Pierre Simon Laplace

Pierre-Simon Laplace

Pierre-Simon Laplace (17491827). Posthumousportrait by Madame Feytaud, 1842.

Born 23 March 1749Beaumont-en-Auge, Normandy,France

Died 5 March 1827 (aged 77)Paris, France

Nationality FrenchFields Astronomer and MathematicianInstitutions cole Militaire (17691776)Alma mater University of CaenAcademicadvisors

Jean d'AlembertChristophe GadbledPierre Le Canu

Doctoral students Simon Denis PoissonKnown for

Signature

Pierre-Simon LaplaceFrom Wikipedia, the free encyclopedia

Pierre-Simon, marquis de Laplace (/lpls/; French: [pj sim laplas]; 23 March1749 5 March 1827) was a French mathematician and astronomer whose work waspivotal to the development of mathematical astronomy and statistics. He summarizedand extended the work of his predecessors in his five-volume Mcanique Cleste(Celestial Mechanics) (17991825). This work translated the geometric study ofclassical mechanics to one based on calculus, opening up a broader range ofproblems. In statistics, the Bayesian interpretation of probability was developedmainly by Laplace.[2]

Laplace formulated Laplace's equation, and pioneered the Laplace transform whichappears in many branches of mathematical physics, a field that he took a leading rolein forming. The Laplacian differential operator, widely used in mathematics, is alsonamed after him. He restated and developed the nebular hypothesis of the origin ofthe solar system and was one of the first scientists to postulate the existence of blackholes and the notion of gravitational collapse.

Laplace is remembered as one of the greatest scientists of all time. Sometimesreferred to as the French Newton or Newton of France, he possessed a phenomenalnatural mathematical faculty superior to that of any of his contemporaries.[3]

Laplace became a count of the First French Empire in 1806 and was named amarquis in 1817, after the Bourbon Restoration.

Contents1 Early years2 Analysis, probability and astronomical stability

2.1 Stability of the solar system3 On the figure of the Earth

3.1 Spherical harmonics3.2 Potential theory

4 Planetary and lunar inequalities4.1 JupiterSaturn great inequality4.2 Lunar inequalities

5 Celestial mechanics6 Black holes7 Arcueil8 Analytic theory of probabilities

8.1 Inductive probability8.2 Probability-generating function8.3 Least squares and central limit theorem

9 Laplace's demon10 Laplace transforms11 Other discoveries and accomplishments

11.1 Mathematics11.2 Surface tension11.3 Speed of sound

12 Politics12.1 Minister of the Interior12.2 From Bonaparte to the Bourbons12.3 Political philosophy

13 Religious opinions13.1 I had no need of that hypothesis13.2 Views on God13.3 Excommunication of a comet

14 Honors15 Quotations16 See also17 References18 Bibliography

18.1 By Laplace18.1.1 English translations

Pierre-Simon Laplace - Wikipedia, the free encyclopedia http://en.wikipedia.org/wiki/Pierre-Simon_Laplace

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18.2 About Laplace and his work19 External links

Early years

Many details of the life of Laplace were lost when the family chteau burned in 1925.[4] Laplace was born in Beaumont-en-Auge,Normandy in 1749. According to W. W. Rouse Ball,[5] he was the son of a small cottager or perhaps a farm-laborer, and owed hiseducation to the interest excited in some wealthy neighbors by his abilities and engaging presence. Very little is known of his earlyyears. It would seem that from a pupil he became an usher in the school at Beaumont; but, having procured a letter of introduction tod'Alembert, he went to Paris to advance his fortune. However, Karl Pearson[4] is scathing about the inaccuracies in Rouse Ball'saccount and states:

Indeed Caen was probably in Laplace's day the most intellectually active of all the towns of Normandy. It was here thatLaplace was educated and was provisionally a professor. It was here he wrote his first paper published in the Mlanges ofthe Royal Society of Turin, Tome iv. 17661769, at least two years before he went at 22 or 23 to Paris in 1771. Thusbefore he was 20 he was in touch with Lagrange in Turin. He did not go to Paris a raw self-taught country lad with only apeasant background! In 1765 at the age of sixteen Laplace left the "School of the Duke of Orleans" in Beaumont and wentto the University of Caen, where he appears to have studied for five years. The 'cole Militaire' of Beaumont did notreplace the old school until 1776.

His parents were from comfortable families. His father was Pierre Laplace, and his mother was Marie-Anne Sochon. The Laplacefamily was involved in agriculture until at least 1750, but Pierre Laplace senior was also a cider merchant and syndic of the town ofBeaumont.

Pierre Simon Laplace attended a school in the village run at a Benedictine priory, his father intending that he be ordained in the RomanCatholic Church. At sixteen, to further his father's intention, he was sent to the University of Caen to read theology.[6]

At the university, he was mentored by two enthusiastic teachers of mathematics, Christophe Gadbled and Pierre Le Canu, who awokehis zeal for the subject. Laplace did not graduate in theology but left for Paris with a letter of introduction from Le Canu to Jean leRond d'Alembert.[6]

According to his great-great-grandson,[4] d'Alembert received him rather poorly, and to get rid of him gave him a thick mathematicsbook, saying to come back when he had read it. When Laplace came back a few days later, d'Alembert was even less friendly and didnot hide his opinion that it was impossible that Laplace could have read and understood the book. But upon questioning him, he realizedthat it was true, and from that time he took Laplace under his care.

Another version is that Laplace solved overnight a problem that d'Alembert set him for submission the following week, then solved aharder problem the following night. D'Alembert was impressed and recommended him for a teaching place in the cole Militaire.[7]

With a secure income and undemanding teaching, Laplace now threw himself into original research and in the next seventeen years,17711787, he produced much of his original work in astronomy.[8]

Laplace further impressed the Marquis de Condorcet, and already in 1771 Laplace felt that he was entitled to membership of the FrenchAcademy of Sciences. However, in that year, admission went to Alexandre-Thophile Vandermonde and in 1772 to Jacques AntoineJoseph Cousin. Laplace was disgruntled, and at the beginning of 1773, d'Alembert wrote to Lagrange in Berlin to ask if a position couldbe found for Laplace there. However, Condorcet became permanent secretary of the Acadmie in February and Laplace was electedassociate member on 31 March, at age 24.[9]

On 15 March 1788,[10][4] at the age of thirty-nine, Laplace married Marie-Charlotte de Courty de Romanges, a pretty eighteen-and-a-half-year-old girl from a good family in Besanon.[11] The wedding was celebrated at Saint-Sulpice, Paris. The couple had a son,Charles-mile (17891874), and a daughter, Sophie-Suzanne (17921813).[12][13]

Analysis, probability and astronomical stabilityLaplace's early published work in 1771 started with differential equations and finite differences but he was already starting to thinkabout the mathematical and philosophical concepts of probability and statistics.[14] However, before his election to the Acadmie in1773, he had already drafted two papers that would establish his reputation. The first, Mmoire sur la probabilit des causes par lesvnements was ultimately published in 1774 while the second paper, published in 1776, further elaborated his statistical thinking andalso began his systematic work on celestial mechanics and the stability of the solar system. The two disciplines would always beinterlinked in his mind. "Laplace took probability as an instrument for repairing defects in knowledge."[15] Laplace's work onprobability and statistics is discussed below with his mature work on the analytic theory of probabilities.

Stability of the solar system


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Spherical harmonics.

Sir Isaac Newton had published his Philosophiae Naturalis Principia Mathematica in 1687 in which he gave a derivation of Kepler'slaws, which describe the motion of the planets, from his laws of motion and his law of universal gravitation. However, though Newtonhad privately developed the methods of calculus, all his published work used cumbersome geometric reasoning, unsuitable to accountfor the more subtle higher-order effects of interactions between the planets. Newton himself had doubted the possibility of amathematical solution to the whole, even concluding that periodic divine intervention was necessary to guarantee the stability of thesolar system. Dispensing with the hypothesis of divine intervention would be a major activity of Laplace's scientific life.[16] It is nowgenerally regarded that Laplace's methods on their own, though vital to the development of the theory, are not sufficiently precise todemonstrate the stability of the Solar System,[17] and indeed, the Solar System is understood to be chaotic, although it happens to befairly stable.

