Knowledge and Meaning ... Chaos and Complexity

What are models good for? Taking a largely pedagogical view, the following essay discusses the semantics of measurement and the uses to which an observer can put knowledge of a process’s structure. To do this in as concrete a way as possible, it first reviews the reconstruction of probabilistic finite automata from time series of stochastic and chaotic processes. It investigates the convergence of an observer’s knowledge of the process’s state; assuming that the process is in, and the observer also uses for internal representation, that model class. The conventional notions of phase and phase-locking are extended beyond periodic behavior to include deterministic chaotic processes. The meaning of individual measurements of an unpredictable process is then defined in terms of the computational structure in a model that an observer built.