Sunday, April 16, 2006

Chaos Talk

Well tonight I went to a talk on chaos by James Yorke, one of the fathers of chaos theory. It was a fairly nontechnical talk, but was fairly interesting nonetheless. Dr. Yorke was a very engaging speaker, and had lots of examples of chaos.

When a scientist talks about chaos, they mean something very specific: sensitivity to initial conditions. The basic idea is that in a chaotic system a small change in the initial setup results in a large change in the results, the classic example being the butterfly flapping it's wings and causing a storm thing. So what can we do then, if all these systems are chaotic and will deviate widely depending on initial conditions (and just about everything is chaotic if you look at a long enough time scale)? Well chaos theory can help some (by providing estimates of how much accuracy you should need in the initial conditions), but mostly you just need to keep actively adjusting things as they go wrong. He made an amusing analogy about how planned economies such as in the Soviet Union don't deal with the chaos of economies as well as capitalism does, which my be one more factor explaining why communism has been less successful.

My own thoughts on this is that out of the chaos comes predictable patterns, so that while the short term or small scale properties of a system are chaotic, the long term or large scale properties are not, and can be predicted accurately. For example, take four mirrored balls, make a pyramid of them so that there are three balls on the bottom and one on top. There will be four holes in the pyramid. If you shoot a photon into a hole it will follow a chaotic pattern, it is effectively impossible to predict where it will be at any time, or where it will come out of. If however you shine red, green, and blue light (or any three colors, really) into three of the holes and look into the last one there will be a fractal pattern, which is very complicated (infinitely so if you want to get technical), but also very orderly and in principle predictable.

This has combined with the book I'm reading A Different Universe by Robert Laughlin, which deals with the idea of emergence. The basic idea of emergence is that the large scale properties of a system are different from the small scale properties of it, for example there is nothing in H2O molecules that is "liquid" individually, but when you put them together (at room temperature) they form a stable configuration we call water. My own 2 cents is that emergence is an effect of stable chaos on a large enough scale. Each water molecule follows a chaotic path, but you can predict what the whole liquid will do.

And I think the perfect example of all this is DC Beltway traffic ;)

1 comment:

uncrazy99 said...

I like to make a habit of researching things that I notice or hear about that seem interesting to me, and picking up random non-fiction books at the local library and reading up on all sorts of topics.

The chaos theory is something that has kept coming up in my pursuits - most recently in an episode of CSI I watched tonight. It seems so hard to fathom, but on the other hand, it makes perfect sense.

Besides the book you mentioned, do you know of any other books on the chaos theory that may be interesting to me? I'm a high school junior, and I'm just interested in reading and learning more.

Thanks.