by pat » Tue Apr 03, 2007 4:49 am
Say that you're trying to model the behaviour of some complicated system like the way convection currents move in a pot of water or the weather or something.
Suppose, you put in an input value of 0.3999293929113 for one of the inputs to your model. Now, say that you want to re-run the simulation again tomorrow, but instead of 0.3999293929113, you accidentally type 0.3999293929118. You might think, "Well, my results might be off a tiny bit, but the inputs agree to 12 decimal places so I should still be in the same ballpark."
If your system is chaotic, you may well not be in the same ballpark at all any longer.
Chaos theory is the study of what kinds of systems show this behaviour, what kind of way can we measure how bad the problem is, and are there overarching things we can still say about the system even if the details are hopelessly dependent on the exact initial conditions.