Pierre Louis Maupertuis

Pierre-Louis Moreau de Maupertuis (July 17, 1698 – July 27, 1759) was a French mathematician, philosopher and man of letters. He is often credited with having invented the principle of least action.

Biography
Maupertuis was born at Saint-Malo, France, to a moderately wealthy family of merchant-corsairs. He was educated in mathematics by a private tutor, and upon completing his formal education his father secured him a largely honorific cavalry commission. After three years in the cavalry, during which time he became acquainted with fashionable social and mathematical circles, he moved to Paris and began building his reputation as a mathematician and literary wit. In 1723 he was admitted to the Académie des Sciences.

His early mathematical work revolved around the vis viva controversy, for which Maupertuis developed and extended the work of Isaac Newton (whose theories were not yet widely accepted outside England) and argued against the waning Cartesian mechanics. In the 1730s, the shape of the Earth became a flashpoint in the battle among rival systems of mechanics. Maupertuis, based on his exposition of Newton (with the help of his mentor Johan Bernoulli) predicted that the Earth should be oblate, while his rival Jacques Cassini measured it astronomically to be prolate. In 1736 Maupertuis acted as chief of the French Geodesic Mission sent by King Louis XV to Lapland to measure the length of a degree of the meridian. His results, which he published in a book detailing his procedures, essentially settled the controversy in his favor. The book included an adventure narrative of the expedition, and an account of the Käymäjärvi Inscriptions. On his return home he became a member of almost all the scientific societies of Europe.

After the Lapland expedition, Maupertuis set about generalizing his earlier mathematical work, proposing the principle of least action as a metaphysical principle that underlies all the laws of mechanics. He also expanded into the biological realm, anonymously publishing a book that was part popular science, part philosophy, and part erotica: Vénus physique. In that work, Maupertuis proposed a theory of generation (i.e., reproduction) in which organic matter possessed a self-organizing “intelligence” that was analogous to the contemporary chemical concept of affinities, which was widely read and commented upon favorably by Georges-Louis Leclerc, Comte de Buffon. He later developed his views on living things further in a more formal pseudonymous work that explored heredity, collecting evidence that confirmed the contributions of both sexes and treated variations as statistical phenomena.

In 1740 Maupertuis went to Berlin at the invitation of Frederick II of Prussia, and took part in the Battle of Mollwitz, where he was taken prisoner by the Austrians. On his release he returned to Berlin, and thence to Paris, where he was elected director of the Academy of Sciences in 1742, and in the following year was admitted into the Académie française. Returning to Berlin in 1744, again at the desire of Frederick II, he was chosen president of the Prussian Royal Academy of Sciences in 1746, which he controlled with the help of Leonhard Euler until his death. His position became extremely awkward with the outbreak of the Seven Years' War between his home country and his patron's, and his reputation suffered in both Paris and Berlin. Finding his health declining, he retired in 1757 to the south of France, but went in 1758 to Basel, where he died a year later. Maupertuis' difficult disposition involved him in constant quarrels, of which his controversies with Samuel König and Voltaire during the latter part of his life are examples.

Evolution
Some historians of science point to his important works in biology as significant precursors in the development of evolutionary theories, specifically the theory of natural selection. Other writers contend that his remarks are cursory, vague, or incidental to that particular argument. See "Venus Physique" (1745), or its English translation, Boas (1966), for details. Other valuable references include Stephen Jay Gould's The Flamingo's Smile (1987), Desmond King-Hele's Erasmus Darwin (1963), Peter J. Bowler's Evolution: The History of an Idea (1983), and Bentley Glass' Forerunners of Darwin (1959). He also was one of the first to consider animals in terms of variable populations, in opposition to the natural history tradition that emphasized description of individual specimens.

Below is a translation from Vénus Physique, followed by the original French passage:

"Could one not say that, in the fortuitous combinations of the productions of nature, as there must be some characterized by a certain relation of fitness which are able to subsist, it is not to be wondered at that this fitness is present in all the species that are currently in existence? Chance, one would say, produced an innumerable multitude of individuals; a small number found themselves constructed in such a manner that the parts of the animal were able to satisfy its needs; in another infinitely greater number, there was neither fitness nor order: all of these latter have perished. Animals lacking a mouth could not live; others lacking reproductive organs could not perpetuate themselves... The species we see today are but the smallest part of what blind destiny has produced..."

