Ionasphere's Chaos Theory Intro

The Ionasphere, ©2001

CHAOS THEORY

Chaos Theory and Complex Dynamical Systems: Consciousness and Healing, (©2001)
Chaos Consciousness and Healing, (from Dreamhealing, ©1992)
Human Dimensions of Chaos Theory, (from Dreamhealing, ©1992)
Chaos As the Universal Solvent, (©1993)
Chaos Theory and Jung's Psychological Complexes, (©1993)
Self-Organization in Biological Systems: Chaos and Antichaos, (©1993)
Dreaming and the Self-Organizing Brain: David Kahn, Stanley Krippner, and Allan Combs

Links:
CHAOSOPHY JOURNAL, Iona Miller, Editor: http://www.oocities.com/iona_m/
Society for Chaos Theory in Psychology and Life Sciences: http://www.societyforchaostheory.org
Asklepia Foundation: Chaos, Consciousness, and Healing:http://asklepia.org
DynaPsych, Ben Goertzel: http://www.goertzel.org/dynapsych/
Brief Intro to C.T.: http://www.imho.com/grae/chaos/chaos.html
Chaos and Fractals: http://www.mathjmendl.org/chaos/

Chaos Theory describes the behavior of non-linear dynamic systems, fractal geometry, and the complex, systematic behavior of nature as well as our nature, consciousness and health.  It describes in eloquent equations deterministic ordered randomness, dimensionality, reflexive feedback loops, boundary conditions and integration.  It is the realm of the irrational, paradoxical, of rich values and structure, self-generative and self-iterating, of self-organizing (autopoietic) emergent creativity, stretched time and folded space, inherent unpredictability, yet boundaried and geometric.  The domain of global behavior, open systems, criticality, sensitive dependence, strange attractors, fluctuations, turbulence, perturbations, thresholds, trajectories, bifurcations, phase transitions, temporal density, reiteration, synchronicity, resilience, the "butterfly effect," subquantal chaos (ZPE), dynamic geometrization, probability, relativity, disruption, coherence and stochastic resonance, synergetics and tensegrity, self-reflection, nested cycles, the breakdown of order with sudden transitions, the creative and evolutionary "edge."  Chaotic systems are apparently acausal, inherently qualitative, sustained by complex feedback loops, and disproportionately responsive.


CHAOS THEORY & COMPLEX DYNAMICAL SYSTEMS
Its Emergence in Human Consciousness and Healing

Iona Miller and Graywolf Swinney, ©2001

Yea verily, I say unto you
A man must have chaos yet within him
to birth a dancing star.

--Nietzsche

To this day God is the name by which I designate all things which cross my willful path violently and recklessly, all things which upset my subjective views, plans and intentions and change the course of life for better or worse.

--Carl Jung, 1961

Chaos Theory and CDS are multidisciplinary approaches employed in divers fields from physics to sociology, from neuropsychology to engineering. Spontaneous self-organizing dynamics is the non-linear basis for a rigorous alternative to linear, reductionistic thinking.  As such, it heralds a rebirth of science.

Fractal Art, the result of graphically displaying the elegant mathematical descriptions of Chaos Theory, shows us the hidden infinity of forms and structures which unfurl from the infinity of possibilities that mirror and duplicate the shapes unfolding in nature within and around us.  Fractals emerge from attractors.  An attractor is simply the characteristic behavior of a dynamical system changing over time.

animated fractal: vclutq.gif
Image by J.C. Sprott
http://sprott.physics.wisc.edu/fractals/vclutq.gif

The holistic mind is a complex dynamical system, (CDS).  The language of CDS and Chaos Theory is now revealing a point-of-view, or metamodel, which provides a universal language for psychology which is competent to deal with the complexities of interactive change and yet is relatively easy to communicate.  The holistic unity involves phenomenology, mind, brain, behavior, and environment.  The dynamical systems' point of view extrapolates a worldview: healing emerges by immersion in the undifferentiated state of chaotic consciousness and emerges via creative self-organization.

Degree of awareness is related to the magnitude of attractors.  Jumps in magnitude result in jumps in awareness.  Attractors of the mind may undergo subtle bifurcations or splits among possibilities.  Bifurcations occur when a system rests right between two attractors.  A tiny change in the system's state can then push the system in one direction or another.  For example, the transition from one state of consciousness to another is represented as a sudden or dramatic jolt which knocks the system out of its attractor, and leads it along a trajectory toward another attractor.

