Perspective: Sloppiness and emergent theories in physics, biology, and beyond

Mark K. Transtrum, Benjamin B. Machta, Kevin S. Brown, BRYAN DANIELS, Christopher R. Myers, James P. Sethna

Research output: Contribution to journalArticle

108 Scopus citations

Abstract

Large scale models of physical phenomena demand the development of new statistical and computational tools in order to be effective. Many such models are "sloppy," i.e., exhibit behavior controlled by a relatively small number of parameter combinations. We review an information theoretic framework for analyzing sloppy models. This formalism is based on the Fisher information matrix, which is interpreted as a Riemannian metric on a parameterized space of models. Distance in this space is a measure of how distinguishable two models are based on their predictions. Sloppy model manifolds are bounded with a hierarchy of widths and extrinsic curvatures. The manifold boundary approximation can extract the simple, hidden theory from complicated sloppy models. We attribute the success of simple effective models in physics as likewise emerging from complicated processes exhibiting a low effective dimensionality. We discuss the ramifications and consequences of sloppy models for biochemistry and science more generally. We suggest that the reason our complex world is understandable is due to the same fundamental reason: simple theories of macroscopic behavior are hidden inside complicated microscopic processes.

Original languageEnglish (US)
Article number010901
JournalJournal of Chemical Physics
Volume143
Issue number1
DOIs
StatePublished - Jan 1 2015
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

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    Transtrum, M. K., Machta, B. B., Brown, K. S., DANIELS, BRYAN., Myers, C. R., & Sethna, J. P. (2015). Perspective: Sloppiness and emergent theories in physics, biology, and beyond. Journal of Chemical Physics, 143(1), [010901]. https://doi.org/10.1063/1.4923066