Chaos << KAY os >> theory is a field of science that deals with complex and irregular processes. Physical processes that are chaotic include the changing of weather patterns, the collision of billiard balls, and the orbital movement of particles in Saturn’s rings. Scientists study chaotic systems, sets of objects that, as a whole, display chaotic behavior. In the case of a collision of billiard balls, the main objects in the system would be the balls, the playing surface of the table, and the cushions at the sides of the playing surface.
Scientists once thought that, with enough information, they could make exact predictions about chaotic systems. The science of chaos has shown, however, that it is difficult to predict the long-range behavior of such complex systems. There are two reasons for this difficulty: (1) a chaotic system has what scientists call a sensitive dependence upon initial conditions, and (2) it is difficult to obtain enough information about those conditions.
Sensitive dependence upon initial conditions means that a tiny difference in starting conditions can lead to much different results. For example, in a complex billiards shot, a small error in the player’s aim would cause only a slight change in the cue ball’s path at first. With each collision, however, the ball would veer farther from the intended path.
The early parts of the path would be relatively easy to predict. A scientist would measure such factors as the location of each ball, the speed and direction of the cue ball, and the friction between the balls and the playing surface. The scientist would then use these measurements in physics equations. To predict the path after each successive collision would be increasingly difficult, however. The scientist would need more information about the initial conditions. Not only would the measurements have to be more precise, but also more measurements would be needed. For example, the scientist might need to know how level the playing table was.
Suppose there were much less friction between the balls and the playing surface. The cue ball would not slow down as much, there would be more collisions, and the measurements would have to be even more precise and extensive. If the amount of friction were small enough, the prediction would require so much information that it would not be practical to try to obtain all of it.
Although scientists cannot make long-term forecasts of chaotic systems, they can make reasonably accurate short-term predictions. They do this by discovering and applying general patterns of behavior in the systems. For example, meteorologists (scientists who study the weather) have analyzed the development of weather patterns in different places over various lengths of time. They have then used their analyses to make useful five-day forecasts available in many parts of the world. See Weather (Weather forecasting).
See also Poincaré, Henri.
