidden symmetries span not just the physical substrate of brain but also the emergent structures of mind and allow us to conceptualize neuroscience and psychology as one continuum.

 

We formalize our approach using the non-Euclidean geometry of binary N-Space and the hierarchical language of binary trees and binary combinatorial spaces. We show that this formalism corresponds to a wealth of empirical evidence and gives us a powerful and very general way of describing the structures and processes of brain and mind. One which is binary, bifurcating, doubling, digital, grid-like and discrete. This unifying language then allows us to conceptualize all the various aspects of brain and mind as a single all encompassing hierarchical structure. So that the motivational, homeostatic, symbolic, sub-symbolic and neural substrate are brought together in a single conception and unity.

 

With this unifying organizational principle, concept and language, we are then able to show that all the seemingly separate processes of brain and mind, are really the expression of a single underlying recursive process. Furthermore this symmetry of process extends not just to how brains and minds work, but also to how brains come into being, i.e. neurogenesis. So that the entire brain theory is able to be succinctly expressed as a single recursive process deriving from a single atom of recursion. In the same way that our brains and minds derive from the originator recursive atom of the fertilized egg.

 

The preceding, allows us to explain and implement recursive self modification and recursive self reference, which are some essential features of intelligence and consciousness. This is through the introduction of a feedback loop whereby, the underlying recursive process creates and augments structure through instantiating mappings in combinatorial space. In turn the structures so created, themselves encode mappings which go on to further express the original process but in augmented form. So in the strangest of strange loops, the original recursive atomic seed, extends itself through mapping, then feeds back on itself recursively to better extend it self, and so on and so forth. Finally we use this to explain the full significance of the Polar Frontal Cortex, a brain region involved in recursive thought processes and show why this facility is key to understanding consciousness and explaining human intelligence over that of animals.

 

Introduction :

The complex and difficult problem of understanding the brain and mind

 

The puzzle of how the brain works and the nature of the mind, remains one of the biggest unsolved problems in science and exists as one of its last great frontiers. It is the holy grail of modern times and its final solving would have massive implications, commercial, educational, medical, philosophical, social and political. Not least of the implications would be the creation of true artificial intelligence and the impact this would have on the world.

 

After earlier optimism in the 1950s and 1960s when cognitive scientists thought the problem of mind would be solved in a decade; instead the problem has turned out to be quite intractable and fiendishly difficult. In a recent interview Noam Chomsky said, 'The work in [AI] of about 60 years has not really given any insight, to speak of, into the nature of thought and organization of action and so on.' and that, 'We're eons away from [a theory of being smart]'.  In a similar comment the Physicist and popular science writer David Deutsche said, "No brain on Earth is yet close to knowing what brains do. The enterprise of achieving it artificially — the field of 'artificial intelligence' has made no progress whatever during the entire six decades of its existence." In 1979 Francis Crick wrote that ‘[The Study of the Brain] is conspicuously lacking a broad framework of ideas’, yet 35 years later it is still looking for this 'broad framework'. This sort of sentiment is also echoed by several other prominent researchers and thinkers. But what is the impasse? Why has this, yes complex, but finite object frustrated all attempts to understand its workings? Why have the answers been so elusive? This is one of the things we seek to answer.

 

Today when a lot of specialists are asked when will we finally come to understand the brain and create true AI, a typical answer is sometime 50 to 100 years in the future. Sometimes a more optimistic estimate is given, say 10 years or so, but this is never accompanied by any sort of clear picture of how this might come about. Perhaps the lowest bound estimate was given by John McCarthy one of the pioneers of AI and the person credited with coining the expression 'artificial intelligence'. He said words to the effect that there is the possibility that someone has already figured it all out, but 'he hasn't told us about it yet'. Along similar lines David Deutsche, while being quite negative about the state of AI and theoretical brain science, he has also expressed the hopeful view that, [ I ] can agree with the AGI[Artificial General Intelligence] is imminent camp', and that it is, ‘plausible just a single idea stands between us and the breakthrough, but it will have to be one of the best ideas ever.'

 

I believe we already know quite a lot about this single 'break-through' idea and also we already know that it is one of the best ideas ever, because this idea is really the key idea behind all of science. This idea is called Symmetry. And Symmetry is the key idea behind all science because when we ask what is science, then a fair and immediate answer would be that science is the process of discovering the patterns in nature and physical reality, and then describing those patterns in the form of mathematical constructs. But science is more that that, because it involves not just capturing the patterns in nature but also the patterns behind the patterns, the meta-patterns and unifying patterns. That is finding the overarching patterns which show that all the seemingly separate and unrelated patterns are really just different manifestations of the same underlying pattern. The word which best describes this process is Symmetry and it is the property which enables Science.

The concept of symmetry in science allows us to conceptualize and understand seemingly separate phenomena as really being the same thing. So for instance electricity and magnetism were considered as separate things but then came the idea of electromagnetism and that behind these different manifestations are the same underlying. Later on the concept of electromagnetic spectrum brought together the phenomena of electricity, magnetism and light. It means there is an underlying symmetry which is behind all them. And they transform into each other, so for instance light from the sun via a solar panel can put electric charge into the battery of an electric car which then uses magnetic force to translate that electricity into motion. That motion may be translated back into electricity when the car brakes through the action of the magnets in the braking dynamos and stored back into the battery of the car. Later on that electric charge may be converted back into light through the cars headlights. So here we have many instances of transformation but all the while something stays the same or invariant in the laws of physics which describes in one conception all these separate manifestations.

This unifying process using the property of symmetry proceeds in science.  Physicist have already unified the electromagnetic force with some of the other forces of nature, i.e. the strong and weak nuclear forces, and a unification together with the force of gravity still pending. This is still a work in progress and is driven by a belief that there exist unifying symmetries in nature.. So that what is initially seen and diverse and different, will turn out to be really various facets of the same simplifying underlying theory. We have a directly analogous situation in the brain and mind sciences, with a vast and myriad array of data, facts and findings waiting for some sort of simplifying and unifying understanding to clarify matters. When we understand that it is symmetry that is behind the process of science then there is no reason to suppose that it should be otherwise with respect to brain and mind science.

 

 

Symmetry, Self Similarity and Recursivity

 

We are proposing is that it is this property of Symmetry together with the related properties of Self Similarity and Recursivity which when used together will enable us to properly understand the structure and workings of the brain and mind. We’ll introduce the idea of Self-Similarity here but explain it in more detail a little later. When some ‘thing’ or some object has the property of Self Similarity then it is said to be 'Fractal', an expression coined by the Mathematician Benoit Mandelbrot in the 1970s who is credited with inventing Fractal Geometry. Implicit in notion of Self Similarity is the idea of nested symmetry and also recursivity; this we’ll also explain soon. So a convenient shorthand for expressing the systematic application of the ideas of symmetry, self similarity and recursivity for the purpose of understanding the brain and mind is to call what comes out of this process a 'Fractal Brain Theory’. Though its full title would be the Fully Symmetrical, Self Similar and Recursive Theory of the Brain and Mind. All of these terms may be unfamiliar to a lot of readers, so in we'll be elaborating more fully on what is meant by Symmetry, Self-Similarity and Recursivity in the context of understanding the brain and mind.

Symmetry, Self Similarity and Recursivity are really such fundamental concepts and as we will show, they are also extremely power tools for understanding what is the nature of mind and how the brain works. It often doesn’t seem obvious at all how these concepts can be applied to understanding the brain. With all the asymmetry and dis-symmetry that exists in the organization of the brain it may seem inappropriate to even consider the principle of symmetry in relation to thinking about brain and mind. However often it is the case that superficial and complex asymmetries masks the underlying and simple symmetry behind it all. Also the self-similar or fractal nature of brain organization is not immediately apparent, and sometimes there can be objection to the very notion of a ‘fractal brain’ theory. Once again it is not through superficial inspection that the self-similar nature of the brain is revealed. We are proposing that self-similarity, symmetry and the related concept of recursivity; are really the fundamental organizing principles of the brain and the key to understanding the process of mind. If the symmetry and self-similarity inherent in the structures and processes of brain and mind were obvious then we would have worked out how the brain works many years ago and the advent of true artificial intelligence would be a historical detail. Therefore we first need to make clear what we mean by symmetry, self similarity and recursivity in order that we then be able to systematically apply these principles to understanding the brain and mind. We will show that there exists a unifying conception of brain and mind which is fully symmetrical, self similar and recursive. And furthermore that these principles apply all the way from the scale of the entire brain right down to the most basic representational building blocks of brain and mind. When it is fully understood how fundamental these principles are then likewise an all encompassing understanding of brain and mind derived from them will have some very special, fundamental and foundational properties.

What is Symmetry?

Two key concepts behind the idea of Symmetry are that of Transformation and Invariance. So what is a transformation? An object, shape, representation, mathematical equation or some form of abstract entity may undergo a variety of different forms of change. For instance an object can be twisted, stretched or otherwise distorted and rules of derivation and logic can be applied to mathematical equations to generate new ones. Also genes can undergo mutations and also other forms of more pre-programmed modification. These are all instances of transformation. While these transformations are able to generate potentially infinite variation and difference, i.e. a myriad number of different shapes, mathematical equations or gene sequences. At the same time underlying all the differences are qualities which are preserved or conserved, and which are said to stay invariant. So in the case of a simple shape undergoing the basic transformations of translation, scaling and rotation. Even though from the original shape a variety of different patterns are formed, behind all this is still the same invariant original shape and if we reverse the transformations then we arrive back at exactly the same original form. See diagram below. And likewise the same sort of reasoning can be applied to the domain of mathematical equations, genes and abstract forms. These transformations are known as symmetries, and if we fully understood the nature of these transformations then we would likewise see fully the invariance or commonality of pattern, underlying all the seeming variety. The application of the principle of symmetry is discovering what these transformations are in order to simplify and understand complex and varied phenomena in terms of a more manageable and preferably minimal set of invariant factors. i.e. basic geometric shapes, simple mathematical equations describing the laws of physics, or the letters of the genetic code from which all DNA is constructed.

Symmetry.jpg

This way of looking at Symmetry may seem a bit different from what is taught in high school maths lessons, where we learn about a shape undergoing certain transformations and which as a result appears exactly the same as the original instance. So for instance we learn that a square being rotated at right angle increments will appear as exactly the same square and that it has rotation symmetry with itself. And the same square by reflecting along the vertical y axis going down the middle of the square will produce a transformed image that looks virtually identical to the original and so is said to have mirror symmetry. Here we have the idea of transformation and invariance in its purest and simplest form. Where the transformations are the most basic and the invariance is most apparent. In these most basic instances of symmetry, a shape undergoes some basic transformations, i.e. rotations and reflections, and end up appearing to the eye exactly the same.

When we talk about symmetry being applied to understanding the brain and being the key concept behind science, we are a talking about this basic high school conception of symmetry but in a much extended, augmented and embellished form. But the same basic idea remains, of things being transformed and at the same time something staying the same or invariant. And we can even extend this idea to different members of the same animal species, where of course no two animals are exactly the same, and there will be an infinity of differences between them. And then we can further extend the idea to looking at the structures of the brain to find the underlying commonality behind the diversity. So when we are applying the idea of symmetry to understanding the brain then we are no longer dealing with simple perfect geometric forms such as perfect squares or perfect equilateral triangles but the more messy world of neurons and brain circuits. But still the same principles of transformations producing an array of variation while preserving an underlying invariance, can still be applied. Later we shall learn that with a few levels of abstracting away some of the more superficial and random seeming features of the brain, then we will arrive at a very compact description of the entire brain, which does have perfect mathematical symmetry. This along with perfect self-similarity and perfect recursivity. We need to introduce a lot of experimental evidence and also some bridging concepts in order to do this. This we will do in due course. But for now we’ll move on to explaining self-similarity.

What is Self-Similarity?

Self-Similarity is a property of an object or thing when it is made up of smaller copies of itself at various scales and potentially to infinitesimally tiny scales or resolutions. So for instance you can take a basic shape and make smaller copies of that shape and place these smaller copies within itself. And then in turn you can take each of these smaller copies and likewise make even smaller copies of these copies and similarly place them within their parent copies from which they were derived. And you could imagine continuing this process without limit. This would produce patterns or shapes which would have the property of being self similar at all scales or can be said to be a fractal. So fractals are conceptual objects or abstract shapes which have this property of being self similar at all scales right down the infinitesimally small. In physical reality things can never be self-similar to infinite levels of consideration but still the application of the idea of self-similarity is very useful when trying to understand natural phenomena. An interesting perspective on what is the nature of self-similarity is to think of it as nested symmetry, which would then relate to the earlier discussion. See diagram below where we had the origin brain shape from earlier, but this time we’ve made smaller copies of itself and placed these copies within itself. We’ve then repeated this process a few more times, i.e. recursively. We'll be discussing recursivity more.

Self Similarity and Recursivity.jpg

Another way to visualize self-similarity is to imagine russian dolls but with many smaller russian dolls contained in the next size down. The diagram below illustrates this concept with what we normally think of as russian dolls at the top of the diagram but with our augmented version of the concept below it. The two augmented russian dolls more towards the right of the diagram represent progressively ‘zoomed’ in versions of the original biggest and enclosing doll, drawn to the left most side.

1b1d4 RussianDolls-Diagram.jpg

And below are a few geometric forms to further illustrate the concept of self-similarity or fractalicality. The object to the right most side below is a vegetable called romanesque broccoli or cauliflower and is an example of a natural fractal. Note here again we have structures which are made up from smaller 'self-similar' copies of the overall form.

1b1f6 Fractal_pyramid.jpg1b1g808.jpg1b1d907cauliflower-fractal.jpeg

What is Recursivity?

Recursivity or recursion refers to the property that certain processes have when they are repeated applied upon themselves. So that the result of the process is repeatedly fed back into itself to produce another result, and so on and so forth. This can be in the form of mathematical equations, where we feed in a number into an equation to get another number, and in turn put this new number back into the equation to get a third etc. Also natural processes such as mitosis or cell division can be described as recursive. This is the process of the cells in our body repeatedly and recursively dividing into two. It is what enables a single cell that is the fertilized egg, to become all the 35 trillion or so cells in our body. So from the single cell, through the recursive process of mitosis we get two cells. The process is then repeated on these two cells to get 4, then repeated again to get 8 and so on. We may also call mitosis a divergent recursive process because of the way it starts from a single point and produces a spreading or diverging set of myriad new points. An example of a process working in the opposite converging way would be the idea of idea in a sports tournament where 8 competitors paired off to play each other in a quarter final round, the 4 winners of which are paired off in the semi-finals, to produce 2 finalists made to compete in the finals, which produces the eventual winner. See diagram below. We could extend this idea to encompass arbitrary numbers of contestants. And this process would be convergent because we start from a whole load of contestants and end up with a single winner.

Tennis-Tournament.jpg

So these three examples of an iterative mathematical function, biological cell division and a sporting arrangement; gives us an idea of what is meant by a recursive process. When this recursivity is combined with the ideas of self-similarity and symmetry, then we have the most important fundamental concepts for understanding the brain and mind in place.

We will now talk about the brain itself, and start our analysis by trying to find some common organizational patterns or ‘fuzzy’ symmetries, to gain an initial sense of order and overarching pattern. Later we translate our fuzzy symmetries into something more crystalline and definite.

Some underlying and recurring organizational patterns behind the brains complexity.

 

The brain has been called the most complex object known to humankind and at times it seems bewilderingly so. With its around 10s of billion neurons, trillions of synapses and 100 000+ kilometres of wiring all contained in the space of our skulls. To some brain researchers it seems like a total mess, a ‘kluge’ or the result of a long series of haphazard accidents. But underneath this superficial disorganization and mind numbing complexing lies a stunning simplicity. Through the systematic application of the principles of symmetry, self similarity and recursivity we can show that there exist organizational principles and common underlying patterns, which allow us to fully comprehend brain and mind.

 

So we start with some obvious repeating patterns in the brain, then move to demonstrating ones which are increasingly less obvious. Some of these patterns have only been able to be discerned as a result of quite recent research in the neurosciences. And then we move to underlying common patterns or symmetries which are quite abstract.

 

First of all, we consider the cerebral cortex or neo-cortex (two completely interchangeable terms) and the neo-cortical columns from which it is entirely constructed. This part of the brain comprises most of the brain mass in the skull ~80% and is what we normally understand as brain. It consists of all the crinkly folds and ridges we see when looking at a brain. But its real structure is that of a flat sheet a few millimetres in thickness and covering an area of approximately 2 and a half feet squared. By scraping out all the white matter which are the nerve fibre tracts connecting up all the different regions and columns of the neo-cortex then it is possible to literally flatten it out. The diagrams below left show a depiction of a flattened out human cerebral cortex and the size of this ‘flat sheet’ relative to a whole brain. The diagram below left does the same for one hemisphere of a macaque monkey cerebral cortex.

2c Human Cortex Flattened.jpg2da Cortical Map.jpg

 

This flat sheet is made up of a few million cortical columns which are like cylinders, with a diameter of ~0.3 millimetres and a length corresponding to that of the cortex itself i.e. 2-3 millimetres. This makes up the ‘grey matter’ of the cerebral cortex, as the cell bodies give a greyish appearance to naked eye. All the white matter or fibre tracts connecting up the cerebral cortex, arises from neurons located within the cortical columns. The really amazing thing is that all of these cortical columns share a same basic design and contain roughly the same number of neurons arranged in a stereotypical manner within all the columns. With certain neuron types and certain patterns of connectivity arranged in a very ordered and stereotypical manner, throughout all the cortical columns making up the neo-cortex. Of course no two cortical columns will be exactly the same, and there does exist a lot of variation between columns existing in different regions of the neo-cortex. Nonetheless underlying all the variation and difference is commonality and invariance in basic design. What’s more, this basic blueprint seems to be preserved through the evolutionary process, so that the cerebral cortex of a mouse brain is likewise made up of the same columnar building blocks, of roughly the same diameter, containing roughly the same number of neurons, the same neuron types, and following the same stereotypical blueprint also found in the human brains. So that even though the neocortical is stupendously complex, at the same time there exists a lot of repeating pattern, symmetry and organization.

Below  left is a diagrammatic presentation of some cortical columns. Below middle is a diagram of the distribution and size of neuron cell bodies from various regions of cerebral cortex showing some variation. And below right is a diagram showing the main neuron classes found within the cell columns.

2fa Capture.JPG2fb Agranular Transitional & Granular Cortex.jpg2fCerebral Cortex Neurons in Layers.jpg

 

The same line of reasoning and analysis we’ve just applied to the neo-cortex can also be applied to the cerebellar cortex and also the striatum, which together with the auxiliary structure of the thalamus, makes up most of the rest of the brain. The cerebellar cortex can likewise be flattened into a sheet like structure, which is also made up of a stereo-typical modular architecture. These are referred to cerebellar ‘complexes’ and ‘micro-complexes’. With these basic modular building blocks which are around 0.5 millimetres in length, the entire flat sheet of the cerebellar cortex is constructed. The structure of a cerebellar complex is simpler than that of a cortical column of the neo-cortex. The design is also evolutionarily more ancient, so that the stereotypical design of the basic cerebellar circuit, has been preserved from shark brains right up to human brain. Going even further back, even the brain of a lamprey, a primitive form of fish and very ancient animal, contains rudimentary cerebellar circuitry.

The diagrams below left, show the the relative position of the cerebellum to the rest of the brain and a cross section of it shows if extremely folded nature. The diagram below centre shows a drawing of an animal cerebellum. Here some body maps of the animal are drawn in to show which parts of the cerebellum handle which parts of the animals body. The cerebellum displays topographic mapping in its representation of the body. The diagram below right depicts a flattened human cerebellum. We can see from the scale indicator that the extent of this flattened cerebellum from top to bottom is about 60 cm or 2 feet. We can see why it has to be so intricately folded in order to cram this considerable surface area into such a small space.

2jb dCerebellum---Cross-sections-in-3-Species.jpg2jc Cerebellum Projection Map.jpgCropped Flattened Cerebellum.jpg

The diagram left below show the the striatum in human brain, depicted in green and shows where it is located within the brain.The same sort of reasoning that we applied to the neocortex and cerebellum likewise applies to the striatum, So again we find stereotypical organizational patterns throughout all the striatal areas in the brain. The stereotypical pattern of striatal organization and neuronal makeup as found in a human brain is also the same basic design found in the striatum of birds and reptiles. And so like the neocortex and cerebellum we are seeing brain structures preserved through the course of evolution. The diagram below right depicts a part of the striatum called the putamen which both humans and many other mammals possess. A body map is drawn onto the diagram of an animal putamen, showing which zones within it, handle the control which parts of the animals body. Here again we see topographical mapping, with relative spatial relationships between different parts of the body preserved.

2ka Striatum.jpg2kc Basal Ganglia Diagram.JPG

 

The analysis so far has mainly dealt with quite obvious basic symmetries or invariant patterns. We can proceed now with exposing commonalities of pattern which are less obvious. A very important one ties together the three main structures of the brain we have so far considered and gives an important clue as to their functioning as an integrated unity. It involves the way both the cerebellum and striatum interact with the neo-cortex. Both these structures separately form what are known as ‘closed loops’ between themselves and the neo-cortex and in both cases the thalamus is used as an intermediate relaying structure. There are many such closed loops working in parallel and separate ones for each different sub-region of the neo-cortex. Such that specific subregions of the neo-cortex will work in conjunction with specific sub-regions of cerebellar cortex and striatum etc. Later on we be explaining how this loops may represent time but for now the main thing is this symmetry of closed loop structuring that links the cerebral cortex to the striatum and cerebellum.

We bring now into our discussion of the main structures of the brain, what can be described as the emotion centres. These are the centres of the brain involved in motivation and homeostasis and include such structures as the hypothalamus, amygdaloid nuclei and parts of the cerebral cortex such as the orbital frontal cortex and subgenual anterior cingulate cortex. We have already described how the striatum forms closed loops with regions of the cerebral cortex. What was discovered and confirmed quite recently is the idea that this striatal loop structure also extends to the emotion centres. So that the hypothalamus and the amygdala structures also have their corresponding striatal closed loops with which they interact. So in the case of the hypothalamus, its various nuclei interact with a once mysterious structure called the lateral septum. We now know this structure has the same stereotypical architecture as the rest of the striatum and forms separate closed loops with each of the hypothalamic nuclei; each separate region of the hypothalamus working in conjunction with its own area of lateral septum. And in relation to the amygdaloid nuclei, we now know that a sub-region known as the central nucleus of the amygdala also can be understood as ‘striatal’ and forming the same closed loops with the rest of the amygdala. In fact all the emotion centres we mentioned share the same underlying striatal-like organization. We’ll be discussing the emotional centres a lot more later in this paper.

What we have then is a common striatal organizational pattern which is found through-out large parts of the brain and covers all the anterior and prefrontal neocortex together with the emotion centres. Also a similar extension of our understanding of the cerebellar cortex has also occurred in recent years so that a part of the brain once thought to be involved mainly in the coordination of movement (like the striatum) has likewise been extended to cover the emotion centres and also the cognitive areas. What this means is that we have common organizational principles that cover most of the brain and encompass, neo-cortex, striatal structures, cerebellar cortex and the emotion centres. We will demonstrate later on and in much more detail, important symmetries which span all the emotion centres together with neo-cortex, cerebellum and striatal structures and show how they can be conceptualized as sharing the same underlying design and mode of operation.

We’ll complete our initial quite superficial overview of brain anatomy with a description of another recurring pattern found throughout the brain which brings together everything we’ve talked about so far. It is a basic recurring ‘fuzzy’ symmetry which we’ll elaborate upon much more later and show that it is key to understanding what it is that brains and mind are doing. And we’ll also be formalizing these fuzzy and vague symmetries into very definite and precise mathematical ones.

A Basic Overarching Pattern in Brain Organization

The basic pattern which seems to be recurring all over the brain is that of a tree, like the sort we find in our gardens and in parks but with a special addition which we’ll describe in a moment. So if we imagine a tree then we have its trunk, which is its body, and then we have all the main branches coming off the trunk, and the progressing branching into the twigs and leaves of the tree. But there are also the roots which we don’t normally see because they are underground. And like the branches above ground, the roots also branch out progressively, further and further into the depths of the earth. Apart from superficial appearance, there is a very important difference between the roots of a tree, versus the branches and leaves. It has to do with the main flow of nutrients going through the tree. That is, water and nutrients from the soil, flow through the roots in a converging recursive process towards the trunk or body of the tree. In turn, the flow continues through the branches and leaves of a tree but in a diverging recursive process away from the trunk. This is analogous to the earlier sports tournament and cell division examples used earlier to illustrate convergent and divergent recursive processes respectively. As we shall see, this inflow and outflow, tree like converging and diverging branching pattern is something that is found everywhere in the organization of the brain. And whereas in the case of botanical trees, it is water and plant nutrient that is being moved around, in the trees of brain and mind it is information that is flowing in and flowing out.  If we needed an simple overall concept, or analogy for understanding brain and mind, then this would be it. But the trees of the brain would have an additional feature that is not found in our everyday trees. This is the idea that the tree structures and processes found all over the brain, loop back upon themselves so that some of the outflow of the divergent branches are feed back into the ‘roots’ of the corresponding convergent inflow going back to the original starting place. This is best illustrated by consider examples of this in the brain. So we’ll go through a load of brain structures existing at various scales to support these ideas, ending with a look at the entire brain.

