The Mathematics of Discontinuity

Abstract

Somehow it is appropriate if ironic that sharply divergent opinions exist in the mathematical House of Discontinuity with respect to the appropriate method for analyzing discontinuous phenomena. Different methods include catastrophe theory, chaos theory, fractal geometry, and synergetics theory. All have been applied in economics in one way or another.

“On the plane of philosophy properly speaking, of metaphysics, catastrophe theory cannot, to be sure, supply any answer to the great problems which torment mankind. But it favors a dialectical, Heraclitean view of the universe, of a world which is the continual theatre of the battle between logoi, between archetypes.” René Thorn, 1975 “Catastrophe Theory: Its Present State and Future Perspectives,” p. 382

“Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.” Benoit B. Mandelbrot, 1983 The Fractal Geometry of Nature, p. 1