Journal Article

What Are the New Implications of Chaos for Unpredictability?

Charlotte Werndl

in The British Journal for the Philosophy of Science

Published on behalf of British Society for the Philosophy of Science

Volume 60, issue 1, pages 195-220
Published in print March 2009 | ISSN: 0007-0882
Published online January 2009 | e-ISSN: 1464-3537 | DOI: http://dx.doi.org/10.1093/bjps/axn053
What Are the New Implications of Chaos for Unpredictability?

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From the beginning of chaos research until today, the unpredictability of chaos has been a central theme. It is widely believed and claimed by philosophers, mathematicians and physicists alike that chaos has a new implication for unpredictability, meaning that chaotic systems are unpredictable in a way that other deterministic systems are not. Hence, one might expect that the question ‘What are the new implications of chaos for unpredictability?’ has already been answered in a satisfactory way. However, this is not the case. I will critically evaluate the existing answers and argue that they do not fit the bill. Then I will approach this question by showing that chaos can be defined via mixing, which has never before been explicitly argued for. Based on this insight, I will propose that the sought-after new implication of chaos for unpredictability is the following: for predicting any event, all sufficiently past events are approximately probabilistically irrelevant.

Introduction

Dynamical Systems and Unpredictability 2.1

Dynamical systems

2.2

Natural invariant measures

2.3

Unpredictability

Chaos 3.1

Defining chaos

3.2

Defining chaos via mixing

Criticism of Answers in the Literature 4.1

Asymptotic unpredictability?

4.2

Unpredictability due to rapid or exponential divergence?

4.3

Macro-predictability and Micro-unpredictability?

A General New Implication of Chaos for Unpredictability 5.1

Approximate probabilistic irrelevance

5.2

Sufficiently past events are approximately probabilistically irrelevant for predictions

Conclusion

Journal Article.  9964 words.  Illustrated.

Subjects: Philosophy of Science ; Science and Mathematics

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