Chance and Chaos. David Ruelle. Princeton University Press.

Chance and Chaos Book Cover Chance and Chaos
David Ruelle
Princeton University Press
October 23, 1991

The mathematical physicist David Ruelle takes what he calls a “walk among the scientific results of the twentieth century.” It is, he says a “walk guided by chance, literally, since the study of chance will be the thread that I shall follow.” How do scientists look at chance, or randomness, and chaos in physical systems? In answering this question for a general audience, Ruelle writes in the best French tradition: he has produced an authoritative and elegant book – a model of clarity, siccinctness, and a humour bordering at times on the sardonic. Even those with no special knowledge of mathematics or physics can comfortably follow him on his “walk,” as he views several kinds of chaotic systems – the complicated, erratic course of a stream, for instance, or the data that produce certain varieties of “computer pictures,” or the weather, so unpredictable except over a very short term.

Using the weather is an example of chaos par excellence, Ruelle shows how an absurdly small event can produce dramatic results in only a few weeks. After short discourses on probabilities, lotteries and horoscopes, determinism, and the theory of games, he explains the situation of chaotic systems: any tiny alteration in their state at time zero creates later changes that grow exponentially with time. These systems thus exhibit a startling “sensitive dependence on initial condition.” Besides examining such situations, Ruelle explores the relationship to entropy, information, complexity, black holes, algorithmic complexity, Gödel’s theorem, and the mysterious phenomena of hydrodynamic turbulence and “strange attractors.” He also comments perceptively on the role of chance and genetics, meteorology, economics, and history. Anyone who joins him on the skilfully guided tour will gain new insight into many of the most important ideas underlying modern science.

David Ruelle, Professor of Theoretical Physics at the Institut des Hautes Etudes Scientifiques, Bures-sur-Yvette, is the author of Statistical Mechanics, Thermodynamic Formalism, and Elements of Differentiable Dynamics and Bifurcation Theory.