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Butterfly effect: Difference between revisions
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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”. | 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 to vergence is not accountable solely for atomic differences in the initial configuration, but for ongoing atomic differences throughout the pendulums cycle. The systems are ''path''-dependent, not ''initial-condition''-dependent. The longer the the system continues the more dependent the system will be on on the infinity if subsequently intervening causes. Unless the pendulum is somehow powered, the laws of thermodynamics predict that it will in a short time period come to rest. Over time, then, even insoluble mathematical operations converge. We can see this path dependency to be noise. For an unpowered jointed pendulum, the signal is is, over time, clear. However you start it, 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, but that they ''cannot''. These systems are so [[complex]] — so ''ontologically indeterminate'' — that it is ''theoretically'' impossible to predict how they will behave. | |||
Butterfly wing-flaps are discrete independent events. Unless you are prepared to hypothesise some kind of spooky quantum butterfly entanglement, one butterfly flapping its wings will not make more or less likely another butterfly’s decision to do the same, let alone any of the other environmental factors that might cause a tropical storm. | Butterfly wing-flaps are discrete independent events. Unless you are prepared to hypothesise some kind of spooky quantum butterfly entanglement, one butterfly flapping its wings will not make more or less likely another butterfly’s decision to do the same, let alone any of the other environmental factors that might cause a tropical storm. | ||