What Could Be Worse than the Butterfly Effect?

Abstract

Our understanding of classical mechanics (CM) has undergone significant growth in the latter half of the twentieth century and in the beginning of the twenty-first. This growth has much to do with the explosion of interest in the study of nonlinear systems in contrast with the focus on linear systems that had colored much work in CM from its inception. For example, although Maxwell and Poincaré arguably were some of the first to think about chaotic behavior, the modern study of chaotic dynamics traces its beginning to the pioneering work of Edward Lorenz (1963). This work has yielded a rich variety of behavior in relatively simple classical models that was previously unsuspected by the vast majority of the physics community (see Hilborn 2001). Chaos is a property of nonlinear systems that is usually characterized by sensitive dependence on initial conditions (SDIC). In CM the behavior of simple physical systems is described using models (such as the harmonic oscillator) that capture the main features of the systems in question (Giere 1988).