Shapes and patterns emerge from the mysterious infinity of chaos.  This is also true of the images which can be observed in our stream of consciousness.  Sudden shifts in awareness arise from the suddeness of bifurcations in nonlinear dynamic systems.  These forms reach deep inside, resonate with our spirit and foster a sense of connection.

In Chaos Theory, forms emerge, dissolve, and reform through the creative process known as autopoietic self-organization.  It demonstrates the unfolding of creative process itself, the emergence of form or structure from formlessness and chaos.  Strange attractors, principles or forces that interact with complexity, are hybrids with roots in both chaos and structure which influence and shape the emergent structures.

Chaos is ubiquitous in nature, hidden in the most ordered and solid-seeming places.  It is found in the following dynamical processes, and more:

* In the eloquent blueprint of dynamic behavior, pure spontaneity, thresholds, beginning with the choatic fluctuation of Zero-Point Energy (ZPE) underlying the formation of all matter/energy;

* in emergent patterns, connectivity, diversity, the self-assembly rules of nature, beginning with the structure of the atom and its particles/waves, to molecular collectives and permeating organic and inorganic matter;

* in the universal set of building rules, networks, events, coherent wholes, dimensional embedding, and the synergetic achitecture of life and biological organization from simple carbon compounds to complex cells and tissues, adaptability;

* in the guided design of organic structures, viability, from the unfolding of genetic patterns to tensegrity and cytoskeleton geometry, to microtubule assembly in nerves, to the rhythms of a beating heart and the flow of blood through it, global behavior;

* in global behavior and the dynamical system of the mind, panpsychism, psychological complexity, sentience and emergent properties, pattern recognition, genesis of intelligence, reality discrimination, raw awareness, attention, meaningfullness, perception-cognition loops, refocusing, creative inspiration, consequences, memory, self-sustenance/structure maintenance, perceptual chunking, time distortion, point of view/relativity, significance/correspondence (beliefs, concepts, attitudes, emotions, behavior), attributions, restructuring, adaptive learning, spontaneous healing;

* in the complex interactions of the neural firing patterns of our brain, and the dynamics of thought especially during dreaming, creative imagination, connectivity, even enlightenment--the biology and psychology of consciousness itself with its tightly knit fabric of subprocesses;

* in the infinite complexity of recurrence in wilderness and natural phenomena, such as the hierarchichal organization of tiers within tiers of systems within systems, and evolutionary adaptation;

* in the primordial elemental turbulence and churning complexity of white water, fire, air, and even earth as well as the quintessence, plasma;

* in the formation and motion of the planets and their path around the sun;

* in the scattering complexity of the stars and galaxies, and the moment of the Big Bang, from which the universe emerged, in the acceleration and expansion of spacetime from vacuum fluctuation.

Wherever we look, from the Microcosm to the Macrocosm, the sub-quantal to the Cosmic, chaos or non-linear dynamics and complexity is either right in sight or hidden just below the surface.  Notions of form, pattern, geometry and structure an be found at the deepest levels of both matter and the psyche.  Its domain lies at the edges of knowledge where our perceptions of structure and order end.  Yet chaos reveals in its own depths, hidden degrees of order and structure that resonate with the soul and reveal to us the basic forms and structures repeated throughout nature and throughout our nature.  Topology and geometrical relationships are a more fundamental way of understanding both matter and consciousness.

Chaos Theory underlies the fundamental laws of nature and natural processes, and implies a universe of evolution and constant re-creation.  Structure arises in the moment and is in resonance with its environment.  But in a universe of constant evolution each form eventually becomes dissonant as the evolving environment surrounding it changes.

Chaos Theory restores the balance to the entropic forces which lead to the decay and death of outworn systems.  It is the means of creative self-organization which arises from the undifferentiated disorder that lurks within the processes of creation.  Chaos holds infinite possibilities of new form, and these forms are eventually revealed and emerge from chaos as new structure.  This is also an apt way to describe consciousness dynamics, such as thought, spontaneous behavior and creativity.  Reality is neither structure nor chaos, but a process in which structure and chaos dance between form and formlessness.  This is the eternal cycle of death and renewal, the dance of Shiva.

