Anti-Chaos

SELF-ORGANIZATION IN BIOLOGICAL SYSTEMS
The Holistic Patterning Process of Chaos and Antichaos

by Iona Miller, ©1993

ABSTRACT:  Self-organization is an emergent property of systems and organisms, including human beings.  Chaotic dynamics governs the emergence of this new order from apparent randomness.  The deep coherence of the overall process implies hidden or missing information for holistic patterning within the apparent "noise" or randomness of chaotic processes.

"When nature must correctly respond to a sequence of events whose nature and arrival time are essentially random, then nature uses the richness of chaos to nondeterministically solve its problem, probability one.  Using direct or indirect feedback, nature uses and controls chaos to achieve its goals.  But should not this fact embolden us to accept the challenge: 'What nature can do; man can do better'? Indeed, man has already begun to use and control chaos..."

                                                                               --Joseph Ford, THE NEW PHYSICS

DETERMINISTIC RANDOMNESS

Chaos is ubiquitous in nature, and human experience.  Chaos is the source of missing information whose absence we notice when we cannot perceive the underlying order.  It is fundamental uncertainty -- Mystery -- beyond human understanding.  Joseph Ford calls it "a paradox hidden inside a puzzle shrouded by an enigma."  He calls evolution "chaos with feedback."

In amplifying the mytheme of Chaos Theory we can continue our poetic, metaphorical approach to the scientific research, finding some valuable analogies for CCP within the theory's biological applications.  Chaos permits systems to randomly explore their every dynamical possibility.  Embracing chaos through CCP offers exciting variety, richness of choice, a cornucopia of opportunities.

In far from equilibrium conditions, when the constraint is sufficiently strong, biological systems can adjust flexibly to the environment.  Deterministic randomness or chaos opens the system to novel solutions possible within the particular context.

Chance alone decides which of these probabilistic solutions is realized.  Among the many choices, the solution (selection) of "probability one" confers a historical dimension, or memory, on the evolutionary process of the organism, and affects its further evolution.

Nonequilibrium enables a system to transform part of the energy communicated from the environment into an ordered behavior of a new type--the dissipative structure--which is characterized by symmetry-breaking, multiple choices, and correlations of a macroscopic range.  Thus, complexity is born from self-organization, which arises inevitably as a consequence of the laws of physics when suitable conditions are fulfilled.

Living systems, including human beings, function definitely under conditions far away from equilibrium.  An organism as a whole continuously receives fluxes of energy (e.g. the solar influx used by plants for photosynthesis) and of matter (in the form of nutrients), which it transforms into quite different waste products evacuated to the environment.  At the cellular level inhomogeneities, inequalities and highly nonequilibrium states are the origin of processes such as the conduction of nerve impulses, glycosis, respiration, and embryonic development.

We suggest that chaotic patterning may govern embryonic development through symmetry breaking within the electromagnetic field projected by the DNA.  Within the primitive neural tube, this process creates the "blueprint" or biohologram for the organism, directing the location and differentiation of specialized tissues and organs.  For a detailed description of this notion, see "Embryonic Holography," Chaosophy '93 Journal.

Development is a transition phenomena, during which constraints in the environment give rise to new levels of organization.  The concerted behavior of large numbers of cells enables the organism to respond flexibly to a hostile environment.  (The same happens in the context of society or culture.)

Chaotic dynamics projects a coherent global patterning throughout the proximity of the organism which directs the developmental process.  Feedback loops of electromagnetic information are set up within the hollow neural tube, which subsequently manifests as the physical substratum of the nervous system.

The nonmanifest "magnetic" core of the organism functions like a "strange attractor" exerting global patterning effects.  It is analogous to the notion in physics that gravity is a basic organizing factor in the universe mediating the passage from equilibrium to nonequilibrium and enabling in this way microscopic events to manifest themselves at a global scale.

Differentiated matter is the outcome of primordial nonequilibrium.  Ordinary phase transitions are smooth, but nonequilibrium phase transitions (chaotic transitions) are discontinuous.  They can be likened to the so-called "punctuated equilibrium" of the evolutionary process, which adds the factor of self-organization to the process of natural selection.  Many of the "punctuations" of the evolutionary process are believed to be the results of environmental catastrophe.

Discontinuous transitions provide for an increased flexibility which leads to adaptability.  Thus, evolution is the marriage of selection and self-organization (Kauffman, 1991).

