Overview

Poincaré's 1892

“Will the two principles of Mayer and Clausius assure to it foundations solid enough to last for some time?”

In the Brussels school of thermodynamics, Poincaré’s work had an influence on Belgian thermodynamicist Théophile de Donder, between 1911 and 1914.

Irreversibility debate

In short, Poincaré 1900 article on the three body problem argued that three particles in a system can at various times reverse to their original starting positions. This logic, in turn, directly conflicted with German physicist Rudolf Clausius’ 1854 argument that in all real processes such a transformation would “not be reversible”, in that the forward and return forces involved would not compensate each other exactly. [4]See main: Irreversibility

This tension sparked a string of follow-up articles: “Mechanism and Experience” (Poincaré, 1893), “On a Theorem of Dynamics and the Mechanical Theory of Heat” (Zermelo, 1894), “Reply to Zermelo’s Remarks on the Theory of Heat” (Boltzmann, 1896), “On the Mechanical explanation of Irreversible Processes” (Zermelo, 1896), and “On Zermelo’s Paper: ‘On the Mechanical Explanation of Irreversible Processes” (Boltzmann, 1897). [5]

Poincare is said to have concluded, according to physical economics historian Philip Mirowski, that classical thermodynamics and Hamiltonian dynamics were incompatible, because no function of coordinates and momenta could have the properties of the Boltzmann entropy function. [6]

Economics

In circa 1905, Poincare wrote the following in a letter to Leon Walras: [7]

“Can satisfaction be measured? I may say that one satisfaction is greater than another, because I prefer one to the other; but I cannot say that one is two or three times greater than another … Satisfaction then is a magnitude, but not a measureable magnitude. Now is a magnitude that is not measureable therefore not amenable to mathematical theory? By no means. Temperature, for instance (at any rate before the term ‘absolute temperature’ had acquired a signification with the rise of thermodynamics), was a non-measureable magnitude. It was arbitrarily defined and measured by the expansion of mercury. It might quite as legitimately have been defined by the expansion of any other substance and measured by any function of that expansion,provided that it was a continually increasing function. Likewise, in the present case, provided that the function continually increases along with the satisfaction which it represents.”

(add discussion)

IQ | Mislabel

Poincare, as commonly cited among IQ and genius discussions, so poorly on the Binet IQ, to note, that he was judged an imbecile (IQ=35). [8]See main: Mislabeled geniuses and IQ tests

Hauriou

Poincaré's 1892

Education

Poincaré graduated from the École Polytechnique in circa 1876, then studied mathematics and engineering at the École des Mines, graduating with a degree in ordinary engineering in 1879, and completed his PhD in science with a dissertation “On the Properties of Functions defined by Differential Equations”, under the supervision of French mathematician Charles Hermite, at the University of Paris, finishing in circa 1879. He then lectured at Caan University for a term before becoming a professor at the University of Paris, in 1881, where he remained for the rest of his career, holding chairs in mechanics, mathematical physics, probability, celestial mechanics, and astronomy.

References

1. Poincaré, Henri. (1890). “On the Three-body Problem and the Equations of Dynamics” (“Sur le Probleme des trios corps ci les equations de dynamique”),

2. (a) Poincaré, Henri. (1892).

(b) Hauriou, Maurice. (1899).

3. Poincaré, Henri. (1903).

4. Clausius, Rudolf. (1854). "On a Modified Form of the Second Fundamental Theorem in the Mechanical Theory of Heat", (pp. 111-135), in

5. (a) Poincaré, Henri. (1893). “Mechanism and Experience”,

(b) Zermelo, Ernst. (1894). “On a Theorem of Dynamics and the Mechanical Theory of Heat”,

(c) Boltzmann, Ludwig. (1896). “Reply to Zermelo’s Remarks on the Theory of Heat”,

(d) Zermelo, Ernst. (1896). “On the Mechanical explanation of Irreversible Processes”,

(e) Boltzmann, Ludwig. (1897). “On Zermelo’s Paper: ‘On the Mechanical Explanation of Irreversible Processes’”, 60: 392-98.

6. Mirowski, Philip. (1989).

7. (a) Walras, Leon. (1909). “Economique et mecanique” (quoted at end),

(b) Edgeworth, Francis. (1915). “Recent Contributions to Mathematical Economics” (abs) (quote, pgs. 57-58),

8. Rose, Colin and Nicholl, Malcolm J. (1998).

External links

● Henri Poincaré – Wikipedia.