When there is an intrusion or perturbation in a system, centers of dynamic activity are set in motion within the whole system which attract more and more energy toward themselves like mini-blackholes.  Such systems are known in Chaos Theory as "strange attractors."  In chaotic systems, time is "stretched and folded" so that events ostensibly separated in time and space are intimately linked in a non-linear way.

Under the pressure of constant evolution, each form is constantly stressed by the evolving environment toward beginning a process of its dissolution back into chaos.  Periodic chaos purges the old dissonant structures that impede the flow.

A dynamical view emphasizes interconnectedness and self-organization.  Self-organization creates new information in a dynamical system with the development of increasing complexity.  There is growth potential in the self-control of bifurcations to novel attractors.  Anyone can learn to make choices to empower their future and develop new skills, to inhabit new attractors, to explore conjectured attractors, and make informed choices concerning potential trajectories, to affirm and create self.  In complex dynamics, divergent features are perceived as being as important as convergent features.

There are also gradual changes in degree of awareness and the amount of energy expended in a particular process.  In general, the expansion of an attractor requires that more energy be devoted to it; increased forces increase the magnitude; shrinkage of the attractor is accompanied by the lessening of energy requirements by the system.  In Chaos Theory, the notion of psychobiological stability has been considerably liberalized to include psychobiological periodic and chaotic attractors.

Ben Goertzel describes the process of transformation of consciousness in a complex dynamical system--the mind:

“Psychological structures make no sense considered statically; they have to be considered dynamically, as “attractors” of systems that change over time.  There are three kinds of attractors.  There are fixed-point attractors, i.e. equilibrium system behaviors, in which a system does not change over time.  There are periodic attractors, i.e. cyclic system behaviors.  And there are strange attractors -- a grab-bag category covering everything that is neither unchanging nor periodic.  Strange attractors are often chaotic, in that, once a system is locked into a strange attractor, its behavior cannot be predicted in any detail.  But, nevertheless, strange attractors need not be “random,” they can be intricately structured.”

“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.”

Fear of chaos manifests as ontological anxiety or existential dread, a fear of being, a feeling there is no meaning in life; since nothing makes sense, why go on?  Overcoming the anxiety and depressions of contemporary life requires a drastic change in attitude about what is important and what is not.

We can learn to enjoy and find meaning in the ongoing stream of experience, in the process of living itself.  Experience depends on the way we invest psychic energy--on the structure of attention.  This, in turn is related to goals and intentions.  These processes are connected to each other by the self, or the dynamic mental representation we have of the entire system of our goals.

This process is complex, and the notion of complexity is related to the same concept as used by some evolutionary biologists and also described with poetic insights.  Its essence in terms of the psychology of the self is that a complex person is one whose behavior and ideas cannot be easily explained, and whose development is not predictable, but is autopoetic, that is self-organizing emergent order.

Order in consciousness is experienced as flow, optimal experience, healing experience.  Following a flow experience, the organization of the self is more complex than it had been before.  It is by becoming increasingly complex that the self might be said to grow.  The flow state facilitates both differentiation and integration.  The old alchemists used to say, “Only that which has been properly separated can be rightfully joined.”

Complexity also facilitates the integration of autonomous parts.  After each episode of flow a person becomes more of a unique individual, less predictable, possessed of rarer skills.  The complex self is more likely to avoid both selfishness and conformity.

“The self becomes complex as a result of experiencing flow.  Paradoxically, it is when we act freely, for the sake of the action itself rather than for ulterior motives, that we learn to become more than what we were. . .Flow is important both because it makes the present instant more enjoyable, and because it builds the self-confidence that allows us to develop skills and make significant contributions to humankind.” (FLOW; Csikszentmihalyi, 1990).

Flow helps us to integrate the self because in that state of deep concentration consciousness is unusually well ordered.  Thoughts, intentions, feelings, and all senses are focused on the same goal.  Experience is in harmony.  And when the flow episode is over, one feels more “together” than before, not only internally but also with respect to other people and the world and cosmos in general.

THE EDGE OF CHAOS

Chaos and Order are two sides of the seamless fabric of Reality.  New order emerges from the deterministic, self-organizing properties of chaos.  Once known as Chaos Theory, the dynamics of systems far-from-equilibrium, the emerging science at the edge of order and chaos is now known as Complexity, or Complex Dynamic Systems (CDS).  Complex, self-organizing systems, and human beings are certainly among them, are characterized as being adaptive.  The ability of a system to move in and out of chaos gives it the greatest creative advantage.

