Pierre-Simon, marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French scholar and polymath whose work was important to the development of engineering,

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...

, physics, astronomy, and

philosophy Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some ...

. He summarized and extended the work of his predecessors in his five-volume ''Mécanique céleste'' ('' Celestial Mechanics'') (1799–1825). This work translated the geometric study of classical mechanics to one based on calculus, opening up a broader range of problems. In statistics, the Bayesian interpretation of probability was developed mainly by Laplace. Laplace formulated

Laplace's equation In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its properties. This is often written as \nabla^2\! f = 0 or \Delta f = 0, where \Delta = \nab ...

, and pioneered the Laplace transform which appears in many branches of mathematical physics, a field that he took a leading role in forming. The Laplacian differential operator, widely used in mathematics, is also named after him. He restated and developed the nebular hypothesis of the

origin of the Solar System The formation of the Solar System began about 4.6 billion years ago with the gravitational collapse of a small part of a giant molecular cloud. Most of the collapsing mass collected in the center, forming the Sun, while the rest flattened into a ...

and was one of the first scientists to suggest an idea similar to that of a

black hole A black hole is a region of spacetime where gravitation, gravity is so strong that nothing, including light or other Electromagnetic radiation, electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts t ...

. Laplace is regarded as one of the greatest scientists of all time. Sometimes referred to as the ''French

Newton Newton most commonly refers to: * Isaac Newton (1642–1726/1727), English scientist * Newton (unit), SI unit of force named after Isaac Newton Newton may also refer to: Arts and entertainment * ''Newton'' (film), a 2017 Indian film * Newton ( ...

'' or ''Newton of France'', he has been described as possessing a phenomenal natural mathematical faculty superior to that of almost all of his contemporaries. He was Napoleon's examiner when

Napoleon Napoleon Bonaparte ; it, Napoleone Bonaparte, ; co, Napulione Buonaparte. (born Napoleone Buonaparte; 15 August 1769 – 5 May 1821), later known by his regnal name Napoleon I, was a French military commander and political leader who ...

attended the '' École Militaire'' in Paris in 1784. Laplace became a count of the Empire in 1806 and was named a

marquis A marquess (; french: marquis ), es, marqués, pt, marquês. is a nobleman of high hereditary rank in various European peerages and in those of some of their former colonies. The German language equivalent is Markgraf (margrave). A woman wi ...

in 1817, after the

Bourbon Restoration Bourbon Restoration may refer to: France under the House of Bourbon: * Bourbon Restoration in France (1814, after the French revolution and Napoleonic era, until 1830; interrupted by the Hundred Days in 1815) Spain under the Spanish Bourbons: * ...

Early years

Pierre-Simon de Laplace by Johann Ernst Heinsius (1775)

Some details of Laplace's life are not known, as records of it were burned in 1925 with the family château in

Saint Julien de Mailloc Saint-Julien-de-Mailloc () is a former commune in the Calvados department in the Normandy region in northwestern France. On 1 January 2016, it was merged into the new commune of Valorbiquet.Lisieux, the home of his great-great-grandson the Comte de Colbert-Laplace. Others had been destroyed earlier, when his house at Arcueil near Paris was looted in 1871."Laplace, being Extracts from Lectures delivered by

Karl Pearson Karl Pearson (; born Carl Pearson; 27 March 1857 – 27 April 1936) was an English mathematician and biostatistician. He has been credited with establishing the discipline of mathematical statistics. He founded the world's first university st ...

", ''

Biometrika ''Biometrika'' is a peer-reviewed scientific journal published by Oxford University Press for thBiometrika Trust The editor-in-chief is Paul Fearnhead (Lancaster University). The principal focus of this journal is theoretical statistics. It was es ...

'', vol. 21, December 1929, pp. 202–216. Laplace was born in Beaumont-en-Auge, Normandy on 23 March 1749, a village four miles west of Pont l'Évêque. According to

W. W. Rouse Ball Walter William Rouse Ball (14 August 1850 – 4 April 1925), known as W. W. Rouse Ball, was a British mathematician, lawyer, and fellow at Trinity College, Cambridge, from 1878 to 1905. He was also a keen amateur magician, and the founding ...

, his father, Pierre de Laplace, owned and farmed the small estates of Maarquis. His great-uncle, Maitre Oliver de Laplace, had held the title of Chirurgien Royal. It would seem that from a pupil he became an usher in the school at Beaumont; but, having procured a letter of introduction to d'Alembert, he went to Paris to advance his fortune. However,

is scathing about the inaccuracies in Rouse Ball's account and states: His parents, Pierre Laplace and Marie-Anne Sochon, were from comfortable families. The Laplace family was involved in agriculture until at least 1750, but Pierre Laplace senior was also a

cider Cider ( ) is an alcoholic beverage made from the fermented juice of apples. Cider is widely available in the United Kingdom (particularly in the West Country) and the Republic of Ireland. The UK has the world's highest per capita consumption, ...

merchant and ''

syndic Syndic (Late Latin: '; Greek: ' – one who helps in a court of justice, an advocate, representative) is a term applied in certain countries to an officer of government with varying powers, and secondly to a representative or delegate of a universi ...

'' of the town of Beaumont. Pierre Simon Laplace attended a school in the village run at a Benedictine priory, his father intending that he be ordained in the Roman Catholic Church. At sixteen, to further his father's intention, he was sent to the University of Caen to read theology.*. Retrieved 25 August 2007 At the university, he was mentored by two enthusiastic teachers of mathematics, Christophe Gadbled and Pierre Le Canu, who awoke his zeal for the subject. Here Laplace's brilliance as a mathematician was quickly recognised and while still at Caen he wrote a memoir ''Sur le Calcul integral aux differences infiniment petites et aux differences finies''. This provided the first intercourse between Laplace and Lagrange. Lagrange was the senior by thirteen years, and had recently founded in his native city Turin a journal named ''Miscellanea Taurinensia'', in which many of his early works were printed and it was in the fourth volume of this series that Laplace's paper appeared. About this time, recognising that he had no vocation for the priesthood, he resolved to become a professional mathematician. Some sources state that he then broke with the church and became an atheist. Laplace did not graduate in theology but left for Paris with a letter of introduction from Le Canu to Jean le Rond d'Alembert who at that time was supreme in scientific circles. According to his great-great-grandson, d'Alembert received him rather poorly, and to get rid of him gave him a thick mathematics book, saying to come back when he had read it. When Laplace came back a few days later, d'Alembert was even less friendly and did not hide his opinion that it was impossible that Laplace could have read and understood the book. But upon questioning him, he realised that it was true, and from that time he took Laplace under his care. Another account is that Laplace solved overnight a problem that d'Alembert set him for submission the following week, then solved a harder problem the following night. D'Alembert was impressed and recommended him for a teaching place in the '' École Militaire''.Gillispie (1997), pp. 3–4 With a secure income and undemanding teaching, Laplace now threw himself into original research and for the next seventeen years, 1771–1787, he produced much of his original work in astronomy.Rouse Ball (1908). Calorimeter of Lavoisier and La Place plate xi the s1784m49j 3f462600t dl full size

Calorimeter of Lavoisier and La Place plate xi the s1784m49j 3f462600t dl full size

From 1780 to 1784, Laplace and French chemist Antoine Lavoisier collaborated on several experimental investigations, designing their own equipment for the task. In 1783 they published their joint paper, ''Memoir on Heat'', in which they discussed the kinetic theory of molecular motion. In their experiments they measured the specific heat of various bodies, and the expansion of metals with increasing temperature. They also measured the boiling points of ethanol and ether under pressure. Laplace further impressed the

Marquis de Condorcet Marie Jean Antoine Nicolas de Caritat, Marquis of Condorcet (; 17 September 1743 – 29 March 1794), known as Nicolas de Condorcet, was a French philosopher and mathematician. His ideas, including support for a liberal economy, free and equal pu ...

