Computable chaos

Philosophy of Science 59 (2):263-275 (1992)
Abstract
Some irrational numbers are "random" in a sense which implies that no algorithm can compute their decimal expansions to an arbitrarily high degree of accuracy. This feature of (most) irrational numbers has been claimed to be at the heart of the deterministic, but chaotic, behavior exhibited by many nonlinear dynamical systems. In this paper, a number of now classical chaotic systems are shown to remain chaotic when their domains are restricted to the computable real numbers, providing counterexamples to the above claim. More fundamentally, the randomness view of chaos is shown to be based upon a confusion between a chaotic function on a phase space and its numerical representation in Rn
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DOI 10.1086/289666
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Gordon Belot & John Earman (1997). Chaos Out of Order: Quantum Mechanics, the Correspondence Principle and Chaos. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 28 (2):147-182.

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