  We report a similarity between the microscopic parameter dependance of
emergent theories in physics and that of multiparameter models common in other
areas of science. In both cases, predictions are possible despite large
uncertainties in the microscopic parameters because these details are
compressed into just a few governing parameters that are sufficient to describe
relevant observables. We make this commonality explicit by examining parameter
sensitivity in a hopping model of diffusion and a generalized Ising model of
ferromagnetism. We trace the emergence of a smaller effective model to the
development of a hierarchy of parameter importance quantified by the
eigenvalues of the Fisher Information Matrix. Strikingly, the same hierarchy
appears ubiquitously in models taken from diverse areas of science. We conclude
that the emergence of effective continuum and universal theories in physics is
due to the same parameter space hierarchy that underlies predictive modeling in
other areas of science.
