Complexity, Chaos and the Nature of Reality
(A note to Len) Our mathematical models (or our ability, in general, to predict or "understand" a system) must always be bound by an artificial "carving out" of the application domain of understanding specification of scale - including the applicability of our tools to the scale we are working with recognition of the precision we expect or the precision that is even theoretically possible. This visualizes a "fractal" nature of reality (or our models of reality) up to a point, where models at one scale fail at a different one. In "Road To Reality" Penrose attempted to construct a framework for a smooth transition from one model to another (Relativity to Quantum Mechanics, for example). I'm afraid I remained unconvinced but partly because I'm too lazy or too stupid to follow his arguments in detail. In a hypothetical University curriculum in this field (which still needs to be named), I think that scale, chaos, non-linear systems a...