2010: A Mandelbrot Odyssey

January 17, 2012

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While the title of this post is slightly beyond my understanding… Which is mainly because I had nothing to do with creating it… I find myself, nonetheless, publishing this rather off-kilter post, which is about nothing in particular, other than for the sake of sharing a magnificently orchestrated zoom into (and out of) the Mandelbrot Set. Truth be known, the title came from a YouTube video, which I Stumbled upon only the other day. And as it was so beautifully done… Not to mention that I so enjoy Johann Strauss’ classical masterpiece, “The Blue Danube”… And with its analogy to Kubrick and Clarke’s potent cinematic magnum opus, which I also adore so… I just had to post it here for your viewing pleasure (it’s best to view it in 720p HD on a full screen with the volume cranked UP for maximum effect).

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To find out more about the maker of this video, please click here.

And to find out more about “2001: A Space Odessy”, please click here.

OR to hear an explanation of what “2001: A Space Odessy” was all about, then please click here.

And, lastly, to find out more about Alex Gray (who’s artwork I use at the top of this post), please click here.


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Knowing others is wisdom… Knowing yourself is enlightenment.

Lao Tzu

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This is the first part of a series of blogs that I mentioned would be coming… The ones where I was going to do my best to present several ideas which aptly demonstrated that the notion of a ‘self’, a notion which we all seem to cling to so ardently in life, is really nothing more than a sort of grand illusion of consciousness conjured up by the biochemically ‘aware’ molecular systems of our bodies, which – if you’re a human being (or even a bird, perhaps) – use a vocalized type of memetic linguistic patterning to confer ideas, notions, emotions, warnings and/or other data to one another within social groups of a similar species… As it happens, these memes also evolve in a very similar way to the physical bodies that we presently use to convey all these ideas/memes with (after all, we do live in a fractal like universe)… And, it should be mentioned, all of this arose ‘naturally’ from the strange and unexpected relationship between order and chaos inherent within the solar system’s accreted mass of star dust… In fact this same strange and unexpected relationship between order and chaos resides at the heart of all universal phenomena… But more on that later.

For the moment… Please do excuse the length of time it has taken for me to realize this post… However, much patience, practice and research was needed to construct the essence of, what I’m sure many experts on the subject will only consider to be, this very rudimentary study. And perhaps, while I am managing to be humble, I should also add – so as to be totally honest and fair – that I’m really no better off reaching any definitive conclusion about what ‘I’, or rather my ‘self’, actually is either!?!?

In fact… This study has only made me more and more unsure – more unsure than I’ve ever been before – about what constitutes an idea of a ‘self’… Demonstrating for me, at least, that what many of us seem to take for granted as being a ‘certain’, ‘definable’ and ‘constant’ notion of identity and/or existence, upon closer inspection, actually becomes a very vague, intangible and indefinable man-made abstraction centered more around linguistic syntax rather than on direct knowledge or experience alone. I know that might sound quite disconcerting to some… However, it should be noted that it is nothing more than an alternative idea to counter the many commonplace views that presently exist on how the majority of us see our ‘selves’ and our position here in the cosmos today… Not to mention that I feel it might well be a good time to start evolving a bit, both mentally as well as physically.

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The individual has always had to struggle to keep from being overwhelmed by the tribe. If you try it, you will be lonely often, and sometimes frightened. But no price is too high to pay for the privilege of owning yourself.


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I know, I know… Why would anyone want to challenge the socially accepted Western view of the universe that we’re presently running along with… One that seems to set in stone a type of superiority over the rest of life here on Earth… One where the ‘self’ is all pervasive, and yet, it remains silently un-clear and unrevealed to those who need to know the most about it… ? Well, I for one don’t feel that our present state of Being and/or understanding adequately reflects our true circumstance… Let alone our true nature… And, having spoken to many fellow human beings here on Earth recently (so as to clarify whether we’re all functioning properly or not), I have discovered that many of our present problems i.e. over population, food shortages, war, etc… seem to stem from a fundamental error in the way we all perceive how we connect to the environment around us… To be more specific about this error… We all seem to be observing everything we do through an idea – or lens – of ‘self’. One that focuses our minds into modes of specific and present action within the world we presently find our ‘selves’ in.

But why should this way in which we perceiving things actually be a problem? Well… If we were to accept the idea of our ‘self’ somewhat blindly – like many of us do presently – and see ourselves as all being independently standing i.e. our ‘self’ exists separately and independently of everything else (which many of us clearly thinks is the case, seen by most people amassing bank balances, material wealth like gold, jewelry, cars, fashion based clothes, social status, etc)… Then we can actually limit the way that we see, understand and interrelate to everything and everyone else around us here on planet Earth and within the universe… Why? Because if we choose to completely disregard how the notion of ‘self’ came into being, and use only a marginalized approximation of what this unbounded essence of existence really is, then I fear we may mangle and divorce ourselves thoroughly from any real chance that we might have of developing a true and more appropriately connected state of Being that considers who ‘we’ all i.e. all sentient beings, unquestionably are.

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It is astounding that man, the instigator, inventor and vehicle of all these (i.e. political opinions and religious understandings) developments, the originator of all judgments and decisions and the planner of the future, must make himself such a quantité négligeable. The contradiction, the paradoxical evaluation of humanity by man himself, is in truth a matter for wonder, and one can only explain it as springing from an extraordinary uncertainty of judgment – in other words, man is an enigma to himself. This is understandable, seeing that he lacks the means of comparison necessary for self-knowledge. He knows how to distinguish himself from the other animals in point of anatomy and physiology… But as a conscious, reflecting being, gifted with speech, he lacks all criteria for self-judgment. He is on this planet a unique phenomenon, which he cannot compare with anything else. The possibility of comparison and hence self-knowledge would arise only if he could establish relations with quasi-human mammals inhabiting other stars…

Carl Gustav Jung (1875 – 1961)

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I mean… If we could cultivate an understanding of things that is free of ‘self’ centered tendencies and ‘selfish’ attitudes towards natural resources and ecological processes… An attitude that is devoid of all ‘self’ importance… And, thus, prevents our ‘selves’ from taking this idea of a ‘self’ too literally… Thereby relieving most – if not all – of the unnecessary stress and folly that awaits us if we continue with these ‘self’ centered views and relationships i.e. unwittingly promoting deconstructive behavioral patterns within our societies and ecosystems… Then we might well be able to disarm the citadels of ‘self’-importance that we have all imprisoned our ‘selves’ in… And REALLY SEE how ‘we’ all closely interconnect to the world (and universe) around us…

In many ways, this is why this journey to find my ‘self’ was so important… In fact, it’s why I feel it’s a really important journey for us all to undertake. Otherwise we will be cursed to pollute and destroy our delicate ecosystem over and over again, propagating an unsettled karmic pattern from our unenlightened mind streams and resulting behavior patterns, creating a Saṃsāra without end.

Thus, bearing in mind all I’ve written about within this website, it became, for me, a natural evolutionary process to take sometime to ponder over where the true enemy lay hidden… And, by being as humble and as diligent as I possibly could (please bear in mind I still have many faults and, thus, have done only as best as I could with my present defilements of mind, etc…), I managed to catch a glimpse of the enemy within… The enemy within my ‘self’… The one who created all the ‘self’-centered views, stances, opinions, arguments and ways of being that I’ve had, gotten into or done over the years… And I wondered, how can pacify this selfish mode of being… ?

For, once we manage to dismantle this ‘selfish’ perceptive stance, we might well be able to grasp how our present worldview was constructed and, thus, develop a better attitude toward solving our problem of ‘self’ obsession from the inside out rather than trying to do it from the outside in. Nothing we can do outside will ever really permanently change what is going on inside… Why? Well, it’s a bit like what Robert Persig once wrote in “Zen and the Art of Motorcycle Maintenance”…

“But to tear down a factory or to revolt against a government or to avoid repair of a motorcycle because it is a system is to attack effects rather than causes; and as long as the attack is upon effects only, no change is possible. The true system, the real system, is our present construction of systematic thought itself, rationality itself, and if a factory is torn down but the rationality which produced it is left standing, then that rationality will simply produce another factory. If a revolution destroys a systematic government, but the systematic patterns of thought that produced that government are left intact, then those patterns will repeat themselves in the succeeding government again and again. There’s so much talk about the system. And so little understanding.”

In my humble opinion, it’s in building our present conceptualized understanding of things from the inside out that we have created most of our problems here on Earth.

For example, the idea of ‘self’ – which is a designated social construct that allows anyone who can grasp it to relay, say, how they are feeling in relation to the world around them – provides us with the necessary notions/ideas for constructing sentences with, eluding to a “subject” and “object” with regards to some aspect of happening or action, OR change, between – or relative to – the two entities i.e. a subject and an object… From this formulation we derive the ability to describe to others our place in the world around us, along with the changes that effect all within it daily unfolding, and even how they affect our ‘selves’ and each other (see Noam Chomsky’s “Language And Mind”). Thus the notion of a ‘self’ gives us a very handy tool by which we can understand the world around us, conveying what we feel we need to convey to others in order to act with every one’s best interests at heart (or not) and do our best to survive.

Through this conveyance, We i.e. human beings, were able to organize – via the use of language – our ‘selves’ as collective groups who work together more effectively and efficiently as an objective, collective unit, relaying the merits of certain actions, and condemning overly ‘self’-centered interests that broke up group efforts (see Scientific American’s recent article “Groups With Good Social Skills Outperform The Merely Smart“). In this kind of linguistic/collective exchange, the ‘self’ allowed us to find a type of collective ‘fairness’ and/or ‘equanimity’ within the subsequent constructs of moral codes of conduct… Which, in time, became laws of the land.

So the ‘self’ has bestowed us with the advantage of understanding how we – as individuals – would like to be treated morally and, thereby, it allows us to develop a kind of moral, self-referenced exchange that ultimately posits an agreeable universal code of conduct between us all, precluding good living and optimal survival conditions for the majority. This is a type of morality that most of us would agree with one another upon… Why? Because it allows us to see things in relative terms i.e. the body, where our ‘perceived’ center of consciousness ‘seems’ to emanate from (more on this later), is the center of our perspective… And, relative to everything else, we desire a certain amount of ‘happiness‘ from the actions we perform, so that, on the whole, we all lead stress free and healthy lives. Thus, for the most constructive outcome within the complex dynamics of human flourishing, our actions should be morally guided with a concern for the whole… For looking after the interests of the whole precludes looking the interests of the individual.

So… Bearing all this in mind… Perhaps now is a good time for me to introduce the idea that most languages are essentially the same… I know on one level it might sound a bit bizarre i.e. Japanese is certainly not the same as French, which is not the same as English or Tibetan, otherwise we’d all speak like each other… Rather I mean that the syntax of all sentence structure is essentially the same as one another. In order to demonstrate this, I have quoted the following passage, which comes from the introduction to Noam Chomsky’s book, entitled “New Horizons in the Study of Language and Mind.”

Taken from Noam Chomsky’s “New Horizons in the Study of Language and Mind”, this is a Forward by Neil Smith. Cambridge, England: Cambridge University Press. Pp. xvi, 230. Reviewed by Gilbert Harman, Princeton University

Here are seven essays that describe and deplore a philosophical double standard that respects the methods and results of physics, chemistry, and biology but not the methods and results of linguistics and other sciences of the mind.

One sign of the double standard is that, while hardly anyone thinks one can do philosophy of physics without knowing physics, it is all too common for one to think that they can do philosophy of language without knowing linguistics.

Chomsky is, of course, the leading figure in contemporary linguistics. Starting in the 1950s, his development of generative grammar was an important factor in the shift from behavioristic to cognitive approaches to language and mind. Chomsky’s approach takes the goal of linguistics to be to characterize the human faculty of language, noting its differences from the human faculties for general problem solving science. As Chomsky and other linguists tried to give explicit characterizations of the competence of a speaker of a language like English, it became clear that a child learning language simply does not have the sort of evidence available that would enable it to learn the relevant principles from scratch. There is a “poverty of the stimulus.” The child must be prepared to acquire language with these principles in a way that it is not prepared to acquire the principles of, say, physics or quantification theory.

It is clear that normal children acquire a language that reflects their particular linguistic environment. A child brought up in Japan acquires a version of Japanese. The same child brought up in Brazil acquires a version of Portuguese. So, these languages must in some sense reflect some of the same underlying innate principles.

Further reflection along these lines and a great deal of empirical study of particular languages has led to the “principles and parameters” framework which has dominated linguistics in the last few decades. The idea is that languages are basically the same in structure, up to certain parameters, for example, whether the head of a phrase goes at the beginning of a phrase or at the end. Children do not have to learn the basic principles, they only need to set the parameters. Linguistics aims at stating the basic principles and parameters by considering how languages differ in certain more or less subtle respects. The result of this approach has been a truly amazing outpouring of discoveries about how languages are the same yet different.

More recently, there have been attempts to try to explain some of the basic principles on the assumption that the language faculty is close to an ideal engineering solution to a problem of connecting the language faculty with the cognitive system and the articulatory perceptual system. This “minimalist program” remains highly speculative, but whether of not it succeeds, contemporary linguistics as a whole has been a tremendous success story, the most successful of the cognitive sciences.

One would therefore expect that any philosopher of mind or language would make it his or her business to understand the basic methodology and some of the results of this subject. But many philosophers of mind and language proceed in utter ignorance of the subject.

For me, at least, this demonstrates – via the tenets of linguistics – that languages used for communication, a ‘universal’ trait of human beings presently here on Earth, are all essentially structured in very similar ways to one another. This notion of the subjective vs. objective in turn aids, what I can only call, the programming of one’s ‘self’ – via a type of memetic feedback loop – into who they ‘feel’ they presently are in this moment of their lives.

Perhaps it should also be mentioned here that, as we use with such daily regularity a linguistic ‘method’ that defines how separate aspects of the world occur in relation to ourselves i.e. we use sentences that include a plethora of ‘nouns’ or ‘names’ for almost everything we can experience tangibly or intangibly (see the dictionary for a full scope on the number of words that we use to describe things seperately with, coupled with their manmade ‘meanings’/’definitions’) along with how these names/nouns/concepts all interrelate to the separate notion of our ‘selves’… Thus we are unwittingly cementing in place a worldview based on an understanding of ‘separateness’… Of ‘independent’ arising… Where everything seems to have an ‘apparent’ individual identity and meaning, independent of everything else. And, if we don’t check ourselves daily, then we will fall foul of this ‘self’ referential system of thought, and think that everything must be ‘separate’ from everything else… Or even have a ‘meaning’ or a ‘purpose’ of some sort… A meaning that differentiates and/or separates it from other things… !!!
Perhaps that is why many of us feel at a loss when we truly realize that there is no inherent meaning to anything i.e. that everything is ultimately empty… Even the idea of our own lives, which is just a fantastical social construct at best, has no inherent meaning beyond that which we create for our ‘selves’… And, something that has scared me recently (though I must say I am slowly beginning to feel more at ease with the idea now), that there is no inherent meaning, or even concrete definition, to the notion of my – or even your – ‘self.’ I know I still haven’t discussed why the idea of a solid, or ever constant, ‘self’ is perhaps a delusion… But I am getting there slowly…

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Ultimate truth cannot be taught without basis on relative truth.


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After we have seen how everything slots together within linguistic constructs – and understood from which direction we constructed the conceptualized notion of the universe around us – we might well clinch a better method of action with which to resolve most our problems of sustainability and war with… Not to mention that it might well become a highly effective method that will allow us to see how we constructed the notion of our ‘self’ within our relative modes of understanding. For, once that is understood, I believe that we might well give our ‘selves’ the power to ‘self’ realize and actualize our own remedy from within.

It’s a bit like a motorbike… If you don’t know how one is constructed… Or even what a screw does… Or, even, how this basic unit of the motorbike functions i.e. a screw… Then you will never be able to repair it when it breaks down… Just because you know how to drive a bike doesn’t mean you know how to fix it. But when you look at all the parts that gave rise to its coming together… Even how it stays together… Then we will be able to at least take the motorbike apart, bit by bit, undoing the of the basic units that built it up… And, thus, through that process, we’d be able to have a better chance at seeing what is wrong with it and, so, have a better chance of repairing it.

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So as to look at some functions within the mind/brain/body/environmental continuum… I’d like to recap on what we’ve already covered in this blog… Mainly because I feel they contain some very important aspects about how the ‘self’ functions within this here website… For example, the notion of our ‘self’ functioning as a sort of feedback loop (as discussed in Douglas Hofstadter’s book, entitled “I Am A Strange Loop“), along with how analogy can be viewed as the core of cognition, plus how the mind naturally demonstrates that the very process that drives it is based on an engine of nonlinear dynamics i.e. an engine of pure chaos, as well as how we are beginning to use these models of understanding in order to develop artificial intelligence with… Not to mention we have discussed concepts that treat our ‘self’ as nothing more than an amalgamation of ideas/memes that collect over the course of our lives, via a feedback loop between the mind/brain/body/environment continuum, and which are then assimilated into a central memeplex of ‘self’ for relative temporal processing… !!! We’ve also seen how prone to illusion the system of our biomechanical bodies makes us – the very bodies that we use on a daily basis to perceive the world around us with… And, thus, we can see how we should also be aware of the resulting delusions that therefore creep into our own socially constructed understanding about what the nature of reality ‘seems’ to be… !?!? And, bearing that in mind, we’ve even managed to discuss how nothing is permanent and that ‘time’ is really only a conceptualized understanding about how our past memories relate to the only moment that we really have i.e. this present moment… Thus we can begin to understand how we distort the essence of experience with social constructs, like the concept of ‘time’, which we choose to gauge gradients of change with in relation to our own, somewhat ‘self’ biased perspectives, which are usually mainly centered around our own clusters of personalized memories.

I think all these insights are so important to bear in mind… Why? Because rarely do we truly see past these prejudiced, memetically procured views and glimpse at the pure and ultimate nature of everything – and I mean EVERYTHING – which resides in a continually evolving flux of new patterns… Unfolding freely and interconnectedly from one ‘conceptualized’ moment to the next… In fact, there never was any need for conceptualization… Nor was there ever any moment… There was only Being… Being in the now… A Being that was beyond all definition… Continually evolving… Beyond all understanding… Free from any conceptualization…

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None by his own knowledge, or by subtle consideration, will ever really understand these things. For all words and all that one can learn or understand in a creaturely way, are foreign to the truth that I mean and far below it.

John Van Ruysbroeck (1293 – 1381)

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‘Being’ never needed any conceptualization because experience was naturally selected for without it and, so, it spoke completely for its ‘self’… Pure ‘experience’ is unbounded and beyond all dualistic modes of thinking… But once one takes the bitter bite/byte from the fruit that came off the tree of knowledge, we instantly limit our understanding of all things and forget that we are much like butterflies ‘flapping our wings’ of imagination within the parameters of our caged, syntax based existence, ‘using our structured minds’ to shape the world in which we now live… How many of us realize that there is this beautifully unbounded, enchanting, chaotic beast lurking deep within the system of our ‘selves’… ? One that, if ignored, can amplifiy subtle changes to manifest infinitly further down the line, like ‘hurricanes’ ripple off the flutter of a butterfly’s wings… Capable of destroying as much as creating.

Without a better viewpoint of our ‘selves’ and how we relate to the universal system in a karmic manner, it will be very hard for us to develop a pure and compassionate intent that amplifies predominantly constructive modes of living, while diminishing the destructive aspects of actions suitably for optimal flourishing of all sentient beings… For, without constructive modes of living, we only unwittingly harm other sentient beings, including ourselves, much further down the line.

Furthermore… So as free our own existence from a “God created us in his image” induced self-righteousness, which seems to only further this ‘self’ obsession… I’ve also begun to touch on how science, along with other ‘human’ endeavors, are yielding results that clearly demonstrate that ‘We’ all are really nothing more than a bunch of ‘interdependently’ related chemical reactions which are slowly evolving in a closed-off, ‘petri dish’ type of a planetary environment, which is isolated from other planetary ecosystems only through space’s vast and open, inhospitable expanses… Here, on Earth, whether we realize it or not, we are simply ‘doomed’ (though I fear that is very much the wrong word with which to describe life’s bountiful delights with) to do our best to survive and work around any sudden environmental/social/universal changes that might disrupt or hamper our ability to live in stability with the environment and ecosystem we find ourselves in. That is unless, somewhere down the line, we actually forget what our original purpose was.

Here I’d like to take a moment to introduce an article from Paulo Coelho’s blog entitled, “Learned Helplessness”… Perhaps, while reading it, I would beg everyone to consider the plethora of maladies that this modern world – and its medicine – has invented for us i.e. ADHD, anxiety disorder, etc…

The American psychologist Martin Seligman’s foundational experiments and theory of learned helplessness began at University of Pennsylvania in 1967, as an extension of his interest in depression.

A person should be able to walk away from an abusive relationship, for example, or voluntarily quit a stressful job.
A psychological condition known as learned helplessness, however, can cause a person to feel completely powerless to change his or her circumstances for the better.
The result of learned helplessness is often severe depression and extremely low self-esteem.

Learned helplessness can be seen as a mechanism some people employ in order to survive difficult or abusive circumstances.
An abused child or spouse may eventually learn to remain passive and compliant at the hands of his or her abuser, since efforts to fight back or escape appear futile.Learned helplessness results from being trained to be locked into a system. The system may be a family, a community, a culture, a tradition, a profession or an institution.

Initially, a system develops for a specific purpose. But as a system evolves, it increasingly tends to organize around beliefs, perspectives, activities and taboos that serve the continuation of the system. Awareness of the original purpose fades and the system starts to function automatically. It calcifies.

Some experts suggest learned helplessness can be passed on through observation, as in the case of a daughter watching her abused mother passively obey her husband’s commands.
The daughter may begin to associate passivity and low self-esteem with the “normal” demands of married life, leading to a perpetuation of the learned helplessness cycle.

Child abuse by neglect can be a manifestation of learned helplessness: when parents believe they are incapable of stopping an infant’s crying, they may simply give up trying to do anything for the child.

Another example of learned helplessness in social settings involves loneliness and shyness. Those who are extremely shy, passive, anxious and depressed may learn helplessness to offer stable explanations for unpleasant social experiences.

