Unification of Science and Spirit -- Copyright Ben Goertzel 1996

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Chapter 6

MIND AS A COMPLEX SYSETM

    Among my many memories of early childhood, a few stand out with particular vigor. First and foremost, there is Neil Armstrong walking on the moon -- this was around the time of my second birthday, but I remember it as well as anything I've watched on TV since. I understood where the moon was -- way up in the sky -- and that this man, dressed in a funny suit, was walking on it, having just flown there in something faster than an airplane. I was puzzled by "One small step for a man, one great leap for mankind" -- I concluded, not unreasonably, that a "mankind" was some kind of miniature human being, perhaps a sort of midget-monkey hybrid. I wondered why, if they had brought one of these "mankind" creatures along on the spaceship with them, they hadn't shown it on TV.

    Another glowingly vivid memory, from a couple years later, is watching my mother roll out of the hospital in a wheelchair, holding my newborn baby sister in her arms. This was 1970, and the only hospital in Eugene, Oregon was a Catholic hospital, which didn't even allow fathers in the birthing room, let alone big brothers. My mother had disappeared with a big belly, and now returned, a day or two later, with a much smaller belly and a strange shrunken face peeking out of a blanket on her lap. The first thing she did was to explain about the wheelchair; it was a legal requirement, she said. But I was more interested in this tiny, staring thing she was holding. I had known it was coming, but I hadn't been fully prepared for the inertness of a newborn infant. This pink little lump of meat was supposed to be a person?

    Every day I would go over to her crib and watch the baby. Her name, they said, was Becky; but she didn't seem much like a Becky to me. Eventually she learned to fix her eyes on me, to roll over onto her belly, to sit up, to crawl. Somewhere along the line, it seemed to me, this wriggling, screeching bunch of protoplasm that they called Becky had been invaded -- invaded by a person, by an invisible spark of awareness ... invaded by a mind. Clearly the thing that my mother had wheeled out of the hospital had had no mind. It was just a body, it didn't react, it didn't understand. So how had this happened? What an amazing thing -- and yet everybody took it for granted. Everyone knew that somehow a person was going to grow inside this tiny flesh; I had known it too, yet somehow I hadn't quite understood....

    I asked a lot of questions, but no one had any answers. A couple years later I looked in my World Book encyclopedia, and found that equally unsatisfying. The mind was in the brain, they said, or somehow connected with the brain. But what was, really, the connection? I spent hours and hours -- too many hours, perhaps! -- just sitting there empty-faced and quiet, pokingaround inside my mind, trying to feel the intricate contours of my thoughts, my emotions, my knowledge.... I constructed complicated internal movies, complete with soundtracks, representing the ebb and flow of my mental processes. But I couldn't quite put my finger on the essence of the thing.

    ***

    When, as I child, I was asked "What do you want to be when you grow up?", my stock answer was "an astronomer." I pictured myself sitting in an observatory on the peak of a snow-covered mountain, acutely peering into a lense, probing the edge of the observable universe. Quasars, pulsars, black holes -- that was the real stuff. As I grew older, the vision was elaborated. In my spare time, when the sky was clouded over, I would write best-selling science fiction novels. Beautiful women would climb up to my observatory seeking my autograph....

    But by the time I entered university, at age 15, I had become gradually more interested in this fuzzy, peculiar question of understanding the mind. I became particularly excited when I read about something called "artificial intelligence." These people were writing computer programs that were actually supposed to think! Now this, I thought, was a path to real understanding. Computer graphics could render all sorts of weird-looking images; why not the internal movies of my thoughts? If you could take a computer, just as inert and non-reactive as my newborn sister, and somehow cause it to spontaneously grow a self, an inner life, a mind....

    I remembered a children's book I'd once had on "mathematical order and pattern in the real world" or something like that -- it had had a long chapter on crystals. A crystal could just *grow*, just like that, almost out of nothing. All you needed was a seed, a tiny, microscopic seed, and given appropriate conditions, the pattern could spread from that seed to cover a huge area with beautiful forms. Maybe the mind was just the same. Just fill the computer with the right "seed," place it in the right environment, and a mind will grow....

    Of course, I quickly discovered that my strange meanderings about crystals had nothing to do with artificial intelligence research, nor with any other kind of research -- psychology or philosophy of mind -- for that matter. Arrogantly enough, I decided I had little to learn about the mind from any of these fields, and I decided to study mathematics instead. I knew I didn't want to spend my life proving mathematical theorems just for their own sake. But somewhere out there in the mathematical universe, I decided, there must be a language for expressing the stuff that's really important -- the way a baby suddenly grows an awareness, the way feelings float in and out of the mind, the way we construct ideas as complex as that of a ball of gas floating out in the sky fifty parsecs away....

    I remember scouring all the sections of the library looking for clues as to the nature of mind -- mathematics, physics, biology, psychology, computer science,... Then finally, sometime during my first year in graduate school, I discovered the Q section in the library. In the USA Library of Congress system,QA is mathematics, QC is physics, QH is biology, and so forth; but I had never before looked at just plain Q. The Q section was a mishmash of topics, but prominent among them was this thing called General Systems Theory. I could see that publications on this topic had faded out over the past twenty years, and I could sort of understand why: there were a lot more general proclamations than concrete applications. But still, here was a hint, here was something to go on. There were ideas like self-organization and autopoiesis, which explained how structure could emerge out of nothing, or almost nothing ... out of a tiny seed. Today the buzzwords are "complexity science" and "chaos theory", but the basic concepts are the same.

    I remember one moment in great detail, a sort of "Eureka!" experience of the sort one always has after one mulls over some sticky problem for months and months and months.... It was shortly after I "discovered" General Systems Theory; I was lying on the grass in the northwest corner of Washington Square Park, which at that time was largely populated by Rastifarian drug dealers (as opposed to the southeast corner, which the coke dealers had staked out) ... I was supposed to be sitting in partial differential equations class at the Courant Institute a few hundred yards away; instead I was doodling on a piece of paper, trying to use set theory to make a diagram of the mind. Suddenly it struck me that I would never be able to make that diagram. The important thing was the process I was carrying out: I was searching for a diagram to somehow encapsulate the mind.... I was trying to take something big and complicated -- the mind -- and represent it as something little and simple -- a diagram. In other words, I was looking for a pattern.

    I thought back to a previous "Eureka!" experience four years earlier, during which I had intuited, for the first time, that all aspects of mind could be expressed in terms of *pattern* -- pattern recognition, pattern formation, and pattern destruction (looking back, I suspect that the "pattern" idea may have come to me from Douglas Hofstadter's Godel, Escher, Bach, which I read when I was twelve years old; but at the time it felt like a completely original insight). The concepts of pattern and self-organizing system fit together in my mind like two pieces of a jigsaw puzzle. The whole idea of General Systems Theory, I saw, was to build more general patterns out of the special case patterns studied in the sciences. The circles and lines that I was drawing were, in fact, patterns recognized by my visual systems; and, because my handwriting was so bad, the process of recognizing these ink patterns necessarily involved an understanding of the conceptual patterns they were designed to represent. The "I" who was lying on the grass was just a pattern which it, itself had detected; a pattern in the responses which it received from other people. The mind, I felt certain, was some kind of self-organizing network of patterns -- patterns in patterns, patterns among patterns, patterns among patterns in patterns among patterns.... Patterns linking patterns together. Patterns, patterns, patterns! It was "just" a matter of understanding how the network was structured, and how the self-organization worked....

    ***

    That was almost a decade ago. As described in the Preface, I have spent much of the intervening period thinking about the problem of how to construct a mathematical model of mind as a self-organizing network of patterns. And, to be blunt, I feel that I have finally succeeded: I have answered, to my own satisfaction, my childhood question regarding "what on earth is going on with this 'mind' thing."

    Of course, not everyone would agree with me that I have answered this question -- while a small but growing group of other researchers has come to appreciate my views on mind, it may be that no one else would agree with me on every detail! And I'd be the first to admit that my model of mind is not scientifically proven. We simply don't have the technology to conclusively prove or disprove such things. So, at the present time, I would promote my model of mind, not as a scientific fact, but as a way of understanding things.

    I call my model of mind the psynet model -- psy for mind, and net for network. As scientific models go, the psynet model is fairly simple: it doesn't involve twenty-six dimensional strings rolled up into four dimensions, or even elementary calculus.... But, in a way, this simplicity is only to be expected. It would be absurd to think that the mind could boil down to some abstruse mathematical property of some sophisticated equation....

     THE FRAGMENTATION OF PSYCHOLOGY

    Before beginning our exploration of the psynet model, it seems appropriate to make a few general comments about the discipline of psychology, and how my own thinking fits into it (or, does not fit into it). Although I am presently employed at a fairly conservative, high-quality university psychology department, the reader should not be led to believe that my model of mind is a part of mainstream academic psychology. Far from it.

    The psynet model comes out of a tradition of psychological systems theory and "chaos-theoretic" psychology -- a tradition which has evolved gradually over a period of decades, and has reached a sort of critical mass over the past few years. While it has evolved largely within academic psychology, and now involves perhaps a thousand researchers worldwide, it is still very much a "fringe" movement.

    The reason for the evolution of "chaos psychology" or "psychological systems theory" is rather obvious. Complex systems science is a study of systems as wholes, of emergent properties and global qualitative dynamics. And the one thing missing in modern psychology is precisely this: an understanding of the mind as a whole.

    Modern psychological science has a great deal to say about the mind, more than could possibly be reviewed here. However, it does not have a terribly well-defined overall vision of mind. The situation is quite different from, say, theoretical physics, as discussed in Chapter 3. In physics we have generally-accepted theories that make coherent, rigorous and testable statementsabout the overall nature of the world. In psychology, on the other hand, there are no generally-accepted theories of this nature. Instead, modern psychology subdivides mind into numerous components, and says little about the relations between the components. Today, scientific psychology is basically a collection of specialized models of very specific systems and processes.

    The scientific view of mind focuses on the lower levels of being, beginning with the physical realm, and working up through the realms of emotions, creativity and intuition. The spiritual view of mind, on the other hand, focuses on the higher levels of being -- the higher Self, the overmind, and the intuitive feeling of inspiration, working down to the ordinary thinking mind and the emotions. But if one wishes to bring the two together, one immediately runs into trouble, because of this fragmentation of modern psychology. One finds that it is necessary to go beyond current psychological theory, by introducing unifying ideas from someplace else. The psynet model of mind is a result of introducing unifying ideas from complexity science into psychology.

    ***

    Of the numerous components into which modern psychology divides the mind, the largest and most important are perception, action, thought and memory. Other components, such as self and emotion, can be understood in terms of these.

    In terms of these basic components, the understanding of mind implicit in modern psychology may be roughly summarized as follows. The mind takes in information through its perception system. It feeds the information to its thought system, and stores it in its memory system. The thought system decides what kind of actions to take, based on its goals, and passes its decisions to the action system, which determines and carries out specific actions accordingly.

    Each of these principal systems is actually divided into purpose-specific subsystems. For instance, there is short-term memory, which is divided into a visuospatial sketchpad (for memory of visual images), a phonological loop (for memory of words), and a more general working memory. Then there is long-term memory, which is divided at minimum into episodic memory (memory for life experiences), semantic memory (memory for facts), and procedural memory (memory for how to do things, e.g. reading or riding a bicycle). In the area of perception, different sensory systems are largely distinct: for instance, the visual perception system has rather little to do with the tactile perception system.

    Finally, the self is a theoretical model built up by the thought system in order to explain the behavior of the mind and its associated body in the world. Emotions are explained in various ways, for instance as the mind's reactions when the expectations of the thought system are unfulfilled. Consciousness has to do with the focusing of attention, and with short-term memory; it involves the interlinking of thought and perception systems."

    Because of the specialized nature of psychological research, this general way of thinking about the mind is rarely articulated all in one place. However, it is there behind the scenes; and it guides the thinking of mind scientists in several different disciplines. In short, what modern scientific psychology has is an information-processing vision of mind. The mind is viewed as a distributed information processing system, composed of relatively autonomous subsystems, which are in many cases themselves composed of relatively autonomous subsystems.

    The advantages of the information-processing vision are at least twofold. First, it allows one to construct detailed theories of individual subsystems, based on laboratory experiments dealing with highly artificial tasks. And second, it allows one to try to match up mental systems with brain systems, an effort which has met with increasing success in recent years.

    The disadvantages of this vision are, however, also at least twofold, and are equally plain. First, there is no understanding of the mind as a coherent, integrated system, as a unified whole. And second, there is no understanding of the subjective experience of consciousness, of the experience of being a mind.

    ***

    Some researchers have attempted to justify the fragmentation of psychological theory by positing a fundamental "modularity" to the mind. The mind, they argue, is divided into components that function relatively independently from each other. However, the arguments for mental modularity are not at all convincing. One may show, on purely logical grounds, that there is no way to tell from experimental psychology alone whether a given set of phenomena is the result of one integrated system or multiple interacting systems.

    The facts in cognitive neuroscience do not support any strict modular structure for the brain. Even the visual cortex, often considered the most insular "module" of the human mind, has been shown to depend intimately on a variety of other areas of the brain for all aspects of its operation. Neuroscientists never speak of the brain as a modular system, rather as a self-organizing system in which each region feeds into and out of each other region in multiple ways.

