Citizendia
Your Ad Here

"Laplace" redirects here. For the city in Louisiana, see Laplace, Louisiana. LaPlace is a Census-designated place (CDP in St John the Baptist Parish, Louisiana, United States, along the east bank of the Mississippi
Pierre-Simon, marquis de Laplace
Posthumous portrait by Madame Feytaud, 1842
Posthumous portrait by Madame Feytaud, 1842
Born 1749-03-23
Beaumont-en-Auge, Normandy, France
Died March 5, 1827 (aged 77)
Paris, France
Residence France
Citizenship French
Fields Astronomy
Mathematics
Institutions École Militaire (1769-1776)
Known for Work in Celestial Mechanics
Laplace's equation
Laplace Operator/Laplacian
Laplace transform

Pierre-Simon, marquis de Laplace (March 23, 1749 - March 5, 1827) was a French mathematician and astronomer whose work was pivotal to the development of mathematical astronomy. Year 1749 ( MDCCXLIX) was a Common year starting on Wednesday (link will display the full calendar of the Gregorian calendar (or a Events 1174 - Jocelin, Abbot of Melrose, is elected Bishop of Glasgow. Beaumont-en-Auge is a commune in the Calvados department in the Basse-Normandie region in northern France. Normandy (Normandie Norman: Normaundie) is a geographical region corresponding to the former Duchy of Normandy. This article is about the country For a topic outline on this subject see List of basic France topics. Events 363 - Roman Emperor Julian moves from Antioch with an army of 90000 to attack the Sassanid Empire, in a Year 1827 ( MDCCCXXVII) was a Common year starting on Monday (link will display the full calendar of the Gregorian Calendar (or a Common Paris (ˈpærɨs in English; in French) is the Capital of France and the country's largest city This article is about the country For a topic outline on this subject see List of basic France topics. This article is about the country For a topic outline on this subject see List of basic France topics. Legal residents and citizens To be French according to the first article of the Constitution is to be a citizen of France regardless of one's origin race or religion ( Astronomy (from the Greek words astron (ἄστρον "star" and nomos (νόμος "law" is the scientific study Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and The École Militaire (Military School is a vast complex of buildings housing various military teaching facilities located in Paris, France, southeast of the Celestial mechanics is the branch of Astrophysics that deals with the motions of Celestial objects The field applies principles of Physics, historically In Mathematics, Laplace's equation is a Partial differential equation named after Pierre-Simon Laplace who first studied its properties In Mathematics and Physics, the Laplace operator or Laplacian, denoted by \Delta\  or \nabla^2  and named after In Mathematics, the Laplace transform is one of the best known and most widely used Integral transforms It is commonly used to produce an easily soluble algebraic Events 1174 - Jocelin, Abbot of Melrose, is elected Bishop of Glasgow. Year 1749 ( MDCCXLIX) was a Common year starting on Wednesday (link will display the full calendar of the Gregorian calendar (or a Events 363 - Roman Emperor Julian moves from Antioch with an army of 90000 to attack the Sassanid Empire, in a Year 1827 ( MDCCCXXVII) was a Common year starting on Monday (link will display the full calendar of the Gregorian Calendar (or a Common This article is about the country For a topic outline on this subject see List of basic France topics. A mathematician is a person whose primary area of study and research is the field of Mathematics. Historically Astronomy was more concerned with the classification and description of phenomena in the sky while Astrophysics attempted to explain these phenomena Astronomy (from the Greek words astron (ἄστρον "star" and nomos (νόμος "law" is the scientific study He summarized and extended the work of his predecessors in his five volume Mécanique Céleste (Celestial Mechanics) (1799-1825). Celestial mechanics is the branch of Astrophysics that deals with the motions of Celestial objects The field applies principles of Physics, historically This seminal work translated the geometric study of classical mechanics, used by Isaac Newton, to one based on calculus, opening up a broader range of problems. Geometry ( Greek γεωμετρία; geo = earth metria = measure is a part of Mathematics concerned with questions of size shape and relative position Classical mechanics is used for describing the motion of Macroscopic objects from Projectiles to parts of Machinery, as well as Astronomical objects Sir Isaac Newton, FRS (ˈnjuːtən 4 January 1643 31 March 1727) Biography Early years See also Isaac Newton's early life and achievements Calculus ( Latin, calculus, a small stone used for counting is a branch of Mathematics that includes the study of limits, Derivatives

He formulated Laplace's equation, and invented the Laplace transform which appears in many branches of mathematical physics, a field that he took a leading role in forming. In Mathematics, Laplace's equation is a Partial differential equation named after Pierre-Simon Laplace who first studied its properties In Mathematics, the Laplace transform is one of the best known and most widely used Integral transforms It is commonly used to produce an easily soluble algebraic Mathematical physics is the scientific discipline concerned with the interface of Mathematics and Physics. The Laplacian differential operator, widely used in applied mathematics, is also named after him. In Mathematics and Physics, the Laplace operator or Laplacian, denoted by \Delta\  or \nabla^2  and named after Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and

Independently from Immanuel Kant, he formulated the nebular hypothesis of the origin of the solar system and was one of the first scientists to postulate the existence of black holes and the notion of gravitational collapse. Immanuel Kant (ɪmanuəl kant 22 April 1724 12 February 1804 was an 18th-century German Philosopher from the Prussian city of Königsberg In Cosmogony, the nebular hypothesis is the most widely accepted model explaining the Formation and evolution of the Solar System. The formation and evolution of the Solar System is estimated to have begun A black hole is a theoretical region of space in which the Gravitational field is so powerful that nothing not even Electromagnetic radiation (e Gravitational collapse in Astronomy is the inward fall of a massive body under the influence of the force of Gravity.