So in the diagram below, diagram 1./ depicts a typical pyramidal type neuron which makes up around 80% of all the neurons in the cerebral cortex and is really the ‘work horse’ neuron of the brain. Most of the high level information processing in the brain critically involves these neurons. And all the major nerve fibre bundles, that is the white matter found underneath the surface of the neocortex, consists of the axons emanating from pyramidal neurons. So the diagram depicts a small pyramid shaped cell body, hence their name and the dendrites surround it. The arrow heading straight down from the cell body is the axon of the pyramidal cell which will traverse some distance to another part of the neocortex and then branch profusely all around its area of termination. This is not depicted. What is shown is a recurrent connection that splits off from the outward bound axon and which loops back to make connections in the vicinity of the neuron from which it came. However this recurrent part of the axon generally won’t make direct contact with the cell body of the originating neuron. Diagram 2./ depicts a cortical column which would be made up of around 1000 neurons and we have in composite, the same pattern that we described for a single pyramidal neuron. We could have an aggregates of connections flowing in and also flowing out, from and to other cortical columns. And we would likewise have an aggregate feedback loop made up of hundreds of individual nerve fibres splitting off from the output projections to other columns and  flowing back into the same column. In Diagram 3./ we depict entire cortical patches each made up of many thousands of cortical columns. At this scale we can also make out a converging flowing in and diverging flowing out pattern, but this time involving entire patches of neocortex. At this scale there is an aggregate looping back of the recurrent loops deriving from individual columns but what is more important are the closed loops that many patches of neocortex, particularly in the frontal cortex, will form with the striatum and cerebellum.

3c FractalStructureOfBrain.jpg

The diagram below depicts a more complex arrangement of neocortical patches, which would correspond to a whole processing nexus centred in one of the prefrontal cortical regions involved some specific task such as speech or spatial processing. Here the central patch would have its own striatal loop and also a cerebellar loop(not drawn). It would receive various inflows of information from cortical patches around the brain each with their own little nexus of inflow, outflow and looping back activity. Our central prefrontal patch will in turn feed its output to various other centres that are themselves little processing centres with a similar set of inputs and outputs.

3e.jpg

When we come to the entire brain then we can also conceptualize it is a tree structure with an overall recurrent loop. See diagram below. The converging roots would correspond to all the sensory hierarchies starting from the primary sensory cortices of sight, touch, sound etc. All these modalities will form their respective hierarchies with vision being the most complex and elaborated. Also the modalities will converge in some places to form cross modal or multimodal aggregated hierarchies. Eventually all these hierarchies flow inwards and converge upon the hippocampus, with each individual or multimodal sensory input, representing the distilled information coming from the various senses, making up the thickest root segments closest to the zone of ultimate convergence. This is actually the emotion centres and their full integration into the sensory and motor hierarchies will be explained in detail later. From here all the sensory flow of information is feed forwards to the cingulate cortex, which is the start of the diverging out motor and cognitive hierarchies. From here the flow of information spreads outwards. So at this end the initial thick branches of the cingulate cortex will correspond to modalities of action and mental processing. Different regions of the cingulate will drive different activities. So for instance the retrosplenial cortex will be involved in memory access and the posterior cingulate will be involved in internal spatial processing and first person perspective visualization. The anterior & dorsal-medial cingulate cortex will drive reasoning, cognition and language. The regions posterior to these regions are involved movement and motor control. So each of these modes will be like the initial thick branches of a tree, progressively radiating out to greater levels of detail ending up as specific thoughts, language output, movement and behaviours. And even at this whole brain scale we discover fibres tracts emanating out from cingulate areas and looping back to the inflow input zone, i.e. the hippocampus. This is depicted by the blue arrow in the diagram below. In this way the brain forms a massive recurrent loop between its diverging action and converging sensing hierarchies.

3i copy.jpg

So we see this quite basic and simple recurring tree like patterning from the level of neurons right up to the level of the entire brain and various scales in between too. And together with this tree structuring we also find our recurrent loops all over the brain and at various scales, again from the level of neurons to the entire brain.

We’re starting to get an idea of some overarching patterns and modular design principles existing in the brain. Where before we seemed to have a mass of unrelated and hard to fathom physiological and anatomical data. We started off by describing the stereo-typical modular design of the cerebral cortex, cerebellar cortex and extended striatum. Then we described the stereotypical way in which these parts of the brain are wired together, i.e. with the striatum and cerebellum forming closed loops of circular connectivity with the cerebral cortex. We also briefly talked about the emotion centres and described how this striatal and cerebellar closed loop architecture also applied to these important brain areas as well. Thereby highlighting some more recurring organizational patterns. After that we introduced our basic overall organizing pattern found throughout the brain and at various scales i.e. the tree like inflow, outflow branching; and looping back arrangement. All our earlier stereotypically patterned modules which make up the cerebral cortex, cerebellum and striatum, and the cerebellar and striatal closed loops would totally fit into and be accommodated by our overall tree like organizing principle.

So we are getting a sense of least some order amid the bewildering complexity of the brain. However in our analysis of the brain and attempt to demonstrate underlying patterns we are constrained by the vagaries of language and verbal descriptions. Even with our visual and diagrammatic representations of brain we are limited. Towards our goal of fully understanding the brain and mind, we can only go so far with this sort of analogous explanation and graphical means of reasoning. This ‘mathematics of the eye’ as Benoit Mandelbrot described it. We need a more formal mathematical language and means of capturing our ideas in order to take things further. We need to geometrize the problem in order to more clearly see how all the different aspects of the puzzle relate to one another in order that they may be solved. We need to convert our fuzzy symmetries and rough analogies into something totally explicit and definite. So towards this end we need to introduce some abstract ideas that will allow us to completely formalize and precisely describe all the neural organizing patterns we have described so far. Later on we will completely revisit all the neuroscience and brain anatomy that we have been talking about so far. We will be elaborating on it much and then translate all of it into a unified theory of how the brain is organized and how it works.

The importance of abstracting, formalizing and geometrizing

We find that in the history of science it is often a process of geometrization which has enabled us to see things more clearly and explicitly. So it was through the analytical geometry of Rene Descartes which allowed for a more systematic study of the motion of the planets and which paved the way for the invention of the differential calculus by Isaac Newton and Gottfried Liebnitz. And likewise Einstein’s theory of relativity was only made possible by the application of a peculiar sort of non-Euclidean geometry where parallel lines may intersect. And so the same sort of idea may be useful for the task of understanding the brain and mind. What we need is some sort of formal language and abstract geometry that will allow us to fit together all the separate pieces of this vast jigsaw puzzle and see patterns which would otherwise be hidden from us.

In the late 1990s Rodney Brooks, who was then the director of the MIT (Massachusetts Institute of Technology) AI lab, predicted the coming of an, ‘Organizational principle, concept or language, that may revitalize the Mind Sciences in [the 21st Century]’. And separately in a 1996 publication titled, ‘Fractals of Brain, Fractals of Mind: In Search of a Symmetry Bond’, one of the contributing editors talked about the possible existence of what was described as a ‘secret symmetry’, secret in the sense of being undiscovered.  Its uncovering would provide the ‘symmetry bond’ referred to in the subtitle of the book, which would allow us to understand brain and mind as existing on the same continuum where as they put it, ‘mind/brain performs as an indistinguishable one from a formal, neurological and psychological point of view’. The formal abstract geometry we are about to describe will be both an ‘organizational principle, concept or language’, and also one which will allow us to not just bring together all the details of the brain, but also unify brain and mind into a single conception. So what is this formalism? It is the language of binary trees and binary combinatorial codes. These are really the simplest and most basic concepts in computer science and may on first consideration seem unimpressive and limited. Also it will not be immediate clear why these concepts should provide the key to understanding the brain and mind. But science is really the process of explaining the most with the least and as we shall see, there is a very powerful way of looking at the brain which is completely binary, bifurcating, doubling, octaving, griddy and discretized. Also later on we shall demonstrate that these properties are pretty much ubiquitous throughout the brain and also in the description of the data structures of mind. But we first need to explain more clearly what are binary trees and binary combinatorial spaces.

Binary Trees and Binary Combinatorial Spaces

4bDifferent Kinds of Trees - Copy.jpg

The binary tree is one of the most elementary ideas in computer science along with binary combinatorial spaces. And binary codes are the most basic unit of consideration in Claude Shannon’s information theory. Quite simply a binary tree is like the sort of tree we see in our gardens and parks but they have the property that every branching may only fork into two, never 3, 5 or even 4 directly. To the nodes of binary trees we can assign the numbers 0 or 1 and this allows us to represent combinatorial codes. Each of these codes is basically a binary base 2 number where the only digits allowed are 0 or 1, as opposed to the base 10 numbers we normally understand i.e. consisting of digits from 0 and 1 up to 9 and all the numbers in between. With our base 10 numbers we are specifying decimal codes which can theoretical represent any number we could possibly imagine. We could also equivalently represent these quantities in binary base 2 and this is the way digital computers work. So this is what is meant by binary coding. But what is a binary combinatorial space? Here is where we diverge a little from the world of base 10 and decimal numbers.

A binary combinatorial space is where first we consider every combinatorial possibility that a sequence of binary digits may represent, i.e. every number that may be represented by that sequence of binary bits by allocating to it, either 0 or 1. We then treat each combinatorial possibility as a point in abstract space. We then define a distance measure between all these points in abstract space corresponding to every different combinatorial code that may be represented by our sequence of binary digits. This is simply what’s known as the ‘Hamming distance’ between any two different binary sequences. And this is the difference not in the number that the binary sequences represent, but rather the difference in bit pattern when we take two binary sequences, put them side by side, and make a comparison at each corresponding point of the two sequences to see whether they contain the same binary digit or not, i.e. 0 or 1. If both the sequences contain the same digit, i.e. both 0 or both 1, then there is no difference and no additional distance. If however they contain non matching bits, then this point along the two sequences contributes 1 unit of distance to the overall distance measure. And so we do this for every point along the two binary sequences we’re comparing, and we end up with a total tally of the number of bits where the two sequences differ. This is the hamming distance. If both binary sequences were identical then the hamming distance would be zero. If they were not identical then the hamming distance would be greater than zero and this would give an indicator of how different the two binary sequences were.

Because these sequences are being thought of as points in an abstract space, then we now have a way of completely specifying the distance between every single point in this abstract space. This way of looking at things satisfies certain conditions so that mathematicians who study this sort of thing would call this a non-Euclidean metric space. Sometimes this binary combinatorial space is referred to as ‘binary N-space’ with the ‘N’ corresponding to an arbitrary number of binary digits or length of the sequences that we might take into consideration. In this abstract binary N-space we may define points, lines, circles, regions, attractor basins etc. However they will have very different properties from the lines and circles we might define in our normal ‘x, y, z’, Euclidean or Cartesian space, which we normally perceive and think of as space. Some of these special properties of binary N-space make it very suitable for representing things and tolerating errors and also for understanding the brain.

Reconciling Binary Combinatorial N-space with ‘normal’ Euclidean space

We have seen how binary trees give rise to an abstract non-euclidean metric space based on binary codes corresponding with binary digits allocated to binary tree nodes. But our brains and minds need to function in euclidean space, i.e. space as we normally perceive and understand it. We need to be able to use binary trees to represent these normal spatial relationships and the spatially defined objects existing in the space of the reality we inhabit. Fortunately there is a very straight forward way to do this through the recursive sub-dividing of lengths in normal space into two and then allocating these two separated compartments to the two branchings of a node of a binary tree.

The simple diagram below would explain this most effectively. Here we see a series of squares subdivided into a 2-dimensional grid. Drawn together with the blue 2d squares and grids representing normal euclidean space is a binary tree drawn in red. It is drawn in such a way that it is easy to see the correspondence between the nodes of the binary tree and the blue squares representing normal space. It is easy to imagine how the grids can be specified to any resolution and details, i.e. with more branchings of the binary tree. It is also possible to use the same principle to include a third spatial dimension, though this is harder to depict in a static 2 dimensional diagram. In computer science this way of representing space is called Quad Trees. Something similar also occurs in the implementation of Wavelet Transforms which are used in data compression algorithms.

4dj Grid-Tree-3d-view - Copy.jpg

The next diagram below also depicts a binary tree except it is drawn flattened out in the 2d plane. It shows in a different way how we may maps the nodes of a binary tree into normal euclidean space in order to represent it. The binary trees in the diagram below and above are actually topologically equivalent.

5ba TH Grid Binary Tree.JPG

The next diagram shows 2-dimensional grids of increasing resolution, represented by binary trees of increasing branching depth.

4c Making Grids with Binary tree.jpg

Furthermore we may also represent time using binary trees. So that instead of recursively partitioning space into binary subdivisions we instead carry out the same process along the time dimension. So in the next diagram below, instead of using binary trees to represent space, each of the branches subdivide the time dimension. At the bottom end nodes of the temporal tree are depicted eight 2d grids representing spatial information. So taken together this effectively hybrid temporal-spatial binary tree would be able to represent the succession and evolution of spatial information over time.

2ta A Representing Time with Binary Trees.jpg

Now that we’ve described how we can specify euclidean space and time using binary trees, we can then allocate these spaces or contexts, binary values, i.e. 0 or 1, so that these spatial temporal descriptions may also contain a combinatorial code. Or put another way, they become spatial temporal combinatorial codes. We have then a merging of the earlier description of binary combinatorial space, with our binary tree representation of euclidean space. It means that we may take projections from euclidean space and map them onto our binary tree and binary combinatorial space language. This sounds a little complex but a simple example will greatly clarify what is meant by this. When we take a digital photograph, then patterns of light from objects existing in reality are projected by the camera lens onto a 2d surface which converts the light into digital information. This is an example of a projection from euclidean space onto combinatorial space, whereby a photographic scene of converted into a computer file in the camera. All we’re adding on top of this simple commonly used everyday process is a binary tree hierarchical structure on top of the 2d photo plane.

There is a slight problem with mappings from euclidean space to binary combinatorial space. This is that slight changes or transformations in euclidean space can lead to massive hamming distance changes in binary combinatorial space. The solution is that we include all the simple affine transformations in euclidean space, i.e. translation, rotation, scaling and inversion, into our binary trees, and also represent these transformations as binary codes. So if our binary trees represent squares in euclidean space, as depicted in the diagrams above, then these squares are allowed to transform themselves i.e. shift, enlarge/contract and rotate. If a picture is sometimes worth a thousand words, then a short video animation even more so. A relatively simple computer program shows this process in action. See… https://www.youtube.com/watch?v=1CNjZGhWqC0&feature=youtu.be

The Binary Brain and Neuropsychology

 

In this next section we will demonstrate how it is that the binary tree and binary coded way of looking at things is extremely relevant for understanding the brain and mind. Going through quite a diverse array of empirical findings, we show that there is a very powerful way of looking at the brain and structures of mind, which is completely binary, bifurcating, octaving, doubling, griddy and quantized. Furthermore this perspective on things is pretty ubiquitous and generalizing throughout the brain and mind.

Binary Space

We start with considering how we form mental maps of space and the outside world in our heads. A clue as to the workings of this essential facility is provided by case studies of patients suffering from a neurological deficit called hemi-neglect. Sometimes we come to learn better about how something works when it breaks down. This is a case in point. People suffering from hemi-neglect usually have some form of damage to the parietal lobes, which are an area of neocortex which our coordinates movements in space and is known to be involved in forming our mental maps of the worlds. The classic symptom of hemi-neglect syndrome is that those afflicted with it literally lose half their world; both either to perceive it or to imagine it. So the pictures below show what happens when someone with hemineglect is asked to copy some shape or picture. They literally can't place or register details on the neglected side. Asked to draw a clock, they can only place the numbers on one side. Asked to read a word they only register the letters on one side.

 4e Hemi-Neglect-diagram.jpg

When asked to eat a plate of food, they will eat only the food on one side of the plate and stop when that’s all gone seemingly oblivious to the food on the other side of the plate. But when the plate is rotated 180 degrees, so that the remaining food comes into view of the non-neglected side then the test subject starts eating again, only to stop half way again leaving all the food on the non-neglected side untouched. It seems as if there is an underlying binary sub-divisioning in our ability to perceive objects including plates of food and the food on the plate. See diagrams below.

cropped food on plate.jpg

In an experiment on hemineglect sufferers, patients were asked to imagine walking down some street well known. They were asked to name the various buildings located on either side of the street. As might be expected they were unable to recall any of the buildings located on the neglected side. However when they were asked to imagine walking down to the end of the street, turning completely around and walking back the other way, now they were able to name all the previously unrecallable buildings which couldn’t be imagined. But also this time round, the patients had extreme difficulty recollecting the building on the opposite side of the street, which were easily described when imagining walking in the original direction This relates to what psychologists refer to as egocentric spatial mapping. It is our view of the world from the first person perspective and so here again we see a binary partitioning of our egocentric maps. Not just in our ability to perceive but also in our ability to imagine.

When we consider the micro-features of our visual perception which are spatial frequency detectors (which also act as bar detectors) then we discover an interesting doubling in frequency arrangement. The diagram below left shows what is meant by spatial frequency. From what are known as 'Just noticeable difference’ (JND) experiments it seems that the spatial frequencies which are detected by our brains are spaced one octave apart. It is possible to manipulate each sub-band separately from the adjacent sub-bands above and below. So that when a spatial frequency grating with a specific wavelength was repeatedly presented as a target stimulus, it became progressively harder to detect with each presentation. It is as if a specific frequency processing sub-band was getting steadily fatigued and so altering its ability to respond. However when spatial frequency gratings either double in frequency and half the wavelength, or else half the frequency and double the wavelength, i.e. one octave above or one octave below the  original spatial frequency, then these new patterns were able to be detected more easily, in the same way the original stimulus was initially easier to detect. We may map frequencies all an octave apart to correspond with the nodes of a binary tree which thereby encode this doubling and halving pattern. See diagram below right.

4ha Untitled-2.jpg4hb Spatial-Waves-with-Binary-Tree.jpg

Another brain system also displaying a similar frequency doubling pattern to the spatial frequency detectors of the mammalian visual system, is the centres of the brain involved in what is referred to as ‘allocentric’ spatial representation. These involve the recently discovered grid cells found in the hippocampus and auxiliary structures in particular the dentate gyrus. Allocentric spatial mapping refers to where we are in a physical coordinate system and frame of reference. So for instance our GPS (global positioning system) location is an example of an allocentric point of reference. This is kind of spatial processing is also involved in procedure known as  ‘dead reckoning’, where direction, velocity and times of travel can be used to work out where we are in physical reality. It is our x, y location or point on the map. This is different from our egocentric spatial map or first person perspective as discussed earlier. We may stay in the same allocentric location, i.e. standing on the same spot, but we might turn our heads and scan our eyes all over the place to give lots of different egocentric frames of reference, but tied to one unchanging allocentric reference frame. What was discovered in recent years is that there exist special neurons which seem to map out lattice like reference grids over our allocentric x, y floor space. These neurons will only fire in response to the animal being in specific allocentric locations as the test subject moves around an open area of floor space.

4hcb Capture.JPG

The amazing thing is that these special locations where a particular 'grid' neuron fires the most, closely correspond to the vertices of equilateral triangles arranged in a perfectly tessellating grid projected onto the floor space. See diagram below. Alternatively we can think of these special firing zones as being in the centres of perfect hexagons similarly arranged in a perfectly tessellating grid. Furthermore these tessallating grids only come in certain sizes. What’s really interesting for our current purposes is that the scaling factor from one grid size to the next one above or below in size is roughly 1.42. This is a very recent finding and is significant because 1.42 is roughly the square root of 2. This means that if we multiply by 1.42 twice then we come to double the scale of the equilateral triangles or hexagons.

Long version Grid-Cells-Human.jpg

 

So we see this frequency doubling phenomenon with respect to the micro-features of visual perception, i.e. spatial frequency and also in the context of allocentric spatial mapping where in a sense a spatial frequency mesh is projected onto our perception of physical space.

When we turn our attention to the auditory system, the part of the brain most associated with processing frequency and oscillating phenomena, then in the arrangement of the cochlear-topic or tonotopic maps of the auditory cortex then again we discover this frequency doubling arrangement. The frequency processing sub-bands of the auditory cortex are spaced 1 octave apart. See diagram below.

Primary Auditory cortex.jpg

 

More generally, it is possible to take any sort of cortical topographic map or any region of the cortex and represent them using binary trees; thus also making them conform to our binary bifurcating and doubling view of things. This would include visual retinotopic maps, auditory tonotopic maps, the somatotopic maps representing our bodies, the musculature-topic map representing our muscle groups and all the other areas of neocortex involved in more abstract functions. In general all these sorts of topographic brain maps which preserve spatial relationships are involved in a very simple form of spatial mapping. The 2d-laminae which these topographic maps can be thought of as, represent in a sort of pictographic form our senses, musculature, memories and thoughts. Even if this is not intuitive or obviously apparent as in the case of more abstract representations. And so too is it the case that we can use binary trees to reduce and represent any 2d topographic map or any sub-area of cerebral cortex.

 

For as we showed earlier there is a very straight forward way to map binary trees onto any bounded two dimensional plane. All cortical maps are effectively laminar or sheet-like 2d planes, and therefore we can represent them easily using our binary tree spatial mapping scheme described earlier. This gives us a rather boxy and square spatial structuring and some readers may object that the components of real cortical maps are better thought of as being arranged in a more hexagonal pattern. After all, if the brain is made of roughly cylindrical columns, then wouldn’t this pack into a more hexagonal grid? Also from what we find in empirical studies of neocortex and also in relation to our allocentric grids, it seems hexagons or equilateral triangles seem more the norm. Wouldn't this be incompatible with our square view of things? The simple answer is that we can make these alternative tessellating patterns conform to our binary and square way of looking at things. We do this because it allows us to develop the more unified perspective which we seek, while also keeping our grounding in empirical evidence. A diagram or two can save a lot of verbal description so below is depicted a way in which a hexagonal mapping scheme can be perfectly represented with our binary tree and boxy, griddy way of doing things. See diagrams below. The centres of each hexagon may be mapped to a superimposed square grid, drawn in blue, and which may in turn be specified using binary trees.

4hda Hexagons-3.jpg4hdb Hexagons-2.jpg

What we have shown so far is that there is an underlying binary and doubling pattern to a host of brain functions and facilities of mind, that may seem very unrelated and disparate. From egocentric spatial maps, to allocentric spatial maps to all the varieties of topographic cortical map. And from the micro-features of visual perception to the or brain’s processing of auditory sound information. We see throughout all these different ways of thinking about space, this underlying binary, doubling, octaving pattern. When we turn our attention to time then likewise we see pervading underneath and in all manner of ways, this sort of binary structuring. We have discussed the different sorts of spatial representation and we will now discuss temporal representation.

Binary Time

 

At the start of our discussion on the binary nature of time processing and representation in the brain, first we need to show it discrete nature. In the same way that space is demarcated by the peaks and troughs of spatial frequency patterns or the binary sub-divisioning of egocentric maps and compartmentalized around these reference points; likewise time is also partitioned and compartmentalized. Though subjectively we experience a continuous flow of time, we know from physiological data and evidence from neuropsychological experiments, that time is actually chopped up into separated segments and is non-continuously processed by our brains.

 

Brain waves are pretty much all pervasive in the brains of just about any living creature imaginable. The peaks and troughs of these waves synchronize brain activity but also enable and dis-enable it. So for instance in the rabbit, the olfactory bulb (smell brain) and hippocampus (A region involved in memory) oscillate at the theta frequency range ~5-6 htz. When we look at rabbits close up then we can usually see that they are constantly sniffing around very rapidly. This is actually occurring at roughly 5 to 6 htz and is synchronized with the theta brain waves in the olfactory bulb and hippocampus of rabbits. Experiments were performed to try and illicit synaptic LTP (Long term potentiation) in the rabbit hippocampus. LTP is an experimentally induced modification in the synaptic strength of the connection between two brain cells and is believed to be the physiological substrate of our memories. This LTP in rabbit brain components could only be induced when the training stimuli, electrical currents coming from the experimenters micro-electrodes, was timed to coincide with the peaks of the hippocampal theta waves. Otherwise there was no effect and no ‘learning’. We can imagine from these results the idea of the rabbit taking rapid discretized temporal snapshots of the olfactory environment. So therefore in this way time is being partitioned into separate compartments.

 

In another set of experiments this time performed on humans and relating to the ~40 htz gamma wave which is expressed all over the brain, a similar discontinuity of temporal processing was discovered. Here the human test subject was shown some video footage but it had the special property of being shown only 50% of the time and in an oscillating succession of flashes, timed 25 milliseconds apart and therefore shown at ~40 htz. In fact the display of this visual input was synchronized with the phase of the human test subjects visual cortex gamma waves recorded using sensitive non-invasive surface electrodes. When the showing of the bursts of visual input was made to perfectly correspond with the peaks of the visual cortex gamma waves then everything was fine and the subject saw the video perfectly. It was perceived as a continuous stream with no apparent discontinuities. But when the same visual input was merely phase shifted 180 degrees, so that the exact same input was shown but this time synchronized to correspond with the troughs of the visual gamma waves then the subjects saw nothing. This again demonstrates the slicing up and demarcating of time using brain waves.

