Isaac Newton (23 page)

He was committed to his corpuscular theory: that rays of light are “very small Bodies emitted from shining Substances.”
²³
Thus he seemed to take a wrong turn: over the next two centuries, researchers thrived by treating light as waves, choosing smoothness over granularity in their fundamental view of energy. The mathematical treatment of colors depended on wavelength and frequency. Until, that is, Einstein showed that light comes in quanta after all. Yet it was Newton, more than any other experimenter, who established the case for light waves. With an accuracy measured in hundredths of an inch, he had studied colored rings in thin films.
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He found it impossible to understand this as anything but a form of periodicity—oscillation or vibration. Diffraction, too, showed unmistakable signs of periodicity. He could neither reconcile these signs with his corpuscular theory nor omit them from his record. He could not see
how a particle could be a wave, or embody waviness. He resorted to an odd word:
fits
, as in “fits of easy reflection” and “fits of easy transmission.” “Probably it is put into such fits at its first emission from luminous bodies, and continues in them during all its progress. For these Fits are of a lasting nature.”
²⁵

Opticks
stretched to cosmology and metaphysics—the more as Newton extended it in new printings. He could speak with authority now. He used his pulpit to issue a manifesto. He repeated again and again these dicta: that nature is consonant; that nature is simple; that nature is conformable to herself.
²⁶
Complexity can be reduced to order; the laws can be found. Space is an infinite void. Matter is composed of atoms—hard and impenetrable. These particles attract one another by unknown forces: “It is the Business of experimental Philosophy to find them out.”
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He was charging his heirs and followers with a mission, the perfection of natural philosophy. He left them a task of further study, “the Investigation of difficult Things by the Method of Analysis.”
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They need only follow the signs and the method.

As President of the Royal Society he employed two new Curators of Experiments.
²⁹
Sometimes he had them demonstrate or extend features of the
Principia
—once, for example, dropping lead weights and inflated hogs’ bladders from a church tower—but more often he tried to spur experiments on light, heat, and chemistry. One line of experiments explored the electric effluvium, creating a luminous glow, for example, in a glass tube rubbed with cloth, and testing the tube’s attractive power with a feather. Some spirit, it seemed, could penetrate glass, move small objects, and emit light—but what? In revising the
Opticks
he drafted
new “Queries”: for example, “Do not all bodies therefore abound with a very subtle, but active, potent, electric spirit by which light is emitted, refracted, & reflected, electric attractions and fugations are performed …?”
³⁰
He suppressed these; even so, the trail of electrical research in the next century seemed to lead back to the
Opticks
.

“I have only begun the analysis of what remains to be discover’d,” he wrote, “hinting several things about it, and leaving the Hints to be examin’d and improv’d by the farther Experiments and Observations of such as are inquisitive.”
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Active principles—shades of alchemy—remained to be found out: the cause of gravity, of fermentation, of life itself. Only such active principles could explain the persistence and variety of motion, the constant heating of the sun and the inward parts of the earth. Only such principles stand between us and death. “If it were not for these Principles,” he wrote,

the Earth, Planets, Comets, Sun, and all things in them, would grow cold and freeze, and become inactive Masses; and all Putrefaction, Generation, Vegetation and Life would cease.
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Word of the
Opticks
spread slowly through Europe; then a bit faster after a Latin edition appeared in 1706.
³³
Father Nicolas Malebranche, aging theologian and Cartesian, reviewed the
Opticks
with the remark, “Though Mr. Newton is no physicist, his book is very interesting …”
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Rivals who had never managed to dispute his mathematics found new opportunities in his metaphysics. He had spoken of infinite space as the “sensorium” of God, by which he meant to unify omnipresence and omniscience. God, being
everywhere, is immediately and perfectly aware. But the difficult word, suggesting a bodily organ for divine sensation, left him vulnerable to theological counterattack: “I examined it and laughed at the idea,” Leibniz told Bernoulli—these eminent admirers now turned enemies of Newton. “As if God, from whom everything comes, should have need of a sensorium. This man has little success with Metaphysics.”
³⁵
And again Leibniz abhorred Newton’s vacuum. A world of vast emptiness—unacceptable. Planets attracting one another across this emptiness—absurd. He objected to Newton’s conception of absolute space as a reference frame for analyzing motion, and he mocked the idea of gravitation. For one body to curve round another, with nothing pushing or impelling it—impossible. Even
supernatural
. “I say, it could not be done without a miracle.”
³⁶

