Everyone is God
The Prophecies are Now
The Nature of Reality
Psychedelia past and present
'Everyone is God' is the truth behind all World Religion
The unification of World Religion
Science and Religion
The Problems of the World today
Prophecies from around the World
Artificial Intelligence
Fractal Brain Theory

Update 02/03/22 - See the videos below for the latest developments involving the application of the Fractal Brain Theory towards the goal of creating True Artificial Intelligence


The following text is excerpts from the Fractal Brain Theory Book which may be purchased from Amazon and Barnes Noble. We include the Preface and the introductory Chapter 1 their entirety.


The Fractal Brain Theory


This book is the result of a long process spanning over 25 years. It has been a quest to create artificial intelligence along with the aim of understanding how the brain and human mind works. Along the way, the journey came to involve a diverse range of ideas from mathematics, computer science, biology and the physical sciences. Out of this has emerged a unified theory of Brain, Mind, Artificial Intelligence, Functional Genomics, Ontogenesis and Evolution. In the pages that follow, we will be elaborating on this novel and quite revolutionary way of looking at all of these topics.

Where did the journey begin? It really started early on in my life with a strong influence from Science Fiction in the form of toys, comics, magazines, films and TV shows. 1970s popular culture, seemed to be saturated with all things Sci-Fi. A recurring theme which, was an almost indispensable feature of anything to do with Sci-Fi, was robots and artificial intelligence. From an earlier age I was completely fascinated by these sorts of things, they really caught my imagination and would later strongly shape the course of the rest of my life.

A particular film really sparked my imagination, which seems to have also inspired many other artificial intelligence (AI) questers, and this was the 1982 classic BladeRunner, which I finally managed to see after hiring it from the local video shop in around 1985. It crystallized for me, in my young mind, the purpose of my life, which was to figure out how the brain works and create artificial intelligence from that understanding.

I was already caught-up in the home computer craze which was sweeping the UK and much of the industrialized world in the early 1980s. In my teens I was obsessed with computers and anything to do with them. Coupled with this burgeoning interest in AI, it took over my life. I had always thought before then, that I would become a doctor. I was good at maths and science and it seemed like a natural thing to aspire to. After my AI epiphany, then a new course was set. Around age 17 I started spending all my time learning anything and everything I could, which I thought relevant to my goal. I would constantly be talking about all things computers, AI and neural networks at school, it seemed like it was the only thing I could think about.

In my last year in high school I got a place to study at an academic institution, Imperial College, which at that time was a major centre for AI and computer science research, and it seemed like a logical next step. At this point I was set for a conventional research path.

In the Summer holiday before I was about to start university I ordered and got hold of the neural network AI ‘bible’ of the time, which was a two volume set called ‘Parallel Distributed Processing’. As I collected them from a local bookshop and walked home, I was so excited, I thought I held the future of AI and the key to my destiny in my hands. But as I read through the books and learned about what was the state of the art at that time, my excitement turned to disappointment.

I realized that the ideas in those books, which would in later decades re-emerge as the popular deep learning from of AI, wouldn’t lead to true intelligence, as I understood it. Also, I already had an understanding of the other sort of symbolic or ‘good old fashioned AI’, which I knew was barely intelligent, and far removed from the human variety. Therefore I came to the conclusion that the way that AI was being done in academia and the corporate world wasn’t the way forward. It was all so very uninspiring. So I had to find my own path, which deviated very much from other approaches being pursued at the time, and which today’s most popular forms of AI are a continuation of.

This book is, therefore, about an approach to artificial intelligence which is very different from anything that has come before or is currently in fashion today. I came to formulate a new kind of AI and an original formulation of what is the process of the brain and the nature of intelligence.

The path I took instead was that I saw neuroscience and psychology - the understanding of the human brain and human behaviour - as the real key to creating truly intelligent machines. This involved a lot of reading and study which continued over many years, along with the formation of concepts which I had to invent to make sense of the wide array of things I was learning, and for which no good theories already existed at all. So I had to create my own.

For all the myriad and bewildering components of the human brain and its related physiology, I had to form my own conceptions to make sense of things. Over the years, and over the decades, the different and diverse concepts I invented in my imagination linked-up and became integrated with one another. I also came to form overarching concepts with which I could unify many of the component concepts. Eventually, after many years, I succeeded in bringing everything together into a single unified conception. One of the key ideas which enabled me to do this is the idea of symmetry. This went hand in hand with the idea of self-symmetry or self-similarity, which is the idea of fractals, and so we have the Fractal Brain Theory, which is the title of this book.

Fractal geometry has been called the ‘geometry of nature’ and, from the perspective of this book, this is highly appropriate, as the single most important influence on the formulation of the Fractal Brain Theory has probably been nature. I have always had a fascination with living things. From the outset of this project I have used the natural world to provide metaphors and analogies from which I have been able to formulate my conceptions about the brain and its functioning. This led eventually to a rather dramatic discovery, and a fundamental aspect of the Fractal Brain Theory. I came to realize that the central ideas relating to life and biology, such as genes, genomes, ontogenesis (biological development) and evolution, are all fully manifested in the workings of the brain and mind. I came to see that with a certain level of abstraction, the correct way of visualizing things and the right mathematics, there exists an essential unity between what is intelligence and what is life. They are really manifestations of a deeper underlying process, and can be brought together into a unifying theory.

I saw this perspective, and unified theory, as the key to the creation of a new kind of artificial intelligence that would completely overcome the limitations and challenges faced by existing approaches.

Therefore, this book is about the brain and mind, and about biology and living things in general. In addition, and forming a strong undercurrent throughout, either implicitly or explicitly, this book is about artificial intelligence, and the last 80 pages focus entirely on AI.

The purpose of the book is, of course, to disseminate a constellation of novel ideas, but it is also intended to instigate a revolution in the fields of neuroscience, the life sciences, and AI. It shows a new and exciting way of looking at things. Along the way we’ll be covering a host of related topics, including computer science, linguistics, discrete mathematics, formal axiomatic systems, and recursively self modifying functions, providing new ideas and fresh insights into all of these areas.

Throughout the book I’ve avoided using maths formulas as much as possible so that it contains only two very simple - but at the same time powerful and profound - ones, which are explained in a relatively easy to digest way. Making things as easy as possible to grasp has been an aim throughout the writing of this book. In order to convey ideas which are sometimes complex the book contains many diagrams, over 130. This will hopefully make the book more accessible and the specific ideas and concepts easier to understand.

Many of the chapters can be read in isolation. For instance, the final chapter on AI can be read stand-alone by most AI specialists. Also, chapters 7 and 8, which cover biological development and evolution, together comprise something like a mini book within a book. But to get the most out of the book a cover to cover read-through will be best, as later chapters build on ideas introduced in earlier ones.

Thanks goes to the research efforts of all the neuroscientists and biologists (too many to list) without whom, there would no neuroscientific and biological data to integrate and explain. Also to the numerous theorists, computer scientists, mathematicians and thinkers whose books and papers I’ve read over the years, and which have fed into the formulation of my own ideas.

