From Complexity to Creativity -- Copyright Plenum Press, 1997

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Emergent Patterns and Self-Organizing Dynamics in Mental, Computational and Physical Systems

"A book for thinking -- and nothing besides"

Friedrich Nietszche, preface to his never-written book, The Will to Power


I owe particular thanks to those who assisted me, in one way or another, in the development of the ideas reported here. Far more than any of my previous books, this one has been a cooperative venture.

Of course, as the saying goes, any errors that remain in the book are my responsibility alone.

In no particular order, I must acknowledge:

Kent Palmer -- although I know him only by e-mail, he has probably given me much more interesting feedback on my work than anyone else. The work described here on magician systems, abstract algebras and hypercomplex fractals was largely inspired by my dialogue with Kent.

Tony Smith (of Georgia Tech) and Onar Aam, for numerous intriguing e-mail discussions, in a four-way dialogue with myself and Kent that has continued through the second half of 1995, and now, mid-way through 1996, is still remarkably active. The theory of consciousness given here has benefitted particularly from their input: the basic idea of octonionic consciousness was given to me by Onar and Kent.

John Pritchard, a Columbia student and another e-mail acquaintance. His enthusiasm for and feedback on my book Chaotic Logic has been inspiring and educational; and his help in rethinking the Chaos Language Algorithm has been deeply appreciated.

Allan Combs, who has been extremely supportive of my forays into system theoretic psychology. His dual expertise in neuropsychology and transpersonal psychology has made him an excellent resource. In addition to the collaborative work on mood fluctuations reported here, his application of my "cognitive equation" to the dynamics of states of consciousness, as reported in his book Radiance of Being, has been most inspirational.

Matt Ikle' (now at the University of New Mexico, Alamosa), who collaborated on the infinite population size GA work reported here (contributing many thoughtful ideas as well as lots of Mathematica hacking), and is my current collaborator on the SEE model.

Malwane Ananda and Louis Yager, who helped out with the infinite population model in its early stages; and Gennady Bachman, who came up with the proof of the determinant theorem. Harold Bowman, who, as well as being a great friend, helped me to work through some of the mathematical details of the generalized Baker map and random magician networks. The magician system model itself was first worked out in detail by Harold and myself, in a series of early morning sessions in my Las Vegas townhouse; this was also when the connection between magician systems and abstract algebras was first conceived.

Three graduate students at UNLV. Hiroo Miyamoto and Yoshimasa Awata, who wrote the GA-driven fractal inverse problem program, as part of Hiroo's M.S. thesis. Andy Bagdunov, a computer science grad student at UNLV, who wrote a program which I used to evolve melodies by the genetic algorithm, at an early stage of my research on computer music (I never actually used his program, but the routines that he wrote for producing MIDI files have proved very useful).

George Christos, of the Curtin University math department, in Perth -- first, for sending me his papers on dream dynamics prior to my arrival in Australia; and second, for many intriguing discussions on dreaming, consciousness, neural networks, memory and related topics since my arrival in Perth.

The folks on chaopsyc, the Internet listserver of the Society for Chaos Theory in Psychology. This listserver has often been interesting and has, on several occasions, even been useful. Numerous sections of this book existed in their first incarnations as posts to chaopsyc.

The Computer Science Department of Waikato University, where much of this book was written, and a good bit of the work described in it was done. Although I only stayed there fourteen months (1994, and a bit of 1995), it was an extremely productive period for me, and I am grateful to have had the opportunity to work in such a remarkably friendly environment.

The Psychology Department of the University of Western Australia, where I am currently employed. The environment here is truly intellectually stimulating, much more so than any of my previous workplaces. In particular, Mark Randell and Mike Kalish have helped to keep alive my interest in psychological applications of complexity science, and have helped me to nurse along a few ideas, e.g. "mindspace curvature."

My sons Zarathustra and Zebulon. Zebbie has learned to talk during the two-year-long genesis of this book; when I first drafted this Acknowledgements section, one of his newest phrases was "Ben, no work!" He and his big brother Zar have held up extremely well as I have moved them from country to country over the past few years.

And last but not least, my wife Gwen, who deserves thanks both professionally (for her help in formulating the Chaos Language algorithm), and personally.


Cybernetic pioneer Warren McCullough asked: "What is a man, that he may know a number; and what is a number, that a man may know it?" Thinking along much the same lines, my question here is: "What is a creative mind, that it might emerge from a complex system; and what is a complex system, that it might give rise to a creative mind?"