Spontaneous self-organization, or autopoeisis, is a creative, emergent property of chaos, and expresses synchronicity and serendipity.  The very richness of multiple levels of observable interaction, fractal reiteration, allows the system as a whole to undergo spontaneous self-organization.  Thus some genes in a living embryo become nerve cells and other muscle tissue, or bone.

Organisms constantly adapt to the environment and to each other through the self-unfolding of emergent properties--creative evolutionary adaptations.  They actively try to turn what happens to their advantage.  Darwin didn't know about self-organization, matter and life's incessant drive to create order from chaos even in the face of the dissolving ubiquity of the second law of thermodynamics--entropy.

Complex systems, are spontaneous, disorderly and more alive because of it.  The "edge of chaos" is a special balance point in dynamical systems where components never quite synch but also never quite dissolve into total turbulence either.  It is a constantly shifting zone between stagnation and anarchy and spontaneous adaptability.

There is order even in disorder.  There is order, manageable chaos (fractals), and unmanageable chaos.  The fractal dimension expresses the complexity of a particular fractal form.  "Fractal" comes from the Latin fractus, which means broken or fragmented.  Fractals delineate a whole new way of thinking about structure and form.

Magnify a fractal again and again and more detail emerges from its infinitely embedded structure.  The same self-similar pattern repeats, over and over, no matter what level you care to examine.  A single image is infinitely reiterated.  Thus, a wealth of structure emerges from simplicity.

Tiny variations are amplified on every bounce in Chaos Theory through the phenomenon of the "butterfly effect."  When changes approach the catastrophic level, bifurcation, the whole system reorganizes in a cascade.  Thus chance fluctuations can be blown up into gigantic proportions, and change becomes stability.  If a system is in a stable attractor state, small imbalances at a point in the system will tend to be damped out by the fluctuating of the system as a whole.  If it is in such a state, small imbalances at any juncture will be maintained or amplified.

If we look at the "edge of chaos" which self-organizing systems naturally evolve toward, we find four basic principles, as outlined by Stuart Kaufmann (Sci Amer, Jan, 1993):

1)  A system goes through a phase transition from order to randomness if the strength of the interaction between interconnected agents is gradually increased.

2)  A system can perform the most sophisticated computation at the boundary between order and randomness.  Adaptive agents can develop good solutions to extraordinarily difficult problems.

3)  Complex adaptive systems tend to evolve toward the boundary between order and chaos.

4)  Organisms change how strongly they interact with others in such a way that they reach the boundary between order and randomness, thereby maximizing the average fitness of the organisms.

There are certain fundamental characteristics of chaotic systems and each has its analogy and application to the nature of human consciousness and therapeutic treatment in consciousness journeys facilitating the natural healing process.

Sensitivity to initial conditions.  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.  Sensitive dependence on initial conditions means similar causes do not produce similar effects.  Disease is a crisis that is presented to an organism that creates the opportunity to dissolve the old structure and evolve into a new one, better adapted to survival.  We are not limited to any specific technique or practice for healing, but use a deeper understanding of the nature of the healing process itself to create whatever technique is needed for the client at whatever level we are working.

Butterfly effect.  A variance so small it is almost insignificant in the beginning can create vast differences as the system evolves, making it impossible to track or predict.  In the Consciousness Restructuring Process of natural healing, just as one traumatic incident may pattern a lifelong disorder, one healing therapeutic event may completely and permanently restructure the whole system from the most fundamental level.  After a bifurcation there can be no return to the old situation.

Fractal Embedding.  A fractal is an object that reveals more and more detail as it is increasingly magnified, like seeing the universe in a grain of sand.  Self-similarity repeats its conformations from the most fundamental to the most complex level. In CRP, the disease image appears in a myriad of self-similar forms revealed through the levels of the consciousness journey.  One traumatic event can shape a life; one intense therapeutic event can reshape it.