A third example is aging, with the elderly learning to be helpless and concluding that they have no control over losing their friends and family members, losing their jobs and incomes, getting old, weak and so on.

How many times could I have just given up and gone to sit with the rest of the herd, medicated up to my eye-balls, happy and supposedly contented with my lot in the daily routine of ‘supposedly’ well adjusted human endeavor… And done so until eventually, one day, I died… ? Too many times was I given this option… And how many times could I have just proclaimed helplessness within this capitalist society and given up this quest of ‘self’ discovery and operated in only the confines of some syndrome or mental disorder, looking for immediate gratification and comfortable conformity? Again, all too many…

Perhaps when one begins to formulate all this for themselves… And glimpse at a more adequate type of interdependent reality for themselves… They might well suddenly realize that our own need for stability limits the way we view this ever-changing world and universe… And, once that step has been taken, perhaps we can then also begin to glimpse at a humbling reminder that shows us we are all really nothing more than the ‘left-overs’ of matter reconfigured in the present solar system’s accretion process – all of which was constructed naturally, via processes of chaos, from a mass of fused atomic debris which had been expired, like soot from a fire, by past splendiferous burns of long gone suns

Here, perhaps we are somewhat fortunate to have developed a type of organic Life that allows ‘us’ to be present, both here and now, and perceive the wonders of the universe as they unfold around us… Using similar structures and processes to those found in and around the universe so as to guide our perceptive mechanisms and understandings..

Well… I’m sure you can imagine how all this began to sound to a layman like myself… Especially when I began compiling and piecing together all the data and experience I had available to me – which, on the whole, was taken from a vast quagmire of scientific journals, published papers, university/researcher websites, books, video lectures and even going to (though I think ‘sneaking into’ is a far better description of events) a few university lectures in person, as well as some transcendent experiences involving psychedelic drugs and certain meditative techniques – so as to understand a bit more about my place, here, in the unfolding non-linear dynamic of the cosmos…

No doubt, while gorging my ‘self’ on the raw data that ‘I’ had amassed, ‘I’ found my ‘self’ restructuring and rearranging it into streams of, what ‘I’ can only call, an intuitive patterning, or sense of reasoning… One that came from my heart and gut as much as it did my head, all the while filling up the pages of this website with these ‘raw’ ideas… Ideas that relentlessly kept flooding into my mind’s memetic stream… And yet, whilst laying out all these ideas for restructuring, I never knew that I’d be slowly coming back round, ‘full circle’ so to speak, to look back at the observer… At the ‘self’… To see this idea of consciousness looking back at its ‘self’ in an eternal feedback loop… Like someone standing in front of two slightly distorted mirrors faced back in upon each other… And then, when I discovered that the observer, them ‘selves’, can actually shape the way in which the world functions around them simply through the act of perceiving it… !?!? Well… That blew a lot of the ‘supposed’ common sense I had learned from school and society right out of the water.

However, during this process of reflection, the hardest thing for me was trying to pin point where this ‘self’, this observer, actually was… Where ‘I’ actually came from… Why? Because, in trying to discover what my ‘self’ was – this powerful perceiving entity that could shape the universe around it simply by observing – I found my ‘self’ using all the antiquated social constructs that I had been provided with during my childhood and teenage years; concepts and ideas that I had learnt while I was at school and university… And in doing so, I found my ‘self’ needing to ask new questions within questions, so as to to puncture the crusty surface of a hard-baked, almost calcified, social reality… Questions like, if I didn’t use any type of language to communicate with, then, in the absence of any conceptualized notion of a ‘self’, would ‘I’ still be aware of my ‘self’ in the way that ‘I’ presently am, etc… ???

‘I’ mean… Surely if this idea of a ‘self’ was meant to be so obvious a fact… Like, “I think, therefore I am…” ! And as obvious as the existence of a ‘self’ seemingly was… Didn’t there have to be an equally obvious and simple answer about what the ‘self’ actually was/is… An answer that could exist independently of everything else – like language seemed to hint at – without the need to unravel the highly complex and infinitely long chain of cause and effect that brought it all into being… !?!?

But every time I looked at boiling any set of these conceptualized notions about the ‘self’ down into a concise and tidy bit of understanding… I only found endless vagaries, each of which did not quite fit the mark… Each of which didn’t satisfy my need for precision… Each of which required more questions to be asked… And each of which required more answers than the last to be defined and clarified… Spiraling into and endless foray of attach and parry that would apparently lead me to a reachable goal. Oh, how deluded I was.

It eventually became evident that a straightforward and transparent concept of the ‘self’ was not possible. In fact, the solution of my ‘self’ – which I found to be impressively colorful, soluble and ‘seemingly’ apparent in the vocalized solution of syntax which we all used in every day life, much like a dye in water – kept evading any type of concise certainty about what the ‘I’, which was being discussed, actually was. Paradox upon paradox kept layering over one another… I mean… How far could it go? Could these questions go on and on forever and ever… ? Like the way we could go on zooming into and/or out of our present scale of conscious resolution (let’s temporarily forget the apparent limits imposed by the Planck length)?

For example… When I wanted to look at the solidity of my body, where I once thought I perceived my ‘self’ to reside… I wondered whether the ‘self’ could simply be a sum of its physical parts i.e. and enduring form relating to all the atoms in their present structural configurations, connected together in cascading molecular lines/chains of environmental functionality?

But then ‘I’ remembered an idea that was discussed earlier in “An Idea About Who We Really Are“… An idea where the body’s apparent solidity comes into question.

Perhaps here it is a good time to introduce one of those paradoxes that I came across not too long ago, entitled the “Ship of Theseus…” For I feel this adequately allows us to grasp the idea of whether physical (even mental) identity – something that is related to the idea of a ‘self’ – is persistent or not…

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This puzzle has been around since antiquity, probably later than Heraclitus, but not much later. It first surfaces in print in Plutarch (Vita Thesei, 22-23), where the Greek wrote:

“The ship wherein Theseus and the youth of Athens returned had thirty oars, and was preserved by the Athenians down even to the time of Demetrius Phalereus, for they took away the old planks as they decayed, putting in new and stronger timber in their place, insomuch that this ship became a standing example among the philosophers, for the logical question of things that grow; one side holding that the ship remained the same, and the other contending that it was not the same.”

Plutarch tells us that the ship was exhibited during the time [i.e., lifetime] of Demetrius Phalereus, which means ca. 350-280 BCE.

To make the original puzzle clearer… Let me reiterate this idea in planer English… Over the years, the Athenians replaced each plank in the original ship of Theseus as it decayed, thereby keeping it in good repair. Eventually, there was not a single plank left of the original ship. So, did the Athenians still have one and the same ship? Or was it a completely different ship?

But we can liven it up a bit by considering two different, somewhat modernized, versions. On both versions, the replacing of the planks takes place while the ship is at sea. We are to imagine that Theseus sails away, and then systematically replaces each plank on board with a new one (say it is his habit to carry a complete supply of new parts on board as his cargo). Now we can consider these two versions of the story:

Simple version: Theseus completely rebuilds his ship, replaces all the parts, throws the old ones overboard. Does he arrive on the same ship as the one he left on? Of course it has changed. But is it really the original ship?

Let A = the ship Theseus started his voyage on.

Let B = the ship Theseus finished his voyage on.

Our question then is: Does A = B? If not, why not? Suppose he had left one original part in. Is that enough to make A identical to B? If not, suppose he had left two, etc, etc… Where do you draw the line? I mean… If all the new parts came from the same forest… Or even better… If they all came from the same type of tree as the pieces of wood that ship was originally constructed from did, would this allow one to call it the same ship? Or if these pieces of the same tree were carved by the same person… Would it then be the same ship? Then again… Are these just trivialities? And, if so, would it even matter if Theseus stopped along the way and used different types of wood, whatever came to hand, so to speak… Then would this still be the same ship?

The permutations on this paradox are almost endless… For example, if all the atoms in the ship, atoms that have come together after the processes of accretion and evolution that formed us all along with the rest of the solar system that we now see around us today… If these atoms were replaced in exactly the same position and manner… The only difference being that the atomic matter came from a different set of suns… Would Theseus’ ship still be the same ship? Are the processes that made us more important that the material we are built from?? Or is the notion of ‘importance’ its ‘self’ empty of all inherent meaning… And, thus, is inadequate to describe anything ultimately???

In my humble opinion… We can apply this same principle to the physical notion of our ‘self’… For example we have already seen in a prior blog, entitled “An Idea About Who We Really Are” that, over a 15 year period, the human body replaces almost every single cell within its structure. All the material changes within us… Thus, is this body, that you are now using to read these words with, actually the same body that you had several years ago? I know for me, at least, it certainly feels like it is the same body… In fact it feels similar to the body I had 15 years ago… 15 years ago I was 20 years old, and pretty much looked the same… Albeit now I have a few grey hairs and am slightly fatter than I used to be… I know I ‘essentially’ still feel the same now… And I can still do nearly all the same things I used to, etc… But, despite these similar feelings, am I really the same person?

The same happens with experience. Experience shapes the way we react to the world around us. Different experiences cause different memories to be formed… And with these memories, we temporally choose to guide our ‘selves’ through certain situations… So, if we had to two of me… Exactly the same as each other, up to a specific point in time i.e. all the materials and processes that made us both were exactly identical… Along with all the experiences up to that moment in time, etc… Then, if one of me was to experience something completely different to the other… Would that differing experience mean that ‘I’ am no longer my ‘self’?

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Even if the ‘self’ was simply just a sum of its parts and expereinces… We should ask the question… Where should one draw the lines between all these parts i.e. at a molecular level, or at an atomic level, or even at subatomic levels, as with neutrons, protons, electrons, quarks, etc… ?? Or even, where should one draw the line between all these experiences? I mean… What even REALLY constitutes a part??? Isn’t it just the mind grasping at trying to understand the unfathomable process of everything… And, in doing so, procure its own brand of stupid dependability and definition???? Because to define any part properly, shouldn’t we still also include the processes that brought all these individual parts together to function as they do presently, describing, as well, how those processes arose too, and the ones that gave rise to them, ad infinitum?????

But perhaps more pertinently… Do we actually have any real right to divide the flow of an interdependent system up into conceptualized parts? You know, like we feel we do, for example, with borders between countries i.e. separating these interrelated topographies with merely imagined, fracturing lines that stem from our fractured, intellectualized memetic mind streams… I mean… It obvious that these lines simply do not exist in the real world. Nowhere that I have ever been on Earth is there some line that nature left us that denotes who should live where and how they should live or what they should be called… Nowhere!

And even if we did have a right to divide up them up… What would happen if we were to walk around these imagined borders, examining every nook and cranny of the immense majesty and diversity that fell into and out of every facade of their periphery… ? Wouldn’t we also find what Benoît Mandelbrot wrote about in his 1967 paper, published in Science, entitled “How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension“?

Surely with every new question asked, a new level of detail emerges, giving rise to an unbounded and infinite boarder? Just as Lewis Fry Richardson discovered, the length of a given coastline depends on the method used to measure it. Since a landmass has features at all scales, from hundreds of kilometers in size to tiny fractions of a millimeter and below, there is no obvious limit to the size of the smallest feature that should/could not be measured around… And, hence, there is no single well-defined perimeter to the landmass.

In my humble opinion, it is this very idea that should be applied to trying to understand the notion of ‘self.’ For example, when someone asks us the question “who are we?”, various approximations seem to come to mind and, with these approximations, vague assumptions are made about who we are i.e. he/she lives in Tunbridge Wells, wears sunglasses on sunny days, is a vegetarian, etc… And, perhaps, if we were from a scientific disposition, we might also include that we were made from flesh and bone, which in turn is made from proteins, carbohydrates, fats, water, calcium, etc… It doesn’t matter to our conceptualized notions that this flesh and bone changes every few years… Just so long as we can describe what it is that we vaguely want to talk about here and now… !?!?

Just as with landmasses too, various approximations exist when specific assumptions are made about minimum feature size. So… How far can we go on probing the idea of a ‘self’ with out questioning the very logic/ideas/ approximations/processes that created it? Or even the language that we use to describe it? I mean… If we go all the way… ALL THE WAY… Will we not discover that we are really inherently unbounded and indefinable… ?? That we are infinite in a perspective that present social conditioning and understanding has forced us to forget… ???

While looking for my ‘self’, I found that Douglas Hofstadter’s book, entitled, “Escher, Bach and Gödel: And Eternal Golden Braid”, was more pertinent than I had ever really imagined it would be… And recently I’ve found my ‘self’ coming back to it time and again… Because in many ways this search for the ‘self’ reminds me of looking at Gödel’s “Incompleteness Theorems.” Rather than the ‘self’ being a real entity that can be defined logically and reasonably within axiomatic definitions based on “good-old” empirical evidence – evidence that is derived from many types of experimental observation, and then assessed via modes of logical reasoning, so as to posit how it all fits together into a greater, universal picture… Upon a closer inspection, this ‘I’ or ‘self’ seems to merge with, and become part of, the WHOLE universal dynamic… A tiny part of the WHOLE picture… Like a baby Mandelbrot set in the totality of the WHOLE Mandelbrot set… Each of these little sets is dependent on all the totality of the patterns preceding it… Patterns that, if they were any different further upstream, would not have brought it to rest in its present place, shape, size and/or fashion.

Saying that… I doubt that the factors that brought about our “selves” into this present universal moment are quite as simple as zn+1 = zn2 + c… Rather, in my humble opinion, there would have to be – more likely – an infinite amount of describing equations, all entangled and entwined into one another, rippling in and out of sync with each other, feeding back through and around them ‘selves’, making – from a human’s point of view – such an overwhelmingly complex totality of indefinable and unpredictable occurring precisions that one might only be able to describe it as Baruch Spinoza once did… Simply as “God, or Nature” its very ‘self’.

When I began to view the idea of ‘self’ in these terms i.e. that there is this evolving fractal chain of interdependent events, linked by cause and effect – one that gives rise to the notion of ‘self’ – it reminded me somewhat of Kalu Rinpoche’s writing on “Karma, Interdependence and Emptiness.” This unfolding cascade of events stacks up with every conscious and unconscious decision/action creating the karmic patterns that determine the unfolding nature of our reality and, therefore, our circumstance.

I know many of us might well call everything We i.e. humans, do or make or say, even, “man-made…” But in reality it is all a part of the natural flow of things… There is an order there, one that defies comprehension… It’s flow is so uncertain and unpredictable that it flexes with every new action or event that is presented to it… Never does it stay the same… In fact, it is so sensitive to everything, that even a little ripple can manifest huge changes somewhere later down the line… Certain ancient Chinese philosophers once called this the great Tao. It was unspeakable, un-describable, and all pervasive… To talk of it would limit it and destroy its essence… To define it would only end up defiling its purity.

So too with the ‘self’… When we try to define our ‘self’, nothing that we hang on ‘it’ conceptually fits ‘its’ essence properly… Every limiting word presumes a rough approximation of something infinite and unbounded… And to use limitations to describe something which is unbounded is dangerous… It breeds delusion and breaks the delicate balance between what ‘IS’ and what we think ‘it’ is. I’m sure that if we all were to spend most of our time striving for enlightenment, then we would begin to see all this i.e. that we are nothing more than a part of the chaos inherent in a universal – although even the term universal might well seem to limit what I really want to express – system that is continually evolving and unfolding in this present moment. When we let go of our ‘selves’ then we truly become free and we can see that nothing begins or ends… Nor does anything exist independent of everything else, especially in the finite ways that we have been taught to describe the world with.

So… To bring it back round to where we started from… To understand what the ‘self’ is, I found my ‘self’ having to look at all the processes that brought me into being… And while I’m sure I’ve only touched on just a hand-full of these in the infinite majesty unfolding continuously around us… It lays a good idea at the unknowable totality of the interconnectedness we all share with one another AND the universe around us… I know we might well like to describe everything in terms of how it relates to our “selves”… But it would be better not to get too attached to this way of describing things… For it can breed delusion and spread confusion by manifesting fantasies beyond what actually “IS”. I As Douglas Adams once said…

This is rather as if you imagine a puddle waking up one morning and thinking, ‘This is an interesting world I find myself in—an interesting hole I find myself in—fits me rather neatly, doesn’t it? In fact it fits me staggeringly well, must have been made to have me in it!’ This is such a powerful idea that as the sun rises in the sky and the air heats up and as, gradually, the puddle gets smaller and smaller, it’s still frantically hanging on to the notion that everything’s going to be alright, because this world was meant to have him in it, was built to have him in it; so the moment he disappears catches him rather by surprise. I think this may be something we need to be on the watch out for. We all know that at some point in the future the Universe will come to an end and at some other point, considerably in advance from that but still not immediately pressing, the sun will explode. We feel there’s plenty of time to worry about that, but on the other hand that’s a very dangerous thing to say. Look at what’s supposed to be going to happen on the 1st of January 2000—let’s not pretend that we didn’t have a warning that the century was going to end! I think that we need to take a larger perspective on who we are and what we are doing here if we are going to survive in the long term.

I will leave it here for now… The second part to this study of ‘self’ will follow soon.

Having recently been to Dr Bruce Lipton‘s talk, entitled “The Biology Of Belief,” which was held in the Logan Hall of the Institute Of Education in London this last Saturday, the 17th of July 2010, I had reinforced the idea that we are nothing more than a bunch of atomic mechanisms, built from atomic polymers i.e. DNA, proteins, fatty acids, etc… all arranged into intricate cellular clusters, which – given the right circumstances – can function with amazingly natural flows of Being, demonstrating what we can only call, from a self referencing point of view, natural organic movements… And over the years we have – funnily enough – coined these flows to be “Life-Like.”

I really believe that when we begin to see Life in these terms i.e. that Life as we presently know it usually results from the complex interactions of the atomic machinery within an enclosed cellular body, which, if presented with more differentiated versions of itself, can build larger bodies from highly specialised cellular clusters… And then, once in place, out of all this unfolds a nonlinear biology/biochemistry of perceptive functions, all of which came about through the process of what we now know as ‘chaos’ – rather than the result of some divine intervention – and thus becomes nothing more than a complex, naturally occurring chaotic system that ‘intelligently’ reacts and responds, through effective behavioural patterns, to external environmental pressures and stimuli, precipitating survival habits that have been natural selected for… The behavioural patterns allow Life to survive in an ever changing environment, and the chaos inherent in our being affords us the ability to utilise the best survival traits that we can, one of which was the development of self-biased tendencies centred around a distinct notion of “self” and “body” that many of us seem to take for granted on a daily basis.

While I will eventually get around to discussing the reality and validity of the “self” in a future blog (something that is taking me much longer than I had anticipated)… In this blog I’d like try to discuss why this idea of viewing ourselves as a machine is a lot more natural and effective a notion about our “selves” than any previous egocentric notion about what we really are i.e. we were created by one or several Gods, in their own images to be special, etc… Certainly Dr Bruce Lipton’s analogy about us being a group of living cells which function within the confines of this body as a “community” of beings, each performing their own specific roles within the body’s mechanism i.e. just as governments regulate countries and their home economies, while police men arrest criminals, so do certain parts of the central nervous system function as regulators of heart rhythm and bodily temperature, while white blood cells kill of infections from ‘maliciously behaved’ bacteria… This idea of self-similarity within the patterns of Life that we see unfolding here on Earth across all scales and modes of Being will provide us with a very deep and intuitive understanding about the subtle and – what we tend to call – divine aspects of our Being, as well as showing us all how we interconnect and relate to this universally unfolding discourse..

Bearing in mind this ‘rule’ of self-similarity that seems to present itself within and throughout the whole of this universal dynamic so pervasively… And by viewing Life as a type of mechanisation… I am curious as to where – or from which level of scale – the emotive force of Life actually originates from? Is it at the level of the body i.e. does it directly and uniquely come from the sum of all its parts, where each individual part would be able to do nothing whatsoever by itself? Or is this trait of the emotive Life force buried deep down with in the cellular – or even the atomic – matrix? Certainly when we try to address what this experience of Life actually is and how it comes about we can hopefully begin to see it does not only belong to the body as a whole unit, but also comes from the various levels of functionality within the body i.e. at the cellular and atomic levels.

Just as Jung is concerned as much with the individual within society, as the individual is him/her “self” the measure of society, so too we can apply this analogy to the cell and body. Without the individual, society cannot function, let alone exist… And without the cell, the body cannot function or even exist. Life and its dynamism directly stems from the units that comprise the whole. These units, just as much as the whole, are all subject to the same forces and methods of development as each other i.e. those of nonlinear evolution. This ‘Life,’ and its essence, relies upon the parameters of these nonlinear, fractal eddies with their dynamics. These cellular bodies that make up our own larger bodies are driven by and made from the same underlying principles of naturally occurring algorithmic phenomena… Even though at first glance it might not be obvious that they are… But they are. Thus, if these algorithmic patterns reside across all levels of scale, shape and form, why shouldn’t we expect similar ‘intelligences’ to reside across all scales of these naturally occurring systems, whether at the human body’s level or a cellular level? Ultimately it’s up to you what you believe… But to function better I personally would like to know a little bit more about the processes that give rise this “I”; the processes that drive all of Life here on Earth – and possibly beyond too – rather than giving into dogmatic nodes of parrot fashioned understanding.

As Jung once wrote in “The Undiscoverd Self“:

Human knowledge consists essentially in the constant adaptation of the primordial patterns of ideas that were given us a priori. These need certain modifications, because, in their original form, they are suited to an archaic mode of life but not to the demands of a specifically differentiated environment. If the flow of instinctive dynamism into our life is to be maintained, as is absolutely necessary for our existence, then it is imperative that we remould these archetypal forms into ideas which are adequate to the challenge of the present.

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Our denominational religions with their archaic rites and conceptions – justified enough in themselves – express a view of the world which caused no great difficulties in the Middle Ages but has become strange and unintelligible to the man of today. Despite this conflict with the modern scientific outlook, a deep instinct bids him hang on to ideas which, if taken literally, leave out of account all the mental developments of the last five hundred years. The obvious purpose of this is to prevent him from falling into the abyss of nihilistic despair. But even when, a rationalists, we feel impelled to criticise contemporary religion as literalistic, narrowminded and obsolescent, we should never forget that the creeds proclaim a doctrine whose symbols, although their interpretation may be disputed, nevertheless possess a life of their own on account of their archetypal character. Consequently, intellectual understanding is by no means indispensable in all cases, but is called for only when evaluation through feeling and intuition does not suffice, that is to say, with people for whom the intellect holds the prime power of conviction.

