Idealization and modeling

Robert W. Batterman

pp. 427-446

in: Roman Frigg, Stephan Hartmann, Cyrille Imbert (eds), Models and simulations, Synthese 169 (3), 2009.

Abstract

This paper examines the role of mathematical idealization in describing and explaining various features of the world. It examines two cases: first, briefly, the modeling of shock formation using the idealization of the continuum. Second, and in more detail, the breaking of droplets from the points of view of both analytic fluid mechanics and molecular dynamical simulations at the nano-level. It argues that the continuum idealizations are explanatorily ineliminable and that a full understanding of certain physical phenomena cannot be obtained through completely detailed, nonidealized representations.