Pierre Louis Maupertuis : biography
- "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."D Beeson 1992. Maupertuis: an intellectual biography. Oxford.
- 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).
- The crater Maupertuis on the Moon is named after him, as is the asteroid 3281 Maupertuis.
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.