Laplace

LAPLACE, Pierre-Simon, marquis (March 23, 1749 – March 5, 1827) a French mathematician sometimes called the “Newton of France” who contributed to the developing sciences of engineering, mathematics, statistics, physics, and astronomy. He also tentatively attempted to apply mathematics and celestial mechanics to philosophical and theological questions.

His most famous work Mécanique Céleste (Celestial Mechanics, 1799–1825) summarized and extended the work of Galileo and Newton in describing and predicting the motions of celestial bodies. He advanced the work of his predecessors by applying calculus rather than classical geometry to problems of celestial mechanics. In the field of mathematics he developed both the Laplace transform in mathematical physics and the Bayesian interpretation of probability. He survived the French Revolution, was made a count of Napoleon’s Empire in 1806 and was named a marquis in 1817 during the Bourbon restoration of the French monarchy.

AN often-cited but grossly misunderstood incident concerns Laplace’s formal presentation to Napoleon of his Celestial Mechanics. His predecessors, including both Newton and the French mathematician Legrange, had employed the notion of “God” in their work as a way of explaining inconsistencies that could not be accounted for mathematically. Laplace’s application of calculus to these problems had removed the inconsistencies, and he did not need to invoke divine providence or miraculous intervention as an excuse for inexplicable orbits or inaccurate equations.

It is alleged that during the formal presentation Napoleon cynically asked whether it was true that God was nowhere mentioned in Mécanique Céleste, and that Laplace replied Je n’avais pas besoin de cette hypothèse-là. (“I had no need of that hypothesis.”). Often interpreted as a sardonic response in the spirit of Voltaire and the Encyclopedists, Laplace’s answer simply means that he had not needed to invoke divine intervention as an excuse for an incomplete theory of celestial mechanics.

However, it is uncertain whether this version of the interaction is accurate. In old age, being informed that this incident would be cited in his biography, Laplace fervently requested that it either be omitted or explained. The only eyewitness account of this encounter is found in the the diary of the British astronomer Sir William Herschel dated August 8,1802:

The first Consul [Napoleon] then asked a few questions relating to Astronomy and the construction of the heavens to which I made such answers as seemed to give him great satisfaction. He also addressed himself to Mr Laplace on the same subject, and held a considerable argument with him in which he differed from that eminent mathematician. The difference was occasioned by an exclamation of the first Consul, who asked in a tone of exclamation or admiration (when we were speaking of the extent of the sidereal heavens): ‘And who is the author of all this!’ Mons. De la Place wished to shew that a chain of natural causes would account for the construction and preservation of the wonderful system. This the first Consul rather opposed. Much may be said on the subject; by joining the arguments of both we shall be led to ‘Nature and nature’s God’.

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

A Philosophical Essay on Probabilities, Pierre-Simon Laplace, transl. F.W.Truscott & F. L. Emory, (John Wiley & Sons, New York: 1902) pp. 4-5	Essai philosophique sur les probabilités Pierre-Simon Laplace (Bachelier Paris, 1840) pp. 4-6
WE ought then to regard the present state of the universe as the effect of its past state and as the cause of the one which is to follow. Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective situation of the beings who compose it—an intelligence sufficiently vast to submit these data to analysis—it would embrace in the same formula the movements of the greatest bodies of the universe and those of the lightest atom; for it, nothing would be uncertain and the future, as the past, would be present to its eyes.	Nous devons donc envisager l’état présent de l’univers, comme l’effet deson état antérieur, [p.4] et comme la cause de celui qui va suivre. Une intelligence qui, pour uninstant donné, connaîtrait toutes les forces dont la nature est animée, et lasituation respective des êtres qui la composent, si d’ailleurs elle était assezvaste pour soumettre ces données à l’analyse, embrasserait dans la mêmeformule les mouvemens des plus grands corps de l’univers et ceux du plus légeratome : rien ne serait incertain pour elle, et l’avenir comme le passé, seraitprésent à ses yeux.
THE human spirit offers, in the perfection which it has been able to give to astronomy, a feeble idea of this intelligence. Its discoveries in mechanics and geometry, added to that of universal gravity, have enabled it to comprehend in the same analytical expressions the past and future states of the system of the world. Applying the same method to some other objects of its knowledge, it has succeeded in referring to general laws observed phenomena and in foreseeing those which given circumstances ought to produce. All these efforts in the search for truth tend to lead it back continually to the vast intelligence which we have just mentioned, but from which it will always remain infinitely removed. ^[p.5]This tendency, unique to the human race, is that which renders it superior to animals; and their progress in this respect distinguishes nations and ages and constitutes their true glory.	L’esprit humain offre, dans la perfection qu’il a su donner àl’Astronomie, une faible esquisse de cette intelligence. Ses découvertes enMécanique et en Géométrie, jointes à celle de la pesanteur universelle, l’ont misà portée de comprendre dans les mêmes expressions analytiques, les étatspassés et futurs du système du monde. En appliquant la même méthode àquelques autres objets de ses connaissances, il est parvenu à ramener à deslois générales les phénomènes observés, et à prévoir ceux que descirconstances données doivent faire éclore. Tous ces efforts dans la recherchede la vérité, tendent à le rapprocher sans cesse de l’intelligence que nousvenons de concevoir, mais dont il restera toujours infiniment éloigné. Cette tendance, propre à l’espèce humaine, est ce qui la rend supérieure [p.5] aux animaux ; et ses progrès en ce genre, distinguent les nations etles siècles, et font leur véritable gloire.

Laplace's personal faith and spirituality remain contentious points of debate, especially among those who posit a radical divide between science and religion. Devotees of the Enlightenment, whether deists or atheists have ardently tried (and still try) to claim Laplace as one of their own. Certainly he did not believe in a “God of the gaps” Who could be invoked as an excuse for inadequate mathematics. And it must be noted that reticence to speak on matters of religion would have been a necessary survival skill throughout the first seventy year of his life, encompassing as it did the French Revolution, the Terror, and the First Republic, all of which Laplace survived. But perhaps worth noting in this respect is what he wrote to his son at he age of sixty:

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June 17, 1809
IT is with regret, my dear one, that I see you leaving Metz without being able to kiss you and give you my blessing. I hope you will do yourself honor in the noble career (of arms) which you [intend to] pursue.	« C'est avec bien du regret, mon ami, que je te vois partir de Metz sans que je puisse t'embrasser et te donner ma bénédiction. J'espère que tu te feras honneur dans la noble carrière (des armes) que tu vas parcourir.
You will be my consolation and that of your mother.	Tu seras ma consolation et celle de ta mère.
I pray to God that He watch over your days. Always keep Him present in your thoughts, as well as your father and your mother.	Je prie Dieu qu'il veille sur tes jours. Aie-le toujours présent à ta pensée, ainsi que ton père et ta mère 2. »


Napoleon		Laplace