 

Moving on, when we consider the relationship between the main brain waves that have been classified and given labels then again we see a doubling, octaving, powers of two pattern in their relative frequencies. This is not by design, but merely the frequencies around which the power spectra from the EEG (electroencephalogram) recordings were grouped and so were given specific names. First to be discovered in the early 20th century are the alpha waves at around 10 htz. Then we have the theta waves at ~5-6 htz, the beta waves at ~20 htz and gamma waves at ~40 htz. When we arrange these waves in the diagram below then once again we see this octaving frequency doubling pattern. Neuropsychologist now believe that these waves interact with one another and that the lower frequencies harmonically nest the progressively higher ones. In music the most harmonic interval is the octave, and it is easy to see how a harmonic nested temporal representation scheme would most natural employ this octaving spacing of relative brain wave frequencies. Neuroscientists believe that these brain waves are in turn nested in even lower frequency brain waves, i.e. delta waves, and these may even have fractional frequencies or wavelengths extending to several seconds. It would be interesting to see if these lower frequency waves likewise fit into our binary doubling patterning scheme of things.

4i Brain-Waves-Diagram - Copy.jpg

While we are still waiting for clarification on the exact nature of these lower frequency oscillations with wavelengths spanning even a whole second or more; at the same time we do know a lot about another rhythmic oscillatory phenomenon which the brain processes and which features regular periodic behaviour spanning into the minute range and more. This is music and again we discover an underlying binary doubling structure to it. In the forms of music which are most accessible, easy to listen, easy to remember, most popular and arguably easiest for the brain to process then we find a certain doubling pattern in the grouping of the beat patterns behind it. The kinds of music this particular grouping pattern would apply to are pop music, folk, rock and also importantly what’s know as ‘common time’ classical music with the 4/4 time signature denoting 4 beats to a measure made of quarter notes. When we look at the overall structure of these kinds of music then usually there will a certain grouping of the beats in a doubling, powers of two binary structure. So 4 beats will be grouped into 8, then this will make longer agglomerations of 16 beats, which in turn form composite structures of 32 beats etc. These structures might form the verses and choruses of a pop song say, which are then linked up like modular building blocks. This gives us a very regular patterned rectangular or boxy structure to the way most music is constructed. See diagram below.

4lb Music-and-Binary-Bifurcation-height-1200.jpg

While there also exist a variety of funny time signatures and other less ordered musical arrangements, in the kinds of music which we most instantly appreciate there does seem to be this doubling structure behind it. After all, one or two music theorists over the years have said then any collection of arbitrary and even random series of sounds will if, listened to enough, start to sound like a sort of music to the ear. There may be some truth in this. It is certainly true that when sounds are grouped together in a certain sort of way, i.e. in our binary grouping structure, then it can immediate sound like music and we are able to process and also remember it with ease. Sometimes we have that feeling of, ‘not being able to get that tune out of my head’. And sometimes we will hear some popular song or melody just once and have almost perfect or at least very good recall of it afterwards. It would make perfect sense that this was happening because the music was structured in such a way, as to make it as easy as possible for the brain to process. And if, as we believe, the underlying structuring of the brains spatial and temporal representations are inherently binary then those kinds of music which we would find the most accessible and easy to process would be exactly those kinds of music which follow an underlying binary doubling structuring pattern. And we know that this is indeed the case.

We can also apply this sort of reasoning to simple nursery rhymes for children, limericks and some common structures used in poetry. Again there’s a certain meter and patterning of time which again fits into the same sort of organization as the popular sorts of music described earlier. And of course song lyrics are words set to music and also have this same basic accessibility even when read as poetry without the music behind it.

When we further consider the nature of language itself then we discover more binary structure behind it. In fact all human languages as well as computer programming languages and even the language of logic, can be broken down and analyzed in terms of binary trees. This follows from the work of people like Noam Chomsky and a host of others. So in the diagrams below we see simple sentences structured as simple binary trees forming more complex ones which are also binary structured. We can take this process to ever increasing degrees of complexity to form extremely complex linguistic constructs, but still they will obey this binary structuring.

4la Chomsky-binary-1-Height-1200.jpg4lb Chomsky-binary-2-height-1200.jpg

This binary view of language, be it human language or computer code, is very interesting especially when we relate it to the preceding discussing of spatial and temporal representation, which we have shown to both have an inherently binary structure underlying it. Furthermore we demonstrated this binary order in all the kinds of spatial mapping, i.e. egocentric, allocentric and topographic; and also showed how this binary structuring can be seen in many temporal scales, from some various millisecond ranges, right up to the time periods spanned by sections of music. This spatial and temporal aspect of what it is our brains and minds process is sometimes referred to as the ‘sub-symbolic’ level, by artificial intelligence researchers and cognitive scientists. And of course language processing would make up the corresponding ‘symbolic’ level. What all this means is that we have then a single unifying ‘language’ or formalism for describing both the ‘symbolic’ and ‘subsymbolic’ levels. As we will demonstrate later on, this allows us to fully explain how the two levels inter-operate and also to show that they really exist on the same symmetric, self-similar and recursive continuum. So that the spatial, temporal subsymbolic and symbolic and really just manifestations of a deeper underlying symmetry or invariant factor.

Having a common conceptual language to think about the symbolic together with the spatial and temporal sub-symbolic allows us to better understand how these different aspects interact in our brains and minds. And obviously they do. For instance we symbolize, i.e. we describe with words and sentences, the complex spatial and temporal input we see with our eyes and hear with our ears. And vice-versa we may register a stream of words while reading from a book and from them reconstruct in our imagination sights, sounds and even complex social situations happening in specific circumstances or locations. So the spatial and temporal, i.e the so called sub-symbolic becomes symbolized and the symbolic becomes spatialized and temporalized.

Within the sub-symbolic there is also an important interchangeability between time and space that goes on in the way we process and perceive the world. A complex spatial scene is serially broken down in time by scanning our gaze repeated over the image over a certain extended time period in order to register all the salient details contained within it. It is only the simplest of images, a road sign say, that we are able to process in one shot or in very few sequential operations. And in our actions a complex task is carried out over several different physical locations. It is serialized and carried out one specific sub-task at a time. Also something which is so obvious we never think about it. When going from two spatial locations, i.e. from ‘a’ to ‘b’ as we say, it is never spontaneous but involves a journey that occurs over a certain length of time so that a spatial distance becomes expressed as a time period.

Going the other way the temporal is also spatialized. Things or sensory patterns that are spread out over time may be represented spatially. So music and spoken language which are phenomena occurring spread out over time, may be representing on a sheet of paper spatially as music notation or the written word. Sometimes it is said that a composer will ‘see’ the entire score of music in his or her head, and the construction of sentences is sometimes visualized in our minds as we formulate them. Also we represent time in terms of numbers, i.e. hours, minutes and seconds, this is obvious; but what is less well known is that in our minds we spatialize enumerations. Neuropsychologists have discovered a ‘number line’ by which we represent numbers spatially as if arranged in order along a line going from left to right in our minds. They discovered that this ‘number line’ was processed by exactly those same brain regions which handle physical spatial processing. So this is another way that time becomes space.

This interoperability and interchangeability between space and time, i.e. the parallel and the serial becomes very important when it comes to implementing the brain theory in software and eventually directly in hardware. These ideas in relation to the quest to create artificial intelligence will be discussed in a later chapter. The reconciling of the symbolic and subsymbolic which is known as the ‘symbol grounding problem’ in the field of artificial intelligence has not been solved satisfactorily. And a universal and general way to represent time is an important current issue in AI as is the issue of integrating time into existing hierarchical spatial representation schemes. A way of showing the total inter-relatedness of the symbolic, spatial and temporal would obviously be very useful towards these ends. The fact that this integration is also grounded in actual brain physiology and neuropsychological evidence is a bonus. Furthermore once we adopt this way of 'doing’ AI, the reverse engineering the brain approach, then it is also much easier to integrate new findings from the brain and mind sciences into our inventions.

The Binary Neural Substrate of the Brain

Thus far in our survey of the binary brain and mind, we have mainly considered quite high level functioning and emergent phenomena. So we have talked about various spatial and temporal representations. Also we has discussed language and brain waves. Now we show that our binary perspective extends all the way down to the underlying physical substrate of brain organization and physiology. The binary nature of the brain even extends to the very process by which brains come into being i.e. neurogenesis, which is a subset of the process by which our bodies come into being i.e. ontogenesis. This is because every cell that makes up our brains and our bodies, is created in the binary cell divisioning process called mitosis, whereby one cell becomes two, becomes four, becomes eight, then to sixteen, thirty two, sixty four etc. in powers of  two or doubling increments. This is what we shall discuss next because it can provide the means by which brains can contain so many inter-operating sub-components that are so exactly laid out and intricately interconnected in a very specific way to produce the detailed hardwiring of our brains. It is very reasonable to conjecture that the binary cell sub-divisioning process of mitosis may be the key to understanding not just how our brains come into being, but also how it comes to be so precisely organized.

 Mitosis.jpg

So we start life from being a fertilized egg. This singularity from which the human form begins, starts to recursively subdivide as we have already described. And from this process of mitosis, every cell in our body is produced. Along the way we assume a variety of intermediate forms. A few weeks into this process of ontogenesis starting from a fertilized egg, we become something like a flat disc already made of many millions of cells. Then this flatted form rolls up and folds up in intricate ways to start generating our body layouts and more complex morphological forms. See diagrams below.

4oa Human TriLaminar Disc.jpg4oc Human Neural Tube.jpg

Sometimes in order to conceptualize things better, physiologists imagine what it would be like if this complex folding of our initial flat disc like form didn’t occur and we stayed as a flat sheet. This is called a flat-map. So we can depict a flat map for our brains with all its diverse regions and sub-components. So in diagram below left we have a flat map of the cerebral cortex and in diagram below right we have a flat map of the hypothalamus. We could potentially specify flat maps for every region and all the structures of the brain.

4ogHuman Cortex Flat Map.jpg4og Hypothalamus Flat Map.jpg

The question is, how do the different cells in the demarcated regions of the flat map ‘know’ what to be? How do we come to be able to define all the many different regions in the first place? There are two answers to this question and both of them play a role in this process of specifying the layout and functioning of the cells contained in our bodies and brains. The two ways are known as intrinsic and extrinsic. An analogy will help us to understand these concepts more easily. We may ask how do we as people come to be the way we are. And the answer is that it is a combination of nature and nurture. i.e. our behaviour and the way we look is determined by our genetic endowment that we receive from our parents and also from the environment in which we develop and live our lives. The genetic component can be said to be intrinsic and the environmental influences can be called extrinsic. And so it is with the cells in our bodies including brain cells. They know what to be through extrinsic factors, i.e. their surrounding chemical environment and also intrinsic factors which means the cell lineage from which they are derived. As the process of cell division proceeds, then at certain points changes will occur in the DNA of the dividing cells and also what are known as epigenetic factors will also modify the cells. These genetic and epigenetic changes made to cells undergoing mitosis or cell division will be passed on to all future cells which derive from them. So each such modification will start a new lineage with all the future progeny cells containing the change. This will affect ‘intrinsically’ how these cells function and interact with other cells. So this combination of intrinsic and extrinsic influence, determines how cells act and what they are, much the same with people.

Extrinsic factors certainly do play an important role in the development and arrangement of our bodies and brains. This can be through the creation of chemical gradients across certain body regions which may provide relative spatial information to inform cell development. But when it comes to precisely specifying the extremely complex and intricate components and subcomponents of the brain, merely relying on chemical gradients and extrinsic factors to determine cell development becomes limited. The problem with chemical environments is that they diffuse, so if we are to use them for determining exact brain regions then the problem is how do we prevent all the chemical markers for all the different regions from diffusing across to other regions. And we’re still left with the problem of how to specify these myriad sub-regions in the first place. A much simpler solution would be to use intrinsic factors to determine cell functioning and also in order to exactly specify all the different regions of the brain. Because the process of cell division is binary then each new specification of lineage and genetic or epigenetic modification will be occurring in a binary diverging way. With each ‘lineage’ beginning at the branching of a binary tree and all future progeny belonging to this lineage may be represented as nodes of a binary tree corresponding to the mitosis binary cell divisioning process emanating from it. These sub-branchings may in turn contain more genetic and epigenetic modifications specifying sub-lineages and sub-sub-lineages and so on and so forth to create a binary map of all the cells in our bodies and brains. This binary tree of cell divisioning and genetic/epigenetic specification of lineage may be flattened out and represented as a 2-dimensional plane using a special 2-d fractal representation of a binary tree. The diagrams below illustrate this idea.

5b Grid-Tree-3d-view.jpg5ba TH Grid Binary Tree.JPG

A simple computer program helps us visualize this process of specifying cell lineages in order to specify different brain regions. It simply involves the creation of a 2-d flattened binary tree like the one in the diagram above. Some simple computer code then detects mouse clicks on any of the nodes of the binary tree depicted in the flattened tree diagram as T junctions. This selects that node. The program then translates this into the shading and marker slightly darker blue of all the enclosing boxes of the subnodes or progeny nodes below the selected node. So for instance by clicking on the very centre node which corresponds to the top node of the entire binary tree, then the entire grid is colored a slightly darker blue. If we do the same with any node then a griddy sub-region corresponding to the space containing all its progeny nodes will likewise be shaded a slightly darker shade of blue. If a picture can be worth a thousand words then a short video more so. This link to a short screen capture video shows the program action...

We can use this program and binary demarcation process to create a variety of patterns to arbitrary levels of depth and complexity. So the diagram below left is an example and immediately to the right of it is another example but created in such a way that it is symmetrical along the midline y-axis.

8nRandom infojel Mondrain map.jpg     8oinfojel brain.jpg

In the diagram below is the same diagram as above right but juxtaposed with some flat maps of the cerebral cortex and the hypothalamus. What this is meant to show graphically is the idea that we may specify a pattern of demarcations using our computer program that may potentially exactly correspond with the specification of all the different regions of real brains. And because we are proposing that real brains are specified in detail with exactly the same binary demarcation process then this is not merely an analogy but rather a demonstration of a direct correspondence between the workings of the computer program and the way that real brains are specified and formed. Of course there are complications to this picture, in that in real brain cells will migrate from one region to another but we are mainly interested in the specifying of detailed regional cortical maps and the myriad main sub-components of brain, not in the specification of every neuron or support cell in the brain. What would be the case in real brains would be a small set of cells which would play this precise regional specifying role acting as markers and demarcators. All the other cells would operate within the guidelines and signposts provided by this special subset of cells. This would be akin to the operation of hox-genes and the exact specifying of overall body plans in ontogenesis.

5dc Flat-Map-&-Digitized-Brain.jpg

So in this way with our computer program we have created a sort of ‘digitized’ brain which is completely specified in the language of binary trees. Through a sub-divisioning and demarcating of the different regions of real brains, myriad spatial contexts are created into which real neurons and support cells may be located. In the creation of our digitized brain map and computer likeness of a brain we are able to place digital neurons and digital spatial/temporal representations. This is where we discover a fantastic set of insights. Because we have already shown that the way the brain represents symbol, space and time; also has an inherent binary digital structure underlying it. All the various spatial maps, topographic maps and representations of temporal sequential information, together with our linguistic symbolic facilities also are inherently binary and digital in nature. Therefore this content of mind fits perfectly together with these contexts of brain, for they are expressed in the same binary language. What this means is that it is very straight forward to place within our digitized brain, all our digitized topographic maps, all our digitized representations of space and time and all our digital symbolic structures of language. Once we have the physical substrate of brain and the representational structures of mind expressed in the same underlying language then this opens up the possibility for us to conceptualize brain/mind and all the things contained within it, i.e. our thoughts, memories, skills together with all the subcomponents of perception and action, as a single integrated whole and single all encompassing structure. We’ll discuss this much more later on.

We’re starting to see a gradual blurring and intersection between the worlds of neuroscience and neuropsychology on the one hand, and the world of computer science on the other. Perhaps it can seem a little odd, the juxtaposition of curvy rounded organic flat map structures with our griddy computer generated likeness of a brain map. However very recent research seems to have demonstrated at least in the wiring of the brain, a systematic grid like arrangement governing how brains are interconnected. Through new very high resolution brain scanning technology and some complex mathematical analysis, it was discovered as recently as 2012, that the nerve fibres connecting up the different regions and subregions of the cerebral cortex are routed in an almost perfectly grid structured way, much like the square road layout of American cities. So in our brains and brains of monkeys also studied, the fibre tracts connecting the cerebral cortex can go across and up but never diagonally. Therefore the fibres may run parallel to each like computer ribbon cables or else intersect only at perfect 90 degree right angles. See diagram below of an actual scan of this fibre arrangement. The researchers found that this pattern holds true at all scales analyzed from an overall whole brain scale to the smaller various levels of cerebral sub-patches. Furthermore this griddy arrangement also seems to hold true for many subcortical structures and even the spinal cord. This griddy wiring pattern found in reals brains would be a perfect fit for connecting up the right angled orthogonally organized structures of our digitized brain.

5dd large - Copy.jpg

We may add to our current discussion of the binary brain substrate and griddy nerve fibre wiring patterns, the fact that there is also a ubiquitous pattern to how nerve fibres branch and which is always binary. The branching of the axons or nerve fibres which project output signals forwards from neurons, always branch in a bifurcating binary manner, never in trifurcations, quad-furcations or quint-furcations. And the same for every dendrite branching backwards from a neuron making up the complex dendritic ‘arbor’ or tree-like profusion collecting signals from other neurons to relay to the cell body. Essentially all the axonal and dendritic ‘trees’ existing in our brains actually are binary trees. When we consider the signals that travel along axons, i.e. action potentials, then this too can be considered as essentially binary or digital in nature that is on or off. And the release of neurotransmitters at the end of an axon relaying information to the dendrite of another neuron is quantized. This rounds off our digital, binary, quantized, boxy and griddy picture of physical brain structure and all the interconnections between all its various sub-structures.

Later on we show how our boxy binary digitized brain is an even better fit for modelling real brains than superficial inspection would suggest. Not only does our digitized brain and real brains have in their formation an underlying binary digital code for the exact specification of their respective sub-components. Furthermore, In the same way that there is an orthogonal or right angled boxy structure to our digital brain, likewise there is an orthogonal organizing principle to be found in the neocortex itself to go along with the griddy wiring underlying it. This paves the way for a complete digitization of real brains through a process whereby our theoretical computer generated binary brain is able to map systematically to all the relevant information process components of real brain. This opens up a whole new way to do what is know as ‘Whole Brain Emulation’ or WBE for short. It really takes the Artificial Intelligence theorist Ray Kurzweil’s idea of abstracting away all the non essential details for brain emulation to the absolute maximum. Things don’t get any more abstract or minimal than binary trees and binary combinatorial spaces in computer science. Whole brain emulation using this approach will produce many orders of magnitude improvements in computational efficiency and performance advantage over projects such as the Waterloo University Spaun project and Henry Markram’s whole brain simulation plans. It also has the advantage of being based on a comprehensive brain theory at the outset. When we add fractal time and dynamic recursive processes to our fractal digitized brain then we will be able to show how it can be made to come to life. Amazingly in the operation of this digitized brain will be the subsumption of many of the best ideas and algorithms in artificial intelligence and computer science which we’ll explain in some final sections. What we think is about to happen is a complete unification of neuroscience and psychology together with some of the most important ideas in computer science and artificial intelligence, into a single overarching conception.

But for now we will continue this section on the binary neural substrate of the brain by examining how our binary tree way of looking at time and temporal representation may be implemented by actual neural physiological mechanism. We’ve covered the physiology of the binary structural spatial. Now we consider how binary time may also be given its physiological basis.

The Neurophysiological Basis of Binary Time

Earlier we examined some time dependent phenomena from what may be described as a higher level neuropsychological level. That is we talked about some of the properties of surface brain waves, music and language in order to demonstrate a common binary doubling pattern underlying them all. What we do now is to show how and why this binary patterning comes about. We seek to explain the neurophysiological basis for time representation and time processing.

Time is such an important dimension in our lives and in the operation of our minds. Without it nothing much would happen. It is central, fundamental and all pervading and we would expect that it is implemented by some aspect of our brain architecture which is likewise all pervading. The perfect candidate for this role would be the recurrent loops found throughout the brain, in every structure and at every scale. Cortical columns feedback upon themselves and the individual layers within columns do likewise. The entire brain contains a massive recurrent loop projecting back upon itself and importantly the cortical areas of the prefrontal cortex along with some special posterior areas form recurrent closed loops with the cerebellum and striatum. Here we have a lot of empirical evidence to suggest that these two important structures, i.e. the cerebellum and striatum, are heavily involved in the temporal processing and the representation of ordered sequential information. I believe we can perfectly extrapolate this time handling property of these cerebellar and striatal closed loops to all the other kinds of recurrent loops found in all the other areas of the brain and at all scales.

But how would a recurrent looping back arrangement of neural connectivity enable us to represent, recognize and reconstruct temporal information? The answer is that recurrent loops allows us to represent two consecutive moments in time in the simplest way imaginable, that is as the two diverging branches of a binary tree. This is because one branch can represent ‘past’ and the other branch can represent ‘future’. Taken together these two branches have represented a demarcation in time. These two branches may further divide to produce four branches in total which may represent ‘distant past’, ‘near past’, near future’ and ‘distant future’. This process can be recursive iterated to produce representations of time to any resolution required. But how does a recurrent loop come to represent a temporal binary tree of the sort we have just described? This comes about due to two reasons. They are firstly the fact which we explained earlier, that time is discretized into separate compartments by the action of brain waves. Secondly there is a delay in the time it takes for the signal coming from any brain component travelling along one of these recurrent paths to loop back upon itself. As long as this delayed looping back signal is integrated with the set of signals coming in at the next time compartment, then this allows us to represent the conjugation or joining of the information relayed by the current ‘fresh’ signal together with the information carried by the recurrent signal which relates to the previous time compartment. So in a very simple manner we may register the succession of two time steps i.e.( t ) & ( t + 1 ) ,which we might also refer to as past and future and make correspond with the two nodes of a binary branching. We can iterate this process to produce tree structures encoding more than 2 time steps. See diagram below. And if we can register temporal sequences we can also reconstruct them to form temporal combinatorial codes. The orange arrows in diagram below right, show this reconstructing of the next step in the sequence based on the previous registration of a particular sequence in a particular order.

4ma  Temporal-loops-1.jpg

The finest temporal resolution that this proposed physiological mechanism will be operating at would be ~40 htz or the gamma range. The gamma wave is ubiquitous all over the brain. This is due to its arising from the properties of the gamma-aminobutyric acid A receptor subtype which has a refractory period of ~25ms or a fortieth of a second. Gamma phase locking has been proposed as a mechanism by which representations spread out all over the brain are coordinated and synchronized with each other. This gamma phase locking across distant different regions of the brain has been observed. However it is now thought that the lower frequency brain waves are also involved in the synchronizing of the information processing in different regions of the brain. This brain wave phase locking and in particular with respect to gamma waves, has even been proposed as a candidate for the neural correlate of consciousness. What is also interesting for our discussion of temporal looping structures is the expression of gamma waves in the cerebellum and striatum; and the empirical finding that gamma phase locking occurs across these structures as well, together with the cerebral cortex.

Concerning the modification of the synaptic connections involved in these looping time structures, it is significant the time intervals involved in the established phenomenon of spike time dependent plasticity STDP, fits into our gamma compartmentalized and binary conjugated picture of things. STDP describes the phenomenon where two correlating neural signals will only cause a change in synapse strength if they both arrive within a critical time window. STDP is most strongly elicited within time difference intervals between the two signals of 25ms or so. At the ~50ms mark, which would correspond with two non adjacent time compartments more than a single time slot apart, then the strength of STDP falls to zero. Though 40 htz gamma would be nested in the lower frequencies i.e. 20 htz beta, 10 htz alpha and 5 htz theta etc; it would be at this 25 ms time seam that the adjacent temporal building blocks of behaviour and mind will be welded together.

The idea of our brains working at an underlying basic 40 htz gamma wave resolution may be related to the fact that it is around the 20 htz mark that repetitive beats starts to become tone. At or below around 20 beats a second then we are able to discern separated beat events but above this then we start to only register a low frequency tone with our ears. The lowest tonal range that the cochlear in our ears is able to start detecting is also around 20 htz. If 40 htz is the processing resolution of our brains then it would make sense that we would be able to detect separate beats at 20 hertz or below. Because registering the beats as separate would involve detecting the beats together with the space between the beats. So at 40 beats per second it would be impossible for us to discern the separation so we would only register a constant unchanging signal with our 40 htz sampling of the data. This is where the lowest tonal range of our cochlear takes over to start registering the beats as tone. This 40 htz operating frequency of the brain idea may also be relevant for understanding our perception of video and film, and whether we perceive it as smooth or not. Traditionally film has operated at 24 frames a second and video around 40. If we made film less than 24 frames a second then it starts to be perceived as jerky. A complicating factor in making comparisons with the auditory facility and the processing of beats versus tone, is that our visual system has temporal resolution which is not as sharp as for hearing. It would be interesting to have full account in the future of the significance of the underlying 40 htz gamma wave with respect to video processing by our brains.

We are progressively putting together a general temporal representation scheme for the brain and mind based purely on binary trees. However so far, the approach outlined above will only give us what are known as unbalanced binary trees. See diagram below left. We would also like to be able to represent time with balanced temporal binary trees, i.e. see diagram below right.