One particular problem from observational astronomy was the apparent instability whereby Jupiter's orbit appeared to be shrinkingwhile that of Saturn was expanding. The problem had been tackled by Leonhard Euler in 1748 and Joseph Louis Lagrange in 1763 butwithout success.[18] In 1776, Laplace published a memoir in which he first explored the possible influences of a purported luminiferousether or of a law of gravitation that did not act instantaneously. He ultimately returned to an intellectual investment in Newtoniangravity.[19] Euler and Lagrange had made a practical approximation by ignoring small terms in the equations of motion. Laplace notedthat though the terms themselves were small, when integrated over time they could become important. Laplace carried his analysis intothe higher-order terms, up to and including the cubic. Using this more exact analysis, Laplace concluded that any two planets and thesun must be in mutual equilibrium and thereby launched his work on the stability of the solar system.[20] Gerald James Whitrowdescribed the achievement as "the most important advance in physical astronomy since Newton".[16]

Laplace had a wide knowledge of all sciences and dominated all discussions in the Acadmie.[21] Laplace seems to have regardedanalysis merely as a means of attacking physical problems, though the ability with which he invented the necessary analysis is almostphenomenal. As long as his results were true he took but little trouble to explain the steps by which he arrived at them; he never studiedelegance or symmetry in his processes, and it was sufficient for him if he could by any means solve the particular question he wasdiscussing.[8]

On the figure of the EarthDuring the years 17841787 he published some memoirs of exceptional power. Prominent among these is one read in 1783, reprinted asPart II of Thorie du Mouvement et de la figure elliptique des plantes in 1784, and in the third volume of the Mcanique cleste. Inthis work, Laplace completely determined the attraction of a spheroid on a particle outside it. This is memorable for the introductioninto analysis of spherical harmonics or Laplace's coefficients, and also for the development of the use of what we would now call thegravitational potential in celestial mechanics.

Spherical harmonics

In 1783, in a paper sent to the Acadmie, Adrien-Marie Legendre had introduced what are now known asassociated Legendre functions.[8] If two points in a plane have polar co-ordinates (r, ) and (r ', '), where r ' r, then, by elementary manipulation, the reciprocal of the distance between the points, d, can be written as:

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

The sequence of functions P0k(cos) is the set of so-called "associated Legendre functions" and their usefulness arises from the factthat every function of the points on a circle can be expanded as a series of them.[8]

Laplace, with scant regard for credit to Legendre, made the non-trivial extension of the result to three dimensions to yield a moregeneral set of functions, the spherical harmonics or Laplace coefficients. The latter term is not in common use now .[8]

Potential theory

This paper is also remarkable for the development of the idea of the scalar potential.[8] The gravitational force acting on a body is, inmodern language, a vector, having magnitude and direction. A potential function is a scalar function that defines how the vectors willbehave. 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 geometricreasoning. Laplace described Clairaut's work as being "in the class of the most beautiful mathematical productions".[22] However,Rouse Ball alleges that the idea "was appropriated from Joseph Louis Lagrange, who had used it in his memoirs of 1773, 1777 and


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1780".[8] The term "potential" itself was due to Daniel Bernoulli, 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 inLaplace's sense) until George Green's 1828 An Essay on the Application of Mathematical Analysis to the Theories of Electricity andMagnetism.[23][24]

Laplace applied the language of calculus to the potential function and showed that it always satisfies the differential equation:[8]

An analogous result for the velocity potential of a fluid had been obtained some years previously by Leonhard Euler.[25][26]

Laplace's subsequent work on gravitational attraction was based on this result. The quantity 2V has been termed the concentration ofV 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.Laplace's equation, a special case of Poisson's equation, appears ubiquitously in mathematical physics. The concept of a potentialoccurs in fluid dynamics, electromagnetism and other areas. Rouse Ball speculated that it might be seen as "the outward sign" of one ofthe a priori forms in Kant's theory of perception.[8]

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 solelyon distance from the centre point, and an angular or spherical part. The solution to the spherical part of the equation can be expressedas a series of Laplace's spherical harmonics, simplifying practical computation.

Planetary and lunar inequalities

JupiterSaturn great inequality

Laplace presented a memoir on planetary inequalities in three sections, in 1784, 1785, and 1786. This dealt mainly with theidentification and explanation of the perturbations now known as the "great JupiterSaturn inequality". Laplace solved a longstandingproblem in the study and prediction of the movements of these planets. He showed by general considerations, first, that the mutualaction of two planets could never cause large changes in the eccentricities and inclinations of their orbits; but then, even moreimportantly, that peculiarities arose in the JupiterSaturn system because of the near approach to commensurability of the meanmotions 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 ofsmall whole numbers. Two periods of Saturn's orbit around the Sun almost equal five of Jupiter's. The corresponding difference betweenmultiples of the mean motions, (2nJ 5nS), corresponds to a period of nearly 900 years, and it occurs as a small divisor in theintegration of a very small perturbing force with this same period. As a result, the integrated perturbations with this period aredisproportionately 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 ofLaplace's discoveries, the tables of the motions of Jupiter and Saturn could at last be made much more accurate. It was on the basis ofLaplace's theory that Delambre computed his astronomical tables.[8]

Lunar inequalities

Laplace also produced an analytical solution (as it turned out later, a partial solution), to a significant problem regarding the motion ofthe Moon. Edmond Halley had been the first to suggest, in 1695,[27] that the mean motion of the Moon was apparently getting faster, bycomparison with ancient eclipse observations, but he gave no data. It was not yet known in Halley's or Laplace's times that what isactually occurring includes a slowing down of the Earth's rate of rotation: see also Ephemeris time History. When measured as afunction of mean solar time rather than uniform time, the effect appears as a positive acceleration.

In 1749, Richard Dunthorne confirmed Halley's suspicion after re-examining ancient records, and produced the first quantitativeestimate for the size of this apparent effect:[28] a rate of +10" (arcseconds) per century in lunar longitude, which was a surprisinglygood result for its time and not far different from values assessed later, e.g. in 1786 by de Lalande,[29] and to compare with values fromabout 10" to nearly 13" being derived about century later.[30][31] The effect became known as the secular acceleration of the Moon,but until Laplace, its cause remained unknown.

Laplace gave an explanation of the effect in 1787, showing how an acceleration arises from changes (a secular reduction) in theeccentricity of the Earth's orbit, which in turn is one of the effects of planetary perturbations on the Earth. Laplace's initial computationaccounted for the whole effect, thus seeming to tie up the theory neatly with both modern and ancient observations. However, in 1853,J. C. Adams caused the question to be re-opened by finding an error in Laplace's computations: it turned out that only about half of theMoon's apparent acceleration could be accounted for on Laplace's basis by the change in the Earth's orbital eccentricity.[32] Adamsshowed that Laplace had in effect considered only the radial force on the moon and not the tangential, and the partial result thus hadoverestimated the acceleration; when the remaining (negative) terms were accounted for, it showed that Laplace's cause could only


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Laplace's house at Arcueil.

explain about half of the acceleration. The other half was subsequently shown to be due to tidal acceleration.[33]

Laplace used his results concerning the lunar acceleration when completing his attempted "proof" of the stability of the whole solarsystem on the assumption that it consists of a collection of rigid bodies moving in a vacuum.[8]

All the memoirs above alluded to were presented to the Acadmie des sciences, and they are printed in the Mmoires prsents pardivers savants.[8]

Celestial mechanicsLaplace now set himself the task to write a work which should "offer a complete solution of the great mechanical problem presented bythe solar system, and bring theory to coincide so closely with observation that empirical equations should no longer find a place inastronomical tables." The result is embodied in the Exposition du systme du monde and the Mcanique cleste.[8]