    All in all, it seems clear that the current fragmentation of psychological theory is a result, not of an underlying fragmentation of the mind, but of the inability of current concepts and analytical methods to deal with the complex, subtle interdependence of the mind.

    But if psychology cannot deal with the complex, holistic nature of the mind, then where is one to turn? One might think to turn to neuroscience. However, while partly overcoming fragmentation, modern neuroscience suffers from a different complexity-induced ailment: an amazingly rapid change in basic ideas. One might say that, while the disorganization of psychology is spatial, that of neuroscience is temporal. Neuroscience reveals layer upon layer of complexity, but at present anyway, it does not clarify complexity.

    Christof Koch and Joel Davis, in their preface to the recent book Large-Scale Neuronal Theories of the Brain, point out that over the whole history of neuroscience, only two theories or models of brain function have survived their birth by more than a decade: the Hodgkin-Huxley model of the neuronal action potential, and the correlation model of motion perception in beetles and flies. Furthermore, it is no coincidence that these two theories date from the 1950's. The peculiar truth is that neuroscience changes so quickly these days that even a very good theory is lucky to survive two or three years before obsolescence. Rather than being a place from which to draw ideas about overall mental structure, neuroscience is a discipline that would itself benefit greatly from ideas about overall mental structure, were there another discipline able to provide them.

    So, all this is why, in order to gain a deeper understanding of mind than is provided by conventional psychology or neuroscience, while still remaining within the basic framework of empirical science, more and more psychologists have begun to turn to the emerging sciences of chaos and complexity. Complexity science focuses on integration rather than fragmentation; it gives a remarkably fine-grained picture of "fluffy" concepts like interdependence and emergence. It holds out the promise of a scientific understanding of the whole mind.

    In the US, the applications of chaos theory to psychology have been enthusiastically promoted by the Society for Chaos Theory in Psychology and the Social and Life Sciences. Outside the US, there has also been a great deal of research activity. In Australia, for example, one has only to attend the biannual Australian Complex Systems or Australian Mathematical Psychology conferences, and one will encounter a surprising variety of work applying complexity-science concepts to psychological phenomena.

    ***

    The promise of chaos and complexity for science is obvious. Frustratingly, however, the mind is not only complex enough to baffle psychologists and stymie neuroscientists -- it is also complex enough to stymie all of the standard mathematical models of complex systems science!

    Complexity science, in the main, consists of the study of a few standard computational models. We have cellular automata, we have iterations and differential equations on vector spaces, we have genetic algorithms and classifier systems, and we have neural networks. But it turns out that these models at best capture only limited aspects of mental structure and dynamics. The structure of mind is something that goes beyond any of these useful "complex systems archetypes."

    At bottom, of course, the brain can be modeled as a huge system of nonlinear differential equations. Hodgkin and Huxley demonstrated this, on the neuronal level at any rate, way back in the 1950's. But we lack the mathematical or computational tools to understand the global properties of a system of equations this large and complex; and so the mathematical theory of dynamical systems has proved effectively useless for the task of modeling mind.

    Neural networks, on the other hand, are complex systems models explicitly intended to mimic brain structure, but in actual fact they ignore all but one level of brain structure: the neuron level. In the brain, neurons are sandwiched between chemistry and large-scale architecture; one of the major lessons of modern neural network theory is that the neuron level is not enough. This is, it would seem, the underlying reason why neural network models have currently fallen out of favor in cognitive psychology, despite their lasting and even increasing popularity in computer science and engineering.

    Scientists have shown that "toy" neural networks with 50 -10,000 neurons can be trained to solve all sorts of problems, including practical computing problems and problems faced by the human brain. But the training methods used in computational experiments rarely bear more than a distant resemblance to neurodynamics, and even where training methods are more realistic, the networks have to be supplied with carefully engineered representations of their input. In the end, the problem of training a network of 50-10,000 neurons to solve a problem is quite different from the problem of understanding how a network of 100 billion neurons trains itself to solve a problem.

    ***

    And this is where my own research comes in. I have worked under the assumption that what we need is an entirely new approach to the mind -- a new vision which does not merely paste together psychological and complex-systems ideas, but in some sense transcends the both of them. The psynet model is a new complex systems model, aimed directly at modelling mental processes. It is not a modification of existing models such as neural networks, classifier systems, and differential equations. It is intended to be appropriate to psychology in the same sense that genetic algorithms are appropriate to biology, and differential equations are appropriate to physics. It was arrived at, as described in the Preface, by a combination of deep meditative introspection and consideration of scientific data.

    The use of complexity science to model the mind might seem a purely scientific and mathematical endeavor, having nothing to do with spirituality. In fact, though, the deeper one probes the mind using the conceptual tools of chaos and complexity, the more one finds oneself revisiting ideas from spiritual psychology. Both spiritual psychology and complex-systems psychology lead one to focus on the emergent patterns and self-organizing structures of the mind, rather than on the low-level details of individual information-processing systems.

    Previous presentations of the psynet model have focussed on the scientific side of things; here the discussion will be more weighted toward the spiritual and phenomenological side. But the model itself lies on neither side. It lives precisely in the middle of the Great Smoky Dragon. It can be extended out to either end of the Dragon, to annamaya (or quantum-maya) or vignanamaya and anandamaya. But it lives in the middle level. It speaks of the systems that span pranamaya, manomaya and vignanamaya -- the thought-emotion complexes that make up ourpsychosocial selves, and guide our feelings, thoughts and behaviors.

    The key weaknesses of scientific psychology -- lack of an overall perspective on the mind and lack of insight into conscious experience -- are precisely the two strong points of the spiritual view of mind. The psynet model bridges the two perspectives, by taking the point of view that mind is a system of interacting, intercreating processes. The information-processing structures postulated by scientific psychology are understood as autopoietic subsystems of an overall mental process system -- having the peculiar (sur)reality of self-producing strange attractors.

     THE PSYNET MODEL

    The psynet model of mind does not easily break down into parts. It has an holistic structure that reflects the holistic nature of the mind. For expository purposes, however, it seems useful to present the model in the somewhat unnatural form of a list of axioms. These axioms may seem somewhat opaque on first reading, because all the terms used have not yet been "officially" defined -- this will be done in the following paragraphs. However, they should help the reader to get the basic flavor of the model, before getting into the details.

  1. Minds are made of pattern/processes (i.e., processes that recognize and create patterns)

  2. Minds are systems of inter-creating pattern/processes (i.e. they are magician systems)

  3. Thoughts, feelings and other mental entities are structural conspiracies, i.e., autopoietic subsystems of the mind magician system

  4. The structural conspiracies of the mind join together in a complex network of attractors, meta-attractors, etc.

  5. This network of attractors approximates a fractal structure called the dual network, which is structured according to at least two principles: associativity and hierarchy.

    To explicate these ideas, let us begin at the beginning, with the question of the stuff of mind. One of the key questions of the philosophy of mind has always been what the mind is made of. Is the mind made of physical material -- molecules, atoms, particles, quarks? If it is not physical, then what kind of beast is it? A mathematical structure? Something carved out of the bones of angels, perhaps?

    According to the psynet model, the mind is made of pattern/processes. This is an ugly coinage, but the fact is that there is no single word in English to denote a process which: 1) exists to recognize patterns, and 2) is itself one of the patterns which it recognizes. A pattern/process is both a verb and a noun. The concept that mind is made of pattern/processesreflects a very deep philosophical perspective, which I call the "pattern philosophy."

    In fact, the idea that pattern is the stuff of mind can be traced back at least to Hume. With a generous interpretation, it can be traced as far back as Plato. But the idea only came into its own within the past century. Most notably, it is the root idea behind Charles S. Peirce's "pragmatic" philosophy, Gregory Bateson's system-theoretic "ecology of mind", and Benjamin Lee Whorf's linguistic anthropology.

    To Peirce, Whorf and Bateson, the concept of pattern is primary and needs no elucidation. There is a great deal of truth in this view; after all, in any theory one must take some concept as undefined. As I demonstrated in The Structure of Intelligence, however, it is also possible to frame the concept of pattern in the language of the theory of computation. In doing so one is explaining something simple in terms of something complicated, but one is also making the hitherto philosophical notion of "pattern" mathematically concrete. Basically, the idea is that a process is a pattern in a certain entity if

     -- the result of the process is a good approximation of the entity

     -- the process is simpler than the entity

To make this idea precise one must answer two questions: what's a "result," and what is "simpler"? For example, if an "entity" is a binary sequence, and a "process" is a computer program, then the simplicity of an entity or a process may be defined as its length. Pursued further, these considerations would lead us to Gregory Chaitin's theory of "algorithmic information,"in which program length is analyzed in the context of the theory of universal computation -- but this would lead us too far astray from the issues of current interest.

    ***

    To see more clearly the relation between pattern and mind, one may define the "structure" of a system as the set of patterns in that system. Then one is led to the idea, that, perhaps, the mind is part of the structure of the brain -- or the structure of the body, more generally. This places mind in the realm of abstract processes rather than the realm of physical processes. If a mind is a collection of processes that are patterns in the brain, then it exists fundamentally in mathematical space rather than physical space.

    This way of thinking about mind suggests that everything has some degree of mind -- a conclusion which is very much in accordance with spiritual ideas. However, we need not conclude that everything has an equal amount of mind. Mind is structure, but not all structure is equally "mental." Mind is, more specifically, structure that has to do with intelligent behavior. The more intelligent the behaviors a structure is associated with, the more "mental" that structure is.

    And, of course, "intelligence," if one wishes to give a formal definition, may also be specified in terms of pattern/processes. I.Q. tests measure intelligence in a particular social, cultural and biological context, but they donot measure general intelligence. In the most general sense, intelligence is nothing more or less than the ability to solve complex problems in difficult environments. That is, an intelligent system, must be able to solve problems in environment that are that are unpredictable on the level of detail, but somewhat predictable on the level of overall pattern. Rephrased in terms of patterns, one may say: an intelligent system is able to solve subtly patterned problems relating to subtly patterned environments.

    One crucial concept here is subjectivity. We have said that, in the psynet model, a mind is an abstract entity; it resides in the Platonic realm of mathematical constructions. And mind is also, to a certain extent, an observer-dependent entity, because the definition of structure depends on the observer's measure of complexity. While perhaps controversial from the perspective of the philosophy of mind, these definitions do have the benefit of utility: they give a unifying framework within which one may go on to make concrete statements about the nature of mentality.

    Finally, another crucial concept is emergence. Most simply, we may say that a process is emergent between two entities to the extent that it is a pattern in the "union" of these entities but not in either entity individually. Consider for instance the part of this sentence preceding the semicolon, and the part of this sentence following the semicolon; the meaning of the sentence does not exist in either part alone, but only emergently in the juxtaposition of the two parts. "Emergence" is a pragmatic version of the old idea of Gestalt; all the examples of gestalt in perception are also examples of emergent pattern. Mind would seem to make ample use of emergence -- to consist of patterns emergent among patterns emergent among patterns....

    ***

    I have remarked above that the concept of pattern may be defined in terms of computation. However, in Chapter 2 we have seen that computation has a deep physical meaning. Quantum computation is different from classical computation. This leads us to the question of whether it is possible to define pattern in a purely physical way.

    For instance, one might define the complexity of a certain behavior relative to a given physical system as the minimum amount of energy which the system must expend in order to act out that behavior; or, perhaps, as the average amount of energy which the system expends when it acts out the behavior. This alternate approach is not nearly so elegant as the theory of computational complexity; however, it has the great advantage of placing energy and algorithmic information on the same scale, and in this way showcasing the underlying unity of "reality" and "mind."     According to this physicalistic approach, it makes no sense to ask for the complexity of some thing. One must, instead, ask for the complexity of a behavior. This presents a slight conceptual problem: given a string of numbers, a sentence, a picture, a cat or any other particular object, there are many different kinds of behaviors involving that object. Suppose, forexample, the "object" in question is a string of words, say a children's rhyme:

        Ding, dong bell

        Pussy's in the well

        Who put her in?

        Little Jackie Thin.

        Who took her out?

        Little Johnny Stout.

        What a naughty boy was that

        to try and drown the pussycat

What behavior should be used to gauge the complexity of this verse? Three different choices come to mind. There is the behavior of producing the rhyme, once it is already "known." There is the behavior of learning the rhyme, of storing it in the memory for future production. And, finally, there is the behavior of maintaining the rhyme in memory, of not forgetting it. These behaviors are not distinct: learning and maintenance will necessarily require production. But each one requires a certain amount of energy.

    Beginning from the energetic point of view, computational complexity emerges as a very special case. Suppose one focuses on maintenance, and asks: what is the minimum amount of energy required to maintain the string in random access memory? And suppose that the physical system in question is precisely a digital computer. This computer stores the string as a certain program: a certain sequence of 0's and 1's. If the computer is configured so that the energy required to maintain a 0 is the same as the energy required to maintain a 1, then the energy required to remember the string is proportional to the length of the program used to compute the string. The minimum energy needed for the computer to remember the string is the length of the shortest program for computing the string, or in other words the "algorithmic information" of the string.