, and already by 1771 Laplace felt entitled to membership in the

French Academy of Sciences The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV of France, Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific me ...

. However, that year admission went to Alexandre-Théophile Vandermonde and in 1772 to Jacques Antoine Joseph Cousin. Laplace was disgruntled, and early in 1773 d'Alembert wrote to

Lagrange Joseph-Louis Lagrange (born Giuseppe Luigi LagrangiaGillispie (1997), p. 5 In 1773 Laplace read his paper on the invariability of planetary motion in front of the Academy des Sciences. That March he was elected to the academy, a place where he conducted the majority of his science. On 15 March 1788, at the age of thirty-nine, Laplace married Marie-Charlotte de Courty de Romanges, an eighteen-year-old girl from a "good" family in Besançon. The wedding was celebrated at

Saint-Sulpice, Paris , image = Paris Saint-Sulpice Fassade 4-5 A.jpg , image_size = , pushpin map = Paris , pushpin label position = , coordinates = , location = Place Saint-Sulpice6th arrondis ...

. The couple had a son, Charles-Émile (1789–1874), and a daughter, Sophie-Suzanne (1792–1813).

Analysis, probability, and astronomical stability

Laplace's early published work in 1771 started with

differential equations In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...

and finite differences but he was already starting to think about the mathematical and philosophical concepts of probability and statistics.Gillispie (1989), pp. 7–12 However, before his election to the ''Académie'' in 1773, he had already drafted two papers that would establish his reputation. The first, ''Mémoire sur la probabilité des causes par les événements'' was ultimately published in 1774 while the second paper, published in 1776, further elaborated his statistical thinking and also began his systematic work on celestial mechanics and the stability of the Solar System. The two disciplines would always be interlinked in his mind. "Laplace took probability as an instrument for repairing defects in knowledge."Gillispie (1989). pp. 14–15 Laplace's work on probability and statistics is discussed below with his mature work on the analytic theory of probabilities.

Stability of the Solar System

Sir Isaac Newton had published his ''

Philosophiae Naturalis Principia Mathematica Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some ...

'' in 1687 in which he gave a derivation of Kepler's laws, which describe the motion of the planets, from his laws of motion and his

law of universal gravitation Newton's law of universal gravitation is usually stated as that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distanc ...

. However, though Newton had privately developed the methods of calculus, all his published work used cumbersome geometric reasoning, unsuitable to account for the more subtle higher-order effects of interactions between the planets. Newton himself had doubted the possibility of a mathematical solution to the whole, even concluding that periodic divine intervention was necessary to guarantee the stability of the Solar System. Dispensing with the hypothesis of divine intervention would be a major activity of Laplace's scientific life.Whitrow (2001) It is now generally regarded that Laplace's methods on their own, though vital to the development of the theory, are not sufficiently precise to demonstrate the stability of the Solar System, and indeed, the Solar System is understood to be

chaotic Chaotic was originally a Danish trading card game. It expanded to an online game in America which then became a television program based on the game. The program was able to be seen on 4Kids TV (Fox affiliates, nationwide), Jetix, The CW4Kids ...

, although it happens to be fairly stable. One particular problem from observational astronomy was the apparent instability whereby Jupiter's orbit appeared to be shrinking while that of Saturn was expanding. The problem had been tackled by Leonhard Euler in 1748 and Joseph Louis Lagrange in 1763 but without success.Whittaker (1949b) In 1776, Laplace published a memoir in which he first explored the possible influences of a purported luminiferous ether or of a law of gravitation that did not act instantaneously. He ultimately returned to an intellectual investment in Newtonian gravity.Gillispie (1989). pp. 29–35 Euler and Lagrange had made a practical approximation by ignoring small terms in the equations of motion. Laplace noted that though the terms themselves were small, when integrated over time they could become important. Laplace carried his analysis into the higher-order terms, up to and including the

cubic Cubic may refer to: Science and mathematics * Cube (algebra), "cubic" measurement * Cube, a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex ** Cubic crystal system, a crystal system w ...

. Using this more exact analysis, Laplace concluded that any two planets and the Sun must be in mutual equilibrium and thereby launched his work on the stability of the Solar System.Gillispie (1989), pp. 35–36 Gerald James Whitrow described the achievement as "the most important advance in physical astronomy since Newton". Laplace had a wide knowledge of all sciences and dominated all discussions in the ''Académie''. Laplace seems to have regarded analysis merely as a means of attacking physical problems, though the ability with which he invented the necessary analysis is almost phenomenal. As long as his results were true he took but little trouble to explain the steps by which he arrived at them; he never studied elegance or symmetry in his processes, and it was sufficient for him if he could by any means solve the particular question he was discussing.

Tidal dynamics

Dynamic theory of tides

While

explained the tides by describing the tide-generating forces and Bernoulli gave a description of the static reaction of the waters on Earth to the tidal potential, the ''dynamic theory of tides'', developed by Laplace in 1775, describes the ocean's real reaction to tidal forces. Laplace's theory of ocean tides took into account friction, resonance and natural periods of ocean basins. It predicted the large amphidromic systems in the world's ocean basins and explains the oceanic tides that are actually observed. The equilibrium theory, based on the gravitational gradient from the Sun and Moon but ignoring the Earth's rotation, the effects of continents, and other important effects, could not explain the real ocean tides. Newton's three-body diagram

Since measurements have confirmed the theory, many things have possible explanations now, like how the tides interact with deep sea ridges and chains of seamounts give rise to deep eddies that transport nutrients from the deep to the surface. The equilibrium tide theory calculates the height of the tide wave of less than half a meter, while the dynamic theory explains why tides are up to 15 meters. Satellite observations confirm the accuracy of the dynamic theory, and the tides worldwide are now measured to within a few centimeters. Measurements from the

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satellite closely match the models based on the

TOPEX TOPEX/Poseidon was a joint satellite altimeter mission between NASA, the U.S. space agency; and CNES, the French space agency, to map ocean surface topography. Launched on August 10, 1992, it was the first major oceanographic research satellite. ...

data. Accurate models of tides worldwide are essential for research since the variations due to tides must be removed from measurements when calculating gravity and changes in sea levels.

Laplace's tidal equations

In 1776, Laplace formulated a single set of linear

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function. The function is often thought of as an "unknown" to be sol ...

s, for tidal flow described as a

barotropic In fluid dynamics, a barotropic fluid is a fluid whose density is a function of pressure only. The barotropic fluid is a useful model of fluid behavior in a wide variety of scientific fields, from meteorology to astrophysics. The density of most ...

two-dimensional sheet flow. Coriolis effects are introduced as well as lateral forcing by gravity. Laplace obtained these equations by simplifying the fluid dynamic equations. But they can also be derived from energy integrals via Lagrange's equation. For a fluid sheet of average thickness ''D'', the vertical tidal elevation ''ζ'', as well as the horizontal velocity components ''u'' and ''v'' (in the latitude ''φ'' and longitude ''λ'' directions, respectively) satisfy Laplace's tidal equations: :

\frac &+ u \left( 2 \Omega \sin( \varphi ) \right) + \frac \frac \left( g \zeta + U \right) =0, \end

where ''Ω'' is the angular frequency of the planet's rotation, ''g'' is the planet's gravitational acceleration at the mean ocean surface, ''a'' is the planetary radius, and ''U'' is the external gravitational tidal-forcing potential. William Thomson (Lord Kelvin) rewrote Laplace's momentum terms using the

curl cURL (pronounced like "curl", UK: , US: ) is a computer software project providing a library (libcurl) and command-line tool (curl) for transferring data using various network protocols. The name stands for "Client URL". History cURL was fi ...

to find an equation for vorticity. Under certain conditions this can be further rewritten as a conservation of vorticity.

