But this article, which looks at the career of Maupertuis himself, indicates that the eighteenth century, though it may have been an era of light, was not always an era of sweetness, and not merely because it was divided into pro- and anti-Enlightenment factions. Sometimes, there were political divisions among the supporters of the Enlightenment. (See the interview with Richard Brookhiser in the June issue of Navigator.) Sometimes, there were personal divisions among them. (Voltaire, as Maupertuis discovered, could turn viciously on his friends.) Sometimes, too, there were philosophical divisions within the Enlightenment, and, among these, the greatest were the divisions between the followers of Sir Isaac Newton on the one hand and the followers of René Descartes and Gottfried Wilhelm Leibniz on the other. It was these philosophical divisions that shaped the early life of Maupertuis, although it was personal enmity that shaped the end of his life.
At the age of sixteen, Maupertuis was sent to Paris to study the Scholastic philosophy of the day and found it unsatisfying. At nineteen, he took up music but simultaneously developed a strong interest in mathematics. After studying with some of the most prominent mathematicians of the day, Maupertuis was elected to the Academy of Sciences in 1723 (probably as an assistant). Combining two of his early interests, his first paper was on the form of musical instruments. Over the next five years, however, Maupertuis presented several more purely mathematical papers.
In 1728, when he turned 30, Maupertuis undertook a journey to London that would change his life. He had been educated in France, where the physical theories of René Descartes still dominated. For example, Cartesians held that the planets were carried around the sun by a vortex of matter, like leaves in a whirlpool. Even those who appreciated the greatness of Newton, such as the president of the Academy, Bernard le Bovier de Fontenelle (1657-1757), defended these Cartesian vortices against Newton's theory of gravitation, because the latter seemed to be an occult force. But Maupertuis, as a result of his trip to England, was converted to Newtonianism and became its leading champion on the Continent.
Returning to France, he joined up with a mathematical prodigy, Alexis-Claude Clairaut, who was also a Newtonian. Born in 1713, Clairaut learned to read from Euclid's Elements and mastered calculus at the age of nine. He presented his first paper to the Academy at 13 and, at the age of 18, became its youngest member. Maupertuis, who also seems to have become an associate of the Academy in 1731, collaborated with Clairaut on a stream of papers. Then, in 1732, he brought out the first major Newtonian essay to be written by a Frenchman: Discours sur les différentes figures des asters (Discourse on the Different Shapes of the Heavenly Bodies). This work brought him to the attention of Voltaire and Voltaire's friend, the Marquise du Châtelet, whom Maupertuis instructed in Newtonianism. The following year, Maupertuis solidified his position as France's leading Newtonian by publishing an essay on the shape of the earth.
A Spherical Earth
Contrary to popular myth, the roughly spherical nature of the earth has long been known, probably since 500 B.C. Aristotle certainly argued for the idea, and, in the third century B.C., Eratosthenes calculated the Earth's circumference to a remarkable exactitude, with an error of perhaps 10 to 20 percent. In 1669, astronomer Jean Picard (1620-82) performed a more accurate experiment, which gave a diameter for the earth of 7796 miles, and this was the figure Newton used in developing his theory of gravitation. That theory led to an interesting conclusion, one that would put an end to the belief that the earth is a perfect sphere. Newton calculated that, given the gravitational and "centrifugal" forces acting on the earth, as a result of the earth's own mass and spin, the planet should be slightly flattened at the poles. To be precise, the equatorial radius should be 1/230 longer than the north-south radius. (In fact, it is about 1/300 longer.)
Now, in the same year that Picard made his measurement, Louis XIV invited the Italian astronomer Gian Domenico Cassini (1625-1712) to France, and by 1671 Cassini was director of the Paris Observatory. In that position, he had many triumphs. But Cassini's significance to the life of Maupertuis was that in 1683 he and his son Jacques (1677-1756) made measurements of the earth that indicated the planet was in fact somewhat elongated at the poles, exactly contrary to Newton's hypothesis. Jacques Cassini realized that the issue could best be settled by making two measurements of a degree of latitude along a line of longitude, one measurement near a pole and one near the equator. The end points of the one-degree arc of latitude could be determined astronomically; the length of the arc could then be determined by a process of surveying called "triangulation" (See map below.) If the earth was flattened at the poles, the arc would be longer at the pole than at the equator.
