Any,
I started out on the Crutchfield et al chapter (which seems a really mellow summary of complexity ideas) and immediately was assaulted by two naive questions. If somebody has the time to set me straight, I would appreciate some help.
(1) About once a month, somebody mentions to me the three body problem, which I take to be that nobody has ever been able to precisely predict even a gravitational system as small as three interacting entitites ( eg, planets) . Yet (as Crutchfield et al point out) we are able to predict eclipses thousands of years in advance. Is the solar system non chaotic? (i.e., not sensitive to initial conditions????). Given that the moon and the sun only cover half a degree of sky, and given that measurements of their position must until recently have been pretty sloppy, how can this be?
(2) The second "question" is really just a "duh" moment about which I would like some comment. I "got" long ago that sensitivity to initial conditions makes it impossible to predict how some simple deterministic systems will behave in the future. And CA's provide us with some wonderful examples of that principle in operation. Today, dawned on me the reverse implications of that fact. The tantalizing possibility exists that for every system, no matter how wierd its behavior, is governed by simple deterministic rules that are obscured by their sensitivity to initial conditions. Is it that possbility that makes you-all so energized about complexity theory.
thanks in advance for any patient commentary.
Nick
Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
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