Strange Attractors. Investigation of the mechanism of turbulence led to the invention of the term strange attractor. The turbulence that is described by strange attractors is “turbulence in time” -- deterministic chaos, or temporal chaos.  Graphic depictions of attractors allow us to map a dynamical system’s behavior in discreet-time or phase-space.  Roughly speaking, an attractor is what the behavior of a system settles down to, or is attracted to.  A system may have several attractors.  Strange attractors are the core of unpredictable variation with limits.  For humans this means any perturbation from conception onward can be a determining factor in structure and personality.  Personality traits can be construed as strange attractors of behavior.  Natural chaos allows adaptation and self-organization for evolutionary change.

Bifurcation.  Amplifying a situation, intensifying it, leads to de-stabilization.  This leads to a phase transition; phase instabilities or turbulence in a system lead to the possibility of bifurcations.  Near bifurcation, systems present large fluctuations.  Such systems “hesitate” among various possible directions of evolution.  Even 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.  Healing is an ever-present potential.

The Edge of Chaos.  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.  Chance plays its role at or near the point of bifurcation, after which deterministic processes take over once more until the next bifurcation.  Thus, nonequilibrium, the flux of matter and energy, is a source of order.  The highest mean fitness is at the phase transition between order and chaos.  Complex adaptive systems adapt to and on the edge of chaos.  In CRP all the action lies in going just beyond the boundary from the known and comfortable into the fear, pain, and challenge.

Chaotic Consciousness. There is a fundamental field of unstructured consciousness prior to energy or form, the bornless field.  A return in the journey to this state evokes spontaneous healing and creative self-reorganization.  At the quantum level, strange attractors influence the emergence of consciousness and its interactions with other fields to create the essence of self and external reality.  In Bohm’s model, consciousness can be either enfolded as potential structure or a field, or it can be manifested or unfolded as structure in the space-time universe.  In enfolded or potential form, it is outside of space-time reality.

Autopoietic self-organization; creativity and self-actualization.  Human EEG shows significant fractal structure, suggesting the brain inherently resides in a state of self-organized criticality, where a small stimulation can set it into fluctuation where the response distribution is fractal.   In CRP therapy, small changes in this process result in whole person changes in a healthier direction.  This process is creative; healing is biological creativity. Freud made the discovery that when man could overcome his fears, face his pathology, and seek to comprehend it, he grew healthier.  Rollo May was among the first to carry this insight further: when we willingly choose to face our being in the same manner, seeking to comprehend it, allowing awareness of its terrors, passions and transiency, we become most truly human and self-actualized.

Emergence.  Central to any understanding of consciousness and the brain, emergence is a process by which order appears “spontaneously” within a system.  When many elements are allowed to mingle, they form patterns among themselves as they interact.  When the mind lets go of its rational order and enters into unstructured chaos it emerges later with a new structure.

Placebo Effect.  Medicine is just beginning to use the mind-body connection for healing.  By giving a dummy drug at least 30% of patients experience the same pain relief as with true painkiller.  The same pain-killing “pill” can stop gastric secretion in ulcer patients, lower blood pressure or fight tumors, for instance.  But this effect requires no “pill” to initiate spontaneous healing; the pill itself is meaningless.  The body has the ability to produce any biochemical response once the mind has been given the appropriate suggestion, which is converted into the body’s intention to cure itself.  We can bypass the deception of the sugar pill and directly to the intention, (Chopra, 1989, 1993; Weil).

Dreams/REM.  Dreams are complex dynamic systems; they embody the very nature of chaos. They are uncensored messages from the twilight zone of chaos-order and communicating with us at the most basic sensory levels imaginable.  Dreaming reflects a pivotal aspect of the processing of memory, and helps us form strategies for survival and adaptation.  They are complex, incorporating self-image, fears, insecurities, strengths, grandiose ideas, sexual orientation, desire, jealousy, and love.  Their unusual character is a result of the complex associations that are culled from memory.  When the mentored recalls a dream thread, it facilitates reentering REM for the rest of the journey.

Chaos Theory and Healing

Graywolf describes Chaos Theory and its relationship to healing in his new book, Holographic Healing (©2001).

In the early sixties at MIT, a physicist-mathematician Edward Lorenz was commissioned to utilize the new computers entering into our culture in an attempt to model weather patterns in order to make possible better long-range weather forecasts.  He failed, but as is often the case in science, noticed some interesting things in this failure.  He noted that the factors that create weather are very complex and intricately interrelated and that systems that are this complex are extremely sensitive to even the tiniest variations in initial conditions.  A variance so small it is almost insignificant in the beginning can create vast differences as the system evolves, making it impossible to track or predict.

