Abstract

The discovery of sensitive dependence on initial conditions (SDIC) in nonlinear models runs counter to the textbook vision of CM, a vision guided by an almost exclusive focus on linear systems. Therefore, it is important to clearly distinguish between linear and nonlinear systems along with establishing some basic terminology (§I). The notions of SDIC and chaos also need clarification, since they play crucial roles in sensitive dependence (SD) arguments. This will require some discussion of Lyapunov exponents as well as the relationship between nonlinear dynamics and chaos (§II and Appendix). For the sake of concreteness, it will also be useful to focus on the Laplacean vision for classical particle mechanics (e.g., Bishop 2002b, 2003 and 2005a), particularly the crucial notion of unique evolution (§III). The SD argument can then be stated in a clear form and its defenses, criticisms and limitations assessed in the more general context of nonlinear dynamics (§IV). Concluding remarks follow (§V).