On the figure of the Earth

During the years 1784–1787 he published some memoirs of exceptional power. Prominent among these is one read in 1783, reprinted as Part II of ''Théorie du Mouvement et de la figure elliptique des planètes'' in 1784, and in the third volume of the ''Mécanique céleste''. In this work, Laplace completely determined the attraction of a spheroid on a particle outside it. This is memorable for the introduction into analysis of spherical harmonics or Laplace's coefficients, and also for the development of the use of what we would now call the gravitational potential in celestial mechanics.

Spherical harmonics

In 1783, in a paper sent to the ''Académie'', Adrien-Marie Legendre had introduced what are now known as

associated Legendre function In mathematics, the associated Legendre polynomials are the canonical solutions of the general Legendre equation \left(1 - x^2\right) \frac P_\ell^m(x) - 2 x \frac P_\ell^m(x) + \left \ell (\ell + 1) - \frac \rightP_\ell^m(x) = 0, or equivalently ...

s. If two points in a plane have polar co-ordinates (''r'', θ) and (''r'' ', θ'), where ''r'' ' ≥ ''r'', then, by elementary manipulation, the reciprocal of the distance between the points, ''d'', can be written as: :

\frac = \frac \left 1 - 2 \cos (\theta' - \theta) \frac + \left ( \frac \right ) ^2 \right^.

This expression can be expanded in powers of ''r''/''r'' ' using Newton's generalised binomial theorem to give: :

\frac = \frac \sum_^\infty P^0_k ( \cos ( \theta' - \theta ) ) \left ( \frac \right ) ^k.

The sequence of functions ''P''⁰_''k''(cos φ) is the set of so-called "associated Legendre functions" and their usefulness arises from the fact that every function of the points on a circle can be expanded as a series of them. Laplace, with scant regard for credit to Legendre, made the non-trivial extension of the result to three dimensions to yield a more general set of functions, the spherical harmonics or Laplace coefficients. The latter term is not in common use now.

Potential theory

This paper is also remarkable for the development of the idea of the scalar potential. The gravitational

force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a p ...

acting on a body is, in modern language, a vector, having magnitude and direction. A potential function is a

scalar Scalar may refer to: *Scalar (mathematics), an element of a field, which is used to define a vector space, usually the field of real numbers * Scalar (physics), a physical quantity that can be described by a single element of a number field such ...

function that defines how the vectors will behave. A scalar function is computationally and conceptually easier to deal with than a vector function. Alexis Clairaut had first suggested the idea in 1743 while working on a similar problem though he was using Newtonian-type geometric reasoning. Laplace described Clairaut's work as being "in the class of the most beautiful mathematical productions". However, Rouse Ball alleges that the idea "was appropriated from Joseph Louis Lagrange, who had used it in his memoirs of 1773, 1777 and 1780". The term "potential" itself was due to

Daniel Bernoulli Daniel Bernoulli FRS (; – 27 March 1782) was a Swiss mathematician and physicist and was one of the many prominent mathematicians in the Bernoulli family from Basel. He is particularly remembered for his applications of mathematics to mechan ...

, who introduced it in his 1738 memoire ''Hydrodynamica''. However, according to Rouse Ball, the term "potential function" was not actually used (to refer to a function ''V'' of the coordinates of space in Laplace's sense) until George Green's 1828

An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism ''An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism'' is a fundamental publication by George Green in 1828, where he extends previous work of Siméon Denis Poisson on electricity and magnetism. The ...

.W.W. Rouse Ball ''A Short Account of the History of Mathematics'' (4th edition, 1908)
/ref> Laplace applied the language of calculus to the potential function and showed that it always satisfies the differential equation: :

\nabla^2V= +
 +
 = 0.

An analogous result for the velocity potential of a fluid had been obtained some years previously by Leonhard Euler. Laplace's subsequent work on gravitational attraction was based on this result. The quantity ∇²''V'' has been termed the concentration of ''V'' and its value at any point indicates the "excess" of the value of ''V'' there over its mean value in the neighbourhood of the point.

, a special case of Poisson's equation, appears ubiquitously in mathematical physics. The concept of a potential occurs in

fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) an ...

, electromagnetism and other areas. Rouse Ball speculated that it might be seen as "the outward sign" of one of the '' a priori'' forms in Kant's theory of perception. The spherical harmonics turn out to be critical to practical solutions of Laplace's equation. Laplace's equation in spherical coordinates, such as are used for mapping the sky, can be simplified, using the method of separation of variables into a radial part, depending solely on distance from the centre point, and an angular or spherical part. The solution to the spherical part of the equation can be expressed as a series of Laplace's spherical harmonics, simplifying practical computation.

Planetary and lunar inequalities

Jupiter–Saturn great inequality

Laplace presented a memoir on planetary inequalities in three sections, in 1784, 1785, and 1786. This dealt mainly with the identification and explanation of the

perturbations Perturbation or perturb may refer to: * Perturbation theory, mathematical methods that give approximate solutions to problems that cannot be solved exactly * Perturbation (geology), changes in the nature of alluvial deposits over time * Perturbatio ...

now known as the "great Jupiter–Saturn inequality". Laplace solved a longstanding problem in the study and prediction of the movements of these planets. He showed by general considerations, first, that the mutual action of two planets could never cause large changes in the eccentricities and inclinations of their orbits; but then, even more importantly, that peculiarities arose in the Jupiter–Saturn system because of the near approach to commensurability of the mean motions of Jupiter and Saturn. In this context ''commensurability'' means that the ratio of the two planets' mean motions is very nearly equal to a ratio between a pair of small whole numbers. Two periods of Saturn's orbit around the Sun almost equal five of Jupiter's. The corresponding difference between multiples of the mean motions, , corresponds to a period of nearly 900 years, and it occurs as a small divisor in the integration of a very small perturbing force with this same period. As a result, the integrated perturbations with this period are disproportionately large, about 0.8° degrees of arc in orbital longitude for Saturn and about 0.3° for Jupiter. Further developments of these theorems on planetary motion were given in his two memoirs of 1788 and 1789, but with the aid of Laplace's discoveries, the tables of the motions of Jupiter and Saturn could at last be made much more accurate. It was on the basis of Laplace's theory that

Delambre Jean Baptiste Joseph, chevalier Delambre (19 September 1749 – 19 August 1822) was a French mathematician, astronomer, historian of astronomy, and geodesist. He was also director of the Paris Observatory, and author of well-known books on th ...

computed his astronomical tables.

