The Clockwork Universe: Isaac Newton, the Royal Society, and the Birth of the Modern World - Edward Dolnick (2011)

Part III. Into the Light

Chapter 50. Only Three People

From the beginning, the Principia had a reputation for difficulty. When Newton brushed by some students on the street one day, he heard one of them mutter, “There goes the man that writt a book that neither he nor any body else understands.” It was almost true. When the Principia first appeared, it baffled all but the ablest scientists and mathematicians. (The first print run was tiny, between three and four hundred.) “It is doubtful,” wrote the historian Charles C. Gillispie, “whether any work of comparable influence can ever have been read by so few persons.”

The historian A. Rupert Hall fleshed out Gillispie’s remark. Perhaps half a dozen scientists, Hall reckoned, fully grasped Newton’s message on first reading it. Their astonished praise, coupled with efforts at recasting Newton’s arguments, quickly drew new admirers. In time popular books would help spread Newton’s message. Voltaire wrote one of the most successful, Elements of Newton’s Philosophy, much as Bertrand Russell would later write ABC of Relativity. An Italian writer produced Newtonianism for Ladies, and an English author using the pen name Tom Telescope wrote a hit children’s book.

But in physics a mystique of impenetrability only adds to a theory’s allure. In 1919, when the New York Times ran a story on Einstein and relativity, a subheadline declared, “A Book for 12 Wise Men.” A smaller headline added, “No More in All the World Could Comprehend It.” A few years later a journalist asked the astronomer Arthur Eddington if it was true that only three people in the world understood general relativity. Eddington thought a moment and then replied, “I’m trying to think who the third person is.”

Two features, beyond the difficulty of its mathematical arguments, made the Principia so hard to grasp. The first reflected Newton’s hybrid status as part medieval genius, part modern scientist. Through the whole vast book Newton relies on concepts from calculus—infinitesimals, limits, straight lines homing in ever closer to curves—that he had invented two decades before. But he rarely mentions calculus explicitly or explains the strategy behind his arguments, and he makes only indirect use of calculus’s labor-saving machinery.

Instead he makes modern arguments using old-fashioned tools. What looks at a glance like classical geometry turns out to be a more exotic beast, a kind of mathematical centaur. Euclid would have been baffled. “An ancient and venerable mathematical science had been pressed into service in a subject area for which it seems inappropriate,” writes one modern physicist. “Newton’s geometry seems to shriek and groan under the strain, but it works perfectly.”

There are almost no other historical examples of so strange a performance as this use/nonuse of calculus. To get something of its flavor, we have to imagine far-fetched scenarios. Think, for instance, of a genius who grew up using Roman numerals but then invented Arabic numerals. And then imagine that he conceived an incredibly complex theory that relied heavily on the special properties of Arabic numerals—the way they make calculations easy, for instance. Finally, imagine that when he presented that theory to the world he used no Arabic numerals at all, but only Roman numerals manipulated in obscure and never-explained ways.

Decades after the Principia, Newton offered an explanation. In his own investigations, he said, he had used calculus. Then, out of respect for tradition and so that others could follow his reasoning, he had translated his findings into classical, geometric language. “By the help of the new Analysis [i.e., calculus] Mr. Newton found out most of the Propositions in his Principia Philosophiae,” he wrote, referring to himself in the third person, but then he recast his mathematical arguments so that “the System of the Heavens might be founded upon good Geometry.”

Newton’s account made sense, and for centuries scholars took it at face value. He knew he was presenting a revolutionary theory. To declare that he had reached startling conclusions by way of a strange, new technique that he had himself invented would have been to invite trouble and doubt. One revolution at a time.

But it now turns out that Newton did not use calculus’s shortcuts in private and then reframe them. “There is no letter,” declared one of the most eminent Newtonians, I. Bernard Cohen, “no draft of a proposition, no text of any kind—not even a lone scrap of paper—that would indicate a private mode of composition other than the public one we know in the Principia.” The reason that Newton claimed otherwise was evidently to score points against Leibniz. “He wanted,” wrote Cohen, “to show that he understood and was using the calculus long before Leibniz.”

This is curious, for Newton had understood calculus long before Leibniz, and so it would have made perfect sense for him to have drawn on its hugely powerful techniques. But he did not. The reason, evidently, was that he was such a geometric virtuoso that he felt no impulse to deploy the powerful new arsenal that he himself had built. “As we read the Principia,” the nineteenth-century scientist William Whewell would write, “we feel as when we are in an ancient armoury where the weapons are of gigantic size; and as we look at them, we marvel what manner of men they were who could use as weapons what we can scarcely lift as a burden.”