Pierre Louis Maupertuis
Encyclopedia
Pierre-Louis Moreau de Maupertuis (mopɛʁtɥi; Saint-Malo
, 17 July 1698 – Basel
, 27 July 1759) was a French
mathematician
, philosopher and man of letters. He became the Director of the Académie des Sciences, and the first President of the Berlin Academy of Science, at the invitation of Frederick the Great.
Maupertuis made an expedition to Lapland
to determine the shape of the earth. He is often credited with having invented the principle of least action
; a version is known as Maupertuis' principle
– an integral equation that determines the path followed by a physical system. His work in natural history has its interesting points, since he touched on aspects of heredity
and the struggle for life.
, 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 arc 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 Austria
ns. 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.
. Other writers contend that his remarks are cursory, vague, or incidental to that particular argument. Mayr's verdict was "He was neither an evolutionist, nor one of the founders of the theory of natural selection
[but] he was one of the pioneers of genetics
". Maupertuis espoused a theory of pangenesis
, postulating particles from both mother and father as responsible for the characters of the child. Bowler credits him with studies on heredity, with the natural origin of human races, and with the idea that forms of life may have changed with time.
Maupertuis was a strong critic of the natural theologians
, pointing to phenomena incompatible with a concept of a good and wise Creator. He was also 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.
The difficulty of interpreting Maupertius can be gauged by reading the original works. Below is a translation from Vénus Physique, followed by the original French passage:
A nearly identical argument may be found in Maupertuis' 1746 work Les loix du mouvement et du repos déduites d'un principe metaphysique (translation: s:Derivation of the laws of motion and equilibrium from a metaphysical principle). King-Hele (1963) points to similar, though not identical, ideas of thirty years later by David Hume
in his Dialogues Concerning Natural Religion
(1777).
The chief debate that Maupertuis was engaged in was one that treated the competing theories of generation (i.e. preformationism
and epigenesis
). His account of life involved spontaneous generation of new kinds of animals and plants, together with massive elimination of deficient forms. These ideas avoid the need for a Creator, but are not part of modern thinking on evolution. The date of these speculations, 1745, is concurrent with Carolus Linnaeus
's own work, and so predates any firm notion of species
. Also, the work on genealogy
, coupled with the tracing of phenotypic characters through lineages, foreshadows later work done in genetics.
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 distance 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 distance 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? (See also the corresponding principles of stationary actions by Lagrange
and Hamilton
).
suggested that Immanuel Kant
's "most important and brilliant doctrine" - contained in the Critique of Pure Reason
(1781) - was asserted by Maupertuis:
Saint-Malo
Saint-Malo is a walled port city in Brittany in northwestern France on the English Channel. It is a sub-prefecture of the Ille-et-Vilaine.-Demographics:The population can increase to up to 200,000 in the summer tourist season...
, 17 July 1698 – Basel
Basel
Basel or Basle In the national languages of Switzerland the city is also known as Bâle , Basilea and Basilea is Switzerland's third most populous city with about 166,000 inhabitants. Located where the Swiss, French and German borders meet, Basel also has suburbs in France and Germany...
, 27 July 1759) was a French
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, philosopher and man of letters. He became the Director of the Académie des Sciences, and the first President of the Berlin Academy of Science, at the invitation of Frederick the Great.
Maupertuis made an expedition to Lapland
Lapland (region)
Lapland is a region in northern Fennoscandia, largely within the Arctic Circle. It streches across Norway, Sweden, Finland and the Kola Peninsula . On the North it is bounded by the Barents Sea, on the West by the Norwegian Sea and on the East by the White Sea...
to determine the shape of the earth. He is often credited with having invented the principle of least action
Principle of least action
In physics, the principle of least action – or, more accurately, the principle of stationary action – is a variational principle that, when applied to the action of a mechanical system, can be used to obtain the equations of motion for that system...
; a version is known as Maupertuis' principle
Maupertuis' principle
In classical mechanics, Maupertuis' principle is an integral equation that determines the path followed by a physical system without specifying the time parameterization of that path. It is a special case of the more generally stated principle of least action...
