Chapter 3

ABSTRACT:  A brief introduction to the discovery of chaos theory and its applications to understanding human awareness and behavior.  The mathematics of deterministic chaos underlies the growth patterns of nature and our nature. There is an implicate order in chaos. But we don't need to understand the math to see that expression in our physiology and psychology.  Chaos is our fundamental essence.  It is inherent in the self-organizing matter within us.

Creation came out of chaos, is surrounded by chaos and will end in chaos.

                                                                           --Anonymous

Despite their training, psychoanalysts have a dread of unconscious meaning, which really translates into a dread of chaos.

                                                                          --Robert Langs

CREATION, CONSCIOUSNESS, AND CREATIVITY

According to classical Greek myth, only Chaos existed in the beginning.  The random element eventually produced Gaea, the deep-breasted earth or matter, from within infinite potential.  For matter to exist, the force of attraction also had to appear (super-celestial Eros).  Uranus, the starry heavens, is Gaea's first-born child.

In other words, the first descent of matter into the threshold of concrete existence came from a chaotic matrix.  This cosmic trinity of chaos, matter, and attraction lies at the heart of chaos theory.  It bears directly on another Greek archetype that we all share--the psyche.  Just as the ancient pantheon provided a foundational orientation for the Greeks, chaos theory can provide us with a model for constructing cognitive maps.

By embracing the chaos in our lives--learning to re-honor the principle--we can begin balancing out millennia of identification which held that only order equates with "good."  Part of our cultural heritage is the programming that we should stave off chaos at every point. Some speculate this was a patriarchal reaction against the ancient matriarchal, chaos cultures.

Sometimes it is psychologically more fruitful to "let go" of  control, pass through that de-structured state, and discover what happens on the other side.  Chaos is definitely part of the process of creativity.  It generates the new order spontaneously from deep within itself.

What makes it imperative for us to embrace the new scientific paradigm implied by chaos theory?  By rejecting chaos, you reject Gaea.  And she is not only the Earth, the love of the planet, the integrity of life forms, but also love of your own physical embodiment.  Whatever the essence of chaos is, we are that.  By rejecting it, we run the danger of rejecting our selves.

Chaos is the essence of life.  Chaos is essential to health.  Research has shown that chaos in bodily functions signals health, while periodic behavior can foreshadow disease.  Whether Eros (the principle of attraction) is evident in the mathematics of a strange attractor or in human behavior, there is a resonance with Chaos and Gaea.

Chaos has laws of its own, which harmonize with order.  Chaos describes the structural growth patterns in nature, and the patterns of breakdown, entropy, or decay.  It describes systems far-from-equilibrium, not just the rarely found stable state.  It applies to all complex dynamic systems, which certainly includes human beings.  It provides a new perspective on reality.  Adaption of this perspective into our worldview helps us understand whole systems.

Chaos theory leads to a new vision of matter, one no longer passive, as described in the mechanistic worldview, but one associated with spontaneous, creative, orderly activity.  This scientific frontier is fertile ground for new metaphors and models.  It will help us solve some of our practical problems, both personal and global.

Throughout history many innovative discoveries have come through the process of reverie, daydreaming, or inspiration.  Research has also shown that the greater the mental challenge, the more chaotic the activity of the subject's brain (Rapp).  After incubating a solution in the chaotic state, we seem to "get a brainstorm."

Certain brainstates, high in virtually random, chaotic activity are conducive to creativity.  Let's hope that by "letting go" of our old rigid structures and beliefs, and letting chaos back into our lives consciously, that we can find more of those creative solutions.  Both scientific and intuitive apprehensions of chaos will lead the way.

A NEW DIALOGUE WITH NATURE

Chaos theory came on the scientific scene in the late 1970s.  It was introduced by a self-motivated group of Santa Cruz scientists.  As students they had to fight their faculty to pursue their fascination with this unorthodox subject.  After its initial presentation, chaos became a buzzword in many disciplines, as scientists thought of ways it applied in their fields. Even more interesting, scientists began crossing over fields, developing multidisciplinary approaches.

Chaos is not entirely random, but is an occult, "hidden," or implicate order within nature.  Cosmology, weather prediction, animal migration patterns, quantum mechanics, and more were affected.  We now have terms like "quantum chaos," and chaotic planetary motion.  Chaos is a major influence from the microcosm to the macrocosm.

Some astronomers even postulate a cosmic Great Attractor toward which all the local galaxies are moving.  Is the earth, our solar system, and galaxy really on a pilgrimage to the Great Attractor?  Technically, the attractor isn't only "out there."  Our galaxy is part of the attractor, whatever it is.  With a sphere influence of 300 million light-years, it is one of the most gigantic known entities in the cosmos.  And, it may have relatives!

At the other end of the scale, it appears that chaos is found in the distribution levels of certain atomic systems and wave patterns (Gutzwiller, 1992).  Chaotic systems lie beyond the description of normal perturbation theory.  Quantum chaos may be a way of linking quantum systems and chaotic systems.  One interesting property of chaotic systems of quantum energy is that they cannot be decomposed.  Chaos also shows up in the way electrons scatter.

