Confidence in cause-and-effect relationships has long been a hallmark of scientific thought. Scientists like to believe that once they know the initial values of all variables in a situation, they can then predict with a fair degree of certainty what events are likely to follow.

Yet, scientists have also long realized that this simplistic view of nature is often inaccurate. Even when conditions are known, unexpected consequences may follow. Such behavior is described as chaos. Although chaos has been studied for more than a century, it was given that name only in 1975 by James Yorke and Tien-Yien Li at the University of Maryland.

The great French mathematician Henri Poincaré is often regarded as the founder of mathematical chaos theory. In the 1890s, Poincaré tried to solve mathematical problems involving the interaction of three planets. He worked with a set of deterministic equations that he expected to...