Finding a Horseshoe on the Beaches of Rio

A mathematician discussing chaos is featured in the movie "Jurassic Park". James Gleich's book "Chaos" remains on the best seller list for many months. The characters of the celebrated Broadway play "Arcadia" of Tom Stoppard discourse on the meaning of chaos. What is chaos? Chaos is a new science which establishes the omnipresence of unpredictability as a fundamental feature of common experience. A belief in determinism, that the present state of the world determines the future precisely, dominated scienti c thinking for two centuries. This credo was based on certain laws of physics, Newton's equations of motion, which describe the trajectories in time of states of nature. These equations have the mathematical property that the initial condition determines the solution for all time. Thus lies the mathematical and physical foundation for deterministic philosophy. One manifestation of determinismwas the rejection of free will and hence even of human responsibility. At the beginning of this century, with the advent of quantum mechanics and the revelations of the German scientists, Heisenberg, Planck, and Schrodinger, the great delusion of determinism was exposed. At least on the level of electrons, protons, and atoms it was discovered that uncertainty prevailed. The equations of motion of quantum mechanics produce solutions which are probabilities evolving in time. In spite of quantum mechanics, Newton's equations govern the motion of a pendulum, the behaviour of the solar system, the evolution of the weather and many situations of everyday life. Therefore the quantum revolution left intact many deterministic dogmas. For example, well after the second world war, scientists held the belief that long range weather prediction would be successful when computer resources grew large enough. In the 1970's the scienti c community recognized another revolution, called the theory of chaos, which deals a death blow to the Newtonian pic-