CoChat
Sign Up
Cited by 193Mathematical Dynamics and FractalsChaos, Complexity, and EducationPhilosophy of Biology and Scientific Explanation

What Are the New Implications of Chaos for Unpredictability?

Open access
Werndl, Charlotte·2009·The British Journal for the Philosophy of Science
DOI 10.1093/bjps/axn053
Open this paper in CoChat — free accountOpen PDF

Abstract

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. Introduction2. Dynamical Systems and Unpredictability 2.1. Dynamical systems2.2. Natural invariant measures2.3. Unpredictability3. Chaos 3.1. Defining chaos3.2. Defining chaos via mixing4. 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 irrelevance5.2. Sufficiently past events are approximately probabilistically irrelevant for predictions6. Conclusion

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1093/bjps/axn053

Cites

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Despite being unpredictable, chaotic systems have recognizable features.

    “Despite being unpredictable, chaotic systems have recognizable features (May 1976; Werndl 2009).”

    From Religion as a Complex and Dynamic System (2013) · cites this paper as Werndl 2009

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Cites

No references could be resolved yet.

Research works printed but not linked: 50

  1. Arnold V. I., [1968]: Ergodic Problems of Classical Mechanics
  2. Batterman R. W., 1996, Foundations of Physics, 26, 307, 10.1007/BF02069475 · DOI
  3. Belot G., 1997, Studies in History and Philosophy of Modern Physics, 28, 147, 10.1016/S1355-2198(96)00025-1 · DOI
  4. Benedicks M., 1993, Inventiones Mathematicae, 112, 541, 10.1007/BF01232446 · DOI
  5. Berger A., Chaos and Chance: An Introduction to Stochastic Aspects of Dynamics, 10.1515/9783110866216 · DOI
  6. Berkovitz J., 2006, Studies in History and Philosophy of Modern Physics, 37, 661, 10.1016/j.shpsb.2006.02.003 · DOI
  7. Bishop R. C., 2003, Erkenntnis, 58, 169, 10.1023/A:1022003805614 · DOI
  8. Bowen R., 1977, Israel Journal of Mathematics, 28, 161, 10.1007/BF02759791 · DOI
  9. Brin M., [2002]: Introduction to Dynamical Systems
  10. Chernov N., [2006]: Chaotic Billiards
  11. Chirikov B. V., 1979, Physics Reports, 52, 264, 10.1016/0370-1573(79)90023-1 · DOI
  12. Cornfeld I. P., Ergodic Theory, 10.1007/978-1-4615-6927-5 · DOI · Paper page
  13. Dahan-Dalmedico A., M, 94
  14. Devaney R., An Introduction to Chaotic Dynamical Systems
  15. 10.1093/bjps/axi138 · DOI
  16. Earman J., 1971, Journal of Philosophy, 68, 729, 10.2307/2024946 · DOI
  17. Eckmann J., 1985, Reviews of Modern Physics, 57, 617, 10.1103/RevModPhys.57.617 · DOI
  18. Ford J., P, 71
  19. Jakobson M. V., 1981, Communications in Mathematical Physics, 81, 39, 10.1007/BF01941800 · DOI
  20. Leiber T., 1998, Synthese, 113, 357, 10.1023/A:1004944713074 · DOI
  21. Lichtenberg A. J., [1992]: Regular and Chaotic Dynamics
  22. Lighthill J., 1986, Proceedings of the Royal Society of London, Series A, 407, 35
  23. Lorenz E. N., 1963, Journal of the Atmospheric Sciences, 20, 130, 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2 · DOI
  24. Luzzatto S., 2005, Communications in Mathematical Physics, 260, 393, 10.1007/s00220-005-1411-9 · DOI
  25. Lyubich M., 2002, Annals of Mathematics, 156, 1, 10.2307/3597183 · DOI
  26. 10.1086/288941 · DOI
  27. Mañé R., Ergodic Theory and Differentiable Dynamics, 10.1007/978-3-642-70335-5 · DOI
  28. Martinelli M., 1998, Mathematics Magazine, 71, 112, 10.1080/0025570X.1998.11996610 · DOI
  29. May R. M., 1976, Nature, 261, 459, 10.1038/261459a0 · DOI · Paper page
  30. Mayer D., 1983, Journal of Statistical Physics, 31, 309, 10.1007/BF01011584 · DOI
  31. Miller D., P. Weingarnter and G. Schurz (eds), Law and Prediction in the Light of Chaos Research, 14
  32. Montague R., D, 70
  33. Moser J., Stable and Random Motions in Dynamical Systems, 10.1515/9781400882694 · DOI
  34. Nillsen R., 1999, Mathematics Magazine, 72, 14, 10.1080/0025570X.1999.11996693 · DOI
  35. Ott E., Chaos in Dynamical Systems, 10.1017/CBO9780511803260 · DOI
  36. Peitgen H., [1992]: Chaos and Fractals: New Frontiers of Science
  37. Robinson C., Symbol Dynamics, and Chaos
  38. Ruelle D., 1997, Complexity, 3, 26, 10.1002/(SICI)1099-0526(199709/10)3:1<26::AID-CPLX8>3.0.CO;2-C · DOI
  39. Schurz G., P. Weingarnter and G. Schurz (eds), Law and Prediction in the Light of Chaos Research, 41
  40. Schuster G., [2005]: Deterministic Chaos: An Introduction
  41. Smith L. A., 1999, Quarterly Journal of the Royal Meteorological Society, 125, 2855, 10.1002/qj.49712556005 · DOI
  42. Smith P., Explaining Chaos, 10.1017/CBO9780511554544 · DOI
  43. Stone M. A., 1989, American Philosophical Quarterly, 26, 123
  44. van Lith J., 2001, Studies in History and Philosophy of Modern Physics, 32, 581, 10.1016/S1355-2198(01)00027-2 · DOI
  45. Weingartner P., P. Weingarnter and G. Schurz (eds), Law and Prediction in the Light of Chaos Research, 88
  46. Wiggins S., Introduction to Applied Nonlinear Dynamical Systems and Chaos, 10.1007/978-1-4757-4067-7 · DOI
  47. Young L., XIIth International Congress of Mathematical Physics (Brisbane), 9
  48. Young L., 2002, Journal of Statistical Physics, 108, 733, 10.1023/A:1019762724717 · DOI
  49. Zaslavsky G. M., Hamiltonian Chaos and Fractional Dynamics, 10.1093/oso/9780198526049.001.0001 · DOI
  50. Ziehmann C., 2000, Physics Letters A, 271, 1, 10.1016/S0375-9601(00)00336-4 · DOI