Probably the first popular book to discuss chaos theory was ORDER OUT OF CHAOS: MAN'S NEW DIALOGUE WITH NATURE, by Ilya Prigogine, published by Bantam in 1984.  By far, the most widely read has become James Gleick's now-classic, CHAOS: MAKING A NEW SCIENCE (1987).  Others, like THE TURBULENT MIRROR, Briggs and Peat, (1989), have sought to express the theory more simply, and poetically.

Some books have focused on the computer graphics, known as fractals, which have emerged from this new science.  Their natural beauty holds an aesthetic fascination.  Even the art world discovered chaos through fractals.  Images of dynamic fractals are used in discos, like light shows.   Chaos software has brought them to the home PC. Chaos moved through science into the arts and humanities.

Chaos bears on our consciousness, physiology, perception, and psychology.  We can learn a lot from what chaos theory tells us about the nature of reality.  Most of reality, instead of being orderly, stable, and equilibrated, is fluctuating and boiling with change, disorder, and process.

Little fluctuations in subsystems combine through positive feedback loops, becoming strong enough to shatter any pre-existing organization.  In chaos theory, this crucial moment is known as bifurcation.  At this point the disorganized system either disintegrates into chaos, or leaps to a new higher level of order or organization.  Through this means, order arises spontaneously from disorder through self-organization.

When a system is far-from-equilibrium, the slightest flux can be amplified into structure-annihilating waves.  Chaos theory helps us think in terms of these fluctuations, feedback amplification, dissipative structures, and bifurcations.  It provides pause for reconsidering the nature of time and the role of chance during transformation from one state to another.

Chance plays its role at or near the point of bifurcation, after which deterministic processes take over once more until the next bifurcation.  But, of course, we can never determine when the next bifurcation will arise.  Chance rises phoenix-like to take its place among physical processes.  Thus, nonequilibrium, the flux of matter and energy, is a source of order.

In the new concept of matter, matter is active.  Paradoxically, matter leads then to irreversible processes, yet irreversible processes (entropy) organize matter (negentropy).  Chaos theory is therefore a new evolutionary paradigm, based in dynamics and thermodynamics.  Irreversibility seems to be a source of order, coherence, or organization.

Time, reality, and reversibility/irreversibility  are closely related.  The implication is that "time" is a real dimension, not merely introduced through human observation.  Irreversibility is not a universal phenomenon, but it is not necessarily subjective, either.  Our human reality is embedded in the flow of time.

It appears that our consciousness creates that sense of time flow by information processing, but it may be a given.  The question then becomes, "what is the specific structure of dynamic systems that permits them to distinguish past and future?"  If we can answer that, and determine the minimum complexity involved, perhaps we can be more precise about the roots of time in nature.

The irreversibility of time is itself closely connected to entropy.  To make time flow backward we would have to overcome an infinite entropy barrier.  Natural systems contain essential elements of randomness and irreversibility.  After a bifurcation there can be no return to the old condition.  Time has both linear and nonlinear qualities.  Time might be described, rather than as a flow, as a dimensional manifold of infinite processes, the ultimate feedback loop.

All biological systems are dissipative structures which are self-organizing (DNA) and self-iterating (reproduction).  The type of system which evolves is critically dependent on the conditions in which the structure is formed.  We can speculate that the gravitational field of earth, as well as EM fields play an essential role in the selection mechanism of self-organization [see EMBRYONIC HOLOGRAPHY, Miller and Webb, 1973].

Chaos theory has caused us to reexamine the concept of matter as inert and without consciousness.  It expresses its own quality of consciousness and determinism, a type of awareness also seen in some quantum phenomena.

According to Prigogine, in equilibrium matter is "blind," but in far-from-equilibrium conditions it begins to be able to perceive, to "take into account," in its way of functioning, differences in the external world (such as weak gravitational or electrical fields). [see THE DIAMOND BODY on scalar physics, Miller and Miller, 1982].

Prigogine and Stengers comment further on the so-called consciousness of dynamic systems:

Near bifurcation, systems present large fluctuations.  Such systems seem to "hesitate" among various possible directions of evolution, and the famous law of large numbers in its usual sense breaks down.  A small fluctuation may start an entirely new evolution that will drastically change the whole behavior of the macroscopic system.  The analogy with social phenomena, even with history is inescapable.  Far from opposing "chance" and "necessity," we now see both aspects as essential in the description of nonlinear systems far from equilibrium.  This is very different than the static view of classical dynamics or the evolutionary view associated with entropy.

Perhaps this is one intuitive perception the Greeks had when they deified these principles.  "Necessity" is the goddess Ananke, while "chance"  and opportunism corresponds with Hermes.  The whole pantheon evolves through these principles from the pure chaos of the source.

In FACING THE GODS, James Hillman points out the common identity of Necessity and Chaos with anxiety:

The psychological viewpoint sees Necessity and Chaos not only as explanatory principles only in the realm of metaphysics; they are also mythic events taking place also and always in the soul, and they are the fundamental archai of the human condition.  To these two principles the pathe (or motions) of the soul can be linked.

