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2020年11月16日 (一) 21:31的版本

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{{Infobox scientist

{{Infobox scientist

{信息盒科学家

|name = Henri Poincaré

|name = Henri Poincaré

|name = Henri Poincaré

|other_names = Jules Henri Poincaré

|other_names = Jules Henri Poincaré

其他名字 = 儒勒·昂利·庞加莱

|image = PSM V82 D416 Henri Poincare.png

|image = PSM V82 D416 Henri Poincare.png

82 D416 Henri Poincare.png

|caption = Henri Poincaré
(photograph published in 1913)

|caption = Henri Poincaré
(photograph published in 1913)

摄于1913年

|birth_date = (1854-模板:MONTHNUMBER-29)29 1854

|birth_date =

出生日期

|birth_place = Nancy, Meurthe-et-Moselle, France

|birth_place = Nancy, Meurthe-et-Moselle, France

出生地: 南希，默尔特-摩泽尔省，法国

|death_date = 17 July 1912(1912-07-17) (aged 58)

|death_date =

死亡日期

|death_place = Paris, France

|death_place = Paris, France

死亡地点: 法国巴黎

|residence = France

|residence = France

居住地: 法国

|nationality = French

|nationality = French

| 国籍: 法国

|fields = Mathematics and physics

|fields = Mathematics and physics

| fields = 数学和物理

|workplaces =

. The first systematic study of topology.

Http://www.maths.ed.ac.uk/~aar/papers/poincare2009.pdf.第一个系统的拓扑学研究。

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On celestial mechanics:

关于天体力学:

Poincaré believed that arithmetic is synthetic. He argued that Peano's axioms cannot be proven non-circularly with the principle of induction (Murzi, 1998), therefore concluding that arithmetic is a priori synthetic and not analytic. Poincaré then went on to say that mathematics cannot be deduced from logic since it is not analytic. His views were similar to those of Immanuel Kant (Kolak, 2001, Folina 1992). He strongly opposed Cantorian set theory, objecting to its use of impredicative definitions[citation needed].


However, Poincaré did not share Kantian views in all branches of philosophy and mathematics. For example, in geometry, Poincaré believed that the structure of non-Euclidean space can be known analytically. Poincaré held that convention plays an important role in physics. His view (and some later, more extreme versions of it) came to be known as "conventionalism".[1] Poincaré believed that Newton's first law was not empirical but is a conventional framework assumption for mechanics (Gargani, 2012).[2] He also believed that the geometry of physical space is conventional. He considered examples in which either the geometry of the physical fields or gradients of temperature can be changed, either describing a space as non-Euclidean measured by rigid rulers, or as a Euclidean space where the rulers are expanded or shrunk by a variable heat distribution. However, Poincaré thought that we were so accustomed to Euclidean geometry that we would prefer to change the physical laws to save Euclidean geometry rather than shift to a non-Euclidean physical geometry.[3]


On the philosophy of mathematics:

关于数学哲学:

Free will

Poincaré's famous lectures before the Société de Psychologie in Paris (published as Science and Hypothesis, The Value of Science, and Science and Method) were cited by Jacques Hadamard as the source for the idea that creativity and invention consist of two mental stages, first random combinations of possible solutions to a problem, followed by a critical evaluation.[4]


Although he most often spoke of a deterministic universe, Poincaré said that the subconscious generation of new possibilities involves chance.

It is certain that the combinations which present themselves to the mind in a kind of sudden illumination after a somewhat prolonged period of unconscious work are generally useful and fruitful combinations... all the combinations are formed as a result of the automatic action of the subliminal ego, but those only which are interesting find their way into the field of consciousness... A few only are harmonious, and consequently at once useful and beautiful, and they will be capable of affecting the geometrician's special sensibility I have been speaking of; which, once aroused, will direct our attention upon them, and will thus give them the opportunity of becoming conscious... In the subliminal ego, on the contrary, there reigns what I would call liberty, if one could give this name to the mere absence of discipline and to disorder born of chance.[5]


Poincaré's two stages—random combinations followed by selection—became the basis for Daniel Dennett's two-stage model of free will.[6]


Bibliography

Other:

其他:

Poincaré's writings in English translation

Popular writings on the philosophy of science:

  • Poincaré, Henri

Exhaustive bibliography of English translations:

详尽的英语翻译书目: (1902–1908), The Foundations of Science, New York: Science Press {{citation}}: line feed character in |author= at position 16 (help)CS1 maint: extra punctuation (link); reprinted in 1921; This book includes the English translations of Science and Hypothesis (1902), The Value of Science (1905), Science and Method (1908).

