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Laplace’s Demon and the Adventures of His Apprentices

Published online by Cambridge University Press:  01 January 2022


The sensitive dependence on initial conditions (SDIC) associated with nonlinear models imposes limitations on the models’ predictive power. We draw attention to an additional limitation than has been underappreciated, namely, structural model error (SME). A model has SME if the model dynamics differ from the dynamics in the target system. If a nonlinear model has only the slightest SME, then its ability to generate decision-relevant predictions is compromised. Given a perfect model, we can take the effects of SDIC into account by substituting probabilistic predictions for point predictions. This route is foreclosed in the case of SME, which puts us in a worse epistemic situation than SDIC.

Research Article
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Work for this article has been supported by the London School of Economics’s Grantham Research Institute on Climate Change and the Environment and the Centre for Climate Change Economics and Policy funded by the Economics and Social Science Research Council and Munich Re. Frigg acknowledges financial support from the Arts and Humanities Research Council–funded Managing Severe Uncertainty project and grant FFI2012-37354 of the Spanish Ministry of Science and Innovation (MICINN). Bradley’s research was supported by the Alexander von Humboldt Foundation. Smith would also like to acknowledge continuing support from Pembroke College, Oxford. We would like to thank Wendy Parker, David Stainforth, Erica Thompson, and Charlotte Werndl for comments on earlier drafts and helpful discussions.