Psychology has already recognized the faceless, nameless Chaos, this "sacred and crazy movement" in the soul, as anxiety, and by naming it such, psychology has directly evoked the Goddess Ananke, from whom the word anxiety derives.  If anxiety truly belongs to Ananke, of course, it cannot be "mastered by the rational will."

This creation process continues to this day, through every moment, a dance of creation and destruction.  It takes place in the quantum flux, as virtual entities pop in and out of physical manifestation.  It takes place in the crucible of new and dying stars, galaxies, and perhaps our entire universe.  Chaos may even be the ground state of multiple universes.

MEASURES OF COMPLEXITY AND CHAOS

Turbulence was one of the key phenomena that motivated the resurgence of interest in nonlinear dynamical systems.  It was, after all, investigation into the mechanisms for turbulence that led to the invention of the term "strange attractor" in 1971.  The turbulence that is described by strange attractors is "turbulence in time"--deterministic chaos, or temporal chaos in current terminology.

In the past decade, a vocabulary for the quantitative characterization of temporal chaos was developed.  It has been used to describe and analyze an incredible variety of phenomena in practically all fields of science and engineering.  The dimensions of strange attractors, the entropies, and Lyapunov exponents describing motion on the attractors, have been used to analyze heartbeats, brainwaves, chemical reactions, lasers, the economy, flames, radiation, and fluid flow.

Yet this vocabulary is not sufficient to describe turbulence, for its complex nature exists in time and space.  Time evolution is seamlessly united with the quantitative characterization of spatial complexity.  Turbulence is dynamical, nonlinear spatio-temporal complexity.

Dimensions, entropies, and Lyapunov exponents [don't worry about this one; there is no test later] have become the standard measures of temporal chaotic behavior.  Dimensions lend themselves to computer modeling of fractal attractors.

Fractals visibly demonstrate harmonies that may not be apparent within the mathematical formulas.  Graphic generators make this beauty visible, where it speaks to us geometrically, intuitively.

The large variety of fields in which dimensions, entropies, and exponents have been used to characterize temporal evolution is an indication of the extent to which these quantities have become elements of a scientific vocabulary that is now nearly universal.

These quantities are used to characterize astrophysical data, dendritic growth, electroencephalographic and electrocardiographic data, nerve fibers, epidemics, etc.  As one of the most basic applications of these methods, dimensions have been used to discriminate between chaos and noise.

Nonlinear dynamical systems produce complex temporal or spatial patterns by stretching and folding regions of phase-space in an iterative way.  Space and time get folded like so much multi-layered pastry dough [more on this aspect shortly].  As a result of the unfolding procedure, the dynamics is described as a sequence of deterministic paths (blocks of symbols) which appear as random in time, with given transition probabilities.

This would seem to imply that chaos underlies the implicate order [see Bohm, WHOLENESS AND THE IMPLICATE ORDER].  It has already been shown as an influence in quantum probability, the mechanism of quantum flux.  Chance and necessity may not be widely separated phenomena--they may be two sides of the same chaotic coin.

A large variety of physical systems exhibit seemingly disordered (turbulent, chaotic) spatio-temporal behavior which, behind its apparent irregularity, hides a high degree of organization.  The observation that low-dimensional nonlinear dynamical systems are able to generate aperiodic bounded solutions gave rise to an increasing interest in the study of chaotic behavior, which led to the definition of strange attractors.  These objects have been geometrically described in terms of fractal dimensions and, dynamically, by means of Lyapunov exponents and metric entropies.

Their future time evolution can be predicted only for finite (relatively short) times, although they are fully deterministic, because of the exponential amplification of the uncertainty on the initial conditions.  Highly structured patterns can be produced, which are not necessarily related to chaotic motion.

Examples of "complex" behavior are provided by biological systems, hydrodynamic flows, spin glasses, neural networks, fractals, cellular automata, and nonlinear dynamic systems.  It is easy to show that entropy and Lyapunov exponents are not useful indicators for the characterization of complexity.

THE MAIN FEATURE OF SELF-GENERATED COMPLEXITY IS THE PRESENCE OF AN ITERATIVE MECHANISM WHICH TRANSFORMS THE INFORMATION CONTAINED IN THE INITIAL CONDITIONS IN A DETERMINISTIC WAY.  IN THIS SENSE, IT IS POSSIBLE TO VIEW COMPLEXITY AS ELABORATED SIMPLICITY.

There are mechanisms for the creation of defects.  In deterministic systems, several mechanisms can lead to their formation, including initial conditions and phase instabilities.  VORTICES can be induced by initial conditions, such as dislocations.

Phase instability plays a crucial role in the creation of defects.  Transitions which involve vortices, as for example the Hopf bifurcation, lead to patterns which are described in terms of a phase.  These transitions are in some sense "phase breaking" transitions.

More complicated patterns, as for example standing waves, require more than a single phase.  In more than one dimension, large enough systems can sustain vortices.  Phase fluctuations eventually become large enough to break, locally in space and time, this "phase only" description.