Books

Laplace now set himself the task to write a work which should "offer a complete solution of the great mechanical problem presented by the Solar System, and bring theory to coincide so closely with observation that empirical equations should no longer find a place in astronomical tables." The result is embodied in the ''Exposition du système du monde'' and the ''Mécanique céleste''. The former was published in 1796, and gives a general explanation of the phenomena, but omits all details. It contains a summary of the history of astronomy. This summary procured for its author the honour of admission to the forty of the French Academy and is commonly esteemed one of the masterpieces of French literature, though it is not altogether reliable for the later periods of which it treats. Laplace developed the nebular hypothesis of the formation of the Solar System, first suggested by Emanuel Swedenborg and expanded by Immanuel Kant, a hypothesis that continues to dominate accounts of the origin of planetary systems. According to Laplace's description of the hypothesis, the Solar System had evolved from a globular mass of incandescent gas rotating around an axis through its centre of mass. As it cooled, this mass contracted, and successive rings broke off from its outer edge. These rings in their turn cooled, and finally condensed into the planets, while the Sun represented the central core which was still left. On this view, Laplace predicted that the more distant planets would be older than those nearer the Sun.Owen, T. C. (2001) "Solar system: origin of the solar system", '' Encyclopædia Britannica'', Deluxe CDROM edition As mentioned, the idea of the nebular hypothesis had been outlined by Immanuel Kant in 1755, and he had also suggested "meteoric aggregations" and tidal friction as causes affecting the formation of the Solar System. Laplace was probably aware of this, but, like many writers of his time, he generally did not reference the work of others. Laplace's analytical discussion of the Solar System is given in his ''Mécanique céleste'' published in five volumes. The first two volumes, published in 1799, contain methods for calculating the motions of the planets, determining their figures, and resolving tidal problems. The third and fourth volumes, published in 1802 and 1805, contain applications of these methods, and several astronomical tables. The fifth volume, published in 1825, is mainly historical, but it gives as appendices the results of Laplace's latest researches. Laplace's own investigations embodied in it are so numerous and valuable that it is regrettable to have to add that many results are appropriated from other writers with scanty or no acknowledgement, and the conclusions — which have been described as the organised result of a century of patient toil — are frequently mentioned as if they were due to Laplace. Jean-Baptiste Biot, who assisted Laplace in revising it for the press, says that Laplace himself was frequently unable to recover the details in the chain of reasoning, and, if satisfied that the conclusions were correct, he was content to insert the constantly recurring formula, "''Il est aisé à voir que ... ''" ("It is easy to see that ..."). The ''Mécanique céleste'' is not only the translation of Newton's '' Principia'' into the language of the

differential calculus In mathematics, differential calculus is a subfield of calculus that studies the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus—the study of the area beneath a curve. ...

, but it completes parts of which Newton had been unable to fill in the details. The work was carried forward in a more finely tuned form in Félix Tisserand's ''Traité de mécanique céleste'' (1889–1896), but Laplace's treatise will always remain a standard authority. In the years 1784–1787, Laplace produced some memoirs of exceptional power. The significant among these was one issued in 1784, and reprinted in the third volume of the ''Méchanique céleste''. In this work he completely determined the attraction of a spheroid on a particle outside it. This is known for the introduction into analysis of the potential, a useful mathematical concept of broad applicability to the physical sciences.

Black holes

Laplace also came close to propounding the concept of the

. He suggested that there could be massive stars whose gravity is so great that not even light could escape from their surface (see escape velocity). However, this insight was so far ahead of its time that it played no role in the history of scientific development.

Arcueil

In 1806, Laplace bought a house in Arcueil, then a village and not yet absorbed into the Paris

conurbation A conurbation is a region comprising a number of metropolises, cities, large towns, and other urban areas which through population growth and physical expansion, have merged to form one continuous urban or industrially developed area. In most ca ...

. The chemist Claude Louis Berthollet was a neighbour – their gardens were not separatedFourier (1829). – and the pair formed the nucleus of an informal scientific circle, latterly known as the Society of Arcueil. Because of their closeness to

, Laplace and Berthollet effectively controlled advancement in the scientific establishment and admission to the more prestigious offices. The Society built up a complex pyramid of

patronage Patronage is the support, encouragement, privilege, or financial aid that an organization or individual bestows on another. In the history of art, arts patronage refers to the support that kings, popes, and the wealthy have provided to artists su ...

. In 1806, Laplace was also elected a foreign member of the

Royal Swedish Academy of Sciences The Royal Swedish Academy of Sciences ( sv, Kungliga Vetenskapsakademien) is one of the Swedish Royal Academies, royal academies of Sweden. Founded on 2 June 1739, it is an independent, non-governmental scientific organization that takes special ...

Analytic theory of probabilities

In 1812, Laplace issued his ''Théorie analytique des probabilités'' in which he laid down many fundamental results in statistics. The first half of this treatise was concerned with probability methods and problems, the second half with statistical methods and applications. Laplace's proofs are not always rigorous according to the standards of a later day, and his perspective slides back and forth between the Bayesian and non-Bayesian views with an ease that makes some of his investigations difficult to follow, but his conclusions remain basically sound even in those few situations where his analysis goes astray. In 1819, he published a popular account of his work on probability. This book bears the same relation to the ''Théorie des probabilités'' that the ''Système du monde'' does to the ''Méchanique céleste''. In its emphasis on the analytical importance of probabilistic problems, especially in the context of the "approximation of formula functions of large numbers," Laplace's work goes beyond the contemporary view which almost exclusively considered aspects of practical applicability. Laplace's Théorie analytique remained the most influential book of mathematical probability theory to the end of the 19th century. The general relevance for statistics of Laplacian error theory was appreciated only by the end of the 19th century. However, it influenced the further development of a largely analytically oriented probability theory.

Inductive probability

In his ''Essai philosophique sur les probabilités'' (1814), Laplace set out a mathematical system of

inductive reasoning Inductive reasoning is a method of reasoning in which a general principle is derived from a body of observations. It consists of making broad generalizations based on specific observations. Inductive reasoning is distinct from ''deductive'' re ...

based on probability, which we would today recognise as Bayesian. He begins the text with a series of principles of probability, the first six being: # Probability is the ratio of the "favored events" to the total possible events. # The first principle assumes equal probabilities for all events. When this is not true, we must first determine the probabilities of each event. Then, the probability is the sum of the probabilities of all possible favoured events. # For independent events, the probability of the occurrence of all is the probability of each multiplied together. # For events not independent, the probability of event B following event A (or event A causing B) is the probability of A multiplied by the probability that, given A, B will occur. # The probability that ''A'' will occur, given that B has occurred, is the probability of ''A'' and ''B'' occurring divided by the probability of ''B''. # Three corollaries are given for the sixth principle, which amount to Bayesian probability. Where event exhausts the list of possible causes for event ''B'', . Then :::

\Pr(A_i \mid B) = \Pr(A_i)\frac.

One well-known formula arising from his system is the rule of succession, given as principle seven. Suppose that some trial has only two possible outcomes, labelled "success" and "failure". Under the assumption that little or nothing is known ''a priori'' about the relative plausibilities of the outcomes, Laplace derived a formula for the probability that the next trial will be a success. :

\Pr(\text) = \frac

where ''s'' is the number of previously observed successes and ''n'' is the total number of observed trials. It is still used as an estimator for the probability of an event if we know the event space, but have only a small number of samples. The rule of succession has been subject to much criticism, partly due to the example which Laplace chose to illustrate it. He calculated that the probability that the sun will rise tomorrow, given that it has never failed to in the past, was :

\Pr(\text) = \frac

where ''d'' is the number of times the sun has risen in the past. This result has been derided as absurd, and some authors have concluded that all applications of the Rule of Succession are absurd by extension. However, Laplace was fully aware of the absurdity of the result; immediately following the example, he wrote, "But this number .e., the probability that the sun will rise tomorrowis far greater for him who, seeing in the totality of phenomena the principle regulating the days and seasons, realizes that nothing at the present moment can arrest the course of it."

