The Role of the Observer in Uniform Systems

Abstract

Starting from models of particular interest for the physicist, there has evolved in the course of years, with different emphasis and varying degrees of abstraction, a vast literature of mathematical structures known collectively as “general dynamical systems [1].” In this area of investigation, the analysis of particular systems has often led to the study of more general media, i.e., of “host” systems in which a variety of “guest” systems can be embedded. Great conceptual economy and, at the same time, great flexibility, is achieved by considering media that are arbitrarily extended and uniform. For example, while a differential equation of the form x = -f(x) describes a single, isolated oscillator, partial differential equations such as those of the electromagnetic field in a homogeneous medium may be made to describe, with a suitable choice of initial conditions, systems of waves of many kinds, including particle-like “packets” of waves. In the discrete domain, a particular sequential process realized by a specialized piece of hardware, may be reproduced by assigning appropriate initial conditions (stored program) to a more uniformly structured, general-purpose computer.