9y1 Representing Time with Binary Trees2 - Copy.jpg4ca Representing Time with Binary Trees.jpg

We can solve this problem by spreading out the temporal representation over more than one or several spatially adjacent brain components. These separate components interact with their adjacent neighbours and would be arranged in a ordered lateral hierarchy. These brain components might be adjacent cortical areas or patches but they may also be smaller lower level structures. In the diagrams below we refer to these adjacent spatial brain components as patches but the same principles which the diagrams depict may be generalized to other sorts of laterally ordered adjacent structures. So we need to explain the diagrams below in more detail. In the diagram below left we have three laterally ordered adjacent patches. The binary branchings depicted below each patch represent simple two step time representations, i.e. ‘a to b’ below patch 1 would be a serial representation contained in it, which registers state ‘a’ transitions over time to state ‘b’. And so on for all the other lettered binary branchings. The dashed orange arrows represents a temporal nesting relationship between the different binary branchings across the different adjacent patches. So a single time state in patch 1 would correspond to two time states in patch 2. i.e. state ‘a’ in patch 1 expands into state ‘c’ and state ‘d’ in patch two as indicated by the hatched arrow coming from ‘a’. What’s really important is that the different patches do their time transitions at different frequencies with patch 1 being the lowest frequency and at the top of the hierarchy and patch 3 being at the highest frequency and lowest down in the hierarchy. Also significant is that the differences in frequency from one level to the next is in octaves i.e. a doubling or halving in frequency. What this means is that we are able iterate through the lateral interactions of the 3 adjacent patches and the 2 step temporal transitions contained within them, to represent a balance binary tree.  So the diagram below right would representing 8 successive temporal transitions at the highest frequency i.e. ‘g’, ‘h’, ‘i’, ‘j’, ‘k’, ‘l’, ‘m’, ‘n’ etc and which would be happening in patch 3. With the transitions in patch 2 i.e. ‘c’, ‘d’, ‘e’, ‘f’, occurring at half the frequency of patch 3. Then in turn patch 1 i.e. ‘a’, ‘b’, working at the half the frequency of patch 2 and a quarter of the frequency of patch 3. The two diagrams below are in a sense equivalent. The one to left emphasizes the separate two step transitions represented by the 3 patches, whereas the one to the right shows more clearly the implicit spatial-temporal structure that emerges from the operation and interaction of the 3 patches over time.

9y2Temporal-loops-2.jpg9y3Temporal-loops-3.jpg

Apart from laterally interacting adjacent patches of neocortex, judging from recent findings, this way of producing balanced temporal binary trees may also take place within a cortical column and between adjacent layers in it. Within most of the layers in a column we will find recurrent connections within a layer, i.e. layers projecting to themselves. And we also have lateral interaction between adjacent layers. See diagram below depicting recurrent connections with layers of mouse primary sensory cortex.

What has also been fairly recently discovered is that different layers within a cortical column will express different operating frequencies. This is a new area with lots of new data and recent findings are still conflicting but it seems we do have gamma and beta waves expressed separated out in different columns. This would provide at least rudimentary balanced binary temporal tree handling potential within a column. Future research may add more clarity and give further support for the ability of cortical columns to represent time in this way. We certainly know that individual cortical columns are able to process temporal information. For instance in the visual cortex columns we find neurons which recognize a moving bar of light or spatial frequency grating projected onto its receptive fields. And in the primary auditory cortex, in columns there we find neurons which respond to changes in pitch over time. We suggest that it is the recurrent loops found there operating within and between the various layers of cortical columns which is the physiological mechanism for implementing this facility. It would do this using a combination of unbalanced and balanced binary temporal trees.

Incorporating Fractal Binary Time into our Fractal Binary Digitized Brain

And so we have provided an overview of how the underlying architectural characteristics and physiology of our brains can enable it to represent time using binary hierarchical structures. It fits together with earlier sections which are relevant to our understanding of binary time. For instance in our initial broad overview of brain anatomy where we demonstrated the ubiquitousness of recurrent looping back nerve fibre arrangements. We find this looping arrangement all over the brain and at every scale, from the level of neurons right up to the level of the whole brain itself, and all levels in between. Also earlier we described binary doubling in the frequency ranges of the major named brain waves i.e. theta, alpha, beta, gamma. And in most types of popular music and in all human languages we found binary structuring. From a neuropsychological perspective we found binary bifurcating and doubling underlying structure in all the various types of spatial mapping i.e. egocentric, allocentric and topographic. This then fitted together with a completely binary decomposition of how brains come into being through binary cell division and how different brain regions are specified and how brains are wired up. This gave us the concept of a digitized brain. We described how these binary neuropsychological structures of spatial mapping, perception, music and language may be fitted neatly into our digitized brain because they were expressed in the same underlying language, i.e. that of binary trees and binary combinatorial codes. It is the most natural next step to add into our accumulating unified picture of brain and mind, the physiological means by which time is represented. So we simply map our explanations of the underlying mechanisms behind binary temporal representations straight into our digitized brain. We discover a seamless fitting in of these ideas due once again to the fact that they are expressed in the same underlying binary discretized language. So therefore to our digitized brain we add digitized recurrent time loops at all scales and all sub-regions to represent binary digitized time in order to animate artificial digitized minds. This is another way that we continue to reduce all the various aspects of brain and mind to our theoretical binary vision. Once we incorporate and map all the recurrent looping structure found in real brains into our theoretical digitized artificial brain then we fully give it the ability to represent time in the same way that real brains do. And just as binary structure underlies our neuropsychological temporal representations of language, music and movement etc. so it will be the case that our artificial minds will represent time in the same way.

A single all encompassing hierarchical classification structure for brain and mind

We’ve already come a long way. We have surveyed a large array of neuro-psychological, physiological and anatomical data. Starting from finding simple basic repeating patterns or symmetries in the brain, i.e. the stereotypical repeating modular design of cortical columns and cerebellar complexes etc; and the overall tree like repeating symmetry with a pattern of inflow like the roots of the tree, a pattern of outflow like the branches and leaves together with a recurrent looping back arrangement (not found in everyday trees). We then moved onto showing the underlying binary structure behind our spatial, temporal and symbolic representations. We continued our binary reduction to include the structures and wiring patterns of the brain, also explaining the physiological basis of representing time. We no move to integrate all of this into a single conception. From simple symmetries, to the single unifying language of binary trees and binary combinatorial spaces we would like to bring all of this together into a single unifying structure. We know that this structure must exist, because all the myriad aspects of our minds and the physical substrate of our brains, operate as an integrated oneness and single whole. The questions is how? and also what is the structure of this integration. We will demonstrate that the integrated entirety of our brains and minds exist as an all encompassing unified hierarchy and that naturally this will be a single binary hierarchy expressed in the language of binary trees.

An analogy will explain better what we are trying to achieve. In the age of information our lives so depend on and are enhanced by the use of computers. And this involves the creation and consumption of a massive and diverse range of data stored as files, from photos, movies, songs, letters to database data, invoices, webpages and computer program files. These files exist in a plethora of different formats i.e. songs in mp3 or AAC format, videos in mp4 or H264 format and word processing documents etc. all with their own way of representing things. The diversity and complexity of all these representation schemes is mind boggling. Also all the files we use, create and consume are scattered all over the place, on our hard drives, backup devices, on the cloud, in cyberspace servers, on our smart phones and memory keys. But imagine if all of these myriad thousands or even millions of files could be placed in a single classification structure and all of them accessible from this integrated collector of all the computer files in our lives, past, present and future. As if every computer file we’ve ever worked with or used and will ever do so in the future was stored on a single gigantic hard drive with a single directory structure. Also imagine if all the different files, all the video, sound, text, computer code and data files were all expressed in a common universal format. One language to capture all of them.

Even furthermore, imagine that this universal format for content, i.e. all these individual files was also the same as the format for context. We need to explain this further. There are various languages and structures for locating and placing computer files and content, i.e. the directory structure of operating systems by which files on our hard drives are located and accessed. And then there are the URLs (Universal Resource Locators) and web addresses by which all the content of the world wide web is addressed. So imagine that we also had a universal single language that could span all these different domains, from the whole internet to that of individual computers. And then imagine that this language of context was exactly the same as the language of content used to represent all the files accessible by the internet and on each computer in the world. This is what I believe is happening in the brain. The language for context is the same as the language for content. So that context and content existed in a single continuum and unifying conception. So the language for space is same as that for time, past and future i.e. context is the same of the language for describing our thoughts, memories, actions and perceptions, i.e. content. And the language for describing composites is the same as that for describing component. This is the language of binary trees and binary combinatorial spaces. This way of looking at things allows us to conceptualize the entire brain and all the structures of mind as a single unity and all encompassing hierarchy. This is what we do next and we’ll be introducing a few new concepts along the way and also a few innovations that enable this unification to happen.

In order to explain our all encompassing unifying conception of brain and mind we will first revisit our binary digitized brain in which we were able to map every other other binary concept so far discussed, which includes all of our discussions of relating to neuropsychology, neurophysiology and anatomy. So below are two diagrams which we’ve also introduced in earlier sections. The one on the left representing our flat grid digitized brain and the one on the right being a drawing of an actual flattened out cerebral cortex of a macaque monkey. Here the different regions are numbered and the areas involved in visual processing are colored in.

5db infojel brain.jpg2da Cortical Map simplified.jpg

 On superficial inspection the rounded borders between all the different cortical regions of the monkey brain see far removed from the boxy components of our digitized brain. In this there seems little resemblance. The monkey brain parcellation of regions doesn’t look much the chequerboard layout of our digital brain. But underlying the arrangement of cortical patches in the monkey brain is also an underlying boxy arrangement. This is because there is a special meaning to the traversals along adjacent cortical patches in certain special direction of traversal, but also in the orthogonal or right angle direction. As we step between adjacent patches of cortex along these special directions then we find that the successive patches form a lateral chain of interacting processing units. But if go in the orthogonal direction then then patches also form a chain but the meaning of the processing that chain is different. However these processing chains of special meaning are not formed in the diagonal direction, though diagonally adjacent patches may share some interconnection. So in the diagrams below we have some examples of these special directions traversing through various areas of cerebral cortex. In the diagram below left, we have a view into the midline inner side of the brain and a thick curved line and smaller lines orthogonal to it. This curvy line comes about due to the curvy folded nature of the brain. In fact if we match up the region numbers in this diagram of the human, i.e. 25, 32 and 24, to the white region at the very top of the flattened macaque monkey map, then we see that here the regions are arranged more in a straight line. In the diagram bottom right, we’ve marked in some of these special directions in colored lines which again are orthogonal or parallel to each other but never diagonal. We can do this sort of orthogonal griddy overlay onto every part of the cortex. It is as if there is an underlying original chequerboard which was involved in the initial formation of the brain, but in the course of brain development, some of the squares were removed, some we greatly enlarged, some shrunken down and all of it distorted, rounded off and stretched. But still the orthogonal relationships between the different patches of cortex remain.

5ld Medial PFC.JPGJust side view.jpg

But what then is this ‘special meaning’ as we traverse these laterally ordered patches of cerebral cortex, in these special directions or in directions orthogonal to it. What is the relationship between the adjacent patches are we traverse across them. The answer is that these adjacent patches of cortex will be chained together into processing hierarchies. The cortical patches at one end of the chain belonging to the top of these hierarchies and those on the opposite end belonging to the bottom, with middle patches at intermediate levels of the hierarchy. So for instance the the bottom red line in the diagram above right traverses the speech hierarchy. The very bottom contains regions of areas 6 and 4, which are involved in the coordination of physical movements involved in speech articulation. Higher up the hierarchy we have regions, 44, 45a & 45b, involved in word and sentence production respectively, and even higher up, we have regions like 47/12, involved in semantics. And we also have hierarchies for all various sorts of movement, touch, hearing all the other things that brains handle. The most complex hierarchies are those involved in visual processing. So that we have sensory hierarchies and motor hierarchies. We also have cognitive hierarchies and even our emotion centres i.e. the hypothalamus, amygdala, orbital frontal cortex and subgenual anterior cingulate cortex can be conceptualized as a hierarchy. And these brain hierarchies are often physically expressed over a succession of cortical areas laterally adjacent to each other in a chain and a traversal over them reflect or special direction lines which we may draw over the cortex.

In order to better understand these brain hierarchies and see how they fit into the bigger picture we need to introduce some new ideas. We also need to explicitly show this hierarchical thinking fits in with our binary tree and binary combinatorial picture of brain and mind we have been steadily putting together. And we do this show that there a hierarchical and binary overall organizing principle in the brain by which all its components, sub-components and all its various spatial, temporal and symbolic representations contained within it are ordered. So we’ll proceed to explicit define some basic concepts in relation to the properties of binary trees.

The Concepts of Top-Down and Bottom-Up

As with any hierarchies, the ones contained in the lateral relationships between adjacent cortical patches in the brain have a top end and a bottom end. The top may be likened to the apex of a pyramid and the bottom end to the pyramid’s base. The top of the hierarchy may also be seen to correspond with the root node of a binary tree with the diverging nodes branching from it forming the intermediate levels. The terminal ‘leaf’ nodes of binary trees may then be considered at the bottom of the hierarchy. If we move up and down this binary tree then naturally the direction going from the single root node to the many end nodes would be described as ‘Top-Down’. Then conversely a traversal in the opposite direction would be called ‘Bottom-Up’. /* See diagram below (make diagram */.

The Concepts of Context and Containment.

We may continue to attach meanings and define terms relating to the properties of binary trees. Two important and related concepts which may be mapped to our binary tree perspective would be that of context and containment. This is quite intuitive. Any node of a binary tree can be said to define a context. It can be imagined as a conceptual box into which we may place things, which in our little  binary tree universe would be other binary trees. So these contexts essential ‘contain’ all the subnodes that derive from our contextual reference tree node, i.e. all nodes branching from it. Vice versa all nodes can be said to be ‘contained’ in the root node from which they derive. /* See diagram below */ So in this way we are able to formally define what we mean by context and containment in terms of the relationships between the nodes of binary trees.

Top-Bottom-&-binary-trees-3d-view.jpg

We may also closely relate the concepts of top-down and bottom-up to that of context and containment. And once again we do this by looking at them in terms of binary tree relationships. It is simply that the top parent binary tree node is the overarching context and container. So as we go top to bottom then the nodes branching from the parent are contained by it. And vice versa any node more to the bottom of the tree pyramid is contained within the context of all the parent nodes that sit above it. Because it may be the case that our binary tree will generally have multiple levels of branching to create a multiple step hierarchy, then we will have a succession of nested contexts each containing the next russian doll style. And any node may in turn, going the other way, be contained in a surrounding onion skin of multiple nested contexts.

/* need to show that binary trees then describe physical nesting in the brain */

The idea of context is a very important one as too are those of top-down and bottom-up. We believe that in the structuring of the brain and the operation of the mind, they are all pervasive and fundamental. Also they are closely tied in with the even more fundamental ideas of self-similarity and recursivity, and also by the same token symmetry. And these are the basic concepts on which this theory of brain and mind are grounded. What we are trying to demonstrate here is that all the spatial and temporal structures of brain and mind which we have so far discussed, which includes practically all of it, can be conceptualize as a single top-down hierarchy and unifying all encompassing classification structure of of nested contexts But we need to go deeper in our understanding of these concepts and show that the concepts of top-down, bottom-up, context and containment also apply not just describing physically nested brain structures but also in the lateral relationships between those structures, and even to the all the temporal relationships of brain and mind. So next we digress into a discussion of the concepts of spatial and combinatorial coding in order that we may show this extended meaning to the ideas of top-down and context etc.

The Concept of Spatial Coding

We can explain the concept of spatial coding by continuing with our tour of binary trees. In the simple 4 node binary tree depicted in the diagram below, the four nodes may be considered as four different demarcated spaces or contexts. And each of these contexts may be directly mapped to something we’d like to represent. So the four nodes may each directly correspond to one of the four members of the rock band the Beatles, i.e. John, Paul, George, Ringo. Alternatively each of the 4 nodes may be used to represent numbers. So the first node might represent ‘0’, the second ‘1’, the third ‘2’ etc. as shown in the diagram. This is spatial coding where we map each thing we would like to represent onto some location or object, in our examples we’re using the nodes of a simple binary tree. We might also use individual stones, separate knots on a piece of string, or sea shells. But this is rather limiting. What if we wanted to represent more things, i.e. more people and more numbers. A simple answer would be that we simply generate a bigger binary tree with more nodes, enough to represent all the things we want. Or gather enough stones or sea shells. In the case of binary trees we may potentially extend the process to infinity /* see diagram bottom righ*/  or at least to very large numbers but still this would be a clumsy inelegant method of representation; we would also run up against limitations to this way of doing things. In order to circumvent these constraints the solution would be to employ what is know as combinatorial coding. Which we’ll explain next.

4df Cell-Divisioning-Binary-Tree1.jpg4dg Cell-Divisioning-to-Infinityi.jpg

The Concept of Combinatorial Coding

At first the name of this idea may sound a little intimidating but it is something that we use everyday and which we are actually totally familiar with. The letters you’re reading and the numbers decimal numbers we use are examples of combinatorial codes. By arranging the letters of the alphabet in different ‘combinations’, including spaces and puncuation, then we are able to construct sentences and convey meaning. And by stringing together a set of numerals from 0 to 9, then we are able to represent numbers. These are all examples of combinatorial coding. We are especially interested in the simplest combinatorial code there is which binary combinatorial coding and which works in exactly the same way as letters of the alphabet and numerals except we only have two letters or numerals to play with which are ‘0’ and ‘1’, ‘off’ and ‘on’. So in the same way there exists a finite ‘space’of possible combinations of a certain length of letters or numerals, by stringing together a certain length of zeros and ones, we may represent a variety of binary combinations again existing in a finite ‘space’ of possibilities.

In the diagram below we graphically depict all the possible combinations that may be created using 4 binary digits (which is 16), and they are represented by the sideways branching tree expanding towards the right. Each branch of this ‘sideways’ tree corresponds to the doubling in the number of possibilities we may represent as we steadily increase the number of binary digits we use. Starting from 1 digit and progressing to using all 4. These 4 digits correspond to the 4 nodes of our original 4 branch binary tree, depicted bottom left with each node numbered in blue. And by place either a ‘0’ or a ‘1’ into each of these boxes then we are able to represent all 16 combinatorial possibilities, all of them listed to the far right of the diagram. We might want to call this lateral combinatorial coding in the sense that the binary digits and the 4 nodes of the original binary tree exist laterally next to one another. This is to distinguish it from another variation on this theme we are going to explore next which we’ll call temporal or time based binary combinatorial coding.

4dh Spatial-Combinatorial-Coding.jpg

We’ll continue our analysis with an explanation of Temporal Binary Combinatorial Coding. This also uses binary trees but with the exception that we are now using the two branches of any node to represent time, i.e. past or future, instead of merely left or right. This means we are really looking at a single node or context of a binary tree and representing different states this node can exist in over a set of discrete time intervals. And we are representing these snapshots in time using a binary tree. For ease of explanation we consider a simple case of 4 temporal transitions using a four node temporal binary tree. Also we’ll only consider that our node over which time is being represented can be in one of two states, i.e. 0 or 1. See diagram below left side. This means we can carry out exactly the same line of reasoning as we used earlier in consider how 4 separate nodes ‘laterally’ placed side by side could represent a combinatorial code of 16 possibilities. Only now, instead of considering a lateral traversal over 4 distinct binary tree nodes, we are looking at a 4 time step temporal traversal over the same node. This means that in exact the same way 4 separate binary nodes can represent 16 combinations, a single node can likewise also represent these 16 combinations if it is allowed to be in 4 binary states, i.e. 0 or 1, over 4 time consecutive time slots. So the two diagrams depicting ‘Lateral’ and ‘Temporal’ Combinatorial coding are essentially exactly the same, except the spatial lateral dimension has been replaced by a sequential temporal one.

4di Temporal-Combinatorial-Coding.jpg

Furthermore we can combine our concepts of Lateral and Temporal Combinatorial coding just discussed, and make them work together. So continuing with our original basic 4 node binary tree, first will allow those four nodes to represent a four digit binary combinatorial code of 16 possibilities. Now we add time. Instead of considering time for a single node representing a single binary digit, instead we combine the time dimension, over all four nodes. And if we consider 4 temporal transitions over these 4 spatial nodes, as in our original explanation of temporal combinatorial coding, then instead of 16 temporal possibilities, we end up with 65536 spatial/temporal binary combinatorial possibilities. /* See diagram below */

4dj Combining-Spatial-with-Temporal-Code.jpg

So from a simple spatial coding scheme with our simple 4 node binary tree to using combinatorial coding, we’ve gone from being able to represent 4 things to being able to represent over 65 thousand. And we do this while still basing our much augmented representation scheme on our original 4 node simple binary tree. What we have done is to allow these four nodes to laterally connect up and also added temporal loops to chain our sequential states of our 4 node tree in time. But this is what we find in the brain, i.e. its components laterally connect up with one another, and also as describe earlier, these can be represented over a succession of different states over time using binary trees. So we can combine this these ideas of spatial versus lateral and temporal combinatorial coding, into our evolving picture of the brain and mind. In fact we have a perfect fitting in of these concepts into our ‘digitized brain’, which in turn maps onto a weallth of anatomical, neurophysiological and neuropsychological data as earlier discussed. It is very easy to transplant our simple 4 node analysis to our digitized brain which may contain billions of such nodes. We may also now use what we have learned about combinatorial coding using binary trees, to more fully explain the meaning of top-down, bottom-up, context and containment.

The concepts of Context and Top-Down in relation to Binary Combinatorial Codes

We now return to our discussion of the ideas of context and top-down and extend them to show how they can be applied to understanding the laterally spatial relationships between brain regions as well as the time dimension applied to these regions and the representations of mind. Now that we have an understanding of what we described as lateral and temporal combinatorial codes in terms of our binary tree language, we seek to show that the concepts of top-down and context also apply to them. How does this work?

If we start again with our simple 4 node ‘spatial coding’ binary tree then the concepts of top-down and context apply in exactly the same way as already explained. /* See diagram make diagram */ The concepts of top-down and context would also apply to the lateral combinatorial codes created from these 4 nodes if we ordered them. So for instance we may say node 1 is the top and node 4 is the bottom, and their given number would exactly reflect the order they were in the hierarchy. Given this ordering of the nodes there would emerge a sideways top-down bottom-up structure which would directly correspond to the 16 way branching binary tree representing all the combinatorial codes the original 4 nodes may represent. And the concepts of context and containment would be captured by this emergent binary tree.

/* diagram here */

An analogy to better explain this would be that of computer operating system directory structures. These may either be specified as a series of names of folders and sub-folders and sub-sub-folders, else they may be graphically depicted as a set of nested folders. So folders will ‘contain’ folders and act as contexts, and it makes sense to talk about a top folder which contains within it the nested ones (bottom in our scheme of things). /* see diagram below */

5nk  Computer-Directories - Copy.jpg

We may also apply this line of reasoning to temporal combinatorial codes. Here again we order each time frame involved in our temporal code, and this would naturally corresponded with the ordering in time. A succession of discrete events happening over time are inherently ordered. But in relation to our binary tree, top-down and contextual way of looking at things we need to conceptualize the first time event in a sequence as that which corresponds to the top or our time hierarchy, and the last event as corresponding to the bottom. In this way the past would ‘contain’ the future and any future state would be ‘contained’ in the sequence of past events. This makes intuitive sense because it is easy to think about where we are now as being in the context of what we just done in the immediate past. For instance walking around a city we naturally think about our current location in relation to the succession of directions we followed to get there. If we made a different turn at a certain time then we may be in a completely different context. Also in life we sometimes think that the ‘place’ we are in, in terms of the context of what happened in the past. And so it is with our simple temporal combinatorial code, binary tree scheme but in a more abstract, explicitly defined and formalised way. /* See diagram bottom left make diagram */ Furthermore we may apply in exactly the way this top-down, bottom-up contextual way of looking at things to our hybrid spatial and temporal binary codes. /* See diagram bottom right make diagram */

And so we have extended our initial conception of what is meant by top-down and bottom-up, context and containment, i.e. the simple spatially nested kind, to include the lateral and temporal kind. Effectively this comes about by laterally conjoining our initial spatial nodes and also chaining them in time. This creates lateral and temporal combinatorial codes, but it also creates emergent logical binary tree structures over which we may also apply the concepts of top-down, bottom-up, context and containment. Therefore there is a close relationship between between these concepts. on the one hand, and on the other the intrinsic properties binary trees and binary combinatorial spaces. Our binary language is able to capture these concepts of top-down, context etc. and vice versa these concepts allow us to see binary trees in a whole new way. This perspective is most important for our theory of brain and mind which seeks to reduce all relevant aspects of the puzzle to the language of binary trees and binary combinatorial spaces which earlier sections have dealt with.

So now that we’ve explicitly defined these important concepts we can now use them to understand our binary brains and binary minds. So we leave this quite abstract discussion of binary trees and binary combinatorial codes, contexts and the meaning of top-down etc. to return to looking at the brain.

The Ubiquitousness and Importance of Top-Down and Bottom-Up relationships in the Brain

Here we will be examining the brains physical, lateral and temporal relationships to see how they can be understood in terms of the concepts of top-down, bottom-up, context and containment. This is with the aim of expressing the entire brain as an integrated top-down hierarchy of nested contexts containing all the brains sub-regions and all the things represented by our minds. In turn these representations of mind will be continuous with and exist as nested top-down sub-hierarchies. So that brain and mind will come to be seen as a single all encompassing representational unity. This is the sought after ‘symmetry bond’ between brain and mind. We will show that the ‘secret symmetry’ is secret no more.