The former was published in 1796, and gives a general explanation of the phenomena, but omits all details. It contains a summary of thehistory of astronomy. This summary procured for its author the honour of admission to the forty of the French Academy and iscommonly esteemed one of the masterpieces of French literature, though it is not altogether reliable for the later periods of which ittreats.[8]

Laplace developed the nebular hypothesis of the formation of the solar system, first suggested by Emanuel Swedenborg and expandedby Immanuel Kant, a hypothesis that continues to dominate accounts of the origin of planetary systems. According to Laplace'sdescription of the hypothesis, the solar system had evolved from a globular mass of incandescent gas rotating around an axis through itscentre 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 predictedthat the more distant planets would be older than those nearer the sun.[8][34]

As mentioned, the idea of the nebular hypothesis had been outlined by Immanuel Kant in 1755,[34] and he had also suggested "meteoricaggregations" and tidal friction as causes affecting the formation of the solar system. Laplace was probably aware of this, but, like manywriters of his time, he generally did not reference the work of others.[4]

Laplace's analytical discussion of the solar system is given in his Mchanique cleste 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. Thefifth volume, published in 1825, is mainly historical, but it gives as appendices the results of Laplace's latest researches. Laplace's owninvestigations embodied in it are so numerous and valuable that it is regrettable to have to add that many results are appropriated fromother writers with scanty or no acknowledgement, and the conclusions which have been described as the organized result of a centuryof patient toil are frequently mentioned as if they were due to Laplace.[8]

Jean-Baptiste Biot, who assisted Laplace in revising it for the press, says that Laplace himself was frequently unable to recover thedetails in the chain of reasoning, and, if satisfied that the conclusions were correct, he was content to insert the constantly recurringformula, "Il est ais voir que..." ("It is easy to see that..."). The Mcanique cleste is not only the translation of Newton's Principiainto the language of the differential calculus, but it completes parts of which Newton had been unable to fill in the details. The work wascarried forward in a more finely tuned form in Flix Tisserand's Trait de mcanique cleste (18891896), but Laplace's treatise willalways remain a standard authority.[8]

Black holes

Laplace also came close to propounding the concept of the black hole. He pointed out that there could be massive stars whose gravity isso great that not even light could escape from their surface (see escape velocity).[35]

ArcueilMain article: Society of Arcueil

In 1806, Laplace bought a house in Arcueil, then a village and not yet absorbed into the Parisconurbation. Claude Louis Berthollet was a neighbourtheir gardens were notseparated[36]and the pair formed the nucleus of an informal scientific circle, latterly known asthe Society of Arcueil. Because of their closeness to Napoleon, Laplace and Bertholleteffectively controlled advancement in the scientific establishment and admission to the moreprestigious offices. The Society built up a complex pyramid of patronage.[37] In 1806, Laplacewas also elected a foreign member of the Royal Swedish Academy of Sciences.

Analytic theory of probabilities


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In 1812, Laplace issued his Thorie analytique des probabilits in which he laid down many fundamental results in statistics. The firsthalf 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 theBayesian and non-Bayesian views with an ease that makes some of his investigations difficult to follow, but his conclusions remainbasically sound even in those few situations where his analysis goes astray.[38] In 1819, he published a popular account of his work onprobability. This book bears the same relation to the Thorie des probabilits that the Systme du monde does to the Mchaniquecleste.[8]

Inductive probability

While he conducted much research in physics, another major theme of his life's endeavours was probability theory. In his Essaiphilosophique sur les probabilits (1814), Laplace set out a mathematical system of inductive reasoning based on probability, whichwe 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.1.The first principle assumes equal probabilities for all events. When this is not true, we must first determine the probabilities ofeach event. Then, the probability is the sum of the probabilities of all possible favored events.

2.

For independent events, the probability of the occurrence of all is the probability of each multiplied together.3.For events not independent, the probability of event B following event A (or event A causing B) is the probability of A multipliedby the probability that A and B both occur.

4.

The probability that A will occur, given that B has occurred, is the probability of A and B occurring divided by the probabilityof B.

5.

Three corollaries are given for the sixth principle, which amount to Bayesian probability. Where event Ai {A1, A2, ...An}exhausts the list of possible causes for event B, Pr(B) = Pr(A1, A2, ...An). Then

6.

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

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 theprobability 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 calculatedthat the probability that the sun will rise tomorrow, given that it has never failed to in the past, was

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 concludedthat 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 [i.e., the probability that the sun will rise tomorrow] is far greater forhim who, seeing in the totality of phenomena the principle regulating the days and seasons, realizes that nothing at the present momentcan arrest the course of it."[39]

Probability-generating function

The method of estimating the ratio of the number of favorable cases to the whole number of possible cases had been previouslyindicated by Laplace in a paper written in 1779. It consists of treating the successive values of any function as the coefficients in theexpansion of another function, with reference to a different variable. The latter is therefore called the probability-generating function ofthe former. Laplace then shows how, by means of interpolation, 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 afinite difference equation.[8]

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 commandover the processes of analysis. In 1805 Legendre had published the method of least squares, making no attempt to tie it to the theory ofprobability. In 1809 Gauss had derived the normal distribution from the principle that the arithmetic mean of observations gives themost probable value for the quantity measured; then, turning this argument back upon itself, he showed that, if the errors of observationare normally distributed, the least squares estimates give the most probable values for the coefficients in regression situations. These


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two works seem to have spurred Laplace to complete work toward a treatise on probability he had contemplated as early as 1783.[38]

In two important papers in 1810 and 1811, Laplace first developed the characteristic function as a tool for large-sample theory andproved the first general central limit theorem. Then in a supplement to his 1810 paper written after he had seen Gauss's work, heshowed that the central limit theorem provided a Bayesian justification for least squares: if one were combining observations, each oneof which was itself the mean of a large number of independent observations, then the least squares estimates would not only maximizethe likelihood function, considered as a posterior distribution, but also minimize the expected posterior error, all this without anyassumption as to the error distribution or a circular appeal to the principle of the arithmetic mean.[38] In 1811 Laplace took a differentnon-Bayesian tack. Considering a linear regression problem, he restricted his attention to linear unbiased estimators of the linearcoefficients. 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 "best" in the sense that they minimized the asymptotic varianceand thus both minimized the expected absolute value of the error, and maximized the probability that the estimate would lie in anysymmetric interval about the unknown coefficient, no matter what the error distribution. His derivation included the joint limitingdistribution of the least squares estimators of two parameters.[38]

Laplace's demonMain article: Laplace's demon

In 1814, Laplace published what is usually known as the first articulation of causal or scientific determinism:[40]

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 acertain 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 movementsof the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and thefuture just like the past would be present before its eyes.

Pierre Simon Laplace, A Philosophical Essay on Probabilities[41]

This intellect is often referred to as Laplace's demon (in the same vein as Maxwell's demon) and sometimes Laplace's Superman (afterHans Reichenbach). Laplace, himself, did not use the word "demon", which was a later embellishment. As translated into Englishabove, he simply referred to: "Une intelligence... Rien ne serait incertain pour elle, et l'avenir comme le pass, serait prsent sesyeux."

Even though Laplace is known as the first to express such ideas about causal determinism, his view is very similar to the one proposedby Boscovich as early as 1763 in his book Theoria philosophiae naturalis.[42]

Laplace transformsMain article: Laplace transform#History

As early as 1744, Euler, followed by Lagrange, had started looking for solutions of differential equations in the form:[43]

In 1785, Laplace took the key forward step in using integrals of this form in order to transform a whole difference equation, rather thansimply as a form for the solution, and found that the transformed equation was easier to solve than the original.[44][45]

Other discoveries and accomplishments

Mathematics

Amongst the other discoveries of Laplace in pure and applied mathematics are:

Discussion, contemporaneously with Alexandre-Thophile Vandermonde, of the general theory of determinants, (1772);[8]Proof that every equation of an even degree must have at least one real quadratic factor;[8]Laplace's method for approximating integralsSolution of the linear partial differential equation of the second order;[8]He was the first to consider the difficult problems involved in equations of mixed differences, and to prove that the solution of anequation in finite differences of the first degree and the second order might always be obtained in the form of a continuedfraction;[8] andIn his theory of probabilities:

de Moivre-Laplace theorem that approximates binomial distribution with a normal distribution


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Laplace.

