From a Beautiful Mind;
Here is an outtake from the best paper I've read on Chaotic Systems, The author Amara, deals mostly with cosmic dust, but she wrote this paper in 1988. Full paper at the link. This Outtake takes control, argument wise, from the very foundations of current Chaos makers. amara.com
EMERGENT ORDER: A PHILOSOPHICAL DISCUSSION
µ Emergent Order: A Philosophical Discussion
The ideas of some of the previous sections lead to a concept which I’ll call "emergent order."
Chaotic systems are completely unpredictable but when an attractor is found, some stable (by
"stable" I mean a perseverance of form through time) structure emerges from the combination
of individual elements.Eac h element has its own goal due to some constraints, and through the
elements’ connections and combination of their properties, an unplanned, unpredictable order arises.
I like to think of this order as a type of attractor.
What systems exhibit emergent order? There are at least three: 1) Markets, 2) Ecologies/Evolution,
and 3) Minds.
In all three of these systems, there is the concept that millions of things are operating under
similar constraints (while at the same time operating in unique local conditions).In Markets, people
are constrained by rights.In Ecologies, living creatures are constrained by the environment and other
creatures.In a Mind, the neurons are constrained by the physiology of the brain.
In Free Market Economics people exchange goods in a mutually reinforcing process.The prices
and wages form themselves into an overall pattern.Adam Smith called such patterns invisiblehand
explanations: "Every individual intends only his own gain, and he is in this, and in so many
other cases, led by an invisible hand to promote an end which was no part of his intention." Other
characteristics of Free Market Economics are that it’s very di.cult to predict events- one can’t
possibly know all there is to know about the system.E.ects such as weather, human being’s
decisions and technological innovations have widespread in.uence.So is the overall pattern an
attractor? There have been speculations in the early days of chaos research that cotton prices
followed Lorenz’s chaotic attractor.If such an attractor exits, then it represents a stable long-term
behavior.It seems likely that any interference would induce an instability.The interference would
entail someone or something (Kings, Governments...) trying to impose a single or small number
of goals upon it.Since each element already has its own goals, this higher-order goal(s) wrecks
havoc.F riedrich Hayek and Milton Friedman make this point with regard to government attempts
to stabilize the economy and the money supply: the e.ect of attempting to stabilize a complex
system arti.cially often increases the instability rather than decreases it.
An ecology is also a complex system.I’m lumping Evolution into this category because the
two are very interrelated- the time-scales are the main di.erence.(Ev olution time-scales are considerably
longer.) Like Free Market Economics there is no central controller, i.e. the control is
"distributed." The order that emerges is unplanned and unpredictable. As in all three of these
systems there is no analytic solution- the only way to calculate it is to "run it out." A system with
this property can be called "computationally incompressible." What sort of stable structures occur
in a Ecological/Evolutionary system? One can conjecture that given a large enough "lattice," selfreproducing
and self-organizing structures would probably appear.These could be the attractors.
It has also been noted by Paul Ehrlich that attempts by Man to arti.cially stabilize an ecosystem
often increases its instability.The maximum stability occurs when no attempt is made to simplify
the system by imposing a single or small number of goals upon it.
The third system- a Mind- has analogous processes.Marvin Minsky conjectures that Mind is an
emergent property of the interaction of many "agents." Agents are the algorithms while the neurons
are the hardware.The agents do simple unintelligent tasks and are not signi.cant individually, but
their interaction perform amazingly complex processes.One can speculate that the attractor here
is simply the Mind itself.
More similarities can be found in these three systems.
In all three of these systems recursion exists- make your output your next input and keep running
the system.As described in the section on Information Theory, what you get over time is
more a function of the process itself than of initial conditions.Information is created and destroyed.
This leads to the concept of "irreversibility." I would speculate that these three systems exhibit irreversibility.
Y ou cannot look at their present information state and infer their history of information
processing.
