Fri, 2 Jun 2000

The idea embodied by deterministic chaos in a system (such as the motion of several planets about a sun, or the weather here on earth, or the stock market, etc.) is the following:

despite the fact that the system is deterministic, it has the
property that imprecise knowledge of the initial condition may
lead to unpredictability after some finite time.

For instance, with the best possible measuring instruments, we can only (even in theory) predict the weather about one week ahead of time and no further. In other words, we lose predictability in a finite time (namely, one week). This is because, being human, we have imprecise knowledge about things. Exact knowledge is beyond our reach. Thank God, some might say.

comet chaos! I suppose you, yes even you, are an example of a chaotic system. You're much more complicated than the weather! Someone might think they know your "state" (your initial condition) and they might even know the laws governing how your state (moods, thoughts, ambitions, etc.) changes with time. But any imprecision in the measurement of your state will lead to total unpredictability in a short amount of time. This is part of what makes interpersonal interaction so interesting - people are unpredictable and it's interesting to see what they'll do next. It's also why dropping balls on to the floor or throwing them up in the air is quite boring - the system is simple and not very chaotic so we know exactly what the ball will do.

And by the way, I am not saying unpredictable, capricious, irresponsible behavior in people is a good thing. I'm just talking about math and the reality of the unpredictability of human behavior. We all get to make moral choices, and that's beyond the scope of mathematical chaos (at present).