In order to emphasise this re-equation that we need i.e. to understand that we are part of a whole ecosystem of Earth, just as a cell is part of the body’s ecosystem, it is here that I’d like to present an article which I read not too long ago in the New Scientist magazine… One that tackles this issue of where emotive Life comes from. When we see that Life’s organic flow resides across all levels of being i.e. atomic, cellular, bodily, biospherically, or even within the planet and its solar system, we might begin to understand that some of our older religious notions of the divine state of existence that We – that is, all Life – experience no longer need to be fantasised over or marginalised in any inaccurate way whatsoever. Now, through the doors of science, we can directly see the mechanisms of Life at work, and thus ‘understand’ the essence behind their patterns and interdependent interactions, all through which we gain the essence of our Being. Natural ordering comes from the patterns of chance and chaos, which give rise to development and originality within all universal systems, whether biological or otherwise. These systems, if given favourable circumstances/environments in which to start, can then begin the arduous process of developing into complex systems of environmentally perceptive and adaptive systems. Human beings are even beginning to use these recursive patterns – which have been called the “Thumb Print Of God” – in their technological developments i.e. to develop semi intelligent robotic systems that can learn fast and develop effective solutions to presented problems in ways that surpass anything we’ve tried or known before.

Thus, with these many new observations, I believe it is time to re-write our archetypal programming. Just as when I first saw the Mandelbrot Set on a postcard from a friend while at school and immediately recognised its tortuous, writhing flow as something so familiar and deeply ingrained in my being… So too do all ‘Gods’ leave this same feeling of familiarity… Of spirituality… And of deep connection to the whole… Here lies an answer to a new understanding… That self-similarity resides within all units of the whole… If you find intelligence within the body… Then why not within cell too… Or even in the atom… After all, one essence is usually found within the other, and so permeates through the entire being. Certainly atoms are just as discerning as human beings are… We all choose what we will or won’t react/socialise/breed with. Does this intelligence then go deeper? Intelligence that can be found within the proton, neutron and/or electron… And, if so, then why not even in the quark… Or the God particle…. Etc, etc, etc… ?

The Secrets Of Intelligence Lie Within A Single Cell

Late at night on a sultry evening, I watch intently as the predator senses its prey, gathers itself, and strikes. It could be a polecat, or even a mantis – but in fact it’s a microbe. The microscopic world of the single, living cell mirrors our own in so many ways: cells are essentially autonomous, sentient and ingenious. In the lives of single cells we can perceive the roots of our own intelligence.

Molecular biology and genetics have driven the biosciences, but have not given us the miraculous new insights we were led to expect. From professional biologists to schoolchildren, people are concentrating on the minutiae of what goes on in the deepest recesses of the cell. For me, however, this misses out on life in the round: it is only when we look at the living cell as a whole organism that wonderful realities emerge that will alter our perception not only of how single cells enact their intricate lives but what we humans truly are.

The problem is that whole-cell biology is not popular. Microscopy is hell-bent on increased resolution and ever higher magnification, as though we could learn more about animal behaviour by putting a bacon sandwich under lenses of increasing power. We know much about what goes on within parts of a cell, but so much less about how whole cells conduct their lives.

Currently, cell biology deals largely with the components within cells, and systems biology with how the components interact. There is nothing to counterbalance this reductionism with a focus on how whole cells behave. Molecular biology and genetics are the wrong sciences to tackle the task.

Let’s take a look at some of the evidence for ingenuity and intelligence in cells that is missing from the curriculum. Take the red algae Rhodophyta, in which many species carry out remarkable repairs to damaged cells. Cut a filament of Antithamnion cells so the cell is cut across and the cytoplasm escapes into the surrounding aquatic medium. All that remains are two fragments of empty, disrupted cell wall lying adjacent to, but separate from, each other. Within 24 hours, however, the adjacent cells have made good the damage, the empty cell space has been restored to full activity, and the cell walls meticulously realigned and seamlessly repaired.

The only place where this can happen is in the lab. In nature, the broken ends of the severed cell would nearly always end up remote from each other, so selection in favour of an automatic repair mechanism through Darwinian evolution would be impossible. Yet something amazing is happening here: because the damage to the Antithamnion filament is unforeseeable, the organism faces a situation for which it has not been able to adapt, and is therefore unable to call upon inbuilt responses. It has to use some sort of problem-solving ingenuity instead.

We regard amoebas as simple and crude. Yet many types of amoeba construct glassy shells by picking up sand grains from the mud in which they live. The typical Difflugia shell, for example, is shaped like a vase, and has a remarkable symmetry.

Compare this with the better known behaviour of a caddis fly larva. This maggot hunts around the bottom of the pond for suitable scraps of detritus with which to construct a home. Waterlogged wood is cemented together with pondweed until the larva has formed a protective covering for its nakedness. You might think this comparable to the home built by the testate amoeba, yet the amoeba lacks the jaws, eyes, muscles, limbs, cement glands and brain the caddis fly larva relies on for its skills. We just don’t know how this single-celled organism builds its shell, and molecular biology can never tell us why. While the home of the caddis fly larva is crude and roughly assembled, that of the testate amoeba is meticulously crafted – and it’s all made by a single cell.

The products of the caddis fly larva and the amoeba, and the powers of red algae, are about more than ingenuity: they pose important questions about cell intelligence. After all, whole living cells are primarily autonomous, and carry out their daily tasks with little external mediation. They are not subservient nanobots, they create and regulate activity, respond to current conditions and, crucially, take decisions to deal with unforeseen difficulties.

“Whole living cells are not subservient nanobots, they respond and take decisions”

Just how far this conceptual revolution about cells could take us becomes clearer with more complex animals, such as humans. Here, conventional wisdom is that everything is ultimately controlled by the brain. But cells in the liver, for example, reproduce at just the right rate to replace cells lost through attrition; follicular cells create new hair; bone marrow cells produce new circulating blood cells at a rate of millions per minute. And so on and on. In fact, around 90 per cent of this kind of cell activity is invisible to the brain, and the cells are indifferent to its actions. The brain is an irrelevance to most somatic cells.

So where does that leave the neuron, the most highly evolved cell we know? It ought to be in an interesting and privileged place. After all, neurons are so specialised that they have virtually abandoned division and reproduction. Yet we model this cell as little more than an organic transistor, an on/off switch. But if a red alga can “work out” how to solve problems, or an amoeba construct a stone home with all the “ingenuity” of a master builder, how can the human neuron be so lowly?

Unravelling brain structure and function has come to mean understanding the interrelationship between neurons, rather than understanding the neurons themselves. My hunch is that the brain’s power will turn out to derive from data processing within the neuron rather than activity between neurons. And networks of neurons enhance the effect of those neurons “thinking” between themselves. I think the neuron’s action potentials are rather like a language neurons use to transmit processed data from one to the next.

Back in 2004, we set out to record these potentials, from neurons cultured in the lab. They emit electrical signals of around 40 hertz, which sound like a buzzing, irritating noise played back as audio files. I used some specialist software to distinguish the signal within the noise – and to produce sound from within each peak that is closer to the frequency of a human voice and therefore more revealing to the ear.

Listening to the results reprocessed at around 300 Hz, the audio files have the hypnotic quality of sea birds calling. There is a sense that each spike is modulated subtly within itself, and it sounds as if there are discrete signals in which one neuron in some sense “addresses” another. Could we be eavesdropping on the language of the brain?

For me, the brain is not a supercomputer in which the neurons are transistors; rather it is as if each individual neuron is itself a computer, and the brain a vast community of microscopic computers. But even this model is probably too simplistic since the neuron processes data flexibly and on disparate levels, and is therefore far superior to any digital system. If I am right, the human brain may be a trillion times more capable than we imagine, and “artificial intelligence” a grandiose misnomer.

I think it is time to acknowledge fully that living cells make us what we are, and to abandon reductionist thinking in favour of the study of whole cells. Reductionism has us peering ever closer at the fibres in the paper of a musical score, and analysing the printer’s ink. I want us to experience the symphony.

by Brian J. Ford

Despite the authors final sentiments, I still feel that this reductionism does provide us with certain, otherwise unobtainable, clarities for understanding the similarities between the processes within and without… After all, one needs to know how to make paper and ink, and understand something about the musical scoring technique before they can write a symphony down for the future enjoyment of others…

To find out where I sourced this article from, please click here.

And to learn more about Dr Bruce Lipton and some of the brilliant work he is doing, please click here.

Comic… !?

July 5, 2010

What can I say… Too much XAOS and a funny five minutes gave rise to these two little oddities.

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If you’d like to learn more about the M-Set and why our world is a fractal world, then please click here.

OR if you’d like to learn more about nonlinear dynamical systems, please read James Gleick’s “Chaos: The Making Of A New Science.” The first three people to E-mail me by clicking here will receive a free copy of the book! Just remember to enter the address you’d like the book to be delivered to…

Language… Meaning… Understanding… It’s all about higher concepts ‘globing’ together to create the aspects of cognition, via modes of analogy, that we all use in our everyday lives to impart meaning to, and thus construct, the world that we ‘know’ around us.

Here in this talk, Hofstadter pertinently demonstrates his encyclopaedic knowledge about the development of human language and how the meaning behind words manifest, as concepts develop from their base level ideas, for example “ball,” into higher levels of complexity, as new words are developed to further complement and describe these basic parental precepts – perhaps stemming from new inventions which are driven by new discoveries, from both the empirical and non empirical fields of cognition – into aspects of “roll,” “wheel,” “car,” “moving,” “hovercraft,” “floating,” “flying,” etc… In this endless game of semantic development and lexical evolution, we begin to glimpse at the inherent emptiness behind the words we all so readily use in our lives, and, thus, see how they are really nothing more than eloquent “grunts” that contain mental images of meaning that allow us Human Ape men/women to understand one another and get our ‘points’ across to each other.

In many ways this is a good point of entry for us to see and to begin to understand how words and their meanings come about… From there we can then see that mental categories begin to shape the axiomatic world in which we live. Once we can understand this, we might have a better chance to really grasp the fundamental aspects that lie behind both the Buddhist idea of “Emptiness” and Kurt Gödel’s “Incompleteness Theorems.” *

Interestingly enough… As Hofstadter discusses “word blends” and “phrase blends,” I think we can begin to see a pertinent analogy between feedback loops of all sorts i.e. language here randomly mutates into simple amalgamations of “originality,” much like “video feedback loops” create modified patterns of slightly iterated imprints of what was only just on the visual screen.

Regarding language… This evolution and development of lexical complexity stems from seemingly random conjoining of phonemes, subtle phonetic variances and little – or even crass – syntactical errors, which mostly stem from when two ideas intermingle within the mind of the speaker and are thus ejected into the conversation stream without too much consideration. This process allows a rich source of new etymological meanings to flourish and develop within – initially – small social circles of friends/colleges… Or if particularly ‘catchy,’ they might then spread across wider groups as successful “memes” via infectious minds through any form/medium of social communicability.

In many ways it is this type of evolutionary self-similarity that keeps language alive and “thinking” on its toes – always forcing it to move forwards into new realms of functionality to suite the current semantic landscapes of our ever-changing, ever-evolving social networks and scientific/technological habits. Within these linguistic and memetic structures we may even find multidimensional configurations where complex patterns modulate old ideas into modern modes of ever more complex types of understanding… Old frameworks of thinking are slowly battered into new designs, and then the two co-exist in a sort of symbiosis with one another. And ever iterating forms of lingual cunningness flow from out lips… Just as the Mandelbrot set increases in complexity the further we zoom into its boundary, so language seems to increase in complexity the further We – as human beings – progress in developing ideas, our knowledge database, our inventions and with new observations… In many way these two particular types of pattern i.e. aural language and visual fractals, run parallel to one another in similar veins of iterative novelty. One is mimicking the other… Except it is not an “exact” replica… It is merely uses the same iterative mathematical ideas to regenerate and reorganise itself with.

Here Hofstadter describes a process where two ideas are torn apart and allowed to intermingle in the speaker’s own fractal mind, thus recombining/assimilating into an endless array of sometimes intentional, but probably mostly unintentional, hip analogies. Analogies are all about self-similarity. Hence, in my mind I become some strange feedback loop, reiterating what I have already heard and seen in my life thus far, remixing, recombining and experimenting with neoteric verbal adage to describe new modicums and meanderings concerning my experiential existence… And thus, through my will alone, my “I” become a Möbius strip of etymological and memetic reform, playing with all of you – my iterated equals – in evolution and natural selection’s ancient game.

To find out more about Douglas Hofstadter, please click here.

* This exposé about the illusion of self and the delusion of most types of knowledge – in the light of the Buddhist precept of “Emptiness” and Kurt Gödel’s “Incompleteness Theorems” – is coming in a future blog…

Here are some stills from Talysis - a short film that Paul Prudence made for the Crystalpunk Workshop for Soft Architecture held in Utrecht, Holland in Autumn 2005. The film explored elements of self-organisation and crystallisation - autocatalytic replication and recursive symmetry using digital video feedback.

I vividly remember seeing my first “video feedback loop” (VFL) some 18 years ago while I was round at Mike and Penny Leander‘s home on Devonshire Street in London. Basically I knew their sons Luke and Rudi via school and, because we shared that mangled lust for “living-it-large,” we kindled a friendship that was forged over many good times, wild experiences and grooves of saturnalia. Though while I won’t divulge too much about our hedonistic escapades, lest I digress into a wild nostalgic stroll down memory lane and thereby forget the reason for my writing, I will “briefly” set the scene… As it seemed that an array of natural events were conspiring to posit an idea about the way in which the universe functioned as a whole. For it was this very idea that became a powerful defining aspect which shaped the rest of my life…

To be precise, my first “VFL” experience occurred about three or four months after our G.C.S.E. exams had finished. Summer was over and it had became very clear that winter was prematurely reaching out through autumn’s colorful spectacle, dragging us reluctantly back into her dark and frosty embrace. The 92₃ term of A-Level studies was already well underway by then, and notions of chemistry, physics, economics and math were weighing more on the mind than they normally did. Every morning, while drawing the curtains, I couldn’t help but notice the varying circadian patterns of wild ice crystals that has grown in the cold of night before over the single paned windows… And, as I marveled at their structure before heading off to the gym, I couldn’t help but notice how similar they were to ferns… These in turn resembled many other structures that I had recently become aware of through my studies. So I began to wonder whether there was some kind of mold that interlinked everything together in an intricately ordered, yet probabalistic way. As a direct result of viewing these ice crystals, I felt compelled to do some research into why these beautiful structures came about. And having just studied the phsyical chemistry of water in class i.e. hydrogen bonding, I had found out that chaos was beating at their heart. Thus I went to the school book store and ordered the first book that appealed to my senses: “The New Scientist Guide To Chaos,” which had been published earlier that year.

Having read both Darwin’s “On The Origin Of Species” and “The New Scientist Guide To Chaos”, much began to spin through my mind… Was there really a key to the order of the universe, one that could give rise to infinite diversity? Could there be such a rich and complex divergence of natural chemistry so that it never quite repeated itself exactly, giving credence to Darwin’s “theory” of evolution, allowing natural processes to slowly generate new wondrous bio-mechanical machines that were interlinked from the dawn of life to the present moment in a long chain of progeny and modification? All my teachers were saying “nonesense” to me. But still these ideas came back even stronger… Then all of sudden, almost as a tonic to this internal philosophical monolog, one of those much needed half term breaks sprung up… Needless to say it provided me with a deep sigh of well earned relief… So off we all scampered, heading to wherever and/or whomever would have a marauding mischievous teenager, or two, for a week!

I myself went home to see the parents. And having spent most of the week in their sanguine company, eating and walking our way through the country side, I began to grow restless for some company of equal stature to my own growing appetites. I needed to put family business to one side and reclaim the reigns to the torrent of the questions I had been pondering over before this holiday. Thus, at the end of the week, I rang Luke and Rudi to find out what they had planned for their “last weekend of freedom…” And the very next day I found myself on a train heading up from the country side to the great city of London, where an assorted company of “friendlies” awaited my arrival before the games and revelry of the weekend began. All the journey I began to imagine fractal patterns in the bustle of human life. And any conversation that I overhead began to yield shapes of self-similarity through out their syntax… Self-referencing was key to the transition of conversational subject matter. Could this be associated with the M-Set too? Churning over these ideas in my mind, I marched down from Baker Street tube in a gleeful stride of exuberance, and pressed the intercom on the front door of the Leander’s residence. Eventually the silence gave way to that electric crackle, and I could hear, behind the muffled inquiry as to who it was from Luke, a clamorous wild cheer of a salute! No doubt the day’s events spiraled beautifully upwards from there on in with an updraft of good company and vivid imaginations. As I launched some of my ideas into the general conversation’s flow, I was inspired by new insights and suggestions from the others.

On the whole, the night went very well… Luke, Rudy, Clay, Amy, Lucy, Cheds and myself were all smiling hard through out. But as all good things do, the adventure finally came to an end as twilight began press through the gloomy neon glow from the clouds above… We had foraged deep into the city’s heart and explored the myriad of lives unfolding in the realtime rhythm of London’s never ending pulse… Swaying from fatigue, we were justly full of sumptuous new experiences, feeling content and alive from all the noctural action. Home was on our minds… And the idea of a comfortable pad to hide from the harsh “reality” of the coming day was a warming thought. So when we arrived back inside, it was with a hearty sense of lightheaded and youthful joy that we declared it was now time to chill out and relax… Somewhere in between putting the kettle on and the cups of tea that followed, we decided that the Orb’s “Adventure’s Beyond The Ultraworld” and the KLF’s “Chillout” would provide the perfect soundtrack to our morning’s laid back groove. And so it was…

But as young restless minds go, banter never ceased for one moment, and wacky ideas, games and practises kept coming out… The party, it seemed, didn’t take well to lying down. Eventually some of the energy did dissipate, and Rudi decided it would be a good idea to interview us all with their new video camera while we all lounged languidly into the “sofa Sunday” that lay ahead. What insights these interviews yielded into our states of mind, I cannot honestly remember. But after our parley, we decided it was a good idea to play back the footage to check our responses for any incriminating evidence that might give us away to any parental veiwing. And it was here that the magical moment unfolded… Sometime in between connecting the camera up to the television and playback, Rudi managed to point the it’s lens back at the flickering screen. And something amazing happened… Patterns started cascading across the television’s screen… Light, reflected from the sparsely lit room, was being picked up and thrown back into the screen’s gliding image… Like a kaleidoscopic array of lights that flickered through interlinking present moments to form a familiar spiraling shape, they slightly modified their position into nearby zones of similarity, evolving into ever changing eddies of wondrous delight in a dream like sequence of order. Every tilt of the camera cast a direction for new pattern to follow, and I was instantly hooked on these beautific arrangements… Nothing could tare away my gaze from the majestic tapestry of Escher-esque delineations that ran across the screen like rain glitters from leaves while streaming down through bright sunlit forests. I had fortunately seen the M-Set for the first time earlier that year, when Emily Mander had sent me three postcards, containing various assorted zooms into the M-Set, down from Manchester. I still don’t quite know what inspired her to send them to me but, as all good friends do, she knew they contained something that would allure me… Thus I immediately recognized the similarity between the two patterns and all the thoughts about evolution, ice crystals and ferns joined to together in one big loop. After that moment, rarely did those images leave my mind… I came back to them time and again, wondering about their beauty and familiarity. It was almost as though the universe was offering up this obvious pattern to which many were so oblivious.

Many years passed as these trains of though grew and grew into an ever deeper understanding about the whole… And it wasn’t until I finished university and had moved into my own home, that I got a chance recreate these mesmerizing visual patterns for myself. After a landing a steady job and a lot of saving, I eventually I got myself a secondhand television set from the local sound and vision centre in Epsom, Surrey. And after a few months more of penny pinching, I purchased a cheap, but decent, digital video camera off eBay… On the day that the camera arrived, I switched off my cellphone and set up my first VFL! Not once did the thrill wear off… And over the next few years, right up until I sold my television set, I would get up in the middle of the night and film new footage of heterogeneous self-organizing patterns, using nothing more than the “cathode ray tube” (CRT) television as a canvas, a mirror and a Canon XL-1 video camera for the visual feedback “brush.” The “reams” of looped feedback patterns that were generated all resembled the fractal structures I had witnessed in the M-Set and throughout life’s journey so far. No doubt it was a key to understanding nature’s process.

To date I have amassed well over one hundred hours of video feedback loops, all recorded onto DV tape, using various sources for initiating the patterns i.e. neon lights, lava lamps, pictures, people dancing, etc… To initiate a pattern, all one does is simply place the light object in between the CRT and the video camera… And off they flow. One day I will get around to transferring these cascades onto my YouTube account for everyone’s viewing pleasure. But for the moment, the bulk of my feedback loops will remain in the musical domain.

The Alan Turning monument in Bletchley Park.

As a sort of note about the inspirational chord that was struck within me, I wanted to post the following video which discusses how feedback loops tie into what Alan Turing was working on between 1952 and his untimely death in 1954 i.e. morphogenesis and the math of pattern formation. Reason being is that I feel it ties into the essence of all things within this universe flow, including all the Life here on earth. In 1952 Turing published one paper on a then unique and previously unheard of subject. It was entitled, “The Chemical Basis of Morphogenesis,” which put forth the Turing hypothesis for pattern formation. However, it wasn’t until well after his death that the scientific community began to realize the full importance of his work within the domains of the biological and evolutionary sciences. Since then, science has realized that Turing himself single handedly set the foundations for a new and refined understanding about how Life might “simply” have come about as a result of nothing more than natural phenomena.