Microscopic events may be the basis of self-organization, but chaotic dynamics pumps up their effect into macroscopic range through correlations of states (resonance) and coherence (entrainment).  Self-organization rests on the ability of nonlinear far-from-equilibrium dynamical systems to create and sustain states of matter displaying regulatory and other remarkable properties, which would be exceedingly improbable under equilibrium conditions (stasis).

Deterministic chaotic states imply the existence of correlations in the macroscopic range, having little to do with intermolecular interaction forces.  It is a matter of correlation, rather than force.  Information is the active agent, providing the "missing information" for organismic structuring and patterning.  This global wave of information (consciousness) is responsible for the extraordinary coherence that can arise and express as self-organization.

In a sensitive system, only a relatively small amount of input information is required to reap a large quantity of output.  We can thus form an image of how order emerges in a system.  According to Nicolis (1989),

"In somewhat anthropomorphic terms, order appears to be a compromise between two antagonists: the nonlinear chemical-like process, which through fluctuations sends continuously but incoherently 'innovating signals' to the system, and the transport-like process which captures, relays and stabilizes them.  Disturbing the delicate balance between these two competing 'actors' leads to such qualitative changes as an erratic state in which each element of the system acts on its own, or, on the contrary, a 'homeostatic' fossil-like state in which fluctuations are crushed and a full uniformity is imposed.  Complexity and self-organization appear therefore to be limited on both sides by two different kinds of states of disorder."

Nonlinear physics of far-from-equilibrium systems is the physics of unstable motions, of bifurcations, of probabilistic behavior, of multiple choices, and of self-organization.  Nonequilibrium constraints and  nonlinear dynamics are ubiquitous in real-world phenomena.  It is therefore legitimate to expect that these new concepts should provide the natural framework within which certain key features of our natural environment can be investigated.

A significant aspect of nonequilibrium physics and self-organization is the emergence of new levels of description brought out by the underlying dynamics.  In the vicinity of a bifurcation point a considerable reduction of description can be achieved owing to the emergence of collective variables.

The phenomena of bifurcation is best understood by introducing the appropriate order parameter (presenting problem), rather than by arguing in terms of the entire set of variables (deep context) present in the problem.  In certain classes of dynamical systems it becomes natural to introduce a still higher level of abstraction, and speak of symbols, codes, complexity and information.

CRP is thus employed therapeutically when the participant is at a supercritical juncture which may result in either breakdown (emergency) or increased adaptability (emergence).  At the point of bifurcation, an individual can facilitate the unfolding of the emergent process through creatively cooperating with it.

By facilitating therapeutic randomness in consciousness more creative solutions become possible.  The unfolding, moment by moment patterning or unfolding of our own self experience is conditioned by degrees of freedom (or constraints) imposed by our organismic flexibility.

Through "morphing" of the situation, either creative solutions fill "the void."  Or, pathological nonsolutions lead to decay or degradation of the system as no solid ground emerges from which to rebuild new, stable dynamic order.  This creative holistic patterning is introduced into the human system through the psyche as nonmanifest, yet phenomenological images, symbols, and patterning information.

Both pathological and healthy feedback loops strengthen with each repetition through the process of iteration.  Each round or iteration deepens "the groove in the mind," which keeps the pattern going.  Intervention in pathological loops begins to break them up with chaotic intermittency until they disintegrate completely.  Due to intermittency, the old order may reassert itself periodically at unpredictable times.

Within the context of the consciousness journey, the instability of motion associated with chaos allows the system to explore continuously in state space, thereby creating information and complexity in the form of aperiodic sequences of symbols.  Being the result of a physical mechanism, these sequences are produced within probability one: the selection of a particular sequence out of a very large number of a priori equiprobable ones simply does not arise.

In a way, the dynamical system generating chaos acts as an efficient selector rejecting the vast majority of random sequences and keeping only those compatible with the underlying rate laws (ability to receive and decode information).  Equally important, the irreversibility incorporated in these laws gives rise to a preferred direction of reading and allows for the existence of attractors enjoying asymptotic stability and thus reproducibility.  Probabilistic behavior influences adaptive strategy.

Nicolis points out that,

The insertion of the symbolic concepts of complexity and information into physics achieved by chaotic dynamics establishes a highly interesting link between physical sciences on the one side, and cognitive sciences on the other.   This remarkable synthesis is likely to give rise to important advances in such areas as biological evolution or the development of computing devices.

