What Are the New Implications of Chaos for Unpredictability?
By Charlotte Werndl. British Journal for the Philosophy of Science, 2009
183 citations recorded by the source corpus.
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. 1. Introduction 2. Dynamical Systems and Unpredictability 2.1. Dynamical systems 2.2. Natural invariant measures 2.3. Unpredictability 3. Chaos 3.1. Defining chaos 3.2. Defining chaos via mixing 4. 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? 5. A General New Implication of Chaos for Unpredictability 5.1. Approximate probabilistic irrelevance 5.2. Sufficiently past events are approximately probabilistically irrelevant for predictions 6. Conclusion Introduction Dynamical Systems and Unpredictability 2.1. Dynamical systems 2.2. Natural invariant measures 2.3. Unpredictability Dynamical systems Natural invariant measures Unpredictability Chaos 3.1. Defining chaos 3.2. Defining chaos via mixing Defining chaos 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? Asymptotic unpredictability? Unpredictability due to rapid or exponential divergence? 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 Approximate probabilistic irrelevance Sufficiently past events are approximately probabilistically irrelevant for predictions Conclusion
Subfields: Economics and Econometrics, Statistical and Nonlinear Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/74c5b3c3a39263062c4c07ef8943f5b2a317b96a
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Economics and Econometrics
In Statistics and Probability
Citations in the corpus
- Big Data Research in Information Systems: Toward an Inclusive Research Agenda (2016, background): “Chaos theory studies the behavior of dynamic systems that are highly sensitive to initial conditions, where small changes in initial conditions can yield widely diverging outcomes (Gleick, 1987; Sprott, 2003; Werndl 2009).”