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Defining Chaos

Published online by Cambridge University Press:  01 April 2022

Robert W. Batterman
Robert W. Batterman*
Affiliation:
Department of Philosophy, Ohio State University
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Abstract

This paper considers definitions of classical dynamical chaos that focus primarily on notions of predictability and computability, sometimes called algorithmic complexity definitions of chaos. I argue that accounts of this type are seriously flawed. They focus on a likely consequence of chaos, namely, randomness in behavior which gets characterized in terms of the unpredictability or uncomputability of final given initial states. In doing so, however, they can overlook the definitive feature of dynamical chaos—the fact that the underlying motion generating the behavior exhibits extreme trajectory instability. I formulate a simple criterion of adequacy for any definition of chaos and show how such accounts fail to satisfy it.

Type
Research Article
Information
Philosophy of Science , Volume 60 , Issue 1 , March 1993 , pp. 43 - 66
Copyright
Copyright © Philosophy of Science Association 1993

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Footnotes

†

I would like to thank Mark Wilson for numerous helpful discussions, without which I would still be confused on many points. Naturally, any mistakes and confusions which still remain are entirely my own. I would also like to thank Jim Joyce for comments on a very early draft of this paper. This work was supported by the National Science Foundation under grant No. DIR-9012010.

‡

Send reprint requests to the author, Department of Philosophy, Ohio State University, 350 University Hall, 230 N. Oval Mall, Columbus, OH 43210, USA.

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