In quantum field theory, for instance, there has been considerable success in in showing how a theory appropriate for some range of energy scales is related to a theory for another range via a process of renormalization (Bain 2012). Renormalization provides a kind of limiting relationship between theories at different scales despite the fact that the reductive Schema R typically fails because of divergences related to singular limits. The physics at one scale is relatively independent of that at some higher energy (shorter length). In effect, renormalization is a mathematical scheme for characterizing how the structure of interactions changes with changing scale: it turns out that the domain characterized by some lower energy (or larger length) scale is surprisingly and remarkably decoupled from that of higher energies (or smaller lengths). In other words, the decoupling entails that the higher energy regime does not much effect the behaviors and character of the lower energy regimes.