J. Barkley Rosser, Jr., James Madison University, Harrisonburg, VA

Abstract: We consider the precursors to the discovery of sensitive dependence on initial conditions by Edward Lorenz (1963) in his model of climatic fluid dynamics. This will focus on work in various disciplines that imply either such sensitivity, irregular endogenous dynamic patterns, or fractal nature of an attractor, as is also found in the attractor underlying the model Lorenz studied. Going from ancient hints in Anaxagoras through nineteenth century mathematics and physics, the main areas of such development will be argued to have been in celestial mechanics, oscillators, and economics.

Keywords: butterfly effect, Poincare, Rayleigh, Plank, Cantor set, fractal dimension, Alfred Marshall, oscillators, Goodwin