In my humble opinion, it is in this powerful realization that Life suddenly finds a new perspective of relevance i.e. that We, as human beings, are nothing more than the result of billions of years of pattern formation that has arisen from all the star dust found here on planet Earth. We are fortunate to be a part of this wild and unfolding universal beauty… And it is Chaos’ hand that makes everything similar and yet uniquely different. No doubt there are many planets/worlds where these wondrous moments of Life have never been fortunate enough to have had a chance to arise i.e. Mercury, Venus, Mars, Jupiter, Saturn, Uranus, Neptune and Pluto. And it would do us immense good to remember this whenever/however we can i.e. whether we are reminded through feedback patterns from video art, OR through the more commonplace and daily memetic feedback loop created through the media industries’ reporting of current events which guide our minds into the current belief systems that we use to understand the world around us. For when we begin to see this humbling truth, we can then begin to realize the danger that a single story can pose from humanity i.e. one religious doctrine, and how it might exclude other important ideas from the evolutionary game of memes and natural selection. After all, mankind’s Life is currently highly dependent on ideas… And, if these ideas never evolved, then our memes/ideas/technology/art/language/etc… would be still very much like the single celled cyanobacteria of Proterozoic times.

Life is a loop… And it feeds back onto itself… Just like a VFL. Much in the same way that some leaves might use feedback regulation between the plant hormone auxin and its efflux carrier, which is a basic chemical feedback loop, to create the wondrously beautiful and varied leaf venation patterns that we all can see throughout the plant kingdom… So mankind uses the memetic feedback loop of media and current social modes of understanding to define its relation to the surrounding and ever changing enviroment. Always shifting, ever iterating, developing into new heady modes of survival and creative means of Being, we continually do our best to better ourselves as a part of the whole that we come from, so that we may realize our true potential for understanding and carrying on “healthy” patterns of creation.

If you would like to learn more about Dr Graham McDonald at Salford University, please click here.

Or to learn more about Bletchly Park and/or Alan Turing, please click here and/or here respectively.

Cells Go Fractal

January 17, 2010

Sometime in early 2002, having just been to my first (and last) ever football match (with my then flatmate, Mr Ralph Pool) so as to watch Arsenal play at their “legendary” Highbury Stadium, a group of us dispersed into the nearby public house (The Highbury Barn) so that we might sit down and discuss the merits and faults about the way “WE” had just played.

No doubt Arsenal were victorious… So all was good! But, as the match had been against West Bromwich Albion, I could hardly find anything particularly radiant to enthuse about, as it couldn’t have been that tricky-a-match for the then “Dream Team” of football to clinch. It was more a case of Arsenal playing it defensive and warding off any attack from the Albion. Thus, after five minutes of over enthusiastic raving from everyone at the table (bar myself), I was somewhat numb to my core over this sort of narcissistic “bottle” chatter. Nonetheless, as I had made myself a promise to give this “football craze” a go for just one day (mainly because everyone I knew was into it), I felt obliged to stay on and do my best to get involved in the footie flow… After another five minutes I was very close to a state of Transmarginal Inhibition, mainly from the mind crushing boredom that I was experiencing over the slow-mo recapitulation on Arsenal’s “amazing” victory… And having still not had anything constructive spring to mind so as to “pitch” into the conversation with, I decided that the only way forward for these egocentric modes of footie babbling was to imbibe more of the good, inebriating organic solvent, “ethanol…” The final aim being that, at worst, my tongue might loose and I might disperse my then not-too-sunny disposition… Or at best I might push through the Transmarginal Inhibition and actually come to love football like I might a son or daughter of my own. !?!? After all, alcohol isn’t called “the social lubricant of the mind” for nothing now, is it…

Thus I marched up to the bar and ordered everyone another pint of whatever it was they were swilling. As you can imagine, the pub was heaving with good vibes from the victory just past, and the queue was long… While waiting I bumped into a somewhat sheepish looking gentleman with long hair and a maroon colored coat. And as his appearance was of the demeanor that he might be someone who enjoyed football for the essence of coming out together, without getting too overly caught up in the “beauty” of the play, I figured that it might perhaps be a good time to strike up a conversation and get into the groove of footie’s languid lubricious social flow. “Damn good game, eh?” I launched off with. And he turned to me, with his eyes lighting up and rambled on about some amazing tactic of play that Sol Campbell had used to deflect the ball back into midfield for the final goal… “ARSE!” I though, as the beautiful tapestry of eloquent prose which exploded from his mind simply trickled off my own like water from a duck’s back. Thus I stared at him with somewhat vacant eyes, pondering over what to say next from behind a forced smile… But all my mind could muster was, “YES! Marvelous wasn’t it!”

Well… Standing in the awkward silence that followed my seemingly “banal” retort, I noticed the queue wasn’t getting any shorter, especially what with all the foul play that was unfolding at the bar’s brim i.e. queue barging, pushing in, friends taking orders for other friends who couldn’t be bothered to queue, etc… So, pondering on how a ref might bring some order to this bevey rush, I turned back to the maroon coated fellow and asked him how long he had been following Arsenal. “Ever since I was 12, to the present,” he said near enough. As I probed more, I stumbled on what he was currently doing as a job… Low and behold I found out he was doing a Ph.D. in “Fractal Topography” at UCL!!! “WOW!” I remarked… But he glazed over and said, “It’s boring as hell.” After this, I noticed we both tried to bring the conversation back around to what we enjoyed i.e. he tried to engage me in footie banter, and I did my best to reciprocate, after which I’d try to bring the conversation back round to fractals, only to find he didn’t want to talk about “work.” Alas the exchange didn’t last long. But I vividly remember asking him, “Might fractals play any role in evolution or biological diversity?” And he laughed, saying that all fractals were was just pretty mathematical patterns that had no other use what-so-ever. So I suggested that I would trade my football friends for his Ph.D. studies any day. To which the silence re-ensued.

To this very day, I know football is just not my thing… And where as some people ramble on poetically about “this” player touching that kind of defensive play and knocking the ball over to “so-and-so,” who dived and ducked inbetween the defence and then shot a scoring goal like some god… Well, despite the liguistic prose… To me, it’s still just a game where a bunch of talented, hairless monkeys run around a pitch kicking and nudging a ball into nets. Equally so, where some people see my varied ramblings about chaotic discourse within music and non-linear dynamical systems as pointless drivel about computer generated art, I know it touches my soul in a way makes me feel connected to the universe… But this is it. It’s about connection with what you are drawn to. No doubt there are many more footie fans than fractal fans in the world today. But that’s life! And it’s fine… This Ph.D. footie experience was in many ways a humbling reminder about how two people’s views of similar things can vary so drastically that we can sometimes see the beauty within each other’s dislikes. “Beauty is in the eye of the beholder.”

However… On some level, I found this brush with the Ph.D. unsettling… Something in me didn’t want to believe it. Hell… Something in me told me he was a “chump” who was more interested in footie than anything real or viable. And still… I had to listen to him. Here was this Ph.D. – a lad who had obviously been studying the math of complex numbers and iterative patterns/structures for quite some now – and, bearing in mind my then somewhat limited understanding about these aberrant beasts of divine simplicity and complexity, who was I to question his well informed personal view on the matter at hand? None the less, I carried on looking into this phenomenon for many years to come, following a sort of gut instinct that seemed to press me ever onwards, regardless of what others would/might say, and eventually I started to develop better modes of understanding about these wondrous forms of divine order and chaotic patterns. To be fair, my interest in this subject has never waned one iota. And despite the opposition to the idea that fractals are somehow locked deep into the very essence of our being, thus defining what and who we really are, it seems that now science is rediscovering these aspects within nearly all dynamical systems of the world. What more can anyone say!?

But besides all this, there were still many holes in the theory. Well… Until last year, that is, when sometime in November I managed to read probably one of the best articles I could have cared to have read, which I had by chance found in a copy of Nature magazine that I had randomly swiped from my doctor’s surgery one “chesty” morning. It suggested that cells were using fractal mathematics to regulate their own internal cellular biology. And, at the very moment of completion, my gut instinct began to feel vindicated. At long last science was beginning to see how “chaotic” flows can create marvels of ordered wonder that could easily give rise to something as marvelous (and “seemingly” impossible) as Life. Here was that link between the beauty that I had seen in the M Set and experienced in Life. This is how chaos’ beautiful flow caused a wondrous event which give rise to all of the Life here on planet Earth. Here lies the key to seeing how we came into being. This is the same powerful internal mechanism that drives our computers to generate the marvelous serpentine flows seen within the M Set… And which, if transposed onto organic molecular soups full of various compounds, also gives rise to the somewhat random, and yet specific, generation of structured internal cellular order. Don’t ask me about the logic there… Perhaps we have to give up understanding for a moment, and simply feel this essence…

How can we mere mortals ever hope to know the unknowable i.e. the shear and almost eternal complexity of “God, or Nature,” as we “supposedly” think we know ourselves? How can we hope to know what chaos will do next? There’s no point in lying to ourselves… We don’t! We won’t! All we need to know is that dichotomies/paradoxes and chaos are wondrous things indeed… Just as wonderful as the notion of “God.” In fact… If you want to still call these wondrous flows of chaotic pattern formation around us “God,” then I can dig that. I might not agree that there is a “God” as such… But I can trip with the notion of a divinely beautiful and somewhat unknowable force i.e. that of chaos, which gives rise to what Spinoza called “God, or Nature.” And it lies in the heart of all beings, whether we love football, or not. Perhaps it truly is the “Thumb Print Of God?”

So I present the article in question, which was written by Claire Ainsworth and was published on September 4th 2009.

Mathematical Patterns Rule The Behaviour Of Molecules In The Nucleus

The maths behind the rugged beauty of a coastline may help to keep cell biology in order, say researchers in Germany. Fractals — rough shapes that look the same at all scales — could explain how the cell’s nucleus holds molecules that manage our DNA in the right location.

In new experiments, Sebastien Huet and Aurélien Bancaud of the European Molecular Biology Laboratory in Heidelberg, Germany, tracked the movement of molecules within cells in a lab dish, then compared the pattern of movement against mathematical models. Large molecules, they found, moved according to the same rules as small molecules — suggesting that their environment was truly fractal. The team reported their findings this week at the EMBO meeting in Amsterdam.

“It’s a really interesting approach,” says Angus Lamond, a cell biologist at the University of Dundee, UK. “It’s very promising that the fractal model appears to be able to describe the [molecular] behaviour in this way.”

continued here

To find out where I sourced this article from, please click here.

Or to learn more about our fractal universe, please click here.

And for an amazing expose into how the chaotic and fractal world of math can show us how Life arose naturally i.e. without a divine creator, then please check this BBC documentary out, entitled “The Secret Life Of Chaos.”

For the more scientific minds among you, I also present some articles concerning the fractal dimensions of cellular formations that I have found very illuminating:

1. Fractal Organization of Cultivated in vitro Spiculogenous Cells and Larval Spicules of the Sea Urchin Strongylocentrotus nudus

2. A comparative fractal analysis of various mammalian astroglial cell types

3. Fractal Dimension Characteristics Of Human Mesenchymal Cell Stem Cell Proliferation

4. Cell division: Fractal cycling

While I was watching a film the other day, I happened to come across a quote at the end among the credits… And having read it, I found that it touched a deep resonant chord within me about the nature of our reality and Being… And from this “chord” posited a beautifully simple, yet wondrously elegant, understanding about why We came into being…

For… When given the chance to do something… Surely it is in our nature to do, rather than not? Probability is everything… And as chance sometimes provides that possibility, so atoms take a chance on complexity, coming together in a gradually evolving divine countenance of planetary habituation… A habituation that many of us still see as “every-day” Life.

Perhaps as and when we choose to depart from this mundane acceptance of existence, and clearly stride towards a better realization of self, we might begin to See and understand what it is that Sri Aurobindo talks of here…

Sri Aurobindo (Aurobindo Ghosh) (August 15, 1872 December 5, 1950) was an Indian nationalist and freedom fighter, poet, philosopher, and yogi. He joined the movement for India’s freedom from British rule and for a duration (1905 10), became one of its most important leaders, before turning to developing his own vision and philosophy of human progress and spiritual evolution.

The central theme of Sri Aurobindo’s vision is the evolution of life into a “life divine”. In his own words: “Man is a transitional being. He is not final. The step from man to superman is the next approaching achievement in the earth’s evolution. It is inevitable because it is at once the intention of the inner spirit and the logic of Nature’s process”.

The principal writings of Sri Aurobindo include, in prose, The Life Divine, The Synthesis of Yoga, Secrets of the Vedas, Essays on the Gita, The Human Cycle, The Ideal of Human Unity, Renaissance in India and other essays, Supramental Manifestation upon Earth, The Future Poetry, Thoughts and Aphorisms and several volumes of letters. In poetry, his principal work is “Savitri – a Legend and a Symbol” in blank verse.

To find out more about Sri Aurobindo, please click here.

In this essay I propose nothing more than an idea for nature’s own design… And, by doing so, perhaps one may also find a suggestion for mankind’s ultimate drive within this design. While I’m not saying that there is an absolute answer to “Life, The Universe and Everything,” I am offering up an obvious pattern that seems to recur with common-place regularity throughout every “Universal” system that I have ever studied and/or viewed so far… It is a pattern that nature has followed for eons already; whether through the natural laws of physics, via the designs of evolution, or in the memories we all use each day to build our world around us and develop the meanings that we place on it… This idea can even be found at the heart of all poetry, exuding beauty, simplicity and finesse simply by adding metaphorical adage to the rough-hewn strata of every day activities. Simply put… It is the idea behind all patterns of universal discourse… A discource which has been accursed as being “the thumb print of god.” Self-similarity is what we do. It is what we build our minds with, where our notions come from, and even allows art to fulfill its very purpose of attaining mystical appeal. It allows us to copy others and express ideas of our own in a way that others can relate to. It even allows us to successfully copy and use age old techniques for survival, giving the “user” (or, memetically speaking, should that be the “used”?) that cutting edge over other life forms… (???) And no doubt it is a key process that will shine light into our very Being.

So… Firstly, let’s look at the definition of “self-similarity.”


self-similarity (sělf’sĭm’ə-lār’ĭ-tē)

The property of having a substructure analagous or identical to an overall structure. For example, a part of a line segment is itself a line segment, and thus a line segment exhibits self-similarity. By contrast, no part of a circle is a circle, and thus a circle does not exhibit self-similarity. Fractals such the Sierpinski triangle are self-similar to an arbitrary level of magnification; many natural phenomena, such as clouds and plants, are self-similar to some degree. See more at fractal.

Next… Let’s look at the definition of an attractor.


attractor (əˈtræktər)


1. a person or thing that attracts.

2. Physics. a state or behavior toward which a dynamic system tends to evolve, represented as a point or orbit in the system’s phase space.

The basic idea behind an attractor is that a dynamic system will tend toward certain states as time goes on. The simplest form of an attractor is the point attractor. Consider a normal pendulum, it doesn’t matter where you release it from, it will always come to rest in the same position, perpindicular to the ground. This state is the attractor for the system.

Next… Let’s look at the definition of a strange attractor.

Strange Attractor


The truth of the matter is this, there is not yet a formally accepted definition of a strange attractor. Strange attractors tend to arise in dissipative dynamical systems, such as the first pendulum example given above. Dissipative simply means that the system loses energy as time goes on. The Collins Reference Dictionary of mathematics states the definition of a strange attractor as …such that its Hausdorf Dimension is non-integral, or else dependant on initial conditions… Obviously this is not a complete definition, but it does give us a sort of intuitive way of thinking about a strange attractor.

And lastly let’s understand something about measuring dimensions

Hausdorf Dimension

The Hausdorf Dimension is a means of measuring the dimension of a mathematical object. For instance, the dimension of a point is 0, a line resides in 1 dimensional space, a plane 2, and of course our friend 3-space in which we live. So by definition a strange attractor is an object which is neither a point, a line, or a plane!. For example, the dimension of the Rossler Attractor is estimated at between 2.01 and 2.02. To understand what this means, think about this: the equations which describe the Rossler attractor will describe a curve or line in 3 dimensional space for periodic solutions. But when you have a chaotic solution, which is never periodic, that is, it never visits a point which it has previously visited, then the path of the Rossler attractor as a whole (time to infinity) becomes more than a collection of lines, and just slightly more than a collection of planes. The key point is that for a non-periodic solution, the attractor never retraces a previously traveled path. This non-integer dimension is also what qualifies strange attractors as a fractal. A fractal is defined to be any object with a non-integer Hausdorf Dimension.

For further reading, please click here.

And with those four definitions out of the way… I would now like to postulate what my aim within this essay will be, and how I hope to achieve it.

Since the discovery of the Mandelbrot set, many images of its “serpentine” flow have captivated the imaginations of those who have laid eyes on it. The literally “never ending” sequence of divine majesty has held court particularly well with the mystical elements of modern day society i.e. the psychedelic voyagers, healers, pyschics, etc… Not to mention it has even brought an element of the spiritual into math. Something is stired deep inside when people view this marvel of vanilla complexity. But what exactly is “it” that is arroused?

Well… For years Religious and Mystical doctrines have all adorned their sacred texts/ideals with marvelous tapestries of cochlear geometric art and calligraphy. This instinctual linking of the divine with these geometric forms seems to adequately explain how we feel about our lives in the complexity of creation. The images seem to proclaim a deep and beatific connection to the world around us as it unfolds according to God’s will.

Below are a few examples of these decoration:

Fractals vs Religion. The idea of the infinite/God. Bottom mural patterns photographed in Alhambra, Spain.

Fractals vs Religion. The idea of the infinite/God. Bottom mural patterns photographed in Alhambra, Spain.

Imagery from the Book Of Kells vs. The M Set

Imagery from the Book Of Kells vs. The M Set

Ishmael vs. The M Set... More Self-Similarity

Ishmael vs. The M Set... More Self-Similarity

Self similarity occurring across many levels. Buddha and the Buddha Brot. Possibly the Buddhist theory of Interdependent Origination should be more closely examined?

Self similarity occurring across many levels. Buddha and the Buddha Brot. Possibly the Buddhist theory of Interdependent Origination should be more closely examined?

But why did We adorn these icons of our saviours with such tortuous and elaborate imagery? Surely they were just as human as we were, albeit slightly more in tune with the divine aspect of reality… And if they knew the divine better than us, then why did they not speak of such intricate complexity? Well… In many ways they did. Buddhists speak of the theory of Interdependent Origination… And even Jesus and Mohammed were known to have talked of the complexity of life and its boundless beauty.

So… Are we all simply seeing the same thing, just from slightly different perspectives… ? Much in the same way Bertrand Russell describes the way various people might perceive a table from different angles in “The Problems Of Philosophy?” I say, “YES, WE ARE!!!”

In Russia, people have used an idea that embodies the essence of fractals and self-similarity to describe the very notion of family life. Babushka dolls relay the obvious similarities that occur between offspring and their parents. A type of affine process that relates to self-similarity…

A matryoshka doll, also known as a Russian nested doll or a babushka doll, is a set of dolls of decreasing sizes placed one inside the other. "Matryoshka" (Матрёшка) is derived from the Russian female first name "Matryona", and "babushka" is the Russian word for grandmother.

A matryoshka doll, also known as a Russian nested doll or a babushka doll, is a set of dolls of decreasing sizes placed one inside the other. Matryoshka (Матрёшка) is derived from the Russian female first name Matryona, and babushka is the Russian word for grandmother.

To further the Babushka doll idea… As you may have read just recently in the blog entitled “Human Mutation Rate Revealed” each subsequent generation accumulates new mutations in their genome… Mutations that allow subtle differences to arise within the parameters of the predefined DNA blue-prints that come from both mother and father… DNA which must unravel itself and intermingled to mix into a new generation of human being. Certain traits will be more pronounced than others, but all in all the offspring will resemble both their maternal and paternal side in some way. This game of “tag,” has been played for eons… Ever since life took a hold here on Earth… And here, as seen in the potent image of the “babushka doll,” there is an excellent metaphor that elludes to this deep understanding of the “divine” process of self-similarity and the complexity that comes from it. It’s almost as thought we are aware that all natural processes carry within themselves a part of the whole from whence they originated: denoting a recognizable relationship of “similar object-within-similar object…” It is this abstraction that appears in the design of many other natural AND man-made objects that we see all around us daily…

Even in the “cradle of civilization” i.e. Africa, this notion of self-similarity is well understood. As Ron Eglash has shown here, and in his book entitled “African Fractals,” fractal patterns abound and play a very important roll in the way mankind understood (and still understands) his place within the cycles of nature… Africa is not the only place that this ancient process is celebrated.

Most Indian and Southeast Asian temples and monuments exhibit a fractal structure.

Most Indian and Southeast Asian temples and monuments exhibit a fractal structure.

As seen in the above two modest pictures, most Indian and Southeast Asian temples and monuments exhibit a fractal structure: a tower surrounded by smaller towers, surrounded by still smaller towers… The particular examples shown above are Hindu temples. The ideal form gracefully artificed suggests the infinite rising levels of existence and consciousness, expanding sizes rising toward transcendence above, and at the same time housing the sacred deep within. This universe is like a ripe fruit appearing from the activity of the cit [consciousness]. There is a branch of a tree bearing innumerable such fruit. There is a tree having thousands of such branches. There is a forest with thousands of such trees. There is a mountainous territory having thousands of such forests. There is a territory containing thousands of such territories. There is a solar system containing thousands of such territories. There is a universe containing thousands of such solar systems. And there are many such universes contained within what is like an atom within an atom. This is what is known as cit, or the subtle sun, which illumines everything in the world. All the things of the world take their rise in it. Amidst all this incessant activity, the cit is ever in undisturbed repose.

Diagram clearly demonstrating this fractal ideal.

Diagram clearly demonstrating this fractal ideal.

As I might seem like a rambling blogger… I’d like to mention that I am not the only person implying this idea about Indian temple architecture and the cit… Please click here for more details.

No doubt, there is something within us that somehow links us to an idea of the “divine…” Of the infinite… We see the unfolding daily complexity of life… Each action causing its own reaction in a chain of events that unravel from the big bang itself. It is unbounded in nature… And yet bound to what has already been. This is where the infinite truly resides! Perhaps the reason why We, as human beings, express this idea in Self-Similar ways i.e. through religious decree and complex geometrical art, is because deep inside each one of us we use the same structures that nature uses to create the universe around us… Perhaps We are all truly aware of this deep connection that We all share with each other and the cosmos… Even if only subconsciously… And so perhaps We can’t help but intuitively feel this “divine” cosmological phenomenon unraveling around us, and feel the need to express it. Whether We choose to acknowledge it or not, it still courses through our very being each day. We can’t help it. This is what we are… !

