Butterfly effect: Difference between revisions

}}The [[butterfly effect]] is a much misunderstood observation of complexity theory - that the behaviour of a [[complex system]] is highly susceptible to its initial configuration, and small differences in that initial state — in an ecosystem, the flapping of a butterfly’s wing — may mean the [[Systems theory|system]] behaves in vastly  — and quite unpredictably — different ways.

This is ''not'' the same as saying, as people are prone to, that “a butterfly flapping its wings in the Amazon causes a hurricane in China”.  

People who not only should, but do know better, can fall into this trap. “To show what a difference an initial condition can make, consider the double-jointed pendulum”.

Set off two double-jointed pendulums from an apparently identical condition and quickly their trajectories will wildly diverge, it is true. But this divergence is derive solely from atomic differences in the initial configurations of the pendulums, but also — and over time, increasingly — from ''ongoing'' atomic differences as the pendulums cycle. A micro-second into their cycle, those differences in initial condition are important. After half an hour,<ref>assuming the pendulums do not quickly come to rest as, in fact, they will do. See below.</ref> the initial condition differences account for more or less none of the differences in the ongoing behaviour of the pendulums.