He is remembered as one of the greatest scientists of all time, sometimes referred to as a French Newton or Newton of France, with a natural phenomenal mathematical faculty possessed by none of his contemporaries. Sir Isaac Newton, FRS (ˈnjuːtən 4 January 1643 31 March 1727) Biography Early years See also Isaac Newton's early life and achievements [1]

He became a count of the First French Empire in 1806 and was named a marquis in 1817, after the Bourbon Restoration. A count is a Nobleman in European countries The word count comes from French comte, itself from Latin The Empire of the French (1804-1814 also known as the Empire of France, Greater French Empire, First French Empire, French Empire, or A marquess (ˈmɑrkwɪs or marquis (/mɑrˈkiː/ is a Nobleman of hereditary rank in various European monarchies and some of their colonies Following the ousting of Napoleon I of France in 1814 the Allies restored the Bourbon Dynasty to the French throne

Contents

Early life

Pierre Simon Laplace was born in Beaumont-en-Auge, Normandy. Beaumont-en-Auge is a commune in the Calvados department in the Basse-Normandie region in northern France. Normandy (Normandie Norman: Normaundie) is a geographical region corresponding to the former Duchy of Normandy.

According to Rouse Ball ('A Short Account of the History of Mathematics', 4th edition, 1908), he was the son of a small cottager or perhaps a farm-labourer, and owed his education to the interest excited in some wealthy neighbours by his abilities and engaging presence. Walter William Rouse Ball ( 14 August 1850 – 4 April 1925) was a British Mathematician, Lawyer and a fellow Very little is known of his early years, for when he became distinguished he had the pettiness to hold himself aloof both from his relatives and from those who had assisted him. It would seem 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 push his fortune. However, Pearson (1929, Biometrika) is scathing about the inaccuracies in Rouse Ball's account and states that ". Biometrika is a Scientific journal principally covering theoretical Statistics. . Caen was probably in Laplace's day the most intellectually active of all the towns of Normandy. It was here that Laplace was educated and was provisionally a professor. It was here he wrote his first paper published in the Melanges of the Royal Society of Turin, Tome iv. 1766-1769, at least two years before he went at 22 or 23 to Paris in 1771. Thus before he was 20 he was in touch with Joseph Louis Lagrange in Turin. He did not go to Paris a raw self-taught country lad with only a peasant background I In 1765 at the age of sixteen Laplace left the "School of the Duke of Orleans" in Beaumont and went to the University of Caen, where he appears to have studied for five years. The "Ecole militaire" of Beaumont did not replace the old school until 1770.

His father was Pierre Laplace, a cider merchant and his mother was Marie-Anne Sochon. For the non-alcoholic beverage commonly known in the US as "cider" see Apple cider. Merchants function as professionals who deal with Trade, dealing in commodities that they do not produce themselves in order to produce Profit. His parents were from comfortable bourgeois families. Laplace attended a school in the village run at a Benedictine priory, his father intending that he would be ordained in the Roman Catholic Church, and at sixteen he was sent to further his father's intention at the University of Caen, reading theology. Benedictine refers to the Spirituality and Consecrated life in accordance with the Rule of St Benedict, written by Benedict of Nursia in A priory is a House of men or women under religious vows headed by a Prior or prioress In general religious use ordination is the process by which individuals are consecrated, that is set apart as Clergy to perform various religious rites and ceremonies The Université de Caen Basse-Normandie or Caen University is a University in Caen, France. Theology is the study of a god or the gods from a religious perspective [2]

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. Laplace never graduated in theology but left for Paris with a letter of introduction from Le Canu to Jean le Rond d'Alembert. Graduation is the action of receiving or conferring an Academic degree or the associated ceremony Paris (ˈpærɨs in English; in French) is the Capital of France and the country's largest city [2] There is an apocryphal story that, aged nineteen, he solved overnight the 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. The École Militaire (Military School is a vast complex of buildings housing various military teaching facilities located in Paris, France, southeast of the [3]

With a secure income and undemanding teaching, Laplace now threw himself into original research and, in the next seventeen years, 1771-1787, he produced much of his original work in astronomy. Original research is Research that is not exclusively based on a summary review or synthesis of earlier publications on the subject of research [4]