Complexity science is a fashionable topic these days. My perspective on complexity, however, is a somewhat unusual one:

I am interested in complex systems science principally as it reflects on abstract mathematical, computational models of mind. In my three previous books, The Structure of Intelligence, The Evolving Mind, and Chaotic Logic, I have outlined a comprehensive complex-systems-theoretic theory of mind that I now call the psynet model.

This book is a continuation of the research programme presented in my previous books (and those books will be frequently referred to here, by the nicknames SI, EM and CL). One might summarize the trajectory of thought spanning these four books as follows. SI formulated a philosophy and mathematics of mind, based on theoretical computer science and the concept of "pattern." EM analyzed the theory of evolution by natural selection in similar terms, and used this computational theory of evolution to establish the evolutionary nature of thought. CL deviated much further from the main stream of contemporary science, and presented the "cognitive equation" -- an original mathematical formalism expressing the structure and dynamics of mind -- with applications to logic, semantics, consciousness, personality, belief systems, and the philosophy of reality. Now, the present book takes the striking, unorthodox models presented in CL, and seeks to draw them back into the fabric of current science, by applying them to various real-world problems, and connecting them to other theories of complex system behavior.

The synthetic model of mind presented in SI, EM and CL, culminating in the cognitive equation, is given the name psynet model. The psynet model is presented in a new and hopefully more clear way, and the connections between the psynet model and other approaches to complex cognitive systems are drawn out in detail. The table of contents is broad, voyaging through dynamical systems, genetic algorithms, perceptual illusions, fractals, autopoietic systems, consciousness, time series analysis, dreams, personality theory, the World Wide Web, and creativity. But even this broad array of topics barely touches the possible applicability of the psynet perspective. The point is not to say the last word on any particular topic, but rather to sketch out a general point of view, which has detailed points to make about every aspect of the mind, and has many points to make about the more complex aspects of the non-mental world as well.

The diverse interconnections presented here teach us something about the psynet model, they teach us something about the mental and physical worlds, and, last but not least, they also teach us something about the other complex systems models that are discussed. It is very interesting to see how standard complex systems models must be extended in order to deal with the immense complexity of the mind. For instance, the theory of polynomial iterations must be extended to hypercomplex numbers, rather than merely complex numbers. Genetic algorithms must be extended to incorporate ecology and spatial distribution. Attractor theory must be extended to the study of emergent formal languages in trajectories. Neural network theories must be made to shift their emphasis to the structure of interconnection between neuronal groups or modules.

Some of the explorations presented here are fairly technical; others are almost entirely nontechnical. Some report concrete scientific research; others are more speculative. What ties the various chapters together, however, is the focus on the interface of complexity and mind. The relation of mind and complexity is a big question, and I certainly do not pretend to have fully resolved it. But I believe I have made some progress.

In order to guide the reader who may have fairly specific interests, I have divided the book into four parts. This division is only a rough one, but it serves to break up the journey from simple mathematical models to subtle human feelings into comprehensible segments.

Part I., The Complex Mind-Brain, outlines the psynet model and gives some related ideas that lie fairly close to the model itself -- the application of the model to brain modeling, and the relation of the model to theories of perception. Chapter 2, in particular, gives the conceptual framework for the remainder of the book.

Part II., Formal Tools for Exploring Complexity, is more technical and the nonmathematical reader might be wisest just to skim it over. It reviews ideas from dynamical systems theory, genetic algorithms, and abstract algebra, and shows how these ideas can be extended beyond what is usually done, to provide tools for thinking about and analyzing the mind. This material provides the conceptual and scientific inspiration for the ideas in the following Parts.

Part III., Mathematical Structures in the Mind, gives a series of loosely related applications of the ideas of Parts I and II to various psychological phenomena: consciousness, dreaming, language production, self-formation, and even the possibility of intelligence on the World Wide Web.

Finally, Part IV., The Dynamics of Self and Creativity, leaves the mathematical precision of Part II even further behind, and attempts to deal with the stickier problems of personality psychology. What do these complex systems models tell us about why people act the way they do? The culmination is the final chapter, which combines personality-psychology ideas with complex-systems ideas to arrive at a novel, synthetic theory of creativity.


I will now give a more detailed summary of the contents of the individual chapters.

