3.3 Determinism and Chaos
If the world were governed by strictly deterministic laws, might it still look as though indeterminism reigns? This is one of the difficult questions that chaos theory raises for the epistemology of determinism.
A deterministic chaotic system has, roughly speaking, two salient features: (i) the evolution of the system over a long time period effectively mimics a random or stochastic process—it lacks predictability or computability in some appropriate sense; (ii) two systems with nearly identical initial states will have radically divergent future developments, within a finite (and typically, short) timespan. We will use “randomness” to denote the first feature, and “sensitive dependence on initial conditions” (SDIC) for the latter. Definitions of chaos may focus on either or both of these properties; Batterman (1993) argues that only (ii) provides an appropriate basis for defining chaotic systems.
A simple and very important example of a chaotic system in both randomness and SDIC terms is the Newtonian dynamics of a pool table with a convex obstacle (or obstacles) (Sinai 1970 and others). See Figure ...
If the world were governed by strictly deterministic laws, might it still look as though indeterminism reigns? This is one of the difficult questions that chaos theory raises for the epistemology of determinism.
A deterministic chaotic system has, roughly speaking, two salient features: (i) the evolution of the system over a long time period effectively mimics a random or stochastic process—it lacks predictability or computability in some appropriate sense; (ii) two systems with nearly identical initial states will have radically divergent future developments, within a finite (and typically, short) timespan. We will use “randomness” to denote the first feature, and “sensitive dependence on initial conditions” (SDIC) for the latter. Definitions of chaos may focus on either or both of these properties; Batterman (1993) argues that only (ii) provides an appropriate basis for defining chaotic systems.
A simple and very important example of a chaotic system in both randomness and SDIC terms is the Newtonian dynamics of a pool table with a convex obstacle (or obstacles) (Sinai 1970 and others). See Figure ...
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