Laplace further impressed the Marquis de Condorcet, and even in 1771 Laplace felt that he was 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 at the However, in that year, admission went to Alexandre-Théophile Vandermonde and in 1772 to Antoine-Joseph Cousin. Alexandre-Théophile Vandermonde ( 28 February 1735 – 1 January 1796) was a French Musician and Chemist who Laplace was disgruntled and early in 1773 canvassed a move to Berlin. Berlin is the capital city and one of sixteen states of Germany. However, Condorcet became permanent secretary of the Académie in February and Laplace was elected associate member on 31 March. Events 307 - After divorcing his wife Minervina, Constantine marries Fausta, the daughter of the retired Roman Emperor [5]

He was married in 1788 and his son was born in 1789. [6]

Analysis, probability and astronomical stability

Laplace's early published work in 1771 started with differential equations and finite differences but he was already starting to think about the mathematical and philosophical concepts of probability and statistics. A differential equation is a mathematical Equation for an unknown function of one or several variables that relates the values of the A finite difference is a mathematical expression of the form f ( x + b) &minus f ( x + a) Probability is the likelihood or chance that something is the case or will happen Statistics is a mathematical science pertaining to the collection analysis interpretation or explanation and presentation of Data. [7] 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. Celestial mechanics is the branch of Astrophysics that deals with the motions of Celestial objects The field applies principles of Physics, historically The Solar System consists of the Sun and those celestial objects bound to it by Gravity. The two disciplines would always be interlinked in his mind. "Laplace took probability as an instrument for repairing defects in knowledge. "[8] 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 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. Sir Isaac Newton, FRS (ˈnjuːtən 4 January 1643 31 March 1727) Biography Early years See also Isaac Newton's early life and achievements The Philosophiæ Naturalis Principia Mathematica ( Latin: "mathematical principles of natural philosophy" often Principia In Astronomy, Kepler's Laws of Planetary Motion are three mathematical laws that describe the motion of Planets in the Solar System. A planet, as defined by the International Astronomical Union (IAU is a celestial body Orbiting a Star or stellar remnant that is Newton's laws of motion are three Physical laws which provide relationships between the Forces acting on a body and the motion of the Newton 's law of universal Gravitation is a physical law describing the gravitational attraction between bodies with mass 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. Calculus ( Latin, calculus, a small stone used for counting is a branch of Mathematics that includes the study of limits, Derivatives Geometry ( Greek γεωμετρία; geo = earth metria = measure is a part of Mathematics concerned with questions of size shape and relative position 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. A miracle is an event believed to be caused by interposition of Divine intervention by a Supernatural being in the Universe by which the ordinary operation Stability can refer to Aircraft flight Stability (aircraft In atmospheric fluid dynamics atmospheric stability, a measure of the turbulence Dispensing with the hypothesis of divine intervention would be the major activity of Laplace's scientific life. [9] As of 2007, it is generally regarded that Laplace's methods on their own, though critical to the development of the theory, are not sufficiently precise to demonstrate the stability of the solar system. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. [10]

One particular problem from observational astronomy was the apparent instability whereby Jupiter's orbit appeared to be shrinking while that of Saturn was expanding. Observational astronomy is a division of the astronomical Science that is concerned with getting data in contrast with Theoretical astrophysics which is The problem had been tackled by Leonhard Euler in 1748 and Joseph Louis Lagrange in 1763 but without success. [11] 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. In the late 19th century " luminiferous aether " (or " ether " meaning light-bearing aether, was the term used to describe a medium for the propagation He ultimately returned to an intellectual investment in Newtonian gravity. [12] 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. The European Space Agency 's INTErnational Gamma-Ray Astrophysics Laboratory ( INTEGRAL) is detecting some of the most energetic radiation that comes from space For other uses see Time (disambiguation Time is a component of a measuring system used to sequence events to compare the durations of Laplace carried his analysis into the higher-order terms, up to and including the cubic. 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. [13] Gerald James Whitrow described the achievement as "the most important advance in physical astronomy since Newton". Gerald James Whitrow ( June 9 1912, Kimmeridge, Dorset - June 2, 2000) was a British Mathematician, cosmologist [9]

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. Symmetry generally conveys two primary meanings The first is an imprecise sense of harmonious or aesthetically-pleasing proportionality and balance such that it reflects beauty or [4]

On the figure of the Earth

During the years 1784-1787 he produced 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 Méchanique céleste. In this work, Laplace completely determined the attraction of a spheroid on a particle outside it. Equation A spheroid centered at the origin and rotated about the z axis is defined by the implicit equation \left(\frac{x}{a}\right^2+\left(\frac{y}{a}\right^2+\left(\frac{z}{b}\right^2 This is memorable for the introduction into analysis of spherical harmonics or Laplace's coefficients, and also for the development of the use of the potential, a name first used by George Green in 1828. In Mathematics, the spherical harmonics are the angular portion of an Orthogonal set of solutions to Laplace's equation represented in a system of The Mathematical study of potentials is known as Potential theory; it is the study of Harmonic functions on Manifolds This mathematical George Green ( 14 July 1793 &ndash 31 May, 1841) was a British Mathematician and Physicist, who wrote [4]

Spherical harmonics

Spherical harmonics
Spherical harmonics

In 1783, in a paper sent to the Académie, Adrien-Marie Legendre had introduced what are now known as associated Legendre functions. Adrien-Marie Legendre ( September 18 1752 – January 10 1833) was a French Mathematician. Note This article describes a very general class of functions [4] 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{1}{d} = \frac{1}{r'} \left [ 1 - 2 \cos (\theta' - \theta) \frac{r}{r'} + \left ( \frac{r}{r'} \right ) ^2 \right ] ^{- \tfrac{1}{2}}.