– an integral equation that determines the path followed by a physical system. His work in natural history has its interesting points, since he touched on aspects of heredity
Heredity
Heredity is the passing of traits to offspring . This is the process by which an offspring cell or organism acquires or becomes predisposed to the characteristics of its parent cell or organism. Through heredity, variations exhibited by individuals can accumulate and cause some species to evolve...
and the struggle for life.
Biography
Maupertuis was born at Saint-MaloSaint-Malo
Saint-Malo is a walled port city in Brittany in northwestern France on the English Channel. It is a sub-prefecture of the Ille-et-Vilaine.-Demographics:The population can increase to up to 200,000 in the summer tourist season...
, France
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan 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
Paris
Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...
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
Vis viva
In the history of science, vis viva is an obsolete scientific theory that served as an elementary and limited early formulation of the principle of conservation of energy...
controversy, for which Maupertuis developed and extended the work of Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...
(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
Johann Bernoulli
Johann Bernoulli was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family...
) predicted that the Earth should be oblate, while his rival Jacques Cassini
Jacques Cassini
Jacques Cassini was a French astronomer, son of the famous Italian astronomer Giovanni Domenico Cassini.Cassini was born at the Paris Observatory. Admitted at the age of seventeen to membership of the French Academy of Sciences, he was elected in 1696 a fellow of the Royal Society of London, and...
measured it astronomically to be prolate. In 1736 Maupertuis acted as chief of the French Geodesic Mission
French Geodesic Mission
The French Geodesic Mission was an 18th-century expedition to what is now Ecuador carried out for the purpose of measuring the roundness of the Earth and measuring the length of a degree of longitude at the Equator...
sent by King Louis XV
Louis XV of France
Louis XV was a Bourbon monarch who ruled as King of France and of Navarre from 1 September 1715 until his death. He succeeded his great-grandfather at the age of five, his first cousin Philippe II, Duke of Orléans, served as Regent of the kingdom until Louis's majority in 1723...
to Lapland to measure the length of a degree of arc 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
Käymäjärvi Inscriptions
The Käymäjärvi Inscriptions refers to inscriptions on a stone approximately 52.5 cm high and 105 cm wide, engraved with characters similar to those found in runic alphabets...
. On his return home he became a member of almost all the scientific societies of Europe.
 |
 |
| Maupertuis' opinion |
Cassini's opinion |
After the Lapland expedition, Maupertuis set about generalizing his earlier mathematical work, proposing the principle of least action
Principle of least action
In physics, the principle of least action – or, more accurately, the principle of stationary action – is a variational principle that, when applied to the action of a mechanical system, can be used to obtain the equations of motion for that system...
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
Chemical affinity
In chemical physics and physical chemistry, chemical affinity is the electronic property by which dissimilar chemical species are capable of forming chemical compounds...
, which was widely read and commented upon favorably by Georges-Louis Leclerc, Comte de Buffon
Georges-Louis Leclerc, Comte de Buffon
Georges-Louis Leclerc, Comte de Buffon was a French naturalist, mathematician, cosmologist, and encyclopedic author.His works influenced the next two generations of naturalists, including Jean-Baptiste Lamarck and Georges Cuvier...
. He later developed his views on living things further in a more formal pseudonymous work that explored heredity
Heredity
Heredity is the passing of traits to offspring . This is the process by which an offspring cell or organism acquires or becomes predisposed to the characteristics of its parent cell or organism. Through heredity, variations exhibited by individuals can accumulate and cause some species to evolve...
, collecting evidence that confirmed the contributions of both sexes and treated variations as statistical phenomena.
In 1740 Maupertuis went to Berlin
Berlin
Berlin is the capital city of Germany and is one of the 16 states of Germany. With a population of 3.45 million people, Berlin is Germany's largest city. It is the second most populous city proper and the seventh most populous urban area in the European Union...
at the invitation of Frederick II of Prussia
Frederick II of Prussia
Frederick II was a King in Prussia and a King of Prussia from the Hohenzollern dynasty. In his role as a prince-elector of the Holy Roman Empire, he was also Elector of Brandenburg. He was in personal union the sovereign prince of the Principality of Neuchâtel...
, and took part in the Battle of Mollwitz
Battle of Mollwitz
The Battle of Mollwitz was fought by Prussia and Austria on April 10, 1741, during the early stages of the War of the Austrian Succession. It was the first battle of the new Prussian King Frederick II, in which both sides made numerous military blunders but Frederick the Great still managed to...