Chapter One reviews some ideas regarding dynamical systems, genetic algorithms and autopoietic systems, which will be useful in following chapters.

Then, Chapter Two reviews the psynet model, the cornerstone of most of the following chapters. As compared to previous publications, the model is given a very dynamical twist -- it is interpreted to portray the mind as a collection of interacting, intercreating pattern-recognition and pattern-creation processes, residing on and dynamically creating a "mental graph." Mental entities such as thoughts, feelings, perceptions and actions are viewed as attractors of spatiotemporal pattern/process dynamics. The essence of mental structure is an high-level emergent meta-attractor called the "dual network," which consists of synergetic hierarchical and heterarchical structures.

Chapter Three gives a newly detailed psynet-theoretic model of the brain. Loose connections between the psynet model, the cell assembly theory of mind/brain, and Neural Darwinism have been made before. Here these general connections are used to formulate a specific psynet/cortex correspondence, in which the two aspects of the dual network are mapped onto the two orthogonal structures of the cortex (pyramidal neurons and cortical layers).

Chapter Four introduces a principle from perceptual psychology, form-enhancing distance distortion or "mindspace curvature." This principle emerges from the study of simple geometric illusions, but it has implications beyond vision. It is used to solve an outstanding problem within the psynet model as previously formulated, namely the initial impetus for the formation of the dual network.

Chapter Five -- beginning Part II -- turns to pattern -- a much-undervalued concept which is central to the psynet model. It is shown that the theory of algorithmic pattern allows one to give a complete formalization of complex systems science, by defining such key terms as system complexity and emergence. Then attention is turned to a new tool for recognizing patterns in dynamial data, the Chaos Language Algorithm or CLA. The CLA, it is argued, indicates how the psynet model can eventually be put to empirical test. An exploratory application of the CLA to data on mood fluctuations is reported.

In Chapter Six, the relation between the psynet model and genetic algorithms is elucidated. Some mathematical results about the dynamics of the GA are summarized, and it is argued that the behavior of the GA with crossover is more "mind-like" than the behavior of the GA with mutation only. Finally, it is shown that a spatially distributed genetic algorithm, with ecology included, can serve as a simple implementation of the psynet model. The genetic algorithm is viewed as an abstract "ideal form" of certain types of mental creativity.

Chapter Seven is an extended mathematical improvisation on the theme of "magician systems." Magician systems, collections of entities that collectively transform and annihilate each other, are central to the rigorous formulation of the psynet model. However, they have been studied very little, and it is not clear where they fit in along the spectrum of applied mathematics concepts. Here magician systems are formulated in terms of directed hypergraphs, and then in terms of hypercomplex algebras and yet more abstract, three-operation algebras. Magician system dynamics (and as a consequence, psynet dynamics) is shown to have to do with polynomial and rational iterations on these n-dimensional algebraic spaces.

Chapter Eight, starting off Part III, leaves mathematics behind and turn to a psychological problem: the question of consciousness. The nature of "raw consciousness" or raw experience is not entered into; the focus is rather on how this raw consciousness is elaborated into structured, subjective states of mind. The first half of the chapter is fairly non-adventurous, and merely expands upon the concept of the "perceptual-cognitive loop" as introduced in CL. The second half of the chapter is the most speculative part of the book; it presents a detailed algebraic theory of states of consciousness, based on the magician system algebras of Chapter Seven and the quaternionic and octonionic algebras in particular.

Chapters Nine and Ten apply the psynet model, and complex systems ideas in general, to two specific psychological problems: the nature of sentence production, and the purpose of dreams. First, sentence production is viewed as a process of fractal growth, similar to biological ramification. It is modeled in terms of L-systems, and evidence for this model is sought in the structure of child language.

Then, dreaming is considered in the context of the Crick-Mitchison hypothesis, which states that "the purpose of dreams is to forget." Hopfield net simulations of this hypothesis are considered, and then it is asked: how might similar phenomena be gotten to arise from the psynet model? The answer leads one to a theory of dreams that is surprising similar to conventional psychoanalytic theories. Dreaming does not simply help one forget, it helps one loosen the grip of overly dominant autopoietic thought-systems.

Chapter Eleven turns toward a topic that will preoccupy much of the remainder of the book: the self. It points out the importance of the psychosocial self for knowledge representation, and argues that until artificial intelligence embraces artificial selfhood, it is bound to failure. The emergence of the self from the dual network is discussed; and the notion of A-IS, or artificial intersubjectivity in artificial life worlds, is discussed more thoroughly than in CL.