In essence he defined the butterfly effect, one of the better known principles of Chaos Theory.  It states that air perturbations caused by the fluttering of a butterfly’s wings in Kansas can, in the complexity of factors affecting weather, hypothetically result in a typhoon in Indochina.  He in essence demonstrated that long-range weather forecasting was impossible and for this reason, his data and speculations lay dormant and obscure in a journal paper.  But it is just such failures that often open the cracks to later scientific advances, and this one set the stage for Chaos Theory.

The old story about "For the want of a nail, the horseshoe was lost. And for want of the horseshoe the horse was lost . . . " is a message to pay attention to details.  Perhaps, however, the real power of the story has more to do with the intricacy, interconnectedness and complexity of things and the butterfly effect.

Although obscure, a number of mathematicians and scientist from fields as diverse as biology, chemical engineering, demographics, and those studying stock market and futures price variations and trends, began exploring this chaos theory.  Although operating on the fringes of science, they became convinced that this new study of non-linear dynamics had much to offer to our understanding of how many reality phenomena operate, for example stock market or futures variations.  Indeed the realization gradually began to emerge that a new science was being birthed.

A major step happened in 1980, when a mathematician at Bell Labs named Mandelbrot, was using computers to explore the mysteries of indeterminate or non-linear equations.  These equations do not have a discrete solution, but instead create an endless string of non-repeating numbers, or have an infinite number of solutions. Pi is an example of the first type.  It is the ratio of the circumference of a circle to its diameter. The solution is a value of 3.1417 . . . but the numbers that follow the decimal stretch on to infinity yet never in any observable pattern.

By applying simple repeated reiterating mathematical operations to such non-linear equations, plotting the results in graphic form using the speed and patience of newer computers, he discovered that complex and beautiful geometric shapes began to emerge from the complexity of the chaos in the equations.   After only a short time he felt very familiar with these patterns at deep levels of his being. They were somehow fundamentally a part of his reality both inside and out; in his own words they were “part of his subconscious.”

This elegant form of  Mathematics is known as Fractal Geometry, and can be readily produced on the screens of computers. It is the mathematics of chaos or complexity.  Beautiful forms unfold out of the complexity, reach into infinite depths and reveal hidden patterns that repeat and repeat in a familiarity of structure and change that resonates with the soul.  The Mandlebrot set has been called the most complex mathematical structure known.

This geometry eloquently unveils the depths of chaos or as it is also known, non-linear dynamics or complexity. It produces a hidden infinity of forms and structures from the infinity of possibilities in chaos that mirror and duplicate the shapes unfolding in nature about us.  In a fractal we can watch a cloud form or a tree evolve, or discover an intricacy of shape that resembles the nervous and the circulatory systems in the human body.

If you focus in on a small segment, a tiny piece of a fractal pattern and journey deep within it, expand it, you eventually encounter the segment you entered, only it is not quite the one you entered but slightly changed.  This depth of “almost” repetition goes on into infinity, shapes ever evolving and changing.  Fractal geometry opens us to a reality of infinite beauty, depth, and complexity in which forms and shapes emerge from the mysterious infinity of chaos.  These forms reach deep inside, resonate with our spirit and foster a sense of connection, belonging, and home.

One of the author's (Graywolf) own introduction to this form of mathematics came in 1983, while it was still a relatively obscure mathematical concept:

One of my clients, when I had lived in Michigan, was a mathematics professor at a local college. We had terminated therapy when I moved from Michigan to Oregon, but he had traveled west to pursue some further work with me.  We chose to do this on a four day hiking journey on the trail that follows the wilderness section of the lower Rogue River.

While contemplating the rugged beauty of the mountains and the wild chaotic waters of the river, he told me of a new form of mathematics that was inserting itself into academic circles. “It is the mathematics of indeterminacy,” he told me, “and deals with non linear and complex phenomena.” In our further discussions of it, he went on to predict that it would affect my work in psychology and consciousness and open the doors to understanding many of the phenomena that remained unsolved in nature and human experience.  Although I did not reconnect with it for six or seven years he has proven to be correct on all counts.

