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Maupertuis

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Posted by Harvey on June 7, 2002 21:39:40 UTC

Richard,

I can't find too much in the way of Maupertuis either. He doesn't have the same level of visibility as his colleagues whom he heavily influenced (Euler, Voltaire, Newton, etc). Which is quite strange given that he anticipated Darwin's theory of natural selection, Mendel's theory of genetics, given credit for first inventing the principle of least action (key to quantum theories), introducing Newton's gravitational theory into Europe, etc.

In any case, he did have enough influence for others to widely know his theological beliefs. C.S. Pierce's father, Benjamin Pierce, knew of Maupertuis even in the United States who is quoted as saying this about Maupertuis:

"When in the case of the fixed forces of nature, the initial and final positions of the system are given, as well as the intial power with which the system is moving, the variation of the characteristic function vanishes, and, therefore, the function is generally a maximum or a minimum. The action expended by the system, which is measured by this function, is also a maximum or a minimum; or in other words, the course by which the total expenditure of action is a macimum or a minimum. But it is obvious, that in most cases and always when the paths in which the various bodies move, cannot correspond to the macimum of expended action, and, therefore, in most cases the system moves from its given initial to its final position with the least possible expenditure of action. Many examples can, however, be given, in which the expended action is, in some of its elements a maximum, although, even in those cases, the expenditure is a minimum at each instant or for any sufficient short portion of the paths of the bodies. This principle of the least action was first deduced by Maupertuis throught an a priori argument from the general attributes of Deity, which he thought to demand the utmost economy in the use of the powers of nature, and to permit no needless expenditure or any waste of action. This grand proposition which was announced by its illustrious author with the seriousness and reverence of a true philosopher, is the more remarkable that, deried from purely metaphysical doctrines, and taken in combination with the law of power, which likewise reposes directly upon a metaphysical basis, it leads at once to the usual form of the dynamical equations." (Physical & Celestial Mechanics, Boston. Little, Brown & Co., 1855 p. 316).

I think Benjamin Pierce also held a view very similar to this:

http://plato.stanford.edu/entries/peirce-benjamin/#Bib

Unfortunately I don't have access to Maupertuis' Essai de Cosmologie (1750) otherwise I would be happy to give you quotes directly from that interesting essay. I sure would like to get my hands on that 18th century book (i.e., a translation into English) but I don't think it exists. Too bad since not only is the principle of least action introduced, but also the principle of natural selection and I think the groundwork for genetics. Not bad for one essay!

The great attraction to this coming from one guy is that no one can be accused of ad hoc introduction of the least action principle to account for evolutionary theory. It appears that Maupertuis was able to use least action to derive an almost modern equivalent to evolutionary theory (far more advanced than Lamarkian theory which followed Maupertuis but prior to Darwin).

This man deserves a statue!

Warm regards, Harv

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