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Book Review: Chaos by James Gleick

This book, first published in 1988, but still in print ten years later, may be considered outdated by those with special knowledge of the subject. However, in relating the interesting developments that took place in the first three decades, in which advocates of chaos theory struggled to recognize it as a legitimate branch of science, the book is of great interest to science-educated laymen and the serious general reader.

The author explains that progress in science is traditionally related to solving problems that can be simplified by neglecting small effects and deriving mathematical formulas to represent the interaction of only one or two main factors that affect the behavior of the subject of study. He uses as an example the well-known formula for the motion of a simple pendulum that ignores the effect of air resistance. A lot of progress was made in this area, but scientists were increasingly faced with situations where the influence of small factors could not be ignored. The first of these was in weather forecasting.

Failures in weather forecasting during World War II led to an awareness that weather is influenced by many small influences none of which can be ignored. In the 1950s, meteorologists began to solve the problem with the help of computers. Early work has shown that small changes in initial conditions can lead to large changes in outcome. Under some conditions patterns may emerge, while others lead to widespread and random fluctuations known as chaos.

Biologists who study how populations of organisms change over time have also encountered chaos. According to the basic formula for 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, and so on, until it is in a region of chaos. and unpredictable changes.

The author gives several examples of relatively simple formulas that, when calculated several times on a computer, determine regions of calm and regions of chaos thousands of times. Some computer outputs in the chaos region when displayed graphically show complex patterns that resemble natural forms and are repeated at any scale of presentation. These are the now well-known and much-admired Mandelbrot fractal images.

After showing examples of how simple single formulas can create chaos when repeated calculations on a computer, the author adds some confusion by stating on page 264 that ‘… three differential equations (for chaos) are minimal. needed, as Poincare and Lorenz had. to show.’ This disjointed narrative raises an unanswered question in the reader’s mind. Nevertheless, James Gleick’s book is of lasting value as a fascinating account of the discovery of a new scientific tool for clarifying the complexity of nature.

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