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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jul 01, 2015
- Source ID
- 10.1063/1.4923066
Entities
People
- Benjamin B. Machta
- Bryan C Daniels
- Christopher R. Myers
- James P. Sethna
- Kevin Scott Brown
- Mark K Transtrum
Organizations
- Brigham Young University
- Cornell University
- John Templeton Foundation
- National Science Foundation
- Princeton University
- United States Army Research Laboratory
- University of Connecticut
- University of Wisconsin–Madison