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

\frac{1}{d} = \frac{1}{r'} \sum_{k=0}^\infty P^0_k ( \cos ( \theta' - \theta ) ) \left ( \frac{r}{r'} \right ) ^k.

The sequence of functions P0k(cosф) 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. In Mathematics, the polar coordinate system is a two-dimensional Coordinate system in which each point on a plane is determined by In Mathematics, a power series (in one variable is an Infinite series of the form f(x = \sum_{n=0}^\infty a_n \left( x-c \right^n = a_0 + In Mathematics, the binomial theorem is an important Formula giving the expansion of powers of Sums Its simplest version says In Mathematics, a sequence is an ordered list of objects (or events The Mathematical concept of a function expresses dependence between two quantities one of which is given (the independent variable, argument of the function Circles are simple Shapes of Euclidean geometry consisting of those points in a plane which are at a constant Distance, called the In Mathematics, a series is often represented as the sum of a Sequence of terms That is a series is represented as a list of numbers with [4]

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. Three-dimensional space is a geometric model of the physical Universe in which we live As of 2007, the latter term is not in common use. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Every function of the points on a sphere can be expanded as a series of them. "Globose" redirects here See also Globose nucleus. A sphere (from Greek σφαίρα - sphaira, "globe [4]

Potential theory

This paper is also remarkable for the development of the idea of the scalar potential. A scalar Potential is a fundamental concept in Vector analysis and Physics (the adjective 'scalar' is frequently omitted if there is no danger of confusion [4] The gravitational force acting on a body is, in modern language, a vector, having magnitude and direction. In Physics, a force is whatever can cause an object with Mass to Accelerate. A potential function is a scalar function that defines how the vectors will behave. A scalar function is computationally and conceptually easier to deal with than a vector function.

Alexis Clairault had first suggested the idea in 1743 while working on a similar problem though he was using Newtonian-type geometric reasoning. Alexis Claude de Clairault (or Clairaut) ( May 3, 1713 – May 17, 1765) was a French Mathematician and Laplace described Clairault's work as being "in the class of the most beautiful mathematical productions". [14] 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". [4]

Laplace applied the language of calculus to the potential function and shows that it always satisfies the differential equation:[4]

\nabla^2V={\partial^2V\over \partial x^2 } + {\partial^2V\over \partial y^2 } + {\partial^2V\over \partial z^2 } = 0

- and on this result his subsequent work on gravitational attraction was based. A differential equation is a mathematical Equation for an unknown function of one or several variables that relates the values of the The quantity \nabla^2V 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. Laplace's equation, a special case of Poisson's equation, appears ubiquitously in mathematical physics. In Mathematics, Laplace's equation is a Partial differential equation named after Pierre-Simon Laplace who first studied its properties In Mathematics, Poisson's equation is a Partial differential equation with broad utility in Electrostatics, Mechanical engineering and Theoretical Wherever a vector force acts on a body, the concept of a potential can be applied and Laplace's equation occurs in fluid dynamics, electromagnetism and other areas. Fluid dynamics is the sub-discipline of Fluid mechanics dealing with fluid flow: Fluids ( Liquids and Gases in motion Electromagnetism is the Physics of the Electromagnetic field: a field which exerts a Force on particles that possess the property of According to some writers this follows at once from the fact that \nabla^2 is a scalar operator. Rouse Ball speculated that it might be seen as "the outward sign" of one the "prior forms" in Kant's theory of perception. Immanuel Kant (ɪmanuəl kant 22 April 1724 12 February 1804 was an 18th-century German Philosopher from the Prussian city of Königsberg [4]

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 Earth (say), and an angular or spherical part. In Mathematics, the spherical coordinate system is a Coordinate system for representing geometric figures in three dimensions using three coordinates the radial The sky is the part of the Atmosphere or of Outer space visible from the surface of any Astronomical object. In Mathematics, separation of variables is any of several methods for solving ordinary and partial Differential equations in which algebra allows one to re-write an The solution to the spherical part of the equation can be expressed as a series of Laplace's spherical harmonics, simplifying practical computation.