Elaborating on this train of thought, Chapter Twelve raises the question of the psychology of the World Wide Web. As the Web becomes more intelligent, and becomes populated with intelligent agents, might it someday become a mind? Might it develop self-awareness? The possibility of the Web developing a magician-system/dual-network structure, as described by the psynet model, is briefly discussed.

Finally, the last three chapters, constituting Part IV, turn to the difficult and imprecise, but very rewarding, topic of human personality. Chapter Thirteen reviews the notion of the dissociated self, and argues that a self is in fact a multi-part dynamical system. The essence of human personality, it is argued, lies in the dynamics of various subselves. Martin Buber's distinction between I-You and I-It interactions is reformulated in terms of emergent pattern recognition, and it is argued that healthy personalities tend to display I-You interactions between their various subselves.

In Chapter Fourteen, applications to the theory of romantic love and the theory of masochism are outlined. These applications are sketchy and suggestive -- they are not intended as complete psychoanalytic theories. The point, however, is to indicate how ideas from complexity science, as represented in the psynet model, can be seen to manifest themselves in everyday psychological phenomena. The same dynamics and emergent phenomena that are seen in simple physical systems, are seen at the other end of the spectrum, in human thought-feeling-emotion complexes.

Finally, in Chapter Fifteen, the nature of creativity is analyzed, in a way that incorporates the insights of all the previous chapters. The theory applies to either human or computer creativity (although, up to this point of history, no computer program has ever manifested even a moderate degree of creativity, as compared to the human mind). The existence of a dissociated "creative subself" in highly creative people" is posited, and the dynamics of this creative subself is modeled in terms of the psynet model and the genetic algorithm. The experience of "divine inspiration" often associated with creativity is understood as a result of a consciousness-producing "perceptual-cognitive loop" forming part of a greater emergent pattern. In general, previous complex systems models are seen as manifestations of particular aspects of the complex creative process. Creativity, the wellspring of complexity science and all science, is seen to require all of complexity science, and more, for its elucidation.

The Character of the Book

This book is written -- perhaps optimistically -- with two different audiences in mind. The first is the small community of researchers who are themselves involved in exploring the relations between complexity science and the mind. And the second is a much larger group, consisting of individuals with some knowledge of mathematics and computing, who have an interest in the mind, and in one or more of the topics touched on by complexity science, but who have not studied cognitive science or complexity science in any detail. The categories that come to mind here are psychologists, computer scientists, engineers, physicists, biologists, sociologists, mathematicians and philosophers -- but the list need not end there. For instance, the material on evolving computer art and music might be of particular interest to artists and musicians with a technical bent.

It bears repeating that what I provide here is not a systematic treatise, but rather a network of interconnected theoretical, computational and mathematical investigations. Like Nietzsche, I tend to believe that "the will to a system is a lack of integrity." The various chapters do build on each other, and they move in a common direction toward an understanding of creativity as a complex process. However, the path that they follow is not a straight one, and there are numerous ideosyncratic digressions along the way. What I present here are, in essence, structured improvisations on the themes of the psynet model, creativity and complexity science.

The technical level of the book is somewhat lopsided. The chapters on Dynamics and Pattern, Evolutionary Dynamics and Magician Systems are relatively technical, whereas the last chapters on personality dynamics are almost entirely nontechnical, and could probably be understood by the general reader. Of course, I would prefer everyone to read the whole book carefully. However, I must admit that a fairly decent understanding can probably be obtained by reading only the "easy" parts. What I would suggest for the reader with minimal mathematical background, and small tolerance for formulas, is to skip the three chapters mentioned above, flipping back to them only as cross-referencing and curiosity require.

Some readers may be disturbed by my heady mixture of "finished" research projects, raw philosophical speculations, and promising scientific beginnings. However, my feeling is that his mixture is entirely appropriate to the subject matter. After all, at the present time, both complex systems science and cognitive science may in themselves be considered "promising beginnings." Both are exciting intellectual adventures, in which philosophy and science are entangled in a most intriguing and confusing way. In this sense, the present book embodies Marshall McLuhan's principle "the medium is the message." Its network of deeply interlinked concepts, results and speculations reflects the structure of complex systems much more accurately than would a standard linear text focusing on a single narrowly defined "topic," or arguing for a particular, simply defined logical "point." By putting the various subfields of complexity science together, toward a common but complex goal, one begins to form an understanding of the way complex systems themselves are put together to make our universe.




