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The Symmetry, Self-Similarity and Recursivity theory of Brain and Mind

This brain theory that is in the process of being revealed to world may also be given the longer title of, ‘The Symmetry, Self-Similarity and Recursivity theory of Brain and Mind’. This is quite an effort to say, and so it is a useful and convenient shorthand to refer to the theory as the ‘Fractal Brain Theory’. The word Fractal implies Symmetry, Self-Similarity and Recursivity so the title ‘Fractal Brain Theory’ is an entirely appropriate as well as useful shorthand. We’ll go through each of these foundational concepts in turn in order to give a better idea of the significance and power of the Fractal Brain Theory.

Symmetry

Symmetry is such an amazingly powerful idea. In fact if the entire process of science had to be summed up in a single word, then a good candidate for this word would be ‘symmetry’. Science can be said to be the process of discovering the patterns of nature and the Universe. But it is more than that, because science is also the process of discovering the patterns behind the patterns. That is, the meta-patterns and unifying patterns, which show us how all the seemingly separate patterns are really manifestations of the same underlying pattern. And so we have the same problem in the brain, where we are confronted with a dizzying and myriad array of facts and findings with no obvious and apparent way of seeing any overarching pattern behind it all. So it makes perfect sense that the idea of symmetry should be applicable. Indeed if symmetry is behind the very process of science itself, then why should the search for a scientific understanding of the brain be any other way? And so then the problem becomes, how to apply this powerful concept towards that goal and this is not at all obvious. The specific ways that the symmetries behind the law of physics are explored in science, don’t translate in any sort of direct or intuitive way to the study of the brain. The symmetry of mathematical equations or of regular geometric forms, seems far removed from the organic messiness and irregularities of biology and brain. And at first glance and superficial inspection, the brain seems so full of asymmetry and dissymmetry. So one of the problems that the fractal brain theory solves and is how to interpret the brain and mind, using some of the most cutting edge findings in neuroscience and some bridging ideas from mathematics, in order to see clearly the underlying and unifying symmetries behind it all. Physicist believe that there is an overarching ‘supersymmetry’ that unifies all the natural laws of the Universe, though this idea is still in the process of being fully worked out. By the same token, the Fractal Brain Theory is able show that likewise there is an overarching symmetry that is able to explain and account for all the diverse phenomena of brain and mind. With this underlying symmetry we are able to reduce all the vast complexities of the brain and mind into a very elegant and compact description. And so symmetry forms an important foundation of the brain theory.

Self-similarity

 

The idea of Self Similarity is synonymous with idea of something being ‘fractal’, hence the name Fractal Brain Theory. An object that is self-similar or fractal contains smaller copies of its overall form within itself repeated and at many smaller scales. A useful way of looking at self-similarity is to think of it as nested symmetry, where a pattern repeatedly contains copies of itself within itself. A much used example of self similarity is that of a tree, where the diverging pattern of branchings coming off the main trunk is repeated in a similar way in its branches and even in the veins of its leaves. So a tree can be described as self similar and fractal. Fractal geometry which was discovered in the 1970s has been called the geometry of nature. Tradition geometry deals with straight lines, regular triangles, squares, circles and the like. Fractal geometry seems far better suited to describing complex natural forms such as mountains, clouds and snowflakes; as well as organic structures such as plants, animals, people and even entire cities. It is even suggested by leading scientists that the entire universe may have fractal structuring. And so quite appropriately the Fractal Brain theory is the application of the idea of self-similarity in the context of understanding the natural phenomenon of brain and mind. It is an approach which has been suggested and tried before in the past few decades but which came up against hurdles which at the time seemed insurmountable. And on superficial inspection and with a limited understanding of the brain, then it is not at all apparent that the brain can be understood as being fractal. But with the benefit of recent empirical findings from neuroscience and a novel way of interpreting the data, then the Fractal Brain Theory is able to show how indeed the brain and mind can be conceptualised as being perfectly fractal and completely self-similar. And this sets up a lot of the conceptual groundwork for the brain theory and gives the theory its organizing principle..

Recursivity

Recursivity really is a universal process and the process of life itself can be considered as recursive. The process by which life comes into being, starting from a fertilized egg, dividing into two, then recursively and repeatedly dividing into 4, 8, 16 and so on, to give rise to all the cells in your body, this is an example of a recursive process. And the process of sexual reproduction, and the diverging and converging lines of family trees, generation recursively following upon generation is another example of recursion. Some thinkers even imagine the entire Universe and everything that happens in it as one big recursive process, so the idea of recursivity is pretty deep. Recursivity is a key concept that underlies computer science and the workings of all computers. The Fractal Brain theory shows that this phenomenon of recursivity is fundamental for understanding how the brain and mind works.

