Application of Kolmogorov Complexity to Advanced Problems in Mechanics

Authors

Vladik Kreinovich, The University of Texas at El PasoFollow
Isaak A. Kunin

Publication Date

5-2004

Comments

UTEP-CS-04-14.

To appear in: Proceedings of the Advanced Problems in Mechanics Conference APM'04 St. Petersburg, Russia, June 24-July 1, 2004

Abstract

In the 1960s, A.N. Kolmogorov described the main reason why a mathematical correct solution to a system of differential equations may be not physically possible: Traditional mathematical analysis tacitly assumes that all numbers, no matter how large or how small, are physically possible. From the engineering viewpoint, however, a number like 10^{10^10} is not possible, because it exceeds the number of particles in the Universe. In this paper, we extend Kolmogorov's ideas from discrete objects to continuous objects known with given accuracy epsilon, and show how this extension can clarify the analysis of dynamical systems.