So from our discussion of the concepts of top-down, bottom-up, context and containment in relation to binary spatial, lateral and temporal combinatorial codes, we discovered there are 3 varieties of top-down and context. The first involves physically nested contexts, with spatially distinct components nested in enclosing spatial contexts. The second emerges from the lateral relationships between these spatial components, and works in the same way as the nested folders and logical contexts used by computer operating systems. The third involves the contexts and top-down relationships emerging from temporal relationships and a succession of combinatorial codes expressed in time.

All three of these varieties of the expression of the concepts of top-down and context, have their counterparts in the brain and also in the structures of mind. The most obvious is the physical russian doll like nesting of components in the brain, i.e. neurons contained in neocortical cortical columns, which are contained in macro columns, which are contained in the cortical patches and which in turn are all contained in the entire neocortex. So here the entire neocortex would be the top and overall context and container. And as we go down this physical nesting structure then we would be considering the intermediate nested levels, all the way down to neurons and even further to sub-components of neurons. Here we have physical contexts and components physically contained or nested within larger structures.

The second expression of top-down and context would be what most neuroscientists think about when they use the expression ‘top-down’. That is when it emerges from the brains lateral hierarchical relationships. As we described in an earlier section all over the brain we discover these lateral hierarchical relationships between cortical patches and sub-patches. So we have all the various sensory and motor hierarchies. The ‘bottom’ of these hierarchies corresponding to primary sensory and motor cortex, connected most directly to the senses and muscle groups. And as we ascend these hierarchies then we have the secondary, and then tertiary sensory and motor areas etc.

An important feature of these lateral cortical brain hierarchies is in the very specific laminar projection patterns of the connections between their adjacent levels. There is very a specific top-down pattern and a very specific bottom-up one, for both the sensory and motor side. These projections will project from very specific layers of the neocortex, and terminate likewise only in certain layers. So for both the sensory and motor hierarchies, the top-down connections always begin from the deep layer 5 and project to superficial layer 1. In the opposite direction, the bottom up projections always start from layers 2 or 3 and terminate in layer 4.

The diagrams below depict these laminar specific projections. The blue arrows represent the top-down projection pattern, and the green arrows represent the bottom-up pattern for both the sensory and motor side. The relative thickness of the arrows is meant to show the general flow of information processing, not the strength or numbers of fibres in the connections. So there is a flow of information from our senses to the brain areas which recognize and categorize those sensations in a bottom-up direction. Whereas on the motor side there is a flow of information from abstract plans and intentions to the complex spatial temporal coordination of movements, in a top-down direction. However even with the sensory side there is a lot of feedback or top-down input at work. Still there seems to be an asymmetry in time, between sensing and doing. In sensing we seem to go bottom-up forwards in time, whereas in doing, we see to go top-down forwards in time. This is like a neuron, where in the sensing dendritic end the flow of information going forwards is bottom-up and converging to the cell body. Whereas the axon side goes top-down with signals diverging from the cell body. So the relative thickness of the blue and green arrows in the diagrams of the sensory and motor hierarchies below, reflect this asymmetry.

Cropped Sensory Only-Hierarchy.jpg

Cropped-Motor Only-Hierarchy.jpg

So we have seen that the motor hierarchies and sensory hierarchies are connected in a very specific laminar pattern. The diagram below depicts these two hierarchies side by side. The motor hierarchies depicted in blue corresponds with regions of the neocortex on the frontal anterior half of the brain.The sensory hierarchies, drawn in green are generally found on the back posterior side. The arrows going up and down the two hierarchies are designated top-down or bottom-up to explicitly show that this concept and also the corresponding specific laminar projection patterns, pervades the entirety of the neocortex.

Simple-Cortical-Hierarchy.jpg

These frontal and posterior sides of the brain are very tightly interconnected by a whole load of major fibre tracts. The diagrams below show some of these major fronto-posterior fibre tracts as found in macaque monkeys. Generally speaking humans will also have analogues to these fibre bundles, the longitudinal fasciculi, which connect up  areas in front of the brain with corresponding areas at the back. And these fronto-posterior connections are also reciprocal, i.e. frontal cortex projects back and vice versa the receiving posterior cortex will send a set of return connections. It is a quite often related fact that generally speaking, the major fibre bundle which connects up the left and right sides of our brain, the corpus callosum, is thicker in women than it is in men. This have generated no end of speculation as to how this might relate to function and manifest behaviour. What is not so well known is the finding that the longitudinal fascicuingli, connecting up the frontal action side to the posterior sensing side, are generally thicker in men. No doubt this will also stimulate a lot of speculation.

3k  PFC Connections to Posterior Cortex - Summary.jpg

Importantly these fronto-posterior projections also have a very specific projection pattern in that a cortical area at a certain level in the sensory or motor hierarchy, will tend to be mainly connected reciprocally to the areas on the othesamee at the same ‘status’ or hierarchical level. So primary sensory cortex will tend to connect to primary motor cortex, secondary sensory with secondary motor etc. And these fronto-posterior connections are also very specific in the layers of neocortex from which they arise. Because these fronto-posterior connections also obey the top-down, bottom-up rule of layer 5 to layer 1 verses layers 2 or 3 to layer 4 respectively. But in this case the top-down bottom-up relationship is between motor and sensory areas at the same hierarchical level. What we find is that the front to back or fronto-posterior projections follow the top-down laminar pattern, whereas the reciprocal posterior sensory half to anterior action side projections follow the bottom-up laminar pattern. So the diagram below shows these fronto-posterior projections added to our earlier diagram with the top-down or bottom-up pattern matched with the flow of information represented by the arrows. This explicitly shows the concept of top-down and bottom-up working across the frontal doing/cognitive and posterior sensing/conceptualizing sides of

Cortical-Hierarchy.jpg

There is one further finding which further fills in our picture of top-down and bottom-up relationships in the brain comes from fairly recent research by Helen Barbas and colleagues at Boston University USA. Actually a lot of work relating to laminar projection projections or structural predictors of top-down bottom-up relationships comes from her lab. Here we’re interesting in some specific findings which show that the frontal cortex will not always have a top-down higher up the hierarchy relationship with the various areas of the brain in the posterior side. What was discovered is that a sensory region in the posterior side which is higher in rank or level of the hierarchy than a motor or cognitive region in the anterior side; will actually project in a top-down pattern to the it. And vice versa that lower level frontal region will project back in a bottom up pattern. Apparent this result was quite unexpected and surprised some neuroscientists who generally thought of the frontal cortex as exerting a top-down effect on the posterior cortex. Therefore this adds another layer of detail to our top-down bottom-up map of the brain. And so depicted in the diagram below are these top-down bottom-up relationships between posterior and anterior regions of the brain which exist in adjacent levels of the sensory motor hierarchy. So taken together with reciprocal connections happening between regions at the same level in the hierarchy, the addition of these ‘diagonal’ connections forms a sort of zig zag pattern.

Cortical-Hierarchy-+-Barbas-fainter-back-arrows.jpg

Once we can see this zig-zag pattern and top-down ordering of the regions in both the frontal and posterior sides of the brain, then it may be useful for conceptual and theoretical reasons to order both hierarchies into a single hierarchy which interleaves both front and posterior regions of neocortex. So the diagram below depicts this combined top-down hierarchy.

Interleaved-Hierarchy.jpg

The Emotion Centres are also Hierarchical and Top-Down

We now include in our survey of the hierarchical and top-down/bottom-up relationships in the brain, the emotion centres. We introduced these earlier but will talk about them more in order to show that they too fit into our hierarchical top-down way of looking at things. These are the hypothalamus, amygdala, orbitofrontal cortex (OFC). We’ll talk about them in turn and demonstrate they may be conceptualized as existing in a mainly 3 tiered or layered hierarchy with the hypothalamus at the top, the amygdala in the middle and the orbital frontal cortex at the bottom.

The hypothalamus is a very important and central (literally and figuratively) part of the brain. It is really the well spring of motivation and this is closely related to it involvement in homeostasis which is maintenance of the most basic conditions which allows us to stay alive, i.e. maintaining correct bodily temperature, water levels, glucose(energy) or fat levels etc. It is also involved in sex and orgasm. In its homeostatic function it really performs its function in the most basic way imaginable. In order to regulate internal body temperature it actually measures the temperature of the blood and triggers responses if these measurements deviate from the optimal. For instance if the blood is too warm, the hypothalamus may trigger sweating. If too cold then it may cause shivering, surface blood vessels to constrict and piloerection of the small hairs on our skin; all of which helps our bodies to stay warm. In case of food or hunger regulation, then it does this by directly measuring the amount of glucose and fatty acids in our blood. In the case of water regulation it measures the osmotic balance between membranes in special cells which give a direct indicator of the amount of water in the blood. When all these basic needs are satisfied then we turn our attention of course to sex. The pre-optic nucleus of the hypothalamus seems to play a central role in this activity in terms of motivation sex drive and also in triggering the reward of orgasm. In the human brain the hypothalamus makes up an almost negligible less than 1% of total brain mass, but is arguably the most critical 1% of the entire brain. The diagram below left shows the position of human hypothalamus. The diagram below right show the mouse hypothalamus which is color crimson red. The more pink areas above it, are the mouse striatum and thalamus. We can see that in the mouse the hypothalamus makes up quite a large proportion of total brain mass.

Hypothalamus.jpgVMHvl resized.png

Next to consider is the Amygdala. Its name derives from the greek word for almond because from early anatomical studies its appearance resembled an almond. But more recent studies using a host of modern means of analysis, we now the original almond shape region is actually part of a much larger complex which has been called the ‘Extended Amygdala’ which includes brain areas such as the Bed Nucleus of the Stria Terminalis BNST which were originally thought to be distinct and different structures. This extended amygdala more resembles a ring shape with the original almond placed as a large ‘jewel’ on this ‘ring’. When we say amygdala we really mean extended amygdala. The diagrams below left and middle, show us the relative position and size of the amygdala in the human brain, marked in red. This is the almond shape as the amygdala used to be understood. The diagram below right shows the extended amygdala which is more ring shaped. Much of the original almond in this diagram, is represented by the hatched line structure to the bottom left of this diagram. Only the Central and Medial nucleus( labelled Ce and Me respectively) of the original almond shaped amygdala are colored in.

amygdala.jpg4o4Extended Amygdala.jpg

In its functioning the amygdala adds to and builds on the functioning of the hypothalamus. It is a centre that is known to be heavily involved in emotional processing and motivation, including fear. It’s seems to augment the augment the homeostatic and motivational roles played by the hypothalamus. So  for instance, in the case of food, it is in the amygdala that the processing of salt and sugar tastes from our tongue is processed. This adds more sophistication to our abilities to register nutritional signals and it also enables these factors to become rewarding to us. In the case of sex, if the hypothalamus handles orgasm, then the it seems certain areas of the amygdala handle sexual preference and gender orientation. Though the so called sexually dimorphic nucleus SDN is found in the hypothalamus it is unknown whether this area plays a role in sexual preference, it is only known to be generally bigger in males. So in way the amygdala adds another level of complexity to the sex drive, specifying certain types of individuals we would like to have sex with, i.e. opposite or same sex. In mice and rats all sexual behaviour is driven by the sense of smell and the detection of special scent chemicals known as pheromones. This is why these rodents are able to breed, well like mice and rats, in total pitch blackness of subterranean environments. All pheromone processing is handled by the medial nucleus of the amygdala.

As we continue along our emotional brain hierarchy we come to the orbital frontal cortex. This is actually a part of the neocortex and is located in the part of the brain immediately above the eye sockets or orbits of

our eyes hence its name. The diagram below left shows this area from a viewpoint as if we were looking up at the undersurface of the brain.

4o6Divisions of OFC & Medial PFC.jpg

As already stated we believe it makes sense to place the orbital frontal cortex along a hierarchical continuum that includes the hypothalamus and amygdala. At the same time the orbital frontal cortex itself forms a another self contained hierarchy and continuum. We know from various studies that this part of the brain is involved in emotional processing, reward and registering salience. And we also know that there exists an ordered mapping of these functions along a posterior to anterior or back to front axis. So rewards or emotionally salient stimuli which are more abstract gets handled by sub-regions of the OFC more towards the front and those more ‘concrete’ are handled more at the posterior end. So for instance something like money, moral choices, fine cuisine or art appreciation would hypothetically light up the front most OFC areas. Whereas things like 0.7 hip ratios, shiny skin and hair, rounded breasts and buttocks, which are all indicators of high estrogen and high fertility, would activate those OFC areas more to the back. Also we know in animals that the OFC hard codes for things like a preference for ripe fruit, the sensation of fat in the mouth, and things like the rewarding value of touch and bodily contact.

So all these various encodings of salience and reward would exist in various subcompartments of  the OFC and be arranged in a posterior frontal continuum. We know from anatomical studies that then as we traverse this continuum from back to front then we are going top-down the hierarchy. This would fit in with our idea of make the OFC along with the Amygdala and Hypothalamus, one big hierarchy and continuum. It fits the anatomical connectivity data and it it also makes logical sense. We started with the hypothalamus and amygdala and used the examples of food and sex to illustrate a steady augmentation in the sophistication of how the brain handles these important biological needs and goals. We started with the most basic detection of nutrients in our bodies by the hypothalamus, and basic orgasm. We then added things like salt and sugar detection and processing of with the amygdala, and also gender preference with respect to sex drive. On top of this we can meaningfully connect up the orbitofrontal cortex and the implicit top down hierarchy contained within it. So now to our quest for food we add things like the visual appearance of food, more complex smell and taste processing and also the texture of food in our mouths. And to sexual behaviour we now add complex visual processing of physical attributes, i.e. indicators of health, fertility and strength. Also sexual pleasure associated with touch and bodily contact. Even higher up the scale we could also include those ‘higher’ factors in determining mating preferences, i.e. status, sense of humor, kindness, intelligence etc. would presumably would be handled by the more anterior OFC.

We hypothesized that morale evaluations would also be handled by these most frontal regions. In an interesting study of incarcerated psychopaths an recurring factor was discovered in a subset of those case studies which contained no obvious indicators of circumstances which might have conditioned their later aberrant behaviour, i.e. broken homes, childhood violence or various other deprivations, i.e. a subset of psychopaths who seemed to have perfectly normal upbringings. What was found was that this subset instead had suffered physical trauma to the head which created abnormal functioning of the orbital frontal cortex. Because of its location at the base of the brain, immediately above the eye sockets and against the inside surface of the front of the skull, this particular area is susceptible to damage from automobile accidents. Where a crash and sudden deceleration will cause the brain to crush against the front of the skull thereby potentially causing damage to it, and in particular to the frontal aspects of the orbital frontal cortex. In of these normal upbringing psychopaths this was indeed the case, i.e. some car accident that occurred at some point earlier on in their lives. This would fit in well with the idea that abstract moral considerations would be handled by the anterior orbital frontal cortex.

Together with the moral aspect we could perhaps expect the social aspect to be processed in regions such as the anterior orbital frontal cortex with help from other frontal regions such as the anterior cingulate cortex, which brain scanning studies suggest. The philosopher Foucault said that ‘hell is other people’ but so is too is ‘heaven’ in a sense. It is true that some of our highest pleasures and achievements involve other people, but so do some of deepest anxieties and pains in life. After all we are social animals, our mental world is in large part and also perhaps to the greatest extent social. But how would this fit into our continuum and top-down hierarchy starting from the hypothalamus the centre of most primitive needs. Would the social dimension of our minds merely exist as an elaboration of basic homeostatic, self preserving and sexual drives. In the social game of the quest for status then the link to sexual reproduction is clearer but would all our ‘higher’ moral imperatives likewise be grounded in and derive from the dictates of the hypothalamus? This structural interpretation would say yes to that question. It is interesting that the different distinct creative periods of the great artist Picasso have been linked by art historians to the different times he was involved with his various mistresses. Perhaps this is an example of lust, the hypothalamus the well spring of lust, being the source of higher artistic and mental achievement. It may be possible but maybe in a more indirect way to also ground all the other higher mental realms to more basic requirements. The idea that all our behaviour ultimate reduces to sex, the prime directive is certainly not a new one. This may seem a bit disappointing if sex is considered as low down in our assessment of the important things of civilization and human nature. However if we elevate the sexual creative act to a higher status, even given it a sacred and divine connotations as some traditions do, then this fit well with a hierarchical top-down model of the brain that has the emotion centres at the top of the hierarchy. And which in turn places sexual union at the top of the emotional and motivational sub-hierarchy. After all our most important treasures in life, our children, come from the sexual act. Without offspring then everything else in life and civilization becomes ultimately meaningless. But we’ll turn away from these more speculative considerations to complete our interpretation of the emotion centres using the hierarchical concepts of top-down, bottom-up, context and containment.

The important is that given our ordering of the hypothalamus, amygdala and orbitofrontal cortex along a hierarchical continuum then our earlier definitions of top-down, bottom-up, context and containment, make perfect sense when applied to interpreting the functioning of the emotion centres. So if the hypothalamus is the ‘top’ of the hierarchy and the overall container then using our example of food,  it makes sense to say that registering of salt and sugar by the amygdala exists in the context of satisfying our hunger as dictated by the hypothalamus and its glucose detectors. And in turn the processing by the orbitofrontal cortex of the following, i.e. the visual appearance of food (e.g. ripe fruit) , the texture of food in our mouths (e.g. fatty or oily sensation) and aroma or more subtle taste of food; can likewise be meaningfully thought of a existing in the context of what the hypothalamus is registering i.e hunger. And also in relation to sex. If the hypothalamus is the source of sex drive and orgasm, then gender preference specification by the amygdala exists in the context of what the hypothalamus is doing i.e. sex. In turn all the complex processing of sexual attributes, breasts, buttocks, status, strength and high fertility, only make sense with the context of gender preference, So the top-down hierarchy of the emotion centres is also a nested structure of context and containment.

We continue with our exploration of the emotion centres by introducing some fairly recently discoveries relating to them, which allows us to conceptualize them as existing as part of a single continuum and hierarchy that also includes the rest of the brain. This is a idea which was mentioned briefly earlier and concerns an important support structure that works directly with a lot of the rest of the brain, i.e. the striatum or basal ganglia. The striatum is an important structure that neuroscientists early on believed to be involved only in movement and planning of movements. We now know that it is involved in so much more, i.e. cognition, language, spatial processing, memory and a lot else besides. We also know now that it is also inextricably implicated in emotional processing and that all the emotion centres have an underlying striatal support structure, just like the all of the prefrontal cortex and some special posterior areas. So the diagram below depicts these findings. The three tiers of the emotion centres are shown in grey on the top row or the diagram. And the emotional hierarchy proceeds left to right, with hypothalamus at the top and the orbitofrontal cortex at the bottom. The yellow boxes in the middle row represent the striatal structures that work closely with the emotion centres. The blue boxes at the bottom represent dopamine neurons which project to the yellow striatal structures and which enables them to function properly.

Engines-also-Striatal-like.jpg

We can understand what these striatal structures of the emotion centres are doing from extrapolating what we know from the movement centres. We know that here the striatum is involved in sequence learning of movements evolving in time and in a specific order in time. And in an earlier discussion we showed how these sorts of recurrent loops may represent the time dimension as a binary hierarchy. Therefore it may be reasonable to assume that likewise, these emotional striatal structures are giving the hypothalamus, amygdala and OFC a temporal dimension. And this would make perfect sense, because we are not just interested in emotions and homeostatic indicators as temporally static and unchanging bits of information. We are most interested in how our emotions and homeostatic state changes in time. So we are not merely interested in the state of being hungry, we are even more interested in the change in state over time from hungry to not hungry, and all the associated actions and perceptions that surround that transition. And in relation to sex we are not merely interested in a static sense of feeling lusty or the sense of orgasm in isolation, but rather the sequence of temporal transitions that leads us from lust to orgasm, together with the registering of all the visual, pheromonal, tactile perceptions that evolve over time towards that end goal.

So this allows us to understand why the emotion centres have underlying striatal structure. This striatal structure and way of interpreting what the emotion centres are doing also allows us to fully integrate the emotional top-down hierarchy with the motor and sensory hierarchies which we have already explore in some detail. It is because the motor areas and also the cognitive processing regions of the prefrontal cortex, which make up the front half of the brain, all have this underlying striatal as well. In fact it was in relation to the primary motor and premotor cortices that the striatum was for a long time believed to be mainly associated. It was known early on that neurology diseases which affected the striatal areas of the putamen and caudate nucleus also invariably caused movement disorders, and the connections between the movement cortices and striatum were more easy to discern. Later on it became apparent that the cognitive and language centres of the prefrontal cortex, likewise also worked together inextricably with the striatum. Also some posterior areas of cortex associated with the functions of higher order perception and spatial mapping, i.e. the temporal and parietal lobes respectively were also shown to have the same underlying striatal looping architecture. And so in more recent times the emotion centres have likewise become understood to also have these striatal loops underpinning their normal functioning. Though this was suspected for a long time, it was not so obvious so took a lot more figuring out and experimentation to convincingly demonstrate. Though these important findings may not yet have found their way into neuroscience textbooks or encyclopedias, nonetheless it is accepted by most or even all specialists.

So in our emotional hierarchy as illustrated by the diagram above we have the hypothalamus at the top, with the amygdala in the middle and the orbitofrontal cortex in the middle. The bottom of the emotion hierarchy is shown in the diagram to project to the cognitive cortical areas and which in turn project to the motor areas of neocortex. So we now turn our attention to these other areas of the brain and describe their underlying striatal architecture. We’ll start with the motor cortices.

In the diagram below we depict elements of the motor hierarchy which includes the primary and premotor cortex, together with the supplementary and presupplementary motor areas. Together they may be arranged in a three tier hierarchy.The striatal loops together with the associated dopamine subsystem is shown as in the earlier diagram of the emotion centres. The striatal component most associated with the motor areas of neocortex is a part of the striatum called the putamen. An important feature of all these motor areas is topographic mapping with the entire body and musculature represented in distinct subpatches of movement cortex with these maps duplicated across all the separate levels of the hierarchy. So in a sense these separate body zones would have their own mini hierarchy to represent them. And all the body zones taken together would form a set of parallel concurrent hierarchically nested loops which would coordinate or movements. The bottom of the top-down motor hierarchy sends signals onto the muscles, via a few relay stations, and so cause actual movements and coordinated behaviour. At the other end, the top of the motor hierarchy receives input from the cognitive areas of the brain involved in higher level planning and abstract thought. We turn to these areas next.

Motor-Hierarchy.jpg

The diagram below does the same thing for some representative parts of the cognitive prefrontal cortex, which likewise can be seen as forming top-down hierarchies. The prefrontal has several of hierarchies, one is involved in language processing, another in spatial mapping and another in object processing etc. And as in the previous diagram dealing with the motor areas, here we also show the striatal and dopamine loops. The striatal region most associate with the cognitive areas is called the caudate nucleus. The bottom of the cognitive hierarchy projects into the top of the motor hierarchy, so presumably in this way our abstract thoughts and plans become external movements and behaviour. Going the other way as we ascend the top of the cortical cognitive hierarchy then we start to find interaction with an important part of the striatum called the nucleus accumbens. This striatal area is heavily implicated in the action of addictive drugs and it dopamine projection comes from a small set of neurons called the ventral tegmental area (VTA). This makes up the mesolimbic dopamine pathway of addiction. It seems without exception all addictive substance affect either directly or indirectly this important brain region. This leads to the question of what naturally activates this pathway of addiction instead of addictive drugs and the answer is the emotion centres which are the motivational engines of the mind. This makes intuitive sense and corresponds with our introspection. And also this agrees with neuroanatomy, where there exists direct connectivity from all the centres of emotion, i.e. hypothalamus, amygdala and orbitofrontal cortex to the VTA dopamine neurons. And similarly when we consider the top of our cortical cognitive hierarchy then this receives strong projection from the areas more to the bottom of the emotional hierarchy i.e. the subgenual ACC and amygdala.

Cognitive-Hierarchy.jpg

So we have establish that there exists a common striatal architecture underlying the emotional, cognitive and motor areas of the brain. And we described the hierarchical nature of all these sets of brain areas. We see in the diagrams how the output of one level of each hierarchy will feed into the adjacent level. Moreover we described how each of these major areas, i.e. emotional, cognitive and motor, reciprocally feed into each other, and in a way that they may also be arranged hierarchically. Therefore the next logical step is to conceptualize all of these brain regions and nested subregions as a single top-down hierarchy. This is shown in the diagram below. There is a lot of detail in this composite diagram and some of the labels and fine details may not be so clear. But it is merely the three separate diagrams from earlier, covering the emotional, cognitive and motor areas separately, replicated and joined together with one another end to end to form one big all encompassing top-down hierarchy.

