Through the years Leibniz’s attempts to engage Georg Ludwig had met with about the success one would expect, but the women of the Hanoverian court were as intellectual as the men were crude. While the dukes collected mistresses and plotted murder, their duchesses occupied themselves with philosophy. Georg Ludwig’s mother, Sophia, read through Spinoza’s controversial writings as soon as they were published and spent long hours questioning Leibniz about the views of the Dutch heretic.
Sophia was only the first of Leibniz’s royal devotees. Sophia’s daughter Sophia Charlotte (sister to the future King George) had an even closer relationship with Leibniz. And yet a third high-born woman forged a still closer bond. This was Caroline, a twenty-one-year-old princess and friend of Sophia Charlotte. Leibniz became her friend and tutor. Soon after, Caroline married one of Georg Ludwig’s brothers. When she was whisked off to England in 1714, Caroline became princess of Wales and in time, as the wife of King George II, queen of England. Leibniz had allies in the highest of circles.
But he was stuck in Germany, and none of his royal friends seemed inclined to send for him. From that outpost, he tried to enlist Caroline on his side in his ongoing war against Newton. Their battle represented not just a confrontation between two men, Leibniz insisted, but between two nations. German pride was at stake. “I dare say,” Leibniz wrote to Caroline, “that if the king were at least to make me the equal of Mr. Newton in all things and in all respects, then in these circumstances it would give honor to Hanover and to Germany in my name.”
The appeal to national pride proved ineffective. Newton was all but worshipped in England—as we have noted, Caroline had met him on various grand occasions at court—and the newly arrived king had no desire to challenge English self-regard just to soothe the hurt feelings of his pet philosopher. In any case, King George had his own plans for Leibniz. They did not include science. Leibniz’s chief duty, the king reminded him, was to continue his history of the House of Hanover. He had bogged down somewhere around the year 1000.
The wonders of calculus, and the injustice of Newton’s theft of it, concerned the king not at all. What was life and death for Leibniz was sport for King George. “The king has joked more than once about my dispute with Mr. Newton,” Leibniz lamented.
From his exile in Hanover, Leibniz wrote to Caroline attacking Newton’s views on science and theology. Caroline studied the letters intently—they dealt mainly with such questions as whether God had left the world to run on its own or whether He continued to step in to fine-tune it—and she passed them along to a Newton stand-in named Samuel Clarke. On some questions Caroline wrote directly to Newton himself. Clarke composed responses to Leibniz (with Newton’s help). The correspondence was soon published, and the so-called Leibniz-Clarke papers became, in one historian’s judgment, “perhaps the most famous and influential of all philosophical correspondences.”
But to Caroline’s exasperation, Leibniz persisted in setting aside deep issues in theology and circling back instead to his priority battle with Newton. The princess scolded her ex-tutor for his “vanity.” He and Newton were “the great men of our century,” Caroline wrote, “and both of you serve a king who merits you.” Why draw out this endless fight? “What difference does it make whether you or Chevalier Newton discovered the calculus?” Caroline demanded.
A good question. The world had the benefit of this splendid new tool, after all, whoever had found it. But to Newton and Leibniz, the answer to Caroline’s question was simple. It made all the difference in the world.
Chapter Forty-Four
Battle’s End
From its earliest days, science has been a dueling ground. Disputes are guaranteed, because good ideas are “in the air,” not dreamed up out of nowhere. Nearly every breakthrough—the telescope, calculus, the theory of evolution, the telephone, the double helix—has multiple parents, all with serious claims. But ownership is all, and scientists turn purple with rage at the thought that someone has won praise for stolen insights. The greats battle as fiercely as the mediocre. Galileo wrote furiously of rivals who claimed that they, not he, had been first to see sunspots. They had, he fumed, “attempted to rob me of that glory which was mine.” Even the peaceable Darwin admitted, in a letter to a colleague urging him to write up his work on evolution before he was scooped, that “I certainly should be vexed if anyone were to publish my doctrines before me.”