The two mathematical concepts relevant to this process are algorithmic complexity and information.  Algorithmic complexity measures the length of the shortest description of a given (finite) sequence.  Information is considered to be maximum in sequence, from the enormous number of random sequences.  Like fractals, whose random decimal sequences are "unnameable" because they are infinitely variable, information continues to unfold detailed solutions in a sequence of nonlinear imagery.

According to Schrodinger, DNA is an 'aperiodic crystal,' which cannot be of the form in sequence.  If all random sequences of the nucleotides are equally good candidates for the genetic material, life would amount to selecting one unique event out of a tremendously large number of possibilities.  The a priori probability of such a selection would be completely negligible.

What is needed therefore, is a process capable of producing with high probability a complex, information-rich aperiodic sequence of states.  Moreover, this system should be stable (in the sense of reproducibility) and asymmetric (in the sense of a well-defined direction of reading, as observed in present-day DNA).  Similar reasoning holds for brain activity, the structure of a language, and most probably for music and other forms of art.

As Nicolis puts it,

Now, the self-organized states of matter allowed by non-equilibrium physics provide us with models of precisely this sort of complexity.  Most important among these states ranks, for our present purposes, chaotic dynamics.  Indeed, the instability of motion associated with chaos allows the system to explore continuously its state space, thereby creating information and complexity in the form of aperiodic sequences of symbols.  On the other hand, being the result of a physical mechanism, these sequences are produced within probability one: the selection of a particular sequence out of very large number of a priori equiprobable ones simply does not arise.

In a way, the dynamical system generating chaos acts as an efficient selector rejecting the vast majority of random sequences and keeping only those compatible with the underlying rate laws.  Equally importantly, perhaps, the irreversibility incorporated in these laws gives rise to a preferred direction of reading and allows for the existence of attractors enjoying asymptotic stability and thus reproducibility.

The phenomena of bifurcation (state change) arises in a transition between different modes of behavior, achieved by a cooperation between the deterministic laws of evolution and the fluctuations arising from the system's variability.

Coherent patterns of self-organization are characteristic at all levels of organization: social, organismic, neural, cellular, chemical, electromagnetic, genetic, atomic, etc.  Global recruitment is characteristic of chaotic patterning.  It allows the best balance between random fluctuations, permitting discoveries and innovations.

In contrast, a permanent structure (such as an ossified ego) in an unpredictable environment may compromise the plasticity of the organism, constricting it to a suboptimal regime.  This fossilized uniformity manifests as a rigid ego, left with only a few, rather predictable choices.

The natural antidote for such a condition or state of being is to maintain a high rate of explorations and the ability to develop rapidly temporary structures suitable for exploring any favorable occasion that might arise.  The consciousness journey is a viable means for such exploration.

In other words, randomness presents an adaptive value.  The streaming imagery sequences of the psyche meet the criteria for a milieu within which various symbolic scenarios may be explored and evaluated.  It is a counterbalance, for example, to pathological hypervigilance induced by traumatic stress, or the narrowing of degrees of freedom due to rigidities fossilized as ordinary consciousness.

Nicolis points out that,

Adaptation and plasticity, two basic features of nonlinear dynamical systems, also rank among the most conspicuous characteristics of human societies.  It is therefore natural to expect that dynamical models allowing for evolution and change should be the most adequate ones for social systems.

A dynamical model of a human society begins with the realization that, in addition to its internal structure, the system is firmly embedded in an environment with which it exchanges matter, energy, and information.

...The evolution of such a system is the interplay between the behavior of its actors and constraints imposed by the environment.  It is here that the human system finds its unique specificity.  Contrary to the molecules, the 'actors' of a physico-chemical system...human beings develop individual projects and desires.  Some of these stem from anticipations about how the future might reasonably look and from guesses concerning the desires of the other actors.  The difference between desired and actual behavior acts therefore as a constraint of a new type which, together with the environment, shapes the dynamics.

The high degree of unpredictability emerging from these complex interactions is the essence of human adventure.  Chaotic attractors are potential information-generating devices.  We are thus led to a tantalizing picture of how information, one of the most conspicuous attributes of the human brain, can be linked to, and even emerge from, its dynamical activity.

ANTICHAOS

As fascinating as chaos is, it is only part of the transformative, evolutionary equation.  The emergent order of self-organization has been dubbed "antichaos," (Kauffman, 1991).  Some very disordered systems spontaneously "crystallize" into high degrees of order, much like DNA crystallizes into our physical form.  For example, genes act as a self-regulating network to guide the differentiation into multitudes of cell types.