Planetary inequalities

This memoir was followed by another on planetary inequalities, which was presented in three sections in 1784, 1785, and 1786. This deals mainly with the explanation of the "great inequality" of Jupiter and Saturn. Laplace showed by general considerations that the mutual action of two planets could never largely affect the eccentricities and inclinations of their orbits; and that the peculiarities of the Jovian system were due to the near approach to commensurability of the mean motions of Jupiter and Saturn: further developments of these theorems on planetary motion were given in his two memoirs of 1788 and 1789. It was on these data that Delambre computed his astronomical tables. [4]

It had been observed since ancient times that the Moon's position in the sky was drifting over time. In 1693, Edmond Halley had shown that the rate of the drift was increasing, an effect known as the secular acceleration of the Moon. Edmond Halley FRS (ˈɛdmənd ˈhɔːlɪ ( November 8, 1656 &ndash January 14, 1742) was an English Astronomer Laplace gave an explanation in 1787 in terms of changes in the eccentricity of the Earth's orbit. The equation of time is the difference over the course of a year between time as read from a Sundial and time as read from a Clock, measured in an ideal situation However, in 1853, John Couch Adams went on to show that Laplace had only considered the radial force on the moon and not the tangential, and hence had failed to explain more than half of the drift. John Couch Adams ( June 5 1819 &ndash January 21, 1892) was a British Mathematician and Astronomer The other half was subsequently shown to be due to tidal acceleration. Tidal acceleration is an effect of the Tidal forces between an orbiting Natural satellite ( i [15] However, Laplace was still able to use his result to complete the proof of the stability of the whole solar system on the assumption that it consists of a collection of rigid bodies moving in a vacuum. Stability can refer to Aircraft flight Stability (aircraft In atmospheric fluid dynamics atmospheric stability, a measure of the turbulence In Physics, a rigid body is an idealization of a solid body of finite size in which Deformation is neglected This vacuum means "absence of matter" or "an empty area or space" for the cleaning appliance see Vacuum cleaner. [4]

All the memoirs above alluded to were presented to the Académie des sciences, and they are printed in the Mémoires présentés par divers savants. [4]

Celestial mechanics

Classical mechanics
History of ...
Scientists
Galileo · Kepler · Newton
Laplace · Hamilton · d'Alembert
Cauchy · Lagrange · Euler
This box: view • talk • edit

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. Classical mechanics is used for describing the motion of Macroscopic objects from Projectiles to parts of Machinery, as well as Astronomical objects Newton's laws of motion are three Physical laws which provide relationships between the Forces acting on a body and the motion of the Early Ideas on Motion The Greek philosophers, and Aristotle in particular were the first to propose that there are abstract principles governing nature Galileo Galilei (15 February 1564 &ndash 8 January 1642 was a Tuscan ( Italian) Physicist, Mathematician, Astronomer, and Philosopher Johannes Kepler (ˈkɛplɚ ( December 27 1571 &ndash November 15 1630) was a German Mathematician, Astronomer Sir Isaac Newton, FRS (ˈnjuːtən 4 January 1643 31 March 1727) Biography Early years See also Isaac Newton's early life and achievements Sir William Rowan Hamilton (4 August 1805 &ndash 2 September 1865 was an Irish Mathematician, Physicist, and Astronomer who The Solar System consists of the Sun and those celestial objects bound to it by Gravity. " The result is embodied in the Exposition du système du monde and the Mécanique céleste. [4]

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. [4]

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. In Cosmogony, the nebular hypothesis is the most widely accepted model explaining the Formation and evolution of the Solar System. (born Emanuel Swedberg; February 8 1688–March 29 1772 was a Swedish Scientist, Philosopher, Christian mystic, and Theologian Immanuel Kant (ɪmanuəl kant 22 April 1724 12 February 1804 was an 18th-century German Philosopher from the Prussian city of Königsberg 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. Incandescence is the emission of Light (visible Electromagnetic radiation) from a hot body due to its temperature This page is about the physical properties of gas as a state of matter 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. A planet, as defined by the International Astronomical Union (IAU is a celestial body Orbiting a Star or stellar remnant that is The Sun (Sol is the Star at the center of the Solar System. On this view Laplace predicted that the more distant planets would be older than those nearer the sun. [4][16]

The idea of the nebular hypothesis had been outlined by Immanuel Kant in 1755,[16] and he had also suggested "meteoric aggregations" and tidal friction as causes affecting the formation of the solar system. Immanuel Kant (ɪmanuəl kant 22 April 1724 12 February 1804 was an 18th-century German Philosopher from the Prussian city of Königsberg Tidal acceleration is an effect of the Tidal forces between an orbiting Natural satellite ( i It is probable that Laplace was not aware of this. [4]

Laplace's analytical discussion of the solar system is given in his Méchanique 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 writers with scanty or no acknowledgement, and the conclusions - which have been described as the organized result of a century of patient toil - are frequently mentioned as if they were due to Laplace. [4]

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. Jean-Baptiste Biot (21 April 1774 Paris &ndash 3 February 1862 Paris) was a French Physicist, Astronomer and Mathematician " The Méchanique céleste is not only the translation of the Principia into the language of the differential calculus, but it completes parts of which Newton had been unable to fill in the details. Differential Calculus, a field in Mathematics, is the study of how functions change when their inputs change The work was more finely tuned by Félix Tisserand but Laplace's treatise will always remain a standard authority. François Félix Tisserand ( January 13, 1845 - October 20, 1896) was a French Astronomer. [4]

