Writing Nature’s Greatest Book

The Best of All Possible Worlds: Mathematics and Destiny

by Ivar Ekeland
University of Chicago Press, 207 pp., \$25.00

Ivar Ekeland has a Norwegian name and teaches at the University of British Columbia in Canada, but the style and spirit of his book are unmistakably French. The book is a rapid run through the history of the last four hundred years, seen through the eyes of a French mathematician. Mathematics appears as a unifying principle for history. Ekeland moves easily from mathematics to physics, biology, ethics, and philosophy. The central figure of his narrative is the French savant Pierre de Maupertuis (1698–1759), a man of many talents, who formulated the principle of least action in 1745 in a memoir with the title The Laws of Motion and Rest Deduced from a Metaphysical Principle. The principle of least action says that nature arranges all processes so as to minimize a quantity called action, which is a measure of the effort required to bring the processes to completion. The action of any mechanical motion is defined as the moving mass multiplied by the velocity and by the distance moved. Maupertuis was able to demonstrate mathematically that if a collection of objects moves in such a way as to make the total action as small as possible, then the movement obeys Newton’s laws of motion. Thus the whole science of Newtonian mechanics follows from the principle of least action.

Maupertuis was dazzled by the beauty of his discovery. “How satisfying for the human spirit,” he wrote, “to contemplate these laws, so beautiful and simple, which may be the only ones that the Creator and Ordainer of things has established in matter to sustain all phenomena of this visible world.” He went on to identify action with evil, so that the principle of least action became a principle of maximum goodness. He concluded that God has ordered the universe so as to maximize goodness. The world that we live in is the best of all the possible worlds that God might have created. This simple principle unites science with history and morality. Mathematics is the key to the understanding of human destiny.

One of the contemporaries of Maupertuis was Voltaire, the great skeptic, who demolished Maupertuis’s optimistic philosophy in a book with the title Story of Doctor Akakia and the Native of Saint-Malo. Akakia is Greek for “absence of evil,” and the native of Saint-Malo is Maupertuis. “The native of Saint-Malo,” Voltaire writes, “had long fallen a prey to a chronic sickness, which some call philotimia [Greek for love of honors] and others philocratia [Greek for love of power].” Voltaire’s book sold well and Maupertuis’s day of glory ended. After Maupertuis died, Voltaire made him posthumously ridiculous by writing the novel Candide, in which Maupertuis appears as the optimistic philosopher Pangloss, wandering from one disaster to another but unshaken in his belief that “all is well that ends well in the best of all possible worlds.”

Maupertuis was in fact no Pangloss. He spent only a small part of his time as an optimistic philosopher. He was also a brilliant scientist and a…