 Cropped - Single-Top-Down-Hierarchy.jpg

We add now to our expanding integrated understanding of the brain, an important area introduced much earlier called the cerebellum. This part of the brain has many parallels with the striatum which we’ve just discussed a fair bit. These parallels are listed in the diagram below. So in the same way the striatum forms closed loops via the thalamus with various areas of cortex so does the cerebellum. And also like the striatum, the cerebellum was for a long time thought to be a structure mainly involved in the coordination of movement but later research also showed its heavy involvement in cognition and language. It is thought that same sort of functions it performs for facilitating the fine control of fast and rapid sequences of movements, playing a complex musical piece on a piano say, is also what it is doing with the facilitation of thinking. So hypothetically the fast flow of thoughts in our minds would be likened to the fast movements of a skilled pianists fingers, and both of these activities would be underpinned by the cerebellum. Much the same line of reasoning could also be put forward as a way of  understanding the functioning of the striatum. It is known from empirical studies that both the cerebellum and striatum are heavily involved with automatized sequencing of thoughts, movements and behaviour. This may be described as habit, skills or procedural memory, and would include mental as well as physical habits, skills and procedures. When we incorporate this line of thinking to another parallel of the striatum and cerebellum, i.e. both their involvement in emotional processing, then we may reasonably suppose that emotional habits and so called emotional intelligence, would also make use of these structures. So with their closed loop architecture, which we explained earlier could represent time and sequence information, the striatum and cerebellum would be automating and chaining together our thoughts, emotional responses and also our movements.

Striatum-&-Cerebellum.jpg

A question arising would be, why do we need this apparent replication of functioning and structure between the striatum and cerebellum. The answer is that though while there is symmetry there is also complementarity. While there are parallels between the striatum and cerebellum there also exist important differences in the organization and laminar areas of termination of the cerebellar and striatal closed loops which gives us clues as to the respective roles they play in behaviour and cognition. This relates to the principle of top-down versus bottom-up which one of the major organizing principles of the brain as we’re trying to explain in this section. More specifically the laminar pattern of projection of the closed loop projections from the striatum and cerebellum to the neocortex, terminate in specific and different layers. The closed loop projections from the striatum terminate in superficial layer 1 and those from the cerebellum terminate predominantly in middle layer 4. This is very important because as we explained earlier when we consider the neocortex as a lateral top-down bottom-up hierarchy then the top-down projections between adjacent areas of neocortex terminate in layer 1, whereas the bottom-up projections terminate in layer 4. This was shown in earlier diagrams. The diagram below shows the different laminar termination patterns of the striatum and cerebellum.

1th-StriatumCerebellum-to-CerebralC.jpg

The next diagram, below brings all this data relating to the cerebellum together and shows the cerebellar closed loops added to our earlier diagram, depicting our expanding and increasingly all encompassing top-down hierarchy of brain and mind. It is basically identical to the earlier cortical striatal hierarchy diagram except we’ve added the pathways to and from the cerebellum, which are drawn as red arrows. The various regions of the cerebellum corresponding to the various cortical areas are represented as brown rounded rectangles. Roughly speaking the most lateral or outer portions of the cerebellum deal with the cognitive prefrontal cortex. The more medial parts deal with the motor and premotor cortices and a small area called the ‘vermis’ found at the centre of the cerebellum, is related to emotional regulation. The diagram doesn’t show important relay stations involved in the cerebellar closed loops, such as the thalamus and omits some auxillary structures and circuitry. It shows the overall plan and scheme of things. The diagram packs in a lot of information but tries to accurately represent the specific layer in which the inputs to the neocortex from the cerebellum terminate i.e. layer 4. All in all this diagram represents the entire frontal cortex and the emotion centres, together with the striatal and cerebellar structures which work closely with them. Also depicted are the important dopamine pathways.

 Cropped - Single-Top-Down-Hierarchy-with-cerebellum.jpg

The composite structure just described and depicted in the diagram above would include all the frontal regions of the brain, together with the striatum, cerebellum and subcortical emotion centres. To this unifying structure we may now also weave in all our posterior sensory regions which are tightly interconnected with the frontal regions via the longitudinal fasciculi and other fronto-posterior pathways as described earlier. So in addition to this frontal cortical hierarchy the next and final step would be to also include the sensory top-down hierarchies. These we described in some detail earlier on together with some of the intricacies concerning how the sensory and motor hierarchies are interconnected with one another.The diagram below integrates all the layer specific projection pattern information from the various earlier diagrams. This now gives us an integrated structure that encompasses the entire neocortex, including both the frontal motor and cognitive side with the posterior more sensory oriented side. So the next diagram below shows this integrating of the sensory aspect to our continually expanding all encompassing view of the brain.

Total-Single-Top-Down-Hierarchy---Complete.jpgThis additional complexity needs a little explaining to make things clearer. The sensory hierarchy is depicted at the bottom of the diagram in grey. The color grey to represent grey brain matter. The 6 layered makeup of the sensory cortex is depicted and names of some of the sensory areas are labeled also in grey. The nerve fibres which connect up adjacent regions of the sensory hierarchy are also drawn as curved arrows also in grey. These grey arrows project from and terminate in specific layers reflecting the top-down and bottom-up rule described earlier. What is important to note is that the connections between this sensory hierarchy with all the rest of the frontal cognitive, motor and emotional hierarchy, as well as the cerebellum and striatum; is shown a bright orange long arrow lines. I hope the choice of color makes these new connections stand out. The sensory hierarchy is reciprocally joined to the motor hierarchy, i.e. the upper bank of grey regions in the diagram, by vertical straight orange arrow lines going up and down. These vertical arrow lines are partially obscured by the boxes representing the striatal regions and dopamine neurons in the diagram. These connections are exactly equivalent to those in the earlier diagrams which focused on the interconnection patterns of the frontal cognitive-motor and posterior sensory top-down hierarchies.

What is new and additional are the projections coming from the sensory hierarchy and projecting to the cerebellum and striatum. So far we have only thought about the striatal and cerebellar regions as forming closed loops with particular regions of cognitive or motor cortex and also with the emotion centres. That is receiving projections from a certain area and then return a projection (via the thalamus) to that same area. But there is additional complexity because the striatum and cerebellum will also receive massive inputs from the sensory areas. It is this input together with the projections from the frontal cognitive and motor hierarchy which allows these structures to perform their respective roles and we’ll explain exactly what these are a little later.

So we now have a pretty all encompassing schematic of practically the entire forebrain, though some auxiliary structures have been left out for the sake of clarity. What this diagram shows is all of the neocortex, and paleocortex i.e. hippocampus and cingulate, emotion centres and also striatum and cerebellum, laid out to graphically illustrate its overall structure. What it clearly demonstrates is that all of these central and almost all inclusive structures of the brain exist as a single top-down hierarchy. The concept of top-down, bottom permeates the entire brain, and all the top-down bottom-up relationships existing throughout the brain may be joined up together end to end, top to bottom and bottom to top to form one all encompassing structure. And the striatum and cerebellum fit in the temporal dimension into this top-down structure in the very specific top-down and bottom-up respectively way, they project to the frontal hierarchy.

Though this diagram is complex at the heart of it is a lot of repeating regularity and order. It depicts the overarching order that exists in the overall organization of the brain. However a lot of other ‘messy’ details have been omitted which complicate our precise and ‘clean’ scheme of things. For instance though there does exist a hierarchical ordering between patches of cortices it is generally not the case that a patch at one level of the hierarchy will only project to the adjacent patch. Usually there are also projections which jump ahead two or even several patches. An extreme case would be direct projections from the emotion centres, particular regions of the amygdala dealing with fear, which leap from all the way to project back to early stages of visual processing, very low down the hierarchy. Also what is also omitted for the sake of clarity is that the areas of striatum and cerebellum will receive projections not just from a single sensory or motor area but rather from several adjacent ones. And similarly as suggested earlier, the  reciprocal projections from the frontal cognitive-motor hierarchy to the posterior sensory hierarchies will tend to end up in corresponding levels of the hierarchy, but there will also be some fibres terminating in surrounding levels. So there is also an extremely disordered dimension to brain architecture which may make the brain seem like something designed through a series of accidents and appear as almost random. These extra connections would give the brain the important property of redundancy and resilience. All these extra paths would mean that any damage may be compensated for. Our diagram represents a very neat chain of interacting parts. A function of all the extra connects would compensate for breakages in the chain, either temporary or permanent. Our simplified easy to immediate understand design is also a brittle one. If any link along the top-down hierarchy for whatever reason malfunctions then the entire chain breaks. The extra paths allow for a lot of bypass and rerouting.

We could draw in and superimpose these extra ‘all over the place’ seeming connections into our already complex but relatively neat conception depicted in the diagram above. This would indeed make things seem like a complete mess, it would produce a complete tangle of a diagram. So when we add in all this additional complexity, then this would be the picture of the brain that most people would imagine things to be, a state of unfathomable disorder. However all of this doesn’t contradict the highly ordered and hierarchy top-down bottom-up conception of overall brain architecture we have built up. Because all this additional complexity and ‘messiness’ can be explained in terms of our more simplified model and incorporated into it without altering the overall picture. What we have formulated is an overarching conception of how the brain is put together and the principles behind its structuring. This gives us I believe a solid theoretical base and a broad framework of tightly interconnected ideas with which to them make sense of all the extra details.

Another significant aspect of brain architecture which is not included in our synthesis is the fact that what we have considered as a single top-down hierarchy is actually a hierarchy of nested component cortical sub-hierarchies. So for instance we describe the primary motor areas as being one level of the hierarchy, but this actually the bottom of another top-down hierarchy which takes a more direct route from the hypothalamus, via a few extra levels of cortical areas, called cingulate motor areas. The same is true for the cognitive areas, which are also in themselves, a self contained top-down hierarchy also emanating directly top-down from the hypothalamus via portions of the cingulate cortex next to the anterior cingulate. So instead of having a simple top-down hierarchy consisting of single areas of cortex, we really have different hierarchical top-down stacks radiating from the cingulate cortex, so we would have motor stacks and also various cognitive stack. And each of these top down stacks which also radiate from the hypothalamic area called the mamillary bodies, which projects to the cingulate cortex (via the anterior thalamus) and which would form the top these cortical stacks and sub-hierarchies. These stacks would then be arranged in our overarching top down hierarchy which in turn would also have the hypothalamus at the top of it as shown in the earlier diagrams. The advantage of such an arrangement is that each level of the overall hierarchy, as depicted in the diagram above, may work independently of one another. The overarching hierarchy consisting of all the substacks is involved when we couple our physical actions and motor behaviour to our higher centres of cognition. But the truth of the matter is that we can act without thinking much, and do a lot of thinking without acting. Therefore we are able to decouple these activities from each other and have them operate independently while still driven by our emotions; hence the direct input from the hypothalamus to these sub-hierarchical stacks. These sub-hierarchical stacks within the overarching stack or hierarchy, would be mapped onto the cortex as an orthogonal top-down trend, perpendicular to the axis of the main hierarchy.

Much like all the extra connections on top of our ‘cleaned up’ hierarchical view of things described earlier, this additional complexity of sub-stacks within our hierarchy, would add flexibility and resilience. What we have is an overarching design principle, i.e. a top-down bottom-up hierarchy and various augmentations and additions, which while they complicate the picture, nonetheless still work within our unifying conceptual scheme.

So in this section so far we have worked through a lot of neuroscientific detail in order to gain an understanding of the hierarchical nature of brain organization. We have shown that hierarchical top-down bottom-up patterns of organization are pretty much ubiquitous in the brain. From sensory and motor hierarchies to the emotion centres, together their connections to the striatum and cerebellum we have seen that top-down and bottom-up relationships can be assigned to them all, and also in relation to their interactions with one another. In effect these hierarchies and top-down bottom-up relationships are really really a universal organization principle of the entire brain. And because of this universality we are able to arrange the brain in a single hierarchy and conceptualize all of its constituent components as existing somewhere within it. Once we arrange the brain in this way, then all the brain components, areas and sub-areas may be assigned top-down or bottom-up relationships with one another.

Merging the All Encompassing Top-down Hierarchy with our Binary Brain/Mind

What we’ll do next is to describe a major synthesis. We take our all encompassing top-down hierarchy and integrate this view from neuroanatomy with all the binary tree, binary coding, binary brain, binary time and binary neuropsychology ideas which have already been covered. Also importantly we make use of the detailed way in which we explained how binary trees and binary combinatorial codes can capture the concepts of hierarchy, top-down, bottom-up, context and containment. The diagram below captures the converging and bringing together of all the information we’ve already synthesized into an even greater synthesis. So we’ve brought back our digitized brain which is supposed to represent the whole binary, doubling and discretized view of the brain and mind we built up earlier. And we’ve juxtaposed this with all the hierarchical top down neuroanatomy and brain connectivity.

Cropped - Hierarchy-into-digitized-brain.jpg

The bridging concepts that make this integration possible are the 3 different ways in which our binary language could explicitly represent the concepts of top-down and context etc, and which we explained in a lot of detail earlier. It is useful to recap that binary trees and binary combinatorial codes could do this in 3 different ways. They were firstly in terms of spatial top-down or spatial containment and this mode related to the idea of the branching nodes of binary trees as being contained. Secondly we described the idea of lateral top-down which derived from lateral spatial combinatorial codes; thirdly and lastly we described the notion of temporal top-down which did the same thing with the temporal combinatorial codes which emerged from time sequences of spatial combinatorial codes. It is very easy then to map these formalized binary tree conceptions of top-down and context onto our brain hierarchy, which consist of 1./ spatial nested physical components, i.e. neocortical maps and columns etc. 2./ Brain components arranged in lateral hierarchies and 3./ all of these components chained in time by our ubiquitous recurrent loops. All of these types of structural arrangements found in neuroanatomy then map directly onto our binary tree way of coding hierarchies. And so with our binary language we are able to completely describe all the physical neural top-down hierarchies and subsume them into our digitized binary brain.

This is process is facilitated by using the knowledge that all the octaving doubling brain waves we describe can be incorporated directed into our neural  top-down hierarchy. And in a way that reflects empirical findings. 40 htz gamma would be pretty all pervasive throughout the entire top-down structure including the striatal and cerebellar components. The ~5 htz theta component would be concentrated in the higher levels of the hierarchy, i.e. emotion centres, cingulate cortex and hippocampus. And the 20 htz beta and 10 htz would play synchronizing functions across the most distantly located brain regions; all as suggested by recent empirical findings. We would incorporate our binary time scheme into our single hierarchy at all scales and use this explain the striatal and cerebellar loops. We would also encode all the various cortical laminae in our sensory and cortical hierarchies with our binary language, and use the same code to describe the feature detectors and even individual neurons nested within those cortical patches.

So we take our  whole binary perspective, all these ideas, insights and empirical findings, and we merge it with our unifying and all encompassing brain hierarchy. The binary, griddy, doubling, octaving and digitized view of brain and mind which we built up in earlier sections goes hand in hand with our single hierarchy of all the major information processing brain structures. So that absolutely everything that has been described and explained thus far, becomes brought together into a single integrated perspective. We obtain an all encompassing and all unifying single top-down binary tree hierarchical structure completely describing the information processing essentials of brain and mind.

Now that we have been to arrange the entire brain into a single top-down hierarchy we can use this powerful conceptualization to gain insight into a variety of mental phenomenon and brain activities. For instance we can understand the significance of the laminar specificity of the striatum and cerebellar projections to the neocortex,  when we consider what the top-down versus bottom-up signals traversing down and up the all encompassing hierarchy would be doing. At the top of the hierarchy we have the emotion centres which would register some need i.e. food or water etc. This would set up the body for action and initiate the cascade of activity which will satisfy that need. So we can imagine a top-down flow of information emanating from the emotion centres with the hypothalamus at the top. As the information flows down the various levels of the hierarchy eventually it reaches the bottom motor cortices where actual behaviour and sequences of actions are produced towards the goal of satisfying the need specified by the emotion centres. As signals are sent top-down towards the motor cortex for expression as behaviour there would be a corresponding bottom-up flow of information. This would be feedback concerning the execution of the tasks or the commands going downstream. The feedback signal would provide information about the success or failure of the command and could also integrate sensory input. As we explained earlier, each level of the hierarchy in the frontal cognitive and motor cortices receive information from the same hierarchical level of corresponding posterior sensory brain areas

The processes of brain and mind reduce to a single underlying recursive process.

Earlier using our binary tree language and the concepts of top-down, bottom-up, context and containment we have been able to conceptualize the brain and mind as an all encompassing hierarchical classification structure integrating neural substrate with emergent representational forms. With our unifying organizational principle, concept and language we have obtained our unifying structure and symmetry bond bridging brain and mind. The next thing we may rhetorically ask is the question, is it possible to then to define a single process over this unified structure expressed in our unifying language which may account for all the separate processes happening within it? Does there exist a single algorithm that we may specify to work with this all encompassing data structure that subsumes and captures in its operation, all the separate partial algorithms of brain and mind? The answer is yes. And what is the nature of this algorithm or process? In a related way that all the components and contexts contained in our all encompassing classification structure relate to one another in a hierarchy of contexts and containment that is nested; the single underlying process which works over this nested structure then has the property of being recursive. But there is more to this single underlying process and algorithm. Not only is it able to animate the functions and representations of brain and mind but does even more. It also captures in its operation, the process of how brains come into being, i.e. neurogenesis. Furthermore this underlying recursive process even subsumes in its operation the process by which the functions and representations of brain and mind evolve.

This is one of the truly stunning properties of this symmetry, self similar and recursive Fractal Brain Theory. And where the systematic application of these principles used together with our binary tree and binary combinatorial code language leads. The unification of the structures of brain and mind into a single conception, though an important step, is merely the foundation for an even greater unification. It is the reduction of all these structures together with all the processes of brain and mind that work over them, into a single compact recursive description and algorithm. It is the ability of the theory to show how a series of fundamental but seemingly disconnected processes are really expressions of the same underlying process. This theory shows the common underlying symmetry and enables the unifying of  the four most important processes of brain and mind. They are, 1./ The process by which brain come into being through the binary diverging process of cell division. 2./ The process by which brains laterally connect up with the always binary bifurcating branching of axons and dendrites. 3./ The process by which these laterally conjugated structures are chained in time using our temporal binary trees to encode and express behaviours and thoughts; finally 4./ The process by which these spatial/temporal representations evolve in binary combinatorial space. All of these 4 process are really expressions of the same underlying recursive process. With the right way to see and a little insight then we will come to realize that they are all really doing the same thing. This is what we’ll be explaining in this chapter.

So how do we go about explaining that all the seeming myriad complex processes of brain and mind, at all levels and all scales, actually reduce to a single underlying process and unitary recursive description? We do this by first listing what all the component processes of the brain are and show that they are happen all over the brain and at various scales of consideration. That is, to show that the processes of the brain are symmetrical and self-similar. Next we encode these process using our binary language. We completely describe these processes in terms of the language of binary trees and binary combinatorial codes. To give these processes a positioning to perform their function, we place these processes within our all encompassing top-down hierarchy of context and containment which is of course also binary coded. And we specify their spatial and temporal relationships with each other also using our binary language. If we were able to fully describe the structures of  brain and mind and their hierarchical arrangement, using our binary formalism, then naturally we do exactly the same thing with the processes of brain and mind. We shall see later that this leads to important insights that would be difficult to obtain without our having geometrized the problem and found the most suitable formalism for describing the problem at hand, i.e. understanding the brain and mind.

The component symmetrical and self-similar processes of the brain

 Here we describe what are the most basic and most of the important recurring processes of the brain that are necessary for explaining what is happening in the brain overall, and what is the process of mind. They are, 1./ competing, 3./ conjugating, 3./ sensing, 4./ doing. The last two processes recognizing and reconstructing join up to give rise to two further processes and they are  5./ Mapping and 6./ Intersecting, which both involving a recognizing as well as a reconstructive aspect. We’ll go through each of these processes in turn, describe what they are and how they’re occurring in the brain. Initially our analysis will proceed by analogy but later on we give everything a more definite and formal interpretation.

Starting with the process of competition, this is something that occurs all over the brain in various ways, shapes and forms. So for instance at the molecular level, neurotransmitters compete with other to bind onto receptors. This mechanism is critically involved in the great majority of transmission of signals around the brain. And then synapses will compete with one another along a microscopic patch of dendrite to form connections with the receiving neuron. We know that neurons will compete with one another for nerve growth factors NGF or neurotrophic factors NTP. Like firms competing for business, profits and money to prosperous and strong. So, neurons likewise compete for NGFs and NTFs to stay alive and grow more robustly. Those neurons which lose out in this process, shrivel and even die out completely.

As described early the neocortex is made up of columns. We know that these columns are grouped into competing and mutually inhibiting clusters where each column might represent a variable form of some feature. An example would best illustrate this idea. So for instance in the primary visual cortex we tight clusters of columns which will each represent a bar of light at a slightly different orientation projected onto a particular small patch of the retina. And each of these bar detectors will try to register the bar of light it represents and suppress all of its neighbours in an active inhibitory process. So a bar of light or edge falling on that patch of retina will most strongly activate its corresponding bar detector column which would ‘win’ the competition and fire its signal strongly while suppressing the activity of competing columns. This lateral competition process between columns seems to happen all over the neocortex.

This process of competition also takes place in our minds at the level of entire perceptions. The sensory input from our eyes will give rise to competing interpretations. And in binocular rivalry experiments, two different visual inputs projected to the eyes will not be perceived as a mix of the two images but rather alternate between one of the two. And in a sense, whenever we make a decision then this is like a process of competition. Sometimes it seems as if things are competing for our attention. From monkey experiments, this may be literally true. Several different stimuli attended to in different areas of the monkeys visual field will activate different areas of the lateral intraparietal cortex. The winning area with the highest activity level will correspond to and predict where the monkey fixates its attention. Also our moods seem to compete, i.e. is the glass half full or is it half empty.

Our next component and fundamental brain process is that of conjugation or the process of conjoining the elements that make up our brain in every increasing scales of complexity. So at the neuronal scale, different synapses transferring information from different neurons will join up along a stretch of dendrites. Neurons join up with one another locally and also across far flung regions of the brain. We also know that the micro features of perception join together to form more complex features and which in turn amalgamate to form representations of our sensory world. Also thoughts and behaviours join up over time to form temporal chains of representations. And so on to every higher levels of complexity and extent. Our brains are one massive interconnected web and so too it is with the emergent structures of mind. This compositing, conjugating and chunking process of the brain would be the mechanism by which our thoughts, behaviours, memories, skills and the sum total of our entire knowledge webs would be constructed. And this process occurs at all scales and all over.

Our third and fourth basic and fundamental processes of the brain we’ll discuss together because they’re complementary  intuitively easy to understand and explain using analogy. Essentially the process of sensing and doing corresponds with how we normally understand these terms. Instead of say ‘sensing and doing’ we could equally have called these processes perceiving and acting or recognizing and reconstructing. If we consider a neuron then it is intuitively easy make the analogy that, the dendrites of a neuron receiving all the signals from other neurons, is involved in a process that is akin to sensing as we normally understand it. As we sense with our eyes and ears, so a neuron senses with it synapses all the input signals from other cells. And at the other end the action potential or signal spike emanating from near the neuron’s cell body and transmitting outwards to other neurons is intuitively easy to imagine as the action side or ‘doing’ side of the neuron. And this same way of looking at things can also be applied to a neocortical column, or cortical patch and even the entire brain, with their sensing side receiving signals and funnelling them towards the themselves versus their doing side triggering signals and emanating them outwards to other brain components. This corresponds to the inflow and outflow pattern of organization that we described in an early section was occurring all over the brain and at all scales, including at the level of the entire brain. And where we likened the inflow to the roots of a tree and the outflow to the branches and leaves. So the inflow would correspond with this process of sensing, perceiving or recognizing, whereas the outflow would be that of doing, acting or reconstructing. So seen in this way, if we interpreted this ubiquitous inflow and outflow pattern as sensing and doing, then this process of sensing and doing would likewise be ubiquitous throughout the brain and at all scales.

This tree-like inflow and inflow pattern as a basic orangis something we discuss

8hw Capture.JPG

8p D Bayes.jpg

Recursive-Self-Modification.jpg

The Polar Frontal Cortex

In this section we discuss a very important region of the human brain called the polar frontal cortex. It can be argued that it is this region which gives human intelligence those critical qualities over and above that of animals, including the great apes and cetaceans. It is the difference in human brain anatomy that makes all the difference and we’ll be explaining why. In doing so we are also able to gain valuable insights into what is the nature of intelligence and human thought.

Below is a diagram depicting where polar frontal cortex is located in the brain. In the diagram below left, we have a drawing of a monkey brain and the polar frontal cortex is colored orange and is located right at the front, i.e. the frontal pole of the brain, hence its name. It occupies exactly the same area as Brodmann area 10 and the terms polar frontal cortex and BA10 can be used quite interchangeably. The next two diagrams along to the right, depict the polar frontal region of the human brain also colored in orange, but showing its ventral (looking up) and medial aspects (i.e. the inside view if we split the left & right halves of the brain).

polar frontal 1.jpgpolar frontal 2.jpg

In the absolute and relative size of the polar frontal cortex we find major differences between humans on the one hand and on the other hand apes and monkeys. It was thought for a long time that the entire prefrontal cortex overall was proportionally larger in humans than in animals but this is not as clear as once thought. However the relative size of the polar frontal cortex and regions which have the characteristics of Area BA10 are definitely greatly enlarged in human beings relative to animals. Generally speaking the polar frontal cortex in the human brain has a greater absolute size than most other higher animals but more significantly represents a far greater proportion of total brain mass than any other animal without exception.