In the preparing of the manuscript of this book, and getting it into a better shape, massive thanks goes to Christopher Bennett, Stuart Clark, Peter Douglas, Bronac Ferran, Joe VanMyers, Lynette Robertson, Adoni Edwin Sergiou and Andrew Tudhope.

Thanks goes to my two older brothers Kin Ming Tsang and Wai Fai Tsang, for their help over the years, especially in areas relating to home computers and computer science. Also thanks goes to Emma-Jane Dolphin, Sylvia and Marianne, for being motivating and patient. Special thanks goes to my mother and father, to whom this book is dedicated, for their sacrifice and support.

Wai H. Tsang July 2016


Chapter 1


Humankind has come a long way on its historic journey of understanding the world and the Universe. But there is a huge, glaring and very significant gap in our knowledge waiting to be filled. We are still waiting to learn about how the human brain and mind works. A final theory of brain and mind will be one of the great, if not the greatest scientific discovery of all time. This in turn will be the key to another closely related and highly consequential goal which is the creation of true and fully functioning artificial intelligence.

This book is about the human brain and mind. It is also about the creation of Artificial Intelligence (AI) and the application of our understanding of how brains and minds work, towards the implementation of practical computer technologies. From the outset we fully recognize the tight inter-relatedness of these areas of human study and endeavour, i.e. Neuroscience and the details of brains, Cognitive science and the details of mind, together with Artificial Intelligence and the details of computing machines. This book presents the idea that there exists a single unified solution for the explanation of brain and mind, along with the construction of artificial ones.

The quest to understand the brain and mind and the goal of creating true Artificial Intelligence is so much a part of the spirit of the times or Zeitgeist. Hardly a month goes by without the announcement of some new initiative relating to the brain and mind sciences, or a news item relating to the computer industry’s attempts at creating more ‘intelligent’ machines. The recent spate of films and plays which relate to AI and the puzzles of mind also attest to the increasing awareness as well as the significance of these areas on our culture and in our lives. This book will explore these tightly interrelated themes.

It is widely and intuitively accepted that some of kind of deep understanding of the brain and mind would naturally help towards the goal of creating artificial intelligence, though the opposite may not necessarily be true. What we will be doing in this book is to describe a novel way of understanding the brain and mind, that relates deeply to existing ideas in the field of artificial intelligence and also leads to future innovations. It will become apparent in the pages that follow how deeply connected the engineering domain of AI is to the domain of the brain and mind sciences, though this is not always obvious to experts. So from the outset we view the problem of creating artificial intelligence together with the puzzles of understanding the brain and mind; as really the same problem. In the course of things, we’ll be showing exactly how these three problem domains fuse into a single description which allows us to understand what is the process of brain and mind, and allow us to see a clear path towards creating true AI modelled on that understanding.

The Holy Grail of Modern Times

In early 2014, the scientist Stephen Hawking together with some other top world class minds in a joint statement declared that, ‘Success in creating Artificial Intelligence would be the biggest event in human history’. This may seem like an overstatement but at the same time the full implications of the advent of true AI shouldn’t be underestimated.

If the last industrial revolution was driven by the mechanization of muscle, then the mechanization of mind would likewise lead to another revolutionizing of human affairs. The British inventor and computer pioneer Sir Clive Sinclair said, ‘the next road to greater wealth must come by replacing men’s mind’s with machinery so it’s artificial minds or artificial intelligences that we need’ . The social, commercial, economic and ultimately political implications of the invention of true and fully functioning artificial intelligence are immense and coupled with the ongoing digital revolution in computing and information technologies; it will impact upon almost every aspect of our lives in a relatively short space of time. It’s an invention that will quite literally and profoundly change the world.

So naturally governments have in the past spent, and are planning in the immediate future to spend billions of dollars, euros, renminbi, yen and won, on brain research and the development of artificial intelligence. And these huge sums of money are matched and even surpassed by corporate spending in the same areas. The wealth and money being poured into AI research today is to some extent a reflection of the utility, wealth and money that the technology is expected to generate in return. One of the wealthiest men in the world and co-founder of Microsoft Bill Gates has said, “It’s the holy grail, it’s the big dream that anybody who’s ever been in computer science has been thinking about.”

Leading Futurists, including the renowned inventor Ray Kurzweil, anticipate a unprecedented acceleration in the advance of our technological abilities once a full understanding of the brain and mind, together with creation of true artificial intelligence has been achieved. This has been called the ‘Technological Singularity’ and comes about through a so called ‘intelligence explosion’ which is the process of artificial intelligence progressively and cumulatively creating ever improving versions of itself, which is then able to create accelerated improvements in existing technologies and also new technologies which currently seem beyond the reach of the human mind. For example, fusion power, cures for cancer and other intractable diseases, interstellar space travel, the reversing of the aging process and even indefinite life extension, some futurists believe.

Kurzweil believes that the Technological Singularity will occur around the year 2029 which other experts believe to be a wildly optimistic estimate. This book will present the case that it will actually happen even sooner. But what most futurists agree on is that once the Technological Singularity gets going the cycles of self improvement will occur at relatively short time scales so that the transformations it’ll bring about will happen rather suddenly. We already see this with the advance of technology where product cycles and the rate of technological advance seems to be accelerating. The idea is that once we add true artificial intelligence to the mix then this already accelerating process of technological advancement, will accelerate even further. After all, the advent of human level artificial intelligence has been called ‘Our Final Invention’. It is quite literally the mother of all inventions, for it is the technology that is able to create technology and it is the invention that is able to invent.

So the full implications of our coming to understand the brain and human mind, which would include the creation of true AI, would quite literally and completely reorder the nature of human affairs. It is called the holy grail of modern times partly because it is widely recognized what the attainment of this goal would naturally lead towards. It has existed as a great prize which has excited the minds and imaginations of generations of scientists, philosophers and technologists. The prestige, potential commercial rewards and the excitement of the intellectual challenge that go along with this great task are pretty immense. So over the years, some of the greatest humans minds on the planet have applied their time, focus and careers towards the aim of achieving this sublime goal. Many have pursued this quest of understanding brain and mind, along with the creation of AI.

But the puzzle has turned out to be fiendishly difficult. Even with all the time, money and resources spent by some of the most gifted and talented minds, working within and with the most prestigious academic institutions, the most well funded government agencies and some of the most powerful corporate entities; still there seems to have been little progress towards a full understanding how the human brain and mind works, and only very limited success in creating truly intelligent machines, beyond mere pattern recognition and game playing.

The State of the Art

There seems to be a conceptual blockage. Everyone knows what the great goal is, but there is little idea as to how to get there. The goal of creating true AI and working out how the brain works has turned out to be a profoundly intractable problem. In real terms there has actually been very little in the way of real advances in our understanding of brain and mind, and the creation of AI, despite some of the claims reported in various news headlines now and then. To emphasize this point, we’ll examine some of the views of various leading experts in these areas.