    Of course, the length of the shortest program for computing the string will be different for different computers with different operating systems. But as the programs in question get longer and longer, these differences will become negligible. And similarly, according to the physical Church-Turing Thesis, if one has a physical system X with universal computing potential, then for very complex behaviors the minimum energy required for memory will become virtually independent of the specifics of the system X. For only a finite amount of energy is required to simulate any other physical system Y, to within arbitrary accuracy. Thus the entire theory of complexity may, if one so desires, be rephrased in terms of energy instead of computation.

    This conclusion has interesting implications regarding the physical basis of the evolution of intelligence. The brain has a finite amount of energy, to distribute among a vast number of different tasks. Out of the many possible ways of remembering a given behavior, it will therefore naturally prefer the one which uses less energy. The quest for energy efficiency therefore implies the quest for simplicity. And the quest for simplicity means that, in place of the process X, it will be preferable to choose a simpler process Y which computes X. Inother words, the quest for energy efficiency implies the quest for pattern recognition.

     Magician Systems

    The computer science community has become very excited, in recent years, about the concept of independent software "agents." Agents, in this context, are simply entities that are defined by their actions: they send messages to other agents, they destroy agents, and they produce new agents. They act individually or in conjunction with other agents. A pattern/process, as considered in the psynet model, is a special kind of agent. Pattern/processes act on each other to produce new pattern/processes; and, indirectly, they can lead to one another's destruction.

    Agents, as considered in computer science, are very general. In previous writings, I have introduced a special word to describe the pattern/process agents that make up the mind. This word is "magician." A magician is an agent which acts to transform other agents by processes of pattern-recognition and pattern-formation. The intuition underlying this word is obvious. Mental processes are like magicians, casting magic spells on one another and transforming each other. The mind is a community of magicians, continually transforming one another by their spells.

    Phrased in terms of magicians, the basic dynamic of the psynet model is a very simple one. First of all: the magicians, the pattern/process agents, act on each other. Secondly: the magicians quickly perish. Each magician acts, alone and in conjunction with those other magicians that are close to it, and then it shortly after disappears. In acting it produces new magicians, which proceed to act in their own right. They also mutate, and mutation errors propagate, making the whole system incredibly unpredictable.

    This dynamic is summarized by the term magician system dynamics. A magician system is simply a system of magicians that continually act on one another, transforming one another.

    Magician system dynamics may sound like utter chaos! But it is not; or at least, it doesn't have to be. The reason is the phenomenon of autopoiesis, as discussed in the previous chapter. Systems of magicians can interproduce. A can produce B, while B produces A. A and B can combine to produce C, while B and C combine to produce A, and A and C combine to produce B. The number of possible systems of this sort is truly incomprehensible. But the point is that, if a system of magicians is mutually interproducing in this way, then it is likely to survive the continual flux of magician interaction dynamics. Even though each magician will quickly perish, it will just as quickly be re-created by its co-conspirators. Autopoiesis creates self-perpetuating order amidst flux.

    Some systems of magicians might be unstable; they might fall apart as soon as some external magicians start to interfere with them. But others will be robust; they will survive in spite ofexternal perturbations. These robust magician systems are what I call autopoietic subsystems or "structural conspiracies." The third basic principle of the psynet model, as outlined above, is that thoughts, feelings and beliefs are autopoietic attractors. They are stable systems of interproducing pattern/processes.

    This is where the "crystal forming" dynamics hinted at above comes in. The process of a crystal forming is precisely a process of convergence to an attractor. The single seed, in an appropriate environment, puts the system in the basin of the attractor. Then the system just converges, faster and faster, until it reaches the attractor form. The formation of an autopoietic attractor is just the same as this. Once a few magicians are there, producing each other, the others simply fall into place: and, presto! a mind is formed.

    But this is not the end of the story. If it were, we would have an interesting philosophical view, but nothing more. The really remarkable thing is that there seems to be a structure to these autopoietic attractors. My claim -- the fifth basic principle of the psynet model -- is that they all spontaneously self-organize into a sort of "monster attractor." I call this monster attractor the dual network.

    The dual network, as its name suggests, is a network of pattern/processes that is simultaneously structured in two ways. The first kind of structure is hierarchical: simple structures build up to form more complex structures, which build up to form yet more complex structures, and so forth. The second kind of structure is heterarchical: different structures connect to those other structures which are related to them by a sufficient number of pattern/processes.

    These two structures are seen everywhere in neuroscience and psychology. The whole vast theory of visual perception is a study in hierarchy: in how line processing structures build up to yield shape processing structures which build up to yield scene processing structures, and so forth. The same is true of the study of motor control: a general idea of throwing a ball translates into specific plans of motion for different body parts, which translates into detailed commands for individual muscles. It seems quite clear that there is a perceptual/motor hierarchy in action in the human brain. And those people concerned with artificial intelligence and robotics have not found any other way to structure their perceiving and moving systems: they also use, by and large, perceptual-motor hierarchies.

    On the other hand, the heterarchical structure is seen most vividly in the study of memory. It is obvious that memory is associative. When I think of Jimi Hendrix, say, I automatically think of other things related to Jimi: another black guys with frizzy hair in a movie I saw last week, the snakes on the cover of the Axis, Bold as Love LP, the screeching twisting noise of the guitar in the Jimi song I was listening to this morning,.... The various associative links between items stored in memory form a kind of sprawling network. The kinds of associations involved are extremely various, but can all be boiled down to pattern: if two things are associated in the memory then there is some other mental process which sees a pattern connecting them.

    The heterarchical and hierarchical networks are not separatethings, they are just one network of magicians, one network of autopoietic attractors. The alignment of the two networks has some interesting consequences, that I will go into later. For instance, one can see that, if the heterarchical network is going to match up with the hierarchical network, it will have to be in some sense fractally structured: it will have to consist of clusters within clusters within clusters..., each cluster corresponding to a higher level of the hierarchical network. And one can look at the way the networks reorganize themselves to improve their performance and stability. Every time the heterarchical network reorganizes itself to keep itself associative in the face of new information, the "programs" stored in the hierarchical network are crossed over and mutated with each other, so that the whole dual network is carrying out a kind of evolution by natural selection.

    The connection between these pattern/processes and the brain is, unfortunately not entirely clear at present. We still have much to learn about how the brain works, and so I tend to be very skeptical of attempts to base psychological theories too closely on neurobiology. But one thing that does seem clear, however, is that these abstract "pattern/processes" should be equated with cell assemblies -- groups of interconnected neurons that tend to act in unison. Many neuroscientists have attempted to model the mind as a network of interacting cell assemblies. I am convinced that this is the right way to go; and I am very impressed with the potential of PET and fMRI scans for studying the intricacies of cell assembly dynamics. But we have a long path to tread before we can build up from cell assemblies to neural structures on the scale of autopoietic attractors or dual networks.

    ***

    The key idea of the dual network is that the network of memory associations (heterarchical network) is also used for perception and control (hierarchical network). As a first approximation, one may say that perception involves primarily the passing of information up the hierarchy, action involves primarily the passing of information down the hierarchy, and memory access involves primarily exploiting the associative links, i.e. the heterarchical network. But this is only a first approximation, and in reality every process involves every aspect of the network.

    It turns out that, in order that an associative, heterarchical network can be so closely aligned with an hierarchical network, it is necessary that the associative network be structured into different levels of clusters -- clusters of processes, clusters of clusters of processes, and so on. This is what I have called the "fractal structure of mind." If one knew the statistics of the tree defining the hierarchical network, the fractal dimension of this cluster hierarchy could be accurately estimated.

    It must be emphasized that neither the hierarchical networknor the heterarchical network is a static entity; both are constantly evolving within themselves, and the two are constantly coevolving together. One of the key points of the dual network model is that the structural alignment of these two networks implies the necessity for a dynamical alignment as well. In other words, whatever the heterarchical network does to keep itself well-adjusted must fit in nicely with what the hierarchical network does to keep itself adjusted (and obviously vice versa); otherwise the two networks would be constantly at odds. It stands to reason that the two networks might be occasionally at odds, but without at least a basic foundation for harmonious interaction between the two, a working dual network would never be able to evolve.

    For example, suppose that -- as I have hypothesized in The Evolving Mind -- the hierarchical network evolves new programs by genetic programming, i.e., by the mutation and crossover of subnetworks to form new subnetworks. And suppose that the heterarchical network improves and maintains its associativity by moving the positions of processes and clusters of processes, to see if the new positions give better associativity than the old. These two dynamics mesh naturally together: every time programs are crossed over, clusters are moved; and every time clusters are moved, programs are crossed over. The moving of subnetworks to new locations is a very simple dynamic which is meaningful both hierarchically and heterarchically -- the value of a "move" may be judged simultaneously from the point of view of perception/action (hierarchy) and the point of view of memory (heterarchy).

    But this is only the beginning. In order to rejoin the static view with the dynamic view, one must envision the dual network, not simply as an hierarchy/heterarchy of mental processes, but also as an hierarchy/heterarchy of autopoietic process systems, where each such systems is considered to consist of a "cluster" of associatively related ideas/processes. Each system may relate to each other system in one of three different ways: it may contain that other system, it may be contained in that other system, or it may coexist side-by-side with that other system. The dual network itself is the "grand-dad" of all these autopoietic systems.

    Autopoiesis is thus seen to play an essential role in the dynamics of the dual network, in that it permits thoughts (beliefs, memories, feelings, etc.) to persist even when the original stimulus which elicited them is gone. Thus a collection of thoughts may survive in the dual network for two reasons:

    -- a usefulness relative to the hierarchical control structure, i.e. a usefulness for the current goals of the organism;

     -- autopoiesis

    This line of reasoning may be used to arrive at many specific conclusions regarding systems of thought, particularly belief systems. For purposes of illustration, two such conclusions may be worth mention here:

     -- that many belief systems considered "poor" or "irrational" have the property that they are sustained primarily by the latter method. On the other hand, many very useful and sensible belief systems are forced to sustain themselves byautopoiesis for certain periods of time as well. System theory clarifies but does not solve the problem of distinguishing "good" from "poor" belief systems.

     -- that one of the key roles of autopoietic systems in the dual network is to serve as a "psychological immune system," protecting the upper levels of the dual network from the numerous queries sent up from the lower levels.

    Stability means that a system is able to "absorb" the pressure put on it by lower levels, instead of constantly passing things along to the levels above it. Strong parallels exist between the dynamics of antibody classes in the immune system and the dynamics of beliefs in an autopoietic system -- these are developed in Chaotic Logic, and will be returned to below, from a somewhat different angle.

    So, in the end, one inevitably returns to the dynamic point of view. One sees that the whole dual network is just another autopoietic attractor which survives by the same two methods: structural conspiracy and external utility. Even if one begins with a fairly standard information-processing picture of mind, such as the master network, one eventually winds up with an "anything-goes" magician-theoretic viewpoint, in which a successful mind, like a successful thought system, is one which perpetually and usefully creates itself.

    ***

    The autopoietic-attractor view of thought makes a striking contrast with the data structures typically employed in artificial intelligence programs. For instance, Doug Lenat's CYC project, which was carried out at AT&T from 1984-1994, was an ambitious attempt to to encode commonsense human knowledge in a machine-usable form. But the human mind does not embody its commensense knowledge as a logically consistent list of propositions. What we know as common sense is a self-reproducing system, a structural conspiracy, an attractor for the cognitive equation.

    Abstractions aside, the intuitive sense of this position is not hard to see. Consider a simple example. Joe has three beliefs regarding his girlfriend:

A: She is beautiful

B: I love her

C: She loves me

Each of these beliefs helps to produce the others. He loves her, in part, because she is beautiful. He believes in her love, in part, because he loves her. He believes her beautiful, in part, because of their mutual love relationships.

    Joe's three thoughts reinforce one another. I suggest that this is not the exception but the rule. When Joe looks at a chair obscured by shadows, he believes that the legs are there because he believes that the seat is there, and he believe that the seat is there because he believes that the legs are there. Thus sometimes he may perceive a chair where there is no chair. And thus, other times, he can perceive a chair far moreeffectively than a computer with a high-precision camera eye. The computer understands a chair as a list of properties, related according to Boolean logic. But he understands a chair as a collection of processes, mutually activating one another.

    The legs of a chair are defined partly by their relation with the seat of a chair. The seat of a chair is defined largely by its relation with the back and the legs. The back is defined partly by its relation to the legs and the seat. Each part of the chair is defined by a fuzzy set of patterns, some of which are patterns involving the other parts of the chair. The recognition of the chair involves the recognition of low-level patterns, then middle-level patterns among these low-level patterns, then higher-level patterns among these. And all these patterns are organized associatively, so that when one sees a certain pattern corresponding to a folding chair, other folding-chair-associated patterns become activated; or when one sees a certain pattern corresponding to an armchair, other armchair-associated patterns become activated. But, on top of these dual network dynamics, some patterns inspire one another, boosting one another beyond their "natural" state of activation. This circular action is the work of the cognitive equation -- and, I suggest, it is necessary for all aspects of intelligent perception, action and thought.

