title: Perspective: Sloppiness and emergent theories in physics, biology, and beyond.
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.
authors.affiliation: Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84602, USA.
authors.forename: Mark K
authors.initials: MK
authors.lastname: Transtrum
authors.affiliation: Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersey 08544, USA.
authors.forename: Benjamin B
authors.initials: BB
authors.lastname: Machta
authors.affiliation: Departments of Biomedical Engineering, Physics, Chemical and Biomolecular Engineering, and Marine Sciences, University of Connecticut, Storrs, Connecticut 06269, USA.
authors.forename: Kevin S
authors.initials: KS
authors.lastname: Brown
authors.affiliation: Center for Complexity and Collective Computation, Wisconsin Institute for Discovery, University of Wisconsin, Madison, Wisconsin 53715, USA.
authors.forename: Bryan C
authors.initials: BC
authors.lastname: Daniels
authors.affiliation: Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA.
authors.forename: Christopher R
authors.initials: CR
authors.lastname: Myers
authors.affiliation: Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA.
authors.forename: James P
authors.initials: JP
authors.lastname: Sethna
mesh_terms: D008962:Models, Theoretical; D010825:Physics / Q000379:methods*; D049490:Systems Biology / Q000379:methods*