In relation to the progress made in the cognitive sciences and the field of AI, the linguist and most referenced academic in the world, Noam Chomsky said in 2014 that, ‘The work in the field 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.’ A similar sentiment is voiced by the Oxford physicist and popular science writer David Deutsch who wrote that, “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.” Long time stalwart AI researcher Professor Patrick Winston of MIT (Massachusetts Institute of Technology), lamenting the lack of progress in AI recently joked that, ‘If I thought this is where we would be 50 years ago, I probably would have hung myself!’ . The neuropsychologist Professor Gary Marcus wrote, in relation to the brain sciences, that, ‘after nearly two centuries of research [there are] exactly zero convincing theories of how it all works.’ Nobel Laureate and co-discoverer of the structure of DNA, Francis Crick, wrote in 1979 that the field of neuroscience was, ‘conspicuously lacking a broad framework of ideas’ . And yet 36 years later many neuroscientists still view their field as completely lacking when it comes to theory. The neuroscientist Daniel Glaser of London University (A major hub of neuroscience research), said frankly in 2015 that his field, ‘is pretty much atheoretical which is to say that nobody has any idea what’s actually going on’ and that, ‘neurobiology and artificial intelligence are in a similar situation of being completely lost at the moment.’

In the world of AI, while there have been some successes in producing so called ‘narrow AIs’ that are able to beat the best human opponents in games like, Chess, most recently Go and even TV quiz games like Jeopardy; what’s going on under the hood is something that is far from being intelligent as we’d understand the term in its wider sense. So while IBM’s Deep Blue could beat Gary Kasparov, the World chess champion at the time, it wouldn’t be able to play noughts and crosses. And even though Google’s Go playing AI could beat the World Go champion Lee Se-Dol, it wouldn’t have any idea of how to win or even make an attempt at a simple children’s game like hang man. Also the recent successes with computers winning in games like Jeopardy or Go don’t actually involve any new ideas but rather large teams of humans painstakingly piecing together and tweaking existing methods that have been around for decades, tailored towards very specific and narrowly defined game domains, coupled with masses of computer power to drive these traditional algorithms.

The really elusive goal which still seems distant is the creation of a true general purpose, self learning and self improving artificial intelligence. Even the creators of these better than human game playing AIs think the same, despite their success in creating very effective forms of ‘narrow AI’. So while there is a lot of hype and sensational claims, the actual progress being made towards the greater goal of creating truly intelligent machines is actually very limited.

The Difficulty of Understanding the Brain and Creating AI

We can ask ourselves why the problem of understanding the brain and mind, and the creation of true AI has been so difficult. A simple answer is that in the mind sciences, particularly in neuroscience, there is a heavy emphasis on experiment and data gathering, with very little work going on in the theoretical side of things. While there does exist a sub-field within the mind sciences which calls itself ‘Theoretical Neuroscience’, this involves mainly using ideas and methods from physics which is effective for describing some of the microscopic details and processes of the brain but fails miserably when it comes to saying anything significant about how it all works. So one of the reasons we don’t yet have a great understanding of how the brain works as a whole, is simply that up to the present very little work in the academic institutions is focused on this question in a concentrated way, or with any greatly significant resources devoted to it.

Another reason for the lack of an overall theory of how the brain works is a viewpoint that is expressed by many neuroscientists, which is that one of the problems of their field is that the vast amount of accumulated knowledge is fractured and lacking any overall integration. Henry Markram, who is a distinguished neuroscientist, lamented in a TED talk that he’d find that at conferences the neuroscientists involved didn’t understand one another and that there would even be a lack of standardized nomenclature so that the same thing would be given completely different labels. His billion Euro funded, ‘Human Brain Project’ (HBP), of which he used to be in charge, sought to simulate an entire human brain on a computer. He believes this is a way to bring together in a common format and single place, all the disparate and disconnected knowledge in the brain and mind sciences.

In the field of AI, a similar sentiment is echoed by MIT Professor Patrick Winston who thinks that one of the main impediments which holds back the progress of AI, is what he calls its, ‘mechanistic balkanization’. By this he means that different research groups are narrowly focused on specific mechanisms or very circumscribed approaches leading towards the creation of limited forms of narrow AI, without considering the big picture and what other techniques or approaches have to offer. And also without addressing the really fundamental questions about what is the nature of intelligence.

Another AI researcher Yann LeCun who is a leading light in the currently fashionable form of AI called Deep Learning, which used to be called Neural Networks, expresses similar opinions. While he is focused on his particular mechanistic approach he also recognizes that his field is lacking a ‘good grand model’. In regard to a particular crucial unsolved problem in his sub-field, i.e. unsupervised learning; he believes that everyone is ‘missing a basic principle’ which he believes could be potentially foundational and provide a solution.

So while a lot of research in AI produces quite effective specific solutions to very narrowly circumscribed problems such as board games, spam filtering, targeted advertisement or recommendations systems and self driving cars; there is not very much work going on which might produce the necessary grand models or basic foundational principles. Instead most AI researchers work within their balkanized compartments. One of big names of AI Marvin Minsky (1927 - 2016), reiterated this point with regard to the lack of progress in ‘big picture’ AI when he said quite recently before his death that, “I haven’t seen many advances in recent years, because the money is going more to short-term applications than basic research.”

These sorts of views and the current state of affairs, reflect in general the compartmentalized, narrowly focused and specialized nature of scientific and technological research in academic and corporate research labs. A career as a research scientist or technologist working in academia or the corporate world, necessarily involves a degree of specialization. It’s not so easy to get a paid position as a jack of all trades generalist and completely free ranging thinker. And perhaps the added pressure of coming up with something with either commercial or military application within a certain limited time frame, and within budget constraints, would further add to the narrowing of focus. So most researchers and academics simply don’t have the freedom or the time to think about the really ‘big picture’.

The process of specialization in academia, is not necessarily a disadvantage in a lot of scientific and technological research if the aim is to incrementally make small or even quite significant advances in understanding within specific areas of expertise. However if the problem is more broad and wide ranging, i.e. one that spans many areas of specialization, as would be the case for the understanding of the brain and creating AI; then the traditional modes and pathways of research may be inadequate to the task. So this factor may be contributing significantly to the problem as to why there has been so little real progress towards the great goal under consideration.

If the solution to a problem involves thinking outside of a box, then this may be difficult if the process of achieving a successful academic or corporate research career involves placing oneself into a box in the first place. And it may not even be a viable solution to collect together a load of different experts with the required specializations for understanding the brain and mind, i.e. neuroscience, computer science, maths, psychology, genomics, etc.; into the same team working closely within a tightly circumscribed time frame dictated by funding limitations. Together with the communication overhead, opposing opinions, personality differences and politics that usually afflict such groups. All of these sorts of factors work against synergy and the necessary fusion of ideas that would be necessary to come to grips with multi-faceted and multi-disciplinary problems.