Evaluation of several common definite integrals;[8] andGeneral proof of the Lagrange reversion theorem.[8]

Surface tension

Main article: YoungLaplace equation#History

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

Speed of sound

Laplace in 1816 was the first to point out that the speed of sound in air depends on the heat capacity ratio. Newton's original theorygave too low a value, because it does not take account of the adiabatic compression of the air which results in a local rise in temperatureand pressure. Laplace's investigations in practical physics were confined to those carried on by him jointly with Lavoisier in the years1782 to 1784 on the specific heat of various bodies.[8]

Politics

Minister of the Interior

In his early years Laplace was careful never to become involved in politics, or indeed in life outside the Acadmie des sciences. Heprudently withdrew from Paris during the most violent part of the Revolution.[46]

In November 1799, immediately after seizing power in the coup of 18 Brumaire, Napoleon appointed Laplace to the post of Minister ofthe Interior. The appointment, however, lasted only six weeks, after which Lucien, 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.[47]

Napoleon later (in his Mmoires de Sainte Hlne) wrote of Laplace's dismissal as follows:[8]

Gomtre de premier rang, Laplace ne tarda pas se montrer administrateur plus que mdiocre; ds son premiertravail nous reconnmes que nous nous tions tromp. Laplace ne saisissait aucune question sous son vritable pointde vue: il cherchait des subtilits partout, n'avait que des ides problmatiques, et portait enfin l'esprit des 'infinimentpetits' jusque dans l'administration. (Geometrician of the first rank, Laplace was not long in showing himself a worsethan average administrator; from his first actions in office we recognized our mistake. Laplace did not consider anyquestion from the right angle: he sought subtleties everywhere, conceived only problems, and finally carried the spiritof "infinitesimals" into the administration.)

Grattan-Guinness, however, describes these remarks as "tendentious", since there seems to be no doubt that Laplace "was onlyappointed as a short-term figurehead, a place-holder while Napoleon consolidated power".[47]

From Bonaparte to the Bourbons

Although Laplace was removed from office, it was desirable to retain his allegiance. He was accordinglyraised to the senate, and to the third volume of the Mcanique cleste he prefixed a note that of all thetruths therein contained the most precious to the author was the declaration he thus made of hisdevotion towards the peacemaker of Europe. In copies sold after the Bourbon Restoration this wasstruck out. (Pearson points out that the censor would not have allowed it anyway.) In 1814 it wasevident that the empire was falling; Laplace hastened to tender his services to the Bourbons, and in1817 during the Restoration he was rewarded with the title of marquis.

According to Rouse Ball, the contempt that his more honest colleagues felt for his conduct in the mattermay be read in the pages of Paul Louis Courier. His knowledge was useful on the numerous scientificcommissions on which he served, and, says Rouse Ball, probably accounts for the manner in which hispolitical insincerity was overlooked.[8]

Roger Hahn disputes this portrayal of Laplace as an opportunist and turncoat, pointing out that, likemany in France, he had followed the debacle of Napoleon's Russian campaign with serious misgivings. The Laplaces, whose onlydaughter Sophie had died in childbirth in September 1813, were in fear for the safety of their son mile, who was on the eastern frontwith the emperor. Napoleon had originally come to power promising stability, but it was clear that he had overextended himself, puttingthe nation at peril. It was at this point that Laplace's loyalty began to weaken. Although he still had easy access to Napoleon, hispersonal relations with the emperor cooled considerably. As a grieving father, he was particularly cut to the quick by Napoleon'sinsensitivity in an exchange related by Jean-Antoine Chaptal: "On his return from the rout in Leipzig, he [Napoleon] accosted MrLaplace: 'Oh! I see that you have grown thinSire, I have lost my daughterOh! that's not a reason for losing weight. You are a


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mathematician; put this event in an equation, and you will find that it adds up to zero.'"[48]

Political philosophy

In the second edition (1814) of the Essai philosophique, Laplace added some revealing comments on politics and governance. Since itis, he says, "the practice of the eternal principles of reason, justice and humanity that produce and preserve societies, there is a greatadvantage to adhere to these principles, and a great inadvisability to deviate from them".[49][50] Noting "the depths of misery into whichpeoples 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 unjustlythreatened nations breeds a coalition to which it always succumbs." Laplace argues that "in the midst of the multiple causes that directand restrain various states, natural limits" operate, within which it is "important for the stability as well as the prosperity of empires toremain". States that transgress these limits cannot avoid being "reverted" to them, "just as is the case when the waters of the seas whosefloor has been lifted by violent tempests sink back to their level by the action of gravity".[51][52]

About the political upheavals he had witnessed, Laplace formulated a set of principles derived from physics to favor evolutionary overrevolutionary change:

Let us apply to the political and moral sciences the method founded upon observation and calculation, which has served usso well in the natural sciences. Let us not offer fruitless and often injurious resistance to the inevitable benefits derivedfrom the progress of enlightenment; but let us change our institutions and the usages that we have for a long time adoptedonly with extreme caution. We know from past experience the drawbacks they can cause, but we are unaware of the extentof ills that change may produce. In the face of this ignorance, the theory of probability instructs us to avoid all change,especially to avoid sudden changes which in the moral as well as the physical world never occur without a considerable lossof vital force.[53]

In these lines, Laplace expressed the views he had arrived at after experiencing the Revolution and the Empire. He believed that thestability of nature, as revealed through scientific findings, provided the model that best helped to preserve the human species. "Suchviews," Hahn comments, "were also of a piece with his steadfast character."[52]

Laplace died in Paris in 1827. His brain was removed by his physician, Franois Magendie, and kept for many years, eventually beingdisplayed in a roving anatomical museum in Britain. It was reportedly smaller than the average brain.[4]

Religious opinions

I had no need of that hypothesisA frequently cited but apocryphal interaction between Laplace and Napoleon purportedly concerns the existence of God. A typicalversion is provided by Rouse Ball:[8]

Laplace went in state to Napoleon to present a copy of his work, and the following account of the interview is wellauthenticated, and so characteristic of all the parties concerned that I quote it in full. Someone had told Napoleon that thebook contained no mention of the name of God; Napoleon, who was fond of putting embarrassing questions, received itwith the remark, 'M. Laplace, they tell me you have written this large book on the system of the universe, and have nevereven mentioned its Creator.' Laplace, who, though the most supple of politicians, was as stiff as a martyr on every point ofhis philosophy, drew himself up and answered bluntly, Je n'avais pas besoin de cette hypothse-l. ("I had no need of thathypothesis.") Napoleon, greatly amused, told this reply to Lagrange, who exclaimed, Ah! c'est une belle hypothse; aexplique beaucoup de choses. ("Ah, it is a fine hypothesis; it explains many things.")

In 1884, however, the astronomer Herv Faye[54][55] affirmed that this account of Laplace's exchange with Napoleon presented a"strangely transformed" (trangement transforme) or garbled version of what had actually happened. It was not God that Laplace hadtreated as a hypothesis, but merely his intervention at a determinate point:

In fact Laplace never said that. Here, I believe, is what truly happened. Newton, believing that the secular perturbationswhich he had sketched out in his theory would in the long run end up destroying the solar system, says somewhere that Godwas obliged to intervene from time to time to remedy the evil and somehow keep the system working properly. This,however, was a pure supposition suggested to Newton by an incomplete view of the conditions of the stability of our littleworld. Science was not yet advanced enough at that time to bring these conditions into full view. But Laplace, who haddiscovered them by a deep analysis, would have replied to the First Consul that Newton had wrongly invoked theintervention of God to adjust from time to time the machine of the world (la machine du monde) and that he, Laplace, hadno need of such an assumption. It was not God, therefore, that Laplace treated as a hypothesis, but his intervention in acertain place.

