|Title||Parameter Space Compression Underlies Emergent Theories and Predictive Models|
|Publication Type||Journal Article|
|Year of Publication||2013|
|Authors||Machta, Benjamin B., Chachra Ricky, Transtrum Mark K., and Sethna James P.|
The microscopically complicated real world exhibits behavior that often yields to simple yet quantitatively accurate descriptions. Predictions are possible despite large uncertainties in microscopic parameters, both in physics and in multiparameter models in other areas of science. We connect the two by analyzing parameter sensitivities in a prototypical continuum theory (diffusion) and at a self-similar critical point (the Ising model). We trace the emergence of an effective theory for long-scale observables to a compression of the parameter space quantified by the eigenvalues of the Fisher Information Matrix. A similar compression appears ubiquitously in models taken from diverse areas of science, suggesting that the parameter space structure underlying effective continuum and universal theories in physics also permits predictive modeling more generally.
See also Physicists unify the structure of scientific theories in the Cornell Chronicle (Anne Ju); Jesse Silverberg's Huffington Post blog and Kathryn McGill's vblog Soft Matters with Jim Sethna from The Physics Factor; and (Unedited) Interview of Sethna by Steven Reiner, Stony Brook School of Journalism (smaller version).