So the compartmentalized, specialized and even territorial nature of academia and the corporate research world, is another plausible explanation for the lack of progress in the goals of understanding how the brain works and the creation of fully functioning artificial intelligence. Other factors which are sometimes cited to explain the slow or non existent theoretical progress in the mind sciences and AI include, a lack of funding, missing maths, not enough computing power, missing empirical data, not enough people working on it, etc.

Of course another important reason for the lack of any real understanding of how the brain works or how to create AI, is simply that it is a very difficult puzzle to solve, involving a myriad number of component puzzle pieces spanning many areas of specialization, all interlocking together in an intricate and complex fashion with each puzzle component resistant to being solved in isolation of all the other pieces of the puzzle. We’ll be exploring this idea in greater detail in chapter 11, which is all about AI.

Some Predictions for the Future

So despite some of the claims that we hear about from time to time in the news, the current situation in the academic, government and corporate labs is that, at least within the formal institutional context, we are a long way away from the goal of truly understanding the nature of the brain and human mind, and the advent of true AI. When experts are pressed to give an answer as to when a good understanding of the brain and mind or AI will come, then a typical answer will be that it is decades away.

Christof Koch, one of the world’s leading neuroscientists expressed the view in a recent book called the ‘The Future of the Brain’, that even 50 years hence, we still will not have figured out how the brain works.

The Nobel prize winning neuroscientist Eric Kandel said, ‘Not in my lifetime, not in your lifetime [speaking to a middle aged guy], are we going to understand fully how the brain works. The scope of the problem is so huge and so intricate’. However perhaps mitigating this rather discouraged perspective, in a separate interview Kandel also stated that he believes that, ‘There is an occasional person who will have a remarkable insight that will allow you to see things in a new way, and that will move the field in unexpected directions.’

The philosopher of AI Aaron Sloman said in a 2014 interview that in context of creating AI, ‘Understanding how humans work might enable us to make surrogate humans... I suspect it won’t happen in this century I think it’s going to be too difficult.’ Other estimates for the coming true Artificial Intelligence, coming from practitioners in the field are usually more optimistic usually ranging from 10 years to 50 or more. Geoffrey Hinton who is sometimes referred to as the godfather of Deep Learning which is at the time of writing the most fashionable form of AI, has said recently in 2015 that true AI will arrive, “No sooner than 2070” . But even more pessimistically, Noam Chomsky has recently stated that, ‘a theory of being smart [i.e. Intelligence] we’re aeons away from that.’ In the same interview he even entertained the idea that fully understanding the nature of human intelligence may be something fundamentally forever beyond the grasp of human intelligence.

More optimistically, the neuroscientist and AI expert Demis Hassabis, whose AI company DeepMind is regarded as a leader in the field, is working to a 20 year road map towards the goal of ‘solving intelligence’. But believes that, “We’re decades away from anything that’s nearing human-level general intelligence.” and that “there could be ten or 20 more breakthroughs before we’ve solved what intelligence is.” In a similar statement Microsoft co-founder Paul Allen, who now funds one of the biggest neuroscience labs in the world and helps to guide its direction of research, asked rhetorically in a recent interview, “is it 20 Nobel prizes, 100 Nobel prizes, 500 Nobel prizes before we understand really how the brain works?”

However it seems that points of view on this matter can pretty quickly change. Geoffrey Hinton who we’ve just mentioned, more recently revised his prediction for when human level AI would arrive, shortly after Google DeepMind’s Alpha Go victory over the human champion. He now says, ‘More than five years. I refuse to say anything beyond five years because I don’t think we can see much beyond five years.’ It seems success breeds optimism. The Go playing AI actually uses to a large degree the sort of neural network AI that Hinton has spent his career developing.

There exists another viewpoint altogether which suggests that things may happen far sooner than most people suspect and think may even be possible. Stuart Armstrong of the Future of Humanity Institute, gave a lower bound estimate of 5 years, in a presentation dedicated to the question of when will true AI come, at the 2012 Singularity Summit. So at the current time of writing, i.e. 2015, the great coming could be pretty close. Stuart Russell who co-wrote the most widely used text book in AI has said recently that, “There will have to be more breakthroughs to get to AI but... those can happen overnight.”

Nick Bostrom in his book ‘Super Intelligence’, which at the time of writing is getting read a lot by the AI intelligensia, thinks that what he calls the ‘lone hacker scenario’, of somebody solving the problem of AI much sooner rather than later, is at least ‘conceivable’ in his opinion; and ‘that somebody somewhere will get the right insight for how to do this in the near future’, also ‘that the last critical breakthrough idea might come from a single individual or a small group that succeeds in putting everything together.’ But of course this sort of viewpoint is not shared by everyone, Yann LeCun whom we’ve already mentioned said, ‘“The scenario you seen in a Hollywood movie, in which some isolated guy in Alaska comes up with a fully-functional AI system that nobody else is anywhere close to is completely impossible”

However we’ll Continue our considerations of this ‘outlier’ and ‘outsider’ perspective for the coming of AI. The late great John McCarthy (1927-2011) who is credited with coining the term ‘artificial intelligence’, and who naturally was there at the field’s inception, when asked to give an estimate for how long it would take for the puzzle of AI to be finally and completely solved; he gave a range of possibilities including the usual 50 to 100 years as his future estimate. But he also suggested the tantalizing possibility that someone outside of the academic and corporate institutions has already solved the problem of AI, but ‘he just hasn’t told us yet’. Along similar lines, John Horgan who is a popular science author and former staff writer for Scientific American magazine concluded from his numerous interviews with specialists in the field that, ‘Some mind scientists… prophesy the coming of a genius who will see patterns and solutions that have eluded all his or her predecessors’. And in relation to this idea he quotes Harvard Psychologist Howard Gardner as saying that, ‘We can’t anticipate the extraordinary mind because it always comes from a funny place that puts things together in a funny kind of way.’ Professor Pedros Domingos who is considered to be a leading practitioner in the field of machine learning writes about a ‘master algorithm’ which from the way he describes it is really a general purpose AI. Echoing some of the immediately preceding sentiments he writes that, ‘Somebody could discover [the master algorithm of machine learning] tomorrow or it could take hundreds of years. My gut feeling is that it will happen in our lifetime, and it will probably be someone who is actually not a professional machine-learning researcher.” and that in relation to actually creating the Master Algorithm he thinks that, ‘perhaps it will take an entirely new insight, which may come not from a professional researcher but from an outsider or a student in a dorm.’

This idea that AI together with a fully developed theory of brain and mind may come sooner rather than later, and involving some new idea, is also suggested by David Deutsch, already mentioned earlier, who wrote in an essay a few years back, ‘I can agree with the ‘AGI [Artificial General Intelligence] is imminent camp’: it is plausible that just a single idea stands between us and the breakthrough. But it will have to be one of the best ideas ever.’

