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Computable Chaos

Published online by Cambridge University Press:  01 April 2022

John A. Winnie
John A. Winnie*
Affiliation:
Department of History and Philosophy of Science, Indiana University
*
‡Send reprint requests to the author, Department of History and Philosophy of Science, Goodbody Hall 114, Indiana University, Bloomington, IN 47405, USA.
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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 R”.

Type
Research Article
Information
Philosophy of Science , Volume 59 , Issue 2 , June 1992 , pp. 263 - 275
Copyright
Copyright © Philosophy of Science Association 1992

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Footnotes

†

I am very grateful to Stephen Kellert, Marco Giunti, John Ewing, Zeno Swijtink, Lawrence Husch, and, especially, Linda Wessels for a number of helpful comments and conversations.

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