Henri Poincaré02 Mar 2004 17:07
French mathematician, physicist and methodologist. He essentially invented the modern field of dynamics as part of his study of celestial mechanics, and specifically of the three-body problem. In the course of this work he became, apparently, the first person to discover the mathematical phenomenon of "sensitive dependence on initial conditions" (not his phrase), which provides a new rationale for treating deterministic phenomena as stochastic processes. It is not just, as earlier probabilists had said, that there are a great many causal variables, and we are ignorant of most of them; even in situations where there there are only a few variables, but arbitrarily small differences in the starting initial state can be rapidly amplified into large differences in the latter state, you'll often have no choice but to treat the dynamics as largely random. (This is explained very clearly in his essay "On Chance" in Science and Method.)
Folklore among physicists holds that he almost discovered special relativity before Einstein; I don't know about that, but Galison's book should say one way or the other.
At some point I should try to explain his methodology, which was brilliant, but which I don't believe at all.
- June Barrow-Green, Poincaré and the Three-Body Problem
- HP [The English translation of these three books is now in the
public domain, and there's a one-volume compilation available called The
Value of Science --- retaining typographic errors going back to 1905]
- Science and Method
- Science and Hypothesis
- The Value of Science
- To read:
- Tobias Dantzig, Henri Poincaré: Critic of Crisis
- Mathematics and Science: Last Essays
- New Methods of Celestial Mechanics