ABSTRACT
This introduction presents an overview of key concepts discussed in the subsequent chapters of this book. The book provides a history of author's efforts to bring a nonlinear point of view to psychoanalytic thinking. To understand the influential challenge posed by attempting to use concepts of nonlinear dynamic systems theory, we must explore the role of mathematical ideas in science generally. The study of nonlinear dynamics began in pure mathematics with the work of French mathematician Henri Poincaré who was probably the deepest mathematical thinker of the twentieth century. Doing mathematics may be motivated by any number of factors, such as the belief that studying a particular system will lead to beautiful results or the anticipation that those results will be helpful in some practical problem. In Kant's classification, all mathematical statements are analytic- that is, they must be true by virtue of the underlying logic independent of qualities of the external world.
