Chaos | Research & Encyclopedia Articles

Chaos

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 produce consistent and predictable results. Instead, they produced results that Poincaré described as "so bizarre that I cannot bear to contemplate them." He abandoned further efforts to interpret those results.

Poincaré's work on chaos received little attention from his colleagues. This was also the case with the research of a Dutch engineer, B. van der Pol, two decades later. In 1927, van der Pol observed unexpected and irregular noises in electrical circuits with which he was working. The noises were a source of concern since the equations with which he was working should have produced determinate results in all circumstances. In his research reports, van der Pol made note of these chaotic noises, but made no effort to study them further.

Van der Pol's observations re-surfaced about three decades later, however, as mathematicians began to wonder how supposedly deterministic electrical equations could yield seemingly random results (the noise van der Pol observed). One possible solution was suggested by Steve Smale (b.1930) at the University of California at Berkeley. Smale suggested that chaotic behavior could be produced by some type of generator. He called the generator that he developed a "horseshoe." Smale argued that two numbers almost identical to each other could be run through the equations that made up his "horseshoe" and could end up very different from each other.

Smale's generator principle has become the core of a critical concept in chaos theory. Chaotic behavior, it turns out, is not always entirely random. Instead, it is possible to find certain mathematical boundaries within which that behavior occurs. For example, many forms of chaotic behavior will eventually "settle down" to a region of space called a strange attractor, because it appears to attract the chaotic system. Nevertheless, strange attractors have a complicated structure on all scales of magnification, behavior that is shared with geometric figures now called fractals.

The first study of chaotic behavior in nature was that of MIT meteorologist Edward Lorenz in 1960. Lorenz attempted to use a set of twelve equations to model the Earth's atmosphere and predict weather patterns. He was surprised to find that the introduction of only minute changes in the initial values he used in these equations produced wildly different results.

This sensitivity to initial conditions troubled Lorenz since it showed that weather prediction was likely to be enormously uncertain even if initial data were very good, but not entirely perfect. Lorenz decided to pursue his study of these apparently random results and was able to discover some fundamental characteristics of chaotic behavior.

Scientists now recognize that chaotic behavior occurs in many parts of the natural world. Population changes, human heart beat, economic conditions, chemical reactions, and even galatic orbits all exhibit chaotic patterns in some very important ways. The development of mathematical models for dealing with chaos in different materials brought the 1991 Nobel Prize for physics to the French physicist Pierre-Gilles de Gennes (b.1932).