When an object moves through space, it's attracted by the gravity of planets and stars; its path bends. Depending on the situation, the attractor may deflect the object's motion, capture it into an orbit, or pull it down to destruction.

Similarly, when a system of any sort changes over time, the point that represents it on a graph of its characteristics moves --- and that point may be attracted towards various places in a weird, non-physical phase space.

For instance, a nation's economy has a growth rate, inflation rate, unemployment rate, trade balance, and so forth. A cow has a daily feed consumption, weight, milk production, etc. Those parameters are interrelated: a cow that isn't fed will lose weight and won't produce milk for long. For any system, some combinations of characteristics are stable --- and when the system gets near enough, it falls into that happy place of stability. The cow has a natural weight. She feels hungry and eats more if below it, or is satiated and eats less if above it ... within limits, of course, and providing nothing else interferes. People are the same, as any dieter can testify. A stable configuration like that is a kind of "attractor".

But besides ordinary attractors, some complex systems have "strange attractors" --- regions of phase space which pull a body in, chew on it for a while, and then spit it out again, or which churn a body into a chaotic pseudorandom mess. In an ordinary situation, two systems which start out similar tend to stay similar. Twin cows grow up to resemble each other, other things being equal. But near a strange attractor infinitesimal differences are magnified, until the results are grossly divergent. That's why weather is so hard to forecast beyond a week or two, and perhaps why economics and other areas of human action seem so inscrutable. Tiny changes blossom into a world of difference.

Wednesday, September 01, 1999 at 19:43:16 (EDT) = 1999-09-01


(correlates: FlashInThePan, StupidityAndConspiracy, BeatingExpectations, ...)