permits symmetry breaking—Prigogine calls this order by fluctuations.

With chaotic systems, then, we lose the promise that mathematics has traditionally provided of a precise, God’s eye view over all time, and thus of certainty and predictability. We are left only with calculations in natural time that give us rapidly decreasing accuracy and hence increasing unpredictability. But from some points of view this is not necessarily a problem. As Turing speculated in his discussion of learning, learning requires trial and error, which would be pointless in a perfectly predictable world, and specifically it requires an element of stochasticity. Many others have made the same observation – that stochasticity seems to be a necessary element in any creative process. In physical systems stochastic perturbations are the basis of the symmetry breaking by which systems become increasingly complex and organized. Chaotic dynamics may thus play a positive role by providing a necessary source of stochasticity in physical, biological, and human systems.

Physics, with the major exception of thermodynamics (together with two very specific cases in particle physics: CPT and a case of a heavy-fermion superconductor [@schemm2014]), is characterized by laws that are “time reversible” in the sense that they remain valid if time 