The idea that someone with some new innovation or revolutionary way of approaching things may suddenly appear out the blue has been a recurring sentiment. This book explores and elaborates upon this outlier possibility of things happening sooner rather than later. And not just in relation to the creation of artificial intelligence, but also in relation to the understanding of brain and mind.

In the pages that follow will be a description of a novel and comprehensive unified theory of brain, mind and artificial intelligence. It consists not just of a single breakthrough based on a single idea, echoing David Deutsch’s sentiment, but rather a series of interlocking innovative concepts based on several other fundamental but also tightly interrelated ideas. And one of these ideas, we already know to be ‘one of the best ideas ever’, because it’s really one of the central ideas behind the whole enterprise of science. And if the aim is to gain a scientific understanding of brain and mind, in order to create true artificial intelligence, then this would make sense. This central idea is called symmetry.

Symmetry is such an amazingly powerful idea. 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. So it is the idea of symmetry and closely related idea of symmetry breaking which really provide for us some very useful concepts for understanding this process. And which we’ll explain in more detail in the next chapter.

What is true for the enterprise of science as a whole is also true for the problem of trying to gain a deep and comprehensive understanding of the workings of the human brain and mind. Here 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 ideas of symmetry and symmetry breaking 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 these powerful concepts towards that goal and this is not at all obvious. This is one of the problems that will be explored at length later on in this book.

There are two other ideas which are fundamental to this brain theory and whole approach to things, the details of which will be explained more fully in the next few chapters but we’ll mention and describe in brief outline now. These are the ideas of Self-Similarity and Recursivity.

Self-Similarity is a property an object has if it’s made up of smaller copies of itself and in a sense contains itself. The classic example is that of a tree, so that an entire tree can be seen as an enlarged branch, and so we have Bonsai trees. Closely associated with the idea of self-similarity is that of nested hierarchies, so that the smaller copies are contained within a Russian doll like hierarchical structure so that the entire structure is made up of smaller copies of itself, nested within itself.

Recursivity is the property a process has, if the result of the process is repeatedly fed back into itself again and again, to produce a recursive sequence of outputs. An example of a recursive process would be compound interest, whereby a sum of money is multiplied by a percentage, and the result fed back to calculate the next accumulation of interest.

If we combine these fundamental and interrelated ideas, then we arrive at the notion of a recursively nested hierarchical self-symmetrical, or self-similar, i.e. fractal, structures, together with recursive processes happening over them. These ideas are then systematically applied towards the understanding of the brain and mind.

This theory we will be describing is called the ‘Fractal Brain Theory’ but it 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 and is intimately related to the concepts of Symmetry, Self-Similarity and Recursivity and which we’ll be explaining more fully in the next chapter. So the title ‘Fractal Brain Theory’ is an entirely appropriate as well as useful shorthand. We’ll later be going 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.

The Fractal Brain Theory derives from the systematic application of the fundamental principles of symmetry, self-similarity and recursivity towards the understanding of brain and mind. And this leads to three major theoretical breakthroughs which make up of the main body of the theory.

The three major breakthroughs comprise firstly a single unifying language for describing all the myriad details and facets of the brain as well as the mind. In order to arrive at a unified theory of anything then first of all it is necessary to be able to describe things in a unified format.

Our second breakthrough concept is a single all encompassing unifying hierarchical structure deriving from our unifying language and the experimental data, which allows us to see how everything related to brain and mind comes together as a single integrated whole.

Our third and most surprisingly theoretical breakthrough is the idea that all the various information processing of the brain and the many operations of the mind, may be conceptualized as a single underlying unifying process and that can be captured in a single algorithm. Taken together these properties of the fractal brain theory are set to revolutionize the worlds of theoretical systems neuroscience and artificial intelligence.

We’ll next describe in a little more detail the nature and significance of these theoretical breakthroughs, but elaborate upon them more fully and extensively in the course of this book.
A Single Unifying Language

he 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. Or as they put it, ‘mind/brain performs as an indistinguishable one from a formal, neurological and psychological point of view’.

Professor of Neuro-Psychology and also a commentator on all things AI, Gary Marcus, described recently in a 2014 interview how useful it would be to gain a unified description of the physical brain together with the emergent mind. He wonders whether he’ll see this in his lifetime but believes that such a conceptual breakthrough could potentially revolutionize the field. Separately he has said, ‘What neuroscience needs, desperately, is a theory of how to connect behavior and the language of cognitive psychology to the dynamics of individual neurons. Until then, we will just have data, not true understanding.’

With the coming of the Fractal Brain Theory, the ‘secret symmetry’ is secret no more. We will describe exactly this unifying language for describing all aspects of the brain as well as the 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. Very interestingly this secret symmetry that allows for the unifying of brain and mind also extends to the description of genomic (DNA) structure, coding and functioning.

The single unifying language which allows everything to fall into place, involves a certain kind of mathematization or geometrization that is able to formally capture, all of the important concepts which we mentioned earlier. This involves a particular way of using binary trees, the most basic of data structures in computer science. In chapter 4 we’ll be explaining this structural description and unifying language in great detail. In subsequent chapters we’ll show how it is pretty much ubiquitous in the structures and processes of brain and mind, as well as that of genomics together with the processes of evolution and biological development. On a very simple level neurons or brain cells are literally binary trees and the process of biological development involves binary cell divisioning or mitosis, which we’ll explain more explicitly later on, but as we’ll see this binary, doubling or bifurcating pattern recurs at all levels of brain architecture, the operation of the mind and the process of biological development or ontogenesis. This way of abstracting the problem of brain, mind and genomics using our unifying language, in turn allows us to fully interpret it in terms of the formal mathematical concepts of symmetry, symmetry breaking, recursivity and self-similarity.

One of the strengths of the Fractal Brain Theory is that it does take into account and incorporates a vast amount of empirical facts and findings from neuroscience, psychology and also genomics. It uses the unifying language to describe in a common format, all this great diversity of information. So that the so called ‘parts list of neurobiology’ can be brought together with the ‘parts list of cognition’; and the ‘stuff of meat’ may be reconciled with the ‘stuff of mind’. And in turn all this is in turn brought together with the parts list of genomics and the stuff of molecular biology. This leads to the second major breakthrough the brain theory enables.

One of the very convenient implications of this way of describing brain, mind and genome using the language of binary trees together with the idea of binary combinatorial codes, which we’ll much elaborate upon in chapter 4, is that this is exactly the language of computer science and information theory. So that throughout this book, in our later discussions about brain, mind, genomes, biological development and evolution, even if not explicitly stated then we are also simultaneously talking about artificial intelligence. The translation of the Fractal Brain Theory into the realm of AI and computer science is most straight forward because the Fractal Brain Theory, as well as being a fractal genome theory is also implicitly a theory of fractal artificial intelligence.

Our single unifying language sets up the necessary conditions for our second breakthrough which we’ll discuss next.