    For example, as I argued in Chaotic Logic, and will argue again below, the circular process dynamics described by the cognitive equation are essential to the development of the self/reality belief system. When the human infant constructs a model of the external world, and its own role within this world, it does not do so by a purely rational method. As language acquisition theorists have often observed, knowledge is "bootstrapped." Recognition of nouns and verbs produces understanding of grammar; and understanding of grammar produces recognition of nouns and verbs. Understanding of the mental states of others produces understanding of one's own mental states, and vice versa. Only in this way can understanding come about where there previously was none.

    The failure of AI programs to construct useful internal models of the world should be understood in this light. A model of the world is necessarily a structural conspiracy, a self-producing "organism" of processes. But such an organism can only arise in the context of an at least marginally functioning dual network. The CYC project seeks to bypass the dual network and jump straight to the model of reality, but there is no reason to believe this to be possible.

    Language

    The psynet model is very broad and can be explored in a number of different ways. Most of the published work on the model, however, involves its implications for issues in theoretical psychology, particularly the theory of cognitive science. Here I will consider a few of these applications -- to language, logic and evolutionary theory. These are the applications that will turn out to be particularly applicable tospiritual psychology.

    Let us begin with language -- something which which is very commonly cited as a distinguishing feature of intelligent systems. What does the psynet model have to say about the linguistic mind?

    A language, as conceived in modern linguistics, is a transformation system. It is a collection of transformations, each equipped with its own set of rules regarding which sorts of entities it can be applied to in which situations. By applying these rules, one after the other after the other, to elements of the "deep structure" of thought, sentences are produced. In terms of the dual network, each of these transformation rules is a process with a certain position in the network; and sentences are the low-level result of a chain of information transmission beginning with a high-level structure or "idea."

    In the case of the language of mathematics, the transformation rules are very well understood; this is the achievement of the past 150 years of formal logic. In the case of natural languages, our understanding is not yet complete; but we do know a handful of general transformation rules (e.g. Chomsky's famous "move-alpha"), as well as dozens upon dozens of special-case rules.

    But this formal syntactic point of view is not enough. A set of transformation rules generates an incredible number of possible sentences, and in any given situation, only a miniscule fraction of these are appropriate. A system of transformation rules is only useful if it is amenable to reasoning by analogy -- if, given a reasonable set of constraints, the mind can -- by implementing analogical reasoning -- use the system to generate something satisfying those constraints. In other words, roughly speaking, a transformation system is only useful if structurally similar sentences have similar derivations. This "principle of continuous compositionality" is a generalization of Frege's (1893) famous principle of compositionality. It appears to hold true for natural languages, as well as for those branches of mathematics which we have studied to date.

    This has immediate implications for the theory of semantics, or word meanings. It suggest an idea that, though rather commonsensical, contradicts most of modern "formal semantics" -- namely, that the meaning of an entity is the fuzzy set of patterns that are "related" to it by other patterns. If one accepts this view of meaning, then the connection between syntax and semantics becomes very simple. A useful transformation system is one in which structurally similar sentences have similar derivations, and two sentences which are structurally similar will have similar meanings. So a useful transformation system is one in which sentences with similar meanings have similar derivations.

    It is not hard to see that this property of "continuous compositionality" is exactly what is required to make a language naturally representable and usable by the dual network. The key point is that, by definition, statements with similar meanings are related by common patterns, and should thus be stored near one another in the memory network. So if a transformation system is "useful" in the sense of displaying continuous compositionality, it follows that statements stored near eachother in the memory network will tend to have similar derivations. This means that the same "derivation process," using the same collection of strategies, can be used for deriving a whole group of nearby processes within the network. In other words, it means that useful transformation systems are tailor-made for the superposition of an associative memory network with an hierarchical control network containing "proof processes." So, continuous compositionality makes languages naturally representable and learnable in the dual network.

    As briefly argued in Chaotic Logic, this analysis has deep implications for the study of language learning. Language acquisition researchers are conveniently divided into two camps: those who believe that inborn knowledge is essential to the process of language learning, and those who believe that children learn language "on their own," without significant hereditary input. The psynet model does not resolve this dispute, but it does give a relevant new perspective on the processes of language learning.

    In the language acquisition literature there is much talk of the "bootstrapping problem," which essentially consists of the fact that the different aspects of language are all interconnected, so that one cannot learn any particular part until one has learned of all the other parts. For instance, one cannot learn the rules of sentence structure until one has learned the parts of speech; but how does one learn the parts of speech, except by studying the positions of words in sentences? From the psynet perspective the bootstrapping problem is no problem whatsoever; it is simply a recognition of the autopoietic nature of linguistic systems. Language acquisition is yet another example of convergence to a structural conspiracy, an autopoietic attractor, a strange attractor of pattern/process magician dynamics.

    The question of innateness is thus reformulated as a question of the size of the basin of the language attractor. If the basin is large enough then no innate information is needed. If the basin is too small then innate information may be needed in order to be certain that the child's learning systems start off in the right place. We do not presently know enough about language learning to estimate the basin size and shape; this exercise has not even been carried out for formal languages, let alone natural languages.

    ***

    Finally, it is interesting to apply this analysis of language to the very simple language known as logic. When Leibniz invented what is now called "Boolean logic" -- the logic of and, or and not -- he intended it to be a sort of language of thought. Mill, Russell, and many recent thinkers in the field of artificial intelligence have pursued the same intuition that much thought is just the solution of Boolean equations. But many problems stand in the way of this initially attractive idea.

    For example, there are the "paradoxes of implication." According to Boolean logic, "A implies B" just means "either Bis false, or A is true." But this has two unsavory consequences: a false statement implies everything, and a true statement is implied by everything. This does not accord very well with our intuitive idea of implication.

    And there is Hempel's paradox of confirmation. According to Boolean logic, "All ravens are black" is equivalent to "All non-black entities are non-ravens." But then every piece of evidence in favor of the statement "All non-black entities are non-ravens" is also a piece of evidence in favor of the statement "All ravens are black." But this means that when we observe a white goose, we are obtaining a piece of evidence in support of the idea that all ravens are black -- which is ridiculous!

    All of these paradoxes are easily avoided if, rather than just hypothesizing that the mind uses Boolean logic, one hypothesizes that the mind uses Boolean logic within the context of the dual network. As an example, let us consider one of the paradoxes of implication: how is it that a false statement implies everything? Suppose one is convinced of the truth both of A and of the negation of A, call it not-A. How can one prove an arbitrary statement B? It's simple. The truth of A implies that either A is true, or B is true. But the truth of not-A then implies the truth of both not-A, and either A or B. But on the other hand, if not-A is true, and either A or B is true, then certainly B must be true.

    To put it less symbolically, suppose I love mom and I hate mom. Then surely either I love mom or cats can fly -- after all, I love mom. But I hate mom, so if either I love mom or cats can fly, then obviously cats can fly.

    So what, exactly, is the problem here? This paradox dates back to the Scholastic philosophers, and it hasn't obstructed the development of mathematical logic in the slightest degree. But from the point of view of psychology, the situation is absurd and unacceptable. Of course a person can both love and hate their mother without reasoning that cats can fly.

    The trick to avoiding the paradox is to recognize that the psynet is primary, and that logic is only a tool. The key step in the deduction of B from "A and not-A" is the formation of the phrase "A or B." The dual network, using the linguistic system of Boolean logic in the manner outlined above, simply will not tend to form "A or B" unless A and B are related by some pattern. No one ever thinks "either I love mom or cars can fly," any more than they think "either I love mom or planes can fly." So the dual network, using Boolean logic in its natural way, will have a strong tendency not to follow chains of reasoning like those required to reason from a contradiction to an arbitrary statement.

    But what if some process within the dual network, on an off chance, does reason that way? Then what? Will this contradiction-sensitivity poison the entire dual network, paralyze its reasoning functions? No. For a process that judges every statement valid will be very poor at recognizing patterns. It will have no clue what patterns to look for. Therefore, according to the natural dynamics of the multilevel network, it will rapidly be eliminated.

    This is a very partial view of the position of logic in the dual network -- to complete the picture we would have to considerthe other paradoxes mentioned above, as well as certain other matters. But the basic idea should be clear. The paradoxes of Boolean logic are fatal only to Boolean logic as an isolated reasoning tool, not to Boolean logic as a device implemented in the context of the psynet. In proper context, the species of linguistic system called logic is of immense psychological value.

    Evolution in the Mind

    Finally, let us turn from logic to evolution. Many theorists have expressed the opinion that, in some sense, ideas in the mind evolve by natural selection. Perhaps the most eloquent exposition of this idea was given by Gregory Bateson in his book Mind and Nature: A Necessary Unity. The psynet model provides, for the first time, a rigorous analysis of the evolution/thought connection.

    The largest obstacle that must be overcome in order to apply evolution theory to the mind is the problem of the definition of fitness. Natural selection is, in Herbert Spencer's well-worn phrase, "survival of the fittest." When considering specific cases, biologists gauge fitnesses with their own common sense. If animal A runs faster than its predator, but animal B does not, then all else equal animal A is fitter -- no one needs a formal definition to tell them that. The problem is getting a handle on fitness in general. If one cannot define fitness in any way besides reproductive success, then what one has is just survival of the survivors. And if one cannot define fitness in any way besides case-by-case special pleading, then what one has is a very inelegant theory that cannot be easily generalized to other contexts.

    One way around this problem, I have proposed, is to measure fitness in terms of emergent pattern. In The Evolving Mind, I define the structural fitness of an organism as the size of the set of patterns which synergetically emerge when the organism and its environment are considered jointly. If there are patterns arising through the combination of the organism with its environment, which are not patterns in the organism or the environment individually, then the structural fitness is large. Perhaps the easiest illustration is camouflage -- there the appearance of the organism resembles the appearance of the environment, generating the simplest possible kind of emergent pattern: repetition. But symbiosis is an even more convincing example. The functions of two symbiotic organisms match each other so effectively that it is easy to predict the nature of either one from the nature of the other.

    This emphasis on emergent pattern gives us a new way of thinking about the whole concept of natural selection. We can say that a system "evolves by natural selection" if, among the individuals who make it up, reproductive success is positively correlated with fitness. Then, if one accepts the claim that structural fitness is an important component of fitness, one way to show this is to show this is to show that reproductive success is positively correlated with structural fitness.

    Using this approach to evolution, it is easy to see thatecosystems and immune systems both evolve by natural selection -- this follows immediately from the discussion in earlier chapters. And, according to the principles outlined above, it is clear that psynets do as well. Consider: the "environment" of a process in the psynet is simply its neighbors in the network. So the structural fitness of a process in the psynet is the amount of pattern that emerges between itself and its neighbors. But, at any given time, the probability of a process not being moved in the network is positively correlated with its degree of "fit" in the associative memory. This degree of fit is precisely the the structural fitness! So, survival in current position is correlated with structural fitness with respect to immediate environment; and thus, according to the definitions given, the psynet evolves by natural selection.

    According to this argument, the "individuals" which are surviving differentially based on fitness are, at the lowest level, individual magicians, individual mental processes. By the same logic, clusters of magicians may also be understood to evolve by natural selection. This observation leads up to a sense in which the psynet's evolutionary logic is different from that which one sees in ecosystems or immune systems. Namely, in the psynet, every time a process or cluster is moved in accordance with natural selection, certain processes on higher levels are being crossed over and/or mutated.

    In ecosystem evolution, the existence of "group selection" -- evolution of populations, species or higher taxa -- is a matter of contention. In psynet evolution, because of the presence of the hierarchical network, there is no cause for controversy. Higher-order individuals can explicitly represent and control groups, so that the distinction between groups and individuals is broken down. Group selection is a form of individual selection. In this sense, it would seem that the psynet uses natural selection much more efficiently than other evolving systems, such as ecosystems or immune systems. While ecosystems can, at best, carry out higher-order evolution on a very slow scale, psynets can carry out low-order and higher-order evolution almost simultaneously. This striking conclusion cries out for mathematical and computational investigation.

     Conclusion

    As should be apparent from the foregoing, the mathematical, computational, psychological and philosophical ramifications of the psynet model are complex and extensive. But even so, the basic core of the model is very simple: just magicians buzzing around acting on each other, crystallizing into autopoietic attractors, and finally into a giant dual network meta-attractor, which displays the structures observed in psychology and neuroscience. Almost "something out of nothing" ... but not quite out of nothing; out of the seed of an initial pool of magicians, and out of the mathematical magic of attraction.

    My interest in the mind, I recounted above, was sparked by the birth of my sister Becky. No matter how abstract, ideas always emerge from the everyday, and eventually, if they aregoing to have meaning, they have to come back to the everyday. As I write this, Becky is nearly 26; she lives 10,000 miles away from me (give or take a few) near Seattle. She has a Master's in education and two small children. She does not seem very impressed with my claim that I now finally feel I understand why she has a mind! But as my six year old son Zarathustra watches my two year old son Zebulon learn to conceive his own ideas, and articulate his thoughts, I can see the same kind of amazement that I felt watching my own little sister. It is the amazement of small inklings and learned procedures ("pattern/processes") pulling together into systematic groups, of small groups building up into larger groups, and of the whole mess of self-supporting routines for understanding and doing gradually building itself up into a stable systematic network. It is every bit as amazing as the formation of a crystal out of a tiny seed in solution -- and, if one is willing to take a sufficiently broad point of view, every bit as comprehensible.