HOWEVER… Standing alone, these propositions that I make are nothing more than bold insinuations… Insinuations that might arise from a mind that has become swamped in its own aspirations… Aspirations for demonstrating this “truth” in a hope for peace and unity between all mankind, thereby clouding my reason with foolish dreams and hopes… Prerhaps this is my fate… To suffer from a misguided scoptoma. No doubt…. Without any scientific backing, I wouldn’t expect anyone to take these insinuations any further than the face value with which I have presented them thus far.

And yet, I myself, having scrubbed these realizations from my mind’s eye time and again in order to try to see afresh the patterns of universal flow around me, have always been led back to this idea of self-similarity. And I keep wondering why? Why is it that when I forget about “self-similarity” and look for some other process, some other explanation, I am always called back to see the chain of events that brought me here… Why do I see my own originality fade into a sea of past, present and future efforts? Are we doomed to copy ourselves over and over again for an eternity, providing little modifications along the way, so that the present becomes almost stagnant, while the whole becomes flowing? Whatever the answer is… It’s almost as if some innate force within me is pushing me to describe a deep Knowing, like an almost forgotten connection, that we all share with the universe around us. A connection that is based on the idea of coming together, which in turn is founded on the very “laws of attraction” and beauty that guide us all through the experience of our daily lives.

I am aware that for the layman, this is still nothing more than one BIG postulation… All of it hanging only on mere conjecture. So… In order to rectify this loose canon, I proclaim… Within the confines of this essay, I will provide some whole facts that might suggest why we all, somewhere deep, deep inside, have always felt a strong urge to connect with this process, whether throught Religious ideals or through mystical rites, in order to express this obvious self-similar and unknowable complexity as it unfolds into new modes of understanding. And in doing so, perhaps I might also suggest (with regards to understanding the flow within our minds i.e. something that is chaotic) a reason why my experiences have always demanded my return to similar flows of thought – and therefore perhaps even suggest why Religious doctrines, ones that are seemingly unrelated to one another, are infact so similar

Afterwards I will provide some visual pictures of the patterns at work in the chaos of the universe surrounding you, and allow you deduce your own conclusions (something that I always ask all my readers to do, no matter how trivial and obvious a statement I make). Good old empirical thought has been clearly demonstrating of late that the universe is one large dynamical system… And these systems are built not upon perfect ideals, like those used by Euclid to describe his perfectly flat plane (a rather romantic notion of man’s own making)… But rather they are fractured deeply inside, and so sometimes move with a wild abandon that no mere mortal could ever grasp fully or hope to predict… And yet… By providing you with a series of analogies to suggest these complex patterns inherent in many of these natural everyday dynamical systems I hope that the idea of self-similarity occuring across many areas that are, at first glance, seemingly unrelated to one another, will hopefully posit of its own accord. Then one may See that self-similarity resides not only in nature around us, but within the very machinery that allows us to perceive the universe around us i.e. the human body and brain, in a type of all embracing monism.

This is no doubt a very delicate matter, and will demand your utmost attention, as well as some diligent homework on your part too… For even my “facts” are somewhat vague in my own mind, as I allow intuition to guide my reason and dictate the obvious. Thus I ask the following of each reader…

Firstly, to remain open minded while reading this essay. I am not asking you to believe anything writen (or typed) down here straight off… All I am doing, is establishing an idea, along with evidence for it, so you can then do your own ground work to see if it is a valid “ideal” or not… As Socrates once wrote, “…it is the mark of an educated mind to be able to entertain a thought without accepting it…” Ultimately it is up to you whether or not you decide to agree or disagree with this. And secondly, it IS a pre-requisite that you either have some basic understanding about science (biology, chemistry and physics)… As well as being up to date on current science facts and theories… AND/OR read some of the previous blogs that I have posted here… As without these, it like introducing a Mexican national to a Japanese national in Africa, and expecting them to understand eachother straight off. You dig?

Right… Here I would like to introduce several words and terminologies, most of with which you’re no doubt familiar with, to christen the launch of this epic…


empiricism (em-pir-uh-siz-uh m)

– noun

1. empirical method or practice.

2. Philosophy – the doctrine that all knowledge is derived from sense experience. Compare to rationalism.

3. undue reliance upon experience, as in medicine; quackery.

4. an empirical conclusion.


rationalism – (rash-uh-nl-iz-uhm)

– noun

1. the principle or habit of accepting reason as the supreme authority in matters of opinion, belief, or conduct.

2. Philosophy.
a. the doctrine that reason alone is a source of knowledge and is independent of experience.
b. (in the philosophies of Descartes, Spinoza, etc.) the doctrine that all knowledge is expressible in self-evident propositions or their consequences.

3. Theology. the doctrine that human reason, unaided by divine revelation, is an adequate or the sole guide to all attainable religious truth.

4. Architecture. (often initial capital letter)
a. a design movement principally of the mid-19th century that emphasized the development of modern ornament integrated with structure and the decorative use of materials and textures rather than as added adornment.
b. the doctrines and practices of this movement. Compare functionalism.


Egocentric bias

This occurs when people claim more responsibility for themselves for the results of a joint action than an outside observer would credit them.

Besides simply claiming credit for positive outcomes, which might simply be self-serving bias, people exhibiting egocentric bias also cite themselves as overly responsible for negative outcomes of group behavior as well (however this last attribute would seem to be lacking in megalomania).

This may be because our own actions are more “available” to us than the actions of others. See “availability heuristic.”

Michael Ross and Fiore Sicoly first identified this cognitive bias.

The reason why I mention these terms is to demonstrate that I am aware of them. They will no doubt also come up latter on in this essay too. But… Because I am aware of them, I am also aware that what I am about to postulate may be nothing more than a self biased view centered around my own imposition, which is based more on rationalism than empiricism. But non the less, as I’ve had quite a few E-mails asking for further reading on fractals and where they occur, I am writing this lengthy article to demonstrate how close to home they actually are i.e. they are everywhere!!!

So, without further ado… I will begin by demonstrating that our mind uses fractals patterns with which to think.

In Earl R. Mac Cormac and Maksim Stamenov’s book, entitled “Fractals of brain, fractals of mind: in search of a symmetry bond,” they mention that…

We shall present a case for the use of non-linear dynamical systems like fractals that can give an explanatory account which describes both the behavior that we have traditionally called involuntary (reflex) and that which we have traditionally called voluntary (will).

Considerable evidence has been presented showing that both the firing of individual neurons and the activation of patterns of neurons are nonlinear dynamical systems. Walter Freeman’s investigations of the olfactory bulb of the rabbit concluded not only that olfaction was nonlinear but also that this process could serve as a model for cognition (Freeman 1990). Skarda and Freeman state the following:

The observations that brains employ not only self-organization but chaotic dynamics to produce behavior places yet another nail into the coffin of reductionism. Chaotic phenomena preclude long-term predictions. It may seem paradoxical that a deterministic phenomenon is inherently unpredictable, but in systems that exhibit chaotic behavior, small uncertainties are amplified over time by the nonlinear interaction of a few elements. The upshot is that behavior that is predictable in the short run becomes intrinsically unpredictable in the long term. As a result, physiologists cannot make strict causal inferences from the level of individual neurons to that of neural mass actions, nor from the level of receptor activity to internal dynamics. The causal connection between past and future is cut. (Skarda & Freeman 1990:282)

Gregor Schoner and J. A. S. Kelso agree with these conclusions but cast their nonlinear net to include all neural behavior claiming “that it is possible to understand behavioral pattern generation on several levels of description (kinematic, electromyographic, neuronal) by means of the concepts and tools stochastic nonlinear dynamics.” (Schoner & Kelso 1989:311). This comprehensive claim is correct and we will attempt in this paper to demonstrate that fractals, a subset of nonlinear dynamical systems, can present a scientific explanation of neuronal behavior. Further, positron emission tomographic (PET) studies of cognitive behavior hopefully will confirm the fractal nature of specific neuronal processes…”

“Okay… And so what?” I hear some of you saying… Well… Perhaps to understand how chaos can be fractal, it might be beneficial to understand a bit about nonlinear dynamical systems. Then we can propose why they are fractal, without asking you to simply take my word that they are. So what is a nonlinear dynamical system? They’re a bit like linear dynamical system, in that they have dynamics… But apart from that, the similarity ends there. Here’s the compare and contrast…

Linear dynamical systems (LDS) can be solved exactly… In a LDS, the variation of a state vector (an N-dimensional vector denoted \mathbf{x}) equals a constant matrix (denoted \mathbf{A}) multiplied by \mathbf{x}. This variation can take two forms: either as a flow, in which \mathbf{x} varies continuously with time.

 \frac{d}{dt} \mathbf{x}(t) = \mathbf{A} \cdot \mathbf{x}(t)

or as a mapping, in which \mathbf{x} varies in discrete steps

 \mathbf{x}_{m+1} = \mathbf{A} \cdot \mathbf{x}_{m}

These equations are linear in the following sense: if \mathbf{x}(t) and \mathbf{y}(t) are two valid solutions, then so is any linear combination of the two solutions, e.g. \mathbf{z}(t) \ \stackrel{\mathrm{def}}{=}\  \alpha \mathbf{x}(t) + \beta \mathbf{y}(t) where α and β are any two scalars. The matrix \mathbf{A} need not be symmetric.

Basically, without the mathematical talk, this simply means that a variable changes in some kind of linear manner with relation to its output. This might be a complex linear relationship, so do be aware that, when plotted, it might not look linear. However, when a system qualifies as a linear system, it is possible to use the responses to a small set of inputs to predict the response to any possible input. This can save the scientist enormous amounts of work, and makes it possible to characterize the system completely i.e. it is predictable.

In contrast to LDSs, most nonlinear ones cannot be solved exactly. Occasionally, a nonlinear system can be solved exactly by a change of variables to a linear system. Moreover, the solutions of (almost) any nonlinear system can be well-approximated by an equivalent linear system near its fixed points. Hence, you can see why understanding LDSs and their solutions is a crucial first step to understanding the more complex nonlinear dynamical systems.

So… What is a nonlinear dynamical system (NDS)?

In mathematics, a NDS is a system which is not linear. That is, it is a system which does not satisfy the “superposition principle” i.e. that, for any linear system, the net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually… To put it another way, a NDS is a system whose output is not proportional to its input. Less technically, a NDS is any problem where the variable(s) to be solved for cannot be written as a linear combination of independent components.

The equation X = rx, which is a linear equation, has a solution. However X = rx(1-x), shown above, demonstrates that as r is increased, chaotic behavior can occur. Therefore it is a NDS and has no definitive solution.

The equation X = rx, which is a linear equation, has a solution. However X = rx(1-x), shown above, demonstrates that as r is increased, chaotic behavior can occur. Therefore it is a NDS and has no definitive solution.

The above logistics map shows how chaos can come about in a NDS. The reason why I chose to use a logistics map to demonstrate a NDS is because it is a relatively simple way of demonstrating how a seemingly obvious system can generate totally random outputs i.e. become chaotic. A rough description of chaos is that chaotic systems exhibit a great sensitivity to initial conditions… And the human mind is no exception.

Non Linear Dynamical System

Why are NDSs of interest to scientists? Nonlinear problems are of interest to physicists and mathematicians because most real-world physical systems are inherently nonlinear in nature. Even in neuroscience, nonlinear dynamics has been shown to play a very big hand in brain dynamcis, understanding spatiotemporal inputs to the brain, etc…

However… Nonlinear equations are unsolvable because they give rise to a phenomena called chaos. The weather is famously nonlinear i.e. simple changes in one part of the system produce complex effects throughout, something that we have seen in a previous post, entitled “A Strange Attraction – A Brief Study Of Strange Attractors And Their Implications… In Tribute To Edward Lorenz.”

But it should be noted that just because a system is nonlinear i.e. it is not predicatable, does not mean that it will be in a state of chaos all the time… Even nonlinear systems have stable patterns that can occur within their temporal unfolding – see the diagram below.

Chaos and stability in a nonlinear dynamical system.

Chaos and stability in a nonlinear dynamical system.

As we have already seen earlier in “The Ultimate Hack: Reverse Engineering The Human Brain,” Henry Markram is developing a three dimensional model of the human brain, specifically of the circuitry in the neocortex. Researchers at IBM have teamed up with Markram and his team at L’Ecole Polytechnique Fédérale de Lausanne (EPFL) to build the model using IBM’s Blue Gene supercomputer. The goal is to gradually expand the model until it encompasses the entire brain. How can they do this?

Well… In order to understand how one can model a computer simulation on something so arbitrary like the human brain, one really needs to understand what the brain is, what it’s made up of, and how it all interlinks to form a complete unit. So firstly, let’s look at the neuron, the basic building block of the brain’s structure.

A neuron (also known as a neurone or nerve cell) is an excitable cell in the nervous system that processes and transmits information by electrochemical signaling.

A neuron (also known as a neurone or nerve cell) is an excitable cell in the nervous system that processes and transmits information by electrochemical signaling.

The real work of the brain goes on in these individual cells. An adult brain contains about 100 billion neurons with branches that connect at more than 100 trillion points. I know… A trillion is a big number… And it might not mean a lot to one who does not use it daily. So let’s put it into context. A trillion seconds is 31,688 years. Yeap… That’s 31,688 years… Pretty big, eh? So imagine a hundred trillion seconds… That’s three million, one hunred and sixty eight thousand, eight hundred years… Or numerically, 3,168,800 years! So… Is it any wonder scientists call this dense, branching network a “neuron forest?” Signals traveling through the neuron forest form the basis of memories, thoughts, and feelings… But we’re jumping the gun somewhat.

Neurons exist in a number of different shapes and sizes and can be classified by their morphology and function. The anatomist Camillo Golgi grouped neurons into two types; type I with long axons used to move signals over long distances and type II without axons. Type I cells can be further divided by where the cell body or soma is located. The basic morphology of type I neurons, represented by spinal motor neurons, consists of a cell body called the soma and a long thin axon which is covered by the myelin sheath. Around the cell body is a branching dendritic tree (made up of dentrites, as shown in the diagram above) that receives signals from other neurons. The end of the axon has branching terminals (axon terminal) that release neurotransmitters into a gap called the synaptic cleft between the terminals and the dendrites of the next neuron. The anatomy and the properties of the surface membrane determine the behavior of a neuron. The surface membrane is not uniform over the entire length of a neuron, but is modified in specific areas: some regions secrete transmitter substances while other areas respond to the transmitter. Other areas of the neuron membrane have passive electrical properties that affect capacitance and resistance. Within the neuron membrane there are gated ion channels that vary in type, including fast response sodium channels that are voltage-gated and are used to send rapid signals.

Neurons communicate by chemical and electrical synapses in a process known as synaptic transmission. The fundamental process that triggers synaptic transmission is the action potential, a propagating electrical signal that is generated by exploiting the electrically excitable membrane of the neuron. This is also known as a wave of depolarization.

Also, it should be noted that neurons communicate with one another via synapses, where the axon terminal or en passant boutons (terminals located along the length of the axon) of one cell impinges upon another neuron’s dendrite, soma or, less commonly, axon. Neurons such as Purkinje cells in the cerebellum can have over 1000 dendritic branches, making connections with tens of thousands of other cells; other neurons, such as the magnocellular neurons of the supraoptic nucleus, have only one or two dendrites, each of which receives thousands of synapses… Thus we can begin to see the complexity that is already beginning to manifest from just the variance in cell types and the way they are interconnected…

A computer simulated diagram of the connections between neurons in a rats brain. And bearing in mind a human brain is 40 times larger, the complexity of these interconnections would be vast.

A computer simulated diagram of the connections between neurons in a rats brain. And bearing in mind a human brain is 40 times larger, the complexity of these interconnections would be vast.

So while the traditional “computational metaphor” really is an oversimplified model of the way in which the brain works i.e. where the brain is viewed in a succinct analogy of a computational device similar to that of a computer – the mind serves as a software program controlling the operations of the brain – I feel it very much leaves out the beauty and essence from which its originality stems. You see, human thinking and neuronal processes combine to produce a computational process. And it is this very computational process that is interactive i.e. the mind affects neuronal processes as demonstrated by phenomena like biofeedback and the way memories are stored… AND the brain also affects the mind, as shown by the effects of hallucinogenic drugs upon thinking, leaving the computer analogy way behind.

But due to much diligent research over the years, scientists have no doubt begun to grasp the very idea and essence of what the human brain actually is. You see, much work has been done in understanding the various types of neurons present within the brain, where exactly they are located, the difference between their morphologies i.e. variences in their respective anatomy/structure is, as well as the properties of their surface membranes, all of which determine the behavior of the specific neuron and speed at which they fire and recharge at, their near exact electro-potentials, etc… AND THUS how they interact with one another. This highly sensitive organic molecular “computer” is the driving process for the human body… In fact it is the driving process for most complex multicellular organisms here on Earth. In many ways, if we study the mechanisms within these brain structures, we will begin to peer into how we function… And thus see what we truly are. From all this data that is being amassed on how our brains and bodies work, some people down at IBM are building a near on exact computer simulation out of all this statistical accumulation of scientific data on brains, where by the complex dynamical system of the various neurons is mapped with great precision into mathematical analogies, which are then structure together using highly accurate brain maps, so that a model of the human brain can be brought to life as a virtual simulation. Viewing the brain as a highly complex interacting dynamical system should help researchers understand processes like thought, perception and memory a lot better than if they were to simply chop up the parts and observe them interacting via fMRI. And ultimately these simulations could also shed light on how and why particular parts of the brain malfunction, leading to a better understanding of autism, depression and schizophrenia.

Markram’s team with the IBM researcher are focusing firstly on the neocortex, which is unique to mammals, and accounts for around 85% of the mass of the human brain. It is thought to be responsible for our higher cognitive functions, such as language, learning, memory and complex thought.

According to Markram, the EPFL professor heading up the project, the collaboration is one of the most ambitious initiatives undertaken in neuroscience. “Modelling the brain at the cellular level is a massive undertaking because of the hundreds of thousands of parameters that need to be taken into account.”

Markram expects the simulation to accelerate the pace of brain research, whereby the computer simulation will help show holes with our current understanding of the brain, and thus will be able show researchers where to look and what studies to perform next. This guiding “presearch” could therefore direct current neural research done “in vitro” with a lot of the pre-testing and planning done “in silico”, saving a lot of time and money in physical research. “With certain simulations we anticipate that a full day’s worth of wet lab research could be done in a matter of seconds on Blue Gene,” Markam added.

The model of the brain will be based on 10 years of the wet lab experiments and research that Markram has been a part of at EPFL. The IBM researchers will use this data to build the model of the electrochemical interactions of the human brain on four racks of Blue Gene. The machine will have a very respectable peak processing capacity of 22.8 Teraflops, and will take up about the same space a four fridges.

The model of the brain is just one of the projects allocated time on the machine. Other teams will use Blue Gene to investigate how plasmas might be used in energy production, and how the folding of proteins plays a role in diseases like Creutzfeldt-Jakob Disease, the human variant of BSE, or mad-cow disease.

by Lucy Sherriff

To find out where I sourced the above quote from, please click here.

It is from this unpredicatable interaction between neurons firing across the brain that consciousness and perception comes about. The chaos inherent in the system allows a great versatility to ensure survival in the light of any threatening possibility. Without this chaos, it would be totally deterministic i.e. completely predictable… And this predictability could only serve to ensure stagnation. I’m sure you could imagine how this would effect one’s mental development! To have the same response to all situations clicking over and over again in our brains would turn us into little more than cyclical morons who continue walking into closed doors… Never thinking to find the handle.

For one to catch up with the essence of Chaos, I would like to take a moment to present a pertinent book, entitled “Chaos: Making A New Science,” written by James Gleick, that explains how chaos works in the universe at large… And, in many ways, what a good thing it is. And I highly recommend it as a great starting point to delve further into understanding nonlinear dynamcial systems and Chaos Theory… As a taster, the following quote comes from the back of the book:

Over the last decade, physicists, biologists, astronomers and economists have created a new way of understanding the growth of complexity in nature. This new science, called chaos, offers a way of seeing order and pattern where formerly only the random, the erratic, the unpredictable–in short, the chaotic–had been observed. In the words of Douglas Hofstadter, “It turns out that an eerie type of chaos can lurk just behind a façade of order–and yet, deep inside the chaos lurks an even eerier type of order. ”

The science of chaos cuts across traditional scientific disciplines, tying together unrelated kinds of wildness and irregularity: from the turbulence of weather to the complicated rhythms of the human heart, from the design of snowflakes to the whorls of windswept desert sands. Highly mathematical in its origin, chaos nonetheless is a science of the everyday world, addressing questions that every child has wondered about: how clouds form, how smoke rises, how water eddies in a stream.

In Chaos, James Gleick tells the remarkable story of an idea–an idea that at once frightened and fascinated the scientists who began to explore it. Gleick describes the stunning and unexpected insights of these scientists: Edward Lorenz’s discovery of the Butterfly Effect that underlies weather’s unpredictability and constancy; Mitchell Feigenbaum’s calculation, prompted by his meditations on nature and art, of a universal constant; Benoit Mandelbrot’s concept of fractals, which has created a new geometry of nature.

Chaos is a history of scientific discovery. It chronicles, in the participants’ own words, their conflicts and frustrations, their emotions and moments of revelation. It is a record of a revolution, the birth of a new science. After reading Chaos, you will never look at the world in quite the same way again.

While neurons are remarkably slow relative to components in mordern computers, they still are able to assimilate a complex array of data into the experience we know as “Life”, which we are all (hopefully) having right now. Each cell in the body produces its own highly specific biochemical response/signal, which is produced from an array of factors that affect the cell’s internal and external workings (such as other external chemical messengers triggering internal cellular responses, OR internal cellular concerntrations of molecules rising or falling to initiate an external cellular change), as discussed in the blog “What Is This “Experience” We Call Being Alive… And How Does It Come About?.” This feeds-back into the brain, which in turn feeds-back into the body, and so a cyclical system of experience is born.

The computer program that Markram will be developing with IBM, will be a mathematical representation of the human brain. And, as is the case with NDS (nonlinear dynamical systems), under certain values the computer simulated NDS algorithm will produce chaos, while under other conditions it will produce a stable pattern.