Laplace's younger colleague, the astronomer Franois Arago, who gave his eulogy before the French Academy in 1827,[56] told Fayethat the garbled version of Laplace's interaction with Napoleon was already in circulation towards the end of Laplace's life. Faye writes:[54][55]


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I have it on the authority of M. Arago that Laplace, warned shortly before his death that that anecdote was about to bepublished in a biographical collection, had requested him [Arago] to demand its deletion by the publisher. It was necessaryto either explain or delete it, and the second way was the easiest. But, unfortunately, it was neither deleted nor explained.

The Swiss-American historian of mathematics Florian Cajori appears to have been unaware of Faye's research, but in 1893 he came to asimilar conclusion.[57] Stephen Hawking said in 1999,[40] "I don't think that Laplace was claiming that God does not exist. It's just thathe doesn't intervene, to break the laws of Science."

The only eyewitness account of Laplace's interaction with Napoleon is an entry in the diary of the British astronomer Sir WilliamHerschel. Since this makes no mention of Laplace saying, "I had no need of that hypothesis," Daniel Johnson[58] argues that "Laplacenever used the words attributed to him." Arago's testimony, however, appears to imply that he did, only not in reference to the existenceof God.

Views on God

Born a Catholic, Laplace appears for most of his life to have veered between deism (presumably his considered position, since it is theonly one found in his writings) and atheism.

Faye thought that Laplace "did not profess atheism",[54] but Napoleon, on Saint Helena, told General Gaspard Gourgaud, "I often askedLaplace what he thought of God. He owned that he was an atheist."[59] Roger Hahn, in his biography of Laplace, mentions a dinnerparty at which "the geologist Jean-tienne Guettard was staggered by Laplace's bold denunciation of the existence of God". It appearedto Guettard that Laplace's atheism "was supported by a thoroughgoing materialism".[60] But the chemist Jean-Baptiste Dumas, whoknew Laplace well in the 1820s, wrote that Laplace "gave materialists their specious arguments, without sharing their convictions".[61][62]

Hahn states: "Nowhere in his writings, either public or private, does Laplace deny God's existence."[63] Expressions occur in his privateletters that appear inconsistent with atheism.[3] On 17 June 1809, for instance, he wrote to his son, "Je prie Dieu qu'il veille sur tesjours. Aie-Le toujours prsent ta pense, ainsi que ton pre et ta mre [I pray that God watches over your days. Let Him be alwayspresent to your mind, as also your father and your mother]."[55][64] Ian S. Glass, quoting Herschel's account of the celebrated exchangewith Napoleon, writes that Laplace was "evidently a deist like Herschel".[65]

In Exposition du systme du monde, Laplace quotes Newton's assertion that "the wondrous disposition of the Sun, the planets and thecomets, can only be the work of an all-powerful and intelligent Being".[66] This, says Laplace, is a "thought in which he [Newton]would be even more confirmed, if he had known what we have shown, namely that the conditions of the arrangement of the planets andtheir satellites are precisely those which ensure its stability".[67] By showing that the "remarkable" arrangement of the planets could beentirely explained by the laws of motion, Laplace had eliminated the need for the "supreme intelligence" to intervene, as Newton had"made" it do.[68] Laplace cites with approval Leibniz's criticism of Newton's invocation of divine intervention to restore order to thesolar system: "This is to have very narrow ideas about the wisdom and the power of God."[69] He evidently shared Leibniz'sastonishment at Newton's belief "that God has made his machine so badly that unless he affects it by some extraordinary means, thewatch will very soon cease to go".[70]

In a group of manuscripts, preserved in relative secrecy in a black envelope in the library of the Acadmie des sciences and publishedfor 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".[71] As for the doctrine of transubstantiation, it "offends at the same time reason, experience, thetestimony of all our senses, the eternal laws of nature, and the sublime ideas that we ought to form of the Supreme Being". It is thesheerest absurdity to suppose that "the sovereign lawgiver of the universe would suspend the laws that he has established, and which heseems to have maintained invariably".[72]

In old age, Laplace remained curious about the question of God[73] and frequently discussed Christianity with the Swiss astronomerJean-Frdric-Thodore Maurice.[74] He told Maurice that "Christianity is quite a beautiful thing" and praised its civilizing 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 theinvariability of the laws of nature did not permit of supernatural events.[73] After Laplace's death, Poisson told Maurice, "You knowthat I do not share your [religious] opinions, but my conscience forces me to recount something that will surely please you." WhenPoisson had complimented Laplace about his "brilliant discoveries", the dying man had fixed him with a pensive look and replied, "Ah!we chase after phantoms [chimres]."[75] These were his last words, interpreted by Maurice as a realization of the ultimate "vanity" ofearthly pursuits.[76] Laplace received the last rites from the cur of the Missions trangres (in whose parish he was to be buried)[62]and the cur of Arcueil.[76]

However, according to his biographer, Roger Hahn, since it is "not credible" that Laplace "had a proper Catholic end", the "last rights"(sic) were ineffective and he "remained a skeptic" to the very end of his life.[77] Laplace in his last years has been described as anagnostic.[78][79][80]

Excommunication of a comet


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In 1470 the humanist scholar Bartolomeo Platina wrote[81] that Pope Callixtus III had asked for prayers for deliverance from the Turksduring 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.[82] What Laplaceactually said, in Exposition du systme du monde (1796), was that the Pope had ordered the comet to be "exorcized" (conjur). It wasArago, in Des Comtes en gnral (1832), who first spoke of an excommunication. Neither the exorcism nor the excommunication canbe regarded as anything but pure fiction.[83][84][85]

Honors

The asteroid 4628 Laplace is named for Laplace.[86]His name is one of the 72 names inscribed on the Eiffel Tower.The tentative working name of the European Space Agency Europa Jupiter System Mission is the "Laplace" space probe.

QuotationsI had no need of that hypothesis. ("Je n'avais pas besoin de cette hypothse-l", allegedly as a reply to Napoleon, who had askedwhy he hadn't mentioned God in his book on astronomy.)[8]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 denyphenomena solely because they are inexplicable in the actual state of our knowledge. But we ought to examine them with anattention all the more scrupulous as it appears more difficult to admit them."[87]

This is restated in Theodore Flournoy's work From India to the Planet Mars as the Principle of Laplace or, "The weight ofthe evidence should be proportioned to the strangeness of the facts."[88]Most often repeated as "The weight of evidence for an extraordinary claim must be proportioned to its strangeness."

This simplicity of ratios will not appear astonishing if we consider that all the effects of nature are only mathematical results ofa small number of immutable laws.[89]What we know is little, and what we are ignorant of is immense. (Fourier comments: "This was at least the meaning of his lastwords, which were articulated with difficulty.")[36]

See alsoLaplaceBayes estimatorRatio estimatorList of things named after Pierre-Simon Laplace

References^ S. W. Hawking, The Large Scale Structure of Space-Time(http://books.google.gr/books?id=QagG_KI7Ll8C&vq=),Cambridge University Press, 1973, p. 364.

1.

^ Stigler, Stephen M. (1986). The History of Statistics: TheMeasurement of Uncertainty before 1900. Harvard UniversityPress, Chapter 3.

2.

^ a

b [Anon.] (1911) "Pierre Simon, Marquis De Laplace

(http://www.1911encyclopedia.org/Pierre_Simon,_Marquis_De_Laplace)", EncyclopaediaBritannica

3.

^ a

b

c

d

e

f "Laplace, being Extracts from Lectures delivered by

Karl Pearson", Biometrika, vol. 21, December 1929, pp.202216.

4.

^ W. W. Rouse Ball A Short Account of the History ofMathematics, 4th edition, 1908.

5.

