Pierre-Simon Laplace

French mathematician

• Born: March 23, 1749
• Birthplace: Beaumont-en-Auge, Normandy, France
• Died: March 5, 1827
• Place of death: Paris, France

Laplace made groundbreaking mathematical contributions to probability theory and statistical analysis. Using Isaac Newton’s theory of gravitation, he also performed detailed mathematical analyses of the shape of the earth and the orbits of comets, planets, and their moons.

Early Life

Pierre-Simon Laplace (lah-plahs) was born into a well-established and prosperous family of farmers and merchants in southern Normandy. An ecclesiastical career in the Church was originally planned for Laplace by his father, and he attended the Benedictine secondary school in Beaumont-en-Auge between the ages of seven and sixteen. His interest in mathematics blossomed during two years at the University of Caen, beginning in 1766.

In 1768, Laplace went to Paris to pursue a career in mathematics; he remained a permanent resident of Paris or its immediate vicinity for the rest of his life. Soon after his arrival in Paris, he sought and won the patronage of Jean Le Rond d’Alembert, a mathematician, physicist, and philosopher with great influence among French intellectuals. D’Alembert found Laplace employment teaching mathematics to military cadets at the École Militaire, and it was in this position that Laplace wrote his first memoirs in mathematics and astronomy.

In 1773, Laplace was elected to the Academy of Sciences as a mathematician. This achievement, at the relatively young age of twenty-four, was based upon the merits of thirteen memoirs he had presented to academy committees for review. Some of Laplace’s earliest mathematical interests involved the calculation of odds in games of chance. At a time when there was not yet a field of mathematics devoted to the systematic study of probability, Laplace played a major role in carrying the early development of this topic beyond the rules of thumb of gambling and the preliminary conclusions of earlier mathematicians. In addition, Laplace emphasized the relevance of probability to the analysis of statistics. He believed that, because all experimental data are imprecise to some extent, it is important to be able to calculate an appropriate average or mean value from a collection of observations. Furthermore, this mean value should be calculated in such a way as to minimize its difference from the actual value of the quantity being measured.

Statistical problems of this type inspired Laplace’s initial interest in astronomy. He became intrigued by the process through which new astronomical data should be incorporated into calculations of probabilities for future observations. In particular, he concentrated on the application of Sir Isaac Newton’s law of gravitation to the motions of the comets and planets. Laplace’s interest in physics thus had a strong mathematical orientation. Throughout his career, he retained his early concentration on the solution of problems suggested by the mathematical implications of physical laws; he never devoted himself to extensive experimental investigation of new phenomena. Laplace’s primary motivation was a deep conviction that, even if human limitations prevent an exact knowledge of natural laws and experimental conditions, it is still possible progressively to eliminate error through increasingly accurate approximations.

Very little is known about Laplace’s personal life during these early years. He does not seem to have stimulated strong friendship or animosity. In 1788, he married Marie-Charlotte de Courty de Romanges, who was twenty years younger than himself, and they had two children. Laplace established and maintained comfortable but disciplined living habits, and he retained an undiminished mental clarity to the moment of his death.

Life’s Work

Although a brief summary of Laplace’s life’s work requires some classification by topics and an emphasis on final results rather than chronology, the highly integrated and developmental nature of his research should not be forgotten. For example, mathematical techniques that he invented for the solution of problems in probability theory often were immediately applied to similar problems in physics or astronomy. Because Laplace was particularly interested in approximate or probable solutions and the analysis of error, he repeatedly revised his mathematical techniques to accommodate new data.

Laplace’s contributions to probability theory were both technical and philosophical. This twofold concern is expressed in the titles of the influential volumes in which he summarized his work, Théorie analytique des probabilités (1812; analytic theory of probability) and Essai philosophique sur les probabilités (1814; A Philosophical Essay on Probabilities , 1902).

The Théorie analytique des probabilités was the first comprehensive treatise devoted entirely to the subject of probability. Laplace provided a groundbreaking, although necessarily imperfect, characterization of the techniques, subject matter, and practical applications of the new field. He relied on the traditional problems generated by games of chance, such as lotteries, to motivate his mathematical innovations, but he pointed toward the future by generalizing these methods and applying them to many other topics. For example, because the calculation of odds in games of chance so often requires the summation of long series of fractions in which each term in the series differs from the others according to a regular pattern, Laplace began by reviewing some of the methods he had discovered to approximate the sums of such series, particularly when very large numbers are involved.

