Chaos Theory

Question

I remember reading that a butterfly on the otherside of the world can cause a hurricane on the opposite side, and it’s down to chaos theory, could someone explain what chaos theory is please? Thanks

In: 42

Answer 1

I actually think the “butterfly on the other side of the world can cause a hurricane” example misses the point a little bit–but the way it does is really the essence of chaos theory.

To understand chaos, think about what is *not* chaos. Typically, in math and physics, we are interested in “stable” systems. Roughly this means small changes in input lead to small and well-understood changes in outputs. For example, a continuous function f(x) won’t change that much if you change x. (This is the premise of calculus, of course.) If you throw a dart at a target and your throwing motion is off a little bit, the dart will miss the target by a little bit. The behavior of the system–and its sensitivity to its initial state/conditions–is easy to describe and well understood. Dart went too far to the left? Try aiming a little bit more to the right.

“Chaos” refers to a system sufficiently complex that the relationship between the inputs of the system and the outputs of the system no longer exhibit a clear/obvious relationship. One canonical example people use is billiards: think about how the 15 ball in the corner moves as a function of how you strike the cue ball. It’s basically impossible to calculate in a deterministic way because there’s so much shit going on. It’s too complex.

The butterfly causing a hurricane example is, while provocative, misleading one for two reasons:

1. It suggests that the butterfly is the only initial condition / causal agent in the weather system, but
2. more importantly: the point of chaos theory is not that small things can “cause” huge effects, but that in complex systems, our that colloquial notions of cause and effect are actually inadequate to describe complex systems.

And that’s really I think the point: complex systems that are sufficiently complex that our notions of direct/proximal causation fail.