In regions where large gradients appear, the creation of defects destroys the quasi-long range order induced by the pattern.  In one dimension, defects are spatio-temporal, i.e. they occur at a given spatial position, for a given time.

Lastly, defects can be created in the transient process accompanying a subcritical transition.  Defects play an important role in the spatio-temporal destruction of the order induced by symmetry breaking transition.  The most efficient way to create defects in these non-equilibrium systems is related to phase instabilities.  Experimental evidence of such a defect-mediated picture of turbulence exists.

All this sounds very far afield from human life, but is it really?  Aside from the literal expression of chaos, there is its metaphorical aspect.  If we re-read the above with an intuitive eye, it might provide archetypal insight on depression, nervous breakdown, personality defects, life transitions, phases of development, and other human realities.  [See CHAOS THEORY AND PSYCHOLOGICAL COMPLEXES, Miller, 1991].

Chaos relates directly to information theory.  Quantitative measures of chaos have been developed and used to connect theory and experiment.  All these systems are closed.  Imposing closed boundary conditions means the system "interacts with itself at all times," so the effects of a perturbation to one location cannot escape, but influences the dynamics of the entire system.  This also holds true  for individual human beings.

The primary instability in such systems is absolute and information on the dynamics of spatially distributed, but closed systems may be obtained by studying the temporal behavior at a single location.  Indeed, the vast majority of experimental investigations have assumed the observed chaotic systems have finite spatial extent, without information flows across their boundaries.  Again, also applicable to the individual person.

In open systems, information may enter and leave the system.  It is not always possible to describe the dynamics by the time series at a single, fixed location.  In contrast to closed systems, open systems frequently possess downstream propagating primary instabilities.  In human life, a trauma at a given point will create exponential problems (turbulence) further on in time, until and unless one passes through the chaotic breakdown into a place of healing--into flow.

Technically, spatial development of flow may depend crucially on external forcing, often by low amplitude noise.  For human beings, the healing space is often one with so-called "white noise," like the flowing of a waterfall or ocean surf, or the rustling or whoosh of the wind.  We create the same state internally when we enter the alpha brainwave state.  These are generated by the dynamics of chaos, and their healing, soothing effect on our personality is well known to nearly everyone.

THE PARADOX IN CHAOS

There is order in chaos; randomness has an underlying geometrical form.  Chaos imposes fundamental limits on prediction, but it also suggests causal relationships where none were previously suspected.  In chaotic systems, since there is no clear relation between cause and effect, such phenomena are said to have random elements.

Simple deterministic systems with only a few elements can generate random behavior.  The randomness is fundamental.  Gathering more information does not make it go away.  Randomness generated in this way has come to be called chaos.

A seeming paradox is that chaos is deterministic, not probabilistic.  It is generated by fixed rules that do not involve any elements of chance.  A paradox is a union of opposites in a transcendent third.  In principle the future is completely determined by the past, but in practice small uncertainties are amplified.  Even though the behavior is predictable in the short term, it is unpredictable in the long term.  This is because any effect, no matter how small, quickly reaches macroscopic proportions.

Graphic depictions of attractors allow us to map a dynamical system's behavior in discreet-time or phase-space.  It helps us visualize a complex situation.  Roughly speaking, an attractor is what the behavior of a system settles down to, or is attracted to.

Some systems do not come to rest in the long term but instead cycle periodically through a sequence of states.  An analogy might be the cycling between competing attractors in bi-polar disorder, or manic-depression.  What slight perturbation causes the switch?  A system may have several attractors [complexes, archetypes, subpersonalities?]  The set of points that evolve to an attractor is called its basin of attraction.

STRETCHING TIME AND FOLDING SPACE

The key to understanding chaotic behavior lies in understanding a simple stretching and folding operation, which takes place in the state space.  The orbits on a chaotic attractor are shuffled by this process, much as a deck of cards is shuffled by a dealer.

The randomness of the chaotic orbits is the result of the shuffling process.  The process of stretching and folding happens repeatedly, creating folds within folds ad infinitum.  A chaotic attractor is, in other words, a fractal--an object that reveals more detail as it is increasingly magnified.

Crutchfield, et al describe, in SCIENTIFIC AMERICAN, how chaos mixes the orbits in state space in precisely the same way a baker mixes bread dough by kneading it.  Just imagine rolling out the dough and placing a big drop of food coloring in the center.  As you spread and fold the dough, you create many layers of alternating blue and white.  Then finally the dye becomes thoroughly mixed with the dough.

Chaos works the same way, except that instead of mixing dough it mixes the state space.  The state of the system is located not in a single point but rather within a small region of state space.

The stretching and folding operation of a chaotic attractor systematically removes the initial information and replaces it with new information.  The stretch makes small-scale uncertainties larger, and the fold brings widely separated trajectories together and erases large-scale information.

Thus chaotic attractors act as a kind of pump bringing microscopic fluctuations up to a macroscopic expression.  In humans only small fluctuations in mental processes are required initially to amplify over time into major changes or re-visioning of reality.  To slightly alter experience of a psychological complex is to work directly on the ego.  Any microscopic fluctuations we make in therapy are amplified into real-time.