Probability-generating function

The method of estimating the ratio of the number of favourable cases to the whole number of possible cases had been previously indicated by Laplace in a paper written in 1779. It consists of treating the successive values of any function as the coefficients in the expansion of another function, with reference to a different variable. The latter is therefore called the

probability-generating function In probability theory, the probability generating function of a discrete random variable is a power series representation (the generating function) of the probability mass function of the random variable. Probability generating functions are oft ...

of the former. Laplace then shows how, by means of

interpolation In the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing (finding) new data points based on the range of a discrete set of known data points. In engineering and science, one often has a n ...

, these coefficients may be determined from the generating function. Next he attacks the converse problem, and from the coefficients he finds the generating function; this is effected by the solution of a

finite difference equation A finite difference is a mathematical expression of the form . If a finite difference is divided by , one gets a difference quotient. The approximation of derivatives by finite differences plays a central role in finite difference methods for the ...

Least squares and central limit theorem

The fourth chapter of this treatise includes an exposition of the method of least squares, a remarkable testimony to Laplace's command over the processes of analysis. In 1805 Legendre had published the method of least squares, making no attempt to tie it to the theory of probability. In 1809 Gauss had derived the normal distribution from the principle that the arithmetic mean of observations gives the most probable value for the quantity measured; then, turning this argument back upon itself, he showed that, if the errors of observation are normally distributed, the least squares estimates give the most probable values for the coefficients in regression situations. These two works seem to have spurred Laplace to complete work toward a treatise on probability he had contemplated as early as 1783.Stigler, 1975 In two important papers in 1810 and 1811, Laplace first developed the characteristic function as a tool for large-sample theory and proved the first general central limit theorem. Then in a supplement to his 1810 paper written after he had seen Gauss's work, he showed that the central limit theorem provided a Bayesian justification for least squares: if one were combining observations, each one of which was itself the mean of a large number of independent observations, then the least squares estimates would not only maximise the likelihood function, considered as a posterior distribution, but also minimise the expected posterior error, all this without any assumption as to the error distribution or a circular appeal to the principle of the arithmetic mean. In 1811 Laplace took a different non-Bayesian tack. Considering a linear regression problem, he restricted his attention to linear unbiased estimators of the linear coefficients. After showing that members of this class were approximately normally distributed if the number of observations was large, he argued that least squares provided the "best" linear estimators. Here it is "best" in the sense that it minimised the asymptotic variance and thus both minimised the expected absolute value of the error, and maximised the probability that the estimate would lie in any symmetric interval about the unknown coefficient, no matter what the error distribution. His derivation included the joint limiting distribution of the least squares estimators of two parameters.

Laplace's demon

In 1814, Laplace published what may have been the first scientific articulation of causal determinism: This intellect is often referred to as ''Laplace's demon'' (in the same vein as ''

Maxwell's demon Maxwell's demon is a thought experiment that would hypothetically violate the second law of thermodynamics. It was proposed by the physicist James Clerk Maxwell in 1867. In his first letter Maxwell called the demon a "finite being", while the ' ...

'') and sometimes ''Laplace's Superman'' (after

Hans Reichenbach Hans Reichenbach (September 26, 1891 – April 9, 1953) was a leading philosopher of science, educator, and proponent of logical empiricism. He was influential in the areas of science, education, and of logical empiricism. He founded the ''Gesel ...

). Laplace, himself, did not use the word "demon", which was a later embellishment. As translated into English above, he simply referred to: ''"Une intelligence ... Rien ne serait incertain pour elle, et l'avenir comme le passé, serait présent à ses yeux."'' Even though Laplace is generally credited with having first formulated the concept of causal determinism, in a philosophical context the idea was actually widespread at the time, and can be found as early as 1756 in Maupertuis' 'Sur la Divination'. As well,

Jesuit , image = Ihs-logo.svg , image_size = 175px , caption = ChristogramOfficial seal of the Jesuits , abbreviation = SJ , nickname = Jesuits , formation = , founders ...

scientist Boscovich first proposed a version of scientific determinism very similar to Laplace's in his 1758 book ''Theoria philosophiae naturalis''.

Laplace transforms

As early as 1744,

Euler Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in ma ...

, followed by

Lagrange Joseph-Louis Lagrange (born Giuseppe Luigi Lagrangiadifferential equations in the form: :

z = \int X(x) e^ \,dx\textz = \int X(x) x^a \,dx.

The Laplace transform has the form: :

F(s) = \int f(t) e^\,dt

This integral operator transforms a function of time (

t

) into a function of a complex variable (

s

), usually interpreted as complex frequency.

Other discoveries and accomplishments

Mathematics

Among the other discoveries of Laplace in pure and applied mathematics are: * Discussion, contemporaneously with Alexandre-Théophile Vandermonde, of the general theory of determinants, (1772); * Proof that every equation of an odd degree must have at least one real quadratic factor; *

Laplace's method In mathematics, Laplace's method, named after Pierre-Simon Laplace, is a technique used to approximate integrals of the form :\int_a^b e^ \, dx, where f(x) is a twice- differentiable function, ''M'' is a large number, and the endpoints ''a'' ...

for approximating integrals * Solution of the linear partial differential equation of the second order; * He was the first to consider the difficult problems involved in equations of mixed differences, and to prove that the solution of an equation in finite differences of the first degree and the second order might always be obtained in the form of a continued fraction; * In his theory of probabilities: ** de Moivre–Laplace theorem that approximates binomial distribution with a normal distribution ** Evaluation of several common

definite integral In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with di ...

s; ** General proof of the Lagrange reversion theorem.

Surface tension

Laplace built upon the qualitative work of Thomas Young to develop the theory of capillary action and the Young–Laplace equation.

Speed of sound

Laplace in 1816 was the first to point out that the

speed of sound The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium. At , the speed of sound in air is about , or one kilometre in or one mile in . It depends strongly on temperature as w ...

in air depends on the heat capacity ratio. Newton's original theory gave too low a value, because it does not take account of the adiabatic compression of the air which results in a local rise in temperature and pressure. Laplace's investigations in practical physics were confined to those carried on by him jointly with

Lavoisier Antoine-Laurent de Lavoisier ( , ; ; 26 August 17438 May 1794),
CNRS (

specific heat of various bodies.

Politics

Minister of the Interior

In his early years Laplace was careful never to become involved in politics, or indeed in life outside the ''Académie des sciences''. He prudently withdrew from Paris during the most violent part of the Revolution. In November 1799, immediately after seizing power in the coup of

18 Brumaire The Coup d'état of 18 Brumaire brought Napoleon Bonaparte to power as First Consul of France. In the view of most historians, it ended the French Revolution and led to the Coronation of Napoleon as Emperor. This bloodless ''coup d'état'' overt ...