In 1734, the Academy of Sciences therefore authorized two expeditions. The first, to be headed by Maupertuis, was sent north to Lapland; the second expedition was sent to a region near the equator in what now is Ecuador. The voyage north, which began in May 1736 and lasted over a year, brought many hardships. The team faced blinding snowstorms, and, on the return journey, the expedition's ship was wrecked in the Baltic Sea, fortunately without loss of life, instruments, or records. But when at last Maupertuis reached Paris, in August 1737, he and his apparently Newtonian results met a cold reception. Newton still had few prominent supporters in France, except for Voltaire, and the expedition to Peru had not returned to confirm the northern results.
Following his return from the north, therefore, Maupertuis found respite from ill-wishers by retreating to Saint-Malo and Circy, where Mme du Châtelet and Voltaire made him welcome. He stayed only briefly at Circy, however, before going on to Basel, where, fatefully, he met Samuel König. Returning to Circy with Maupertuis, König behaved so arrogantly that he angered Mme du Châtelet, who as a result also became temporarily estranged from Maupertuis. Meanwhile, he was struggling to analyze the data on the shape of the earth. Finally, in December 1739, he was able to announce the values he had found for a distance of one degree along the meridian in France and in Lapland. They supported Newton's hypothesis that the earth was flattened at the poles. His opponents struck back by pointing out errors in the measurements and corrections had to be made. But the conclusion still held. When the expedition to Peru returned after an arduous three-year journey, it produced a measure for a degree between Quito and Cuenca and this helped to confirm the Newtonian conclusion. Much later, measurements made at the Cape of Good Hope gave a fourth set of confirming data. Maupertuis presented a final revision of the data in Operations to determine the shape of the earth.
On to Berlin
In 1738, Voltaire had recommended Maupertuis to Frederick the Great of Prussia as someone capable of building up the reputation of the Berlin academy of sciences. Frederick made overtures to Maupertuis and the latter visited Berlin after patching up his relationship with Mme du Châtelet. At this point, Maupertuis's studies took a new turn, toward biology. He became involved in the "pre-formation" argument. The task was to explain the emergence of living beings, which are obviously complex organisms. The difficulty was that the Enlightenment believed firmly in two principles: First, the existence of complex order in the universe is due to the actions of a Divine Intelligence. Secondly, the Divine Intelligence intervened in the world and gave order to the universe only once. After that, He left the world to run like a clockwork, according to the natural order He had imparted. Thus, one could invoke divine intervention to explain an initial order but not the emergence of order.
How, then, could one explain the emergence of a complex living organism from an amorphous egg and sperm? One could say, with Descartes, that animals were just mechanisms, so reproduction was just mechanical interaction. But, Fontenelle rejoined, put a male dog-machine next to a female dog-machine and you soon have a third machine. Put one watch next to another and you can wait forever without getting a third watch. About 1670, biologists came up with an answer that, in principle, solved the problem. Eggs and sperm were not as amorphous as they seemed. Inside each egg (or sperm) was a very tiny, pre-formed individual of the species. All that its emergence required was the necessary conditions for growth. The complexity already existed. (Most leading scientists were "ovists," that is, they believed the pre-formed creature existed in the egg; however, two of the era's leading scientists-Anton van Leeuwenhoek and Hermann Boerhaave -were spermists.)
But how would this answer solve the problem of the following generation? Simple. The tiny preformed individual was fully complete and therefore it also had eggs or sperm, and inside those were even tinier pre-formed individuals. And so on. This did not require the existence of an actual infinite, since no species lasts forever. But it did require an enormous set of Russian dolls, one nested inside the other, all created by God at the beginning of time.
In 1744, and again in 1745, Maupertuis argued against this theory by citing one blatant fact. An individual, he said, cannot be preformed in either the egg or sperm of its parents because it inherits characteristics from both. He thus looked for some corporeal contribution from each parent as the basis of heredity.
Principle of Least Action
Meanwhile, in 1745, Maupertuis had accepted Frederick's offer to come to Berlin. There he married, and in March 1746, he was installed as president of the academy. His first paper was "The laws of movement and respose," in which he set forth the famous (and still important) principle of least action. The following analogy is often used to explain the principle:
Suppose you are standing on the beach, at some distance from the water. You hear cries of distress. Looking to your left, you see someone drowning. You decide to rescue this person. Taking advantage of your ability to move faster on land than in water, you run to a point at the edge of the surf close to the drowning person, and from there you swim directly toward him. Your path is the quickest one to the swimmer-but it is not a straight line. Instead, it consists of two straight-line segments, with an angle between them at the point where you enter the water. (Jim Holt, "Least Action Hero," Lingua Franca, October 1999.)