This reflects on our concepts of transformation, and permission for change to occur in a nonlinear manner in personality.  After a brief time interval the uncertainty of the initial conditions covers the entire attractor and all predictive power is lost:  THERE IS SIMPLY NO CAUSAL CONNECTION BETWEEN PAST AND FUTURE.  There is also no psychological mandate to adhere to an outworn self-simulation.  The change can be instantaneous, unfolding over time.  Healing is an ever-present potential.

Chaotic systems generate randomness on their own without the need for any external random inputs.  Based on this, we can make quite a case for allowing clients to develop their own therapeutic metaphors in therapy.  Some therapists "import" teaching tales or metaphors into the process which they feel could help the client.  The imaginal free association of dream healing seems to open them to the flow of their own process and imagery.  Facilitating that process, the therapist functions best as a guide.

Random behavior comes from more than just the amplification of errors and the loss of the ability to predict it; it is due to the complex orbits generated by stretching and folding.  If a system is chaotic, how chaotic is it?  A measure of chaos is the entropy of the motion, which roughly speaking is the average rate of stretching and folding, or the average rate at which information is produced.

CHAOS AND HUMAN PHYSIOLOGY

Nonlinear chaos refers to a constrained kind of randomness, which, remarkably, may be associated with fractal geometry.  Fractal geometry is the basis of human anatomy, but it pervades nature.  Fractal structures are often the remnants of chaotic dynamics.

Wherever a chaotic process has shaped the environment (the seashore, the atmosphere, a geological fault), fractals are likely to be left behind.  Fractals consist of varying size and orientation but similar shape.

Certain neurons (nerve fibers), for instance, have a fractal-like structure.  If one examines such neurons through a low-power microscope lens, one can discern asymmetric branches, called dendrites, connected to the cell bodies.

At slightly higher magnifications, smaller branches on the larger ones are observable.  At even higher magnification, one sees another level of detail--branches on branches on branches.  Although at some level the branching of a neuron stops, idealized fractals have infinite detail.

The details of a fractal at a certain scale are similar (though not necessarily identical) to those of the structure seen at larger or smaller scales.  All fractals have this internal, look-alike property called self-similarity.

Because length is not a meaningful concept for fractals, mathematicians calculate the "dimension" of a fractal to quantify how it fills space.  Self-similarity of a system implies that features of a structure or a process look alike at different scales or lengths of time.  The greater the dimension of a fractal, the greater the chance that a given region of space contains a piece of that fractal.

In the human body fractal-like structures abound in networks of blood vessels, nerves, and ducts.  The most carefully studied fractal in the body is the system of tubes that transport gas to and from the lung.  The heart also exhibits fractal anatomy or fractal architecture.

Fractal branches or folds greatly amplify the surface area available for absorption (as in the intestine), distribution or collection (by the blood vessels, bile ducts, and bronchial tubes) and information processing (by the nerves).  Fractal structures, partly by virtue of their redundancy and irregularity, are robust and resistant to injury.

Fractal structures in the human body arise from the slow dynamics of embryonic development and evolution.  These processes, like others that produce fractal structures, exhibit deterministic chaos.

In the early 1980s, when investigators began to apply chaos theory to physiological systems, they expected that chaos would be most apparent in diseased or aging systems, but contrary to what training and intuition might suggest, the opposite is true.  For example, careful analysis reveals that healthy individuals have heart rates that fluctuate considerably even at rest.

To identify the type of system dynamics (chaotic or periodic), one determines the trajectories for many different initial conditions.  Then one searches for an attractor: a region of phase space that attracts trajectories.

The strange attractor describes systems that are neither static nor periodic.  In the phase space near a strange attractor, two trajectories that started under almost identical conditions will diverge over the short term and become very different over the long term. The system described by a strange attractor is chaotic.

Recent evidence suggests that chaos is a normal feature of other components of the nervous system, including those components responsible for hormone secretion.  This might account for a degree of randomness in mood and emotions, related to secretion of neurotransmitters in the brain.  It might also be the mechanism for a dream "putting a mood on you" after you awaken.  It is a real-time effect of chaos reaching out from the subconscious mind to the conscious.

Chaos can be generated in a model of the olfactory system.  This research appeared in SCIENTIFIC AMERICAN, February 1991.  This model incorporates a feedback loop among the "neurons" and a delay in response times.  There is a recognized importance of time delays in producing chaos.

Why should the heart rate and other systems controlled by the nervous system exhibit chaotic dynamics?  Such dynamics offer many functional advantages.  Chaotic systems operate under a wide range of conditions and are therefore adaptable and flexible.  This plasticity allows systems to cope with the urgent requirements of an unpredictable and changing environment.

However, the periodic patterns in disease and the apparently chaotic behavior in health do not imply that all pathologies are associated with increased regularity.  Controlled chaos may play a roll in the human ability to quickly produce strings of different speech sounds. It seems biological systems may use chaos, and the richness in chaotic behavior, to change their behavior on the fly.

