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..:: Chaos
Revisited ::..
By
Alan Schneider
Chaos Basics
Perhaps the most significant
principal of chaos theory is represented by the butterfly effect,
one of the initial discoveries that helped to launch the science, made
by Edward Lorentz in 1961 (Schueler, 1997, p. 2). Lorentz was involved
in ongoing experiments designed to develop efficient long range weather
forecasts. On one occasion, he was faced with the need to rerun a long
series of computations to verify certain data. Rather than reenter the
data comprehensively, he decided to simply reenter key values in the
sequences, and executed the computer run.
Lorentz was surprised to
discover that the results of the second run were very different
from the initial attempt. He then closely examined the values used in
the second run, and again compared them to the initial run. He noticed
that certain numbers had been slightly rounded off in the process of
entry into the second program. The impact of this apparently
insignificant oversight was amplified through the parameters of the
computer program, and resulted in the observed shift in the outcome.
The butterfly effect refers
to the tendency of chaotic systems to be influenced, or perturbed,
by even the slightest change in initial system conditions.
Something like the beating of a butterfly’s wings, taken into account as
an initial condition, can and does influence an apparently distant
phenomenon, such as the state of the entire atmosphere, across a complex
bridge of subsequent relationships. If these relationships are sensitive
enough, the impact on the atmosphere could conceivably even be notably
catastrophic in character, e.g. the occurrence of tornados in Indonesia
(Seeger, 2002, p. 331). This was clearly the effect of the slight
rounding of the data values seen in Lorentz’s second computer run. He
eventually came to the conclusion that the sensitivity of the weather to
initial conditions at any given time made the long term prediction of
meteorological trends impossible.
Initial sensitivity accounts
for the ongoing manifestation of another cornerstone concept of chaos
theory, non-linearity. Most, if not all, systems seen in the phenomenal
world (the world we literally experience) are more or less
non-linear in function and form. Non-linear is the chaos theory
term describing a process that does not behave consistently across time,
but rather fluctuates unpredictably in response to variables that are
difficult, if not impossible, to directly observe. Human beings agree,
based on observed statistical consistencies, to treat the phenomenal
world as though it is present in a stable configuration, although it is
always subject to, and demonstrating, perturbation. Non-linear systems
are also referred to in the literature as complex systems.
The specific mode of change
in complex systems is bifurcation. This phenomenon occurs when
the system can no longer maintain stability under a given set of initial
conditions, and breaks down into a set of more relatively stable
conditions. The new conditions may or may not be initially more
comfortable from the viewpoint of a human observer, but nonetheless
represent the emergence of self-organization – the movement of
the system process into a new, more stable form (Seeger, 2002, p.
332). Bifurcation and subsequent self-organization are key processes of
social and organizational change and renewal in the chaos paradigm. This
is in contrast to the view of traditional social science that any
chaos-related event is necessarily negative in character.
The causative agent driving
the mechanism of bifurcation is the strange attractor. There are
many forms of attractors seen in the natural world. Static
attractors, such as gravity – which simply exists as a mass-related
consistent force – and dynamic attractors – represented by the
sinusoidal form of alternating current electricity – are easily
identified everywhere. Attractors are the underlying principals that
maintain order in the world. Chaotic strange attractors are a
particular case in which a fixed point of manifestation, and predictable
operation, have given way to a general conceptual region of
action which can produce unpredictable outcomes. All that can be said
with certainty regarding strange attractors is that there is an apparent
force present tending to shape events as they become manifest in real
time and real space. (Seeger, 2002, p. 334).
Strange attractors are
specifically postulated as being unobservable, but still present in
phase space, the mathematical construct used to describe their
characteristics. Phase space can be thought of as a snapshot of a
complex system’s possibilities at a given point in time, where
each special “dimension” corresponds to a variable in the system
(Schueler, 1997, p. 3). Although these possibilities cannot be observed,
since they occur in the future, they can be inferred from the
performance of past observations of many different systems, which are a
matter of concrete record. Hence, the presence of strange attractors can
be inferred as being potentially manifest in all systems, regardless of
their levels of functioning. When a system becomes significantly
unstable, they become active and begin exerting their influence on
outcomes.
