Poincaré and cosmic evolution

MAR 01, 1980

Among his other, better known, studies this nineteenth‐century “mathematical naturalist” enquired into the origin and stability of the solar system, the fate of the universe and the shapes of rotating fluid masses.

DOI: 10.1063/1.2913996

Stephen G. Brush

Henri Poincaré is well known today for his contributions to many areas of mathematics and his popular writings on science. His attempts to apply physical theories to the evolution of the solar system and the rest of the universe are largely forgotten, except by a few specialists. Yet the crisp lucid prose of this brilliant thinker can still help the modern reader to appreciate the worldview of nineteenth‐century science, and provides a useful introduction to a fascinating historical phenomenon that I will call “the mathematician as naturalist” (see the box on page 44).

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References

1. The basic source for Poincare’s technical articles is Oeuvres de Henri Poincaré, Gauthier‐Villars, Paris (1951–1956);
see also Figures d’Equilibre d’une Masse Fluide, Naud, Paris (1902)
and Leçionx sur les Hypotheses Cosmogoniques, second edition, Hermann, Paris (1913).
2. T. B. Jones, The Figure of the Earth, Coronado Press, Lawrence, Kansas (1967);
H. Brown, Science and the Human Comedy, University of Toronto Press, Toronto (1976) chapter 8;
I. Todhunter, A History of the Matliematical Theories of Attraction and the Figure of the Earth, from the Time of Newton to that of Laplace, reprint of the 1873 edition, Dover Publications, New York (1962).
3. W. Thomson, P. G. Tait, Treatise on Natural Philosophy, Clarendon Press, Oxford (1867);
second edition, Cambridge University Press, Cambridge (1879‐1883).
J. Levy, “Poincaré et le Mécanique Celeste,” lecture at The Hague, 1954, published in Oeuvres de Henri Poincaré, Vol. 11, pages 225–232.
4. G. H. Darwin, Mon. Not. Roy. Astr. Soc. 60, 406 (1900), page 411.
5. G. H. Darwin, Phil. Trans. Roy. Soc. London 170, 447 (1879), pages 535–536.
6. S. Chandrasekhar, Ellipsoidal Figures of Equilibrium, Yale University Press, New Haven (1969), page 12;
see also R. A. Lyttleton, The Stability of Rotating Liquid Masses, Cambridge University Press (1953).
7. Chandrasekhar, ref. 6, page 11.
8. J. P. Ostriker, in Stellar Rotation, A. Slettebak, ed., Gordon & Breach, New York (1970)
page 147, and in Theoretical Principles in Astrophysics and Relativity, N. R. Lebovitz et al., eds, University of Chicago Press, Chicago (1978) page 59;
N. R. Lebovitz, Astrophys. J. 175, 171 (1972); https://doi.org/ASJOAB
R. C. Fleck, Jr., Astrophys. J. 225, 198 (1978).https://doi.org/ASJOAB
9. See R. Numbers, Creation by Natural Law: Laplace’s Nebular Hypothesis in American Thought, University of Washington Press, Seattle (1977).
10. J. D. Burchfield, Lord Kelvin and the Age of the Earth, Science History Pubs., New York (1975).
S. G. Brush, The Temperature of History, Franklin, New York (1978) Chapter III;
The Kind of Motion We Call Heat, North‐Holland Pub. Co., Amsterdam (1976) Chapter 14.
L. Badash, Proc. Amer. Philos. Soc. 112, 157 (1968).
11. For the relation of the recurrence theorem to Nietzsche’s “eternal return” and other aspects of 19th‐century culture, see Brush, The Temperature of History, Chapter V.
12. H. Poincaré, Rev. Metaphys. Mor. 1, 534 (1893);
quotation from the translation in S. G. Brush, Kinetic Theory, Vol. 2, Pergamon Press, New York (1966) page 205.
13. Brush, ref. 12, page 206.
14. For translations of the Zermelo and Boltzmann papers see Brush, Kinetic Theory, Volume 2.
15. Oeuvres de Henri Poincaré, Vol. 8, page 538;
translation in Nature, 58, 183 (1898). [The printed text says, twice, entropy always decreases].
The long quotations in the text are from Nature, 58, 184–185 (1898).
16. H. Poincaré, Congress of Arts and Science, Universal Exposition, St. Louis, Vol. I, Houghton, Mifflin & Co., Boston (1905), pages 604–622, quotation from page 610.
Reprinted in The Monist, 15, 1 (1905).
17. See Brush, The Kind of Motion We Call Heat, pages 669–700.
18. For further details on this theory and its history see S. G. Brush, J. Hist. Astron. 9, 1, 77 (1978).https://doi.org/JHSAA2
19. H. Poincaré, Leçons sur les Hypotheses Cosmogoniques, pages 22–23;
J. H. Jeans, Problems of Cosmogony and Stellar Dynamics, Cambridge University Press, London (1919), pages 147–153;
see also G. P. Kuiper, J. Roy. Astron. Soc. Canada 50, 105 (1956).
20. S. G. Brush, in Rutherford and Physics at the Turn of the Century (M. Bunge, W. R. Shea, eds.), Science History Pubs., New York (1979), page 140.

More about the Authors

Stephen G. Brush. University of Maryland, College Park.