Mathematics

Areas of development in mathematics that should interest psychoanalysts explore properties of complex systems, chaos theory, the mathematics of competition and cooperation, and the psychology of mathematics. The computer has served as a laboratory for mathematicians to discover that we have faulty “intuitions” about how systems evolve over time. These “intuitive” ideas often result from systematic education that excludes many phenomena of everyday life. This education in turn derives from limitations in mathematical knowledge. Over the past half-century mathematicians have created an ever richer set of tools for exploring the systems that enter everyday life. Starting with cybernetics, briefly re-emerging with catastrophe theory, and finally developed as chaos theory, hyperbole has obscured the substantial accomplishments of the steps toward a mathematical theory of complex systems.

Conceptually, the big news from chaos theory was that on the one hand the real world is in a deep sense unpredictable and mathematically intractable to the kind of effort that classical physicists hoped would reduce it to a clockwork and, on the other hand, that this unpredictability has meaningful structure. Out of chaos theory came the further development, familiar from fractal graphics, that highly complex structures can emerge from simple underlying processes. The study of these emergent structures is called “complexity theory.” It shows how simply selective processes can result in the emergence of complex systems. While many introductory books on the subject are as content free as they are breathless, J. Cohen and I. Stewart’s 1994 study, The Collapse of Chaos: Discovering Simplicity in a Complex World (New York: Viking), provides a clear comprehensible and intellectually solid introduction to the field. Steven Levy’s Artificial Life, the Quest for a New Creation (New York: Pantheon, 1992) describes one of the more dramatic creations of complexity theory. According to S. Prata in Art