Edward Ott, et al speculate (SCIENCE NEWS, "Ribbon of Chaos," January 26, 1991), that just small disturbances can radically alter a chaotic system's behavior--tiny adjustments can also stabilize their behavior.

The success of this strategy for controlling chaos hinges on the fact that the apparent randomness of a chaotic system is really only skin deep.  Beneath this chaotic unpredictability hides an intricate but highly ordered structure--a complicated web of interwoven patterns of regular, or periodic, motion.

Physicists from the Naval Surface Warfare System in Silver Springs, Maryland, have succeeded in experimentally controlling chaotic behavior in a magnetic ribbon.  Normally, a chaotic system continually shifts from one pattern to another, creating an appearance of randomness.  In controlling chaos, the idea is to lock the system into one particular type of repeating motion.

William Ditto reports, "We don't avoid the chaos; we stay in the chaotic region.  We take advantage of the system's sensitive dependence on initial conditions."  The trick is to exploit the fact that a chaotic system already encompasses an infinite number of unstable, periodic motions, or orbits.  That makes it possible to zero in one particular type of motion, or periodic orbit, or to switch rapidly from one type of motion to another.

In the past, most scientists and engineers considered a chaotic system's extreme sensitivity to initial conditions as something to be avoided.  To ensure that, say, a chemical reaction or a bridge would function reliably and predictably, they tried to design systems that shunned chaos.

However, chaos may offer a great advantage, allowing system designers greater flexibility and making possible systems that adapt more quickly to changing needs.  The Maryland researchers write, "In particular, the future state of a chaotic system can be substantially altered by a tiny perturbation.  If we can accurately sense the state of the system and intelligently perturb it, this presents us with the possibility of rapidly directing the system to a desired state."

If physical and mental states are analogous, imagine what this might mean in terms of therapeutic intervention.  In fact, it is the theory of all therapeutic intervention, but in practice the effect is unpredictable, both in occurrence and change over time.  Psychologist used to conjecture that one third of clients get better, one third get worse, and one third stay about the same.  This formula is debatable, but the healing powers of placebo and normal recovery with time of many ailments are commonly recognized.  Understanding the therapeutic nature of chaos might increase positive results.

CHAOS AND PERCEPTION

Walter J. Freeman (U.C., Berkeley) is the pioneer in applying chaos theory to perception and the interface between sensory-motor information and brain patterns.  He says, "the brain transforms sensory messages into conscious perceptions almost instantly.  Chaotic, collective activity involving millions of neurons seems essential for such rapid recognition." (SCIENTIFIC AMERICAN, February, 1991).

In other words, "brains make chaos in order to make sense of the world."  He has created a new physiological metaphor, where chaotic behavior serves as the essential ground state for the neural perceptual apparatus.  He proposes a mechanism for acquiring new forms of patterned activity corresponding to new learning. (BEHAVIORAL AND BRAIN SCIENCES (1987) 10:2).

Researchers speculate that chaos underlies the ability of the brain to respond flexibly to the outside world and to generate novel activity patterns, including those that are experienced as fresh ideas (also fresh behavior, emotions, belief systems, mythologies, etc.).  Chaos results in meaning-laden perception, a gestalt, that is unique to each individual.  Chaos is implicated in human perception as a multi-sensory phenomenon.

The controlled chaos of the brain is more than an accidental by-product, like "putting your brain in neutral."  Indeed, it may be the chief property that makes the brain different from an artificial-intelligence machine.  One profound advantage chaos may confer on the brain is that chaotic systems continually produce novel activity patterns.

The ability to create activity patterns may underlie the brain's ability to generate insight and the "trials" of trial-and-error problem-solving.  These chaotic patterns have been documented in the olfactory system.  This is the system most efficient for recalling a memory gestalt.

Just recall how an old familiar scent can bring memories flooding back.  Gamma bursts across large cortical regions involved in recognizing visual images have also been found.  Brain patterns are identical whether experiences are imaginal or real-time.  The stimulation to the visual cortex is identical.

In neuroscience, a new paradigm for the general dynamics of perception is emerging.  The brain seeks information, mainly by directing an individual to look, listen, feel, and sniff.  The search results from self-organizing activity in the limbic system (that part of the brain that includes the entorihinal cortex and is thought to be involved in emotion and memory).

It funnels a search command to the motor systems.  As the motor command is transmitted, the limbic system issues what is called a reafference message, alerting all of the sensory systems to prepare to respond to the new information.

And respond they do, with every neuron in a given region participating in a collective activity--a burst.  Synchronous activity in each system is then transmitted back to the limbic system.  There it combines with a similarly generated output from the other sensory systems to form a GESTALT.

Then, within a fraction of a second, another search for information is demanded, and the sensory systems are prepared again by reafference.  Excitatory inputs at synapses generate electric currents that follow in closed loops within the recipient neuron toward its axon, across the cell membrane into the extra-cellular space and, in the space, back to the synapse.