A Single Unifying Structure

Intuitively 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 a 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 or single cohesive and coherent structure. The Fractal Brain Theory introduces a very elegant way of arranging all the various aspects of brain and mind, fitting them all together into a single top-down hierarchical classification structure. This partly derives from having a single unifying language with which to describe everything in the first place. Having a common description for all the separate pieces of the puzzle, is the prerequisite for fitting all the pieces together into a single unifying 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, together with the emergent structures of the mind.

It is an important stepping stone 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 structures, representations and processes. What the Fractal Brain Theory is able to show is that the entirety of brain and mind may be conceptualized as a single tightly integrated and all encompassing hierarchical structure. A Carnegie Mellon University AI researcher Tom Mitchell thinks in relation to creating AI that, ‘it is not obvious to me that we are missing [AI] components.’ but he thinks what is missing is that, ‘we don’t have a good architecture to assemble the [existing AI] ideas.’ So on one level this is something which is provided by the Fractal Brain Theory, exactly the sort of framework that is needed for the integration of the various conceptions of AI as well as that of the mind sciences in general.

The single all encompassing structure of brain and mind in turn leads to the third 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.

A Single Unifying Process and Critical Algorithm

This is the most surprising and perhaps even shocking property of the fractal brain theory. Because it shows that there exists a stunning simplicity behind the inscrutable and mysterious functioning of the brain and mind. The Fractal Brain theory shows how a single unifying recursive process is able to explain all the component sub-processes of brain and mind.

Putting this powerful idea into the context of what some of the leading researchers in the fields of artificial intelligence and theoretical brain science are currently thinking; roughly speaking we have two camps. On one side we have those thinkers who think that underlying the brain and mind is some sort of unifying and ultimately relatively simple answer waiting to be discovered. This viewpoint goes hand in hand with the notion of some critical breakthrough or the elucidation of a set of basic principles which will unlock the puzzle of brain and mind which will then enable the creation of true AI. On the other side we have those thinkers who believe the opposite, that this won’t be the case. So this idea of a critical algorithm and unifying process has already been anticipated to some extent by various researchers in the mind and brain sciences. We’ll discuss this camp first.

For instance Eric Horvitz the head of AI research at Microsoft, has speculated that there may exist a ‘deep theory’ of mind waiting to be demonstrated. Sir Steve Grand who is a prominent British AI theorist and inventor, thinks there may exist a ‘single sentence solution’ behind how the brain works and which would provide the key to creating AI. Several prominent AI and brain researchers such a Jeff Hawkins, Ray Kurzweil (A successful AI implementer and a godfather of the Technological Singularity) and Andrew Ng (Former director of the Stanford AI lab and now head of AI research for Baidu Corp); all believe that there may exist a universal ‘cortical algorithm’ which captures the functionality of all the various different areas of cerebral cortex which together with the related underlying wiring comprises over 80% of the human brain. And we’ve already mentioned Pedros Domingos and his ideas for a Master Algorithm or ‘a grand unified theory of machine learning, akin to the standard model of physics’.

The second camp is represented by researchers like Ben Geortzel who doesn’t believe in the existence of a critical algorithm that could give rise to true AI, saying ‘I don’t think there’s any one algorithm that’s critical to intelligence’ . Nils Nilsson who was the director of SRI (Stanford research institute) AI Lab and author of many books on the subject, ‘doubts’ that an ‘overarching theory of AI will ever emerge’ . Danny Hillis who did pioneering work on massive parallel computers expressed the view that ‘Intelligence is not a unitary thing’ , but rather a collection of rather ad hoc solutions. Marvin Minsky and Doug Lenat both prominent practitioners of the so called GOFAI or ‘good old fashioned AI’, which involves mainly language and symbolic processing; have expressed similar sentiments. Minsky believes that the brain is made up of multiple functional modules that have evolved separately to produce a multitude of different algorithms, what he has called a ‘society of mind’. He has explicitly stated that, ‘My conclusion is that there isn’t any general principle of how people think’ . Lenat’s work holds out to the hope that AI or at least ‘common sense’ for AI will emerge from the collecting together and human hand coding of a myriad number of facts and pieces of knowledge. And then there’s Stephen Wolfram, the creator of Mathematica, who said at the 2011 Singularity Summit, ‘When I was younger I used to think that there would some great idea, some core break through that would suddenly give us Artificial intelligence.’ But now he doesn’t anymore.

The Fractal Brain Theory will give strong support to the first camp and demonstrate what a unified theory of brain, mind and AI looks like. In a sense it gives us something akin to a ‘one sentence solution’, which will be a minimal self modifying recursive function that starts initially as a seed atom, we’ll talk more about this later on. It will show how a ‘deep theory’ of brain and mind naturally derives from a similar process to how all ‘deep’ theories in science come about, i.e. through the application of the principles of symmetry but in a way that is recursively self modifying.

The brain theory demonstrates not a single critical breakthrough or idea but really a whole series of closely inter-related ideas, which do distil into a single algorithm and recursively self-modifying description. It shows that intelligence and the functioning of brain and mind is indeed a unitary thing, that underlying all the myriad complexity is simplicity. And that true AI and common sense emerges not from trying to hard code all the diverse complexity of mind but rather in the discovery of the relatively simple underlying process which generates it in the first place. So far from being a collection of ad hoc solutions, the brain and human intelligence, comes about through the application of an underlying common algorithm to different contexts and the problems within those contexts, and this is how things may seem ad hoc.

Also this symmetry, self-similarity and recursivity brain theory gives us an ‘overarching’ theory, not just of AI, but also one that seamlessly brings together naturally many of the best and recurring ideas in AI, with what we know about brain, mind and genome. It acts as the bridge between different sets of compartmentalized human scientific and technological activities, i.e. Neuroscience, Psychology, Genomics, Artificial Intelligence and Computer Science, thus allowing them to more fully interact and work together.

As we have seen it is already suggested by leading researchers that there may exist a single algorithm for explaining the workings of most of the brain especially the cerebral cortex. But the Fractal Brain Theory goes a lot further. Because what is behind the theory is a universal algorithm and unifying process that is able to span not just the functioning of the cerebral cortex but also that of all the other major auxiliary brain structures comprising the hippocampus, striatum, cerebellum, thalamus and importantly the emotion centres, which are involved in reinforcement learning, and which include the hypothalamus and amygdala. The Fractal Brain Theory is able to demonstrate how a single overarching process is able to account for and explain the purpose and functioning of all these main structures of the brain. Significant for mainstream ideas about brain functioning and neuroscience inspired AI, is that the Fractal Brain Theory shows that the cerebral cortex can’t really be understood without considering the other auxiliary brain structures. Therefore what we are talking about is a single algorithm behind the functioning of the entire brain, the emergent mind and intelligence itself.

As we have already suggested the theory goes even further than this! For not only does it describe how all the functioning of the brain and mind can be captured by a single algorithm, but also that this overarching process extends to the process of how brains and bodies come into being, i.e. neurogenesis and ontogenesis, and even describes the operation of the DNA genomic computer guiding this developmental process. We’ve already hinted at this surprising and remarkable property but we’ll describe it more explicitly now.

