Parameter Space Compression Underlies Emergent Theories and Predictive Models

Abstract

Information Physics Multiparameter models, which can emerge in biology and other disciplines, are often sensitive to only a small number of parameters and robust to changes in the rest; approaches from information theory can be used to distinguish between the two parameter groups. In physics, on the other hand, one does not need to know the details at smaller length and time scales in order to understand the behavior on large scales. This hierarchy has been recognized for a long time and formalized within the renormalization group (RG) approach. Machta et al. (p. 604 ) explored the connection between two scales by using an information-theoretical approach based on the Fisher Information Matrix to analyze two commonly used physics models—diffusion in one dimension and the Ising model of magnetism—as the time and length scales, respectively, were progressively coarsened. The expected “stiff” parameters emerged, in agreement with RG intuition.