The existence of chaos affects the scientific method itself.  The classic approach to verifying a theory is to make predictions and test them against experimental data.  If the phenomena are chaotic, however, long-term predictions are intrinsically impossible.  Chaos demonstrates that a system can have complicated behavior that emerges as a consequence of simple nonlinear interaction of only a few components.

The ability to obtain detailed knowledge of a system's structure has undergone a tremendous advance in recent years.  Yet, the ability to integrate this knowledge has been stymied by the lack of a proper perceptual framework within which to describe qualitative behavior.

The interaction of components on one scale can lead to complex global behavior on a larger scale that, in general, cannot be deduced from knowledge of individual components.  Chaos may provide the possibility of putting variability under evolutionary control.

Even the process of intellectual progress relies on the injection of new ideas and on new ways of connecting old ideas.  Innate creativity may have an underlying chaotic process that selectively amplifies small fluctuations and molds them into macroscopic coherent mental states that are experienced as thoughts.

In some cases the thoughts may be decisions, or what are perceived to be exercise of WILL.  In this light, chaos provides a mechanism that allows for FREE WILL within a world governed by deterministic laws.  In other words, Newton's laws are only local ordinances.  Chaos suggests causal relationships where none were previously suspected.

Studies have discovered chaotic activity in the brain.  Chaos is evident in the tendency of vast collections of neurons to shift abruptly and simultaneously from one complex activity pattern to another in response to the smallest of inputs.

In healing terms, this implies that ONE TRAUMATIC EVENT CAN SHAPE A LIFE; ONE INTENSE THERAPEUTIC EVENT CAN RESHAPE IT.  Trauma can create a large disturbance both immediately and exponentially over time.  Healing spreads out through the individual life like ripples on a pool of water.  This changeability is the prime characteristic of many chaotic systems.  It is not harmful to the brain.  In fact, it may be the very property that makes perception possible.

Consciousness may well be the subjective experience of this recursive process of motor command, reafference and perception.  If so, it enables the brain to plan and prepare for each subsequent action on the basis of past action, sensory input, and perceptual synthesis.

In short, an act of perception is not the copying of an incoming stimulus.  It is a step in a trajectory by which brains grow, reorganize themselves and reach into their environment to change to their own advantage.  Consciousness is not confined to the ordinary state of awareness.

Dreams (and other non-ordinary states) can be used for healing by employing the imagination to create new realities within the psyche which facilitates multi-state education.  This learning can supercede physical history, according to the "changing history" principle of NLP, (Neurolinguistic Programming), wherein a reiteration of past trauma is reprocessed and supercedes the historical version.

The latest dream research has shown that DREAMS HELP US LEARN.  Tasks performed or information gleaned during the day are assimilated into long-term memory during dreams.  Researchers found that those whose dreams were interrupted experienced more difficulty in absorbing what they learned that given day.  The same holds true if what is learned comes through dreamhealing.

The poet William Blake wrote:  "If the doors of perception were cleansed every thing would appear to man as it is, infinite."  Such cleansing would not perhaps be desirable.  Without the protection of the doors of perception -- that is, without the self-controlled chaotic activity of the cortex, from which perceptions spring -- people and animals would be overwhelmed by infinity.  The lack of external driving means the activity is self-generated.  Such self-organization is characteristic of chaotic systems.

Chaos theory is based on the mathematics of nonlinear dynamics.  But it is also a set of attitudes toward complexity--a new way of seeing, that moves from fragmentation toward integration.  It evolved through the discovery of strange attractors (remember, the cosmic principle of attraction, Eros).

Strange attractors can even be plotted in free will, as we have discussed.  The concept of free will as a strange attractor brings up philosophical and theological implications.  Again, it presents a different relationship than a mechanistic model between human beings and the Higher Power.

Chaos theory does suggest that God, in the forefront of science as usual has outstripped us once again.  This is less surprising than you might suppose: science of late, arcane sub-atomic physics in particular, has begun to implicate a higher presence.  The second coming may arrive as fractal geometry on some lab computer screen.  That our universe is irrational and unjust has long been a forceful argument against the Higher Power's existence.  Yet all the randomness we perceive from Big Bang through Big Whimper may, in fact, contain secret, huge rhythms of creation and destiny.  There can be no more tremendous paradox -- suitable to an omnipotent creator -- than order-from-chaos.  No: ORDER-IN-CHAOS.

So even chance--still obstinate, still anarchic--is not incompatible with divine arrangement.  We have begun to apprehend a new description of certainty.  It may have all the traits that characterize disorder and yet be under law, and those who ask, "How can God exist when there is chaos in our universe?" may have answered their own questions.

Research on the chaotic brain is yielding new models of behavior.  Nonlinear dynamics is being used to focus on overall patterns of behavior, describing how stable or unstable they are and pinpointing the circumstances that make them change.

Results are showing that changes in patterns of electrical activity in the brain are linked to changes in behavioral states.  What we used to consider as meaningless background noise, output of large groups of nerve cells in the brain, are evidently quite meaningful.  They just contain so much information, it blurs together and looks like no coherent message.  Our perceptions can't decode it because they respond through an all-or-nothing relay system.