There exists an ‘astonishing hypothesis’ that is an inherent part of the Fractal Brain Theory. It proposes that it is possible to perfectly extrapolate or interpolate the structures and processes of brain and mind into the realm of the genome and DNA. So that a unified theory exists to completely describe the workings of brain and mind together with that of the genome. It is often thought that the genome and the DNA in each cell, somehow functions as a computer. What the Fractal Brain Shows is that the genome functions exactly as a tiny brain. And the relationship is not merely one of analogy but rather, given the correct level of abstracting and a suitable way of mathematizing, then it is possible to see the brain and genome as identical in their workings and structure. So the astonishing hypothesis is that given the mathematical formalism of the Fractal Brain Theory, then it is possible to conceptualize a neuron exactly as a gene, a neuronal network exactly as a gene regulatory network and the genome exactly as a miniature fractal brain. Furthermore within the context of the Fractal Brain Theory, the process of thought and behaviour is exactly as the process of ontogenesis or biological development. But most interestingly also, the process by which thoughts and behaviours change i.e. through learning, innovation or creativity, is exactly the same as the process by which genomes and the biological development is altered i.e. through the process of evolution.

Astoundingly the fractal brain theory is able to show that there is a singular unified description behind the process by which life begins from a fertilized egg, to give rise to bodies, to give rise to brains, to give rise to minds, to give rise to behaviour and all the things that go on in the course of a lifetime, right back to the purposefully directed central goal of our lives which involves the process of fertilizing eggs. And so the cycle begins again. And likewise a unified theory for how these processes of biological development and also those of mind evolve in evolutionary time and the lifetime of an individual respectively. We’ll be discussing these exciting ideas in great detail, in chapters 7 and 8.

So this is the ‘astonishing hypothesis’ behind the Fractal Brain Theory. I’ve borrowed the term from a Francis Crick (of DNA fame) book called ‘The Astonishing Hypothesis’, I read years ago, which presented the commonly accepted but problematic idea that consciousness arises from the physical brain. But the idea we’re putting forth here is that there exists a perfect symmetry between on the one hand the brain, mind, thought, behaviour and learning; and on the other the genome, ontogenesis or biological development and phylogenesis or evolution. Crick was very interested in neuroscience and of course genomics, so if he were alive today then he would find the hypothesis most ‘astonishing’ and wouldn’t object to the borrowing of his book title.

This is a very bold, provocative and dramatic claim that is made for the Fractal Brain Theory. It may seem like a theoretical impossibility or some wild over-extension of thought and over-interpretation of things, but once these aspects of the theory are fully comprehended, then they become a powerful reason why the theory will quickly become accepted and gain adherents.

What at first seems fantastic might not seem so strange when we consider what is indisputable. It is a fact that everything that happens in our lives, everything that happens in our bodies and brains, every cell created, every protein manufactured and every random nerve firing that has ever occurred; and every thought and action that we’ve ever had or performed; All of this has emanated from a fertilized egg. Without this critical first event and tiny singularity in space and time, then everything that follows from it will not have happened.

Following from this thinking, if we can discover a common underlying symmetry of process which shows how all the separate emerging processes share a common underlying template; and if we can use our unifying language to describe all the many separate phenomena including cell division and progenitor field formation (i.e. neurogenesis and ontogenesis), as well as the idea of DNA operating as information processor, along with the various aspects of brain and mind; and then be able to describe all the separate processes as recursive and furthermore be able place all of these processes into a single unifying structure and also to link them all up into a single recursive process. If we can do this, then this great overarching view of things might not seem so incredible. This great unifying algorithm and overarching recursive process is the central idea behind the fractal brain theory and the key to creating true artificial intelligence the author believes.

Also when we consider that this has been the recurring pattern in the progression in science, whereby seemingly disparate concepts, i.e. electricity, light and magnetism; space and time; matter and energy have been shown to be manifestations of the same underlying phenomenon; then the notion that in the life sciences, the seemingly distinct and disparate phenomena of the genomic processes, ontogenesis, evolution or phylogenesis, brain, mind, thought, behaviour and learning; becoming integrated into a unified understanding might not seem so strange after all. Especially when we understand that it is the principle of symmetry which has enabled the historic scientific process of extracting unifying patterns which bring together diverse phenomena and show that they are really manifestations of the same underlying thing. Then we should expect the same when we apply the principle of symmetry towards the understanding of brain, mind and genome. So that unifying principles would similarly emerge as a result.

The Future Significance of the Fractal Brain Theory

Our three major theoretical breakthroughs in systems neuroscience, genomics and AI described, can be thought of as our three fundamental foundational concepts, i.e. symmetry, self-similarity and recursivity, taken to the maximum limit. They are a natural consequence of seeing things in this way and systematically thinking through their implications in relation to the empirical evidence and given facts.

Our single unifying language can be thought of as a single underlying Symmetry behind the entirety of all the diverse aspects of neuroscience, psychology and genomics. Likewise our single unifying structure can thought of as a single all encompassing self-similar fractal of brain and mind, as well as that of biological development and genomic organization. And our single unifying process is the conceptualizing of all the separate component processes of brain, mind and genome happening in all contexts and scales as being the expressions of a single seed recursive function.

These are the very powerful properties of the Fractal Brain Theory, which would suggest that the theory is something quite special and unique. When it is fully digested and accepted that it is possible to understand the brain, mind and genome using the fundamental scientific and mathematical concepts of symmetry, self-similarity and recursivity, in this complete and comprehensive manner; then perhaps the Fractal Brain Theory itself may come to be seen as something likewise fundamental.

In the recent 2015 book ‘The Future of the Brain’, which we’ve already mentioned, is a collection of essays by more than twenty of the world’s leading neuroscientists relating to what they thought was the necessary next steps the field must take. The recurring theme was the need for integration and unification. In particular, firstly the need to unify the mountain of disconnected findings from neuroscience; secondly the need to bridge the neural substrate with cognition and the emergent mind; and thirdly the need to find a mechanistic link between on the one hand all the exciting findings coming from recent research in the field of genomics and molecular biology and on the other all the facts and data from the mind/brain sciences. The three interlinked theoretical breakthroughs arising from the Fractal Brain Theory described earlier provide exactly the means to accomplish the these three necessary unifications. The next steps for neuroscience and the future of the brain which some of the world’s leading experts describe is exactly the need for a unifying language, a unifying structure and a unifying process which is able to span mind, brain and genome.

Another idea which cropped up in several places in the ‘Future of the Brain’ book was the need to develop a computational understanding of the brain. Naturally a fractal brain theory which is able to compactly compress the three necessary unifications just described, into a single self modifying recursive algorithm is the most succinct and parsimonious computation understanding of the mind, brain and genome that is possible. As we’ll see and we’ve already mentioned, the mathematical language of the Fractal Brain Theory is exactly the same as that of computer science and AI.