Andronov, Aleksandr A., and Pontrjagin, Lev. 1937. “Systèmes Grossiers.” Doklady of the Academy of Sciences of the USSR 14:247–51.Google Scholar
Arnold, Vladimir I., and Avez, André. 1968. Ergodic Problems of Classical Mechanics. New York: Benjamin.Google Scholar
Barreira, Luis, and Valls, Claudia. 2012. Ordinary Differential Equations: Qualitative Theory. Washington, DC: American Mathematical Society.CrossRefGoogle Scholar
Batterman, Robert W. 1993. “Defining Chaos.” Philosophy of Science 60:4366.CrossRefGoogle Scholar
Berger, Arno. 2001. Chaos and Chance: An Introduction to Stochastic Aspects of Dynamics. Hamburg: de Gruyter.CrossRefGoogle Scholar
Bradley, Seamus. 2012. “Dutch Book Arguments and Imprecise Probabilities.” In Probabilities Laws and Structures, ed. Dieks, Dennis, Gonzalez, Wenceslao, Hartmann, Stephan, Stoeltzner, Michael, and Weber, Marcel, 317. Berlin: Springer.CrossRefGoogle Scholar
Curd, Thomas M., and Thomas, Joy A.. 1991. Elements of Information Theory. New York: Wiley.Google Scholar
Dempster, Arthur. 1961. “Upper and Lower Probabilities Induced by a Multivalued Mapping.” Annals of Mathematical Statistics 38:325–39.Google Scholar
Earman, John. 1986. A Primer on Determinsim. Dordrecht: Reidel.CrossRefGoogle Scholar
Fan, Shu, and Hyndman, Rob J.. 2012. “Short-Term Load Forecasting Based on a Semi-parametric Additive Model.” IEEE Transactions on Power Systems 27:134–41.CrossRefGoogle Scholar
Frigg, Roman, Smith, Leonard A., and Stainforth, Dave A.. 2013. “The Myopia of Imperfect Climate Models: The Case of UKCP09.” Philosophy of Science 80, no. 5, forthcoming.CrossRefGoogle Scholar
Frigg, Roman, and Werndl, Charlotte. 2012. “Demystifying Typicality.” Philosophy of Science 79:917–29.CrossRefGoogle Scholar
Good, Irving J. 1962. “Subjective Probability as the Measure of a Non-measurable Set.” In Logic, Methodology and Philosophy of Science, ed. Nagel, Ernest, Suppes, Patrick, and Tarski, Alfred, 319–29. Stanford, CA: Stanford University Press.Google Scholar
Hagedorn, R., and Smith, Leonard A.. 2009. “Communicating the Value of Probabilistic Forecasts with Weather Roulette.” Meteorological Applications 16:143–55.CrossRefGoogle Scholar
Hayashi, Shuhei. 1997. “Invariant Manifolds and the Solution of the C1-Stability and Ω-Stability Conjectures for Flows.” Annals of Mathematics 145:81137.CrossRefGoogle Scholar
Jenkins, Geoff, Murphy, James, Sexton, David, Lowe, Jason, and Jones, Phil. 2009. “UK Climate Projections.” Briefing report, Department for Environment, Food and Rural Affairs, London.Google Scholar
Judd, Kevin. 2007. “Nonprobabilistic Odds.” Working paper, University of Western Australia.Google Scholar
Judd, Kevin, and Smith, Leonard A.. 2004. “Indistinguishable States.” Pt. 2, “The Imperfect Model Scenario.” Physica D 196:224–42.Google Scholar
Kellert, Stephen. 1993. In the Wake of Chaos. Chicago: University of Chicago Press.CrossRefGoogle Scholar
Kyburg, Henry. 1978. “Subjective Probability: Criticisms, Reflections, and Problems.” Journal of Philosophical Logic 7:157–80.CrossRefGoogle Scholar
Laplace, Marquis de. 1814. A Philosophical Essay on Probabilities. New York: Dover.Google Scholar
Levi, Isaac. 1974. “On Indeterminate Probabilities.” Journal of Philosophy 71:391418.CrossRefGoogle Scholar
Mañé, Ricardo. 1988. “A Proof of the C1 Stability Conjecture.” Publications Mathématiques de l’Institut des Hautes Études Scientifiques 66:161210.CrossRefGoogle Scholar
McGuffie, Kendal, and Henderson-Sellers, Ann. 2005. A Climate Modelling Primer. Chichester, NY: Wiley.CrossRefGoogle Scholar
McWilliams, James C. 2007. “Irreducible Imprecision in Atmospheric and Oceanic Simulations.” Proceedings of the National Academy of Sciences 104:8709–13.CrossRefGoogle ScholarPubMed
Orrell, David, Smith, Leonard A., Palmer, Tim, and Barkmeijer, Jan. 2001. “Model Error in Weather Forecasting.” Nonlinear Processes in Geophysics 8:357–71.CrossRefGoogle Scholar
Palis, Jacob, and Smale, Stephen. 1970. “Structural Stability Theorems.” In Global Analysis, ed. Chern, Shiing-Shen and Smale, Stephen, 223–31. Proceedings of Symposia in Pure Mathematics 14. Providence, RI: American Mathematical Society.Google Scholar
Peixoto, Marilia C., and Peixoto, Maurício M.. 1959. “Structural Stability in the Plane with Enlarged Boundary Conditions.” Anais da Academia Brasileira de Ciências 31:135–60.Google Scholar
Peixoto, Maurício. 1962. “Structural Stability on Two Dimensional Manifolds.” Topology 2:101–21.Google Scholar
Robinson, Clark. 1976. “Structural Stability of C1 Diffeomorphisms.” Journal of Differential Equations 22:2873.CrossRefGoogle Scholar
Smale, Stephen. 1966. “Structurally Stable Systems Are Not Dense.” American Journal of Mathematics 88:491–96.CrossRefGoogle Scholar
Smale, Stephen 1967. “Differentiable Dynamical Systems.” Bulletin of the American Mathematical Society 73:747817.CrossRefGoogle Scholar
Smith, Leonard A. 1992. “Identification and Prediction of Low-Dimensional Dynamics.” Physica D 58:5076.Google Scholar
Smith, Leonard A. 2002. “What Might We Learn from Climate Forecasts?Proceedings of the National Academy of Sciences of the USA 4:2487–92.Google Scholar
Smith, Leonard A. 2006. “Predictability Past Predictability Present.” In Predictability of Weather and Climate, ed. Palmer, Tim and Hagedorn, Renate, 217–50. Cambridge: Cambridge University Press.Google Scholar
Hagedorn, Renate 2007. Chaos: A Very Short Introduction. Oxford: Oxford University Press.Google Scholar
Smith, Peter. 1998. Explaining Chaos. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Snyder, Ralph D., Ord, J. Keith, and Beaumonta, Adrian. 2012. “Forecasting the Intermittent Demand for Slow-Moving Inventories: A Modelling Approach.” International Journal of Forecasting 28:485–96.CrossRefGoogle Scholar
Suppes, Patrick. 1974. “The Measurement of Belief.” Journal of the Royal Statistical Society B 36:160–91.Google Scholar
Thompson, Erica L. 2013. “Modelling North Atlantic Storms in a Changing Climate.” PhD diss., Imperial College, London.Google Scholar
Walley, Peter. 1991. Statistical Reasoning with Imprecise Probabilities. London: Chapman & Hall.CrossRefGoogle Scholar
Werndl, Charlotte. 2009. “What Are the New Implications of Chaos for Unpredictability?British Journal for the Philosophy of Science 60:195220.CrossRefGoogle Scholar
Williamson, Jon. 2010. In Defense of Objective Bayesianism. Oxford: Oxford University Press.CrossRefGoogle Scholar
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