, Napoleon appointed Laplace to the post of Minister of the Interior. The appointment, however, lasted only six weeks, after which Lucien Bonaparte, Napoleon's brother, was given the post. Evidently, once Napoleon's grip on power was secure, there was no need for a prestigious but inexperienced scientist in the government.Grattan-Guinness (2005), p. 333 Napoleon later (in his ''Mémoires de Sainte Hélène'') wrote of Laplace's dismissal as follows: Grattan-Guinness, however, describes these remarks as "tendentious", since there seems to be no doubt that Laplace "was only appointed as a short-term figurehead, a place-holder while Napoleon consolidated power".

From Bonaparte to the Bourbons

Although Laplace was removed from office, it was desirable to retain his allegiance. He was accordingly raised to the senate, and to the third volume of the ''Mécanique céleste'' he prefixed a note that of all the truths therein contained the most precious to the author was the declaration he thus made of his devotion towards the peacemaker of Europe. In copies sold after the

this was struck out. (Pearson points out that the censor would not have allowed it anyway.) In 1814 it was evident that the empire was falling; Laplace hastened to tender his services to the Bourbons, and in 1817 during the Restoration he was rewarded with the title of

. According to Rouse Ball, the contempt that his more honest colleagues felt for his conduct in the matter may be read in the pages of Paul Louis Courier. His knowledge was useful on the numerous scientific commissions on which he served, and, says Rouse Ball, probably accounts for the manner in which his political insincerity was overlooked. Roger Hahn in his 2005 biography disputes this portrayal of Laplace as an opportunist and turncoat, pointing out that, like many in France, he had followed the debacle of Napoleon's Russian campaign with serious misgivings. The Laplaces, whose only daughter Sophie had died in childbirth in September 1813, were in fear for the safety of their son Émile, who was on the eastern front with the emperor. Napoleon had originally come to power promising stability, but it was clear that he had overextended himself, putting the nation at peril. It was at this point that Laplace's loyalty began to weaken. Although he still had easy access to Napoleon, his personal relations with the emperor cooled considerably. As a grieving father, he was particularly cut to the quick by Napoleon's insensitivity in an exchange related by Jean-Antoine Chaptal: "On his return from the rout in Leipzig, he apoleonaccosted Mr Laplace: 'Oh! I see that you have grown thin—Sire, I have lost my daughter—Oh! that's not a reason for losing weight. You are a mathematician; put this event in an equation, and you will find that it adds up to zero.'"

Political philosophy

In the second edition (1814) of the ''Essai philosophique'', Laplace added some revealing comments on politics and governance. Since it is, he says, "the practice of the eternal principles of reason, justice and humanity that produce and preserve societies, there is a great advantage to adhere to these principles, and a great inadvisability to deviate from them". Noting "the depths of misery into which peoples have been cast" when ambitious leaders disregard these principles, Laplace makes a veiled criticism of Napoleon's conduct: "Every time a great power intoxicated by the love of conquest aspires to universal domination, the sense of liberty among the unjustly threatened nations breeds a coalition to which it always succumbs." Laplace argues that "in the midst of the multiple causes that direct and restrain various states, natural limits" operate, within which it is "important for the stability as well as the prosperity of empires to remain". States that transgress these limits cannot avoid being "reverted" to them, "just as is the case when the waters of the seas whose floor has been lifted by violent tempests sink back to their level by the action of gravity".Hahn (2005), p. 185 About the political upheavals he had witnessed, Laplace formulated a set of principles derived from physics to favour evolutionary over revolutionary change: In these lines, Laplace expressed the views he had arrived at after experiencing the Revolution and the Empire. He believed that the stability of nature, as revealed through scientific findings, provided the model that best helped to preserve the human species. "Such views," Hahn comments, "were also of a piece with his steadfast character." In the ''Essai philosophique'', Laplace also illustrates the potential of probabilities in political studies by applying the law of large numbers to justify the candidates’ integer-valued ranks used in the Borda method of voting, with which the new members of the Academy of Sciences were elected. Laplace’s verbal argument is so rigorous that it can easily be converted into a formal proof.

Death

Laplace died in Paris on 5 March 1827, which was the same day

Alessandro Volta Alessandro Giuseppe Antonio Anastasio Volta (, ; 18 February 1745 – 5 March 1827) was an Italian physicist, chemist and lay Catholic who was a pioneer of electricity and power who is credited as the inventor of the electric battery and the ...

died. His brain was removed by his physician, François Magendie, and kept for many years, eventually being displayed in a roving anatomical museum in Britain. It was reportedly smaller than the average brain. Laplace was buried at

Père Lachaise A name suffix, in the Western English-language naming tradition, follows a person's full name and provides additional information about the person. Post-nominal letters indicate that the individual holds a position, educational degree, accredit ...

in Paris but in 1888 his remains were moved to

Religious opinions

''I had no need of that hypothesis''

A frequently cited but potentially

apocryphal Apocrypha are works, usually written, of unknown authorship or of doubtful origin. The word ''apocryphal'' (ἀπόκρυφος) was first applied to writings which were kept secret because they were the vehicles of esoteric knowledge considered ...

interaction between Laplace and Napoleon purportedly concerns the existence of God. Although the conversation in question did occur, the exact words Laplace used and his intended meaning are not known. A typical version is provided by Rouse Ball: An earlier report, although without the mention of Laplace's name, is found in Antommarchi's ''

The Last Moments of Napoleon ''The Last Moments of Napoleon'' is a book by Francesco Antommarchi, Napoleon I Napoleon Bonaparte ; it, Napoleone Bonaparte, ; co, Napulione Buonaparte. (born Napoleone Buonaparte; 15 August 1769 – 5 May 1821), later known by his regna ...

'' (1825): In 1884, however, the astronomer Hervé FayeFaye, Hervé (1884), ''Sur l'origine du monde: théories cosmogoniques des anciens et des modernes''. Paris: Gauthier-Villars, pp. 109–111Pasquier, Ernest (1898)
"Les hypothèses cosmogoniques (''suite'')"
''Revue néo-scholastique'', 5^o année, N^o 18, pp. 124–125, footnote 1. affirmed that this account of Laplace's exchange with Napoleon presented a "strangely transformed" (''étrangement transformée'') or garbled version of what had actually happened. It was not God that Laplace had treated as a hypothesis, but merely his intervention at a determinate point: Laplace's younger colleague, the astronomer

François Arago Dominique François Jean Arago ( ca, Domènec Francesc Joan Aragó), known simply as François Arago (; Catalan: ''Francesc Aragó'', ; 26 February 17862 October 1853), was a French mathematician, physicist, astronomer, freemason, supporter of t ...

, who gave his eulogy before the French Academy in 1827, told Faye of an attempt by Laplace to keep the garbled version of his interaction with Napoleon out of circulation. Faye writes: The Swiss-American historian of mathematics Florian Cajori appears to have been unaware of Faye's research, but in 1893 he came to a similar conclusion. Stephen Hawking said in 1999, "I don't think that Laplace was claiming that God does not exist. It's just that he doesn't intervene, to break the laws of Science." The only eyewitness account of Laplace's interaction with Napoleon is from the entry for 8 August 1802 in the diary of the British astronomer Sir William Herschel: Since this makes no mention of Laplace's saying, "I had no need of that hypothesis," Daniel Johnson argues that "Laplace never used the words attributed to him." Arago's testimony, however, appears to imply that he did, only not in reference to the existence of God.

Views on God

Raised a Catholic, Laplace appears in adult life to have inclined to

deism Deism ( or ; derived from the Latin ''deus'', meaning "god") is the Philosophy, philosophical position and Rationalism, rationalistic theology that generally rejects revelation as a source of divine knowledge, and asserts that Empirical evi ...