Laplace then proceeded to state what has since come to be called Bayes’s theorem , after an early predecessor of Laplace. This theorem states how to use partial or incomplete information to calculate the conditional probability of an event in terms of its absolute or unconditional probability and the conditional probability of its cause. Laplace was one of the first to make extensive use of this theorem; it was particularly important to him because of its relevance to how calculations of probability should change in response to new knowledge.

The Théorie analytique des probabilités includes Laplace’s applications of his mathematical techniques to problems generated by the analysis of data from such diverse topics as census figures, insurance rates, instrumentation error, astronomy, geodesy, election prognostication, and jury selection. In particular, he gave an important statement of what has since been called the least square law for the calculation of a mean value for a set of data in such a way that the resulting error from the true value is minimized.

A Philosophical Essay on Probabilities has been one of Laplace’s most widely read works; it includes the conceptual basis upon which Laplace constructed his mathematical techniques. Most important, Laplace stated and relied upon a definition of probability that has been a source of considerable philosophical debate. Given a situation in which specific equally possible cases are the results of various processes (such as rolling dice) and correspond to favorable or unfavorable events, Laplace defined the probability of an event as the fraction formed by dividing the number of cases that correspond to or cause that event by the total number of possible cases. When the cases in question are not equally possible (as when dice are loaded), the calculation must be altered in an attempt to include this information. Laplace’s definition thus calls attention to his treatment of probability as an application of mathematics made necessary only by human ignorance.

In one of the most famous passages in A Philosophical Essay on Probabilities, Laplace expresses this view by describing a supreme intelligence with a complete knowledge of the universe and its laws at any specific moment; for such an intelligence, Laplace believed that probability calculations would be unnecessary because the future and past could be calculated simply through an application of the laws of nature to the given perfectly stipulated set of conditions. Because knowledge of natural laws and the state of the world is always limited, probability is an essential feature of all human affairs. Nevertheless, Laplace’s emphasis was not on the negative aspect of this conclusion but on the mathematical regularities to which even seemingly arbitrary sequences of events conform.

The domain in which Laplace saw the closest human approach to the knowledge of his hypothetical supreme intelligence was the application of Newton’s theory of gravitation to the solar system. Since Newton’s publication of his theory in 1686, mathematicians and physicists had reformulated his results using increasingly sophisticated mathematics. By Laplace’s time, Newton’s theory could be stated in a type of mathematics known as partial differential equations. Laplace made major contributions to the solution of equations of this type, including the famous technique of “Laplace transforms” and the use of a “potential” function to characterize a field of force.

Laplace made remarkably detailed applications of Newton’s results to the orbits of the planets, moons, and comets. Some of his most famous calculations involve his demonstration of the very long-term periodic variations in the orbits of Jupiter and Saturn. Laplace thus contributed to an increasing knowledge of the stability and internal motions of the solar system. He also applied gravitation theory to the tides, the shape of Earth, and the rings of Saturn. His hypothesis that the solar system was formed through the condensation of a diffuse solar atmosphere became a starting point for more detailed subsequent theories.

Newtonian gravitation theory became Laplace’s model for precision and clarity in all other branches of physics. He encouraged his colleagues to attempt similar analyses in optics, heat, electricity, and magnetism. His influence was particularly strong among French physicists between 1805 and 1815. By his death in 1827, however, this attempt to base all physics upon short-range forces had achieved only limited success; aside from the mathematical methods he developed, Laplace’s conceptual contributions to physics were not as long-lasting as his more fundamental insights in probability theory.

Significance

Pierre-Simon Laplace’s cultural influence extended far beyond the relatively small circle of mathematicians who could appreciate the brilliant technical detail in his work. In several ways he has become a symbol of some important aspects of the rapid scientific progress that took place during his career as a result of his role in institutional changes in the scientific profession and the implications that have been drawn from his conclusions and methods.

Laplace was very active within the highly centralized French scientific community. As a member of the French Academy of Sciences, he served on numerous research or evaluative committees that were commissioned by the French government. For example, following the French Revolution in 1789, he was an influential designer and advocate of the metric system, which has become the most widely used international system of scientific units. The academy was disbanded during the radical phase of the Revolution in 1793, but in 1796 Laplace became the president of the scientific class of the new Institute of France.

