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The amount of time we can successfully predict the state of a chaotic system depends on three things: how much error we’re willing to tolerate in the forecast; how precisely we can measure the initial state of the system; and a time scale that’s beyond our control, called the Lyapunov time, which depends on the inherent dynamics of the system itself.
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Steven H. Strogatz (Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life)
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Lyapunov time sets a horizon beyond which acceptable prediction becomes impossible. For a chaotic electrical circuit, the horizon is something like a thousandth of a second; for the weather, it’s unknown but seems to be a few days; and for the solar system itself, five million years.
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Steven H. Strogatz (Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life)