In addition to the chaotic
strange attractor and the static attractor, there are three varieties of
dynamic or linear attractor: fixed point, limit cycle, and
toridal. A brief discussion of these more logical, consistent governing
principles readily identifiable in relatively stable systems may
be useful here as an aid to fully understanding the influence of strange
attractors. The fixed point attractor is illustrated by the
center of a system of circular motion, such as the axel to which a wheel
is mounted. The limit cycle attractor is seen in the presence of
two or more limiting conditions or processes that determine the outcome
of some sinusoidal dynamic process – such as the swinging of a clock
pendulum, where gravity and the clock driver mechanism (e.g. spring,
battery, etc.) are the attractors at work. The toridal attractor
is the result of multiple frequencies present in the limit cycle
attractor network. The shifting of the Earth’s axis accounting for the
Astrological Precession of the Equinoxes is such a toridal attractor
system – the limit cycle attractors are the Sun’s gravitational field
and the Earth’s mass. But certain variations in the magnetic fields of
both the Earth and the Sun cause the constellations to appear to “move
backwards” (i.e. counterclockwise) around the North Star, completing one
complete cycle every 24,000 years. As a comprehensive example
here, turbulence can be characterized as the strange attractor
that draws water into chaotic conditions of flow as velocity increases
in an enclosure, such as a pipe. The extent of the phenomenon can
eventually reach cavitation, where flow effectively ceases,
resulting in the “transition” of the turbulent strange attractor into a
linear fixed point attractor – cavitation – accompanied by the
bifurcation of the system into a more stable, predictable configuration
characterized by the absence of fluidic movement. (Schueler, 1997, p.
7).
The Spiritual Implications of Chaos
Theory
The
forms of the strange attractor operating in the mental systems studied
by psychological and spiritual students are the archetypes of the
collective unconscious mind. Archetypes conform to the
description of strange attractors with great consistency. They are
located in a “region” that is unobservable, tend to emerge into
conscious recognition under conditions of systemic stress, and generate
unpredictable outcomes for the individual’s mental state. All collective
archetypes display these characteristics, regardless of the specific
behavioral trends they define. And the Psyche is a phenomenon that lends
itself quite well to the conception of phase space, particularly in the
unconscious regions (Schueler, 1997, pp. 8,9).
As the archetypes emerge into
conscious expression (rendering them susceptible to observation), they
take the form of recognizable cultural images called archetypal
symbols. There are hundreds (perhaps thousands) of known
archetypal symbols, demonstrated in variations across cultures
throughout history, including the Shadow, a repository of all that has
been willfully rejected from conscious recognition, the Hero, a figure
of salvation and redemption, the Couple, symbols of relationship and
involvement, and so on (Schueler, 1997, pp. 9,10).
When chaotic events manifest
in social systems, the results can be intra personally, interpersonally,
and individually traumatic in the extreme, particularly in the
case of relatively long term episodes. One of the results of such long
term chaotic manifestations is the cosmology episode (Sellnow &
Seeger, 2001, p. 170), characterized by the breakdown of the habitual
routines and expectations taken for granted under the pre-chaotic
condition. The individuals experiencing cosmology events frequently have
a sense of the unreality of their circumstances caused by
significant personal and social displacement associated with the chaotic
occurrence. They may tend to question their most basic assumptions
regarding life, truth, and propriety, and seek new comprehensive
spiritual explanations for their circumstances outside what had been
their previously dominant cultural paradigm. The rise and fall of
cultures and social systems demonstrated throughout history
guarantees that the cosmology event will occur with regularity in
human affairs and human consciousness.
The focus of conscious
deliberation on the Physical Plane of expression is the ego, and
this primitive form of sentient awareness does not respond well to
chaotic conditions, a most unfortunate circumstance, since chaos is the
birthplace of all manifestation and all consciousness.
This places human observers on the Physical Plane in more or less
permanent conflict with Creation and the Creator, a
conflict which we must all either lose, or eventually acquiesce to in
spiritual surrender – the distinction resides in the voluntary or
resistive nature of our response. And, ultimately, we are all reabsorbed
as physical organisms into the chaos that created us, do what we will to
postpone this event. The only real hope of existence lies in the access
to total consciousness – the Psyche – and its probable links to
extended manifestations beyond the physical. This is the realm of the
archetypes and archetypal symbols, of the collective level of
consciousness, and of all higher modes of human spiritual expression.
It is here that we must go, and here that we can succeed in our
spiritual quest as spiritual beings, Created in Love and Light by the
Source of Love and Light. We need only take a leap of faith...
References
Schueler, G. (1997). Chaos theory:
Interface with Jungian psychology. Retrieved March 12, 2004, from
Internet Website:
http://www.schuelers.com/chaos/chaos1.htm.
Seeger, M. (2002). Chaos and crisis:
Propositions for a general theory of crisis communication. Public
Relations Review, 28, 329-337.
Sellnow, T., & Seeger, M. (2001).
Exploring the boundaries of crisis communication: The case of the 1997
Red River Valley flood. Communication Studies, 52, 153-176.
- With Love, Alan -
(CR2008, Alan Schneider)
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