For a complementary approach to chaos in the brain, see Karl Pribram's BRAIN AND PERCEPTION, 1991.  He speaks there of a theory of nonlocal cortical processing in the brain, and the geometry of neurodynamics.  But Pribram is now exploring chaos, as his attendance at the first conference on psychology and chaos theory in 1991 shows.  We can eagerly await his conclusions.

NEUROANATOMY AND CHAOS

World famous researcher, E. Roy John  [Brain Research Lab, New York University Medical Center] has edited the definitive book on the MACHINERY OF THE MIND (1990).  It includes integrative processes, strange attractors and synchronization, cognitive functions, visual information processing, human development, and brain imaging.  All are related to chaos theory and the hardwiring of the brain.

Neuroscientists have dissected the brain minutely defining all structure.  They have charted the wetware circuits of nerve pathways and identified some 60 neurotransmitters.  But they could never explain the synergistics of an emotion, idea, act of will, or consciousness itself.

Mathematical metaphors help us visualize the bigger picture.  Chaos theory has led to the discovery of amazing variations among vast collections of neurons.  This is one application of chaos theory, since nonlinear equations can describe many phenomena from the subatomic to cosmic level.

Nonlinear phenomena are sustained by complex loops of feedback in which the outcomes of initial inputs are diverted back into the system at unpredictable points in its cycle.  This certainly bears on many aspects of perception, consciousness, and personality.  In the cult film, EAT THE SUN, the Videru Telemahandi teaches that, "The ecology of the soul is to recycle one's consciousness."

The body uses complex feedback loops to maintain biochemical balance.  These "biological oscillators" lead to reactions which reveal nonlinear dynamics.  The structure emerges around a strange attractor, and the system may vacillate erratically, but it always stays within a bounded range or norm.  The boundaries are strictly defined mathematically, but within the chaos is apparent method in the madness.

PERSONALITY TRAITS AS STRANGE ATTRACTORS

Chaos is not total randomness, but implies an implicate, "hidden", or occult order within the nature of reality.  The strange attractor construct of chaos theory offers a new way to think about personality.  It is exceptionally difficult to predict the specific behavior of an individual, yet if we know a person, his or her behavior seldom suprises us.

The observation that personality varies within limits may be understood within the context of chaos theory.  Specifically, the strange attractor construct is proposed to account for nonperiodic, nonrandom order.

Understanding and predicting human behavior remains a fundamental goal of psychology.  Personality theory developed for this reason.  Yet, accurate prediction of behavior continues to elude personality researchers.

Chaos theory provides a framework within which the puzzling inconsistency of traditional measures of personality can be understood.  The consistency may be there, but in nonlinear form under the guise of the strange attractor's "hidden order."

Personality is inferred from behavior and personality consistency refers to similar behavior in similar situations (cross-situational consistency) and/or similar behavior over time (temporal consistency).  Consistency, here, simply refers to the repeated presentation of the same or similar behavior.

Some theories of personality stress static or stable traits, while other emphasize states or psychodynamics.  Others find that traits and states are virtually indistinguishable and consider the distinction arbitrary.

Regardless of whether personality is governed by characteristic dispositions (traits) or an intrapsychic balance of forces, the effect upon observed behavior is the same; that is, stable internal factors generate behavioral continuity.

The person's interpretation or "mental representation" is his "true situation," not the actual external environment.  Our intuitive belief in the consistency of personality may be derived from a real, but nonlinear, order underlying human behavior.  It forms the basis of self-simulation moving through time.

There is a nonlinear influence in negative feedback the organism perceives.  It molds behavior.  Chaos theory provides tools for identifying complex, nonlinear relationships.  Behavior is variable, but always within the limits and ranges set by the person's structure itself.

Unpredictable variation within limits sounds very much like the operation of a strange attractor.  Chaotic systems have a sensitive dependence on initial conditions.  For humans this means, any perturbation from conception onward can be a determining factor in structure and personality.

If personality or personality traits function as a strange attractor of behavior, then correlations of behavior over time would not be expected to be very high.  Exact behavior would be unpredictable from moment to moment, but would remain within loose boundaries--those of the strange attractor.  All potential behavior would not have an equal probability of occurence.

In contrast, if behavior were random, then every possible behavior would have an equal probability of occurence at any given time.  It would not be surprising to discover that personality traits can be construed as strange attractors of behavior.  Natural chaos allows adaptation and self-organization so it is an evolutionary advantage.

Sensitive dependence on initial conditions ensures that long term prediction of human behavior remains unattainable.  Prediction within limits, as probabilities of certain behaviors, may be possible based on the strange attractor characterizing the personality or personality trait of an individual.

One may have a particular personality trait that seems to operate like a strange attractor at one time, but later the trait enters a phase of periodicity.  Also, types of attractors may differ from trait to trait within a particular individual.

Research may reveal that assessments of personality or a personality trait over time generate data that leads to a fractal correlation dimension.  Such evidence would confirm that personality or that a particular personality trait may be desribed as a strange attractor of associated behavior.  Essentially, the same statements can be made for dynamic states of consciousness, if states and traits are interchangeable.