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start:mathematics:chaos_theory

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Chaos Theory

Chaos theory is the concept that the behaviour of some complex dynamical systems (e.g. global weather patterns) can be extremely sensitive to tiny changes in initial conditions — making long-term predictions about the system impossible.

In 1963, the publication of Edward Lorenz’s groundbreaking paper, 'Deterministic Nonperiodic Flow' in the Journal of Atmospheric Science hailed the beginning of a new field of mathematical study - with applications in meteorology, sociology, physics, environmental science, computer science, engineering, economics, biology, ecology, and philosophy.

And a now-famous talk, also by Edward Lorenz, in 1972 (to the American Association for the Advancement of Science in Washington, D.C.) was entitled 'Predictability: Does the Flap of a Butterfly's Wings in Brazil set off a Tornado in Texas?' and subsequently gave rise to the phrase The Butterfly Effect

Notes.

1) The outcomes of a chaotic system are not truly random - but they can degenerate into what appears to be randomness.

2) Although the flap of a butterfly's wings in Brazil could (in theory) set off a tornado in Texas, the chances of it doing so are astronomically small - thus, accurate predictions about which butterfly and when are essentially zero.

3) An (apparently) chaotic system can also 'spontaneously' fall into organised, or synchronised behaviour - so-called Spontaneous Order - examples are multiple connected-pendulum swings, firefly swarm light emissions, and group neuronal firing.

Suggestion : Predictions about chaotic systems fall into the special category of Known Unknowables.

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