Complexity science is young enough that every book and article written has a measurable effect on the definition of the field. It thus seems worthwhile to pause for a moment and reflect on what complexity science is -- and what it is becoming.

Picking up the book Complexity by Roger Lewin in the Waikato University bookstore, and glancing at the back cover, I was surprised to read the following words:

Complexity theory is destined to be the dominant scientific trend of the 1990's.

But what is it?

It is the unifying theory which states that at the root of all complex systems lie a few simple rules. This revolutionary technique can explain any kind of complex system -- multinational corporations, or mass extinctions, or ecosystems such as rainforests, or human consciousness. All are built on the same few rules.

"Wow!" I thought, and eagerly flipped through the pages to discover these remarkable new rules which had, in all my years of studying systems theory and complexity science, somehow eluded me. To my great disappointment, however, all I found was a well-written description of things that I had known about for years: the Santa Fe approach to complex adaptive systems, the Gaia hypothesis, Daniel Dennett's theory of consciousness, and so on. If one puts aside all the advertising hype, what is left of complexity science? The truth is that, at present, complexity science is not so much a coherent science as a loose collection of subfields. Dynamical systems theory, fractal graphics, neural networks, genetic algorithms, cellular automata, mathematical immunology, and so forth, to name a few examples, are all thriving research areas, and all have a lot to say about the behavior of complex systems. But, as of this writing (late 1994), there really is no "unifying theory" of complex systems. The "theory which states that at the root of all complex systems lie a few simple rules" does not exist.

But there is a glimmer of truth underlying the hyperbole. There may be no "unifying theory," but there is, nevertheless, something very interesting going on with the science of complexity. There is a tantalizing pattern to the connections between the various research areas. Appropriately, the current state of complexity science is best described by ideas from complexity science itself. One might say that the various subfields are undergoing a slow, steady process of convergence -- if not convergence to a fixed point, as some classical philosophies of science would require, then at least convergence to some kind of strange attractor. Or, in a different vocabulary, one might hypothesize that we are now experiencing the beginning stages of a phase transition, in which the network of relationships that defines complexity science suddenly assumes a densely interconnected structure.

It is not clear, at this point, just how far the complex systems research programme is going to be able to push -- or in what direction. Clearly, many properties of real-world systems are indeed system-specific; complex-systems considerations can't tell you everything. But on the other hand, if complex systems ideas prove sufficiently informative in a sufficient variety of situations, they may come to be considered the general background against which more specific properties are to be viewed and investigated. This is clearly, it seems to my biased eye, the direction in which things are going.

At bottom, as has been pointed out forcefully by Sally Goerner (1994), complex systems science is all about interdependence. Computer technology has allowed us to explore the interdependences between various factors which, in previous decades, we were forced to treat as being "approximately" independent. Fractals, chaos, genetic algorithms and so forth all result from this emerging theoretical and empirical acknowledgement of interdependence. It is hardly surprising, then, that the various subdisciplines of complex systems science should also demonstrate an accelerating interdependence!

I suspect that there will never be "unified rules of complexity." Like many others, I believe that we are pushing toward an entirely different kind of science, toward a more fuzzily defined collection of theoretical schema and computational tools. The very structure of complex systems science is, like the details of the Mandelbrot set, something intriguing and unprecedented.

Complexity as a New Kind of Science

In evaluating this idea that complexity science is not only a new science, but a new kind of science, an historical analogy may be useful. Philosophers of science are well aware that history-based sciences like evolution theory and cosmology have to be treated differently from other sciences -- because they, by their very nature, deal with parts of the world that are difficult to experiment on. We cannot build new universes, or evolve new hominids, in order to test our theories. In experiment-based sciences, it is realistic to judge theories by whether they correctly predict the results of experiments, or whether they suggest interesting new experiments. In observation-based sciences like evolution and cosmology, however, the emphasis has to be placed on conceptual coherence. One is looking for theories that explain a wide variety of data with minimally complicated hypotheses. A premium is placed, in history-based science, on a theory's ability to predict the data that will be found in different situations. But the amount of data available is strictly restricted, and the quality of data is limited by sources beyond one's control. So, more than in experiment-based science, it is conceptual coherence that is the deciding factor.