It is important to note that even though both monkey or ape brains and human brains have a polar frontal cortex in the sense they have a front most part of the brain, the underlying architecture and functioning of the corresponding areas is very different. Recent research indicates that the polar frontal cortex of marmoset monkeys is more similar in structure and connectivity pattern to parts of the human brain more to the back of the prefrontal cortex, i.e. lower down the hierarchy. Similar results have been obtained from studies of macaque monkeys. It appears that the polar frontal cortex as it exists in humans may be a quite unique adaptation that is not found in other animals. If the prefrontal cortex may be conceptualized as a top-down hierarchy running front to back, then it seems that humans have one or two extra levels in this hierarchy that is absent in the rest of the animal kingdom. We’ll explain why this gives us such a critical edge and also cognitive abilities that are qualitatively different from even the great apes who are our closest evolutionary relatives.

Given these anatomical differences between the polar frontal cortex of humans and animals we next ask what is this part of the brain doing? The answer to this question regarding the functioning of the polar frontal cortex in humans have only fairly recently come about through brain scanning studies using fMRI (functional magnetic resonance imaging) technology. The diagram below represents the findings of a meta-study of over a 100 separate brain scanning studies into the function of the human polar frontal cortex. By pooling the data from all these separate efforts it was discovered that it is the ability to multi-task and juggle several concurrent activities which seems to be the critical role played by this brain region. This is marked in green in the diagram which reflects that the polar frontal cortex would generally ‘light up’ the fMRI scanner when the test subjects were asked to perform operations that involved an element of multi-tasking to it.

9e Polar Frontal Cortex Scans Composite.jpg

Other studies and theoretical lines of inquiry have suggested that the critical function performed by the polar frontal cortex is complex branching, recursive thinking and behaviour. This would fit in nicely within the context of a recursive brain theory. In fact the two concepts of multi-tasking and recursive thinking are actually tightly interrelated and can be conceptualized as both being the manifestations of a common underlying mechanism. This is where we may draw direct parallel betweens brains and computers. By considering how computers perform multi-tasking and recursive processing we are also able to explain how this may occur in brains. We’ll even show this interpretation is supported by underlying patterns of connectivity and the architectural plan of the brain. So we need to explain how computers implement multi-tasking and recursion and relate this to how humans may likewise perform the same function.

When a computer multi-tasks then generally it is not really doing two or more things at once, rather it does one thing at a time and quickly switches between the different tasks. Of course this would not apply to multi-processor or parallel computers which do simultaneously process many things at the same time. However in order to explain multiprocessing and recursion in the brain, limiting ourselves to talking about single processor computers or CPUs is more appropriate because we only have one brain. We are currently trying to explain the operation of single brains in isolation. So continuing with our single core or microprocessor computer then the way it would multi-task can only be to keep swapping between the different tasks but in order to do this it needs to maintain information about the tasks which it has put on hold, pending its next turn to get processed. It has to store the system state of the task so that it may stop it, carry out another task, and then later return to the original one. It does this by putting all the information relating to the current state of any task onto what is called a stack which is a kind of memory store. Later it will take the information off the stack when it wants to resume the task so it can carry on where it left off. Computer people talk about pushing information onto the stack and popping if off again later. And like the stacks of trays or chairs we normally deal with, the computer stack operates on a last in, first out, or first in last out principle, i.e. things can only be placed or taken off the top of the stack. This is a constraint that our biological brain stacks may not have to strictly obey however. Nonetheless when we multi-task it will generally involve having the temporally store the details of one task as we switch to another, and in turn store the details of that task if we then switched to a third. And correspondingly we would have to recall the details of the various tasks as we returned to them to carry on where we left off.

This operation of placing system state or the information associated with a task onto the stack is also what happens when a computer performs recursive processing and executes recursive functions. To illustrate how recursive processing works in computers we can use an analogy, i.e. we’ll describe a recursively nested set of human activities. This is a pretty contrived example and is not supposed to be totally realistic. So for instance we might be watching a video at home and then realize that we’re really hungry, too hungry to go on watching. So we freeze the video and store the state of that activity in our memories, i.e. where we were in the movie and what had already happened in it onto our mental stack. We proceed to leave the house to get food. We realize we need money so we go into the sub task of going to the cash machine remembering that we are on a quest for food. We go to the cash machine then go into the subtask of entering our PIN or pass code. We get the money. We pop out of the subtask of getting the money and return to the task of getting food from the shop which we’ve remembered. We goto the shop, get the food, eat it then pop out of that task to return to the house and load back into our heads all the details of the movie we were previously watching. We finish watching the movie and then go on with rest of our lives. This a set of activities with a nested recursive structure, each sub-task recursively branching from an overall enclosing task which is in turn enclosed within the overall context of our lives. And if this human form of recursion involves pushing and popping information onto and off a memory store, then this is exactly what happens when computers handle recursive functions. As the computer central processor comes to deal with each branching sub-task then it stores the details of the current task and which is the enclosing context of the new sub-task onto its stack or memory store. The main difference is the strict ordering in how bits of information may be placed or removed in the case of computers and also in the branching depth, which relates to the number of system states that may be placed onto the memory stack. Computers can handle recursive processing involving many millions even billions of branching sub-tasks, a human obvious cannot do this and is challenged to handle much more than several multi-tasks or levels of recursion.

When we examine the major connections of the polar frontal cortex then we discover that is tightly interconnected with exactly those brain areas which would enable it to implement this stack memory ability in order for it to accomplish multi-tasking and recursive thinking. The diagrams below, which come from monkey studies, show the major pathways emanating from the polar frontal cortex. We know from human DTI (diffusion tensor imaging) studies that corresponding pathways exist in humans only they are much thicker but connect to analogous areas. These areas happen to be closely related to memory and semantic functions in human being. So for instance in the diagram below left, these connections link the polar frontal cortex to the superior temporal cortex and temporal pole which in humans mediate higher level language and semantic processing. This would enable the workings of the polar frontal cortex to be symbolized and described in the inner dialogue of our mind speak, that is us talking to ourselves. The diagram below right show the connections to areas of the brain closely associated with memory storage and retrieval i.e. the area marked Pro in the diagram represents the Proisocortex which feeds into the hippocampus and at the end of the yellow connection, the area marked Rsp or Retrosplenial cortex is heavily implicated in memory retrieval. The connections to the Amygdala marked AMG, would presumably enable the representations of the polar frontal cortex to be given emotional salience. So in order to perform its multitasking and role in recursive thinking, the polar frontal cortex is interconnected with precisely those brain areas which would give it the memory stack facility analogous to the sort used by computers when they perform the same sorts of processing.

9i PolarFrontal to TemporalLobe.JPG9g PolarFrontal to RetroSplenial Etc.JPG

It is as if the polar frontal cortex would be able to register the system state of the brain, represent this overview and then store this into memory. Later on reading off what it stored earlier and to bring it back into the focus and attention of mind. But what exactly would the polar frontal cortex be representing and what would it be pushing onto the stack. The answer to this question is found by consider the special location of the polar frontal cortex. It sits at the at the top of a pyramid consisting of all the top-down hierarchies of the cognitive and motor frontal cortex which as explained earlier are interleaved with the posterior sensory hierarchies. So effectively it sits above all the centres of thinking, movement and sensing, though it is lower down the overall hierarchy than the emotion centres. We can imagine at the lowest level of the sensory hierarchy, the primary visual cortex say, the ability of a column to represent a bar of light, at a particular orientation projected on a certain part of the retina. This would be a very simple and localized integration of spatial information i.e. points of light. We can also imagine higher up the hierarchy how these simple primitive features of perception may in turn form more complex features which in turn form objects, and onto complex scenes and an entire flow of recallable memory, say the ability to go through the days events as when we keep a detailed diary and at the end of each day offload from memory the day events into it. If we continue this line of thinking to also consider our actions and thoughts and how they likewise may be moved higher and higher up a corresponding hierarchy to become grouped into ever more complex constructs then we eventually end up in polar frontal cortex which would be in a position to group together the overarching composite constructs of our thoughts and senses. In the same way a simple bar detecting neuron in the primary visual cortex integrates the positions of points of light to represent and detect bars of light; so it is that the polar frontal cortex will be performing this same role across the entire brain and all its representations, by virtue of its sitting at the very top of the all encompassing representational hierarchy. Pyramidal neurons in the polar frontal cortex have the widest branching dendrites with the most synapses in number and concentration in the entire brain, which would underlie its great integrating function.

So as a visual neuron represents a bar of light with its limited overview of a small area of the visual cortex, so in the same way the polar frontal cortex can in a sense represent an overview of the entire brain, symbolize it with its connections to the language and semantic processing areas of the superior temporal lobe and then store this representation on to its memory stack. By keeping a pointer or reference to this memory then it will be able to reload it, after one or a series of recursive subtasks or multi-tasks have been completed. So the polar frontal cortex due firstly to it special strategic positive at the very apex of the representational, motor and cognitive pyramid, also secondly to its connections with centres of language and memory; is thus able to give the brain and mind the very important and powerful facility of recursive branching thinking processes or behaviour and also the ability to smoothly multi-task. Something which is obviously a vital component of human intelligence and something we take for granted. These are also things that animals either are incapable of or either perform in a very limited way.

However there are a host of other very important mental abilities which the polar frontal cortex enables, and a whole set of tricks which makes intelligence what it is. Without these abilities then a person or an artificial intelligence would seem a bit lacking in intelligence. This would mean a subset of low functioning humans but all AI as it exists today. These other special abilities that the polar frontal cortex enables include, recursive language processing, recursive spatial mapping,  recursive self reflection and social thinking, reflective decision making and recursive self modification. How does all this come about? All of these abilities come about and are underpinned by that crucial ability to represent states of mind, tokenize or symbolize these representations and then store them away for later access. And all of these abilities may be mapped to the special position the polar frontal cortex has to all of the respective brain areas in the prefrontal cortex which are know to handle these functions. That is, it sits on the top of the respective tops of all the various cortical hierarchies which process language, spatial mapping, cognition also our sense of self and the social dimension. It sits at the very top of this converging nexus and integrates the highest and most abstract representations involved with all these various aspects of mind. So it is in a unique position to play these very special roles which we’ll be explaining next.

We’ll start by explaining what may be called cognitive recursion. We have used earlier on, the computer analogy of putting system state onto a stack. In the case of the brain, system state would be a state of mind and all the things we happen to be thinking about at any one time. This would also correspond to short term memory. And we proposed that we could represent this mental system state and store it away temporarily while we focus on a whole other set of thoughts or tasks. So in this way we would be doing multi-tasking and recursive thinking in a way directly analogous to how this is implemented in single processor computers. However there are things which we may do with this representation of mental system state which goes beyond simply pushing it onto the memory stack and then popping it off again as we would when doing simple recursive thinking or multitasking. Once we represent our thoughts and mind states then we may look into the memory stack and analyze those representations. We may manipulate those representations and modify them. And we may also join up those representations of mind states with other such representations. If we can represent ourselves thinking and store that representation. It means I can then look at that representation and think about it, i.e. I can think about myself thinking. If I then also represent that mind state and likewise put it on my memory stack, then I would be able to think about myself thinking about myself thinking; and so on and so forth to ever higher orders of self analysis. This useful ability has been referred to as ‘jumping out’ of the system by artificial intelligence research Douglas Hofstadter and he cites it as an ability which is lacking in current AIs. Future artificial intelligences will have artificial polar frontal cortices.

Furthermore with these representations of mind system state stored on my memory stacks, I can not only think about them, I could also modify them and make alterations to these representations. Which means I may not only think about myself thinking, but also modify the representation of myself thinking, then reflect on that modification. I can change the way I think then reflect on those changes and perhaps make further modifications. I can then perhaps make further changes together with another round of reflection and carry on this process repeatedly i.e. recursive self modification. Or perhaps I might make some decision and work through in my mind a simulation of the implications of that decision or course of action. I could store this analysis and then make a modification to the original decision and likewise do the same thing again; and recursively again and again. Then I could compare all the various outcomes I went through in my head in order to decide which decision or modification is best. In this way the polar frontal cortex would be playing a vital role in the process called reflective decision making. This is an important aspect of intelligence which AI researchers have identified and marked out as important but about which they are unclear as to how to proceed in creating it in machines.

 Another facility which comes about quite naturally from these extra manipulations and processing of the memory stack would be the ability to process language recursively and create fully recursive linguistic constructs to arbitrary levels of complexity depending on our memory stack ability, which will be slightly different for different people. This something which really distinguishes human language from that of other animals even the higher apes. Our closest relatives i.e. chimpanzees are not really capable of doing this recursive trick with language. It is believed that bonobo chimpanzees, which are like a variety of super chimp, possess the faint rudimentary beginnings of this ability which even most low intelligence humans do with relative ease. So in the brain this ability would work something like this. Once we have a sentence in mind then using our polar frontal memory stack ability, we would be able to store this away. We could then process another sentence and then attach the original sentence to it as a sub-sentence. And we could carry on this process creating language constructs of ever greater complexity.  When it comes to the processing of language, we may process linguistic structures, store these on the stack and then recursively process sub-structures in much the same way that we would organize our recursive behaviours using our memory stack.

We could do the same thing with our spatial maps of the world as we navigate through reality. In the same way that our linguistic constructs are recursive and hierarchical, the same could be meaningfully said for our representations of physical reality, space and our environments. In the same way sentences recursively branch off from other sentences or are recursively nested within one another the same could be said of the places we represent in our minds. Rooms branch off from corridors, which are nested the floors of buildings, which in turn branch of from streets, which form the network of streets of a city, connected by motorways, nested in countries etc. etc. Also there is another powerful way that comparison of recursive linguistic processing and recursive spatial mapping would be most appropriate. This is because we earlier show that both of these important aspects of the functioning of mind, may both we coded using our binary tree language. In the case of language this is more obvious, but we also showed based on empirical evidence that all the various types of spatial mapping, i.e. allocentric, egocentric and topographic may likewise be represented using binary trees. Therefore the notion that the polar frontal may be using a common mechanism to implement recursive processing and representation of language and spatial mapping would make intuitive sense.

There another area in which recursive thinking would come in useful and that is in the social realm and also in the ability to reflect upon ourselves, our lives and the state we’re in. Caltech neuroscientist John Allman has proposed this to be the central function of the polar frontal cortex and that it is this social thinking which has propelled its evolution and expansion in relative size. No doubt we do spend a lot of time thinking about ourselves, and other people. We also spend a lot of time thinking about ourselves in relation to other people and other people in relation to other people. This important social cognition would likewise make heavy use of the polar frontal cortex as we store our intermediate social deliberations onto the memory stack, then compare or combine these with other social deliberations. So for instance so we size ourselves up,  size up other people and then make a comparison between ourselves and these other people etc. Also we may keep a tally of various associations regarding other people and also ourselves, store this composite representation on our memory stack, make modifications to it and then reflect on it. Then recursively make further modifications and cross comparisons and so on.

So far we have been explaining the recursive role of the polar frontal cortex with respect to some of the separated and various major aspects of mind, i.e. language, spatial mapping, higher cognition and social thinking. However the real power of recursive thinking and the polar frontal cortex comes into play when we combine all these separate modes together and then consider them together as composite representations, but then process potentially all the recursive combinations and permutations of these aspects of mind.

Perhaps the most important example of this is that though we talked earlier about cognitive, linguistic and spatial mapping recursion separately from one another; in reality they are tightly interrelated and work closely together. Obviously our cognition has a major language element to it, after all we internally verbalize our thoughts. Also our reasoning often involves mental manipulations of spatial relationships. And also we verbalize space and time, and we even spatialize language. These words you’re reading represents language spatialized. Sometimes we may use this ability to help in our language construction and reasoning, i.e. writing things out on a piece of paper and thinking about it. The use of space in relation to language or symbols is also important in mathematical reasoning, where we sometimes visualize equations and formulae in our heads. The ability to utilize cross modal recursive processing combining these facilities would underlie much of our cognitive abilities.

Another  example of this sort of synergistic recursive thinking, is that not only do we think about ourselves and other people, but we may also think about what we’re thinking and also what other people may be thinking as well, i.e. their cognitive processes. And we can think about what other people would be thinking if they knew what we were thinking. And then go on to think about what we’d think about that. We may also place our social thinking within the representation of physical contexts and spatial maps. i.e. and then place ourselves and other people in these imagined contexts and then contemplate how we would feel and how we would act. And we could imagine all the different things we might say. And we could imagine the consequences of certains actions or word we might take or say in these circumstances and think about the outcome and what people would think as a result. We could then recursively consider various modified scenarios involves different actions, sentences, different people and different physical circumstances and think about all the various outcomes. We could also think about how we would think in these different circumstances and how we would feel and what other would think and feel etc. etc.

There would be an infinity of possibilities of complex recursive thought involving all the combinations and permutations of people, actions, words, physical circumstances, feelings and intentions and these would be all the things that the polar frontal cortex may potentially be processing. This would give brains a quantum leap in ability over and above what would be the case if this ability did not fully exist. I believe this is really the critical ability that humans have in their mental abilities over that of animals and is a central aspect of the operation of our minds. It is the ability that allows for introspection and self reflection. It is the facility which gives the mind its tremendous power and flexibility. This function of the polar frontal cortex is to effective make the entire brain a fully recursive computer architecture. Because this ability to represent the whole brain and store its system state would effectively enable the recursive process to happen over entire brain states and the all the representations contained within them. Within the context of this symmetry, self-similarity and recursive brain theory where functioning of the component processes of the entire brain is recursive throughout then this polar frontal whole brain recursion is the natural extension of our fully recursive computing architecture. So if we accept there is something fundamental in our unifying underlying recursive algorithm then this polar frontal whole brain recursion we’ve been discussing, makes this recursive algorithm complete. Then by the same token the evolution of this critical and unique part of the human brain is the step which has made our intelligence complete.

The Brain Theory in relation to the ‘Easy’ Problem of Consciousness

This symmetry, self similarity and recursivity brain theory, due to it’s ability bring together so much empirical data about the brain, its anatomy and its function; has the very interesting property of being able to correspondingly bring together most of the popular theories proposed as solution to the ‘easy’ problem of consciousness. Many different ideas relating to the brains functioning and its anatomy have been put forward as candidates for the neural correlates of first person subjective states. The list below includes probably most of the main contenders. The brain theory is able to integrate all of these separate views into one seamless composite. All of these proposals are really different aspects of the brain theory.

FBT-&-Easy-problem-of-Consciousness.jpg

So starting with idea that somehow hierarchical systems and organization is important for understanding consciousness, what we have in the brain theory is the neural substrate and also the emergent structures of mind described in the same language and forming a single all encompassing hierarchical top-down structure. So if it is believed that hierarchical organization has something useful to say about the problem of consciousness then the brain theory would fit in completely with this approach. Interestingly the brain theory is able to integrate the functioning of the striatum and cerebellum within this top-down hierarchy of brain and mind. This is important because these structures are heavily involved with the process of the automatization of behaviour and thought. And this is most relevant because we are conscious of our behaviours and actions before they become automatized. But once they are automatized then we perform them completely unconsciously. So for instance when we first learn to drive a car then we are most aware and fully conscious of all the exact ways to move the controls, but with experience all these skills become automatized and we are no longer conscious of them. Unless we choose to focus on them of course. The brain theory shows how the cerebellum working in conjunction with the striatum is able to form a completely self contained self controlled little loop of activity over a section of the overall brain hierarchy, which may complete some sequence of actions without any guidance from parts of the brain higher up the hierarchy. Hence we have an automatized behaviour that doesn’t require top-down coordinate signals but also one which doesn’t send back bottom-up signals for registering in consciousness.

This completely hierarchical nature of the brain theory and overall description of how the neural substrate relates to mind really subsumes existing ideas of a cognitive global workspace and neuronal gestalts and grounds them in actual physiology and anatomy. It really describes the hierarchical nested structuring of the global workspace and proposes too that all neuronal gestalts are likewise hierarchically organized. This also relates to the idea of structural coherence which sees a connection between the geometry of conscious perception and that of the neural substrate. The formalism in which the brain theory is expressed, i.e binary trees and binary combinatorial codes, uses binary trees to direct map and represent euclidean space. It is then able to completely specify topographic maps and the features contained in them. Also the notion of egocentric mapping and also allocentric mapping is completely integrated into the brain theory and likewise expressed in the language of binary trees. This way of looking at the various kinds of spatial mapping is supported by a lot of empirical evidence as discussed earlier. This would give the notion of structural coherence a firm physiological grounding, and effective integrate this idea as relates to explaining consciousness.

Next we consider the idea of recurrent loops, which in one form or another has been put forward as a neural correlate of consciousness by thinkers such as Gerald Edelman, Paul Churchland and Eric Harth. Recurrent feedback loops exist all over the brain and the entire brain can be thought of as one all encompassing recursive loop. This ubiquitous self reference is an integral part of the brain theory and at all scales and levels. Specifically the theory describes how these recurrent loops can be used to represent time and store sequence memories. The theory fits all these recurrent loops into a single top-down hierarchy which not only describes the physical nesting brain structure but also how recurrent loops can be nested within recurrent loops, acting like wheels within wheels. As earlier described, with the action of the striatum and cerebellum automatizing behaviour and making it unconscious, then this can be seen as some of the nested recurrent loops spinning off on their own and acting autonomously.

A popular proposal for the neural correlate of consciousness is the idea of phase locked brain waves and in particular the approximately 40 hertz gamma wave. For instance this was proposed by Francis Crick of DNA fame and his collaborator Christof Koch. A similar 40 htz proposal was also put forward by Rodolfo Llinas. Nested brain waves grouped together in octave bands are an integral part of how much of the brain functions and a necessary mechanism for discretizing time and synchronizing the coordinated activity of different brain regions. This doubling pattern and nesting of brain waves is mapped to binary trees which represent time in the brain theory. The nodes of these temporal binary trees bind together gestalts of simultaneously active representations or features  in the brain and which will correspond to the peaks of phase locked brain waves. It is also suggested by the brain theory that the 40 hertz gamma is an important temporal resolution baseline, which is grouped by lower frequency brain waves in multiples of octaves.

This binary discretization of time as well as the complete binary discretization of space in the brain theory allows it to totally accommodate our next often cited proposal for solving the problem of consciousness, i.e. the notion that information theory somehow gives us the necessary bridging concept for relating qualia to the physical substrate of the brain. This a view put forward by the philosopher David Chalmers who is credited with emphasizing the idea that there is an ‘easy’ and ‘hard’ problem of consciousness. i.e. the ‘easy’ problem of finding the neural correlates of consciousness, versus the ‘hard’ problem of why those neural correlates should give rise to qualia and subjective states. He thinks that information has aspects which are both physical and ‘phenomenal’. He proposes that information has a dual aspect which may somehow include consciousness as an intrinsic property of an extended view of physical reality. He also acknowledges that his ideas are tentative. Whether this idea has any significance or not, nonetheless the brain theory is able to integrate this idea into its composite account of brain and consciousness. This is because the brain theory is totally expressed in the language of binary trees and binary combinatorial codes which is really the language of information theory, so the idea that somehow consciousness may relate to information theory, is completely captured by this central aspect of the brain theory.

Also while the brain theory deals with normal binary bits and binary combinatorial codes, it is very easy to adapt the theory to accommodate ‘qbits’ i.e. quantum bits and also quantum superposed combinatorial codes. The brain theory goes hand in hand with its implementation on digital computers for it is expressed in the same binary language as our computing inventions and computer codes are specified. The theory also goes hand in hand with its being implemented one day on quantum computers. At least in part. It is believed by some that the brain is capable in special instances of performing as a quantum computer. The mysteries of quantum mechanics, its seeming incompatibility with materialist or physicalist assumptions and strange properties have been proposed as the key to understanding consciousness. The expression of the brain theory in the language of information theory, binary trees and binary combinatorial spaces, and the seamless interface between quantum information and normal information it provides; allows the theory to fully integrate with these quantum physical approaches to understanding consciousness. It does so in a way that abstracts away much of the potentially obfuscating complexity. A lot of the fine details of quantum mechanics reduces to a description in terms of binary codes and qbits (quantum bits). It was the renowned physicist John Wheeler who coined the remark ‘it from bit’, which distilled the idea that all physics including quantum mechanics is ultimately reducible to a set of yes or no questions. The brain theory shows that all brain and mind ultimately reduces to a long serialized chain of yes and no questions.

The idea of the brain as quantum computer is closely associated with idea that the neuronal cytoskeleton and microtubule network that makes up a large part of it, is acting as computing machinery and augmenting the information processing capabilities of neurons as normally understood. The completely binary and discrete nature of the brain theory together with  its expression in the very basic and fundamental concepts of mapping and correlation or convolution (i.e. lock and key), allows it to perfectly interpolate into the microcosm of the cytoskeleton of neurons. If the brain theory can be thought of as ‘fractal’ then the fractal doesn’t end with the cell membrane of neurons, but is able to encompass the finer scale fractal level of microtubules. Furthermore the language and very basic way that the brain theory is expressed also allows it to perfectly accommodate the idea of DNA acting as a computing device. Here the communication and mapping network would be the transmission medium of cytoplasm surrounding the DNA and the messenger signals would be non-coding RNA. With corresponding lock and key receptor regions of DNA, introns and exons, promoter regions, suppressor regions and so on. Once we fully express the idea of DNA and microtubule networks as computing machinery in the same language and concepts as the brain theory, then this opens up the very exciting prospect of showing how all the neurons and information processing cells in the brain together with the microtubules and the DNA in all of these cells; can all work together in a single all encompassing fractal computing architecture. Given its potentially quantum computer abilities, such architectures may have from time to time quantum coherent states that allow it to have extraordinary flashes of insight or the occasional inspired thought.