Three breakthroughs: A unifying language, unifying structure & unifying process

The fractal brain theory is the systematically application of the fundamental principles of symmetry, self-similarity and recursivity towards the understanding of brain and mind. And this leads to three major scientific breakthroughs, which we’ll elaborate in turn…

A Single Unified Language

The first of our breakthrough concepts has been anticipated. It is a way of describing not just all the structures and processes of the physical substrate of the brain but also all the various emergent structures and processes of mind; using a single unifying language. So for instance the 1996 publication, ‘Fractals of Brain, Fractals of Mind: In search of a Symmetry Bond’, described the existence of a ‘secret symmetry’, secret in the sense of being at that point undiscovered, which would allow us to conceptualize the brain and mind as a single continuum and describe it in the same language. This is the ‘symmetry bond’ referred to in the books title. Professor of Psychology and commentator on all things AI, Gary Marcus, described recently in 2014 how useful it would be to gain a unified description of brain and mind, and how this could potentially revolutionize the field. With the coming of the Fractal Brain Theory, the ‘secret symmetry’ is secret no more. We have now exactly this unifying language for describing all aspects of brain as well as mind. It is also a descriptive language which is supported by a vast array of empirical evidence, which suggests that it is not something ad hoc or arbitrary but rather one which reflects fundamental truths about how the brain and mind work. Indeed one of the strengths of the fractal brain theory is that it does take into account and incorporates a vast array of empirical facts and findings from neuroscience and psychology. It uses the unifying language to describe in a common format, all this vast diversity of information. This leads to the second major breakthrough the brain theory enables..

A Single Unifying Structure

Intuitive we know that there must be some sort of unity and integrated structure behind the brain and mind. This is because we know that somehow, all the various myriad aspects of our brains and minds must work together in an unified and coordinated way to achieve our goals and objectives. We know from our experience and introspection that this must be the case, we have this personal sense of oneness and singular wholeness that gives us the impression of self and identity. But it has been very problematic for brain scientists and artificial intelligence researchers to work out how exactly this is the case physiologically and how this may be implemented. Neuroscience exists as an ocean of facts and findings, with no obvious way to fit them all into a unified understanding. In 1979, Francis Crick of DNA fame, wrote that in relation to brain science, “what is conspicuously lacking is a broad framework of ideas in which to interpret these various concepts.” 35 years later, this unifying theoretical framework still seems to be missing. Neuroscientists Henry Markram’s much publicized and very well funded billion euro brain simulation project can be seen as an attempt to integrate all the knowledge of neuroscience which exists into some sort of integrated whole. Here the aim is to merely to bring all the neuroscience together in order to program it into a big computer simulation, but without any theoretical underpinning behind it whatsoever. A leading artificial intelligence researcher named Ben Geotzel is attempting to bring together a lot of existing partial solutions and previous attempts at AI, but is facing an ‘integration bottleneck’, without any clear way to make all the separate pieces fit and work together sensibly.

 In contrast what the Fractal Brain Theory introduces is a very elegant way of arranging all the various aspects of brain and mind, and fitting them all together into a single top-down hierarchical classification structure. This partly derives from the having a single unifying language with which to describe everything. By having a common description for all the separate pieces of the puzzle, this is the prerequisite for fitting all the pieces together into a single structure. Furthermore this unified classification structure also derives from what we know about hierarchical representations and relationships in the brain as suggested by the actual neurophysiological substrate and experimental findings. This gives us a very powerfully integrated and all encompassing overview of brain organization and the emergent structures of the mind which are grounded in the neurophysiological substrate. It is an important step to fully understanding the brain and the creation of true artificial intelligence. After all, many of the biggest names in AI and theoretical neuroscience stress the importance of hierarchical representations and processes. What the fractal brain theory is able show is that the entirety of brain and mind may be conceptualized as a single tightly integrated and all encompassing hierarchical structure.

The single all encompassing structure of brain and mind in turn leads to the third, final and most dramatic breakthrough which the fractal brain theory delivers. Given our all encompassing unifying structure we may then ask, is it possible to define a single overarching process over that structure which captures all the separate processes happening within it. Or put another way, if we can represent the entire brain and mind as a single integrated data structure, then is it possible to specify a single algorithm over that data structure, which captures the functionality of all the partial algorithms of brain and mind? And the answer is yes.