Understanding complex dynamics by visual and symbolic reasoning

Abstract

Professional scientists and engineers routinely use nonverbal reasoning processes and graphical representations to organize their thoughts and as part of the process of solving otherwise verbally presented problems. This paper presents a computational theory and an implemented system that capture some aspects of this style of reasoning. The system, consisting of a suite of computer programs collectively known as KAM, uses numerical methods as a means to shift back and forth between symbolic and geometric methods of reasoning. The KAM program has three novel features: (1) it articulates the idea that “visual mechanisms are useful for problem solving” into a workable computational theory, (2) it applies the approach to a domain of great technical difficulty, the field of complex nonlinear chaotic dynamics, and (3) it demonstrates the power of the approach by solving problems of real interest to working scientists and engineers.