The Ionasphere, ©2001
CHAOS THEORY
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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