Mathematical fortune-telling

Abstract

This is an informal introduction to the physics of dynamical systems and chaos at the level of elementary college calculus and analytic geometry. Terms like state-vector, phase-space, and strange attractor are defined and illustrated. Subsequently, we describe a method to produce forecasts for the behavior of complex nonlinear systems using the past behavior of the system. Finally, examples are provided to illustrate the practical utility of the method. Examples include: forecasting of presidential elections; the logistic, and predator-prey time series; sun spot numbers; human body fat; and arbitrage trading in stocks. Other types of applications in lending, insurance, quality control, noise-reduction, and pattern recognition are also good candidates for this method. Details on various aspects of the method are given in end notes suited for readers other than the complete beginner. © 2001 John Wiley & Sons, Inc.