     MIND AND SPIRIT

    The psynet model is a mathematical model of mind, which I have, in the preceding section, attempted to express in words. It is more abstract than the models generally used in empirical psychology, where one is concerned with modelling very particular phenomena, such as, say "reaching and grabbing," or "word memory" or "perceptual priming" or "face recognition." The psynet model is not a model of behavior in particular experimental or real-life situations -- it is a model of the overall structure of mind, within the context of which particular behaviors are evolved.

    The current focus of my scientific work is to show that this "bird's-eye" view of the mind is useful from a scientific perspective -- that it can help us to write smarter computer programs, and to construct more penetrating psychological experiments. But my focus here is somewhat different. I believe that the psynet model is also of great value philosophically. For it gives us, for the first time, a concrete way of relating the lower levels of being to the higher levels of being. By connecting the physical substrate of mind to the most abstract emergent patterns of mind, in a logically coherent way, it builds a bridge between pranamaya and vignanamaya.

     The Dual Network and the Hierarchy of Being

    The first correspondence between the psynet model and

spiritual psychology, and the basis for many of the further correspondences to be pointed out, is the relation between the hierarchy of being and the dual network. The hierarchy of being posits an hierarchical structure for the whole universe; the dual network posits an hierarchical structure for the mind. These are not two different hierarchies, they are just two different waysof thinking about the same thing. Similarly, the heterarchical structure posited by the dual network is just another way of thinking about the interpenetrative structure of the universe as proclaimed by all wisdom traditions.

    Let us deal with hierarchy first. The dual network bottoms out with perceptual and motor processes -- i.e., with pranamaya, and the interface between pranamaya and annamaya. Proceeding up the dual network, one finds more and more abstract ideas, until one ultimately reaches ideas that are so broad they almost exceed the comprehension of the individual mind. In other words, the top of the dual network as I have considered it is vignanamaya: large intuitive ideas, too subtle and complex to be consciously experienced all at once in an ordinary state of mind.

    What I would claim is that the dual network, as posited in the psynet model, is in fact a miscrosopic view of the manomaya level of being, and the other levels of being that "fringe" this level in the hierarchy. The hierarchy of being is very coarse, treating the individual mind as a single level, but the dual network's hierarchical structure makes finer distinctions; it reveals an hierarchical structure hidden within the manomaya level of the Vedantic hierarchy.

    It would be foolish to claim that the seven levels of the Vedantic scheme were absolutely real -- not to be subdivided or melted together. We have seen that other wisdom traditions divide up the universe in different ways. In the end, the hierarchical structure of the universe is arbitrarily divisible -- one may divide it up into levels, and divide each of the levels up into levels, and so forth, limited only by one's own powers of discernment. The dual network, within the psynet model, is the result of carrying out this division process on the level of Mind.

    ***

    And what about the heterarchical aspect of the dual network, extending "perpendicularly" to the hierarchical aspect? The heterarchical connections in the dual network exist mainly between processes in the same layer of the hierarchical network, but some of them may span layers as well. They represent interdefinitions and associations -- whereas higher levels in the hierarchy represent pattern/processes emergent from lower levels in the hierarchy; each element in the heterarchy represents patterns emergent from its neighbors in the heterarchy.

    In a sense, one might say that the hierarchy is just a special case of the heterarchy. For, both the hierarchy and the heterarchy have to do with emergent pattern. But in the heterarchy, emergence is blatantly mutual on a local level: each pattern/process emerges from its neighbors. In the hierarchy, on the other hand, there is a particular direction, in that a higher level consists of a lot of things that emerge individually from lower-level processes, whereas these lower-level processes do not emerge individually from higher-level proceses.

    This point may require some clarification. Consider a collection of small regions, together making up a large image of a face. The face itself is an emergent pattern, coming out of the small regions as they are put together. It exists on ahigher level, in the hierarchical network. But the small regions are all related to their neighbors -- if you removed a small region, then you could estimate pretty well what that regions was supposed to be, just be looking at its neighbors. On the other hand, the relations between the small regions have even more value when the higher-level pattern of the whole face is taken into account. If a small region is removed, then the fact that it is a region of a face provides extra information that may be quite useful for the task of estimating its contents. So, there are multiple emergent-pattern connections among all the different structures involved, and the relation between one level and another is asymmetric, but is not fundamentally different in kind from the other patterned relations involved.

    In spiritual-psychology terms, heterarchical connections are, quite simply, interpenetrative connections. They are connections by which one pattern/process in the mind is defined by another. The heterarchical network is a network of interdefinition, interpenetration. The spiritual insight that "everything is made of everything else" is captured in the observation that, if one pattern/process in the heterarchical network is removed, it can be substantially replaced by using the information available in its neighbors. Each pattern/process is, at bottom, made up of its relations to other pattern/processes -- so that the mind is a seamless web of interdefinition, pattern, relationship.

    ***

    The dual network, then, mirrors the cosmic hierarchy identified in the Perennial Philosophy. The individual mind emerges as a microcosm of the universe as a whole. Which is, of course, the way it must be. The structures and dynamics of the universe are the structures and dynamics of the individual mind and consciousness -- because, in the end, there is no difference between the universe as a whole and the individual consciousness! The dual network is the universal hierarchy as reflected in the individual; the universal hierarchy is the individual mind as projected into the cosmos at large. The interpenetration between one level and the other is the essence of spiritual being. These two structures, being one, reach out to each other through pattern space; they "fit in" with each other and connect on a level deeper than the obstacles set up within the hierarchy of being. This, ultimately, is the reason why each of us has a need for spiritual growth. Our individual structures and dynamics are reaching out for their estranged "twins," in the universe as a whole. This reaching-out is not a consequence of physical dynamics, nor psychological dynamics per se, but a consequence of the logic of pattern. With a subtle fracal irony, it may be approximately understood as a part of anandamaya, the realm of shifting forms and patterns.

     Consciousness and Attention

    I have just mentioned the dual network as reflective of thestructure and dynamics of individual consciousness. But I have not said much about what this word "consciousness" actually means, in a psychological context. It may perhaps seem that, with all this talk about dynamics, patterns, complex systems, hierarchies and heterarchies, the psynet model has left out the most important part of mind -- consciousness, awareness, the inner feeling of being.

    In fact, though -- as may be inferred from the dual network/ hierarchy of being connection -- awareness has not been omitted from the model. It has just been treated in a subtler way than may be apparent at first glance!

    The problem of the relation between awareness and the dual network is not a psychological problem, it is a philosophical problem. It is the same as the problem of the relation between atman and the Vedantic hierarchy. On the one hand, atman is at the top of the hierarchy; but on the other hand, atman pervades everything!

    These two views of atman are reflected, psychologically, by two different views of consciousness: one view which states that consciousness pervades all aspects of mind and reality; and another view which states that consciousness is particularly associated with certain states of mind, certain parts of mind. There is a genuine contradiction between these two views of consciousness, but this is not, in my view, the kind of contradiction that can be resolved by some kind of clever argumentation, or some devious neurophysiological experiment. Rather, it is a contradiction whose existence is essential to the nature of mind. It is just another reformulation of the contradiction at the heart of wisdom! We have to live and work with these two diverse aspects of consciousness without trying to impose a fallacious reconciliation.

    ***

    The first of these two views of consciousness -- the animist view -- has always come particularly naturally to me. What I mean is that I have always, as a matter of personal intuition, assumed that everything is conscious, whether or not it can communicate with me. As a child, the question that puzzled me about my little sister was not how she became conscious -- I assumed she was always conscious -- but how she came to know and understand. This animist view of consciousness runs through all the world's spiritual traditions, and some recent thinkers (e.g. Nick Herbert in Elemental Mind) have seen it as a natural consequence of modern physics.     

    In the animist view, the raw feeling at the center of consciousness is something that goes beyond the level of Mind. Raw consciousness is an experience of Pure Being; it is Pure Being, brahman, atman. One may talk about states of consciousness, about structures which build themselves up around the experience of Pure Being -- but though this kind of talk is interesting, it does not give any fundamental insight into the nature of raw consciousness, of Pure Being itself, because Pure Being is not the kind of thing one can have insight into.

    ***

    Now let us turn to the second view of consciousness -- the one which holds that consciousness is an aspect of particular mental systems, more than or rather than others. In past publications, I have developed this view of consciousness in the context of the psynet model, in the form of a theory of Perceptual-Cognitive Loops. The basic idea of this theory is a simple one: that a great many phenomena may be understood by viewing consciousness as a feedback circuit joining perceptual processes with cognitive processes.

    The general view of consciousness as a Perceptual-Cognitive Loop has been presented many times, in many different languages, by many different authors. In particular, Edelman's biological theory of consciousness has had a large influence on me. For the present purposes, however, it is perhaps better to cite the work of Treisman and Schmidt, who have argued for a two-stage theory of visual perception. Their theory was evolved in the context of the neurophysiology of vision. The two stages are as follows. First, the stage of elementary feature recognition, in which simple visual properties like color and shape are recognized by individual neural assemblies. Then, the stage of feature integration, in which attention focuses on a certain location and unifies the different features present at that location. If attention is not focused on a certain location, the features sensed there may combine on their own, leading to the perception of illusory objects. The ultimate conclusion is a striking one. The role of attention (i.e., of externally-focussed consciousness) is seen as one of combining disparate features into unified wholes.

    The viewpoint of Treisman and Schmidt will be very useful here. For, in the language of the psynet model, "unified whole" naturally translates into "autopoietic system." Attention is thus viewed as a process which takes in disparate features from the lower levels of the dual network and, using the network's hierarchical and heterarchical structure as a guide, tries to integrate these features into an autopoietic system. These features may be slightly modified, or grouped with other features that were not "really" there; the important thing is that the result is a coherent system that can survive amidst the natural fluctuations of the evolving mind.

    The process by which the brain accomplishes this kind of "coherentization" is not entirely clear. However, it is plain from the logic of the process, as well as from various neurophysiological considerations, that the phenomenon involves some kind of feedback loop between parts of the brain dealing with lower-level, featural information and parts of the brain dealing with higher-level, conceptual information. In terms of the mind rather than the brain, one may summarize the dynamics of this loop in three steps:

1) The perceptual end of the loop sends the cognitive end information consisting of disparate features, with some tentative connections perhaps drawn between them.

2) The cognitive end of the loop modifies the features and links them with other entities stored in memory, seeking to form a coherent autopoietic system integrating the features.

3) The cognitive end sends its conjectural coherentization to the perceptual end, which determines whether the constructed system strays too far from the original features. The perceptual end sends back its report, perhaps containing a few specific suggestions. Unless the report is sufficiently positive, return to Step 2.

In this view, then, consciousness is a process of stepping through the attractor of an autopoietic system, which is itself evolving in order to match its environment (i.e., the information being supplied by the perceptual end of the loop). This is an abstract, schematic model; it is not a detailed model of the neural processes regulating human attention. However, it is concrete enough to guide efforts at neural and psychological modelling.

    ***

    An alternate way to phrase the concept of the Perceptual-Cognitive Loop is in terms of the different levels of being. The three levels involved are Mind, Body and World (manomaya, pranamaya and annamaya). What I have called the cognitive end of the loop is Mind. Perception is precisely the use of Body as a link between Mind and World. The Perceptual-Cognitive Loop is therefore a continual cycling-around of information. Diagrammatically, it is a particular dynamic supported by what I have called the "fundamental triad" of levels of being --

         Mind
       /      \
   World ------ Body

    This view of the Perceptual-Cognitive Loop helps to clarify the relation between the two views of consciousness (animist and specific-system oriented). The Perceptual-Cognitive Loop is, clearly, not a model of raw awareness. There is no good reason why raw awareness should be associated with Perceptual-Cognitive Loops and not with other aspects of the mind. What the Perceptual-Cognitive Loop is, however, is a way of amplifying raw awareness. Pure Being is in everything, but there are degrees of obviousness, and the Perceptual-Cognitive Loop is a way of making Pure Being progressively more and more apparent.

    We are getting back to the essential problem of spiritual psychology: why does the Universal Mind obstruct its own view of itself? Why are there sheaths at all, instead of just Being? Without answering this question, we can still observe that certain elements, arising within the sheaths, seem to have a particular power to penetrate through the sheaths, and give a clear view of Being. This is the nature of the Perceptual-Cognitive Loop. It is just an aspect of mental/physical dynamics, but it is different from other aspects of mental/physical dynamics in its ability to bring Pure Being into the lower levels of the hierarchy.

    In essence, the Perceptual-Cognitive Loop is the loop ofattention. And one of the key elements of the Perennial Philosophy, on which all wisdom traditions agree, is the key role of attention in freeing the mind, in seeing through the sheaths that make the visible universe, and touching the formless core beneath.

    Finally, one might well ask: why does the Perceptual-Cognitive Loop, in particular, have this power? Why not some other kind of structure? This type of question has not been addressed by either spiritual or scientific psychology -- but nevertheless, it is, I believe, fully answerable.