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SOURCES
To conclude this article I would like to point out that, while these three systems are among the
most obvious and important examples of emergent order, emergent order operates on a wide range
of levels:
Atomic
Molecular
Chemical
Human
Markets
The levels of complexity are very di.erent in these systems yet the same processes are operating
at all levels! So the processes of emergent order are "complexity-level-independent." If you recall
from the Fractal section, fractals have this property of "similar on all scales" too.
I tend to view the universe now through my fractal glasses.
Acknowledgments
The author acknowledges the invaluable discussions with F.Bennett on the contents of this
paper especially on the philosophical issues.
o Sources
Abraham, R.H., Shaw, C.D., Dynamics- The Geometry of Behavior Part One: Periodic Behavior,
Aerial Press, Santa Cruz, 1984.
Abraham, R.H., Shaw, C.D., Dynamics- The Geometry of Behavior Part Two: Chaotic Behavior,
Aerial Press, Santa Cruz, 1984.
Barrow, J.D., and F.J. Tipler, The Anthropic Cosmological Principle, Oxford University Press, Oxford,
1988.
Campbell, D., Crutch.eld, J., Farmer, D., Jen, E., (1985) "Experimental Mathematics: The Role
of Computation in Nonlinear Science," Comm of the ACM, 28, p.374-384.
Devaney, R.L. An Introduction to Chaotic Dynamical Systems, Addison Wesley, 1987.
Eckmann, J.-P, Ruelle, D., (1985) "Ergodic Theory of Chaos and Strange Attractors," Rev. Mod.
Phys., 57, p.617-655.
Ehrlich, P. R., Ehrlich, A.H., Population, Resources, and Environment, Freeman, San Francisco,
1970.
Farmer, J. D., Ott, E., Yorke, J.A., (1983) "The Dimension of Chaotic Attractors," Physica, 7D,
p.153-180.
Friedman, M., Friedman, R., Free to Choose, Harcourt Brace Jovanovich, NY, 1980.
Froehling, H., Crutch.eld, J.P., Farmer, D., Packard, N.H., Shaw, R., (1981), "On Determining the
Dimension of Chaotic Flows," Physica, 3D, p.605-617.
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SOURCES
Hayek, F., Unemployment and Monetary Policy, Cato Institute, San Francisco, 1979.
Hofstadter, D.R., "Metamagical Themas: Strange Attractors: Mathematical Patterns Delicately
Poised Between Order and Chaos," Scienti.c American, November 1981, p.22-43.
Hogan, J., Voyage from Yesteryear, Del Rey, 1982.
Gleick, J., Chaos: Making A New Science, Viking Press, 1987.
Minsky, M., The Society of Mind, Simon and Schuster, 1985.
Nozick, R., Anarchy, State, and Utopia, Blackwell, 1974.
Packard, N.H., Crutch.eld, J.P., Farmer, J.D., Shaw, R.S., (1980), "Geometry from a Time Series,"
Physical Review Letters, 47, p.712-716.
Poundstone, W., The Recursive Universe, Contemporary Books, Inc., 1985.
Roux, J.-C., Simoyi, R.H., Swinney, H.L., (1983), "Observation of a Strange Attractor", Physica,
8D, p.257-266.
Shaw, R., (1981), "Strange Attractors, Chaotic Behavior, and Information Flow," Z. Naturforsch.,
36a, p.80-112.
Shaw, R., The Dripping Faucet as a Model Chaotic System, Aerial Press, Inc., Santa Cruz, 1984.
Smith, A., The Wealth of Nations, 1776.
Sparrow, Colin, The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors, Springer-Verlag,
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Wright, R., "Did the Universe Just Happen?", Atlantic Monthly, April 1988, p. 29-44.
Copyright Notice:
I notice that I have the will and the ability to copy this paper.But what about the copy in
your hands? If you have the will and the ability to copy it, that’s great.Willful and able individuals
are the most cost e.ective way for this paper to be distributed.
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