Book Review: Chaos by James Gleick

This book, first published in 1988 but still in print ten years later, is probably regarded as out-of-date by those with special knowledge of the subject. However, in relating the exciting developments that took place in the first three decades, during which the proponents of chaos theory fought for its recognition as a legitimate branch of science, the book retains much interest for the scientifically literate layperson and the serious general reader.

The author explains that progress in science has traditionally involved solving problems that could be simplified by neglecting minor influences and deriving a mathematical formula to represent the interaction of only one or two major factors affecting the behaviour of the subject under study. He uses as an example the well-known formula for the motion of the simple pendulum which ignores the effect of air resistance. Much progress had been made in this way, but scientists were encountering more and more situations in which the influence of minor factors could not be ignored. The first of these was in weather forecasting.

Failures in weather forecasting in World War II helped to lead to an awareness that the weather is affected by many minor influences none of which can be ignored. In the 1950s, meteorologists began to tackle the complexity with the aid of computers. The early work showed that minor changes in the initial conditions could promote big changes in the outcome. Under some conditions patterns might emerge, while others led to wide and random fluctuations that became known as chaos.

Biologists studying how the populations of organisms vary over time also encountered chaos. With a basic formula for a fish population, if a certain parameter has a low value the population is stable, increasing the value the population fluctuates between two levels, then four levels etc, until fluctuating wildly and unpredictably in a region of chaos.

The author gives several examples of relatively simple formulae which when repeatedly calculated on a computer thousands of times define areas of stability and areas of chaos. Some computer outputs in the region of chaos when displayed graphically show complex patterns that resemble natural forms and are repeated at every scale of presentation. These are the now well-known and much-admired Mandelbrot fractal images.

Having shown examples of how single simple formulae when repeatedly calculated on a computer can generate chaos, the author creates some confusion by stating on page 264 that ‘… three differential equations (are) the minimum necessary for chaos, as Poincare and Lorenz had shown.’ This isolated statement puts a question in the mind of the reader that is not answered. Nevertheless, James Gleick’s book has lasting value as a fascinating account of the dawn of a new scientific tool for unravelling the complexity of nature.