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Large scale models of physical phenomena demand the development of newstatistical and computational tools in order to be effective. Many such modelsare `sloppy', i.e., exhibit behavior controlled by a relatively small number ofparameter combinations. We review an information theoretic framework foranalyzing sloppy models. This formalism is based on the Fisher InformationMatrix, which we interpret as a Riemannian metric on a parameterized space ofmodels. Distance in this space is a measure of how distinguishable two modelsare based on their predictions. Sloppy model manifolds are bounded with ahierarchy of widths and extrinsic curvatures. We show how the manifold boundaryapproximation can extract the simple, hidden theory from complicated sloppymodels. We attribute the success of simple effective models in physics aslikewise emerging from complicated processes exhibiting a low effectivedimensionality. We discuss the ramifications and consequences of sloppy modelsfor biochemistry and science more generally. We suggest that the reason ourcomplex world is understandable is due to the same fundamental reason: simpletheories of macroscopic behavior are hidden inside complicated microscopicprocesses.

Sloppiness and Emergent Theories in Physics, Biology, and Beyond