Autonomy and Scales

Abstract

This paper addresses a set of issues involved in modeling systems across many orders of magnitude in spatial and temporal scales. In particular, it focuses on the question of how one can explain and understand the relative autonomy and safety of models at continuum scales. The typical battle line between reductive “bottom-up’’ modeling and “top-down” modeling from phenomenological theories is shown to be overly simplistic. Multi-scale models are beginning to succeed in showing how to upscale from statistical atomistic/molecular models to continuum/hydrodynamics models. The consequences for our understanding of the debate between reductionism and emergence will be examined.