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What Are the New Implications of Chaos for Unpredictability? 总被引:1,自引:0,他引:1
From the beginning of chaos research until today, the unpredictabilityof chaos has been a central theme. It is widely believed andclaimed by philosophers, mathematicians and physicists alikethat chaos has a new implication for unpredictability, meaningthat chaotic systems are unpredictable in a way that other deterministicsystems are not. Hence, one might expect that the question Whatare the new implications of chaos for unpredictability?has already been answered in a satisfactory way. However, thisis not the case. I will critically evaluate the existing answersand argue that they do not fit the bill. Then I will approachthis question by showing that chaos can be defined via mixing,which has never before been explicitly argued for. Based onthis insight, I will propose that the sought-after new implicationof chaos for unpredictability is the following: for predictingany event, all sufficiently past events are approximately probabilisticallyirrelevant.
- Introduction
- Dynamical Systems and Unpredictability
- 2.1 Dynamical systems
- 2.2 Natural invariant measures
- 2.3Unpredictability
- 2.2 Natural invariant measures
- 2.1 Dynamical systems
- Chaos
- 3.1 Defining chaos
- 3.2 Definingchaos via mixing
- 3.1 Defining chaos
- Criticism of Answers in the Literature
- 4.1 Asymptotic unpredictability?
- 4.2 Unpredictability dueto rapid or exponential divergence?
- 4.3 Macro-predictabilityand Micro-unpredictability?
- 4.2 Unpredictability dueto rapid or exponential divergence?
- 4.1 Asymptotic unpredictability?
- A General New Implication ofChaos for Unpredictability
- 5.1Approximate probabilistic irrelevance
- 5.2 Sufficiently pastevents are approximately probabilisticallyirrelevant for predictions
- 5.1Approximate probabilistic irrelevance
- Conclusion
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