, where he was taken prisoner by the Austria
Austria
Austria , officially the Republic of Austria , is a landlocked country of roughly 8.4 million people in Central Europe. It is bordered by the Czech Republic and Germany to the north, Slovakia and Hungary to the east, Slovenia and Italy to the south, and Switzerland and Liechtenstein to the...
ns. 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
Académie française
L'Académie française , also called the French Academy, is the pre-eminent French learned body on matters pertaining to the French language. The Académie was officially established in 1635 by Cardinal Richelieu, the chief minister to King Louis XIII. Suppressed in 1793 during the French Revolution,...
. 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
Leonhard Euler
Leonhard Euler was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion...
until his death. His position became extremely awkward with the outbreak of the Seven Years' War
Seven Years' War
The Seven Years' War was a global military war between 1756 and 1763, involving most of the great powers of the time and affecting Europe, North America, Central America, the West African coast, India, and the Philippines...
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
Basel
Basel or Basle In the national languages of Switzerland the city is also known as Bâle , Basilea and Basilea is Switzerland's third most populous city with about 166,000 inhabitants. Located where the Swiss, French and German borders meet, Basel also has suburbs in France and Germany...
, where he died a year later. Maupertuis' difficult disposition involved him in constant quarrels, of which his controversies with Samuel König and Voltaire
Voltaire
François-Marie Arouet , better known by the pen name Voltaire , was a French Enlightenment writer, historian and philosopher famous for his wit and for his advocacy of civil liberties, including freedom of religion, free trade and separation of church and state...
during the latter part of his life are examples.
- "The brilliance of much of what he did was undermined by his tendency to leave work unfinished, his failure to realise his own potential. It was the insight of genius that led him to least-action principle, but a lack of intellectual energy or rigour that prevented his giving it the mathematical foundation that Lagrange would provide... He reveals remarkable powers of perception in heredity, in understanding the mechanism by which species developed, even in immunology, but no fully elaborated theory. His philosophical work is his most enthralling: bold, exciting, well argued."
Evolution
Some historians of science point to his work in biology as a significant precursor to the development of evolutionary theory, specifically the theory of natural selectionNatural selection
Natural selection is the nonrandom process by which biologic traits become either more or less common in a population as a function of differential reproduction of their bearers. It is a key mechanism of evolution....
. Other writers contend that his remarks are cursory, vague, or incidental to that particular argument. Mayr's verdict was "He was neither an evolutionist, nor one of the founders of the theory of natural selection
Natural selection
Natural selection is the nonrandom process by which biologic traits become either more or less common in a population as a function of differential reproduction of their bearers. It is a key mechanism of evolution....
[but] he was one of the pioneers of genetics
Genetics
Genetics , a discipline of biology, is the science of genes, heredity, and variation in living organisms....
". Maupertuis espoused a theory of pangenesis
Pangenesis
Pangenesis was Charles Darwin's hypothetical mechanism for heredity. He presented this 'provisional hypothesis' in his 1868 work The Variation of Animals and Plants under Domestication and felt that it brought 'together a multitude of facts which are at present left disconnected by any efficient...
, postulating particles from both mother and father as responsible for the characters of the child. Bowler credits him with studies on heredity, with the natural origin of human races, and with the idea that forms of life may have changed with time.
Maupertuis was a strong critic of the natural theologians
Natural theology
Natural theology is a branch of theology based on reason and ordinary experience. Thus it is distinguished from revealed theology which is based on scripture and religious experiences of various kinds; and also from transcendental theology, theology from a priori reasoning.Marcus Terentius Varro ...
, pointing to phenomena incompatible with a concept of a good and wise Creator. He was also 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.
The difficulty of interpreting Maupertius can be gauged by reading the original works. Below is a translation from Vénus Physique, followed by the original French passage:
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 (translation: s:Derivation of the laws of motion and equilibrium from a metaphysical principle). King-Hele (1963) points to similar, though not identical, ideas of thirty years later by David Hume
David Hume
David Hume was a Scottish philosopher, historian, economist, and essayist, known especially for his philosophical empiricism and skepticism. He was one of the most important figures in the history of Western philosophy and the Scottish Enlightenment...
in his Dialogues Concerning Natural Religion
Dialogues Concerning Natural Religion
Dialogues Concerning Natural Religion is a philosophical work written by the Scottish philosopher David Hume. Through dialogue, three fictional characters named Demea, Philo, and Cleanthes debate the nature of God's existence...
