Abstract
The French mathematician, astronomer, physicist, and philosopher Pierre-Simon marquis de Laplace (1749–1827) has been among the most influential scientists in the history.
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In particular, recent numerical simulations established that the motion of planets in the Solar System is chaotic (see entry Chaos), and therefore any prediction of long-term stability (for times larger than a few million years) is meaningless.
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It is important to mention his Mémoire sur les probabilités (1781) in which, after giving the definition of conditional probability, he gave the proof of Bayes’ theorem. And Mémoire sur les approximations des formules qui sont fonctions de trés grands nombres (1786) in which he presented a refinement of Bayes’ theorem for the case of discrete events, assuming a uniform prior.
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One of the fundamental results of the probability theory asserting that the distribution of a sum of independent random variables can be approximated by a Gaussian distribution. The first introduction of the Central Limit Theorem together with the introduction of the Gaussian distribution was due to de Moivre in 1730, but Laplace extended and generalized the theorem to the sum of independent random variables with discrete distribution.
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For the discussion about causal determinism and the most famous statement on Laplace’s demon presented in Essai Philosophique sur les Probabilités (A Philosophical Essay on Probabilities, 1814), we refer the reader to the entry on Determinism.
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We recall that Immanuel Kant was the first who introduced the idea that the Solar System originated from nebulous material in his Allgemeine Naturgeschichte und Theorie des Himmels (Universal Natural History and Theory of the Heavens, 1755) but, as was Laplace custom, he did not mention Kant’s previous work, even if, in this case, it is actually unlikely that Laplace knew the work of Kant. In later times, in 1821, given the general interest that this part had in a large audience, the Book V of the Exposition du système du monde was printed, with some modifications, as an independent volume entitled Précis de l’historie de l’astronomie (Summary of the history of astronomy).
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From the Napoléon’s correspondence “In the Interior, minister Quinette was replaced by Laplace, a first-rate mathematician, but who quickly proved to be a more than mediocre administrator. From his very first work, the officials realized they had made a mistake; Laplace never took a question from its real point of view; he looked for subtleties everywhere, only had problematic ideas, and finally brought the spirit of the infinitesimal into administration”.
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Cencini, M., Puglisi, A., Vergni, D., Vulpiani, A. (2021). Laplace. In: A Random Walk in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-72531-0_18
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DOI: https://doi.org/10.1007/978-3-030-72531-0_18
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