### BIOGRAPHY 8.1 *Pierre Simon, Marquis de Laplace* (1749 -1827)

Pierre Simon de Laplace was born in Beaumont-en-Auge, France, where his father farmed a small estate. At age 20, having finished his studies, Laplace went to Paris and became the protégé of d'Alembert, a renowned mathematician and physicist. Laplace held a variety of positions, ranging from teacher to artillery inspector to favored collaborator of Napoléon Bonaparte (who briefly made him Minister of the Interior). Later, however, Laplace turned against Napoléon and, in a surprising turn of events, was a made a marquis by Louis XVIII. Like his teacher, Laplace achieved great distinction as a mathematician and physicist, making innumerable and crucial contributions to both fields. He dealt with such matters as integral calculus, the theory of chance, corpuscular optics, the chemical physics of heat, the speed of sound, the pattern of the tides, the orbits of comets, and the moons of Jupiter -- to name just a few. In his great treatise, *Mécanique céleste*, he generalized the laws of mechanics and applied them to the motions of the heavenly bodies. In the field of probability and its applications, Laplace systematized and further extended the scattered researches of his predecessors until, with the 1820 edition of his *Théorie Analytique des Probabilités*, the theory of probability as it is presented in Chapter 8 emerged, and it was clear that it owed more to Laplace than to any other mathematician.

Among Laplace's numerous contributions is a statement of what is now called Bayes' theorem that extended the Bayesian case, in which a *priori* probabilities are equal, to a general case, in which they might not be equal. (Laplace, apparently, was unaware of Bayes' earlier essay.) Laplace also must be credited for discovering and demonstrating the major role of the normal distribution (which is mentioned in Chapters 6 and 7 of the text and is discussed fully in Chapter 10), as well as the central-limit theorem (discussed in Chapter 11). Laplace's writings also contain the seeds of ideas that have been carefully studied only in recent times: confidence-interval estimation, hypothesis testing, and regression analysis.

Not only did Laplace make important discoveries, but he also thought it crucial to communicate them to a wide audience so that even those not versed in technical mathematics could share his pleasure and enthusiasm for science. This desire gave rise to verbal paraphrases of his two great treatises as *Exposition du Système du Monde* and the *Essai Philosophique sur les Probabilités*. Consider what he had to say in the latter work:

All events, even those that on account of their insignificance do not seem to follow the great laws of nature, are a result of it just as necessarily as the revolutions of the sun. In ignorance of the ties which unite such events to the entire system of the universe, they have been made to depend upon final causes or upon hazard, according as they occur and are repeated with regularity, or appear without regard to order; but these imaginary causes have gradually receded with the widening bounds of knowledge and disappear entirely before sound philosophy, which sees in them only the expression of our ignorance of the true causes.

Present events are connected with preceding ones by a tie based upon the evident principle that a thing cannot occur without a cause that produces it...
The theory of chance consists in reducing all the events of the same kind to a certain number of cases equally possible, that is to say, to such as we may be equally undecided about in regard to their existence, and in determining the number of cases favorable to the event whose probability is sought. The ratio of this number to that of all the cases possible is the measure of this probability, which is thus simply a fraction whose numerator is the number of favorable cases and whose denominator is the number of all cases possible...
The theory of probabilities is at bottom only common sense reduced to calculus; it makes us appreciate with exactitude that which exact minds feel by a sort of instinct without being able oftentimes to give a reason for it. It leaves no arbitrariness in the choice of opinions and sides to be taken; and by its use can always be determined the most advantageous choice. Thereby it supplements most happily the ignorance and weakness of the human mind.

Laplace never stopped applying the statistical methods he developed. Thus, he helped estimate the population of France (at 25 million in 1802) and worked on questions of life insurance, the validity of trial evidence, and the creation of the metric system.

*Sources*: Adapted from International Encyclopedia of Statistics, vol.1 (New York: Free Press, 1978), pp. 493-499; Dictionary of Scientific Biography, vol.15 (New York: Scribner's, 1978), pp. 273-403. The above quote is from Pierre Simon, Marquis de Laplace, A Philosophical Essay on Probabilities (New York: Dover, 1951), pp. 3-4, 6-7 and 196.