Is that so? As a rule, when you take a limit new things can emerge. For example, pi is the limit of a sequence of rational numbers. For example 3, 3.1, 3.14,

Is that so? As a rule, when you take a limit new things can emerge. For example, pi is the limit of a sequence of rational numbers. For example 3, 3.1, 3.14, 3.141, 3.1415, etc. All these rational numbers are "perfectly predictable", while the digits of pi are not. One could say pi is a "chaotic number", and is the limit of non-chaotic numbers. Nobody would find this paradoxical. Take turbulence, the textbook example of chaos. I can approximate any solution of the Navier-Stokes equation with a sequence of periodic functions (with longer and longer period). Each of these is non-chaotic, but the limit is chaotic. Quantum mechanics converges to classical mechanics when h->0. So, the solutions of Schroedinger's equation (which are all non-chaotic) converge to something that exhibit chaos. Where's the paradox?