MATHEMATICS and nonlinear systems
| Collection | International Encyclopedia of Systems and Cybernetics |
|---|---|
| Year | 2004 |
| Vol. (num.) | 2(1) |
| ID | ◀ 2021 ▶ |
| Object type | General information, Epistemology, ontology or semantics, Methodology or model |
According to R. MAY: “The elegant body of mathematical theory pertaining to linear systems (Fourier analysis, orthogonal functions, and so on) and its sucessful application to many fundamentally linear problems in the physical sciences, tends to dominate even moderately advanced University courses in mathematics and theoretical physics. The mathematical intuition so developed ill equips the student to confront the bizarre behavior exhibited by the simplest of discrete nonlinear systems… Yet, such nonlinear systems are surely the rule, not the exception, outside the physical sciences” (1976, p.467).
The trend to use linear mathematics in social sciences, for instance, has been a stumbling block for the use of systems concepts by sociologists and explains some of their sharp criticism. In J. MARTINO's words in his review of BERLINSKI's “On Systems Analysis”: “There is no proof offered by the systems analysts that social and political systems are at all similar to control systems” (1979, p.18).
MAY advocates the study of 1st order nonlinear difference equations, as a starting point. Since 1976, when he published this paper, a considerable body of new mathematics of nonlinearity has been created.
It should be emphasized however that the first important work on nonlinearity was POINCARÉ's 1889 paper on the three bodies problem and that POINCARÉ himself introduced various topological concepts that led to chaos theory.
See also
Poincar+ Section