Highly publicized institute prizes were regularly offered for essays in physics and mathematics, and Laplace exerted a powerful influence on French physics through the attention he devoted to choice of topic and support for his preferred candidates. He also played an important part in the early organization of the École Polytechnique, the prestigious school of engineering founded in 1795. Although Laplace lived through turbulent political changes, he remained in positions of high scientific status through the Napoleonic era and into the Bourbon Restoration, when he was raised to the nobility as a marquis. Laplace seems to have held few strong political views, and he thus is sometimes cited as an example of a powerful scientist indifferent to social or political conditions.

Aside from his work in probability and statistics, which has quite direct impact on modern societies, other aspects of Laplace’s work have contributed to general perceptions of the goals, limitations, and methods of science. With Newton’s theory of gravitation as his model, Laplace was convinced that, although human knowledge of nature is always limited, there are inevitable regularities that can be expressed approximately with ever-increasing accuracy. Laplace thus has become a symbol of nineteenth century scientific determinism, the view that the uncertainty of the future is only the result of human ignorance of the natural laws that determine it in every detail.

When Napoleon I asked Laplace why God did not play a role in Laplace’s analysis of the stability of the solar system, Laplace replied that he had had no need for such a hypothesis. Laplace thus contributed to a growing association of the scientific tradition with atheism and materialism. Finally, Laplace’s style of mathematical physics has become a primary example of a reductionistic research strategy. Just as the gravitational effect of a large mass is determined by the sum of the forces exerted by all of its parts, Laplace expected all phenomena to reduce to collections of individual interactions. His success in implementing this method contributed to widespread perceptions that this is a necessary component of scientific investigation.

Bibliography

Arago, François. “Laplace.” In Biographies of Distinguished Scientific Men. New York: Ticknor & Fields, 1859. Arago was a student and colleague of Laplace for many years. His essay discusses only Laplace’s work in astronomy and concentrates on his study of the stability of the solar system.

Brush, Stephen G. The Origin of the Solar System and the Core of the Earth from Laplace to Jeffreys: Nebulous Earth. Vol. 1 in A History of Modern Planetary Physics. New York: Cambridge University Press, 1996. Traces the evolution of Laplace’s nebular hypotheses, the most popular nineteenth century explanation for the origin of the solar system.

Fox, Robert. “The Rise and Fall of Laplacian Physics.” Historical Studies in the Physical Sciences 4 (1974): 89-136. This is an excellent summary of Laplace’s efforts to direct French physics according to a research program based upon short-range forces.

Gillespie, Charles Coulston, Robert Fox, and Ivor Grattan-Guiness. Pierre-Simon Laplace, 1749-1827: A Life in Exact Science. Princeton, N.J.: Princeton University Press, 1997. Focuses on Laplace’s research program and his work with the Academy of Science. Includes biographical information from a scientific point of view, a description of Laplace’s efforts to gather young physicists who would work with the Newtonian model in physics, and an overview of the Laplace transform.

‗‗‗‗‗‗‗. “Pierre-Simon Marquis de Laplace.” In Dictionary of Scientific Biography. Vol. 15. New York: Charles Scribner’s Sons, 1978. This chronological survey of Laplace’s scientific career combines discussion of significant concepts with summaries of important mathematical derivations.

Hahn, Roger. Laplace as a Newtonian Scientist. Los Angeles: Williams Andrew Clark Memorial Library, 1967. This short essay describes the philosophical debate concerning the status of laws of nature that occurred during Laplace’s formative period at the University of Caen and his early years in Paris. Laplace’s convictions about the law-governed structure of the universe are traced to his reading of d’Alembert and Marquis de Condorcet.

‗‗‗‗‗‗‗. Pierre Simon LaPlace, 1749-1827: A Determined Scientist. Cambridge, Mass.: Harvard University Press, 2005. Full biography of Laplace by a scholar who has studied him for decades.

Todhunter, Isaac. A History of the Mathematical Theory of Probability from the Time of Pascal to That of Laplace. New York: Chelsea House, 1965. Chapter 10 provides a technical and chronological account of the chief results and some of the derivations found in Laplace’s publications on probability theory.