"The Edge of Chaos"

13 Dec 2010 13:56

The notion is that "complex systems" (sometimes just "complex adaptive systems," both Names Which Must Be Destroyed) tend, in some ill-defined sense, to be poised on the border between order (no change or periodic change) and chaos (aperiodic change), because this is somehow the most flexible and evolvable position; that things "evolve to evolve" to the edge of chaos. --- The notion is that things at the edge-of-chaos are somehow optimized for adaptation and information-processing, and so natural selection would favor things near there, if indeed there isn't some inherent drive towards this edge. (One runs across both versions.)

I think the evolutionary argument, as usually stated, rests of a big mistake about what nervous systems, immune systems, genetic regulatory nets, etc., evolve to do. This is not transmit information from one place to another, or be "flexible" in some abstract sense, but cause actions which enhance the fitness of the organism they happen to be in. (The usual weasel-clauses about inclusive fitness, kin selection, etc., apply.) E. coli doesn't care about information flow in its regulatory network; it wants to be able to eat lactose when nothing else is around.

Now, it's entirely possible that the general argument is wrong, but that the edge of chaos has, after all, very striking properties, and that these are usefully enough to be frequently exploited by living things. So: is the edge of chaos really that special? Melanie Mitchell, Peter Hraber and Jim Crutchfield tried to replicate results which claimed the edge of chaos was very nice for computation, with negative results, back in 1993 ("Revisiting the Edge of Chaos: Evolving Cellular Automata to Perform Computations"; details below).

Given that that the opinion of specialists was never unanimous behind "life at the edge of chaos," and there is every possibility it's wrong, why was this idea picked up by some segments of educated opinion and adopted? --- even adopted pretty widely; I seem to recall Al Gore making some hay with the notion, and hearing that it was being touted by management witch-doctors. The obvious answer is that it fits nicely with some wide-spread prejudices: basically, antinomianism, a dislike of rules and rigidity and formality, a positive relish for rule-breaking. ("The information-transmitting capability of a network is maximized by having the frozen units at the critical threshold for percolation" would not have played in Peoria, or more to the point Manhattan.) But I wonder whether this isn't putting the cart before the horse --- after all, the reason we say that there is an antinomian trend is (among other things) that people increasingly pick up and like ideas like "life at the edge of chaos", so is that supposed explanation more of a tautology?

Another, probably related question is, why did that idea spread, and not others which are associated with it, at least for specialists?

Tracing the rise and (I dare to hope) fall of the edge of chaos among both specialists and the wider public would be very instructive. One could probably do some very pretty epidemiology, identifying the main vectors by which the idea spread, and examining the failure to propagate of counter-ideas. (I'm willing to bet that the news the edge of chaos is in trouble will not spread with anything remotely like the same speed or breadth, and that it will live a long, happy, but not productive life in books on the New Science, the social sciences, and certain strains of literary criticism.)

Notebooks:     Hosted, but not endorsed, by the Center for the Study of Complex Systems