Laplace's house at Arcueil
Laplace's house at Arcueil

Arcueil

Main article: Society of Arcueil

In 1806, Laplace bought a house in Arcueil, then a village and not yet absorbed into the Paris conurbation. The Society of Arcueil was a circle of French scientists who met regularly on summer weekends between 1806 and 1822 at the country houses of Claude Louis Berthollet and Arcueil is a commune in the Val-de-Marne department located in what can be considered as the southern suburbs of Paris A conurbation is an Urban area or Agglomeration comprising a number of Cities, large Towns and larger urban areas that through Population Claude Louis Berthollet was a near neighbour and the pair formed the nucleus of an informal scientific circle, latterly known as the Society of Arcueil. Claude Louis Berthollet ( December 9, 1748 &ndash November 6, 1822) was a Savoyard Chemist who "became vice president Because of Laplace and Berthollet's closeness to Napoleon, they effectively controlled advancement in the scientific establishment and admission to the more prestigious offices. Napoleon Bonaparte (15 August 1769 – 5 May 1821 was a French military and political leader who had a significant impact on the History of Europe. The Society built up a complex pyramid of patronage. Patronage is the support encouragement privilege and often financial aid given by a person or an organization [17]

Laplace and Napoleon

An account of a famous interaction between Laplace and Napoleon is provided by Rouse Ball[4]:

"Laplace went in state to beg Napoleon to accept a copy of his work, and the following account of the interview is well authenticated, and so characteristic of all the parties concerned that I quote it in full. Someone had told Napoleon that the book contained no mention of the name of God; Napoleon, who was fond of putting embarrassing questions, received it with the remark, 'M. Laplace, they tell me you have written this large book on the system of the universe, and have never even mentioned its Creator. ' Laplace, who, though the most supple of politicians, was as stiff as a martyr on every point of his philosophy, drew himself up and answered bluntly, 'Je n'avais pas besoin de cette hypothèse-là. ' [I did not need to make such an assumption. ] 'Napoleon, greatly amused, told this reply to Lagrange, who exclaimed, 'Ah! c'est une belle hypothèse; ça explique beaucoup de choses. ' [Ah, but that is such a good hypothesis. It explains so many things!]"

Black holes

Laplace also came close to propounding the concept of the black hole. A black hole is a theoretical region of space in which the Gravitational field is so powerful that nothing not even Electromagnetic radiation (e He pointed out that there could be massive stars whose gravity is so great that not even light could escape from their surface (see escape velocity). In Physics, escape velocity is the speed where the Kinetic energy of an object is equal to the magnitude of its Gravitational potential energy [18] Laplace also speculated that some of the nebulae revealed by telescopes may not be part of the Milky Way and might actually be galaxies themselves. The Milky Way (a translation of the Latin Via Lactea, in turn derived from the Greek Γαλαξίας (Galaxias sometimes referred to simply Thus, he anticipated the major discovery of Edwin Hubble, some 100 years before it happened. Edwin Powell Hubble ( November 20, 1889 – September 28, 1953) was an American astronomer.

Analytic theory of probabilities

In 1812, Laplace issued his Théorie analytique des probabilités in which he laid down many fundamental results in statistics. Statistics is a mathematical science pertaining to the collection analysis interpretation or explanation and presentation of Data. 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. [4]

Probability-generating function

The method of estimating the ratio of the number of favourable cases, compared 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 Mathematical concept of a function expresses dependence between two quantities one of which is given (the independent variable, argument of the function The latter is therefore called the probability-generating function of the former. In Probability theory, the probability-generating function of a Discrete random variable is a Power series representation (the Generating function Laplace then shows how, by means of interpolation, these coefficients may be determined from the generating function. In the mathematical subfield of Numerical analysis, interpolation is a method of constructing new data points within the range of a Discrete set of 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 f ( x + b) &minus f ( x + a) [4] The method is cumbersome and leads most of the time to a normal probability distribution the so called Laplace-Gauss distribution, not to be confused with the Laplace distribution. The normal distribution, also called the Gaussian distribution, is an important family of Continuous probability distributions applicable in many fields

Least squares

This treatise includes an exposition of the method of least squares, a remarkable testimony to Laplace's command over the processes of analysis. The method of least squares is used to solve Overdetermined systems Least squares is often applied in statistical contexts particularly Regression analysis. The method of least squares for the combination of numerous observations had been given empirically by Carl Friedrich Gauss and Legendre, but the fourth chapter of this work contains a formal proof of it, on which the whole of the theory of errors has been since based. Johann Carl Friedrich Gauss (ˈɡaʊs, Gauß Carolus Fridericus Gauss ( 30 April 1777 – 23 February 1855) was a German This was affected only by a most intricate analysis specially invented for the purpose, but the form in which it is presented is so meagre and unsatisfactory that, in spite of the uniform accuracy of the results, it was at one time questioned whether Laplace had actually gone through the difficult work he so briefly and often incorrectly indicates. [4]