  • 1904. Science and Hypothesis, The Walter Scott Publishing Co.
  • 1913. "The New Mechanics," The Monist, Vol. XXIII.
  • 1913. "The Relativity of Space," The Monist, Vol. XXIII.
  • 1956. Chance. In James R. Newman, ed., The World of Mathematics (4 Vols).
  • 1958. The Value of Science, New York: Dover.


On algebraic topology:


On celestial mechanics:

  • 1892–99. New Methods of Celestial Mechanics, 3 vols. English trans., 1967.
    .
    • 1905. "The Capture Hypothesis of J. J. See," The Monist, Vol. XV.
    • 1905–10. Lessons of Celestial Mechanics.


    On the philosophy of mathematics:

    • Ewald, William B., ed., 1996. From Kant to Hilbert: A Source Book in the Foundations of Mathematics, 2 vols. Oxford Univ. Press. Contains the following works by Poincaré:
      • 1894, "On the Nature of Mathematical Reasoning," 972–81.
      • 1898, "On the Foundations of Geometry," 982–1011.
      • 1900, "Intuition and Logic in Mathematics," 1012–20.
      • 1905–06, "Mathematics and Logic, I–III," 1021–70.
      • 1910, "On Transfinite Numbers," 1071–74.
    • 1905. "The Principles of Mathematical Physics," The Monist, Vol. XV.
    • 1910. "The Future of Mathematics," The Monist, Vol. XX.
    • 1910. "Mathematical Creation," The Monist, Vol. XX.


    Other:

    • 1904. Maxwell's Theory and Wireless Telegraphy, New York, McGraw Publishing Company.
    • 1905. "The New Logics," The Monist, Vol. XV.
    • 1905. "The Latest Efforts of the Logisticians," The Monist, Vol. XV.


    Exhaustive bibliography of English translations:


    See also

    Concepts

    • Poincaré complex – an abstraction of the singular chain complex of a closed, orientable manifold


Theorems

|title=Henri Poincaré. A Life in the Service of Science

|title=Henri Poincaré.为科学服务的一生

|author=Jean Mawhin |journal=Notices of the AMS

作者: Jean Mawhin | journal = AMS 公告

  • Poincaré–Bendixson theorem: a statement about the long-term behaviour of orbits of continuous dynamical systems on the plane, cylinder, or two-sphere.

|date=October 2005 |volume=52 |issue=9 |pages=1036–1044 }}

| date = October 2005 | volume = 52 | issue = 9 | pages = 1036-1044}

  • Poincaré–Hopf theorem: a generalization of the hairy-ball theorem, which states that there is no smooth vector field on a sphere having no sources or sinks.
  • Poincaré separation theorem: gives the upper and lower bounds of eigenvalues of a real symmetric matrix B'AB that can be considered as the orthogonal projection of a larger real symmetric matrix A onto a linear subspace spanned by the columns of B.
  • Poincaré–Birkhoff theorem: every area-preserving, orientation-preserving homeomorphism of an annulus that rotates the two boundaries in opposite directions has at least two fixed points.
  • Poincaré conjecture (now a theorem): Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere.


Other


References

Footnotes

  1. ↑ Yemima Ben-Menahem, Conventionalism: From Poincare to Quine, Cambridge University Press, 2006, p. 39.
  2. ↑ Gargani Julien (2012), Poincaré, le hasard et l'étude des systèmes complexes, L'Harmattan, p. 124, archived from the original on 4 March 2016, retrieved 5 June 2015
  3. ↑ Poincaré, Henri (2007), Science and Hypothesis, Cosimo, Inc. Press, p. 50, ISBN 978-1-60206-505-5
  4. ↑ Hadamard, Jacques. An Essay on the Psychology of Invention in the Mathematical Field. Princeton Univ Press (1945)
  5. ↑ Poincaré, Henri (1914). "3: Mathematical Creation". Science and Method. https://ebooks.adelaide.edu.au/p/poincare/henri/science-and-method/book1.3.html. 
  6. ↑ Dennett, Daniel C. 1978. Brainstorms: Philosophical Essays on Mind and Psychology. The MIT Press, p.293
  7. ↑ "Structural Realism": entry by James Ladyman in the Stanford Encyclopedia of Philosophy


Sources

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