However at that time neither Lorenz's, nor Mandelbrot’s nor the others’ explorations of this field really identified or fully defined the principles of chaos as a fundamental theory about how reality operates. That came in the mid-eighties.  A group of graduate students in physics became interested in chaos and wanted to explore its possibilities. As is not unusual in graduate school, they received little or no support from their academic and doctoral advisors for this unorthodox quest, who suggested they get on with the business of their dissertations and learning science and physics as it was being taught at that time. As is not unusual with graduate students they declined their advisor's advice and met beyond the confines of the university working on their own.  Eventually they formulated much of what is now accepted as chaos theory. They then invited their faculty to a presentation, which was so convincing and well staged that “Chaos Theory” was accepted and soon entered into academic physics.

Chaos theory is still very much in its infancy but it is sweeping throughout the scientific world, rapidly finding application not only in hard sciences, such as physics and chemical engineering, but also in economics, psychology, biology, astronomy, demographics, business management, . . . and on and on. It demonstrates the unfolding of creative process itself, the emergence of form or structure from formlessness and chaos. Strange attractors, principals or forces that interact with complexity, hybrid something's with feet in both chaos and structure influence and shape the emergent structures

In this way perhaps they reveal the faces of the creator or some may prefer the term God. In Taoist philosophy from chaos came the one, which became the two, the yin and yang from which all else is created.  In Christian cannons it is said that out of the darkness (no-thingness, implicate order   or chaos) God first created light (the quantum level of reality that is energy-matter). Once light had been created, the rest of the universe followed. Chaos is found everywhere, hidden in the most ordered and solid seeming places.

Wherever we look chaos or non-linear dynamics and complexity is either right in sight or hidden just below the surface. It takes over at the edges of our knowledge where our perceptions of structure and order end. Yet chaos reveals in its own depths, hidden degrees of order and structure that resonate with the soul and reveal to us the basic forms and structures repeated throughout nature.

Chaos theory implies a universe of evolution and constant re-creation. Structure arises in the moment and is in resonance with its environment. But in a universe of constant evolution each form eventually becomes dissonant as the evolving environment surrounding it changes. The changed surroundings stress the form and begin a process of its dissolution back into chaos.

This latter is known in conventional science as the Law of Entropy which mathematically states that all systems and structures in the universe are tending to increasing states of disorder or chaos. When I first encountered this law in my sophomore physical chemistry course in 1959, I was thrown into depression. My mind would not accept this inevitable grinding down of the universe. It was an unfinished gestalt for me that became completed only when I encountered Chaos Theory and it restored the balance by showing that within this disorder lurk the processes of creation.

Within it, chaos holds infinite possibilities of new form, and these forms are eventually revealed and emerge from chaos as new structure. This also seems an apt way to describe consciousness dynamics such as thought, spontaneous behavior and creativity. This is, in part, how my thoughts seem to emerge and operate. Reality is neither structure nor chaos but a process in which structure and chaos dance, one revolving into the other in a constant cycle of death and renewal. Much like the dance of Shiva.

The models of disease and wellness that we have identified from the CRP, illustrate these principles at work in the human experience. For example: psychologists have long debated why the same experience can result in pathology in one individual yet strengthen another and with a third pass unnoticed. New sciences provide answers. First with respect to chaos theory and the butterfly effect, humans are indeed complex systems and except in a few instances do not operate in linear fashion.

Thus minor perturbations in initial conditions can cause considerable changes in the development of the personality or system, or on the other hand may be damped out having no effect. In other words the butterfly effect. So a minor trauma at an early age in one individual, due to other small differences in the complexity of his being and experience, may heavily affect him and result in a severe neurosis. Another individual might experience a relatively severe trauma at an early age that has little or no effect on his development. In such complex systems there is no clear linear cause-effect chain. The systems interconnecting with other systems are far too complex

A variance so small it is almost insignificant in the beginning can create vast differences as the system evolves, making it impossible to track or predict.