In seeking this mathematical description of neuronal process, we are construction a rational reconstruction rather than a simulation. In looking at brain functions, one can investigate various hierachial levels of explanation beginning with the operation of individual neurons, how their excitatory and inhibitory actions take place through ionic exchanges across membranes that produce changes in electrical potential, as we’ve already discussed…

In Skarda and Freeman’s 1990 paper, entitled “Chaos And The New Science Of
The Brain
,” they postulate the following:

The idea that perception can be explained in terms of feed-forward processing, that it is caused by the stimulus or can be explained as the sum of responses to stumuli, is no longer acceptable. Our model tells us that perceptual processing is not a passive process of reaction, like a reflex, in which whatever hits the receptors is registered inside the brain. Perception does not begin with causal impact on receptors; it begins with the organism with internally generated (self-organized) neural activity that, by re-afference lays the ground for processing of future receptor input. In the absence of such activity, receptor stimulation does not lead to any observable changes in the cortex. Percpetion is a self-organized dynamic process of interchange inaugurated by the brain in which the brain fails to respond to irrelevant input, opens itself to the input it accepts, reorganizes itself, and then reaches out to change its input.

In many ways this is a very logical observation… For example, we need to be able to decern what type of particular object, rushing towards us at speed, might cause our body irreparable damage. For example, a leaf blown towards us in a gust of wind will not do our body any harm if it were to “bash” into us. We recognize (or rather choose NOT to recognize) the leaf as it is blow towards us. However, we have learnt that a spear, which has been hurled through the air at us, will cause our body great harm if the two were to meet… So our brain brings into focus the need to distinguish between the kind of action to be taken in order to either avoid or ignor one of these types of object flying towards us. Either way, the leaf and the spear are still both objects in the physical world… But our brains are able to discern between the two almost instantly, and therefore efficate a reaction that is appropriate i.e. ignor or avoid, and thereby ensure self-preservation.

Skarda and Freeman go on to say:

We suggest that the self-organzing process that replaces environmental input with an internally generated, chaotic activity is one that gives “biological meaning” to the stimulus.

Mac Cormac and Stamenov, having quoted the above in their book “Fractals of brain, fractals of mind: in search of a symmetry bond,” then mention…

Our search, therefore, must be for nonlinear dynamical systems that actively organize themselves into neuronal patterns that result in recognizable cognitive behavior. Rather than beginning with a simple simulation of the firing of a neuron (a sigmoid function) and then building up from that simulation to hierarchial layers as in artificial neural networks, we will attempt to employ nonlinear systems, especially fractals, as rational reconstructions of neural processes.

Mac Cormac and Stamenov next look at the analogies between neuronal processes and glycolysis in order to demonstrate a direct physical relationship between mind and body.

Our search for nonlinear systems to rationally reconstruct neuronal processes begins with the analogy between nonlinear systems that explain the chemical process of glycolysis and the activation of neurons. That analogy arises from the consumption of glucose by neurons when they are activated. But why would one seek an analogy from an underlying physical process to explain cognitive behavior? This seems like trying to explain the meaning of telephone messages by giving an explanation of the physics of how sounds are transformed into electronic signals, transmitted by photons in fiber optics and then reconverted into sounds at the receiving end. Why then can one have any confidence that an underlying physical process can have any integral relationship to a mental process?

Few would deny that physical processes like the activation of neurons and mental processes like recognizing words are related. The question, however, is whether the explaination of how neurons operate is like the explanation of how cognitive acts take place. Hope for such an analogous correlation was provided by a series of ingenious experiments conducted by Georgopoulos and his research group (Georgopoulos et al. 1989:234-236). They trained a rhesus monkey to move a handle in the direction of a light when it came on dim ad perpendicular to and counterclockwise from the direction of the light when it came on bright. During these tasks, they measured the activation of neurons in the motor cortex and constructed a population vector of these neurons. With the bright light, the monkey had to rotate the image 180 degrees and counterclockwise; here was a cognitive task that was measured in a motor cortex, the basis of physical movement. Georgopoulos et al. state:

“The rotation of the neuronal population vector is of particular interest because there was no a priori reason for it to rotate at all. It is also interesting that the population vector rotated consistently in the counterclockwise direction: this suggests that the spatial-motor transformation imposed by the task was solved by a rotation through the shortest angular distance. Given that the mental rotation is time consuming, this solution was behaviorally meaningful, for it minimzied both the time for the animal to get the reward and the computational effort which would have been longer if the rotation had been through 270 clockwise. (Georgopoulos et al. 1989:234-236)

In their abstract for the aritcle, the authors make an even stronger claim: “These results provide direct, neural evidence for the mental rotation hypothesis and indicate that the neuronal population vector is a useful tool for ‘reading out’ and identifying cognitive operations of neuronal ensembles.” (Georgopoulos et al. 1989:234-236) this direct evidence shows that the explanation of a physical neuronal process describes the structure of a cognitive process.

Armed with this insight that a genuine analogy exists in at least one case between a physical and cognitive process, glycolysis offers another possible candidate as a real analogy between physical and cognitive. Benno Hess, Stefan Muller, Theo Plesser and Mario Markus of the Max-Plank Institute fur Ernahrungsphysiologie in Dortmund have investigated the nonlinearity of glycolysis through an ingenious method of capturing the dynamics of the reaction by employing a video camera to record spectrophotometry (Muller et al. 1989, Markus et al. 1988, Hess et al. 1988). Pictures of the spectrophotometry of these reactions reveal not only a scientific beauty but also a suggestive analogy to computer graphics representations of other nonlinear systems like fractals.

They then go on make a very interesting statement about the dynamics of the way in which the brain uses its physical processes to cause mind… The way the mind can effect the physical processes:

Even though cognition and consciousness depend upon neuronal processes for their very existence, each maintains an emergent independence from the brain. Conscious thinking can and does change the physical activity of the brain as in the case of biofeedback where the subject can consciously lower blood pressure, pulse rate and other bodily functions. Mind and body interact as changes in neurotransmitters through drugs direct the contents of thinking. Neuronal processes are a necessary but not sufficient condition for cognition and consciousness. One cannot, however, predict the contents of cognition by fully understanding the organization of neuronal patterns as these activations are nonlinear and self-organizing. The neural chaos described by these nonlinear algorithms is both complex and unpredictable. Calling these systems ‘deterministic’ means that various patterns of neuronal activation can be described by algorithms but not that every future event can be predicted. This is contrary to the more tradtitional assumption that deterministic systems generate precise predictions about future behavior. But these more familiar dterministic systems were composed of linear rather than nonlinear equations. The chaos of nonlinear systems does not imply a formless interdeterminism. Instead, nonlinear dynamical systems can produce a self-organizing organism with rational but unpredictable future behavior.

The brain operates as an organic machine generating self-organized patterns of neuronal activation that yields unpredictable, creative congnitive behavior. Ingredient in this self-organizing machine that produces chaos are both mind and consciousness. Both emerge from neuronal processes in ways that remain mysterious. Each may be a series of subsets of the processes OR they may be a collection of activations of definite geographical areas of the brain.

And there you have it… The brain uses these unpredicatable leaps of chaotic intelligence, something that standard computer programs to date have lacked. It is this inherent chaos that adds intelligence to a dynamical system… If a system, a biological organism for example, has pre-defined set of rules within it that allow it to fuction in a given environment, then it usually only follows a series of commands given to it by the programmer. It’s as basic as that. This system, can be compared to a linear dynamical system i.e. a set input will always provide a given and predicatable output. It follows its programming. However, for something to become intelligent, it needs to have that spark… That “je ne sais quoi” about it. It should be able to vary its own response to things… And it should be able to learn from that new behavior i.e. did it provide a benefit or not to the device, by feeding-back the data to a “situation…” The “situation” being: an input occurs, and rather than following “standard protocol output response”, it varies the output response (called a “varied the output response”) and then performs a reflection upon the “varied the output response” to understand if this provides any benefit over the “standard protocol output response” program. If it does actually benefit i.e. saves time OR saves energy, then this can provide a uselful alternative to the “standard protocol output response”. But futher “tests” will need to be performed by the organism in order to ascertain exactly what situations this new “varied the output response” will be benefical in.

These responses will have to built into a large database of sorts and then cross referenced with eachother. Some of these responses will no doubt provide useful alternatives to “conditioned reflexes” or “standard protocol output responses”. Some will not. But inorder to gauge which are beneficial and which are not, these “self-similar actions” will have to be crossreferenced against a catalogue of “varying situations”. Infact, the organism should be able to crossreference the outcomes with the inputs in many various ways i.e. “self-similar actions” against “varying situations”, “self-similar situations” against “varying actions”, “self-similar situations” against “self-similar actions” in order to find which might be best… And the originality and efficiency with which an organsim mixes these combinations up is determined by nonlinear dynamics…

So perhaps it is with good fervor that the saying, “Chaos often breeds life, while order breeds habit,” arises?

From what we have seen so far, I think we can understand how chaos might actually benefit a living organism, and allow it “evolve” in novel and unpredicatable ways. Mac Cormac and Stamenov go on to state that:

‘Mathematical chaos’ describes the properties of nonlinear dynamical systems, namely, algorithms that are complex and deterministic and yet unpredicatable. For some variables, these algorithms are stable with results clustered around point attractors. For other variables, the results are scattered or chaotic and unpredictable.

Now… This is where it gets interesting. I have no idea whether this has already been documented in some scientific study or not… If it has, then perhaps it is simply that I am not the originator. But… My sensibilities tell me that this idea of a strange attractor can have a parrallel drawn between it and Pavlov’s experiments with behavior in his dogs.

As we have already seen, the brain is essentially a complex nonlinear dynamical system. This fact, however, does not predetermine it to being chaotic all the time… While a nonlinear dynamical system is prone to output chaotically under certain stimuli, it does also have the abiltiy to achieve stable states under certain conditions. As you may have seen in one of the previous links provided (click here to see), it has been thought that people who have been diagnosed with behavioral issues i.e. schizophrenia, depression, bi-polar, etc… tend to exhibit more chaotic neuronal patterns/functioning than healthy minds. Bearing this in mind, I am now going to present an extract from William Sargant’s book entitled “Battle For The Mind”… This will be a lengthy interlude, but please do read it, as it beautifully describes the importance of Pavlov’s own work in reflexes, plus clears the path into the connection between mind and body, which will allow for a deep understanding about how we all, dog, monkey and man, operate alike:

In the course of over thirty years of research Pavlov accumulated a mass of observations on various methods of building up behavior patterns in dogs and then breaking them down again. He interpreted his findings in mechanistic terms which have since been frequently disputed by psychologists and psychiatrists. Yet the findings themselves have been confirmed again and again. Horsley Gantt attributed the absence of any important errors in Pavlov’s work to his ‘painstaking methods, his adequate controls, his habit of giving the same problem to several collaborators working in separate laboratories or institutes, with whom he checked results and supervised experiments…’

Pavlov had won the Noble Prize, in 1903, for research on the physiology of digestion before turning to study what he called the ‘higher nervous activity’ in animals. What changed his line of enquiry was a sense that he could learn little more about digestive functions until he had investigated the workings of the brain and nervous system, which often seemed to influence digestion. He then became so deeply absorbed in the implications of this new study that he concentrated on it until his death in 1936, at the age of eighty-six.

Pavlov was one of the Russian scientists of the old regime whose work Lenin thought valuable enough to encourage after the Revolution; and even though extremely critical of the Soviet regime, Pavlov continued to receive generous support from the government. Both inside and outside Russia he was admired for the courageous attitude he adopted, and only at the very end of his life did he become reconciled to living under a dictatorship. Ironically, he is now regarded as a hero of the Revolution, and no mention is made in recent Soviet publications of his persistent opposition to the regime. Horsely Gantt, revisiting him in 1933, asked why his political attitude was now more conciliatory; and Pavlov replied half jokingly that at the age of eighty-three his heart could no longer stand the strain of infuriated outbursts against the authorities who were sponsoring him. About this time, also, the Nazis had begun to threaten Russia, and Pavlov’s great mistrust of Germany inclined him to abate his hostility to the Russian Government. But though he was now relating his discoveries about animals to problems of human behaviour, it is extremely doubtful whether he ever foresaw that his work could be used as an instrument of Soviet policy. Since he always demanded and obtained freedom of thought for himself, it is unlikely that he would have wished to curtail freedom of thought for others. He insisted on travelling abroad to maintain contact with his scientific colleagues, and won a great ovation when lecturing in England just before his death.

Pavlov cannot therefore be considered a typical scientist of the soviet regime; even if much of his finest work had not been done before the Revolution. Yet the Communists must have found his mechanistic approach to the physiological study of behaviour in dogs and men most helpful while persuing their policy of indoctrination. In July, 1950, a medical directive was issued in Russia for re-orientation of all Soviet medicine along Pavlovian lines – probably partly because of the impressive results obtained by applying Pavlov’s research to political ends. Yet outside Russia its implications still sometimes tend to be ignored.

As soon as Pavlov expressed a desire to apply his experimental findings on animal behaviour to problems of morbid psychology in human beings, the Soviet government placed a near-by psychiatric clinic at his disposal. His first public lecture on this topic was dilivered in 1930: he called it ‘The Trial Excursion of a Physiologist in the Field of Psychiatry.’ It may be that these new interests date from an operation for gall-stones which he underwent in 1927; because he then published his significant ‘A Post-operative Cardiac Neurosis Analysed by the Patient: Ivan Petrov Pavlov.’

Pavlov’s work seemed to have influenced the techniques used in Russia and China for the eliciting of confessions, for brainwashing and for inducing sudden political conversions. His findings, applicable to these, should be easily understood even by the non-technical reader, without the need of spending too much time on the details of his actual experiments. Most of these findings are well reported in a series of Pavlov’s later lectures translated by Horsley Gantt, and published in Great Britain and the United States in 1941 under the title ‘Conditioned Reflexes and Psychiatry.’ Professor Y. P. Frolov’s enlightening book on these experiments, ‘Pavlov and his School’ (1938), has also been translated and published in English. Professor Babkin’s more recent ‘Life of Pavlov,’ however, makes little reference to some of his most important findings from the view point of our study. And though Dr. Joseph Wortis in his ‘Soviet Psychiatry,’ published in the United States, emphasizes the importance in modern Russian medicine of Pavlov’s experimental approach to psychiatric problems, few details are given of the last important phase of Pavlov’s work. An official ‘Life of Pavlov,’ published in Moscow in 1949, written by E. A. Asratyan, also contains many details of Pavlov’s earlier experimental work on conditioned reflexes in animals, but very few details of his later work relevant to conversion and brain-washing techniques. At all events, no publication in English has hitherto explained these for the benefit of ordinary readers but recently a good new translation of Pavlov’s selected works has become available in English.

Thirty years of research convinced Pavlov that the four basic temperaments of his dogs approximated closely to those differentiated in man by the ancient Greek physician Hippocrates. Though various blends of basic temperamental patterns appeared in Pavlov’s dogs, they could be distinguished as such, rather than as new temperamental categories.

The first of these four correspond with Hippocrates’ ‘choleric’ type, which Pavlov named the ‘strong excitatory.’ The second correspond with Hippocrates’ ‘sanguine temperament’; Pavlov named it ‘lively,’ the dogs of this type being a more balanced temperament. The normal response to imposed stresses or conflict situations by both these types was increased excitement and more aggressive behaviour. But whereas the ‘choleric,’ or ‘strong excitatory,’ dog would often turn so wild as to be completely out of hand, the ‘sanguine’ or ‘lively’ dog’s reactions to identical stresses were purposeful and controlled.

In the other two main temperamental types of dog imposed stresses and conflict situations were met with more passivity, or ‘inhibition,’ rather than aggressive responses. The more stable of these two inhibitory temperaments was described by Pavlov as the ‘calm imperturbable types, or phlegmatic type of Hippocrates.’ The remaining temperament identified by Pavlov corresponds with Hippocrates’ ‘melancholic’ classification. Pavlov named it the ‘weak-inhibitory’ type. He found that a dog of this type shows a constitutional tendency to meet anxieties and conflicts by passivity and avoidance of tension. Any strong experimental stress imposed on its nervous system reduces it to a state of brain inhibition and ‘fear paralysis.’

Yet Pavlov found that the other three types, too, when subjected to more stress than they could cope with by usual means, responded in the end with states of brain inhibition. He regarded this as a protective mechanism normally employed by the brain as a last resort when pressed beyond endurance. But the ‘weak inhibitory’ type of dog was an exception: protective inhibition occured more rapidly, and in response to lighter stresses – a difference of the utmost significance to this study.

Pavlov fully recognized the great importance of environment, as well as of constitution, in deciding the final behaviour patterns of his dogs. He found that certain fundamental instincts, such as sex or the need for food, were constantly adapted to changes of the environment by the formation of appropriate behaviour patterns. A dog without a brain cortex (which contains some of the more complicated connections between the main brain centres) might still swallow food placed within its mouth; but it needed a brain cortex and means of forming complicated conditioned reflexes, if it were to learn that food would be given only after an electric shock of a certain definite strength, or after a metronome has been heard beating at one particular rate and no other.

In discussing the ‘weak inhibitory’ type, Pavlov pronounced tha though the basic tempramental pattern is inherited, every dog has been condtioned since birth by varied environmental influences which may produce long-lasting inhibitory patterns of behaviour under certain stresses. The final pattern of behaviour in any given dog will therefore reflect both its own constitutional temperament and specific pattern of behaviour induced by environmental stresses.

Pavlov’s experiments led him to pay increasing care to the need for classifying dogs according to their inherited constitutional temperaments before he subjected them to any of his more detailed experiments in conditioning. This was because different responses to the same experimental stress or conflict situation came from dogs of different temperaments. When a dog broke down and exhibited some abnormal patterns of behaviour, its treatment would also depend primarily on its constitutional type. Pavlov confirmed, for instance, that bromides are of great assistance in resotring nervous stability to dogs who have broken down; but that the doses of sedative required by a dog of ‘strong excitary’ type is five to eight times greater than that required by a ‘weak inhibitory’ dog of exactly the same body weight. In World War II the same general rule applied to human subjects who had temporarily broken down under battle and bombing stress and needed ‘front line sedation.’ The required doses varied greatly according to their temperamental types.

Towards the end of his life, when he was experimentally applying his discoveries about dogs to research in humans psychology, Pavlov gave increasing attention to what happened when the higher nervous system of his dogs was strained beyond the limits of normal response; and compared the results with clinical reports on various types of acute and chronic mental breakdown in human beings. He found that severer and more prolonged stresses could be applied to normal dogs of the ‘lively’ or ‘calm unperturbable’ type without causing breakdown, than to those of the ‘strong excitatory’ and ‘weak inhibitory’ types.

Pavlov came to believe that this ‘transmarginal’ (it has also been termed ‘ultraboundary’ or ‘ultramaximal’) inhibition which eventually overcame even the two former types – changing their whole behaviour dramatically – could be essentially protective. When it occurred, the brain might have no other means left of avoiding damage due to fatigue and nervous stress. He found a means of examining the degree of protective transmarginal inhibition in any dog at any given time: by using his salivary gland conditioned reflex technique. Thought the dog’s general behaviour might seem normal, at first sight, the amount of saliva being secreted would tell him what was beginning to happen in it brain.

In these tests, the dog would be given a definite signal, such as the beating of a metronome at a certain rate, or the passing of the a weak electric current into its leg, before being given food. After a time the signal would provoke an anticipatory flow of saliva, without the need of letting the dog see or smell the food. A conditioned reflex having thus been established in the brain between a signal and the expectation of food, the amount of saliva secreted could be precisely measured in drops, and any changes in the response of the brain conditioned reflexes and induced patterns, could be plainly registered.

Here let me digress by emphasizing the relevance of Pavlov’s experiments on condtioned reflexes to the ordinary happenings of everyday human life. Much human behaviour is the result of the conditioned behaviour patterns implanted in the brain, especially during childhood. These may persist almost unmodified, but more often become generally adapted to changes of environment. But the older the person, the less easily can he improvise new conditioned responses to such changes; the tendancy thn is to make the environment fit his, or her, increasingly predictable responses. Much of our human life consists also in the unconscious following of conditioned reflex patterns originally acquired by hard study. A clear example is the way a car-driver builds up numerous and varied conditioned responses before being able to negotiate a crowded city street without paying much conscious attention to the process – this is often called ‘driving automatically.’ If the driver then gets into the open country, he will change to a new pattern of automatic behaviour. The human brain is, in fact, constantly adapting itself reflexly to changes of environment; although, as with car-driving, the first lessons in any given process may demand difficult, and even tedious, efforts of concentration.

Human and canine brains are obliged to build up a series of both positive and negative conditioned responses and behaviour patterns. Most people in business and the Armed Forces learn by experience to behave negatively in the presence of their superiors; and positively, even perhaps aggressively, in that of their juniors. Pavlov showed that the nervous system of dogs developes extraordinary powers of discrimination in building up these positive and negative responses. He showed that a dog can be made to salivate when a tones of 500 vibrations a minute is sounded, if this is a food signal; but not if the rate is only 490, and no food can therefore be expected.

Negative conditoned responses are no less important that the positive ones, since the members of civilized societies must learn how to control normal aggressive responses almost automatically, though sometimes obliged to release them in a split second when a vital emergency arises. Emotional attitudes also become both positively and negatively conditioned: one learns an almost automatic revulsion from certain classes of people, and an automatic attraction to others. Even such words as Catholic and Protestant, Worker and Employer, Socialist and Conservative, Republican and Democrat, evoke very strong conditioned responses.

One of Pavlov’s most important findings was exactly what happens to conditioned behviour patterns when the brain of a dog is ‘transmarginally’ stimulated by stresses and conflict beyond its capicity for habitual response. He could bring about what he called a ‘rupture in higher nervous activity’ by employing four main types of imposed stresses.

The first was, simply, an increased intensity of the signal to which the dog was conditioned; thus he would gradually increase the voltage of the electric current applied to its leg as a food signal. When the electric shock became a little too strong for its system, the dog began to break down.

A second powerful way of achieving the same result was to increase the time between the giving of the signal and the arrival of food. A hungry dog might be conditioned to receive food, say, five seconds after the warning signal. Pavlov would then greatly prolong the period between a signal and the giving of food. Signs of unrest abd abnormal behaviour might become immediately evident in the less stable of his dogs. He found, in fact, that the dogs’ brains revolted against any abnormal prolongation of waiting under stress; breakdown occurred when a dog had to exert very strong or very protracted inhibition. (Human beings, too, often find prolonged period of anxious waiting for an event more trying than when it finally comes).

