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.

The systems are ''[[Path-dependent|path''-dependent]], not ''initial-condition''-dependent. The longer the the system continues the more dependent the system will be on the infinity of subsequently intervening causes.  

And there is another thing: unless the pendulums have perpetual motion,<ref>Impossible, of course.</ref> or are ''powered'' they will, in a short time period, come to rest. All pedulums tend to rest. Their initial conditions are ultimately irrelevant. Over time, then, even insoluble mathematical operations converge. We can see this [[path dependency]] to be [[Signal-to-noise ratio|''noise'']]. The signal, as signals always do, becomes clearer over time. However you start a pendulum — however different its configuration, size, weight or jointedness — it ''will end up in entropic rest''.

For a complexity theorist, the butterfly’s wing [[metaphor]] makes the point not that hurricanes ''can'' be reduced to their infinitesimal operating causes and therefore predicted, but that they ''cannot''. These systems are so [[complex]] — so ''ontologically indeterminate'' — that it is ''theoretically'' impossible to predict how they will behave.