(presumably his considered position, since it is the only one found in his writings). However, some of his contemporaries thought he was an

atheist Atheism, in the broadest sense, is an absence of belief in the existence of deities. Less broadly, atheism is a rejection of the belief that any deities exist. In an even narrower sense, atheism is specifically the position that there no ...

, while a number of recent scholars have described him as

agnostic Agnosticism is the view or belief that the existence of God, of the divine or the supernatural is unknown or unknowable. (page 56 in 1967 edition) Another definition provided is the view that "human reason is incapable of providing sufficient ...

. Faye thought that Laplace "did not profess atheism", but Napoleon, on

Saint Helena Saint Helena () is a British overseas territory located in the South Atlantic Ocean. It is a remote volcanic tropical island west of the coast of south-western Africa, and east of Rio de Janeiro in South America. It is one of three constitu ...

, told General Gaspard Gourgaud, "I often asked Laplace what he thought of God. He owned that he was an atheist." Roger Hahn, in his biography of Laplace, mentions a dinner party at which "the geologist

Jean-Étienne Guettard Jean-Étienne Guettard (22 September 1715 – 7 January 1786), French naturalist and mineralogist, was born at Étampes, near Paris. In boyhood, he gained a knowledge of plants from his grandfather, who was an apothecary, and later he qualif ...

was staggered by Laplace's bold denunciation of the existence of God". It appeared to Guettard that Laplace's atheism "was supported by a thoroughgoing

materialism Materialism is a form of philosophical monism which holds matter to be the fundamental substance in nature, and all things, including mental states and consciousness, are results of material interactions. According to philosophical materiali ...

". But the chemist

Jean-Baptiste Dumas Jean Baptiste André Dumas (14 July 180010 April 1884) was a French chemist, best known for his works on organic analysis and synthesis, as well as the determination of atomic weights (relative atomic masses) and molecular weights by measuring v ...

, who knew Laplace well in the 1820s, wrote that Laplace "provided materialists with their specious arguments, without sharing their convictions".Kneller, Karl Alois. ''Christianity and the Leaders of Modern Science: A Contribution to the History of Culture in the Nineteenth Century'', translated from the second German edition by T.M. Kettle. London: B. Herder, 1911
pp. 73–74
Hahn states: "Nowhere in his writings, either public or private, does Laplace deny God's existence." Expressions occur in his private letters that appear inconsistent with atheism. On 17 June 1809, for instance, he wrote to his son, "''Je prie Dieu qu'il veille sur tes jours. Aie-Le toujours présent à ta pensée, ainsi que ton père et ta mère'' pray that God watches over your days. Let Him be always present to your mind, as also your father and your mother" Ian S. Glass, quoting Herschel's account of the celebrated exchange with Napoleon, writes that Laplace was "evidently a deist like Herschel". In ''Exposition du système du monde'', Laplace quotes Newton's assertion that "the wondrous disposition of the Sun, the planets and the comets, can only be the work of an all-powerful and intelligent Being". This, says Laplace, is a "thought in which he ewtonwould be even more confirmed, if he had known what we have shown, namely that the conditions of the arrangement of the planets and their satellites are precisely those which ensure its stability". By showing that the "remarkable" arrangement of the planets could be entirely explained by the laws of motion, Laplace had eliminated the need for the "supreme intelligence" to intervene, as Newton had "made" it do. Laplace cites with approval Leibniz's criticism of Newton's invocation of divine intervention to restore order to the Solar System: "This is to have very narrow ideas about the wisdom and the power of God." He evidently shared Leibniz's astonishment at Newton's belief "that God has made his machine so badly that unless he affects it by some extraordinary means, the watch will very soon cease to go". In a group of manuscripts, preserved in relative secrecy in a black envelope in the library of the ''Académie des sciences'' and published for the first time by Hahn, Laplace mounted a deist critique of Christianity. It is, he writes, the "first and most infallible of principles ... to reject miraculous facts as untrue". As for the doctrine of transubstantiation, it "offends at the same time reason, experience, the testimony of all our senses, the eternal laws of nature, and the sublime ideas that we ought to form of the Supreme Being". It is the sheerest absurdity to suppose that "the sovereign lawgiver of the universe would suspend the laws that he has established, and which he seems to have maintained invariably". Laplace also ridiculed the use of probability in theology. Even following Pascal's reasoning presented in Pascal's wager, it is not worth making a bet, for the hope of profit – equal to the product of the value of the testimonies (infinitely small) and the value of the happiness they promise (which is significant but finite) – must necessarily be infinitely small. In old age, Laplace remained curious about the question of GodHahn (2005), p. 202. and frequently discussed Christianity with the Swiss astronomer Jean-Frédéric-Théodore Maurice. He told Maurice that "Christianity is quite a beautiful thing" and praised its civilising influence. Maurice thought that the basis of Laplace's beliefs was, little by little, being modified, but that he held fast to his conviction that the invariability of the laws of nature did not permit of supernatural events. After Laplace's death, Poisson told Maurice, "You know that I do not share your eligiousopinions, but my conscience forces me to recount something that will surely please you." When Poisson had complimented Laplace about his "brilliant discoveries", the dying man had fixed him with a pensive look and replied, "Ah! We chase after phantoms 'chimères''" These were his last words, interpreted by Maurice as a realisation of the ultimate " vanity" of earthly pursuits.Hahn (2005), p. 204. Laplace received the last rites from the curé of the Missions Étrangères (in whose parish he was to be buried) and the curé of Arcueil. According to his biographer, Roger Hahn, it is "not credible" that Laplace "had a proper Catholic end", and he "remained a skeptic" to the very end of his life. Laplace in his last years has been described as an agnostic.

Excommunication of a comet

In 1470 the humanist scholar

Bartolomeo Platina Bartolomeo Sacchi (; 1421 – 21 September 1481), known as Platina (in Italian ''il Platina'' ) after his birthplace (Piadena), and commonly referred to in English as Bartolomeo Platina, was an Italian Renaissance humanist writer and gastro ...

wrote that Pope Callixtus III had asked for prayers for deliverance from the Turks during a 1456 appearance of Halley's Comet. Platina's account does not accord with Church records, which do not mention the comet. Laplace is alleged to have embellished the story by claiming the Pope had " excommunicated" Halley's comet. What Laplace actually said, in ''Exposition du système du monde'' (1796), was that the Pope had ordered the comet to be " exorcised" (''conjuré''). It was Arago, in ''Des Comètes en général'' (1832), who first spoke of an excommunication.

Honors

* Correspondent of the Royal Institute of the Netherlands in 1809. * Foreign Honorary Member of the American Academy of Arts and Sciences in 1822. * The asteroid

4628 Laplace 46 may refer to: * 46 (number) * 46 (album), ''46'' (album), a 1983 album by Kino (band), Kino * "Forty Six", a song by Karma to Burn from the album ''Appalachian Incantation'', 2010 * One of the years 46 BC, AD 46, 1946, 2046 {{Number disambiguat ...

is named for Laplace. * A spur of the Montes Jura on the Moon is known as Promontorium Laplace. * His name is one of the 72 names inscribed on the Eiffel Tower. * The tentative working name of the

European Space Agency , owners = , headquarters = Paris, Île-de-France, France , coordinates = , spaceport = Guiana Space Centre , seal = File:ESA emblem seal.png , seal_size = 130px , image = Views in the Main Control Room (1205 ...