Pavlov’s third way of producing a breakdown was confuse them by anomalies in the conditioning signals given – continued positive and negative signals being given one after the other. The hungry dog became uncertain what would happen next, and how to face these confused circumstances. This could disrupt its normal nervous stability – just as happens with human beings.

A fourth way of producing a breakdown was to tamper with a dog’s physical condition, fevers, or by disturbing its glandular balance. Though the three other means listed above failed to produce a breakdown in a particular dog, this might be engineered later by using the same sort of stresses immediately after the removal of its sexual glands, or during an intenstinal disorder. The advantage taken of debilitation and other changes of bodily function in human beings for their political and religious conversion will be discussed later. In some cases, Pavlov’s findings may have been exploited; in others, anticipated.

Pavlov found not only that after castration or intestinal disorders a breakdown might occur even in temperamentally stable dogs; but also that the new behaviour pattern occurring afterwards might become a fixed element in the dog’s way of life, though it had long recovered from the debilitating experience.

In the ‘weak inhibitory’ type of dog new neurotic patterns thus implanted could often be readily removed again: doses of bromide might be enough to achieve this – though they did not alter the dog’s fundamental weakness of temperament. But in ‘calm imperturbable’ or ‘lively’ dogs who needed castration, for instance, before they could be nervously disrupted, Pavlov found that the newly implanted pattern was more often ineradicable once the dog had recovered its normal physical health. He suggested that this was die to the natural toughness of the nervous systems in such dogs. The new patterns of behaviour had been difficult to implant without a temporarily induced debilitation; now they might be held with as much tenacity as the old.

The relevance of this last experiment to similar changes of behaviour in humans hardly needs to be emphasized: towards the end of a long period of physical illness, or after a period of severe debilition (sometimes produced by enforcing fasting), people of ‘strong character’ are often known to make a dramatic change in their beliefs and convictions. If they then recover strength, they may remain true to the new orientation for the rest of their lives. Case-histories of people ‘converted’ in times of famine or war, or in prison, or after harrowing adventures at sea, or in the jungle, or when brought to destitution by their own self-will, are frequent. The same phenomenon is often observed in both psychotic and neurotic patients who have suffered from glandular operations, fevers, loss of weight and the like, and only then developed their abnormal patterns of behaviour: if they had strong previous personalities, these new patterns may persist long after physical recovery.

Pavlov established that the ability of a dog to resist heavy stress would fluctuate according to the state of its nervous system and its general health. But once protiective ‘transmarginal’ inhibition had been induced, some very strange changes in the functioning of the dog’s brain took place. And these changes could not only be measured with some precision by the amounts of saliva secreted in response to conditoned food stimuli, but were not liable, as when human beings have analogous experiences, to subjective distortions: there was no question, that is to say, of the dogs trying to explain away or rationalize their behaviour after having been subjected to these tests.

There distinct and progressive stages of ‘transmarginal’ inhibition were identified by Pavlov in the course of his experiments. The first he called the ‘equivalent’ phase of cortical brain activity. In this phase, all stimuli,of whatever strength, resulted only in the same amounts of saliva being produced. the observation is comparable to the frequent reports by normal people in periods of intense fatigue, that there is very little difference between their emotional reactions to important or trivial experiences. And though the feelings of a normal, healthy person will vary greatly, according to the strength of the stimuli experienced, nervously ill people often complain that they become unable to feel sorrow and joy as acutely as before. As the result of fatigue abd debilitation, in fact, a man may find to hs chagrin that the excitement at receiving a legacy of ten thousand pounds is no higher than if it were one of sixpence; his condition then probably approximates to the ‘equivalent’ phase of exhausted cortical activity identified by Pavlov in his dogs.

When even stronger stresses are applied to the brain, the ‘equivalent’ phase of transmarginal inhibition may be succeeded by a ‘paradoxical’ phase, in which weak stimuli produce livelier responses than stronger stimuli have done. The reason for this is not far to seek: the stronger stimuli are now only increasing protective inhibition; but the weaker ones still produce positive responses. Thus the dog refuses food accompanied by a strong stimulus, but accepts it if the stimulus is weak enough. This paradoxical phase can also occur in human behaviour where the emotional stress is heavy, as will be shown in a later chapter. On such occasions, the individual’s normal behaviour has been reversed to a degree that seems quite irrational not only to a detached observer, but to the patient himself – unless either of them happens to have studied Pavlov’s experiments on dogs.

In the third stage of ‘protective’ inhibition, which Pavlov called the ‘ultra-paradoxical,’ positive conditoned responses suddenly switch to negative one; and negative ones to positive. The dog may then, for instance, attach itself to a laboratory attendant whom it has previously disliked, and try to attack the master whom it has previosuly loved. Its behaviour, in fact, becomes exactly the opposed to all its previous conditioning.

The possible relevance of these experiments to sudden religious and political conversion should be obvious even to the most sceptical: Pavlov has shown by repeated and repeatable experiment just how a dog, like a man, can be condtioned to hate what it previously loved, and love what it previously hated. Similarly, one set of behaviour patterns in man can be temporarily replaced by another that altogether contradicts it; not by persuasive indoctrination alone, but also by imposing intolerable strains on a normally functioning brain.

Pavlov also showed that when transmarginal inhibition began to supervene in a dog, a state of brain activity similar to that seen in human hysteria might result. This can cause an abnormal suggestability to the influences of the environment. His case-histories frequently include reports on hypnodial or hypnotic states in dogs. Clinical reports on the behaviour of human beings under hypnosis, as well as in various conditions of hysteria, abound in description of abnormalities corresponding with those noted in Pavlov’s ‘equivalent,’ ‘paradoxical’ and ‘ultra-prardoxical’ phases of break down in dogs. In states of human fear and excitement the most wildly improbable suggestions can be accepted by apparently sensible people; as in August, 1914, a rumour that Russian soldiers were travelling through England ‘with snow still on their boots’ swept the country, and was so circumstantial that for a while it affected German stratagy; or as in the earlier stages of the Second World War, rumour continually reported the English renegade William Joyce (‘Lord Haw-Haw’) as having mentioned in a broadcast that the church clock of a particular village – the name of which always varied with the telling – was three minutes slow.

What I propose is that there are basins of attraction within the mind of us all. Let me draw on the analogy of the earlier idea of a point attractor, as I expressed within the definition of “attractor” at the beginning of this essay. For a moment, let’s think of the same pendulum. Now place three magnets as the vertices of an equilateral triangle with the pendulum at rest in the center. Each time you swing the pendulum it will come to rest either in the center i.e. the lowest point to the gravitational attraction, or will favor one of the three magnets. Each of these attraction points i.e. the three magnets OR the gravity, are point attractors. The image below shows the cumulative pattern of the pendulum within the attractor basins of this system. Each of the heart shaped regions in the center corresponds to the final state of the pendulum coming to rest favoring a particular magnet. The black areas correspond to the border between attractor basins…


Now let’s jump back to the human brain for a moment… I reckon similar patterns are hidden in the way the brain functions. Why? Well… We already know attraction basins exist within the mind, allowing the interplay of deeply instinctual drives, drives that have been naturally selected for over billions of years of evolution, to posit within behaviour, thus providing the organism with a better ability to survive, by using the best survival traits/techniques/actions available to them. Basically, these traits/techniques/actions, centered in the structure of the brain, ensure that the species carries on producing and surviving… So far, so good I hope. Current humans (and our distant relatives) survived natural selection for good reason… They were better adapted, both physically and mentally, to adapt and live/survive in their surrounding (and ever changing) environment. They developed habits and routines that allowed them to successfully (success = remain alive) with what ever came at them, whether is was a tiger, a disease or drought. This flexible mind, coupled with the constant, yet slow, mutation rate, allowed them to evolve and adjust the ever changing pressures of their surrounding environment. So the current hierarchy between the various controlling aspect of the body and mind, (a hierarchy that still governs us all deeply today) were all naturally selected for… And thus they are, by themselves, point attractors that exist around various structural nodes within the brain that provide particular modes of being to come into play and/or function for healthy, natural bodily activities and normal reflex human behaviour. An example of a point attractor within the brain is seen in the Right Temporal Parietal Junction (or RPTJ for short) that allows us to interpret what other people are thinking/gesturing/signalling/etc… Within these structures, certain varying patterns of neuronal firing occur as various inputs are received and interpreted… No doubt these are, as we have already seen, centered in a complex and chaotic dynamical feedback system of the whole body. After the system (the complete human body as a whole) interprets the stimuli, chemical cues manifest and cause further specific/relevant neuronal firing to posit relevant behavior for the organism… As this occurs, many other channels are triggered that will filter along into other areas of the brain, affecting other nodes… Producing subtle patterns that give rise to healthy OR (in the case of a malformed brain) unhealthy actions. This chemical and molecular interplay occurs much in the way that we’ve already seen in Bruce Lipton’s lecture entitles “The Biology Of Perception,” which can be viewed here.

These regulatory areas of the brain provide critical responses that have been hardwired into the structure of our Central Nervous System (CNS) and allow us to perform the various functions that we perform daily in society. No doubt these functional groups of neurons in the brain, when triggered, will act in varying overriding strengths (as determined by just how critical the “input” signals are), making the organism depart from a normal stable stasis, and move into a different awareness/mode of being. It is my guess that these regulatory areas of the brain will interlink together via various channels, whether directly or indirectly, and will posit relevant interaction, much in the same way strange attractors operate i.e. they allow certain behavioural patterns to remain in a continual steady flux, but when triggered into chaotic oscillation, they allow us to glean advantages over old dogmatic methods of being, and thus provide us with new suitable solutions (OR actions) with which to advance with into these environmental changes OR “problematic” encounters. These attractors are at work in the minds of both healthy and “mentally unstable” individuals alike. The only difference being that the healthy mind has these attractors functioning within fairly stable and predictable parameters i.e. they respond to their evironment, their friends, family and relevant life experiences with healthy, “normal” and accepted behavioral responses/patterns…

Briefly then… As a graphical analogy to what we’ve been discussing so far… Let’s just take look at the chaos that can arise out of a nonlinear dynamical system… Here the chaos within the system is plotted on a Cathode Ray Oscilloscope machine to yield a Strange Attractor pattern within phase space.

So behavioural responses, which are results of basins of attraction centered around specific functional groups within the brain, are no doubt a result of two factors:

i) the structure of the brain itself within an individual – determined by nutrition provided during the formative years of the individual’s growth, and the stimulus provided during this growth, and type of stimulus i.e. positive or negative.

ii) the experiences an individual has throughout their formative years i.e. between birth and the ages of 15 to 18 – determined by the family’s religious disposition, social circles, education, etc…

These inputs of “nurture and nature” build the system. And thus, these factors directly have a role in determining how the organism will react in its later years to specific environmental stimuli i.e. whether it will allow an individual to function within the real world normally according to current social values, or whether they will be prone to negative and destructive behavior patterns. Either way, I think that there are literally patterns of mind that will be able to be observed; patterns that will determine whether they fall into Pavlov’s ‘strong excitatory,’ ‘lively,’ ‘calm imperturbable’ or the ‘weak-inhibitory’ character types. Because as the mind forms, the attractors at work will be molded and pulled into a finalized shape or rhythm that the individual will use, there-onwards in their life, to process all the input data for the rest of their lives.

No doubt if this is the case, then stable/healthy cycles between the “basins” of attraction (which should be able to be modeled, roughly, by mathematical simulations based on current observations) should provide a particular phase space pattern to demonstrate as much i.e. the nonlinear dynamical system has a steady and stable flow to it, similar to what is seen in diagram b) of the “Chaos and stability in a nonlinear dynamical system,” which was shown near the beginning of this essay. However, when undue stress is applied to the subject, and the ‘equivalent,’ ‘paradoxical’ or ‘ultra-paradoxical’ phases of transmarginal inhibition are approached, the steady dynamics of the “normal” human mind will perhaps begin to exhibit signs of instability, OR chaos. These states will no doubt start to manifest in behavioural anomalies i.e. non recognition of family members and/or friends, etc…, and might well provide plots in phase space like those seen in c), d) and maybe even e) of the “Chaos and stability in a nonlinear dynamical system” diagram. ?

Right… For now I would now like to return to Mac Cormac and Stamenov.

‘Mathematical chaos’ describes the properties of nonlinear dynamical systems, namely, algorithms that are complex and deterministic and yet unpredicatable. For some variables, these algorithms are stable with results clustered around point attractors. For other variables, the results are scattered or chaotic and unpredictable. For still other variables, the results unexpectedly cluster around strange attractors and may even oscillate between or amoung them. These strange attactors may have a dimension that is not an integer and hence are fractal.

Examples of mathematical chaos abound in the history of mathematics; nonlinear dynamical systems are not new. The relative newness of this field arises from the realization that these equations can be used to model physical phenomena allowing for the abrupt changes like the shift from laminar flow to turbulence in the flow of air over a wing. The ability of the modern digital computer to produce the results of hundreds of thousands of iterations of these nonlinear equations has also provided an impetus for an exciting and continuing investigation of chaos…

…Nonlinear dynamical systems offer the possibility of describing an interrelated network or neurons that move abruptly from chaos to stable patterns. Self-organized slight perturbations of initial values or the values of constants in the algorithms, force transitions from chaos to stable patterns and from stable patterns to chaos. These properties of nonlinear systems present an opportunity to give a mathematical description of neuronal processes. But which kind of nonlinear algorithm should we seek to model neuronal activation?

I think Markram and his team at L’Ecole Polytechnique Fédérale de Lausanne (EPFL) are well on the way to understanding which nonlinear algorithm is, OR set of nonlinear algorithms are, to be used for their computer model of the human brain.

Just to return one last time to what Mac Cormac and Stamenov have writen in their book “Fractals of Brain, Fractals of Mind: in Search of a Symmetry Bond”:

Fractals are related to mathematical chaos in an unusual manner. Mandelbrot claims that “every known ‘strange’ attractor is a fractal.” He expands on this claim by exploring the concept of “strange.”

“Whether or not all fractal attractors are strange is a matter of semantics. Increasing numbers of authors agree with me that for the most purposes an attractor is strange when it is a fractal. This is a healthy attitude, if strange is taken to be a synonym to ‘monstrous,’ ‘pathalogical,’ and other epithets once applied to individual fractals.” (Mandelbrot 1983:197)

Although the formal relationship between fractals and nonlinear dynamic systems remians unclear, some fractals seem to be a geometrical subset of nonlinear systems even though not all nonlinear systems are fractals. Amoung fractals, the property of resemblance would seem to be an extremely useful analogy in attempting to model the nonlinear activation of neurons. When fractals are scaled up or down with larger or smaller values, topological patterns recur unexpectedly over and over again. This poperty is called ‘resemblance.’ Since neuronal activations during various cognitive tasks involves at least some similarities in the areas of the brain activated, a property of resemblance in mathematical rational reconstrcutions would be desirable. Unfortunately, however, many fractals than can be used to model biological forms involve geometrical inversion of their forms (and are called self-inverse fractals) and do not possess the property of resemblance (self-similarity) (Mandelbrot 1983: 166-179). Even some of these fractals, howeverm are ‘nearly’ self-similar and perhaps it is those which we shall seek in our investigation of congintive neuroscience. Many random fractals possess the property of self-affinity; even though their patterns do not exactly resemble the each other in scaling, they are affine, meaning that they possess some similar properties but not exact resemblance. Richard Voss states: “This non-uniform scaling, where shapes are (statistically) invariant under transformations that scale different coordinates by different amounts, is know as self-affinity” (Voss 1988:44). This is the property necessary for a mathematical reconstruction of patterns of neuronal activation: statistical similarity with differences in detail at different scales.

A zoom into the Mandelbrot set...

A zoom into the Mandelbrot set...

Fractals also offer one advantage of representing temporal changes in geometrical forms for explaining cognitive neuronal processes. Neurons activate over time in various regions of the brain often physically separated. The dynamics of fractals allows for temporal and spatial changes. The Mandelbrot set, one of the most interesting and robust fractals, combines aspects of self-similarity with aspects of infinite change.

zn+1 = zn2 + c

where z is a variable and c complex number.


The Mandelbrot set can be displayed graphically by beginning z=0 and then iterating the algorithm for various values of c. If one fixes c and then varies z in the field of complex numbers, beautiful Julia sets are obtained (Douady 1986). While Julia sets are self-similar, the Mandelbrot set exhibits patterns that are affine. It is most likely that if neuronal processes can be represented by fractals, they will be rationally reconstrcuted by random fractals or fractals like the Mandelbrot set that are infinitely varied, complex and unpredictable, but still self-organized.

A Julia set plot showing julia sets for different values of c. The plot, when showing the distribution of c in the complex plane, resembles the Mandelbrot set.

A Julia set plot showing julia sets for different values of c. The plot, when showing the distribution of c in the complex plane, resembles the Mandelbrot set.

The mathematics of chaos, especially fractals many of which are subsets of chaos, offer a ideal series of algorithms to rationally reconstruct the nonlinear self-organizing activation of neurons. In a search for the mathematical algorithms which reconstruct how billions of interconnected neurons are activated to account for both motor and cognitive actions, one must find representations that are nonlinear, that form recurring patterns, that are capable of self organization, and that move rapidly from order to disorder. Fractals fulfill all of these requirments. There are both deterministic and random fractals, with the latter and perhaps the former combining determinism and unpredictability. And all fractals posses a property either of exact resemblance or at least self similarity (affine) under scaling. But which fractals rationally reconstruct which neuronal processes? We must find an emprical method of discovering which nonlinear algorithms (fractals) will represent which neuronal processes.

And perhaps this is also something that Markram and his team will discover as they run and develop their software into an ever more similar/exacting model of the human mind… Perhaps they will literally see these almost kaleidoscopic patterns unfolding as sensory data are input into the complex structure of the central nervous system, interpreted and then output back into patterns that never repeat exactly the same way twice, always unfolding in new and original ways, giving the system freedom from stagnation… Making possible evolution.

A depiction of Lorenz's water wheel experiment.

A depiction of Lorenz's water wheel experiment.

Just a Lorenz discovered the chaotic patterns inherent in his equations by varying the input data to only a few decimal places i.e. ignoring several thousandths of a unit of accuracy, into his Royal McBee computer… Another system, that of a water wheel, show above demonstrates nonlinear dynamical fluctuations in its flow… At the top, water drips steadily into containers hanging on the wheel’s rim. Each container leaks steadily from a small hole in its base. If the input stream of water is slow, the top of containers never fill fast enough to overcome friction, but if the input stream is faster, the weight starts to turn the wheel. The rotation might become continuous. Or if the input stream is so fast that the heavy containers swing all the way around the bottom and start up the other side, the wheel might then slow, stop, and reverse its rotation, turning first one way and then the other.

As James Gleick mentions in his book entitled, “Chaos: The Amazing Science Of The Unpredictable”:

A physicist’s intuition about such a simple mechanical system – his pre-chaos iintuition – tells him that over the long term, if the stream of water is never varied, a steady state would evolve. Either the wheel would rotate steadily or it would oscillate steadily back and forth, turning first in one direction and then the other at constant intervals. Lorenz found otherwise.

Three equations, with three variables, completely described the motion of this system. Lorenz’s computer printed out the changing values of three variables: 0-10-0; 4-12-0; 9-20-0; 16-36-2; 30-66-7; 54-115-24; 93-192-74. The three numbers rose and then fell as imaginary time intervals ticked by, five times steps, a hundred time steps, a thousand.

To make a picture from the data, Lorenz used each set of three numbers as coordinates to specify the location of a point in three-dimensional space. Thus the sequence of numbers produced a sequence of points tracing a continuous path, a record of the system’s behaviour. Such a path might lead to one place and stop, meaning that the system had settled into a steady state, where the variables for speed and temperature were no longer changing. Or the path might form a loop, going around and around, meaning that the system had settled into a pattern of behaviour that would repeat itself periodically.

A Lorenz attractor 3D plot (a plot in phase space) demonstrating the way inwhich the data lines up. Here there are two attractor basins, demonstrated by the two points around which the circular patterns group.

A Lorenz attractor 3D plot (a plot in phase space) demonstrating the way inwhich the data lines up. Here there are two attractor basins, demonstrated by the two points around which the circular patterns group.

Being able to see the Lorenz attractor with its 3D graphical nomenclature always helps, I've found...

Being able to see the Lorenz attractor with its 3D graphical nomenclature always helps, I've found...

Lorenz’s system did neither. Instead, the map displayed a kind of infinite complexity. It always stayed within certain bounds, never running of the page but never repeating itself, either. It traced a strange, distinctive shape, a kind of double spiral in three dimensions, like a butterfly with its two wings. The shape signaled pure disorder, since no point or pattern ever recurred. Yet… Within this disorder, a new order was discovered.

Here, it is my guess that Markram and his team at L’Ecole Polytechnique Fédérale de Lausanne (EPFL), as they begin running their computer simulation of the human brain, piecing it together bit by bit as they go along, will see strong evidence pointing towards the existence of “strange attractors” at work within the “neuronal forest.” Some of these “strange attractors” might be so complex in nature that they might even demand several dimensions of phase space to be plotted out. No doubt these attractors will begin to be linked to behavioural patterns i.e. sex drive, flight and fight responses, conginitive functions, etc… And eventually, as the simulation becomes more and more complete in structure, as well as tuned to function just like a real human brain does, the EPFL team will begin to see “strange attractors” within “strange attractors…”

Perhaps now might be a good time to have a look at what makes you, you…

The price we pay for being self-aware, is the understanding the ultimate demise of ourselves. As Spinoza once said, “A free man thinks of nothing less than of death, and his wisdom is not a meditation upon death but upon life…”

As you will have seen… When Professor du Sautoy goes out to the Wisconsin Psychiatric Institute, he observes that there is an important difference between the waking mind and mind “at rest/in sleep.” While awake, it seems that there is cross talk between various sides of the brain i.e. between the different centers of regulation within the neocortex. When du Sautoy has Transcranial Magnetic Stimulation (TMS) while awake (seen at about 42 mins into the documentary) he sees that the graphical recording of his own brain’s activity shows simulated areas of the brain as red. From this recording he can clearly see that when areas of his brain were stimulated by TMS, there were also other areas on the opposite side of the brain demonstrating stimulation… Almost as though there was some “secondary-stimulation” resulting from an interconnection between the different areas of his brain. However… When a subject was asleep, and the same proceedure was performed on their brain i.e. simulation of certain brain areas by TMS, the “secondary-stimulation” usually seen in subject who were awake, was NOT observed!!! Thus, as Professors Marcello Massimini and Marcus du Sautoy rightly observe, “consciousness is about the interconnectivity between the different elements of the brain.” It is my guess that various control centers of the brain cross-talk in chaotic ways; ways that are similar to “strange attractor” plots in phase space, producing chaotic patterns of mind… Perhaps if this “secondary-stimulation”, OR this cross-talk between various parts of the mind, was observed more closely, then nonlinear dynamics (OR chaos theory) would best describe the dynamical interactions between regulatory nodes of brain, which are posited as modes of mind, and behavioral modifications. The chaos inherent in our minds is the essence of what we perceive to be consciousness. But currently, I am awaiting the definitive proof of this conjecture from the world of science. Is there anyone reading this who can test my theory for me???