Cited by

Sorted by citations

Authors
Werndl, C.
Affiliations
University of Cambridge (GB)
Corresponding author
Werndl, Charlotte
ORCID
Werndl, Charlotte
Venue
The British Journal for the Philosophy of Science
Publisher
University of Chicago Press
Published
2009-03-01
Volume
60
Issue
1
Pages
195-220
ISSN
  • 0007-0882 (ISSN-L)
  • 1464-3537
DOI
10.1093/bjps/axn053
OpenAlex
W2111479915
Cited by
193
References
0
Citations by year
2026: 6 · 2025: 3 · 2024: 6 · 2023: 10 · 2022: 10 · 2021: 11 · 2020: 13 · 2019: 11 · 2018: 12 · 2017: 10 · 2016: 8 · 2015: 9 · 2014: 16 · 2013: 10 · 2012: 10
FWCI
22.75
Type
journal article
Language
en
Open access
Locations
  • The British Journal for the Philosophy of Science (publishedVersion)
  • London School of Economics and Political Science Theses Online (London School of Economics and Political Science) (submittedVersion)
  • HighWire Press Open Archive (submittedVersion)
Funders
University of Cambridge
Topics
  • Physical Sciences › Mathematics › Mathematical Physics › Mathematical Dynamics and Fractals
  • Social Sciences › Education › Chaos, Complexity, and Education
  • Social Sciences › Arts and Humanities › History and Philosophy of Science › Philosophy of Biology and Scientific Explanation
Keywords
chaos, unpredictability, mixing, deterministic systems, dynamical systems, exponential divergence, philosophy of physics

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review