(1777).
The chief debate that Maupertuis was engaged in was one that treated the competing theories of generation (i.e. preformationism
Preformationism
In the history of biology, preformationism is either the specific contention that all organisms were created at the same time, and that succeeding generations grow from homunculi, animalcules, or other fully formed but miniature versions of themselves that have existed since the beginning of...
and epigenesis
Epigenesis
Epigenesis may refer to:* Epigenesis , describes morphogenesis and development of an organism* By analogy, a philosophical and theological concept, part of the concept of spiritual evolution* The Epigenesis, a 2010 album by Melechesh...
). His account of life involved spontaneous generation of new kinds of animals and plants, together with massive elimination of deficient forms. These ideas avoid the need for a Creator, but are not part of modern thinking on evolution. The date of these speculations, 1745, is concurrent with Carolus Linnaeus
Carolus Linnaeus
Carl Linnaeus , also known after his ennoblement as , was a Swedish botanist, physician, and zoologist, who laid the foundations for the modern scheme of binomial nomenclature. He is known as the father of modern taxonomy, and is also considered one of the fathers of modern ecology...
's own work, and so predates any firm notion of species
Species
In biology, a species is one of the basic units of biological classification and a taxonomic rank. A species is often defined as a group of organisms capable of interbreeding and producing fertile offspring. While in many cases this definition is adequate, more precise or differing measures are...
. Also, the work on genealogy
Genealogy
Genealogy is the study of families and the tracing of their lineages and history. Genealogists use oral traditions, historical records, genetic analysis, and other records to obtain information about a family and to demonstrate kinship and pedigrees of its members...
, coupled with the tracing of phenotypic characters through lineages, foreshadows later work done in genetics.
Least Action Principle
The principle of least actionPrinciple of least action
In physics, the principle of least action – or, more accurately, the principle of stationary action – is a variational principle that, when applied to the action of a mechanical system, can be used to obtain the equations of motion for that system...
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 distance 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 distance 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? (See also the corresponding principles of stationary actions by Lagrange
Lagrange
La Grange literally means the barn in French. Lagrange may refer to:- People :* Charles Varlet de La Grange , French actor* Georges Lagrange , translator to and writer in Esperanto...
and Hamilton
William Rowan Hamilton
Sir William Rowan Hamilton was an Irish physicist, astronomer, and mathematician, who made important contributions to classical mechanics, optics, and algebra. His studies of mechanical and optical systems led him to discover new mathematical concepts and techniques...
).
Relation to Kant
Arthur SchopenhauerArthur Schopenhauer
Arthur Schopenhauer was a German philosopher known for his pessimism and philosophical clarity. At age 25, he published his doctoral dissertation, On the Fourfold Root of the Principle of Sufficient Reason, which examined the four separate manifestations of reason in the phenomenal...
suggested that Immanuel Kant
Immanuel Kant
Immanuel Kant was a German philosopher from Königsberg , researching, lecturing and writing on philosophy and anthropology at the end of the 18th Century Enlightenment....
's "most important and brilliant doctrine" - contained in the Critique of Pure Reason
Critique of Pure Reason
The Critique of Pure Reason by Immanuel Kant, first published in 1781, second edition 1787, is considered one of the most influential works in the history of philosophy. Also referred to as Kant's "first critique," it was followed by the Critique of Practical Reason and the Critique of Judgement...
(1781) - was asserted 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).
Honors
- The crater MaupertuisMaupertuis (crater)Maupertuis is the remnant of a lunar impact crater that is located in the northern part of the Moon's near side. It lies in the stretch of rugged terrain north of Sinus Iridum, a bay in the northwestern corner of Mare Imbrium...
on the MoonMoonThe Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...
is named after him, as is the asteroid 3281 Maupertuis3281 Maupertuis3281 Maupertuis is a main-belt asteroid discovered on February 24, 1938 by Y. Vaisala at Turku. The crater was named for the French mathemetician and astronomer Pierre Louis Maupertuis .- External links :*...
.