Another idea that was tentatively put forward by neurophysiologist William Calvin, is that it is the competitive processes found all over the brain and at all scales, i.e. darwinian competition, which could be the neural correlate of consciousness. This is related to Gerald Edelman’s idea of neural darwinism who has claimed that his theory ‘explains’ consciousness. This idea of evolution happening in the brain, is probably one instance where research in theoretical neuroscience, philosophy and artificial intelligence gets it right in thinking about the mind though perhaps not with respect to consciousness. This idea that the process of evolution is happening in the brain and mind. In AI this is manifest as the study of genetic algorithms and evolutionary programming. It is the epistemological idea of memes and already mentioned we have neural darwinism in neuroscience. This idea is intuitively appealing because we get a sense of the evolution of our thoughts and behaviours simply through introspection and also from observing others, especially babies and young children. That there should exist a corresponding evolutionary mechanism operating in the neural substrate to enable this observable evolution that seems to take place makes sense. As described earlier, the process of evolution is an inseparable and intrinsic part of the brain theory. And which it does in the most exquisite and integrated way, through a mode of operation of the unifying recursive algorithm. As described earlier these evolving explorations into binary combinatorial space are also accompanied by a competitive darwinian selection process. These evolving explorations are happening at all places and levels of the all encompassing top-down hierarchy, so that therefore the competitive selection process would correspondingly be all pervasive. This would allow the brain theory to fully incorporate the idea that somehow darwinian competition may give rise to consciousness.

So taken all together, with our unifying theory of brain and mind we may also unify a lot of, perhaps most of the main ideas suggested as solutions to the easy problem of consciousness. This integrated solution would surely serve as an augmented hybrid turbo charged souped up contender for answering the ‘easy’ problem of consciousness. But we may then ask ourselves would it have anything to say about the ‘hard’ problem of explaining why qualia should arise from these correlations. And the answer is no not matter how accurate or comprehensive our set of composite correlations. Even in this aggregated answer there is absolutely nothing to suggest why this conglomeration of significant brain properties and functionalities would give rise to first person subjective states and qualia.

But the hard problem is hard if not impossible because it rests on false and flawed assumptions. It makes the presupposition that consciousness and qualia necessary arise from or are caused by the brain. It derives from the common misconception that there are only two options for understanding consciousness. Which are commonly and mistakenly understood to be either, on the one hand what can be described pretty interchangeably as materialism or physicalism and on the other hand dualism, which supposes the first option in addition to some other irreducible ‘stuff’. This narrow and limited view of things ignores the other very sound and in contemporary times mostly forgotten ontological idea of Idealism. This is the notion that it is consciousness which is primary and the ground of all existence. A proposition that was believed to be the true state of things by many of the greatest minds all through out history, all over the world. It goes hand in hand with the idea that physical reality is somehow illusory. But how can a symmetry, self-similarity and recursivity brain theory completely and fully revive this ancient and most controversial ideas for the 21st century? If reality is illusory then how can we explain what is behind the illusion? How may we reduce everything to consciousness? How may this fractal brain theory setup the conditions for a dramatic return of the recurring heresy?

Bibliography

Frontal Lobes and Cerebral Cortex

Principles of Frontal Lobe Function, Second Edition - Eds. Donald T. Stuss & Robert T. Knight 2013

Principles of Frontal Lobe Function - Eds. Donald T. Stuss & Robert T. Knight 2002

The Frontal Lobes - Eds. Jarl Risberg & Jordan Grafman 2006

The Executive Brain - Elkhonon Goldberg 2001

The Genius Engine - Kathleen Stein 2007

The Prefrontal Cortex - Joaquin Fuster 1989

The Prefrontal Cortex, 4th Edition - Joaquin Fuster 2008

The Orbital Frontal Cortex - Eds. David H. Zald & Scott L. Rauch 2006

The Human Frontal Lobes - Eds. Bruce L. Miller & Jeffrey L. Cummings 2007

The Cerebral Cortex - Vernon B. Mountcastle 1999

Cortical Memory Functions - C.M. Fair 1992

Corticonics, Neural Circuits of the Cerebral Cortex - M. Abeles 1991

Cingulate Neurobiology and Disease - Brent Vogt 2009

The Hippocampus Book - Editors Anderson, Morris, Amaral, Bliss & O'Keefe 2007

Memory and Higher Functions

Concise Learning and Memory - John H. Byrne 2008

Memory - Alan J. Parkin 1993

Human Memory - Allan Baddeley 1990

Memory and Brain - Larry R. Squire 1987

Computational Neuroscience of Vision - Edmund T. Rolls & Gustavo Deco 2002

Mirrors in the Brain - Giacomo Rizzolatti & Corrado Sinigaglia 2006

Basal Ganglia, Cerebellum and Subcortical Structures

Subcortical Structures and Cognition - Leonard Koziol & Deborah Ely Budding 2010

Handbook of Basal Ganglia Structure and Function - Heinz Steiner and Kuei Y. Tseng 2010

Frontal-Subcortical circuits in Psychiatric and Neurological Disorders

- Eds David G. Lichter & Jeffrey L. Cummings 2001

A Theory of the Striatum - J. Wickens 1993

The Behavioural Neuroscience of the Septal Region - Ed. Robert Numan 2000

The Mesolimbic Dopamine System - Eds. P. Wilner & J. Scheel-Kruger 1991

Anatomy of Neuropsychiatry

- Lennart Heimer, Gary W. Van Hoesen, Michael Trimble & Daniel S. Zahm 2008

Exploring the Thalamus and its Role in Cortical Function - S. Murray Sherman and R.W.Guillery 2006

The Neural Basis of Motor Control - Vernon B. Brooks 1986

The Cerebellum and Adaptive Control - John S. Barlow 2002

The Amygdala - Ed. John P. Aggleton 1992

The Amygdala, 2nd Edition - Ed. John P. Aggleton 2000

The Human Amygdala - Paul J. Whalen and Elizabeth A. Phelps 2009

The Brain and Emotion - Edmund T. Rolls 1999

Textbooks and Encyclopedias

Encyclopedia of Neuroscience 3rd Ed - George Adelman and Barry H. Smith 2004

Encyclopedia of Neuroscience - Editor in Chief Larry R. Squire 2008

Principles of Cognitive Neuroscience - Ed. Dale Purves 2008

Neuroscience 4th Edition - Ed. Dale Purves 2008

The Students Guide to Cognitive Neuroscience - Jamie Ward 2006

Cognition, Brain and Consciousness: Introduction to Cognitive Neuroscience

- Eds. Bernard J. Baars & Nicole M. Gage 2007

Introducing Neuropsychology 2nd edition - John Stirling and Rebecca Elliot 2008

Physiology of Behaviour, Ninth Edition- Neil R. Carlson 2007

Physiology of Behaviour, 8th Edition - Neil R. Carlson 2004

Physiology of Behavior by Neil R. Carlson 1991

The Fundamentals of Human Neuropsychology 6th Edition - Bryan Kolb & Ian D. Whishaw 2008

Principles of Neural Science 4th Ed - Eric R. Kandel and James H. Schwartz and Thomas M. Jessell 2000

The Biology of Behaviour and Mind - Bruce Bridgeman 1988

The Human Brain, An Introduction to its Functional Anatomy 6th Edition - John Nolte 2008

The Synaptic Organization of the Brain - Gordon M. Shepherd 1990

Handbook of Brain Microcircuits - Gordon Shepard & Sten Grillner 2010

Functional Neuroanatomy - Adel K. Afifi & Ronald A. Bergman 2005

Atlas of Functional Neuroanatomy - Walter J. Hendelman 2006

Neurochemistry

Drugs and the Brain - Solomon Snyder 1986

Noradrenergic Neurons - Marianne Fillenz 1990

Neuronal Serotonin - Editors N. N. Osborne and M. Hamon 1988

Neural Activity and the Growth of the Brain - Dale Purves 1994

Body and Brain - Dale Purves 1990

Dopamine - Handbook of Chemical Neuroanatomy Vol 21 - Eds S. B. Dunnett, M. Bentivoglio, A. Bjorklund, T. Hokfelf 2005

Popular Neuroscience and Psychology Books

The Undiscovered Mind - John Horgan 1999

From Brains to Consciousness - Ed. Steven Rose 1998

Principles of Brain Evolution - Georg F. Streidter 2005

On Intelligence - Jeff Hawkins 2004

The 21st Century Brain - Steven Rose 2005

Rhythms of the Brain - Gyorgy Buzsaki 2006

Broca's Region - Editors Yosef Grodzinsky & Katrin Amunts 2006

The Universe Within - Morton Hunt 1983

Windows on the Mind - Erich Harth 1985

In the Palaces of Memory - George Johnson 1992

Secrets of Sleep - Alexander Borbley 1988

The Dreaming Brain - J. Allan Hobson 1990

Sleep - J. Allan Hobson 1995

Newton's Madness - Harold L. Klawans 1990

Toscanini's Fumble - Harold L. Klawans 1989

The Man Who Mistook His Wife For a Hat - Oliver Sacks 1985

Brain Washing - Kathleen Taylor 2004

The Computational Brain - Churchland and Sejnowski 1989

Computer Science and Artificial Intelligence

Artificial Intelligence - Patrick Winston 1992

Artificial Intelligence: A Modern Approach 3rd Ed - Peter Norvig and Stuart Russell 2010

Natural Computing - Dana

Algorithmics - David Harel

The Quest for Artificial Intelligence - Nils J. Nilsson 2010

Bio-Inspired Artificial Intelligence - Dario Floreano and Claudio Mattiussi 2008

Bioinformatics -Pierre Baldi and Soren Brunak 2001

Memory and the Computational Brain - C.R Gallistel and Adam Philip King 2010

Computer Vision and Image Processing - Dr Tim Morris 2003

The Singularity is Near - Ray Kurzweil 2005

How to Create a Mind - Ray Kurzweil 2013

The Brain Makers - Harvey Newquist 1994

Data Compression - Peter Symes

The Data Compression Book - Mark Nelson 1996

Data Compression Handbook 4th Ed - David Salomon 2007

Fractal Data Compression -

Digital Image Processing - Nick Efford

Parallel Distributed Processing - Vols I & II - Eds Jay Rumelhart & David McClelland

Cognizers - R. Colin Johnson and Chappell Brown 1988

Neurocomputing - Robert Hecht-Nielsen 1990

Studies in Geometry - Leonard M. Blumenthal and Karl Menger 1971

Sparse Distributed Memory - Pentti Kanerva 1988

Fuzzy Logic: Dan McNeill and Paul Freiberger (1 Apr 1994)

Speech Recognition : Theory and C++ Implementation - Lucio Ricotti and Lucio Prina Ricotti 1999

Artificial life - Ed. Chris Langton 1989

Artificial Life - Stephen Levy 1992

The Recursive Universe - William Poundstone 1985

Labyrinths of reason - William Poundstone 1988

Godel, Escher, Bach - Douglas R. Hofstadter 1979

The Fifth Generation - Edward Feigenbaum 1983

Out of their Minds - Dennis Shasha and Cathy Lazere 1995

The Connection Machine - Danny Hillis 1985

Advanced Computer Architectures - Dezso Sima, Terence Fountain, Peter Kacsuk 1997

The Creative Computer: Machine Intelligence & Human Knowledge - Donald Michie & Rory Johnston 1985

The New Turing Omnibus - A.K. DEWDNEY 2003

Beginning Logic - E. J. Lemmon 1971

Logic - Wilfred Hodges 2001

PROLOG Programming for Artificial Intelligence - Ivan Bratko 1988

Engines of Logic - Martin Davies 2000

Interfacing with C - Howard Hutchings 1995

Science and Mathematics

Symmetry - Ian Stewart 2007

From Cardinals to Chaos - N. G. Cooper, Roger Eckhardt and Nancy Shera 1989

The large, the small and the human mind - Roger Penrose 1997

The Emperor's new mind - Roger Penrose 1989

Evolution, The Grand Synthesis - Ervin Laszlo 1987

Introducing Mathematics - Sardar, Ravetz & Van Loon 1999

The Fabric of Reality - David Deutsch 1997

The Blind Watchmaker - Richard Dawkins 1986

The Web of Life - Fritjof Capra 1996

Chance and Chaos - David Ruelle 1991

Randomness - Deborah J. Bennett 1998

Introducing quantum theory - McEvoy & Zarate 1996

Information - Hans Christian von Baeyer 2003

Information and the internal structure of the Universe - Tom Stonier 1990

The Colors of Infinity - Various 2004

Fractal Geometry - Lesmoir-Gordon, Rood & Edney 2000

The Bit and the Pendulum - Tom Siegfried 2000

The Quantum Brain - Jeffery Satinover 2001

Introducing chaos - Sardar & Iwona 1998

Makers of Mathematics - Stuart Hollingdale 1989

Chaos under control - Peak & Frame 1994

Frontiers of Complexity - Coveney & Highfield 1995

Between inner space and outer space - John D. Barrow 1999

A Brief History of Time - Stephen Hawking 1988

The Universe in a nutshell - Stephen Hawking 2001

Small world - Mark Buchanan 2002

Complexity - Mitchell M. Waldrop 1992

Complexity - Roger Lewin 2001

Complexity - Melanie Mitchell 2009

The User Illusion - Tor Norretranders 1998

Chaos - James Gleick 1987

Searching for Certainty - John Casti 1992

The Broken Dice - Ivar Ekeland 1994

The New Quantum Universe - Anthony Hey and Patrick Walters 2003

The Trouble With Physics - Lee Smolin 2006

Who's afraid of Schrodinger's cat - Ian Marshall & Danah Zohar - 1997

Meta Maths, The Quest for Omega - Gregory Chaitin 2005

New Theories of Everything - John Barrow 2007

A Passion for Mathematics - Clifford A. Pickover 2005

The End of Time - Julian Barbour 1999

Endless Universe, Beyond the Big Bang - Paul J. Steinhardt & Neil Turok 2007

Deciphering the Cosmic Number - Arthur I. Miller 2009

Who got Einstein’s office? - Ed Regis 1988

Programming the Universe - Seth Lloyd 2007

Information and the Nature of Reality - Eds Paul Davis and Niels Henrik Gregersen 2010

The Mind of God - Paul Davies

The Evolution of Reason - William S. Cooper 2004

The Mystery of the Aleph - Amir D. Aczel 2000

Decoding the Universe - Charles Seife 2007

Relevant Neuroscience Papers

Efferent Association Pathways from the Rostral Prefrontal Cortex in the Macaque Monkey

Michael Petrides1,2 and Deepak N. Pandya - The Journal of Neuroscience, October 24, 2007

ANTERIOR PREFRONTAL CORTEX: INSIGHTS INTO FUNCTION FROM ANATOMY AND NEUROIMAGING

Narender Ramnani* and Adrian M.Owen - Nature Reviews Neuroscience 2004

Damage to the Fronto-Polar Cortex Is Associated with Impaired Multitasking

Jean-Claude Dreher¤a*, Etienne Koechlin¤b, Michael Tierney, Jordan Grafman*, 2008

The frontopolar cortex and human cognition. Evidence for a rostrocaudal hierarchical organization within the human prefrontal cortex - Kalina Christoff and John D. E. Gabrielli 2000

Two Phylogenetic Specializations in the Human Brain

JOHN ALLMAN, ATIYA HAKEEM, and KARLI WATSON 2002

The role of the rostral frontal cortex (area 10) in prospective memory: a lateral versus medial dissociation

Paul W. Burgess a,∗, Sophie K. Scott b, Christopher D. Frith c 2003

Is the rostro-caudal axis of the frontal lobe hierarchical?

David Badre*‡ & Mark D’Esposito - Nature Reviews Neuroscience 2009

Mechanisms of hierarchical reinforcement learning in corticostriatal circuits 1: Computational Analysis

Michael J. Frank David Badre 2009

The prefrontal cortex and flexible behavior

Helen Barbas1,2 and Basilis Zikopoulos - 2007

Causal role of the prefrontal cortex in top-down modulation of visual processing and working memory

Theodore P Zanto, Michael T Rubens, Arul Thangavel & Adam Gazzaley 2011

Sensory Pathways and Emotional Context for Action in Primate Prefrontal Cortex

Helen Barbas, Basilis Zikopoulos, and Clare Timbie 2010

Short frontal lobe connections of the human brain

Marco Catani a,1,*, Flavio Dell’Acqua a,b,c,1, Francesco Vergani d, Farah Malik a,

Harry Hodge a, Prasun Roy a, Romain Valabregue e and Michel Thiebaut de Schotten a - 2012

THE HUMAN ORBITOFRONTAL CORTEX: LINKING REWARD TO HEDONIC EXPERIENCE

Morten L. Kringelbach 2005 Nature Reviews Neuroscience

A new perspective on the role of the orbitofrontal cortex in adaptive behaviour

Geoffrey Schoenbaum, Matthew R. Roesch, Thomas A. Stalnaker and Yuji K. Takahashi - 2009 Nature Reviews Neuroscience

The Organization of Networks within the Orbital and Medial Prefrontal Cortex of Rats, Monkeys and Humans

 - D. Ongur and J.L. Price 2000

Differential role of the orbital frontal lobe in emotional versus cognitive perspective-taking

Catherine A. Hynes 1, Abigail A. Baird, Scott T. Grafton ∗2005

Orbital Versus Dorsolateral Prefrontal Cortex.

 Anatomical Insights into Content Versus Process Differentiation Models of the Prefrontal Cortex

DAVID H. ZALD 2007

CONTROL OF GOAL-DIRECTED AND STIMULUS-DRIVEN ATTENTION IN THE BRAIN

Maurizio Corbetta and Gordon L. Shulman 2002

Typologies of attentional networks

Amir Raz and Jason Buhle 2006

THE ROLE OF FIXATIONAL EYE MOVEMENTS IN VISUAL PERCEPTION

Susana Martinez-Conde*, Stephen L.Macknik* and David H.Hubel‡ 2004

A new neural framework for visuospatial processing

Dwight J. Kravitz*, Kadharbatcha S. Saleem‡, Chris I. Baker*and Mortimer Mishkin‡ 2011

A COMMON REFERENCE FRAME FOR MOVEMENT PLANS IN THE POSTERIOR PARIETAL CORTEX

Yale E. Cohen* and Richard A. Andersen‡ 2002

Layer-dependent attentional processing by top-down signals in a visual cortical microcircuit model

Nobuhiko Wagatsuma, Tobias C. Potjans, Markus Diesmann and Tomoki Fukai 2011

Top-Down Influences in Sensory Processing

Charles D. Gilbert1,* and Mariano Sigman1,2 - 2007

Functional role of the supplementary and pre-supplementary motor areas

Parashkev Nachev*‡, Christopher Kennard‡ and Masud Husain* 2008

The importance of being agranular: a comparative account of visual and motor cortex

Stewart Shipp* 2005

Structure and function of the cerebral cortex -

Stewart Shipp - 2007 Current Biology Vol 17 No 12

The anterior insula and human awareness

A. D. (Bud) Craig 2009

Pattern in the Laminar Origin of Corticocortical Connections - Helen Barbas 1986

Cortical Structure Predicts the Pattern of Corticocortical Connections - H. Barbas and N. Rempel-Clower 1997

Laminar Distribution of Neurons in Extrastriate Areas Projecting to Visual Areas V1 and V4 Correlates with the Hierarchical Rank and Indicates the Operation of a Distance Rule

Pascal Barone, Alexandre Batardiere, Kenneth Knoblauch, and Henry Kennedy 2000

Interlaminar Connections in the Neocortex Alex M. Thomson and A. Peter Bannister 2003

The Laminar Pattern of Connections between Prefrontal and Anterior Temporal Cortices in the Rhesus Monkey is Related to Cortical Structure and Function

 - Nancy L. Rempel-Clower and Helen Barbas 2000

Diversity of laminar connections linking periarcuate and lateral intraparietal areas depends on cortical structure

M. Medalla1 and H. Barbas1,2006

Laminar and modular organization of prefrontal projections to multiple thalamic nuclei

D Xiao2, B Zikopoulos1, and H Barbas - 2010

Thalamic Input to Distal Apical Dendrites in Neocortical Layer 1 Is Massive and Highly Convergent

Pablo Rubio-Garrido, Flor Pe´ rez-de-Manzo, Ce´ sar Porrero, Maria J. Galazo,  Francisco Clasca - 2009

What does the retrosplenial cortex do?

Seralynne D. Vann*, John P. Aggleton* and Eleanor A. Maguire‡ 2009

PRIMATE ANTERIOR CINGULATE CORTEX: WHERE MOTOR CONTROL, DRIVE AND COGNITION INTERFACE

Tomá˘s Paus 2001

PAIN AND EMOTION INTERACTIONS IN SUBREGIONS OF THE CINGULATE GYRUS

Brent A. Vogt 2005

The integration of negative affect, pain and cognitive control in the cingulate cortex

A. J. Shackman, Tim V. Salomons, Heleen A. Slagter, Andrew S. Fox, Jameel J. Winter, Richard J. Davidson 2001

Neural connections of the posteromedial cortex in the macaque

         Josef Parvizi*†, Gary W. Van Hoesen*‡, Joseph Buckwalter*‡, and Antonio Damasio*§ 2006

Quantitative Architecture Distinguishes Prefrontal Cortical Systems in the Rhesus Monkey

- S.M Dombrowski, C. C. Higetag and H. Barbas

NEW INSIGHTS INTO THE FUNCTIONS OF THE SUPERIOR TEMPORAL CORTEX

Hans-Otto Karnath 2001

Neuronal Oscillations in Cortical Networks

Gyo¨rgy Buzsa´ki1* and Andreas Draguhn2 2004

Synaptic mechanisms of synchronized gamma oscillations in inhibitory interneuron networks

Marlene Bartos*, Imre Vida‡ and Peter Jonas 2007

Layer-specific network oscillation and spatiotemporal receptive field in the visual cortex

Wenzhi Sun and Yang Dan1 2009

DYNAMIC PREDICTIONS: OSCILLATIONS AND SYNCHRONY IN TOP–DOWN PROCESSING

Andreas K. Engel*, Pascal Friesठand Wolf Singer|| 2001

THE BRAINWEB: PHASE SYNCHRONIZATION AND LARGE-SCALE INTEGRATION

Francisco Varela*, Jean-Philippe Lachaux*, Eugenio Rodriguez‡ and Jacques Martinerie* 2001

The role of phase synchronization in memory processes

Juergen Fell and Nikolai Axmacher 2011

Spectral fingerprints of large-scale neuronal interactions

         Markus Siegel1*, Tobias H. Donner2* and Andreas K. Engel - 2012

Dissociating the role of the medial and lateral anterior prefrontal cortex in human planning

Etienne Koechlin*†, Gregory Corrado*, Pietro Pietrini*, and Jordan Grafman*‡ 2000

The role of the basal ganglia in habit formation

Henry H. Yin* and Barbara J. Knowlton - 2006

Mechanisms of Hierarchical Reinforcement Learning in Cortico--Striatal Circuits 2: Evidence from fMRI

David Badre and Michael J. Frank - 2011

Frontal-striatal circuit functions: Context, sequence, and consequence

JEAN A. SAINT-CYR 2003

The temporal lobe is a target of output from the basal ganglia

FRANK A. MIDDLETON* AND PETER L. STRICK 1996

ROLE OF A LATERALIZED PARIETAL-BASAL GANGLIA CIRCUIT IN HIERARCHICAL PATTERN PERCEPTION: EVIDENCE FROM PARKINSON’S DISEASE

         Haline E. Schendan, Ph.D.1,3, Melissa M. Amick, Ph.D1,2, and Alice Cronin-Golomb, Ph.D.1 2009

Activity of striatal neurons reflects dynamic encoding and recoding of procedural memories

         Terra D. Barnes1*, Yasuo Kubota1*, Dan Hu1, Dezhe Z. Jin1,2 & Ann M. Graybiel - 2005

Subcortical loops through the basal ganglia

John G. McHaffie1, Terrence R. Stanford1, Barry E. Stein1, Ve´ ronique Coizet2 and Peter Redgrave2 2006

Behavioral Functions of the Mesolimbic Dopaminergic System: an Affective Neuroethological Perspective

Antonio Alcaro1,3, Robert Huber1, and Jaak Panksepp - 2007

Active perception: sensorimotor circuits as a cortical basis for language

Friedemann Pulvermüller and Luciano Fadiga - 2010

A parieto-frontal network for visual numerical information in the monkey

Andreas Nieder* and Earl K. Miller 2004

COUNTING ON NEURONS: THE NEUROBIOLOGY OF NUMERICAL COMPETENCE

Andreas Nieder 2005

INTERACTIONS BETWEEN NUMBER AND SPACE IN PARIETAL CORTEX

Edward M. Hubbard, Manuela Piazza, Philippe Pinel and Stanislas Dehaene - 2005

The representation of semantic knowledge in the human brain

Karalyn Patterson*, Peter J. Nestor‡ and Timothy T. Rogers - 2007

The cortical organization of speech processing

Gregory Hickok and David Poeppel - 2007

Two Types of Thalamocortical Projections from the Motor Thalamic Nuclei of the Rat: A Single Neuron-Tracing Study Using Viral Vectors

Eriko Kuramoto, Takahiro Furuta, Kouichi C. Nakamura, Tomo Unzai1, Hiroyuki Hioki, Takeshi Kaneko - 2009