When elements engage simultaneously, a system is synchronous.  The degree of entrainment of processes determines the degree of coherence or integration of the system and its ability to unfold the potentiality of the explicating information.

As the system passes from one unique state to another, it goes through a succession of states called the trajectory of the network.  Random networks (or systems of entrainment) have a finite number of states.  Therefore, a system is inclined to eventually reenter a state it has previously encountered.

If the system proceeds to the same successor state as it did before, it consequently repeats old states.  With intervention it discontinuously leaps to an unpredictable state initiating a novel pattern of response--it tries something new.

Left to themselves, any network (system of neural entrainment, or state of consciousness) will eventually settle in its cycle (basin of attraction) and remain there, unless perturbed.  There are two types of perturbation with analogies in CCP:  minimal perturbations (random) and structural perturbations (facilitated deconstruction).

A minimal perturbation is a transient flipping of binary element to its opposite state of activity (i.e. mood swing, enantiodromia).  If such a change does not move a network outside its original basin of attraction, the network will eventually return to its original state cycle.  But if the change pushes the network into a different basin of attraction, the trajectory of the network will change: it will flow into a new state cycle and new recurrent (iterating) patterns of network behavior.

According to Kauffman, the stability of attractors subjected to minimal perturbations can differ.  Some can recover from any single perturbation, others from only a few, whereas still others are destabilized by any perturbation.  This certainly sounds like an analogy to human coping skills, ways of dealing with stress, trauma, and unexpected catastrophe.

Changing the activity of just one element may unleash an avalanche of changes in the patterns that would otherwise have occurred.  The changes are "damage," and they may propagate to varying extents throughout a network.  It is this propagation which amplifies over time, congealing consciousness in restricted, dysfunctional patterns.

A structural perturbation is like a permanent mutation in the connections or functions of a network.  Like minimal perturbations, structural perturbations can cause damage, and networks may vary in their stability against them.  This process is revealed in the human immune system, and its ability to fend off ever-present cancer cells, for example.  a system can change from chaotic behavior to ordered behavior.

Therapeutic intervention contains a random element.  Because the successor to any state is essentially random, almost any perturbation that flips one element sharply changes the network's subsequent trajectory.  Thus, minimal changes typically cause extensive damage--alterations in the activity patterns--almost immediately.  Because the systems show extreme sensitivity to their initial conditions and because their state cycle increase in length exponentially, they are characterized as chaotic.

Despite chaotic behaviors, when order begins to emerge the number of possible state cycles and basins of attraction becomes very small.  About two thirds of all the possible states fall within the basins of only a few attractors--sometimes just one.  Most attractors claim relatively few states--a limited repertoire of psychological responses.

The stability of an attractor is proportional to its basin size, which is the number of states on trajectories that drain into the attractor.  Big attractors are stable to many perturbations, and small ones are generally unstable.  Therefore, we can deduce that the more global or holistic neural patterning is, the more stable the resultant state and behavior.

In the chaotic process, networks (entrainments of neural systems) diverge after beginning in very similar states; in emergent order, similar states tend to converge on the same successor states fairly soon.

HOMEOSTASIS, FROZEN CONSCIOUSNESS, AND TRANSFORMATION

"Frozen" elements in a system are incapable of changing state, unless they are deconstructed through structural perturbation.

Ordered networks are characterized by a homeostatic quality: networks typically return to their original attractors after perturbations.  Homeostasis is a property of all living things.  Random networks which exhibit emergent order develop a frozen core, or a connected mesh of elements that are effectively locked into either an active or inactive state.

According to Kauffman, the frozen core creates interlinked walls of constancy that "percolate" or grow across the entire system.  As a result, the system is partitioned into an unchanging frozen core and islands of changing elements.  It is easy to see a metaphorical description of the ego and pathology formation in this description.

These islands are functionally isolated: changes in the activities of one island cannot propagate through the frozen core to other islands.  The system as a whole becomes orderly because changes in its behavior must remain small and local.  But at what price--inflexibility in states of consciousness?  The "islands" of creative change become isolated, unintegrated, or inaccessible.  Low connectivity is a sufficient condition for orderly behavior to arise in disordered switching systems.  Order radically limits the potentiality of the system--its degrees of freedom.

Entrainment can work positively or negatively.  If the degree of bias exceeds a critical value, then "homogeneity clusters" of elements that have frozen values link with one another and percolate across the network.  The dynamic behavior of the network becomes a web of frozen elements and functionally isolated islands of changeable elements.  Is this not the description of an ossified awareness?