^ a

b *O'Connor, John J.; Robertson, Edmund F., "Pierre-Simon

Laplace" (http://www-history.mcs.st-andrews.ac.uk/Biographies/Laplace.html), MacTutor History of Mathematics archive,University of St Andrews., accessed 25 August 2007

6.

^ Gillispie (1997), pp. 347.^

a

b

c

d

e

f

g

h

i

j

k

l

m

n

o

p

q

r

s

t

u

v

w

x

y

z

aa

ab

ac

ad Rouse Ball

(1908)8.

^ Gillispie (1997), p. 59.^ Hahn (2005), p. 99. However, Gillispie (1997), p. 67, gives themonth of the marriage as May.

10.

^ Hahn (2005), pp. 9910011.^ Gillispie (1997), p. 6712.

^ Hahn (2005), p. 10113.^ Gillispie (1989), pp. 71214.^ Gillispie (1989). pp. 141515.^

a

b Whitrow (2001)16.

^ Celletti, A. & Perozzi, E. (2007). Celestial Mechanics: TheWaltz of the Planets. Berlin: Springer. pp. 9193.ISBN 0-387-30777-X.

17.

^ Whittaker (1949b)18.^ Gillispie (1989). pp. 293519.^ Gillispie (1989), pp. 353620.^ School of Mathematics and Statistics (http://www-history.mcs.st-andrews.ac.uk/Biographies/Laplace.html),University of St Andrews, Scotland.

21.

^ Grattan-Guinness, I. (2003). Companion Encyclopedia of theHistory and Philosophy of the Mathematical Sciences(http://books.google.com/?id=f5FqsDPVQ2MC&pg=PA1098&lpg=PA1098&dq=laplace+potential+1784). Baltimore: JohnsHopkins University Press. pp. 10971098. ISBN 0-8018-7396-7.

22.

^ W. W. Rouse Ball A Short Account of the History ofMathematics (4th edition, 1908) (http://www.maths.tcd.ie/pub/HistMath/People/Clairaut/RouseBall/RB_Clairaut.html)

23.

^ Green, G. (1828). An Essay on the Application of MathematicalAnalysis to the Theories of Electricity and Magnetism.Nottingham. arXiv:0807.0088 (//arxiv.org/abs/0807.0088).

24.

^ Kline, Morris (1972). Mathematical thought from ancient tomodern times, Volume 2. Oxford University Press. pp. 524525.ISBN 0-19-506136-5.

25.


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^ Euler, Leonhard (1756/57). "General principles of the motion offluids". Novi. Comm. Acad. Sci. Petrop.: 271311.

26.

^ Halley, Edmond (1695), "Some Account of the Ancient State ofthe City of Palmyra, with Short Remarks upon the InscriptionsFound there" (http://rstl.royalsocietypublishing.org/content/19/215-235/160.full.pdf), Phil. Trans., vol.19 (16951697),pages 160175; esp. at pages 174175.

27.

^ Dunthorne, Richard (1749), "A Letter from the Rev. Mr.Richard Dunthorne to the Reverend Mr. Richard Mason F. R. S.and Keeper of the WoodWardian Museum at Cambridge,concerning the Acceleration of the Moon"(http://rstl.royalsocietypublishing.org/content/46/491-496/162.full.pdf), Philosophical Transactions (16831775), Vol. 46(17491750) #492, pp. 162172; also given in PhilosophicalTransactions (abridgements) (1809), vol.9 (for 174449),p669675 (http://www.archive.org/stream/philosophicaltra09royarich#page/669/mode/2up) as "On theAcceleration of the Moon, by the Rev. Richard Dunthorne".

28.

^ de Lalande, Jrme (1786), "Sur les equations seculaires dusoleil et de la lune" (http://www.academie-sciences.fr/membres/in_memoriam/Lalande/Lalande_pdf/Mem1786_p390.pdf),Memoires de l'Academie Royale des Sciences, pp. 390397, atpage 395.

29.

^ North, John David (2008), Cosmos: an illustrated history ofastronomy and cosmology. University of Chicago Press, Chapter14, at page 454 (http://books.google.com/books?id=qq8Luhs7rTUC&pg=PA454).

30.

^ See also P Puiseux (1879), "Sur l'acceleration seculaire dumouvement de la Lune" (http://archive.numdam.org/article/ASENS_1879_2_8__361_0.pdf), Annales Scientifiques del'Ecole Normale Superieure, 2nd series vol. 8, pp. 361444, atpp. 361365.

31.

^ J. C. Adams (1853), "On the Secular Variation of the Moon'sMean Motion" (http://rstl.royalsocietypublishing.org/content/143/397.full.pdf), in Phil. Trans. R. Soc. Lond., vol.143 (1853),pages 397406.

32.

^ Roy, A. E. (2005). Orbital Motion (http://books.google.com/?id=Hzv7k2vH6PgC&pg=PA313&lpg=PA313&dq=laplace+secular+acceleration). London: CRC Press. p. 313.ISBN 0-7503-1015-4.

33.

^ a

b Owen, T. C. (2001) "Solar system: origin of the solar

system", Encyclopaedia Britannica, Deluxe CDROM edition34.

^ See Israel (1987), sec. 7.2.35.^

a

b Fourier (1829)36.

^ Crosland (1967), p. 137.^

a

b

c

d Stigler, 197538.

^ Laplace, Pierre Simon, A Philosophical Essay on Probabilities,translated from the 6th French edition by Frederick WilsonTruscott and Frederick Lincoln Emory. New York: John Wiley &Sons, 1902, p. 19. Dover Publications edition (New York, 1951)has same pagination.

39.

^ a

b Hawking, Stephen (1999). "Does God Play Dice?"

(http://web.archive.org/web/20000708041816/http://www.hawking.org.uk/lectures/dice.html). Public Lecture.Archived from the original (http://www.hawking.org.uk/lectures/dice.html) on 8 July 2000.

40.

^ Laplace, A Philosophical Essay, New York, 1902, p.4.Template:Nice translation, but it's not the one in this edition.

41.

^ Cercignani, Carlo (1998). "Chapter 2: Physics beforeBoltzmann". Ludwig Boltzmann, The Man Who Trusted Atoms.Oxford University Press. p. 55. ISBN 0-19-850154-4.

42.

^ Grattan-Guinness, in Gillispie (1997), p. 26043.^ Grattan-Guinness, in Gillispie (1997), pp. 26126244.^ Deakin (1981)45.^ Crosland (2006), p. 3046.^

a

b Grattan-Guinness (2005), p. 33347.

^ Hahn (2005), p. 19148.^ Laplace, A Philosophical Essay, New York, 1902, p. 62.(Translation in this paragraph of article is from Hahn.)

49.

^ Hahn (2005), p. 18450.^ Laplace, A Philosophical Essay, New York, 1902, p. 63.(Translation in this paragraph of article is from Hahn)

51.

^ a

b Hahn (2005), p. 18552.

^ Laplace, A Philosophical Essay, New York, 1902, pp. 107108.(Translation in this paragraph of article is from Hahn.

53.

^ a

b

c Faye, Herv (1884), Sur l'origine du monde: thories

cosmogoniques des anciens et des modernes. Paris: Gauthier-Villars, pp. 109111

54.

^ a

b

c Pasquier, Ernest (1898). "Les hypothses cosmogoniques

(suite)" (http://www.persee.fr/web/revues/home/prescript/article/phlou_0776-5541_1898_num_5_18_1596). Revueno-scholastique, 5o anne, No 18, pp. 124125, footnote 1

55.

^ Arago, Franois (1827), Laplace: Eulogy before the FrenchAcademy, translated by Prof. Baden Powell, Smithsonian Report,1874

56.

^ Cajori, Florian (1893), A History of Mathematics. Fifth edition(1991), reprinted by the American Mathematical Society, 1999, p.262. ISBN 0-8218-2102-4

57.