Ne pourrait-on pas dire que, dans la combinaison fortuite des productions de la nature, comme il n'y avait que celles où se trouvaient certain rapport de convenance qui puissent subsister, il n'est pas marveilleux que cette convenance se trouve dans toutes les espèces qui existent actuellement? Le hasard, dirait-on, avait produit une multitude innombrable d'individus; un petit nombre se trouvait construit de manière que les parties de l'animal pouvaient satisfaire à ses besoins; dans un autre infiniment plus grand, il n'y avait ni convenance, ni ordre: tous ces derniers ont péri; des animaux sans bouche ne pouvaient pas vivre, d'autres qui manquaient d'organes pour la génération ne pouvaient se perpétuer... les espèces que nous voyons aujourd'hui ne sont que la plus petite partie de ce qu'un destin aveugle avait produit...

A nearly identical argument may be found in Maupertuis' 1746 work Les loix du mouvement et du repos déduites d'un principe metaphysique (its English translation). Desmond King-Hele (1963) points to similar, though not identical, ideas expounded roughly thirty years later by David Hume in his Dialogues Concerning Natural Religion (1777).

The question of who deserves priority for the discovery of the principle of natural selection has long been of particular interest to historians and biologists. Charles Darwin himself, in his foreword to the 6th edition of the Origin of Species, credited Aristotle with foreshadowing the concept of natural selection, and stated that "the first author who in modern times has treated it in a scientific spirit was Buffon". Darwin's fame rests on being the first to develop and publish the concept as a well supported scientific theory, rather than being the first to suggest the concept.

With regard to Maupertuis the question is whether or not Maupertuis had (1) an internally coherent, yet externally robust, theoretical system, (2) an atheistic system or, at a minimum, a non-mystical and thus, scientific system, and/or (3) a broad, overarching theory that tied together all of the available evidence. The chief debate that Maupertuis was engaged in was one that treated the competing theories of generation (i.e. preformationism and epigenesis) indicating that, if Maupertuis was indeed involved in evolutionary speculations, then natural selection may have followed intuitively from clear thinking about the mechanism of biological generation and propagation.

The date of these speculations, 1745, being concurrent with Carolus Linnaeus's own work, predate any firm notion of species, excepting, of course, Aristotle's. Also, the work on genealogy, coupled with the tracing of phenotypic characters through lineages, foreshadows the later work done by Gregor Mendel. The juxtaposition of these subjects suggests that the Modern evolutionary synthesis, while certainly more quantitative, rigorous, and scientific, may have been a rather late addition to a philosophical framework that could already be considered "discovered". In summary, Maupertuis' text is suggestive and deserving of closer scrutiny by scientists and historians, as well as the general public.

Least Action Principle
The principle of least action states that in all natural phenomena a quantity called ‘action’ tends to be minimized. Maupertuis developed such a principle over two decades. For him, action could be expressed mathematically as the product of the mass of the body involved, the distance it had traveled and the velocity at which it was traveling.

In 1741, he gave a paper to the Paris Academy of Sciences, Loi du repos des corps, (Law of bodies at rest). In it he showed that a system of bodies at rest tends to reach a position in which any change would create the smallest possible change in a quantity that he argued could be assimilated to action.

In 1744, in another paper to the Paris Academy, he gave his Accord de plusieurs lois naturelles qui avaient paru jusqu’ici incompatibles (Agreement of several natural laws that had hitherto seemed to be incompatible) to show that the behaviour of light during refraction – when it bends on entering a new medium – was such that the total path it followed, from a point in the first medium to a point in the second, minimised a quantity which he again assimilated to action.

