Chaos theory was popularized by the publication of James Gleick’s 1987 best-selling book Chaos, primarily an exposition of chaos in natural science. The potential role of chaos theory in economics and finance was made prominent by the Santa Fe Institute’s publication of a volume in 1988. It has been carried into the realm of “phynance”—the merger of physics and finance—most spectacularly by Doyne Farmer and Norman Packard, whose phynance exploits are chronicled by Thomas Bass in his 1999 book The Predictors. As a result of these works, chaos theory became an important and growing field in the study of the nonlinear dynamic behavior of economic and financial systems.
Through chaos theory, physicists discovered that many phenomena in the universe previously thought to be random (unpredictable, exhibiting no pattern) are not random but exhibit a significant pattern. To oversimplify, chaos theory holds that there is a pattern to the seeming randomness of physical events occurring in the universe. Thus, systems that appear to be stochastic (to involve only random motion or behavior under conventional linear modeling) may be deterministic, or exhibit more complex internal dependence than simple linear modeling reveals.
Chaos theory has its roots in the nineteenth-century work of Henri Poincare´ , a French mathematician and physicist who studied the famous three-body problem. Newton, using his laws of motion and gravitation, proved that it was possible to calculate accurately the future positions and velocities of two mutually attractive material bodies. Neither Newton nor anyone since, however, has been able to do so for three or more bodies.
This three-body problem reveals itself repeatedly to scientists sending space probes to Mars and other planets: They chart a course directed to where the planet will be in its orbit when the probe arrives (not where the planet is upon sending the probe), but midcourse corrections are nevertheless necessary because Newtonian physics can predict accurately only the interaction of two bodies, not three. (This has led some probes to be lost in space.)
Poincare´ attributed the three-body problem to nonlinearities inherent in multibody systems as the result of which “small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter.” This insight, now the unifying core of chaos theory, is known as “sensitive dependence upon initial conditions.”
The classic example of sensitivity to initial conditions is the butterfly effect in meteorology. Its pioneer in the early 1960s was the MIT meteorologist Edward Lorenz, who said, “The dynamical equations governing the weather are so sensitive to the initial data that whether or not a butterfly flaps its wings in one part of the world may make the difference between a tornado occurring or not occurring in another part of the world.”
Picture an empty hockey rink. A person places a puck at midice and then rolls it toward the far end of the rink. He measures the angle of his hit, the angle of the puck’s impact, and the angle of its rebound. He keeps measuring the puck’s angles of impact and rebound as the puckbounces around the rink.
Assuming no friction, a rule of puckmotion in the rinkis that it will emerge from impacting a side of the rinkat precisely its angle of approach (a similar thing will be familiar to anyone who has played billiards). That rule means we have defined a deterministic system under which the future position of the puckat any time can be forecast perfectly (assuming its actual or average speed is known).
But now assume that the initial position of the puckis varied by a few degrees, even an infinitesimally small variation, not observed by or known to the forecaster. The forecaster’s predictions of the puck’s location after it hits the first one or two sides may be imprecise— off by some small amount—but the imprecision will be negligible.
The amount of error will grow exponentially, however, with each subsequent impact. In a short time the forecast will be wide of the mark. Disturbing the measure of the puck’s initial position causes its movement to appear random and unpredictable, whereas knowing that measure enables precise prediction. It is this sensitive dependence on initial conditions that is the signal characteristic of chaotic systems. To detect its presence, Lorenz and his followers developed a couple of fascinating tools.
Read More : Next Wave Of Chaotic Market Movement