Inductive probability

While he conducted much research in physics, another major theme of his life's endeavours was probability theory. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. Probability theory is the branch of Mathematics concerned with analysis of random phenomena In his Essai philosophique sur les probabilités, Laplace set out a mathematical system of inductive reasoning based on probability, which we would today recognise as Bayesian. Induction or inductive reasoning, sometimes called inductive logic, is the process of Reasoning in which the premises of an argument are believed Probability is the likelihood or chance that something is the case or will happen Bayesian probability interprets the concept of Probability as 'a measure of a state of knowledge'. One well-known formula arising from his system is the rule of succession. In Probability theory, the rule of succession is a formula introduced in the 18th century by Pierre-Simon Laplace in the course of treating the Sunrise problem Suppose that some trial has only two possible outcomes, labeled "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. Probability is the likelihood or chance that something is the case or will happen

\Pr(\mbox{next outcome is success}) = \frac{s+1}{n+2}

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 only have 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(\mbox{sun will rise tomorrow}) = \frac{d+1}{d+2}

where d is the number of times the sun has risen in the past times. 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 [i. e. , the probability that the sun will rise tomorrow] is 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. "

Laplace's demon

Main article: Laplace's demon

Laplace strongly believed in causal determinism, which is expressed in the following quote from the introduction to the Essai:

“ We may regard the present state of the universe as the effect of its past and the cause of its future. In the History of science, Laplace's demon is a hypothetical "demon" envisioned in 1814 by Pierre-Simon Laplace such that if it knew the precise location Determinism is the philosophical Proposition that every event including human cognition and behaviour decision and action is causally determined An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes. ”

This intellect is often referred to as Laplace's demon (in the same vein as Maxwell's demon). Maxwell's demon was an 1867 Thought experiment by the Scottish Physicist James Clerk Maxwell, meant to raise questions about the possibility Note that the description of the hypothetical intellect described above by Laplace as a demon does not come from Laplace, but from later biographers: Laplace saw himself as a scientist that hoped that humanity would progress in a better scientific understanding of the world, which, if and when eventually completed, would still need a tremendous calculating power to compute it all in a single instant.

Laplace transforms

Main article: Laplace transform#History

As early as 1744, Euler, followed by Lagrange, had started looking for solutions of differential equations in the form:[19]

z = \int X(x) e^{ax} dx and z = \int X(s) x^s dx. In Mathematics, the Laplace transform is one of the best known and most widely used Integral transforms It is commonly used to produce an easily soluble algebraic A differential equation is a mathematical Equation for an unknown function of one or several variables that relates the values of the

In 1785, Laplace took the key forward step in using integrals of this form in order to transform a whole difference equation, rather than simply as a form for the solution, and found that the transformed equation was easier to solve than the original. "Difference equation" redirects here It should not be confused with a Differential equation. [20][21]

Other discoveries and accomplishments

Mathematics

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

Surface tension

Main article: Young-Laplace equation#History

Laplace built upon the qualitative work of Thomas Young to develop the theory of capillary action and the Young-Laplace equation. In Physics, the Young&ndashLaplace equation is a Nonlinear Partial differential equation that describes the Capillary pressure difference sustained Thomas Young (13 June 1773 &ndash 10 May 1829 was an English Polymath who contributed to the scientific understanding of vision, Light Capillary action, capillarity, capillary motion, or wicking is the ability of a substance to draw another substance into it In Physics, the Young&ndashLaplace equation is a Nonlinear Partial differential equation that describes the Capillary pressure difference sustained

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. Sound is a vibration that travels through an elastic medium as a Wave. Temperature and layers The temperature of the Earth's atmosphere varies with altitude the mathematical relationship between temperature and altitude varies among five Ideal gas relations For an ideal gas the heat capacity is constant with temperature Newton's original theory gave too low a value, because it does not take account of the adiabatic compression of the air that results in a local rise in temperature and pressure. This article covers adiabatic processes in Thermodynamics. For adiabatic processes in Quantum mechanics, see Adiabatic process (quantum mechanics A gas compressor is a mechanical device that increases the Pressure of a Gas by reducing its Volume. Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface Laplace's investigations in practical physics were confined to those carried on by him jointly with Lavoisier in the years 1782 to 1784 on the specific heat of various bodies. Specific heat capacity, also known simply as specific heat, is the measure of the heat energy required to increase the Temperature of a unit quantity [4]

Political ambitions

As Napoleon's power increased Laplace begged him to give him the post of minister of the interior. Napoleon, who desired the support of men of science, agreed to the proposal, but a little less than six weeks saw the close of Laplace's political career. Napoleon's memorandum on his dismissal is as follows:[4]

Géomètre de premier rang, Laplace ne tarda pas à se montrer administrateur plus que médiocre; dès son premier travail nous reconnûmes que nous nous étions trompé. Laplace ne saisissait aucune question sous son véritable point de vue: il cherchait des subtilités partout, n'avait que des idées problématiques, et portait enfin l'esprit des `infiniment petits' jusque dans l'administration. (Geometrician of the first rank, Laplace was not long in showing himself a worse than average administrator; since his first actions in office we recognized our mistake. Laplace did not consider any question objectively: he sought subtleties everywhere, only conceived problems, and finally carried the spirit of "hair-splitting" into the administration. )