Maupertuis formulated his version of the least action principle as stating that "in all the changes that take place in the universe, the sum of the products of each body multiplied by the distance it moves and by the speed with which it moves is the least possible." The principle was later clarified and expounded by the great mathematician Leonhard Euler (1707-83), who was at the Berlin Academy with Maupertuis; by Joseph-Louis Lagrange (1736-1813), whom Maupertuis and Euler were unable to lure to Berlin; and, in the nineteenth century, by Sir William Rowan Hamilton (1805-65), the brilliant Irish mathematician and astronomer.
Max Planck once paid tribute to the least-action principle in the following terms:
The highest and most coveted aim of physical science is to condense all natural phenomena
which have been observed and are still to be observed into one simple principle. Amid the more
or less general laws which mark the achievements of physical science during the course of the
last centuries, the principle of least action is perhaps that which . . . may claim to come nearest
to this ideal final aim of theoretical research. (Holt, "Least Action Hero.")
In an odd way, however, this principle was to prove the undoing of Maupertuis. His protégé, Samuel König, was elected to the Berlin Academy in 1749 and came for a visit, at which time he was warmly welcomed by Maupertuis. But two years later, König did something bizarre. Though a friend of Maupertuis and a devoted Leibnizian, he accused Maupertuis of plagiarizing the least action principle from Leibniz-and then he attacked the principle. His charge of plagiarisn was based, he said, on a letter that Leibniz had written to Johann Hermann. Maupertuis demanded that König produce the letter, but he could show only what he said was a copy. The original was supposedly with the estate of a Swiss named Henzi, who had recently been executed for participating in a conspiracy. An exhaustive search found no trace of the letter in Henzi's effects, and Maupertuis demanded the Academy take action against König.
Through greatly upset by the affair, Maupertuis managed to produce some of his most significant work at this time, reporting on a biology investigation he had carried out. The System of Nature (1751) emerged from his study of polydactylism (having more than the normal number of fingers and toes). This was the first careful and explicit analysis of a dominant hereditary trait in man, and it showed that polydactylism is transmitted through either the male or female parent. As a result, Maupertuis postulated the existence of hereditary particles present in the eggs and semen of parents, corresponding to the parts of the fetus to be produced. These particles would come together by chemical attraction, each particle from the male parent joining a corresponding particle from the female parent. At certain times, the maternal character would dominate; at other times the paternal character. Maupertuis also envisaged the occasional occurrence of wholly new particles. Lastly, Maupertuis thought it possible that new species might originate through the geographical isolation of such variations. In a tribute to Maupertuis, the biologist Ernst Mayr called him "one of the pioneers of genetics" (The Growth of Biological Thought, 1982).
Yet during these triumphs, the König affair would not go away. In 1752, a hearing was held, from which Maupertuis absented himself. The letter cited by König was declared to be inauthentic and undeserving of credit. König resigned from the Academy-only to issue a public appeal and defense. Voltaire, who was jealous of Maupertuis's influence with the Prussian king, took up König's cause in September 1752 and accused Maupertuis of plagiarism and error, persecution of honest opponents, and tyranny over the Academy. In Diatribe du Docteur Akakia, Voltaire poured invective on ideas that Maupertuis had expressed in various of his works. In Micromégas, he made fun of the voyage to Lapland. Frederick supported Maupertuis and tried to restore good feelings but in vain. Maupertuis could not understand the character of König, whom he had sponsored, or of Voltaire, whose adulation and friendship had turned so quickly to malice and vituperation. Pursued by an unceasing volley of Voltaire's most savage satires, Maupertuis became despondent and withdrew to Saint-Malo until the spring of 1754, when he returned to Berlin at Frederick's insistence. But in 1756 Maupertuis again left for France, deciding to return home by way of Switzerland. He went to Toulouse, and then set out again in May 1758. At Basel, he was warmly welcomed by Johann (II) Bernoulli but was too ill to proceed. On July 27, 1759, he died and was buried at Dornach.
In the Dictionary of Scientific Biography, Bentley Glass says of Maupertuis that "above all he was proud, both of his intelligence and of his accomplishments, and to attack either was to wound him deeply." Indeed, in the end, the wounds to his public reputation proved fatal.
This article was originally published in the July/August 2000 issue of Navigator magazine, The Atlas Society precursor to The New Individualist.