The theory of evolution by natural selection is a wonderfully simple idea. It explains the observed diversity of species, and the nature of the fossil record; it connects closely with genetics, and the practices of animal and plant breeding. Similarly, the Big Bang theory explains a huge number of astronomical phenomena, including the distribution of matter in the universe, the cosmic background radiation. Neither of these theories is directly testable in the classic sense -- but both are fabulous science.

Just as history-based sciences have to be treated differently, so, I claim, does complexity science. By its very nature, it deals with high-level emergent patterns, which behave differently from the simple physical quantities studied by other natural sciences. Complex systems have a variety and variability that makes reliable experimentation difficult. Different types of complex systems are similar in many abstract, subtle ways, which are difficult to rigorously characterize. They are not similar enough to be accurately modelled with the same equations, but they are similar enough that, when viewed on a coarse level, they display behaviors that are "identical in character."

Many researchers believe, with Lewin, that complexity science will eventually become like traditional, experiment-based science -- that researchers will find precise equations for the relations between complex systems. They believe that the current focus on qualitative models and vaguely-defined "archetypal" behavior is just a transitional phase. Of course, this is possible. But, looking at what complexity science actually is, we see something quite different from sciences like, say, solid-state physics, protein chemistry, mineralogy or haematology. We see a science that is based on fuzzily-defined but intuitively recognizable abstract forms -- a science that manifests, in the most striking possible way, Plato's notion of abstract Ideas which are only approximated by real entities, in various different ways.

A science of this nature, I claim, should be judged differently than other kinds of science. It should be judged, firstly, by the archetypal patterns it provides, and how these patterns help us to understand particular complex systems; and secondly, by the analytical and computational tools it provides, and how these tools help us to tease out the ways the archetypal patterns manifest themselves in particular systems. At any rate, that is the spirit in which the ideas reported here were conceived, and are presented.

Complexity and Psychology

The main disciplines touched on here are mathematics, computer science and psychology. The relation between complexity science and mathematics and computing needs little note. The relation between complexity science and the discipline of psychology, however, may be a less obvious matter.

The first point to be noted is the remarkable extent to which theoretical psychology is currently fragmented. The concepts used to model perception are by and large completely different from those used to model personality, which in turn are different from those used to model cognition, etc. While there are bound to be significant differences between different aspects of mental process, it seems likely that there is more underlying commonality than current theory reveals.

Two examples will serve to illustrate this point. First: memory. While cognitive psychologists tend to speak in terms of memory systems, the cognitive neuroscientists tell us that memory, as an independent entity, does not exist. The brain does not store inactive "memory tokens"; it contains active processes, which construct the neural activity patterns we interpret as memories, and often do other things as well.

In a similar way, until very recently, perceptual psychologists tended to speak of perceptual processing systems as independent modules. However, input from cognitive neuroscience has consistently contradicted this, and has taught us that much of vision processing (to name only the sense mode that has received the most attention) is based on interconnections with cognitive, motor and emotional centers of the brain.

In one case after another it is revealed that, what psychologists model as separate systems operating under their own principles, are actually carried out by the brain in an interconnected and unified way. This fact has led several researchers to construct general "complex systems theories" of mental process, emphasizing the interconnectedness and the self-organizing nature of the mind/brain. My own psynet model falls in this category, as does Kampis's component-systems model, and the Abrahams' dynamical-systems psychology.

From the point of view of psychology, these system-theoretic models are excessively general (and my own model is no exception here). They speak of the general structure of mental systems, rather than of what is particular to human intelligence. However, they are superior to mainstream psychological theories in one very important respect: they give a concrete vision of mind as a whole. Thus it is of intense interest, psychologically speaking, to extend these models in a more concrete and definite direction, by looking for general, complex-systems-theoretic principles of human mental function.

This is the importance of complexity science for psychology. But what of the importance of psychology for complexity science? The study of psychological systems, as pursued here, has several lessons to teach us regarding complexity science in general. Most of all, it leads to a vision of complexity which centers on emergent pattern and autopoiesis, rather than the numerical details of low-dimensional iterations.