    The looping of information through an individual mind's Perceptual-Cognitive Loop is in esence the same as the looping of information through the universe as a whole. This is the basic form of form-creation. One senses, one groups and solidifies, one acts; one senses, one groups and solidifies, one acts; and so on, ad infinitum. This is how each of us creates our own universes out of the shifting pattern-continuum of anandamaya; and this is how the universe itself emerges from anandamaya. Each time we go through the loop, our subjective time-loop pulses once; and the time-loop of the universe as a whole is just a kind of synchronized version, a superposition of all the individual time-loops of the individual consciousnesses of every entity in the universe.

    ***

    It is time to recall the concepts of states of consciousness, as defined by Allan Combs in Radiance of Being. In Chapter 2 we discussed states of consciousness in a purely non-mathematical way. But, as Combs points out, they also have a very natural interpretation in terms of dynamical systems theory. States of consciousness are attractors of neural dynamical systems. Specifically, they are strange attractors of systems of interacting, interproducing neural processes. Each process in the mind acts on other processes, producing new processes and stabilizing old ones: this interaction and intercreation of processes is the dynamics of the mind. Mental structures are the attractors of this process dynamics. States of consciousness are best viewed as strange attractors with "wings" -- each wing corresponding to a certain state of mind, within that state of consciousness. While in a certain state of consciousness, a mind can move back and forth between different wings, different states of mind. Some wings (states of mind) may be more closely connected than others.

    In chaos theory terms, the transition between one state of consciousness and another is represented as a jolt which knocks the system out of its attractor, and leads it along a trajectory toward another attractor. This model predicts that transition between states of consciousness should be a sudden and dramatic process -- very much a discrete shift rather than a continuous gradation. And indeed, the discrete nature of shifts between states of consciousness has long been established in the consciousness literature, in particular by the work of Charles Tart, who seems to had a strong influence on Combs. Much of the literature of various wisdom traditions pertains to shifting between one state of consciousness and another -- how to attainpositive shifts, prevent negative ones, or bring the movement between states of consciousness under control of one's will.

    The Perceptual-Cognitive Loop is the essence of the ordinary waking state of consciousness. It is essential to our being. But just as the ordinary waking state is not the only state of consciousness, the Perceptual-Cognitive Loop is not the only abstract structure that is important for consciousness. A state of consciousness such as "enlightenment" will require a different kind of structure -- a notion to which we will shortly return.

     Happiness and Other Emotions

    So much for consciousness, for the moment. Now what about emotion? Feelings?

    It has become common, in recent years, to view emotions almost entirely on the level of pranamaya -- to view the human being as a biological machine, whose feelings are driven by hormones, neurotransmitters, and so forth. This is a valid point of view: indeed, emotion is centered in pranamaya, and the effects of biology on mood, feeling and thought are real and important. But in the end, this is only part of the story.

    Body chemistry, brain chemistry and mental structure are connected by a network of complex, nonlinear feedback relations. While your chemistry affects what you think, what you think also affects your chemistry. Unhappy thought structures lead to unhappiness-producing chemicals, and unhappiness-producing chemicals lead to unhappy thought-structures. In the end, all the levels of being are engaged with one another, and emotion is not something that resides on any one particular level, but rather something that has to do with the relations between hierarchical levels in the mind and universe.

    So, instead of beginning with brain chemicals and pranamaya, I will begin, once again, with consciousness. As it turns out, the spiritual, animist approach to consciousness ties in naturally with modern theories of emotion. George Mandler, a leading cognitive scientist, has argued that emotion should be divided into two aspects, hot and cold. The "cold" aspect of emotion is the structure of emotion; and the hot aspect of emotion is "cold" emotion plus consciousness. According to the animist view, the "hot" aspect of emotion is raw consciousness -- unanalyzable atman. On the other hand, the "cold" aspect of emotion is scientifically understandable: it is pattern, structure. What we experience as feelings are patterns linked up with Pure Being.

    Leaving aside the hot aspect of emotion, then, we may ask: what is the structure of emotion? The key to this question was, I believe, provided over a hundred years ago by a French psychologist named Paulhan. What Paulhan suggested was that an emotion is an unfulfilled desire. In recent years this idea has been adopted and refined by many cognitive psychologists, but the essence has remained unchanged.

    In the context of the dual network, what Paulhan's idea means that an emotion is a command passed down the perceptual-motor hierarchy, which is not obeyed. Suppose that a shaperecognition process asks its subsidiary line recognition processes for some lines in a certain place. If they cannot find any such lines, then the shape recognition process experiences "cold" emotion.

    Experientially, it is most interesting to apply this idea to the emotions of happiness and unhappiness. Unhappiness always involves, on some level, things not going the way part of one's mind expects them to. But what about happiness? How is happiness a result of unfulfilled expectations?

    One answer to this is contained in the oft-made observation that repetition makes pleasure grow dimmer. Happiness is happiness, in large part, because of the contrast with previously experienced sadness. And sadness is sadness, in large part, because of the contrast with previously experienced happiness.

    Another, complementary answer is that happiness is a feeling of increasing unity, of increasing order, of everything coming together; while sadness is a feeling of decreasing unity, of everything falling apart. In terms of emergent pattern, we may say that happiness is a feeling of emergent pattern growing -- the intuitive recognition of a new order tying together disparate, sensations, actions, ideas. Unhappiness is a feeling of emergent pattern disappearing -- of emergent structures falling apart, leaving only their components. Happiness leaves behind the expectations of a lower level in favor of the expectations of a higher level; unhappiness leaves behind the expectations of a higher level in favor of a lower level.

    Viewed in terms of the hierarchy of mind and being, this is an important conclusion indeed. We may say that happiness is a result of the unification of different levels of the hierarchy, while unhappiness is a result of the dislocation of different levels of the hierarchy. Both are a result of change: one a result of increasing cross-level unification (emergent pattern), another a result of decreasing cross-level unification.

    The hierarchy of being is an hierarchy of koshas or sheaths -- surfaces blocking parts of Pure Being from perceiving their true nature. What we have concluded is that happiness and unhappiness result from decrease or increase in the "thickness" of these koshas. Happiness results when Being is brought closer to itself; unhappiness results when Being is moved further away from itself.

    Of course, from a spiritual point of view, this conclusion is not in the remotest degree surprising. Of course happiness is aligned with some kind of cosmic unity or harmony, and unhappiness with cosmic disharmony. What could be plainer? The present discussion of emotion is a classic example of scientific ideas being used to "reinvent the wheel." But, as discussed in the Preface, it is of interest and importance to see that the wheel can be reconstructed in this type of way. The Paulhanian theory of emotion, which states that emotions are unfulfilled expectations being passed through the hierarchical network, does not at first sight appear to have anything whatsoever to do with the spiritual quest. But a careful analysis, in the context of the psynet model, shows that the two are closely connected! The mind and the universe are working in the same way, because, of course, the two are ultimately only one.

    By piercing the levels in our own minds, we pierce thelevels of the universal hierarchy. The two hierarchies are one and the same. Individual happiness is universal happiness. Familiar as it may sound, it bears repeating: We are all parts of the same unbroken whole.

     The Creative Experience

    We have aligned the dual network with the hierarchy of being, discussed the role of attentional processes in penetrating illusion, and revealed happiness to be identical with the unification of levels in the cosmic hierarchy. But this is just the beginning. We have not yet approached the main question of spiritual psychology, which is: Why does the universe obscure itself from itself? Why are there sheaths at all, instead of just ultimate being?

    I will approach this question indirectly, by way of the question of creativity. Creative inspiration is an altered state of consciousness which has a great deal to teach us about the structure of the universe. In the following chapter I will discuss a number of examples of creative inspiration in detail. Here I will give an abstract, psychological theory of creativity, and explore its implications for the nature of mind in general.

    ***

    I will begin with an account of my own personal experience of creativity. In the Preface, I described some of the experiences that led up to the writing of this book. But I did not describe the actual experience that I had while writing the book -- the experience I generally have while writing about abstract ideas. My best writing and thinking is done in the state of awareness that the psychologist Czentsikmihalyi has aptly called "flow." Among the many altered states of consciousness I have experienced or read about, creative flow is the one that interests me the most.

    The best description of creative flow that I can think of is fluidity. Abstract ideas, forms, shapes, structures appear and move about in the mind with astonishing fluidity. This fluidity can come upon one in different ways. One can be working along, in an ordinary and mundane matter -- and then all of a sudden one finds one is flying! Or, one can empty the mind, concentrate utterly, and wait -- simply wait until the proper state of mind "sinks in."

    Creative flow is a state of absolute concentration, in which the physical world virtually ceases to exist -- there is only the world of forms and structures, taking the guise of sounds or words or equations ... forms and structures moving around each other, interpenetrating each other, mutating each other and combining with one another to create new forms.... The ideas are there -- they are solid and present, moving and alive -- but yet they are not rigid and definite as they would appear in an ordinary state of mind. They are flexible and flowing, and thisis the source of their creativity. In short they are semi-real -- they are an hyperreality.

    Many children seem to sink into the creative trance easily and frequently. In early youth I fell into it often, while simply musing in the backyard, or walking along the road, manipulating ideas and imaginations. Now, I can still encounter creative flow in this way -- particularly while walking to work in the morning -- but it more often occurs when I am actively doing something I am good at: writing about ideas, improvising or composing music, thinking about mathematical structures, etc. Occasionally it even emerges when I am doing something I am not so good at, say computer programming or drawing.

    This feeling of creative trance is somewhat similar to what people feel sometimes when playing sports. As a mediocre athlete, I myself have experienced this only occasionally, but often enough to know that it is a genuine phenomenon! Usually, on the tennis court, I'm consciously planning my shots, and watching them go awry. But there are rare occasions when I play so smoothly that the process becomes automatic. The shots just keep pounding out and working, one after the other. One moment flows into the next effortlessly and delightfully. It's a fairly unstable state: a few minutes of bad luck can leave me distracted, or annoyed, or perhaps even smashing my racket on the ground like John MacEnroe! I'm not about to give up my day job. But the point is that there is a kind of flowing, happy state the mind seems to get into when it succeeds at doing something absorbing and challenging.

    Flow can arise in many different contexts -- but it rarely seems to arise when watching TV, or picking up pins off the ground, or drinking beer. There are certain preconditions. According to Cziksentmihalyi's research, the flow state occurs when one partakes of a creative activity that stretches one's abilities, but not beyond the limit. One is creating, one is making -- one's being is absorbed in the activity, but one is not straining and struggling. One is shaping one's immediate reality, shaping the future from the past, in a continuous way, from each moment to the next. One is getting high on creating the one thing that is absorbing one's attention -- on creating one's immediate, subjective world.

    ***

    Cziksentmihalyi was the first to document the existence of "flow" as a state of consciousness, from the point of view of scientific psychology. However, a great many artists have remarked upon the same phenomenon, albeit in less rigorous terminology. One thing which is apparent from the remarks of various creative people is that, in the flow state, one gets a vividly hyperrealistic view of the world. In the "white heat" of artistic creation, reality melts into illusion forming semireality, and inspiration flows from what was previously solid and immovable.

    In fact, I would make the strong claim that, in general, the creative act tends to involve perceiving the world as virtual, as hyperreal. Creative artists and scientists, at the moment ofcreation, have always intuitively understood the virtuality of the world: this is the irresistable seduction of the creative act.

    Another way to say this is to say that the creative act blurs the distinction between mental structures and physical structures. The state of creative flow reveals deep parallels that exist between the physical object and the creative work -- and I mean not only paintings, poems and the like but also such abstract objects as philosophical ideas, scientific theories and mathematical theorems. Physical objects are self-organizing, self-supporting systems: their solidity does not come from outside themselves, but rather from within themselves, from the way each part helps to support the whole. And the task of the creator is to create entities which are self-organizing and self-supporting in this same way -- to create, out of the hyperrealistic state of creative insight, entities which have the same aura of reality as the physical world.

    And, of course, the task of the creative person is also, in a different way, the task of every one of us, as a complex human being. In the end, we are all creative people. Each one of us, each day, in a barely conscious way, must work to bring together our various subselves into a coherent self-supporting whole. To construct something with a semblance of solidity and permanence out of the fluid flow of situations, emotions, reactions. Too often this is accomplished by letting one part of the mind squelch the others. Or, in the confused and neurotic person, it is not accomplished at all. The productive, well-adjusted personality is a work of mindspace sculpture, comparable in cohesiveness and aliveness to other natural phenomena.

    The creative trance, then, is the trance of world-creation. The ideas in this book, at the moment of writing them, were my subjective world, and process of creating such ideas is in many ways similar to the processes by which objects, personalities and experiences emerge out of the collective unconscious. There is a logic of creation, and there is a joy of creation; and as humans, we are privileged to understand both of these in especially intricate ways.

    ***

    The most intense and striking description of creative flow I have ever seen was given by Nietzsche in his autobiography, Ecce Homo:

        Has anyone at the end of the eighteenth century a clear idea of what poets of strong ages have called inspiration? If not, I will describe it. -- If one has the slightest residue of superstition left in one's system, one could hardly resist altogether the idea that one is merely incarnation, merely mouthpiece, merely a medium of overpowering forces. The concept of revelation -- in the sense that suddenly, with indescribable certainty and subtlety, something becomes visible, audible, something that shakes one to the last depths and throws one down --that merely describes the facts. One hears, one does not seek; one accepts, one does not ask who gives; like lightning, a thought flashes up, with necessity, without hesitation regarding its form -- I never had any choice.

