Butterfly effect: Difference between revisions

Set off two double-jointed pendulums from an apparently identical condition and quickly their trajectories will wildly diverge, it is true. But this divergence does not 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 continue on their periods. 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.

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''.