Of course, everyone recognizes that complexity is all about "emergence," in some sense -- but in practice, most work in complex systems science still has to do with studying numerical variables. I believe that, particularly in discussing very complex systems such as psychological systems, it is necessary to push even further in the direction of emergence, and to treat algorithmic pattern/processes, rather than numerical variables, as the main topics of discourse. The self-organization and interproduction of patterns must be kept at the forefront. Magician system models, as introduced in Chaotic Logic, are stressed here, as a way of capturing this kind of abstract, autopoietic pattern dynamics.

This new angle on standard complex systems models presented here serves to balance the "hard science" bias which one finds in most complexity science. Complexity science evolved primarily within physics, computer science and applied mathematics, with some input from biology, chemistry, economics, etc. The complexity/psychology connection has only very recently attracted significant attention. Here I look at complex systems ideas and models from a theoretical-psychology perspective -- to see how thse models must be extended in order to deal with that most complex of systems, the mind. This exercise is, I believe, valuable for cognitive science and complexity science in particular, as well as for the psynet model in particular.

Background Reading in Complexity Science

Despite the wide sweep of the ideas, this is fundamentally a research monograph and not a textbook. In particular, it is not a good introduction to the study of complex systems. Thus it may be appropriate to give a few suggestions for background reading for the reader who is not "up to speed" regarding the emerging science of complexity.

First of all, since I have critiqued the blurb on the cover of Lewin's Complexity, I must say that -- while it does suffer, to a certain extent, from the usual sins of omission and lionization -- this is an unusually lucid and intelligent book. Lewin does an excellent job of getting across the general flavor of complexity science as it existed in the early 1990's. This era has already passed, and by now complexity science has become far more diffuse and diverse -- but it is a time period well worth reading about.

A different kind of review of complexity science, more focussed on ideas rather than personalities, is Coveney and Highfield's book Frontiers of Complexity (1995). I have used this book as the main textbook for a liberal arts class, and the students found it enjoyable and readable despite its sometimes intricate scientific detail.

Next, although it is not fashionable to admit it, modern complexity science owes a great deal to the half-century-old discipline of general systems theory. Erich Jantsch's classic The Self-Organizing Universe is an excellent overview of the accomplishments of general systems theory. Sally Goerner's The Evolving Ecological Universe (1994) ties chaos and complexity together with modern work in thermodynamic systems theory and also with more general social trends. Finally, the works of Gregory Bateson, most notably Mind and Nature (1980), are also not to be missed.

Regarding dynamical systems theory in particular, in addition to popular treatments like Gleick's Chaos (1988), there is an abundance of quality texts on all different levels. A popular choice is Robert Devaney's Chaotic Dynamical Systems (1988), which is aimed at upper level undergraduate and first year graduate students in mathematics. A Visual Introduction to Dynamical Systems Theory for Psychology, by Fred Abraham, Ralph Abraham and Chris Shaw (1991), gives a nice overview of basic concepts as well as describing many solid scientific applications.

Regarding genetic algorithms and evolutionary computation, the picture is not so clear -- no one has yet written a comprehensive textbook surveying the full variety of EC theory and applications. The reader who wishes more general background information on EC is therefore referred to not one but four good books reviewing aspects of the "state of the art" in evolutionary computation. Goldberg's Genetic Algorithms for Search, Machine Learning and Optimization (1988) gives the classic treatment of the bit string GA. Michaelewicz, with Genetic Algorithms + Data Structures = Evolution Programs (1993), has written the bible for floating point based GA's and "evolution programs." Koza's massive tomes, Genetic Programming and Genetic Programming II (1990, 1993) make the best case so far for the genetic programming approach. Regarding classifier systems, the best reference is still the classic work Induction (Holland et al, 1986).

The Artificial Life conference proceedings volumes, especially Artificial Life II (Langton et al, 1992), give an excellent survey of applications of evolutionary computation, dynamical systems theory and other ideas to the problem of constructing artificial life forms. Also, Stuart Kauffman's The Origins of Order (1993), though by no means easy reading, summarizes a long list of research projects in complexity science accomplished by Kauffmann and his colleagues over the years.

Finally, the small but important subfield of "system-theoretic cognitive science" is referred to frequently in the following pages. This research is grounded in classical systems theory as much as in modern complexity science; it is exemplified by books such as Francisco Varela's Principles of Biological Autonomy (1978), Vilmos Csanyi's Evolutionary Systems: A General Theory (1989), George Kampis's Self-Modifying Systems in Biology and Cognitive Science (1991), and my own Chaotic Logic, Structure of Intelligence and Evolving Mind.