"Tim Tyler" <[email protected]> wrote in message news:[email protected]... > Guy Hoelzer <[email protected]> wrote or quoted: > > Jim Menegay at [email protected] wrote on 4/28/04 2:44 PM: > > > Guy Hoelzer <[email protected]> wrote in message > > Cosma Shalizi offers some criticism of the whole idea - and winds up > offering a purely mem > > > And, I think that the whole field of "complexity" is plagued by bad > > > choices of terminology and some very, very bad intuitions. > > > Furthermore, I don't see the situation as likely to improve when > > > books can be sold by coining meaningless, but evocatative, phrases > > > such as "the edge of chaos". IMO. > > > > "Edge of chaos" is much more than a catchy phrase. Do you know what it > > means in this context? > > "Edge of chaos" *is* an evocative phrase. > > However... subsequent researchers generally failed to confirm Langton's > suggestion that the location might be of interest in terms of being a > particulary attractive spot for performing computations - and his Lambda > parameter hasn't actually proved to be of much use :-( > etic explanation for the existence of the phrase: > > ``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.'' > > - http://cscs.umich.edu/~crshalizi/notebooks/edge-of- chaos.html > > However... I have to number myself as among those who thinks that > there really /is/ something to Langton's intuitive idea ;-) > > "Self-organised criticality" (e.g. the pile-of-sand/landslide effect) > is the simplest way I know to clearly illustrate to sceptics that > there really /is/ something to the notion that complex systems can > tend to migrate towards the "edge" of zones where chaotic behaviour > arises. Perhaps another example of such "Self-organised criticality" (or at least a similar idea) that is easier to rationalize is the formation of substances into different allotropic forms when stressed by differing environmental conditions such as temp., pressure, or other energy constraints--the formation of water into several different forms of ice, or carbon into graphite, diamond, or buckeyballs/tubes, are beautiful examples of compounds or elements "evolving" under stress to go from one quantitatively changing-properties- regime, through transition points, into another, qualitatively different regime, then so on into others (allotropes having radically different properties such as structures, densities, etc., etc.) Transition points can easily be seen as points on the edge of chaotic boundarys of specific phase diagrams. In fact, they can be viewed as characteristic of many different types of phase changes...even the evolution of a massive star into a neutron star, or black hole, under the influence of gravity may be considered the same type process. Evolution and change...and then more evolution... Quite a beautiful universal process in a way, one which blends order, complexity, and chaos, all together. ...tonyC > -- > __________ > |im |yler http://timtyler.org/ [email protected] Remove lock to reply.