Chaos theory and dynamical systems

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application of Chaos . . . and the direction taken by Michael Schwalbe
. . .
Order and complexity are basic to all systems, by definition;
however, objects are not basic to systems (in fact it is the other way
around). Order is a thermodynamically improbable state of an enduring
configuration. Order and complexity, however, are not synonomous. Complexity
presupposes order, and objects (or things) can be ordered without being
complex. complexity is simply a matter of an object (or thing's) degree
of internal differentiation, and the intricacy of the relationships between
its internally differentiated parts. Object (or thing) complexity can be
measured by the information required to specify the configuration of whatever
constitutes it.
What needs to be stressed is that in dynamical systems, the elements of
the system are not necessarily discrete parts; they may be ephemeral
structures that arise only out of the energy flows that constitute the
system.
Dynamical systems are open to continuous interaction with their
environments. What makes dynamical systems so interesting is that while
(as Reed has noted) they assume that given a complete description of the
starting points of the system (the inputs), the system is basically
deterministic. The interesting part is that, however, in practical terms
the system is unpredictable; since, it is self organizing . . . meaning that
it is capable of capturing information that it itself generates, and then
using the new information as input to the system.
Thus, Chaotic dynamical systems are theoretically capable of evolving
and (in a very odd sense) becoming autogenisis systems (capable of
altering themselves).
Even though dynamical systems operate deterministically, the final outcome
state of the system is not predictable.
What is meant by self-organization is the creation of new information,
by information that has been captured by a selective dynamical system. Order
and complexity effectively create more order and more complexity.

Honestly, I recommend the Schwalbe article to anyone interested in
a concise application in the social sciences.

As well, as I have always said, I believe that some of the concepts
relevant to Chaotic systems and to dynamical systems have a direct
relevance to anthropological study. For example, self-organization and
the unpredictable new order and complexity, based on the function of
old order and complexity, sounds a great deal like Steward's ideas on
multi-linear evolution - particularly when considered in light of an
open system in interaction with its environment.

John O'Brien
Indiana University

PS . . . however, as a post script . . . I do not believe that the kinds
of dynamical patterns identified in by other applications of Chaos theory
necessarily translate automatically into the kinds of structures that
we note in human systems. I would think that it is more probable that
human systems map to material systems in metaphorical ways . . . and that
the basic organizational typologies common to human or cultural systems
need to be recognized before attempting to misapply chaos mathematics to
cultural systems. [OOPS . . . the above should read ". . . identified in
mathematics (such as the Lorenz or butterfly effect, and so forth) by other
applications of Chaos . . ."

John

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