^ Johnson, Daniel (June 18, 2007), "The Hypothetical Atheist"(http://www.commentarymagazine.com/2007/06/18/the-hypothetical-atheist), Commentary.

58.

^ Talks of Napoleon at St. Helena with General BaronGourgaud, translated by Elizabeth Wormely Latimer. Chicago: A.C. McClurg & Co., 1903, p. 276.

59.

^ Hahn (2005), p. 67.60.^ Dumas, Jean-Baptiste (1885). Discours et loges acadmiques,Vol. II. Paris: Gauthier-Villars, p. 255.

61.

^ a

b Kneller, Karl Alois. Christianity and the Leaders of Modern

Science: A Contribution to the History of Culture in theNineteenth Century, translated from the second German editionby T. M. Kettle. London: B. Herder, 1911, pp. 7374(http://www.ebooksread.com/authors-eng/karl-alois-kneller/christianity-and-the-leaders-of-modern-science-a-contribution-to-the-history-of-hci/page-6-christianity-and-the-leaders-of-modern-science-a-contribution-to-the-history-of-hci.shtml)

62.

^ Hahn (1981), p. 95.63.^ uvres de Laplace. Paris: Gauthier-Villars, 1878, Vol. I, pp.vvi.

64.

^ Glass, Ian S. (2006). Revolutionaries of the Cosmos: TheAstrophysicists. Cambridge University Press, p. 108. ISBN0-19-857099-6

65.

^ General Scholium, from the end of Book III of the Principia;first appeared in the second edition, 1713.

66.

^ Laplace, Exposition du systme du monde (http://archive.org/details/expositiondusys05laplgoog), 6th edition. Brussels, 1827,pp. 522523.

67.

^ Laplace, Exposition, 1827, p. 523.68.^ Leibniz to Conti, Nov. or Dec. 1715, in H. G. Alexander, ed.,The LeibnizClarke Correspondence (Manchester UniversityPress, 1956), Appendix B. 1: "Leibniz and Newton to Conti", p.185 ISBN 0-7190-0669-4; cited in Laplace, Exposition, 1827, p.524.

69.

^ Leibniz to Conti, 1715, in Alexander, ed., 1956, p. 185.70.^ Hahn (2005), p. 22071.^ Hahn (2005), p. 22372.^

a

b Hahn (2005), p. 20273.

^ Hahn (2005), pp. 202, 23374.^ Compare Edmund Burke's famous remark, occasioned by aparliamentary candidate's sudden death, about "what shadows weare, and what shadows we pursue".

75.

^ a

b Hahn (2005), p. 20476.

^ Roger Hahn (2005). Pierre Simon Laplace, 17491827: ADetermined Scientist. Harvard University Press. p. 204.ISBN 9780674018921. "The Catholic newspaper La Quotidienne[The Daily] announced that Laplace had died in the arms of twocurs (priests), implying that he had a proper Catholic end, butthis is not credible. To the end, he remained a skeptic, wedded tohis deterministic creed and to an uncompromised ethos derivedfrom his vast scientific experience."

77.

^ Roger Hahn (2005). Pierre Simon Laplace, 1749-1827: ADetermined Scientist. Harvard University Press. p. 202.ISBN 9780674018921. "Publicly, Laplace maintained his agnosticbeliefs, and even in his old age continued to be skeptical aboutany function God might play in a deterministic universe."

78.


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^ Morris Kline (1986). Mathematics and the Search forKnowledge. Oxford University Press. p. 214.ISBN 9780195042306. "Lagrange and Laplace, though of Catholicparentage, were agnostics."

79.

^ Edward Kasner, James Newman, James Roy Newman (2001).Mathematics and the Imagination. Courier Dover Publications.p. 253. ISBN 9780486417035. "Modern physics, indeed all ofmodern science, is as humble as Lagrange, and as agnostic asLaplace."

80.

^ E. Emerson (1910). Comet Lore. Schilling Press, New York.p. 83.

81.

^ C. M. Botley (1971). "The Legend of 1P/Halley 1456". TheObservatory 91: 125126. Bibcode:1971Obs....91..125B(http://adsabs.harvard.edu/abs/1971Obs....91..125B).

82.

^ Hagen, John G. "Pierre-Simon Laplace". CatholicEncyclopedia. New York: Robert Appleton Company. 1913.

83.

^ Stein, John (1911), "Bartolomeo Platina"(http://www.newadvent.org/cathen/12158a.htm), The CatholicEncyclopedia, Vol. 12. New York: Robert Appleton Company

84.

^ Rigge, William F. (04/1910), "An Historical Examination of theConnection of Calixtus III with Halley's Comet"(http://adsabs.harvard.edu/full/1910PA.....18..214R), PopularAstronomy, Vol. 18, pp. 214-219

85.

^ Schmadel, L. D. (2003). Dictionary of Minor Planet Names(5th rev. ed.). Berlin: Springer-Verlag. ISBN 3-540-00238-3.

86.

^ Laplace, Pierre Simon (1814). Essai philosophique sur lesprobabilits (http://books.google.com/books?id=rDUJAAAAIAAJ&pg=PA50#v=onepage&q&f=false).p. 50.

87.

^ Flournoy, Thodore (1899). Des Indes la plante Mars:tude sur un cas de somnambulisme avec glossolalie(http://books.google.com/books?id=6xdk111WDScC&lpg=PA345&vq=laplace&pg=PA344#v=onepage&q=laplace&f=false). Slatkine. pp. 344345.*Flournoy, Thodore (2007).From India to the Planet Mars: A Study of a Case ofSomnambulism (http://books.google.com/books?id=Vnog3NS5aY4C&lpg=PA369&ots=m0VMb2NcR0&pg=PA369#v=onepage&q&f=false). Daniel D. Vermilye, trans.Cosimo, Inc. pp. 369370. ISBN 9781602063570.

88.

^ Laplace, A Philosophical Essay, New York, 1902, p. 177.89.

Bibliography

By Laplace

uvres compltes de Laplace (http://gallica.bnf.fr/Search?ArianeWireIndex=index&lang=EN&q=oeuvres+completes+de+laplace&p=1&f_creator=Laplace%2C+Pierre+Simon+de+%281749-1827%29), 14 vol.(18781912), Paris: Gauthier-Villars (copy from Gallica in French)Thorie du movement et de la figure elliptique des plantes (1784) Paris (not in uvres compltes)Prcis de l'histoire de l'astronomie (http://books.google.com/books?id=QYpOb3N7zBMC)

English translations

Bowditch, N. (trans.) (18291839) Mcanique cleste, 4 vols, BostonNew edition by Reprint Services ISBN 0-7812-2022-X

[18291839] (19661969) Celestial Mechanics, 5 vols, including the original FrenchPound, J. (trans.) (1809) The System of the World, 2 vols, London: Richard Phillips_ The System of the World (v.1) (http://books.google.com/books?id=yW3nd4DSgYYC)_ The System of the World (v.2) (http://books.google.com/books?id=f7Kv2iFUNJoC) [1809] (2007) The System of the World, vol.1, Kessinger, ISBN 1-4326-5367-9Toplis, J. (trans.) (1814) A treatise upon analytical mechanics (http://books.google.com/books?id=c2YSAAAAIAAJ) Nottingham:H. BarnettTruscott, F. W. & Emory, F. L. (trans.) (2007) [1902]. A Philosophical Essay on Probabilities. ISBN 1-60206-328-1., translatedfrom the French 6th ed. (1840)

A Philosophical Essay on Probabilities (1902) (http://www.archive.org/details/philosophicaless00lapliala) on InternetArchive