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 Bourbon Restoration this was struck out. Following the ousting of Napoleon I of France in 1814 the Allies restored the Bourbon Dynasty to the French throne In 1814 it was evident that the empire was falling; Laplace hastened to tender his services to the Bourbons, and on the restoration was rewarded with the title of marquis. The House of Bourbon is an important European Royal house, a branch of the Capetian dynasty. A marquess (ˈmɑrkwɪs or marquis (/mɑrˈkiː/ is a Nobleman of hereditary rank in various European monarchies and some of their colonies The contempt that his more honest colleagues felt for his conduct in the matter may be read in the pages of Paul Louis Courier. Paul Louis Courier ( January 4, 1773 - August 18, 1825) French Hellenist and political writer was born in Paris. His knowledge was useful on the numerous scientific commissions on which he served, and probably accounts for the manner in which his political insincerity was overlooked; but the pettiness of his character must not make us forget how great were his services to science. [4]

He died in Paris in 1827. [4]

Honours

Quotes

References

  1. ^ [Anon. ] (1911) "Pierre Simon, Marquis De Laplace", Encyclopaedia Britannica
  2. ^ a b *O'Connor, John J. The Encyclopædia Britannica is a general English-language encyclopaedia published by Encyclopædia Britannica Inc & Robertson, Edmund F. , “Pierre-Simon Laplace”, MacTutor History of Mathematics archive , accessed 25 August 2007
  3. ^ Gillispie (1997) pp3-4
  4. ^ 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 ae af ag Rouse Ball (1908)
  5. ^ Gillispie (1997) pp5
  6. ^   "Pierre-Simon Laplace". The MacTutor History of Mathematics archive is an award-winning website maintained by John J Catholic Encyclopedia. The Catholic Encyclopedia, also referred to today as the Old Catholic Encyclopedia, is an English-language Encyclopedia published by The Encyclopedia (1913). New York: Robert Appleton Company.  
  7. ^ Gillispie (1989) pp7-12
  8. ^ Gillispie (1989) pp14-15
  9. ^ a b Whitrow (2001)
  10. ^ Celletti, A. & Perozzi, E. (2007). Celestial Mechanics: The Waltz of the Planets. Berlin: Springer, 91-93. ISBN 0-387-30777-X.  
  11. ^ Whittaker (1949b)
  12. ^ Gillispie (1989) pp29-35
  13. ^ Gillispie (1989) pp35-36
  14. ^ Grattan-Guinness, I. (2003). Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences. Baltimore: Johns Hopkins University Press, 1097-1098. ISBN 0801873967.  
  15. ^ Roy, A. E. (2005). Orbital Motion. London: CRC Press, 313. ISBN 0750310154.  
  16. ^ a b Owen, T. C. (2001) "Solar system: origin of the solar system", Encyclopaedia Britannica, Deluxe CDROM edition
  17. ^ Crosland (1967) p. The Encyclopædia Britannica is a general English-language encyclopaedia published by Encyclopædia Britannica Inc 1
  18. ^ See Israel (1987), sec. 7. 2.
  19. ^ Grattan-Guiness, in Gillispie (1997) p. Ivor Grattan-Guinness (Born 23 June 1941 Bakewell, England is a Historian of mathematics and Logic. 260
  20. ^ Grattan-Guiness, in Gillispie (1997) pp261-262
  21. ^ Deakin (1981)
  22. ^ Schmadel, L. D. (2003). Dictionary of Minor Planet Names, 5th rev. ed. , Berlin: Springer-Verlag. ISBN 3540002383.  

Bibliography

By Laplace

English translations

About Laplace and his work

External links

Preceded by
Nicolas Marie Quinette		 Minister of the Interior
Nov - Dec 1799		 Succeeded by
Lucien Bonaparte
Preceded by
Michel-Louis-Étienne Regnaud de Saint-Jean d'Angély		 Seat 8
Académie française
1816 - 1827		 Succeeded by
Pierre-Paul Royer-Collard

The Minister of the Interior (full title Ministre de l’Intérieur et de l’Aménagement du Territoire) in France is one of the most important governmental Lucien Bonaparte Prince Français 1st Principe di Canino and 1st Principe di Musignano (born Luciano Buonaparte; ( May 21, 1775 &ndash Michel Louis Étienne, Comte Regnaud de Saint-Jean d'Angély ( December 3, 1761 &mdash March 11, 1819) was a French This is a list of members of the Académie française (French Academy by seat number L'Académie française, or the French Academy, is the pre-eminent French learned body on matters pertaining to the French language. Pierre Paul Royer-Collard ( 21 June 1763 - 2 September 1845) was a French statesman and Philosopher, leader of the
© 2009 citizendia.org; parts available under the terms of GNU Free Documentation License, from http://en.wikipedia.org
 Dapyx Software network: MP3 Explorer | Ebook Manager | Zenithic