What vexed the mild Darwin sent Newton and Leibniz into apoplectic rages. The reasons had partly to do with mathematics itself. All scientific feuds tend toward the nasty; feuds between mathematicians drip with extra venom. Higher mathematics is a peculiarly frustrating field. So difficult is it that even the best mathematicians often feel that the challenge is just too much, as if a golden retriever had taken on the task of understanding the workings of the internal combustion engine. The rationalizations so helpful elsewhere in science—she had a bigger lab, a larger budget, better colleagues—are no use here. Wealth, connections, charm make no difference. Brainpower is all.
“Almost no one is capable of doing significant mathematics,” the American mathematician Alfred W. Adler wrote a few decades ago. “There are no acceptably good mathematicians. Each generation has its few great mathematicians, and mathematics would not even notice the absence of the others. They are useful as teachers, and their research harms no one, but it is of no importance at all. A mathematician is great or he is nothing.”
That is a romantic view and probably overstated, but mathematicians take a perverse pride in great-man theories, and they tend to see such doctrines as simple facts. The result is that mathematicians’ egos are both strong and brittle, like ceramics. Where they focus their gaze makes all the difference. If someone compares himself with his neighbors, then he might preen himself on his membership in an arcane priesthood. But if he judges himself not by whether he knows more mathematics than most people but by whether he has made any real headway at exploring the immense and dark mathematical woods, then all thoughts of vanity flee, and only puniness remains.
In the case of calculus, the moment of confrontation between Newton and Leibniz was delayed for a time, essentially by incredulity. Neither genius could quite believe that anyone else could have seen as far as he had. Newton enjoyed his discoveries all the more because they were his to savor in solitude, as if he were a reclusive art collector free to commune with his masterpieces behind closed doors. But Newton’s retreat from the world was not complete. He could abide adulation but not confrontation, and he had shared some of his mathematical triumphs with a tiny number of appreciative insiders. He ignored their pleas that he tell everyone what he had told them. The notion that his discoveries would speed the advance of science, if only the world knew of them, moved Newton not at all.
For Leibniz, on the other hand, his discoveries had value precisely because they put his merits on display. He never tired of gulping down compliments, but his eagerness for praise had a practical side, too. Each new achievement served as a golden entry on the résumé that Leibniz was perpetually thrusting before would-be patrons.
In Newton’s view, to unveil a discovery meant to offer the unworthy a chance to paw at it. In Leibniz’s view, to proclaim a discovery meant to offer the world a chance to shout its hurrahs.
In history’s long view, the battle ended in a stalemate. Historians of mathematics have scoured the private papers of both men and found clear evidence that Newton and Leibniz discovered calculus independently, each man working on his own. Newton was first, in 1666, but he only published decades later, in 1704. Leibniz’s discovery followed Newton’s by nine years, but he published his findings first, in 1684. And Leibniz, who had a gift for devising useful notations, wrote up his discoveries in a way that other mathematicians found easy to understand and build upon. (Finding the right notation to convey a new concept sounds insignificant, like choosing the right typeface for a book, but in mathematics the choice of symbols can save an idea or doom it. A child can multiply 17 by 19
. The greatest scholars in Rome would have struggled with XVII times XIX.)47
The symbols and language that Leibniz devised are still the ones that students learn today. Newton’s discovery was identical, at its heart, and in his masterly hands it could be turned to nearly any task. But Newton’s calculus is a museum piece today, while a buffed and honed version of Leibniz’s remains in universal use. Newton insisted that because he had found calculus before anyone else, there was nothing to debate. Leibniz countered that by casting his ideas in a form that others could follow, and then by telling the world what he had found, he had thrown open a door to a new intellectual kingdom.
So he had, and throughout the 1700s and into the 1800s, European mathematicians inspired by Leibniz ran far in front of their English counterparts. But in their lifetimes, Newton seemed to have won the victory. To stand up to Newton at his peak of fame was nearly hopeless. The awe that Alexander Pope would later encapsulate—“Nature and nature’s laws lay hid in night, / God said ‘Let Newton be!’ and all was light”—had already become common wisdom.