Europa Jupiter System Mission is the "Laplace" space probe. * A train station in the RER B in Arcueil bears his name. * A street in Verkhnetemernitsky (near

Rostov-on-Don Rostov-on-Don ( rus, Ростов-на-Дону, r=Rostov-na-Donu, p=rɐˈstof nə dɐˈnu) is a port city and the administrative centre of Rostov Oblast and the Southern Federal District of Russia. It lies in the southeastern part of the East Eu ...

, Russia).

Quotations

* I had no need of that hypothesis. ("Je n'avais pas besoin de cette hypothèse-là", allegedly as a reply to

, who had asked why he hadn't mentioned God in his book on astronomy.) * It is therefore obvious that ... (Frequently used in the ''Celestial Mechanics'' when he had proved something and mislaid the proof, or found it clumsy. Notorious as a signal for something true, but hard to prove.) * "We are so far from knowing all the agents of nature and their diverse modes of action that it would not be philosophical to deny phenomena solely because they are inexplicable in the actual state of our knowledge. But we ought to examine them with an attention all the more scrupulous as it appears more difficult to admit them." ** This is restated in

Theodore Flournoy Theodore may refer to: Places * Theodore, Alabama, United States * Theodore, Australian Capital Territory * Theodore, Queensland, a town in the Shire of Banana, Australia * Theodore, Saskatchewan, Canada * Theodore Reservoir, a lake in Saskatche ...

's work ''From India to the Planet Mars'' as the Principle of Laplace or, "The weight of the evidence should be proportioned to the strangeness of the facts." ** Most often repeated as "The weight of evidence for an extraordinary claim must be proportioned to its strangeness." (see also: Sagan standard) * This simplicity of ratios will not appear astonishing if we consider that all the effects of nature are only mathematical results of a small number of immutable laws. * Infinitely varied in her effects, nature is only simple in her causes. * What we know is little, and what we are ignorant of is immense. (Fourier comments: "This was at least the meaning of his last words, which were articulated with difficulty.") * One sees in this essay that the theory of probabilities is basically only common sense reduced to a calculus. It makes one estimate accurately what right-minded people feel by a sort of instinct, often without being able to give a reason for it.

List of works

* * * * * * * File:Laplace-1.jpg, Volumes 1-5 of Pierre-Simon Laplace's "

Traité de mécanique céleste ''Traité de mécanique céleste'' () is a five-volume treatise on celestial mechanics written by Pierre-Simon Laplace and published from 1798 to 1825 with a second edition in 1829. In 1842, the government of Louis Philippe gave a grant of 40,000 ...

" (1799) File:Laplace-2.jpg, Title page to Volume I of "

" (1799) File:Laplace-3.jpg, Table of contents to Volume I of "

" (1799) File:Laplace-4.jpg, First page of Volume I of "

" (1799)

Bibliography

*
Œuvres complètes de Laplace
', 14 vol. (1878–1912), Paris: Gauthier-Villars (copy from Gallica in French) * ''Théorie du movement et de la figure elliptique des planètes'' (1784) Paris (not in ''Œuvres complètes'') *
Précis de l'histoire de l'astronomie
' *

Alphonse Rebière Alphonse Michel Rebière (Tulle, 1842 – Paris, 1900) was a nineteenth-century advocate for women's scientific abilities. He wrote the book Les Femmes dans la science, published in 1894. Rebière's piece followed the encyclopedia format, listi ...

, ''Mathématiques et mathématiciens'', 3rd edition Paris, Nony & Cie, 1898.

English translations

Bowditch, N. (trans.) (1829–1839) ''Mécanique céleste'', 4 vols, Boston ** New edition by Reprint Services * –

829–1839 8 (eight) is the natural number following 7 and preceding 9. In mathematics 8 is: * a composite number, its proper divisors being , , and . It is twice 4 or four times 2. * a power of two, being 2 (two cubed), and is the first number of t ...

(1966–1969) ''Celestial Mechanics'', 5 vols, including the original French * Pound, J. (trans.) (1809) ''The System of the World'', 2 vols, London: Richard Phillips * _ ''The System of the World (v.1)'' * _ ''The System of the World (v.2)'' * – 809(2007) ''The System of the World'', vol.1, Kessinger, * Toplis, J. (trans.) (1814) A treatise upon analytical mechanics Nottingham: H. Barnett * , translated from the French 6th ed. (1840) ** * , translated from the French 5th ed. (1825)

References

Citations

General sources

* * * * – (2006) "A Science Empire in Napoleonic France", ''History of Science'', vol. 44, pp. 29–48 * * David, F. N. (1965) "Some notes on Laplace", in Neyman, J. & LeCam, L. M. (eds) ''Bernoulli, Bayes and Laplace'', Berlin, pp. 30–44. * * * * * * , delivered 15 June 1829, published in 1831. * * * Grattan-Guinness, I., 2005, "'Exposition du système du monde' and 'Traité de méchanique céleste'" in his ''Landmark Writings in Western Mathematics''. Elsevier: 242–57. * Gribbin, John. ''The Scientists: A History of Science Told Through the Lives of Its Greatest Inventors''. New York, Random House, 2002. p. 299. * * – (1981) "Laplace and the Vanishing Role of God in the Physical Universe", in Woolf, Henry, ed., ''The Analytic Spirit: Essays in the History of Science''. Ithaca, NY: Cornell University Press. . * * * * * (1999) * * Rouse Ball, W.W.

908 __NOTOC__ Year 908 ( CMVIII) was a leap year starting on Friday (link will display the full calendar) of the Julian calendar. Events By place Byzantine Empire * May 15 – The three-year-old Constantine VII, the son of Emperor L ...

(2003) "Pierre Simon Laplace (1749–1827)", in ''A Short Account of the History of Mathematics'', 4th ed., Dover, Als
available at Project Gutenberg
* * * Whitrow, G. J. (2001) "Laplace, Pierre-Simon, marquis de", '' Encyclopædia Britannica'', Deluxe CDROM edition * * * *

External links

* *
Pierre-Simon Laplace
in the

MacTutor History of Mathematics archive The MacTutor History of Mathematics archive is a website maintained by John J. O'Connor and Edmund F. Robertson and hosted by the University of St Andrews in Scotland. It contains detailed biographies on many historical and contemporary mathemati ...

. *
Guide to the Pierre Simon Laplace Papers
at The Bancroft Library *
English translation
of a large part of Laplace's work in probability and statistics, provided b

Pierre-Simon Laplace – Œuvres complètes
(last 7 volumes only) Gallica-Math * "Sur le mouvement d'un corps qui tombe d'une grande hauteur" (Laplace 1803), online and analysed on
BibNum
' (English). {{DEFAULTSORT:Laplace, Pierre Simon 1749 births 1827 deaths People from Calvados (department) 18th-century French mathematicians 19th-century French mathematicians Counts of the First French Empire Determinists Enlightenment scientists French agnostics French deists 18th-century French astronomers French marquesses French physicists Fluid dynamicists Grand Officiers of the Légion d'honneur Mathematical analysts Linear algebraists Members of the Académie Française Members of the French Academy of Sciences Members of the Royal Netherlands Academy of Arts and Sciences Members of the Royal Swedish Academy of Sciences Fellows of the Royal Society Probability theorists French interior ministers Theoretical physicists Fellows of the American Academy of Arts and Sciences University of Caen Normandy alumni