The Fractal Brain Theory exists at the critical juncture towards which all of these predictions for what is the necessary next step for the brain and mind sciences converge.

Recursive Self Modification: The Trick Behind Intelligence

Inevitably the proposal of such a dramatic integrating of the diverse range of phenomena just described leads a person to ask, how can it possibly be the case that a single algorithm is able to account for such a range of diverse and differentiated ones. The process of cell division and functioning of individual nerve cells seems far removed from the level of introspection, the complex thoughts that we have, and the intricate behaviours that we have to perform in our day to day lives. And intuitively the process of evolution happening to genomes seems quite distinct from the processes of learning and creativity happening in our brains and minds. So it would perhaps seem quite implausible that there may exist a single algorithm and process that could span the entire gamut of everything that happens in our bodies and in our lives, from the level of a fertilized egg and the process of the development of our bodies and brains, right up to everything that unfolds in our lives, i.e. all the thoughts and behaviours we express in a lifetime.

However there is a trick which enables the simplest of processes, i.e. cell division, to give rise to the most complex i.e. our intricate thoughts and behaviours. This is recursive self modification. What the Fractal Brain Theory describes and at its heart, is a recursive algorithm or process that is able to generate hierarchical structures. These structures in turn manifest the same process but in a composite, expanded and augmented form. The unifying recursive process then uses these augmented forms to further expand itself to create even more complex and evolved structures, which in turn generate more complex patterns of operation, and so on. Crucial to this process of full recursive self modification is the necessary prerequisite that the function is able to augment itself, so that the modifier is modified, and the generator is able to generate augmented modifiers. Certain other processes or algorithms may involve a form of self modification where the modifier is static and unchanging. We may call this ‘weak’ recursive self modification but we are mainly interested in the variety where the process of transformation itself becomes transformed. So in this book when we talk about recursive self modification it will be implicit that we mean it in this stronger definition of the expression.

So the initial seed process feeds back on itself in this recursive way, to generate our bodies, brains and all our mental representations, thoughts and behaviours. This is really the trick that makes the fractal brain theory tick, and the key to understanding the nature of intelligence. As we’ll see in chapter 8 which focuses on the idea of recursive self modification, it is also fundamental to the process of evolution given the new findings coming from molecular biology or the so called 21st century view of evolution. In the words of prominent evolutionary biologist James Shapiro, ‘Evolution evolves evolvability’. So therefore if we conceptualize evolution as a function, i.e. the function that evolves genotypes and therefore phenotypes, than that function itself evolves through a process of recursive self modification.

This idea of recursive self modification is much discussed in artificial intelligence circles but no one in mainstream and formal institutions really knows how to do it. Many artificial intelligence researchers believe that the process of recursive self modification is one of the factors which could bootstrap ‘super intelligence’ that is able to far out perform human level intelligence. However a common misconception is that this recursively self modifying functioning only emerges above a critical level of complexity that is pretty complex. Many researchers believe that this threshold and its associated level of complexity, is near or above the level of human level intelligence. What the fractal brain shows is that in natural bodies and brains the process of recursive self modification is happening right at the outset, i.e. starting from a fertilized egg and the beginning of life. This is actually quite obvious once we think about it.

Obviously the process of cell division whereby a single cell becomes all the cells in our bodies through a binary divisioning process is recursive. So that one cell becomes two, and each of those two cells recursively subdivides to become four cells, then to eight cells and so on to the trillions of cells that comprise a human body. So like the example recursive process of compound interest described earlier, the result of the cell division process, i.e. more cells, have the same process enacted on it to produce even more cells.

It is not so obvious, but taken as fact now due to advances in molecular biology, that the genome modifies itself using what are known as ‘epigenetic’ mechanisms which alter the algorithmic functioning of the DNA contained in the genome. These pre-programmed epigenetic modifications are repeated recursively in the course of ontogenesis and neurogenesis. While in the course of biological development this form of recursive self modification is preprogrammed and circumscribed, the specifics of how and when this happens, comes about through the process of evolution, which as we’ll be explaining in chapter 8, is fully recursively self modifying in the sense we described earlier.

In the development of the brain it is now also known that the actual DNA itself is modified in a sort of ‘copy and paste’ operation known as ‘retrotransposition’, whereby small sections of DNA are repeatedly inserted into other parts of the Genome. Without going into anymore details, the point is made that the recursive function of cell division, undergoes recursive self modification so that it is therefore an inherent part of the workings of the process by which bodies and brains come into being; and is occurring on an even smaller scale at the level of the operation of the genome. The fractal brain theory shows that this process of recursive self modification is ongoing in the operation of our brains and minds. So the intuitive continuity that must exist from the point at which life begins, i.e. the fertilized egg to all the manifestations of our lives can therefore be described as a single recursive process that is able to modify itself. At the level of human thought and behaviour this ability to recursively self modify is known as learning.

On a much wider societal level the much discussed Technological Singularity can also be described as a recursively self modifying process. It involves a recursive feedback process whereby one generation of artificial intelligence is quickly able to design an augmented and improved next generation of AI. In turn this new generation is able to produce an even better next generation. This process proceeds in a continual recursive positive feedback cycle so as to create the so called ‘intelligence explosion’ and ‘super intelligence’. This is the key ingredient to the instigation of the Technological Singularity which describes a fundamental transformation of the world, human society and beyond, once this super intelligence is applied to the wider social, political, economic, scientific and technological realms. Essentially the entire planet, world society and political economy becomes a single recursively self-modifying positive feedback loop.

The effects of this anticipated transformation are so dramatic that they appear almost mythical and even of a prophetic seeming nature. So much so that speculation concerning the Technological Singularity has been labelled as ‘Apocalypticism for Nerds’. At the very least it’s fairly safe to say that the advent of AI and the realization of this positive feedback loop of recursive self modification of intelligence happening outside of our biological brains, instead on a machine substrate; could effect a transformation of the world that would be just as or probably even more dramatic than the advent of the industrial revolution.

So in the context of our little digression concerning the Technological Singularity, it is a very interesting property of the fractal brain theory that it describes this same process happening in the microcosm of the genome, human brain and emergent mind. So that likewise, human intelligence is made up of a virtuous positive feedback cycle happening in our heads, but constrained by our biological limitations and finite lifespans.

It will be seen as entirely appropriate, once this idea is fully accepted, that the key process that enables true intelligence, i.e. recursive self modification, would be the same trick behind the creating of artificial intelligence; and which in turn enables the power of recursive self modification to happen on a far grander scale to bring about the Technological Singularity. Individual artificial intelligences will then be clearly seen as a fractal microcosm of the macrocosmic Technological Singularity, that it gives rise to, which in turn would be a reflection of the recursively self modifying biological intelligence of our brains and genomes, from which the machine intelligence arises, which according to the ideas to be discussed in the pages to follow, will have been made in the likeness of our image.



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