The battle between the two men smoldered for years before it burst into open flames. In 1711, after about a decade of mutual abuse, Leibniz made a crucial tactical blunder. He sent the Royal Society a letter—both he and Newton were members—complaining of the insults he had endured and asking the Society to sort out the calculus quarrel once and for all. “I throw myself on your sense of justice,” he wrote.
He should have chosen a different target. Newton, who was president of the Royal Society, appointed an investigatory committee “numerous and skilful and composed of Gentlemen of several Nations.” In fact, the committee was a rubber stamp for Newton himself, who carried out its inquiry single-handedly and then issued his findings in the committee’s name. The report came down decisively in Newton’s favor. With the Royal Society’s imprimatur, the long, damning report was distributed to men of learning across Europe. “We take the Proper Question to be not who Invented this or that Method but who was the first Inventor,” Newton declared, for the committee.
The report went further. Years before, it charged, Leibniz had been offered surreptitious peeks at Newton’s mathematical papers. There calculus was “Sufficiently Described” to enable “any Intelligent Person” to grasp its secrets. Leibniz had not only lagged years behind Newton in finding calculus, in other words, but he was a sneak and a plagiarist as well.
Next the Philosophical Transactions, the Royal Society’s scientific journal, ran a long article reviewing the committee report and repeating its anti-Leibniz charges. The article was unsigned, but Newton was the author. Page after page spelled out the ways in which “Mr. Leibniz” had taken advantage of “Mr. Newton.” Naturally Mr. Leibniz had his own version of events, but the anonymous author would have none of it. “Mr. Leibniz cannot be a witness in his own Cause.”
Finally the committee report was republished in a new edition accompanied by Newton’s anonymous review. The book carried an anonymous preface, “To the Reader.” It, too, was written by Newton.
Near the end of his life Newton reminisced to a friend about his long-running feud. “He had,” he remarked contentedly, “broke Leibniz’ heart.”
Chapter Forty-Five
The Apple and the Moon
The greatest scientific triumph of the seventeenth century, Newton’s theory of universal gravitation, was in a sense a vehicle for showing off the power and range of the mathematical techniques that Newton and Leibniz had fought to claim. Both men discovered calculus, but it was Newton who provided a stunning demonstration of what it could do.
Until 1687, Isaac Newton had been known mainly, to those who knew him at all, as a brilliant mathematician who worked in self-imposed isolation. No recluse ever broke his silence more audaciously.
Fame came with the publication of the Principia. Newton had been at Cambridge for two decades. University rules required that he teach a class or two, but this did not impose much of a burden, either on Newton or anyone else. “So few went to hear Him, & fewer that understood him,” one contemporary noted, “that oftimes he did in a manner, for want of Hearers, read to ye Walls.”
As Newton told the story, his rise to fame had indeed begun with the fall of an apple. In his old age he occasionally looked back on his career, and eager listeners noted down every word. A worshipful young man named John Conduitt, the husband of Newton’s niece, was one of several who heard the apple story firsthand. “In the year 1666 he retired again from Cambridge . . . to his mother in Lincolnshire,” Conduitt wrote, “& whilst he was musing in a garden it came into his thought that the power of gravity (which brought an apple from the tree to the ground) was not limited to a certain distance from the earth but that this power must extend much farther than was usually thought. Why not as high as the moon said he to himself & if so that must influence her motion & perhaps retain her in her orbit, whereupon he fell a calculating. . . .”
The story, which is the one thing everyone knows about Isaac Newton, may well be a myth.48 Despite his craving for privacy, Newton was acutely aware of his own legend, and he was not above adding a bit of gloss here and there. Historians who have scrutinized his private papers believe that his understanding of gravity dawned slowly, over several years, rather than in a flash of insight. He threw in the apple, some suspect, simply for color.
