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Pierre-Simon Laplace

1749 - 1827

Pierre-Simon de Laplace

Pierre-Simon de Laplace was a French aristocrat who narrowly escaped the guillotine during the French Revolution. He was the mathematics tutor then friend of Napoleon Bonaparte at the École Militaire in Paris, and briefly became his Minister of the Interior in 1800.

  • Nationality
  • French

  • Subject
  • Mathematics

  • Fields
  • Probability, cosmology, astronomy, statistics

  • Posts
  • Elected to the Académie des sciences ( French Academy of Sciences), 1773.

    Minister of the Interior to First Consul Napoleon Bonaparte, Nov 1799, for six weeks. He was replaced by Napoleon's brother because Laplace was only appointed for political reasons. His lack of interest and therefore aptitude for practical worldly affairs became immediately obvious. As Napoleon himself expressed it: ' cherchait des subtilités partout, n'avait que des idées problématiques, et portait enfin l'esprit des 'infiniment petits' jusque dans l'administration' (..he looked for ever finer points, saw only problems, carried the spirit of 'infinitesimals' even into matters of administration.)

  • Publications
  • Mécanique Céleste (Celestial Mechanics), 5 volumes from 1799–1825.

    Mémoire sur la probabilité des causes par les événements, 1774, was a paper on probability of causes and events.

    Papers on probability and statistics, developing statistical techniques to fill gaps in knowledge, which he applied to his monumental works on celestial mechanics.

    Théorie du Mouvement et de la figure elliptique des planètes, 1784. This publication, along the third volume of his Mécanique Céleste, introduces the concept of gravitational potential, and provides the first mathematical description of spherical harmonics.

    Théorie analytique des probabilités, 1806.

  • Theories
  • Mathematical physics: Laplace transform, Laplace's equation

    Nebular hypothesis: Laplace developed a theory explaining the origin of the solar system, as well as gravitational theory and consequences such as what would become known as black holes, and gravitational collapse.

    Translation of the geometries of classical mechanics to calculus-based methods.

    Development of Bayesian probability

    The Laplace operator $∇^2$, which describes the divergence of slope of a function in Euclidean space.

  • Equations
  • Laplace transform:

    $$F(s) = ∫_{0}^{∞} e^{-st}f(t)dt$$

    where the function $F(t)$ for all positive real numbers $t ≥ 0$, $s$ is the complex number frequency ($s = σ + iω$).

    Laplace's equation:

    $$∇^2φ = 0$$

    where $∇^2$ is the Laplace operator, and $φ$ is a scalar function. The solutions to this elliptic partial differential equation underlie potential theory, and provide the harmonic functions, which have many applications in science.

  • Experiments/Discoveries
  • Dispensing with the necessity of divine intervention: by demonstrating through mathematical treatments of Newton's work on laws of motion and universal gravitation, Laplace showed that Newton's presumption of divine intervention as a necessary requirement to make the cosmos work was unnecessary.

    Laplace concluded that any two planets and the Sun must be in mutual equilibrium. Although a major contribution to the field, Laplace's work did not conclusively explain the stability of the solar system (aka Laplace's Daemon). Today's understanding is that of a chaotic, though stable, system.

    Laplace's Demon

    In a treatise about causal determinism, A Philosophical Essay on Probabilities, Laplace proposes an imaginary all-knowing intelligence ["Une intelligence... Rien ne serait incertain pour elle, et l'avenir comme le passé, serait présent à ses yeux." (An intelligence ... nothing is uncertain to it, and the future like the past is like the present to its eyes)] :

    "We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present to its eyes."

    Laplace did not use the term 'demon' - it was attributed later, in a similar vein to Maxwell's demon (a thought experiment demonstrating a potential case of violation of the second law of thermodynamics).

Sometimes called the 'Newton of France', Laplace's contribution to mathematics and physics cannot be exaggerated. He was a pioneer of the application of calculus to physical problems, a field now referred to as mathematical physics.

Siméon Poisson was a doctoral student of Laplace's.

Laplace proposed a thought experiment, in which a star grew so massive that its gravity was great enough to prevent anything, including light, from escaping its gravitational potential: the black hole - though it was not till the 1960s that the term was applied by John Wheeler.

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