When, and even if, this is demonstrated… Perhaps these patterns will mimic ideas and shapes found in everyday life… ? Perhaps human consciouness will be able to be mapped in much the same way that a sea urchin’s shell can be described by a 4th degree polynomial graphical plot?

The beautifully patterned cases/skeletons of a sea urchin without their spines.

The beautifully patterned cases/skeletons of a sea urchin without their spines.

A fourth degree polynomial pattern trace. Sea resemblance? (Pun intended)

A fourth degree polynomial pattern trace. Sea resemblance? (Pun intended)

But this is something I will leave for time to reveal…

So… So far so good… I HOPE!!! But an important question that we’ve not yet tackled is… Why would the human body choose to use a central nervous system based on fractals??? Well… In many ways, the answer to that is pretty simple. Because fractals are everywhere! And what would be the most efficient system to recognize and sift through any self-similar data set? You guessed it… A fractal system.

If you don’t believe me that fractals exist everywhere, I’m now going to show you just the tip of the iceberg with a few photo collages that I’ve prepared.

The Mandelbrot Set

The Mandelbrot Set

The (Mis)behaviour Of Markets” is the chronicle of Benoit Mandelbrot’s long lasting pursuit of understanding the financial markets. Instead of Brownian motion and Gaussian distribution, as the early 20th century French mathematician Louis Jean-Baptiste Alphonse Bachelier (March 11, 1870 – April 28, 1946) did (like flipping a coin, his idea was that the evolution of asset prices could be conceived of as purely random events, with a 50-50 chance of ticking up or ticking down as the time passes) Mandelbrot based his views on fractal geometry, a mathematical branch he himself originated.

Fractal comes from the Latin word “fractus” meaning broken. The idea is that a shape is broken down into smaller shapes, each echoing the large. Fractals can be found in many places in nature, like the British coast line, branches on a tree, or parts of a rock. The analogy to asset prices is the similarity between different frequencies of stock market data. We know that daily observations look very similar to lower frequency data, such as monthly observations. Hence the self similarity property of the parts to the whole.

Beniot Mandelbrot also wrote an article for Scientific American back in 1999, entitled “How Fractals Can Explain What’s Wrong with Wall Street,” which demonstrates how the geometry that describes the shape of coastlines and the patterns of galaxies also elucidates how stock prices soar and plummet.

Bifurcation diagram of a logistic map, displaying chaotic behaviour past a threshold.

Bifurcation diagram of a logistic map, displaying chaotic behaviour past a threshold.

Another fractal pattern occurs as dynamical system move towards chaotic behaviour. The Feigenbaum constant δ is a universal constant for functions approaching chaos via period doubling. It was discovered by Feigenbaum in 1975 (Feigenbaum 1979) while studying the fixed points of the iterated function f (x) = 1 – μ[x]r and characterizes the geometric approach of the bifurcation parameter to its limiting value as the parameter μ is increased for fixed x.


The plot above is made by iterating the equation f (x) = 1 – μ[x]r (where r = 2) several hundred times for a series of discrete but closely spaced values of μ, discarding the first hundred or so points before the iteration has settled down to its fixed points, and then plotting the points remaining.

Simple systems can also produce chaos without relying on differential equations. An example is the logistic map, which is a difference equation (recurrence relation) that describes population growth over time. Another example is the Ricker Model of population dynamics.

Even these bifurcation diagrams exhibit fractal like properties, called Feigenbaum fractals.

Even these bifurcation diagrams exhibit fractal like properties, called Feigenbaum fractals.

A Bifurication Diagram is basically a probability map that accurately shows the path that a dynamical system can take at each cycle/oscillation at any one time.

This diagram shows "roughly" how the evolution of cyclical variations within a nondynamical system relate to the data shown in a bifurcation diagram...

This diagram shows "roughly" how the evolution of cyclical variations within a nondynamical system relate to the data shown in a bifurcation diagram...

These Bifurication Diagrams also demonstrate a surprising proportionate resemblance between the Mandelbrot Set.

The correspondence between the Mandelbrot Set and the logistic map.

The correspondence between the Mandelbrot Set and the logistic map.

Let’s move on to attractors, as these ideas are very pertinent to what we’ve been discussing above i.e. that brain function is, in its own way, based on fractal principles.

The Lorenz attractor, named after Edward N. Lorenz, is a fractal structure corresponding to the long-term behavior of the Lorenz oscillator. The Lorenz oscillator is a 3-dimensional dynamical system that exhibits chaotic flow, noted for its lemniscate shape. The map shows how the state of a dynamical system (the three variables of a three-dimensional system) evolves over time in a complex, non-repeating pattern.

The Lorenz attractor, named after Edward N. Lorenz, is a fractal structure corresponding to the long-term behavior of the Lorenz oscillator. The Lorenz oscillator is a 3-dimensional dynamical system that exhibits chaotic flow, noted for its lemniscate shape. The map shows how the state of a dynamical system (the three variables of a three-dimensional system) evolves over time in a complex, non-repeating pattern.

An attractor is a set to which a dynamical system evolves after a long enough time. That is, points that get close enough to the attractor remain close even if slightly disturbed. Geometrically, an attractor can be a point, a curve, a manifold, or even a complicated set with a fractal structure known as a strange attractor. Describing the attractors of chaotic dynamical systems has been one of the achievements of chaos theory, as you may have already read in James Gleick’s book entitled “Chaos: Making A New Science.” The term “strange” was coined by David Ruelle and Floris Takens to describe the attractor that resulted from a series of bifurcations of a system describing fluid flow.

The human heart also exhibits chaotic patterns within its rhytmic cycles, again denoting a nonlinear dynamical system.

The human heart also exhibits chaotic patterns within its rhytmic cycles, again denoting a nonlinear dynamical system.

The human heart also has a chaotic pattern. The time between beats does not remain constant; it depends on how much activity a person is doing, among other things. Under certain conditions, the heartbeat can speed up. Under different conditions, the heart beats erratically. It might even be called a chaotic heartbeat. The analysis of a heartbeat can help medical researchers find ways to put an abnormal heartbeat back into a steady state, instead of uncontrolled chaos. For more information, please click here.

A pattern I noticed while calculating Mandelcube pictures... Notice the white lines? Don't they look veins!?

A pattern I noticed while calculating Mandelcube pictures... Notice the white lines? Don't they look veins!?

In studying fractal topography, I also taking a keen interest in generating images of the M set, and its related permutations. One of these is the Mandelcube. And just the other day, while generating the above image using FraxFlame, I noticed an uncanny similarity between vein patterns and the white fibral markings above…

Veins (from the Latin vena) are blood vessels that carry blood toward the heart.

Veins (from the Latin vena) are blood vessels that carry blood toward the heart.

Through out the body there are ever branching pipes, that get smaller and smaller, like trees trucks break into boughs, which break branches, which again break into twigs. This fractal physiology of the human body has been well documented in recent times. James B. Bassingthwaighte, Larry S. Liebovitch and Bruce J. West have done it great justice in their book entitled “Fractal physiology.” Even the structures in the heart are fractal…

Is there any wonder that these dynamical systems then keep arising through out the universe in many different ways, across many different scales???

Is there any wonder that these dynamical systems then keep arising through out the universe in many different ways, across many different scales???

Then there are general phenomenon that seem to be self-similar in an affine away… Spirals of weather systems roughly “match” those found existing within the cosmos on much larger scales. And it’s just mesmerizing to think that within each galaxy, there are near one thousand billions solar systems, most of which have planetary systems that will exude similar weather patterns to Earth’s own.

A satelite view of the Tibetan mountain range... Fractals shapes seen from high above.

A satelite view of the Tibetan mountain range... Fractals shapes seen from high above.

Above, mountains “branch” over the surface of the Earth… Gravity pulling the carving forces for water, ice and rock down into basins (or oceans) of equilibrium. As these forces carve out the higher grounds, their random shapes elude to the divine geometry of Universal flow.

Even trees and plants use fractal structures. Notice the way the tree's branches flow... And how the leaves viens flow.

Even trees and plants use fractal structures. Notice the way the tree's branches flow... And how the leaves viens flow.

All plants arrange their structures in fractal ways… This maximises the surface area of their leaves exposed to sunlight over the day time.

Basic structures, when iterated over and over again, produce the complex patterns we see today... Think about the first single celled organisms, iterated into complex multicellular life... Reproduced with kind permision from Paul Bourke - Research Associate Professor, University of Western Australia.

Basic structures, when iterated over and over again, produce the complex patterns we see today... Think about the first single celled organisms, iterated into complex multicellular life...

Basic shapes and structures, when repoduced over and over again, form patterns out of the whole… This idea stretches from molecules in cells, cells in organisms… Even molecules in planets, planets in solar systems, all the way through to solar systems in galaxies.

Even the simple shape of a bacterium, when iterated over and over again, produces wondrous patterns of self-similarity.

Even the simple shape of a bacterium, when iterated over and over again, produces wondrous patterns of self-similarity.

Even single celled organism produce affine fractal patterns… Click here for more information.

Bearing this last idea about bacterial spread following fractal patterns of growth… Or should it rather be, producing fractal patterns in their growth… Is it any wonder that epidemiologists are finding it very convinient to understand the spread of disease in terms of fractal scaling laws?

1. A fractal model of HIV transmission on complex sociogeographic networks: towards analysis of large data sets

2. Fractal scale-free networks resistant to disease spread

3. The spread of filthy lucre and disease

4. Respiratory-circulatory interactions in health and disease by Steven M. Scharf, Michael R. Pinsky, Sheldon Magder

5. Fractals, graphics, and mathematics education by Michael Frame, Benoît B. Mandelbrot

Expanding this idea of spread and diffusion… In China, scientists have also noticed that the spread of fires is best described with the use of fractal geometry… This is handy as fire-fighters now understand that they should focus on the most recently ignited sites, as suggested by this new fractal mathematical model. One wall of flame may look like another to a fire-fighter on the ground, but the boundaries where a forest fire is growing fastest are more dangerous than the rest… So now better co-ordination for effective fire-fighting can be orchestrated between a ground and airborn team.

Even when one drops some ink onto blotting paper, there are fractals unfolding before your very eyes.

Even when one drops some ink onto blotting paper, there are fractals unfolding before your very eyes.

The fine filaments within the structure of paper provide fine holes woth which ink is absorbed by “capillary action.”

And even as we zoom in, the pattern remains self-similar...

And even as we zoom in, the pattern remains self-similar...

These branches and patterns also occur throughout other systems. A common one being ground water draining through top soil after is rains.

L. Sander & T. Witten made this CGI of a Diffusion Limited Aggregation (DLA) system in 1981... Another fractal structure commonly found in the natural (and man made) world.

L. Sander & T. Witten made this CGI of a Diffusion Limited Aggregation (DLA) system in 1981... Another fractal structure commonly found in the natural (and man made) world.

Diffusion-limited aggregation (DLA) is the process whereby particles undergoing a random walk due to Brownian motion cluster together to form aggregates of such particles. This theory, proposed by Witten and Sander in 1981 [1], is applicable to aggregation in any system where diffusion is the primary means of transport in the system. DLA can be observed in many systems such as electrodeposition, Hele-Shaw flow, mineral deposits, and dielectric breakdown.

Diffusion Limited Aggregation of iron flowers that formed naturally in bedrock...

Diffusion Limited Aggregation of iron flowers that formed naturally in bedrock...

A DLA cluster grown from a copper sulphate solution in an electrodeposition cell.

A DLA cluster grown from a copper sulphate solution in an electrodeposition cell.

DLA can even be seen in the structures of moss and lichens.

DLA can even be seen in the structures of moss and lichens.

A picture of moss growing on a stone.

A picture of moss growing on a stone.

A picture taken from a Mandelbrot zoom that I created in FraxFlame. Notice similarities between the moss covered stone?

A picture taken from a Mandelbrot zoom that I created in FraxFlame. Notice similarities between the moss covered stone?

Even lightening displays a type of DLA fractal structure…

But enough of this demonstration. Find your own fractals! And remember… They might not be as obvious as these visual displays, as we saw with the functioning of Strange Attractors within the human mind.

Now I will have my say…

Just as all life originated from the single celled organisms called stramatolites… Single cells which eventually came together to join and work as one multicellular organism… So, in these early multicellular sheets of algae, each cell initially performing exactly the same tasks as one another… Thin enough so that nurtients and sunlight might be readily available and waste might dufuse easily away into the environment. Similar natural laws that caused the atomic star dust of accretion to assemble into molecular balance in order to meet energetic needs/requirments, providing a beautifully elegant solution via atomic sharing and symmetry, eventually began to work on these very molecules themselves. Basins of chaotic attraction, bestowed upon these molecular communities by their own structural and physical necessitarianism, started to arrange themselves into masses. Characteristics of their energetic dispositions dictated how each molecules unique phsical and chemical properties would impinge upon its own destiny of intermolecular interaction. Some, such as the fatty acids, formed vesicles… Others formed protein-base pair coupled reactions that cycled in these vesicles like Beluzov-Zhabotinsky marvels.

Simple Belousov-Zhabotinsky swirls in naturally occuring reaction. Waves of instability propaagating outwards...

Simple Belousov-Zhabotinsky swirls in naturally occuring reaction. Waves of instability propaagating outwards...


After much time, chance and probablity bequeathed stability within these basins of attraction. And so these Life forms developed a stable reproducability that allowed them to become successful enough to multiply over the surface of this novel and wondrous “petri dish”, suspended in the inky back void of time and space around its central star.

However, as chance is a fickle thing, even crashing in on stability’s own new founded molecular party… Somewhere within these environmentally isolated vesicles (introduced by disfusion, turbulent, or concentration inadequacies) errors were caused by the chaotic instabilities, and new functions were either formed… Or, much more commonly, old functions were terminated. Either way, these “stromatolites” were at times given the opportunity to distiguish themselves from the rest and separate, even mutate, the original plan… So that subtle differences occured within their single celled bodies. Successful ones even developed advantages over the others and began racing ahead with a new found impetus for spreading and consuming.

After many millions of years of steady, vibrant gowth, chemical by products of life i.e. oxygen, built up in the environment… And as all good chemists and physicists now, as partial pressures of gases increase, so do the ability to which they dissolve into solution. So, no doubt, oxygen began to build up in the primordial soups of life… And as we all know so well from experience, as ‘polutants’ build up, so they have an effect on the environment and the creatures living within that environment. As this eponymous oxidating agent ever increased in volume, the pressure it began to place on evolution’s cause began to impact selection. Where as mutations that bestowed abilities to handle the “king of all oxidating elements” in earlier organisms might have gone un-noticed, due to anaerobic evironmental pressures; they were now able to capitalize on the build up of “waste” oxygen from earlier generations. Specializing in “O two” consumption, these organisms were given new chances to interact around new basins of attraction. This idea of evolving didn’t stop there… Chaos wanted to span the eons majestically with new iterative designs. As Life moulded the environment, so the environment moulded Life.

Eventually the limitations of the single celled organisms came about, as sheets of algal cells lnked sides and became the first “crude” multicellular organisms… And as with each new generation of modifications, the odds of mutation stacked higher and higher. And so cells began to clump together, forming algae like sheets that became larger nd larger. Sooner or later, as these clumps of cells began to mutate/differentiate in their own ways within their multi-cellular bodies, they might have discovered symbiosis… Aliances between these differentiations arose, where by one cell’s waste, became another cell’s food. Now these chaotic attractors developed new internalized basins to modulate their own survival/needs with. Eventually radical differences came into being, whereby certain cells could begin to specialize in particular functions for the Whole… Functions that others could not i.e. eyes with which to see, kidneys with which to purify the body with, etc… This ever changing flow eventually gave rise to complex organisms like ourselves, humankind.

Bearing in mind mankind followed similar social ideals to these of the cells journey i.e. was born into a family, would leave the family and then come together again in a new family… We can see that these patterns are repeating. Living organisms are generally following an “affine” fractal pattern. The idea of the whole i.e. survival, is the key… And the patterns used to create survival are essentially the same as they always were, across many different scales… And across time.

Man, as they spread… Originally started out as family groups of hunter gatherers, which eventually grouped together in social groups, aiding in grooming, mating and providing protective measures from predators… Even further down the line these ideals developed into villages, towns, cities, and countries… And even, as we are seeing today, Global Communities. So… Isn’t it becoming obvious? We’re doing the exact same things that all life on Earth has always done, since the day it got its very first, and very sucessful, foot hold here… We’re coming together, and operating in new ways that only large groups of organisms can do… We’re evolving new patterns of thought, like little bodily cells of the Universe, perceiving the majestic wonder in which we’ve ‘suddenly,’ and rather randomly, appeared in. What a lottery ticket We (the molecules on Earth) have been given… That chance to experience Life!

This idea of self-similarity, which we use every day of our waking, sleeping, eating, talking, partying, thinking, studying, dancing lives, is showing us something that we’ve been trying to express through Religions, mystical dances, etc… for EONS! And now we’re beginning to see that nature is showing this obvious pattern of being… Via memes, via scientific research, via mathematical, chaotic and fractal research even… And most deffinitely via artistic expression… We’re copies of copies, no longer originating, but simply evolving ideas and techniques, using the colors of past happenings, with the shading of present experiences, to paint a brighter and more deeply textured future with…

And we should heed the leasons that this ancient process is showing us… That the Butterfly Effect, where small seemingly insignificant gestures can generate instabilities in current flows, which are then amplified further up the line through a chain of turbulent features, so that they become unpredictable eddies of wondrous new possibilities… We should understand the sensitivity of our “petri dish” life here on planet Earth, and know that the way we are consuming and heating out homes, and running our machines with fuels, eating foods that we no longer grow ourselves, are all having effects on the surrounding environment… The period of stable weather systems that we have enjoyed for so long, which we have taken for granted even i.e. summer to mean warm sunny days and winter to mean snowy cold landscapes of white wonder (if you live in the Uk, that is), ar phasing away from our presumptions… Change is certain. Stability never endures for long. Along with the consequences of pollution throughout the food chain, over watering, deforestation, etc… this will all feedback into the chaotic system of Life on Earth. And we should be aware of this! For this is part of the Tao and the way it flows…

To ignore this Wisdom is to ignore the essence of Life itself!!!

As you may have noticed above… We must understand that our minds are sensitive hosts for memetic parasites… Hosts that are based on nonlinear dynamical systems… Systems which can be manipulated and reprogrammed quite a lot easier than any of us would care to imagine. The illusion of “Self,” something that I have blogged about earlier in “Another Take On Reality – Meme, Myself and I“, is an illusion of defining ourselves in a consumerist world. Remember, the term ‘illusion’ is not derogatory. It simply means illusion.

We should be aware of this, and take heed of the divine in ourselves… For the magic of Life itself, is locked within the free flow of chaos. Once we see this, we will begin to ‘See’ deeper into being than we ever have before… And come of this will a new revolution of thought and considerate being… A world where we can affect eachother in new positive ways of being, while maintain a balance with one another, AND the rest of life here on Earth.

No doubt this tipping of the scales was necessary to arrive at these new wondrous discoveries and Knowings. But the burden of mankind on Gaia has not gone un-noticed. We will feel Gaia begin to give way, as our needs crush the delicate balance that has arrisen over the epochs. For now… Chaos is slowly buckling with instability, poised and ready to “reiterate” a new change over the new “butterflies” of mankind. This is, without a doubt, the calm before the storm.

One question that still bothers me deeply is… Why is so hard for mankind to know this truth??? Have these “consumer chains” bound us to their availabilty like Crack or Methamphetamine does to their “addicted” users???


I would like to re-iterate to the reader my own intentions by writing this blog… It is not my aim to disclose a “hidden meaning” to life’s eternal flow. Neither is it to procure new scientific or religious standings. Nor is it my aim to put into disrepute current world views OR Religious ideals. Rather it is to ‘suggest,’ using analogies recently disclosed through science’s accolades (most of which have so far been reviewed within these Blogs) new modes of possible understanding about ‘what’ We, as human beings, are and ‘why’ We came about in this Garden Of Eden that orbits around a bright star of light… One that, like all the others before it, forges all the known matter into what Life has become today. It is an intricate process, with seemingly unrelated parts not fitting in at time… However, all of it, no matter how bizarre or strange, plays a part in the whole, and becomes applified through Chaos’ own design.

The sages of old spoke about this wisdom… And some of us today can see how that wisdom is now based around scientific truths. It’s a puzzle, and a marvelous one at that… One that we should all cherish dearly… And, if given half the chance, it is something we should become ultimately aware of.

But I cannot tell people what to do. It is for you to decide what you do with your lives here on Earth… And it is your choice to decide what to believe. Besides… This could just be nothing more than an egocentric bias that I have for a particular meme that is lodged in my head… A bias that came to mind many moons ago… And just the other day it was once again presented to me while reading an excert about the late Dr Albert Hoffmann, the father of LSD, where he is reportedly quoted as saying:

“I am a figment of my own imagination…

I am a part in this universe…


I am the universe experiencing itself…

I am the universe questioning itself.”

Taken from the New York Times.

Taken from the New York Times.


When you See and Feel this for yourself… You will begin to Know truth.