The Challenge of Macro-Systems

Abstract

Chaos is a word of rich and looming content, implying unpredictable events producing unlimited variety that is not tameable in the territory of order. The grand narrative of mechanics casts chaos as the antagonist of integrability. In the preceding chapter, we demonstrated order in integrability, showing that motion can be transformed into motionless, that is, a superficially dynamic event can be reduced into a complete set of invariant parameters (constants ofmotion). Symmetry is the key to find the invariance. The negation of order, then, means irreducibility or true movement–these properties define chaos in the realm of mechanics. However, more general aspects of chaos should be recognized from a phenomenological viewpoint. In a “macro-system”which includes a tremendous number of interacting parameters, non-integrability (lack of constants of motion) is just obvious, so it cannot be a determining concept characterizing something chaotic. In this chapter, we focus on the “difficulty of prediction” as an aspect characterizing chaos and discuss complex systems from a macroscopic viewpoint.