Chaos

[firemeboy]

Ok, this one has no easy answer. Can anybody sum up the whole idea behind chaos theory, how it is used, etc.?

I was glancing through a book a while ago and they had these colorful pictures of 'chaos' that were interesting. There were patterns and flows in the 'chaos' which I thought was kind of paradoxical.

In addition I just read Timeline by Michael Chrighton (sp?) and he had some weird stuff in there. I don't know if it directly corelates or is a tangent to the chaos theory.

Anyway, and thoughts?

[Ghost Post]

I'd be interested in more info too. There is a book on the subject that was recomended to me. I think it was "Chaos" by James Glick. Not sure about the author's name. Anybody read it? What about other books to try?

Anyway I think that the whole idea is that very complex behavior can result from simple rules. All those cool pictures are generated following some simple set of rules.

[firemeboy]

I read a paper one time about this guy who brought in High school kids and they were trying to show that you could give simple rules to 'objects' and they could do complex actions. They were trying to show that animals in nature may not need much to do amazing things like build Termite mounds.

They had there programagle objects called star turtles I think. Anyway, they asked these kids to program them and see what they could come up with.

One objective was to stack objects into one stack with very few instructions. One kid 'programmed' in the command if you come to an object, pick it up and drop it by another object. This command was so simple and yet the number of objects dropped from 100s to less that 10. Of course they sped up the time and all but it was pretty interesting to see a simple code make these little star turtles be able to take a bunch of objects and make piles.

[Ghost Post]

That's StarLogo, it is based on regular Logo but with thousands of turtles working in parallel. I've seen it. It is pretty neet stuff. There is also a cool traffic simulation that shows how a traffic jam happens.

More info at: http://el.www.media.mit.edu/people/starlogo/

[Ghost Post]

James Gleick's book, "Chaos," is very good, but it doesn't really go so much into chaos theory per se, but it explains the history of chaos theory and the various developments along the way.

[Alfie]

This ancient poem sums it up:

For want of a nail, the shoe was lost;
For want of a shoe, the horse was lost;
For want of a horse, the rider was lost;
For want of a rider, the battle was lost;
For want of a battle, the kingdom was lost!


Good site to look at is http://www.duke.edu/~mjd/chaos/chaos.html

[Andy]

I can't cite a specific reference, but my understanding of the general ideas of chaos theory are that 1) In some systems, repeated application of simple rules over large numbers of components or long periods of time can lead to complex behavior; and 2) In some systems, small changes in initial conditions can result in large changes in final conditions. The implications of these conditions are that in chaotic systems, behavior can be predicted only statistically if at all. For example, in an ideal gas, the rules are simple and the statistical behavior is predictable, but the actual path followed by any one particle is essentially unpredictable if the number of particles is large. In orbital mechanics, the eventual behavior of a particular object (will the earth spiral into the sun?) may depend on immeasurably small variations in initial conditions.

[Amy]

I have also heard the Earth's atmosphere described as a chaotic system. The so-called "butterfly effect" illustrates the idea: if a butterfly in Africa somewhere flutters its wings, that tiny current of air could lead to a change in much bigger air currents, etcetera, producing a rainstorm in Massachusetts (not that they would notice anything odd about that). Anyway, I think this is supposed to explain why it's not possible to predict the weather accurately: a chaotic system just can't be tracked effectively. (Yet it is also true that on a large scale, chaotic systems sometimes produce predictable patterns. You can draw a dot on a piece of paper, then roll dice to determine the direction and distance away of the next dot, and keep doing this, so that you will be drawing dots on the page in an unpredictable, chaotic fashion--but after millions of iterations, you will always produce the same pattern, and no one knows why.)