        A rapture whose tremendous tension occasionally discharges itself in a flood of tears -- now the pace quickens involuntarily, now it becomes slow; one is altogether beside onself, with the distinct consciousness of subtle shudders and one's skin creeping down to one's toes; a depth of happiness in which evern what is painful and gloomy does not seem something opposite but rather conditioned, provoked, a necessary color in such a superabundance of light....

        Everything happens involuntarily in the highest degree but as in a gale a feeling of freedom, of absoluteness, of power, of divinity. -- The involuntariness of image and metaphor is strangest of all; one no longer has any notion of what is an image or metaphor: everything offers itself as the nearest, most obvious, simplest expression....

Nietzsche's experience of inspiration was particularly overpowering. But it differs in intensity, rather than in kind, from the "everyday" inspiration experienced by ordinary creative people.

    Sometimes this "overpowering force" of which one is merely a "medium" is experienced as an actual alien entity. In these relatively rare cases, creative inspiration blurs into paranoid hallucination -- or religious inspiration. The great science-fiction writer Philip K. Dick was an example of this -- as will be discussed in detail in the following chapter. He felt himself being contacted by an artificial intelligence from another star system. This AI being fed ideas into his mind, giving him the plots for his last few novels, especially The Divine Invasion and Valis.

    ***

    Similar, if less extreme, experiences of inspiration have been reported by many scientists. The chemist Kekule' conceived the idea for the benzene ring while in a state of dreamlike reverie. He perceived the benzene molecule as a snake, wriggling around, trying vainly to assume a stable structure. Then, all of a sudden, the snake bit its own tail. Everything was clarified! The molecule was a circle! Calculations revealed that this conjecture was correct. This was a unique molecular structure for its time, in several different ways; it was a landmark in organic chemistry. It is also a beautiful illustration of the role of cultural archetypes in guiding creativity. The snake biting its own tail is a stereotypical image, going back before Western culture to Eastern mythology. Kekule's creative mind spontaneously locked the benzene molecule in with an archetypal image, the snake, and then the cultural repertoire of image transformations did his work for him.

    An impressive survey of creative inspiration was given by the mathematician Jacques Hadamard in his book The Psychology ofMathematical Invention. Hadamard reviews, for instance, the great mathematician Poincare', who conceived the idea for a mathematical structure called Fuschian functions while stepping onto a bus. All of a sudden, the whole structure popped into his head, in complete and elegant form. He had struggled with the problem for some time, but had made little progress, and had shut it out of his conscious mind. But something had been obviously working on it. Had his unconscious posted a query to God, and finally received the answer? Or had some component of his mind simply continued working?

    The great chemist Linus Pauling described this sort of process in a particularly clear way:

    Some years ago I decided that I had been making use of my unconscious in a well-defined way. In attacking a difficult new problem I might work for several days at my desk, making appropriate calculations and trying to find a solution to the problem. I developed the habit of thinking about a problem as I lay in bed, waiting to go to sleep. I might think about the same problem for several nights in succession, while I was reading or making calculations about it during the day. Then I would stop working on the problem, and, after a while, stop thinking about it in the period before going to sleep. Some weeks or months, or even years might go by, and then, suddenly, an idea that represented a solution to the problem would burst into my consciousness.

Pauling won the Nobel Prize in chemistry for his theory of the chemical bond; he also did more than anyone else to found the science of molecular biology, and made important contributions to other areas, such as mineral chemistry and metal chemistry. He described one of his key creative processes as the "stochastic method" -- the free-form combination of facts into novel configurations, leading to original hypotheses. In applying his stochastic method, he relied on his tremendous store of factual information and his outstanding physical and chemical intuition. He also relied on the altered state of consciousness experienced when falling asleep, a state of consciousness in which ideas blend into each other more easily than usual, and on the mysterious, long-term creative processes of the unconscious.

    In physical chemistry proper, Pauling's stochastic guesses displayed an uncanny accuracy. The combinations of facts arrived at by his unconscious were nearly always the same ones present in the physical world! In chemical biology and medicine, his guesses were less accurate, though he still made a number of important discoveries. His creative process apparently did not change from one research area to the other, but the average quality of the results did. It appears that Pauling's ability to see new connections was so powerful, and at the same time so stochastic, that it needed a very solid body of factual knowledge to tie it down. This body of knowledge was there in physical chemistry, but less so in molecular biology, and far less so in medicine. (For a more detailed discussion of Pauling's scientific thought, see the biography Linus Pauling: A Life in Science and Politics, which I coauthored with my father TedGoertzel and my grandparents, Mildred and Victor Goertzel.)

    ***

    It is clearly established, then, that creative individuals in many different areas experience creativity as a kind of sudden rush of ideas, coming into the mind "as though from elsewhere." This is the essence of creative flow. One becomes but a vessel, but a pipeline through which ideas emerge from "on high," taking on definite forms in the physical world.

    The Vedantic hierarchy explains this phenomenon very easily: it postulates that there are two different kinds of thought involved in creative activity. First there is manomaya thought, which is on a level above mere physical or emotional reaction, but which is still based on complex manipulations of ideas derived from the physical world. And then there is vignanamaya thought, which is based on taking intuitions from the upper realms, and using them to guide one's more physicalistic concepts, one's feelings and actions.

    In the first type of thought, the reflexes are in control; in the second, one's higher intuitions are in control. The realm above intuition, anandamaya, is no longer well described as a realm of thought at all; it is a realm of shifting, subtle forms, weaving indescribable patterns. Vignanamaya thought is what I have described and experienced as creative flow.

    ***

    This Vedantic view is an accurate experiential description of creative inspiration. From the modern scientific perspective, however, things are not so simple. Scientifically, the idea that these ideas actually come from elsewhere is preposterous. Clearly, each point of view has its own validity -- one empirical, one experiential. Any theory of creative intuition that wants to be truly comprehensive must take both into account. My question now is, therefore: can any scientific sense be made of the Vedantic-hierarchy view of the creative process?

    In order to answer this question I will return to the psynet model once again. I wish to put forth the proposition that these "higher intuitions" which people (especially creative people) experience are in fact emergent patterns viewed from the inside.

    The train of thought I propose is as follows. Suppose a Perceptual-Cognitive Loop, a consciousness-embodying circuit, comes into being, and engages some of the mental processes involved in creating a broadly-based emergent pattern. How will the emergent pattern look from the point of view of this particular Perceptual-Cognitive Loop? It will look like a pattern, a structure coming from outside consciousness, enforcing itself from nowhere in particular. In short, I propose that the feeling of "creative inspiration" is the feeling of emergent pattern viewed from the inside -- i.e., the feeling of a Perceptual-Cognitive Loop which encompasses only part of a broadly-based emergent pattern.

    In this view, the distinction between Mind as such andIntuition is recovered, from a more scientific point of view. Mental activity involves trying to build up structures and ideas, by various techniques. And intuitive activity involves taking some emergent pattern which has come from "outside," and seeking to build up this particular pattern using the techniques at one's disposal. In the one instance, one is merely working with the immediate low-level patterns that are provided by a certain "neighborhood" of mental processes within the dual network. In the other instance, one is working with an emergent pattern that is "handed down," and using local mental processes to come to grips with this emergent pattern, to make it more workable and comprehensible. The Vedantic identification of different types of thinking is thus cast in more scientific language.

    ***

    Suppose this view of intuition and mind is correct. Then, psychologically speaking, the next step is to ask about the nature of the processes by which a mind seeks to build up its given patterns to match the form of a newly appeared emergent pattern.

    Some people can have vivid experiences of anandamaya, but be unable to bring much of anything down. They pass too quickly through the realm of Intuition. Others, on the other hand, are unable to loosen the grip of reason and emotion, and move into the higher realms. There is a special knack which some minds have for taking flowing patterns from the Overmind, and building up to them using forms from the Mind. The question is: in what does this knack consist?

    The psynet model leads one to the view that there are two basic mechanisms involved here: one corresponding to the hierarchical aspect of the dual network, and one corresponding to the heterarchical aspect of the dual network. The hierarchical aspect of creativity is based on mutating and combining ideas -- computationally speaking, it is modeled moderately well by the genetic algorithm. The heterarchical aspect of creativity, on the other hand, is based on letting the mind flow from one idea to other related ideas -- it is what is loosely called "analogy." The combination of analogy with genetic form-creation is the essence of creative process. These are the tools which the creative mind uses to concretize its intuitions.

    Consider, first, genetic form creation, in the hierarchical network. The idea here is that subnetworks of the dual network are allowed to mutate and to cross over, by swapping processes amongst each other. In The Evolving Mind, I have shown this to occur as a natural consequence in current models of brain dynamics. And it is introspectively very natural as well: we can all feel ourselves forming new ideas by modifying old ones, or putting parts of old ones together in new ways. The question, then, is how freely this is to be allowed to occur. What is the mutation rate, and how much disruption will crossover be allowed to cause? Will networks be allowed to cross over large chunks with each other, possibly leading to totally dysfunctional portions of the dual network? Or will they only be allowed to exchange small sets of processes, thus leading to smallerinnovations, and a smaller risk of serious disruption of function?

    Next, consider the heterarchical network. This can been thought of as a geographical terrain in which nearby regions host similar species. But it is not a static terrain; it is constantly shifting. The different animals must be allowed to constantly migrate around, seeking better locations. Analogy works by taking an entity B and replacing it, in some context, with another entity C that is near B in the heterarchical network. In The Structure of Intelligence I have given a comprehensive analysis of different types of analogy using this framework. But the crucial point here is: Where does the topology of the network come from? What determines whether B and C are close to each other in the first place?

    More interesting and adventurous analogies will arise if the network is allowed to be somewhat daring in its reorganization. Consider, for instance, Kekule's analogy between the benzene molecule and the snake. In his heterarchical network, a "molecule" process and a "snake" process were close together. In most people's minds, this is certainly not the case -- the two processes are stored in largely unrelated areas. Kekule's creative process involved the reorganization of his associative memory network in such a way that these seemingly unrelated concepts were brought together. The point is that the creative process involves "wild" analogies, and wild analogies ensue from experimental reorganizations of the heterarchical network.

    I have been speaking in terms of two separate networks. But of course, the hierarchical and heterarchical networks are in the end the same network. This is the essence of the "dual network" model. So what we find is that experimental reorganizations of the heterarchical network are exactly the same thing as adventurous crossover operations in the heterarchical network. The essential quirk of the highly intuitive mind, it seems, is a willingness to shake things up -- a willingness to mvoe things around in an experimental manner, instead of keeping them structured the same old way.

    In terms of the Perceptual-Cognitive Loop, this suggests that consciousness acts in a slightly different way in the highly creative mind than it does in ordinary people. It still makes ideas into coherent wholes -- but these coherent wholes are not bundled together quite so tightly. Instead of having a thick black line drawn around them, they have a dotted line drawn around them. They can be dissolved at will.

    Intriguingly, but not surprisingly, this conception of creative consciousness mirror's the description of "enlightened consciousness" found, among other places, in Buddhist psychology. The Buddhist psychologists argue that, in ordinary states of consciousness, we too rigidly separate concepts from each other, thus fragmenting our minds. We should separate ideas with dotted lines rather than thick black lines.

    Enlightened individuals such as Zen masters coherentize things in a different and more flexible, reversible way. Thus they are able to be "in the world but not of it" -- they are able to follow the routines and ideas of ordinary life without being dominated by them. My suggestion is that creative individuals operate in much the same way. In creative work, we are able topick up routines and use them without being dominated by them, to a much greater extent than in ordinary existence. This is, to put it prosaically, because the parts of our mind concerned with creativity have mastered a slightly different way of using the Perceptual-Cognitive Loop.

     Confronting the Big Question

    Now, with all these ideas under our belt, we are ready to tackle the big question, the central puzzle of spiritual psychology. This big puzzle is not the nature of consciousness -- spiritual traditions have invariably had the common sense to recognize the unaswerability of this question. It is, rather, how and why raw feeling obstructs itself from itself.

    We have seen that, given the existence of sheaths clothing and fragmenting Pure Being, the mind will attempt to unify the fragmented universe, by bringing the different levels of being together. This is the universal quest for happiness. But why do the sheaths have to be there in the first place? Why does atman not know that it is atman?

    Different religions and wisdom traditions give different answers here. Judaism has the snake in the Garden of Eden; Christianity develops the snake into a full-fledged Devil, with an expansive hell-world to live in and an army of evil cohorts. Gnostic Christianity has its own yet more bizarre mythology, but it also gives a somewhat more psychological answer. The Kingdom of God is here and now, says the Gnostic Jesus. It is our minds that prevent us from recognizing this. Evil is not some external force, evil is merely our own ignorance, our own inability to see.

    Buddhism gives basically the same answer as Gnosticism: the reason atman does not know it is atman is that thought-feeling complexes get in the way. Conceptual rigidities and emotional fixations give fluctuating patterns the illusion of reality. In terms of the psynet model, this idea becomes a statement about autopoiesis. It is autopoiesis, specifically, which constricts the Mind. The rigidity of concepts and the fixation of emotions are a consequence of the holding-together of autopoietic mental process systems.

