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No. 47: Sep-Oct 1986

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Unpredictable Things

Simple spherical pendulums are fixtures of physics labs, to say nothing of grandfather clocks. It is now widely recognized that pendulums can behave chaotically; that is, unpredictably. As the pendulum bob swings farther away from its rest position, the restoring force becomes nonlinear; i.e., not proportional to the displacement. At some combination of displacement and driving frequency, a region of chaos may develop, in which theory is powerless to tell what is going to happen next. "It is not just the behavior of pendulums that has sprung this surprise. Systems as diverse as simple electrical circuits, dynamos, lasers, chemical reactions and heart cells behave in an analogous way and the implications extend far beyond these examples -- to matters such as weather forecasting, populations of biological species, physiological and psychiatric medicine, economic forecasting and perhaps the evolution of society."

(Tritton, David; "Chaos in the Swing of a Pendulum," New Scientist, p. 37, July 24, 1986.)

Comment. Some of the anomalies we record may be the consequence of simple systems gone wild. Chaotic motions of some asteroids and at least one solar system moon are already suspected. Imagine what might happen in much more complex systems, such as biological evolution (hopeful monsters?), brain development (idiot savants?), etc.

From Science Frontiers #47, SEP-OCT 1986. 1986-2000 William R. Corliss