In any case, it wouldn’t have taken an apple to remind Newton that objects fall. Everyone had always known that. The point was to look beyond that fact to the questions it raised. If apples fell to the ground because some force drew them, did that force extend from the tree’s branches to its top? And beyond the top to . . . to where? To the top of a mountain? To the clouds? To the moon? Those questions had seldom been asked. There were many more. What about the apple when it was not falling? An apple in a tree stays put because it is attached to the branch. No surprise there. But what about the moon? What holds the moon up in the sky?
Before Newton the answer had two parts. The moon stayed in the sky because that was its natural home and because it was made of an ethereal substance that was nothing like the heavy stuffing of bodies here on Earth. But that would no longer do. If the moon was just a big rock, as telescopes seemed to show, why didn’t it fall like other rocks?
The answer, Newton came to see, was that it does fall. The breakthrough was to see how that could be. How could something fall and fall but never arrive? Newton’s answer in the case of the moon, a natural satellite, ran much like the argument we have already seen, for an artificial satellite.
We tend to forget the audacity of that explanation, and Newton’s plain tone helps us along in our mistake. “I began to think of gravity extending to ye orb of the Moon,” he recalled, as if nothing could have been more natural. Newton began to give serious thought, in other words, to asking whether the same force that pulled an apple to the Earth also pulled the moon toward the Earth. But this is to downplay two feats of intellectual daring. Why should anyone have thought that the moon is falling, first of all, when it is plainly hanging placidly in the sky, far beyond our reach or the reach of anything else? And even if we did make the large concession that it is falling, second of all, why should that fall have anything in common with an apple’s fall? Why would anyone presume that the same rules governed realms as different as heaven and Earth?
But that is exactly what Newton did presume, for aesthetic and philosophical reasons as much as for scientific ones. Throughout his life Newton believed that God operated in the simplest, neatest, most efficient way imaginable. That principle served as his starting point whether he was studying the Bible or the natural world. (We have already noted his insistence that “it is ye perfection of God’s works that they are all done with ye greatest simplicity.”) The universe had no superfluous parts or forces for exactly the reason that a clock had no superfluous wheels or springs. And so, when Newton’s thoughts turned to gravity, it was all but inevitable that he would wonder how much that single force could explain.
Newton’s first task was to find a way to turn his intuition about the sweep and simplicity of nature’s laws into a specific, testable prediction. Gravity certainly seemed to operate here on Earth; if it did reach all the way to the moon, how would you know it? How would gravity reveal itself? To start with, it seemed clear that if gravity did extend to the moon, its force must diminish over that vast distance. But how much? Newton had two paths to an answer. Fortunately, both gave the same result.
First, he could try intuition and analogy. If we see a bright light ten yards off, say, how bright will it be if we move it twice as far away, to twenty yards distance? The answer was well-known. Move a light twice as far away and it will not be half as bright, as you might guess, but only one-fourth as bright. Move it ten times as far away and it will be one-hundredth as bright. (The reason has to do with the way light spreads. Sound works the same way. A piano twenty yards away sounds only one-fourth as loud as a piano ten yards away.)
So Newton might have been tempted to guess that the pull of gravity decreases with distance in the same way that the brightness of light does. Physicists today talk about “inverse-square laws,” by which they mean that some forces weaken not just in proportion to distance but in proportion to distance squared. (It would later turn out that electricity and magnetism follow inverse-square laws, too.)
A second way of looking at gravity’s pull gave the same answer. By combining Kepler’s third law, which had to do with the size and speed of the planets’ orbits, with an observation of his own about objects traveling in a circle, Newton calculated the strength of gravity’s pull. Again, he found that gravity obeyed an inverse-square law.
Now came the test. If gravity actually pulled on the moon, how much did it pull? Newton set to work. He knew that the moon orbits the Earth. It travels in a circle, in other words, and not in a straight line. (To be strictly accurate, it travels in an ellipse that is almost but not quite circular, but the distinction does not come into play here.) He knew, as well, what generations of students have since had drummed into them as “Newton’s first law”—in modern terms, a body in motion will travel in a straight line at a steady speed unless some force acts on it (and a body at rest will stay at rest unless some force acts on it).
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