Finally, in 1746 he gave a further paper, the Loix du mouvement et du repos (Laws of movement and rest), this time to the Berlin Academy of Sciences, which showed that point masses also minimise action. Point masses are bodies that can be treated for the purposes of analysis as being a certain amount of matter (a mass) concentrated at a single point. A major debate in the early part of the eighteenth century concerned the behaviour of such bodies in collisions. Cartesian and Newtonian physicists argued that in their collisions, point masses conserved both momentum and relative velocity. Leibnizians, on the other hand, argued that they also conserved what was called live force or vis viva. This was unacceptable for their opponents for two reasons: the first that live force conservation did not apply to so-called ‘hard’ bodies, bodies that were totally incompressible, whereas the other two conservation principles did; the second was that live force was defined by the product of mass and square of velocity. Why did the velocity appear twice in this quantity, as squaring it suggests? The Leibnizians argued this was simple enough: there was a natural tendency in all matter towards motion, so even at rest, there is an inherent velocity in bodies; when they begin to move, there is a second velocity term corresponding to their actual motion.

This was anathema to Cartesians and Newtonians. An inherent tendency towards motion was an ‘occult quality’ of the kind of favoured by mediaeval scholastics and to be resisted at all costs.

Today, of course, the concept of a ‘hard’ body is rejected. And mass times the square of velocity is just twice kinetic energy so modern mechanics reserves a major role for the inheritor quantity of ‘live force’.

For Maupertuis, however, it was important to retain the concept of the hard body. And the beauty of his principle of least action was that it applied just as well to hard and elastic bodies. Since he had shown that the principle also applied to systems of bodies at rest and to light, it seemed that it was truly universal.

The final stage of his argument came when Maupertuis set out to interpret his principle in cosmological terms. ‘Least action’ sounds like an economy principle, roughly equivalent to the idea of economy of effort in daily life. A universal principle of economy of effort would seem to display the working of wisdom in the very construction of the universe. This seems, in Maupertuis’s view, a more powerful argument for the existence of an infinitely wise creator than any other that can be advanced.

He published his thinking on these matters in his Essai de cosmologie (Essay on cosmology) of 1750. He shows that the major arguments advanced to prove God, from the wonders of nature or the apparent regularity of the universe, are all open to objection (what wonder is there in the existence of certain particularly repulsive insects, what regularity is there in the observation that all the planets turn in nearly the same plane – exactly the same plane might have been striking but 'nearly the same plane' is far less convincing). But a universal principle of wisdom provides an undeniable proof of the shaping of the universe by a wise creator.

Hence the principle of least action is not just the culmination of Maupertuis’s work in several areas of physics, he sees it as his most important achievement in philosophy too, giving an incontrovertible proof of God.

The flaws in his reasoning are principally that there is no obvious reason why the product of mass, velocity and time should be particularly viewed as corresponding to action, and even less reason why its minimisation should be an ‘economy’ principle like a minimisation of effort. Indeed, the product of mass, velocity and time is mathematically the equivalent of the integral of live force over time. Leibniz had already shown that this quantity is likely to be either minimised or maximised in natural phenomena. Minimising this quantity could conceivably demonstrate economy, but how could maximising it?

Relation to Kant
Arthur Schopenhauer suggested that Immanuel Kant's "most important and brilliant doctrine" - contained in the Critique of Pure Reason (1781) - was asserted (though not yet "proved") by Maupertuis:

Main works

 * Sur la figure de la terre (1738)
 * Discours sur la parallaxe de la lune (1741)
 * Discours sur la figure des astres (1742)
 * Eléments de la géographie (1742)
 * Lettre sur la comète de 1742 (1742)
 * Accord de différentes loix de la nature qui avoient jusqu’ici paru incompatibles (1744, English translation)
 * Vénus physique (1745)
 * Astronomie nautique (1745 and 1746)
 * Les loix du mouvement et du repos déduites d'un principe metaphysique (1746, English translation)
 * Essai de philosophie morale (1749).
 * Essai de cosmologie (1750).

His Œuvres were published in 1752 at Dresden and in 1756 at Lyons; books at: http://www.bookmine.org ; http://www.dprix.com/biblio/mpage.html ;

Honors
The Maupertuis crater on the Moon is named after him.