We have noted in our explorations that the basis of every symptom of disease including psychological ones represents an attempt to resolve or heal an issue. For example from the physical side consider the symptoms of a cold. The fever and sweating, the sneezing and coughing, all force fluids throughout the organism which flushes the virus from it. The tiredness assures rest to strengthen the immune system.   Today's healing, and the structure it assumes, may define tomorrow's disease

Applying this in the field of psychology, consider also the following example. Mary, a small female child, is verbally and physically abused, yelled at and struck by her uncle one evening while her parents are out. Mary is hurt and confused by this and becomes frightened. In her mind the sound becomes a roaring stream of rage and the unexpected pain shocks her. She begins avoiding him in family situations. He is tall, skinny and has a beard. She soon begins avoiding all tall skinny men with beards. By the time she is grown, she feels faint and passes out one day while riding an elevator with a tall, skinny bearded man who has just become her new boss.

Chaos theory would suggest the following. As a small child much of her mind set was unformed potential waiting to take shape. As at the quantum-chaos level, a nothingness waiting to be sensed and give form. The shock and pain of the incident with her uncle captured her full attention and awareness, and became the perception or strange attractor that helped structure some of this unformed mind-set or undifferentiated (free) consciousness into Mary's perceptions (frame of reference) about men. It became a rather rigid consciousness and emotional structure as her organism reacted to the danger and established neural circuitry to remember the threat to her safety and well being.

These type memories are strongly retained, (not necessarily remaining in awareness,) by the organism as a sensory structure or pattern of neural firings to activate and avoid similar dangers in the future. She begins avoiding him because each time she sees him this neural firing pattern activates and she becomes frightened. It is an attempt by the organism to resolve an issue and protect itself. In a large sense it is a healing of the incident with the limited resources available to a small child. As long as the abusive uncle is in her life it is probably a useful survival behavior and attitude to have.

A structure arises out of the chaos in resonance with the existing environment.

From this point on, any sensory input that conforms to the stored structure, a smell, the appearance of a tall bearded man, or even a background sound is enough to activate the circuitry and shape her perception of the situation.  The Child’s   resolution is to flee and in the elevator this is not possible so she flees by fainting. It is embarrassing since the tall bearded man in her current world is a new vice president in her company with whom, as her boss, Mary will have many future dealings. Each time she is in his presence she feels great anxiety and so she is inclined to avoid him, but cannot do so.

It is stressing Mary and she fears losing her job and high position in her company if this anxiety cannot be relieved, because her business forces her into daily contact with him. It is expected of her. She is confused and feels great pressure to act differently and does not understand this strong aversion to him.  She might even develop physical illness and call in sick for work as a means of avoiding him. In actual fact, he is a well-liked and respected gentleman in every way, and revered by his colleagues. Mary's life, however, is unraveling. Her childhood structure is no longer serving her and in fact threatens her continued well being. She is losing sleep, her appetite is off and she's losing weight. Her life is slipping into chaos and she is in crisis.

But in a universe of constant evolution each form eventually becomes dissonant as the evolving environment surrounding it changes. The changed surroundings stress the form and begin a process of its dissolution back into chaos.

We do have a mixed relationship with complexity or chaos. My white water river running experience also illustrates it. The river, as does life, presents stretches of slow and still waters interspersed with chaotic white water of varying intensity. Among other things the aeration of the water in the rapids acts to purify it. In more general terms this may parallel the role of chaos in life.

Each set of rapids purifies the water but inspires fear because in the turbulence is danger, the boat could flip, we could get hung up on a rock, or tossed into the maelstrom, or perhaps even embrace death. But to get down the river we have to go through them. The idea is to stay in the current and avoid the obstacles. This is often easier said than done as the chaotic waters toss us around unpredictably and often control is wrested away from us by the hydraulics of the currents and tossing waves. Then inevitably we come out on the other side of the rapids, most often still in the raft, but occasionally not. As we come out the calm waters welcome us and the fear recedes. We regroup, climb back in the boat if necessary, and begin rowing again.

 But if the calm stretch between rapids is too long, we start getting bored. In its own way the rowing on still waters is just as hard in its monotony as the challenge and fear of the rapids. We only make headway with the effort of our heavy pulling on the oars. We look forward to the next set of rapids and the excitement, and welcome its challenge.

The river is the stream of consciousness that is life. It too is full of the challenges and fear of the chaos and the boredom of the stillness. Staying in the current is the journey. The periodic chaos serves to restructure our life as the rapids purify the water. It serves to purge the old dissonant structures that impede its flow from our consciousness just as the rapids eventually move the rocks that create them.

Copyright 2001, Iona Miller and Graywolf Swinney; All Rights Reserved

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