Multiscale Modeling: Explanation and Emergence

Abstract

I discuss two extreme views about emergence and explanation in the face of the following facts. The continuum equations of fluid mechanics and material behavior (bending of beams) are remarkably successful. They continue to be used for engineering and building purposes despite the fact that they almost completely ignore lower scale structure and detail. In fact, they treat fluids and steel beams as continuous blobs with no lower scale (atomic/molecular) structure whatsoever. The explanatory question is how such equations can be so successful. Extreme reductionists views expect that a bottom-up explanation from the actual fundamental lower scale structure will answer this explanatory question. Extreme emergentist views deny such reductionist pictures and hold that no bottom-up explanation is possible. The paper argues for a more sophisticated analysis that recognizes the importance of structures at scales intermediate between the atomic and the continuum. It is an analysis that appeals to sophisticated mathematics called “homogenization theory.” One can, in fact, provide a nonreductive explanation of the relative autonomy of the continuum equations from the lower scale details.

I would like to thank Julia Bursten for helpful comments. This research was supported by a grant from the John Templeton Foundation.