Norman Packard on Chaos

Chaos is a particular kind of random motion, one that combines both randomness and structure. The system starts somewhere in space and goes along until it falls onto an attractor. With the simplest kind of attractor, a fixed point, the system goes toward a single state and stays there. You see this with a marble in a bowl; it rattles around until it reaches the bottom of the bowl. With a periodic attractor, the system cycles through a sequence of states, like the arm of a metronome left to right and back again in a regular cycle. If you perturb it briefly, it tends to return to its set cycle. The next most complicated kind of attractor – the strange attractor – displays both structure and chaotic motion.

The intrinsic randomness of a chaotic system limits predictability. But the structure of the attractor implies that you can predict part of the time what the system will do. Chaos represents an indeterminate level of predictability between the motion of the planets, which is derivable, and something completely random, like particles in brownian motion. Chaos presents systems that are random in the long run but have just enough structure so that in the short run you can figure out what they’re going to do. The name of the game of my data analysis techniques and learning algorithms is to probe that limit. How far into the future can you predict?

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