About Laplace and his work

Andoyer, H. (1922). L'uvre scientifique de Laplace. Paris: Payot. (in French)Bigourdan, G. (1931). "La jeunesse de P.-S. Laplace". La Science moderne (in French) 9: 377384.Crosland, M. (1967). The Society of Arcueil: A View of French Science at the Time of Napoleon I. Cambridge MA: HarvardUniversity Press. ISBN 0-435-54201-X. (2006) "A Science Empire in Napoleonic France" (http://adsabs.harvard.edu/full/2006HisSc..44...29C), History of Science,vol. 44, pp. 2948Dale, A. I. (1982). "Bayes or Laplace? an examination of the origin and early application of Bayes' theorem". Archive for theHistory of the Exact Sciences 27: 2347.David, F. N. (1965) "Some notes on Laplace", in Neyman, J. & LeCam, L. M. (eds) Bernoulli, Bayes and Laplace, Berlin,pp3044Deakin, M. A. B. (1981). "The development of the Laplace transform". Archive for the History of the Exact Sciences 25 (4):343390. doi:10.1007/BF01395660 (http://dx.doi.org/10.1007%2FBF01395660). (1982). "The development of the Laplace transform". Archive for the History of the Exact Sciences 26 (4): 351381.doi:10.1007/BF00418754 (http://dx.doi.org/10.1007%2FBF00418754).Dhombres, J. (1989). "La thorie de la capillarit selon Laplace: mathmatisation superficielle ou tendue". Revue d'Histoire dessciences et de leurs applications (in French) 62: 4370.Duveen, D. & Hahn, R. (1957). "Laplace's succession to Bzout's post of Examinateur des lves de l'artillerie". Isis 48 (4):416427. doi:10.1086/348608 (http://dx.doi.org/10.1086%2F348608).


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Finn, B. S. (1964). "Laplace and the speed of sound". Isis 55: 719. doi:10.1086/349791 (http://dx.doi.org/10.1086%2F349791).Fourier, J. B. J. (1829). "loge historique de M. le Marquis de Laplace". Mmoires de l'Acadmie Royale des Sciences 10:lxxxicii., delivered 15 June 1829, published in 1831. (in French) Link to article (http://www.academie-sciences.fr/activite/archive/dossiers/Fourier/Fourier_pdf/Mem1829_p81_102.pdf)Gillispie, C. C. (1972). "Probability and politics: Laplace, Condorcet, and Turgot". Proceedings of the American PhilosophicalSociety 116 (1): 120. (1997) Pierre Simon Laplace 17491827: A Life in Exact Science, Princeton: Princeton University Press, ISBN0-691-01185-0Grattan-Guinness, I., 2005, "'Exposition du systme du monde' and 'Trait de mchanique cleste'" in his Landmark Writings inWestern Mathematics. Elsevier: 24257.Hahn, R. (1955). "Laplace's religious views". Archives internationales d'histoire des sciences 8: 3840. (1981) "Laplace and the Vanishing Role of God in the Physical Universe", in Woolf, Henry, ed., The Analytic Spirit: Essays inthe History of Science. Ithaca, NY: Cornell University Press. ISBN 0-8014-1350-8 (1982). Calendar of the Correspondence of Pierre Simon Laplace (Berkeley Papers in the History of Science, vol.8 ed.).Berkeley, CA: University of California. ISBN 0-918102-07-3. (1994). New Calendar of the Correspondence of Pierre Simon Laplace (Berkeley Papers in the History of Science, vol.16ed.). Berkeley, CA: University of California. ISBN 0-918102-07-3. (2005) Pierre Simon Laplace 17491827: A Determined Scientist, Cambridge, MA: Harvard University Press, ISBN0-674-01892-3Israel, Werner (1987). "Dark stars: the evolution of an idea". In Hawking, Stephen W.; Israel, Werner. 300 Years of Gravitation.Cambridge University Press. pp. 199276.O'Connor, John J.; Robertson, Edmund F., "Pierre-Simon Laplace" (http://www-history.mcs.st-andrews.ac.uk/Biographies/Laplace.html), MacTutor History of Mathematics archive, University of St Andrews. (1999)Nikulin, M. (1992). "A remark on the converse of Laplace's theorem". Journal of Soviet Mathematics 59: 976979.Rouse Ball, W. W. [1908] (2003) "Pierre Simon Laplace (17491827) (http://www.maths.tcd.ie/pub/HistMath/People/Laplace/RouseBall/RB_Laplace.html)", in A Short Account of the History of Mathematics, 4th ed., Dover, ISBN 0-486-20630-0Stigler, S. M. (1975). "Napoleonic statistics: the work of Laplace". Biometrika (Biometrika, Vol. 62, No. 2) 62 (2): 503517.doi:10.2307/2335393 (http://dx.doi.org/10.2307%2F2335393). JSTOR 2335393 (//www.jstor.org/stable/2335393). (1978). "Laplace's early work: chronology and citations". Isis 69 (2): 234254. doi:10.1086/352006 (http://dx.doi.org/10.1086%2F352006).Whitrow, G. J. (2001) "Laplace, Pierre-Simon, marquis de", Encyclopaedia Britannica, Deluxe CDROM editionWhittaker, E. T. (1949a). "Laplace". Mathematical Gazette (The Mathematical Gazette, Vol. 33, No. 303) 33 (303): 112.doi:10.2307/3608408 (http://dx.doi.org/10.2307%2F3608408). JSTOR 3608408 (//www.jstor.org/stable/3608408). (1949b). "Laplace". American Mathematical Monthly 56 (6): 369372. doi:10.2307/2306273 (http://dx.doi.org/10.2307%2F2306273). JSTOR 2306273 (//www.jstor.org/stable/2306273).Wilson, C. (1985). "The Great Inequality of Jupiter and Saturn: from Kepler to Laplace". Archive for the History of the ExactSciences. 33(13): 15290. doi:10.1007/BF00328048 (http://dx.doi.org/10.1007%2FBF00328048).Young, T. (1821). Elementary Illustrations of the Celestial Mechanics of Laplace: Part the First, Comprehending the FirstBook (http://books.google.com/?id=20AJAAAAIAAJ&dq=laplace). London: John Murray. (available from Google Books)

External links"Laplace, Pierre (17491827)" (http://scienceworld.wolfram.com/biography/Laplace.html). Eric Weisstein's World of ScientificBiography. Wolfram Research. Retrieved 2007-08-24."Pierre-Simon Laplace (http://www-history.mcs.st-andrews.ac.uk/Biographies/Laplace.html)" in the MacTutor History ofMathematics archive."Bowditch's English translation of Laplace's preface" (http://www-history.mcs.st-andrews.ac.uk/history/Extras/Laplace_mechanique_celeste.html). Mchanique Cleste. The MacTutor History of Mathematics archive. Retrieved2007-09-04.Guide to the Pierre Simon Laplace Papers (http://www.oac.cdlib.org/findaid/ark:/13030/kt8q2nf3g7/) at The Bancroft LibraryPierre-Simon Laplace (http://www.genealogy.ams.org/id.php?id=108295) at the Mathematics Genealogy ProjectEnglish translation (http://www.cs.xu.edu/math/Sources/Laplace/index.html) of a large part of Laplace's work in probability andstatistics, provided by Richard Pulskamp (http://www.cs.xu.edu/math/Sources/index.html)Pierre-Simon Laplace - uvres compltes (http://portail.mathdoc.fr/cgi-bin/oetoc?id=OE_LAPLACE__7) (last 7 volumes only)Gallica-Math

Political officesPreceded by

Nicolas Marie QuinetteMinister of the Interior

12 November 1799 25 December 1799Succeeded by

Lucien Bonaparte

Retrieved from "http://en.wikipedia.org/w/index.php?title=Pierre-Simon_Laplace&oldid=599678669"Categories: 1749 births 1827 deaths People from Calvados 18th-century astronomers 18th-century French mathematicians19th-century French mathematicians Counts of the First French Empire Determinists Enlightenment scientists French agnosticsFrench astronomers French Marquesses French physicists Grand Officiers of the Lgion d'honneur Mathematical analystsMembers of the Acadmie franaise Members of the French Academy of SciencesMembers of the Royal Swedish Academy of Sciences Fellows of the Royal Society Probability theorists French interior ministers


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Theoretical physicists

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Pierre Simon Laplace