Forcing ourselves into a system of low connectivity, or integration, we can "cocoon" our traumas by isolating them from the functional system-at-large.  Kauffman asserts that, "Transient reversals in the activity of a single element typically cannot propagate beyond the confines of an isolated island and therefore cannot cause much damage."

In contrast, if the level of bias is well below the critical value--as it is in chaotically active systems--then a web of oscillating elements spreads across the system, leaving only small islands of frozen elements.  Minimal perturbations in those systems causes avalanches of damage that can alter the behavior of most of the unfrozen elements.  Viola!  Ego death.

This process only can be interpreted as "damage" where it is unwanted.  Voluntary dissolution is neither shattering, nor fragmenting, but a joyous celebration of multiplicity of consciousness.  When this process is fostered, facilitated, utilized, the deconstructive "damage" is an integral, necessary part of the emergent reconstructive process of the evolution of consciousness.

Network behavior can be metaphorically related to the phase states of matter: ordered networks are solid, chaotic networks are gaseous, and networks in an intermediate state are liquid.  Using this model, according to Kauffman,

"If the biases in an ordered network are lowered to a point near the critical value, it is possible to "melt" slightly the frozen components.  Interesting dynamic behaviors emerge at the edge of chaos.  At that phase transition, both small and large unfrozen islands would exist.  Minimal perturbations cause numerous small avalanches and a few large avalanches.  Thus, sites within a network can communicate with one another--that is, affect one another's behavior--according to a power law distribution: nearby sites communicate frequently via many small avalanches of damage; distant sites communicate less often through rare large avalanches."

From this, researchers conclude that parallel-processing networks poised at the edge of chaos might be capable of extremely complex computations.  Extending his metaphor, Kauffman concludes that the complexity of a network can coordinate peaks at the "liquid" transition between solid and gaseous states.

Systems poised in the "liquid" transition state may also have special relevance to evolution because they seem to have the optimal capacity for evolving.  Networks on the boundary between order and chaos may have the flexibility to adapt rapidly and successfully through the accumulation of useful variations.

CRP produces just such "liquifaction" through dissolution of the ego and imagery states by reduction to nonphenomenological, nonobjectified awareness.  It keeps the entire consciousness poised on the brink of chaos, the brink of the abyss, open to holistic repatterning on a global scale.

Just as poised systems typically adapt to a changing environment gradually, a stable, functioning personality will evolve through typical life passages or transitions relatively smoothly.  But if necessary, they can occasionally change rapidly.

On the other hand, the dysfunctional personality is constantly being called to the edge of chaos and invited over the brink.  Staving off this inevitable dissolution takes a great deal of energy, and saps the ability to cope with external reality.  CRP would follow nature's process to its natural conclusion.  In real life this all factors into the process of natural selection, survivability coefficient.

Evolution emerges at the edge of chaos.  It is an "interzone" between states of consciousness or dimensions of experience.  Kauffman and Johnsen have suggested that "the transition between chaos and order may be an attractor for the evolutionary dynamics of networks performing a range of simple and complex tasks."

They discovered that when the organization of successful networks evolved, their behaviors converged toward the boundary between order and chaos.  The liquid transition between ordered and chaotic organizations may be the characteristic target of selection for systems able to coordinate complex tasks and adapt.

Kauffman notes that an abundance of canalizing functions in a network can create an extensive frozen core.  Increasing the proportion of canalizing functions used in a network can therefore drive the system toward a phase transition (bifurcation) between chaos and order.  The more ossified the ego, the more in need of dissolution and holistic repatterning it becomes.  Under supercritical stress, it will either dissolve destructively or creatively.

If psyche's dynamics resonate with the process of natural evolution, health is found at the boundary region between order and chaos.  For example, evolution has tuned adaptive gene regulatory systems to the ordered region near this boundary creating relatively stable yet adaptive physical forms.  The same may be true for self-organizing consciousness in the "liquified" psyche.

REFERENCES

Ford, Joseph, "What is chaos, that we should be mindful of it," in THE NEW PHYSICS, Paul Davies, Ed.; Cambridge University Press, New York, 1989, p. 348-371.

Kauffman, Stuart A., "Antichaos and Adaptation," SCIENTIFIC AMERICAN, August 1991, p78-84.

Nicolis, Gregoire, "Physics of far-from-equilibrium systems and self organization," in THE NEW PHYSICS, Paul Davies, Ed.; Cambridge University Press, New York, 1989, p.316-347.

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