    Autopoiesis stresses the emptiness of thoughts and feelings. If A and B are supporting C, B and C are supporting A, and A and C are supporting B, then where is the fundamental reality? These mental processes are just holding each other up, pulling each other up out of the Nothing. The trick is to realize that this is what is happening: that, in fact, all our mental processes are supporting each other. And the difficulty is that the autopoietic subsystems making up the mind are large and complex: the individual consciousness is only able to experience them in a fragmentary way.

    Suppose one has a system made of A, B and C, but can experience only two elements at a time -- say, A and B. Then one will never be able to experience, all at once, the hollow and self-supporting nature of the whole {A,B,C} thought-system. This is the position we are in all the time, with mental processsystems containing dozens, hundreds, thousands or tens of thousands of elements. We experience only a part of each system, and each part, as we experience it, seems solid and supported -- because it is supported by the other parts!

    Creative geniuses come up with new thought-systems, which are too large for their Perceptual-Cognitive Loops, their individual consciousnesses to handle. Thus they are confronted with original, incomprehensible inspirations. But all of us are filled up with thought-systems of comparable size and complexity to those which occur in the minds of geniuses -- the difference is that we imbibe these thought-systems from our culture!

    We never think of our cultural thought-patterns as coming to us by divine inspiration, but in fact, how do they enter our minds? We never welcome them in. They invade us in a way we cannot fully understand, because the "we" that is doing the understanding is just a collection of Perceptual-Cognitive Loops, with a limited capacity. The incursion of cultural thought-systems into our minds is rather similar to the emergence of tremendous inspirations in the mind of the creative genius.

    ***

    But if the central puzzle of spiritual psychology simply comes down to a matter of size -- to the fact that the size of thought-systems exceeds the capacity of individual consciousness, so that the autopoietic, self-supporting nature of thought-systems gives rise to an illusion of reality -- then what is to be done? How is it possible to experience large thought-systems as wholes, to see the whole, splendid self-supporting nature of the mind at once, and understand the true nature of the world?     The answer is obvious: Experience of the true nature of the mind is only possible if one leaves behind the limitations of the individual stream of consciousness, by achieving a transpersonal perspective. In modern psychological parlance such a state of being is called an "altered state of consciousness." From a spiritual point of view, however, it is rather the individualized, limited state of consciousness that is "altered" from the natural condition of things.

    The point is that an individual's Perceptual-Cognitive Loop can never fully master the thought-systems that control that individual. Individual consciousness will always get a partial view of these large thought-systems, and thus will always see something that looks "solid," instead of purely self-supporting.

The mind creates autopoietic mental process systems, and is then fooled into believing these systems have absolute reality, rather than being temporary, purpose-driven tools. It thus poses itself the puzzle of re-formulating itself in such a way as to maintain these structures without maintaining the attendant illusions. This is the puzzle which wisdom traditions attempt to solve.

    The Perceptual-Cognitive loop is one highly effective method for piercing the sheaths that clothe Being, for bringing awareness and atman into the inert universe. It is the essence of the ordinary, waking state of consciousness. But it is not the only method for piercing the sheaths. There is a transpersonal alternative, and this is what the Buddhist psychologists are talking about when they speak of the differenttype of conscious experience unique to enlightened people.

    In terms of dynamical systems, we may say that the Perceptual-Cognitive Loop is an adaptive autopoietic attractor, which is far more effective at spreading life and awareness than anything else vaguely resembling it. It is more powerful than any other thought-system that lives in its "neighborhood" in the universal pattern/process network, and hence it is frequently selected by the magician dynamics of the individual mind. The transpersonal alternative, the enlightened state of mind, however, is even more effective than the perceptual-cognitive loop.

    States of consciousness, we have said earlier, are attractors of dynamical systems. Here we have two different attractors, one corresponding to ordinary waking consciousness, and the other to enlightened consciousness. Each of these is complex and may subdivide into many different categories. But each has its own integral structure, its own autopoietic, adaptive coherence. The various disciplines taught in wisdom traditions are aimed at lifting mind-systems out of the basin of attraction of (Perceptual-Cognitive Loop dominated) ordinary waking consciousness, and into the basin of attraction of enlightened consciousness.

    The Buddhists speak of the enlightened state of consciousness in terms of bhavanga. They conceive it as a smooth flow of consciousness with no obstructing words, concepts, feelings. I have spoken of it above as a process which puts "dotted lines" rather than "solid lines" around concepts. Now I will phrase it in yet another way. In essence, I believe, what we are talking about is an expansion of the Perceptual-Cognitive Loop into a loop which, with every cycling of information, goes beyond the "everyday" levels of Mind, Body and World, extending through all the levels of being. As in Quanta, physical objects are perceived as webs of relationship. As in Intuition, thoughts and feelings appear as gifts from above, as perfectly formed, aesthetic wholes manifesting their own, subjective truth. As in the realm of Bliss, the body is understood as an ephemeral and ultimately inessential boundary: the Self blends into the Other, revealing both to be emergent forms in a network of patterns, which is floating in the void.

    By extending itself through all the levels of being, this transpersonal Perceptual-Cognitive Loop gains the ability to see the cultural-psychological systems that rule the human mind as wholes. Perceiving these subtle, multi-leveled systems as wholes, the mind can perceive that they are in fact autopoietic systems with no ultimate reality beyond themselves -- that they are systems which justify themselves.

    To put it another way, when operating in this "enhanced mode," the mind can perceive the fundamental hyperreality of mind systems. Mind systems are less than real, in that they only have their own reality; but they are also more than real, in that they produce their own reality, limited though it may be. They are active and alive, while the "objectively real" systems posited by standard Western philosophy are inert, dead, witless.

    ***

    Beyond just spinning metaphor after metaphor, is it possible to say anything more concrete about the enlightened state of consciousness? I think it is. Just as the Perceptual-Cognitive Loop of ordinary waking consciousness is associated with the triad

    Mind
   /     \
World --- Body

one can also isolate a formal structure associated with enlightened consciousness. This formal structure is obtained by adding an extra element to the loop, which I call Being.

    In this way one obtains a loop of the form

  ---------------------------|
  |                          |
Being ---------|             |
  |            |             |
  |            |             |
  |            |             |
  |           Mind           |
  |        /       \         |
  \ World  -------- Body -----

Each step of the loop, in other words, is infused with Pure Being. Instead of merely having a Perceptual-Cognitive Loop that breaks through the sheaths to Pure Being, one has a Perceptual-Cognitive Loop, each element of which is infused with Pure Being.

    This leads us back to what, in the Introduction, I called the interpenetrative view of the universe. The interpenetrative view is an alternative to the hierarchy of being. It places the Perceptual-Cognitive Loop of ordinary waking consciousness at the center, and views the three additional sheaths (Quanta, Intuition and Bliss) as reflecting the direct interaction of Pure Being with the three core levels.

    In the interpenetrative view, one introduces the levels of Quanta, Bliss and Intuition as labels on the links in the above diagram of the enlightened state of mind:

  ---------------------------|
  |                          |
Being ------ Intuition       |
  |            |             |
  |            |             |
Quanta         |           Bliss
  |           Mind           |
  |        /       \         |
  \ World  -------- Body -----

This is different from the hierarchical view of the universe, but it is an equally valid perspective. Rather than a Perceptual-Cognitive Loop it is a loop of spiritual awareness.

    The hierarchical view has its uses: it emphasizes emergent patterns. It shows us how progressive layers of emergent pattern build up, so that each level is ultimately governed by structures that appear to it as ineffable and mysterious. On the otherhand, the heterarchical view is more useful for understanding the relation between ordinary and enlightened states of consciousness. The ordinary state of consciousness is the core Perceptual-Cognitive Loop; the enlightened state of consciousness involves the entire circuit of seven sheaths. Information cycles around the core Perceptual-Cognitive Loop, and at the same time cycles through the other layers, ensuring that the Perceptual-Cognitive Loop is continually aware of the larger (hyperreal and autopoietic) context in which it operates.

    It may seem odd to have the Quanta level in here, as part of the enlightened state of consciousness. After all, it would be absurd to claim that Zen monks automatically incorporated the Schroedinger equation in their state of consciousness. What is meant by Quanta here, however, is not the detailed equations of quantum physics, but merely the philosophical intuitions of quantum reality -- which, as we have seen, are much the same as the intuitions of virtual reality. The basic idea is that physical objects, which appear real and solid from the perspective of ordinary waking consciousness, are actually manifestations of an underlying realm that is only uncertainly

known. Whether this underlying realm is made of quarks and gluons or registers and compilers is not the point. The point is that what was once perceived as solid is now perceived as yet another kind of floating, emergent pattern.

    Just as the individual Perceptual-Cognitive Loop is, in pattern space, one with the cosmic Perceptual-Cognitive Loop; so, in the ultimate continuum of anandamaya, the individual loop of spiritual awareness is one with the universal loop of spiritual awareness. The looping of Perceptual-Cognitive loops is the time-stream; the infusion of the time-stream with Being is time going beyond time. Time emerges from timeless Being, it creates forms in its looping; and then Being re-enters the loop and brings time beyond itself, creating a perspective in which time exists and does not exist, in which forms are real and yet indefinite -- transnihilistic and hyperreal.

     The Timelessness of the Present Moment

    And now it is time for what is either a post-script or a Grand Finale, depending on one's point of view. I have drawn two diagrams, one representing ordinary waking consciousness and the other representing enlightened consciousness. What I am going to show now is that these particular diagrams have a deep mathematical and psychological meaning. They represent two very special algebraic structures, which embody timelessness in a way that other algebraic structures do not. The more complex structures that make up other systems in the world are intrinsically time-bound. It is the time-bound nature of thought-systems and world-systems that is responsible for the sheathing of Being, for the obscuring of Being from itself.

    Of course, these abstract arguments do not carry absolute truth. They are just constructions which I have made, using the conceptual toolbox of modern science and culture. However, they have a great deal to say to us -- us with our scientifically andtechnologically oriented minds.

    The Perceptual-Cognitive Loop, I have said, is the archetype of form-creation. Cycling around from perception to thought to action and back again, definite structures are pulled out of the indefinite form-continuum. And this cycling around does something else as well: it creates time. Time itself is nothing but change; in other words, it is identity superposed with difference. You know time has happened when something is different than it was before -- but is still the same "something." Time occurs when you go around the Perceptual-Cognitive Loop, from one perception to the next.

    There is no time in absolute Being. There is no time in anandamaya. Time emerges from the void, from the seamless continuum of pattern space, and time creates forms. But the present moment, when time is being created -- the present moment itself is timeless. This is the essential paradox of time. The Perceptual-Cognitive Loop, three forms cycling information around and around, has no particular direction at any instant.

    And once one moves to the loop of spiritual awareness, the same thing is true. This structure is timeless as well. One is moving beyond time, incorporating time, but the moment is still timeless.

    This concept of the timelessness of the present moment is being introduced here in a somewhat offhand manner, but it is absolutely essential. For Being itself is timeless, and it is essential that the experienced moment of individual consciousness must reflect the ultimate timelessness of Being. The flow of consciousness corrupts Being, creates sheaths which obscure Being from itself. But the moment of consciousness is in tune with Being, piercing all the sheaths and communing with everything. This is the ultimate paradox of existence, and the basis of all wisdom traditions. By living in the moment, by accepting the flow of forms and patterns, one comes into contact with ultimate Being in the center of the moment of individual consciousness.

    And this beings us to the central point. We have two structures of consciousness, which are mirror images of the hierarchy of Being: but why are these two structures of consciousness so essential? Why not other structures of consciousness as well, or instead? Here is where, quite possibly, pure mathematics comes into the picture. It turns out that there are very few mathematical structures -- very few systems of inter-creating processes -- that embody this feature of timelessness.

    Mathematically speaking, what "timelessness" comes down to in this context is a property called "unique division"; and there are theorems (most notably the Generalized Frobenius Theorem) which state that there are only two finite algebraic structures with unique division which have any naturalness whatsoever. These are called the quaternions and the octonions, and, as I have argued in my book From Complexity to Creativity, these two algebraic structures are exact models of the ordinary and enlightened states of consciousness. The quaternions have three elements called "imaginary basis elements," corresponding to the three components of the Perceptual-Cognitive Loop. The octonions have seven imaginary basis elements, corresponding to the seven components of the loop of spiritual awareness. I have notmentioned these algebraic structures in my philosophical discussions up to this point, but I might as well have. The Vedantic hierarchy of being, re-cast in interpenetrative mode, is the octonions. The Perceptual-Cognitive Loop is the quaternions.

    And so, these "magic numbers" three and seven, which we have found in the Vedantic hierarchy and the analysis of states of consciousness, come straight out of pure mathematics, out of results with arcane names like "the Generalized Frobenius Theorem." But of course, this is not as mysterious as it might at first seem. For, where does mathematics come from in the first place -- if not from the collective unconscious, from anandamaya, from the necessarily-hidden wisdom of the universe as a whole? Mathematics reflects the subtle patterns of the realm of shifting forms -- the same patterns that our great mystics and creative artists lock into, by pure Intuition.