By now he and Newton were in open conflict. Leibniz, four years Newton’s junior, had seen far more of the world—a stoop-shouldered, tireless man of affairs, lawyer and diplomat, cosmopolitan traveler, courtier to the House of Hanover. The two men had exchanged their first letters—probing and guarded—in the late 1670s. In the realm of mathematics, it was paradoxically difficult to stake effective claims to knowledge without disclosure. One long letter from Newton, for Leibniz via Oldenburg, asserted possession of a “twofold” method for solving inverse problems of tangents “and others more difficult” and then concealed the methods in code:

At present I have thought fit to register them both by transposed letters … 
5accdæ10effh11i4l3m9n6oqqr8s11t9v3x:
11ab3cdd10eæg10illrm7n603p3q6r5s11t8vx, 3acæ4egh
5i414m5n8oq4r3s6t4vaaddæeeeeeiijmmnnooprrsssssttuu
.
³⁷

Communicating with Leibniz: The key to the cryptogram
.
(illustration credit 14.1)

He retained the key in a dated “memorandum” to himself. Still, impenetrable though this cryptogram was, Newton had shown Leibniz powerful methods: the binomial theorem, the use of infinite series, the drawing of tangents, and the finding of maxima and minima.

Leibniz, in his turn, chose not to acknowledge these when, in 1684 and 1686, he published his related mathematical work as “A New Method for Maxima and Minima, and Also for Tangents, Which Stops at Neither Fractions nor Irrational Quantities, and a Singular Type of Calculus for These” in the new German journal
Acta Eruditorum
. He offered rules for computing derivatives and integrals, and an innovative notation:
dx, f(x)
, ∫
x
. This was a pragmatic mathematics, a mathematics without proof, an algorithm for solving “the most difficult and most beautiful problems.”
³⁸
With this new name,
calculus
, it traveled slowly toward England, just before word of the
Principia
, with its classic geometrical style concealing new tools of analysis, made its way across the Continent.

Now, decades later, Newton had a purpose in publishing his pair of mathematical papers with the
Opticks
, and he made his purpose plain. In particular, “On the Quadrature of Curves” laid out for the first time his method of fluxions. In effect, despite the utterly different notation, this was Leibniz’s differential calculus. Where Leibniz worked with successive differences, Newton spoke of rates of flow changing through successive moments of time. Leibniz was chunklets—discrete bits. Newton was the continuum. A deep understanding of the calculus ultimately came to demand a mental bridge from one to the other, a translation and reconciliation of two seemingly incompatible symbolic systems.

Newton declared not only that he had made his discoveries by 1666 but also that he had described them to Leibniz. He released the correspondence, anagrams and all.
³⁹
Soon an anonymous counterattack appeared in
Acta Eruditorum
suggesting that Newton had employed Leibniz’s methods, though calling them “fluxions” instead of “Leibnizian differences.” This anonymous reviewer was Leibniz. Newton’s disciples fired back in the
Philosophical Transactions
, suggesting that it was Leibniz who, having read Newton’s description of his methods, then published “the same Arithmetic under a different name and using a different notation.”
⁴⁰
Between each of these thrusts and parries, years passed. But a duel was under way. Partisans joined both sides, encouraged by tribal loyalties more than any real knowledge of the documentary history. Scant public record existed on either side.

The principals joined the fray openly in 1711. A furious letter from Leibniz arrived at the Royal Society, where it was read aloud and “deliver’d to the President to consider
the contents thereof.”
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The society named a committee to investigate “old letters and papers.”
⁴²
Newton provided these. Early correspondence with John Collins came to light; Leibniz had seen some of it, all those years before. The committee produced a document without precedent: a detailed, analytical history of mathematical discovery. No clearer account of the calculus existed, but exposition was not the point; the report was meant as a polemic, to condemn Leibniz, accusing him of a whole congeries of plagiarisms. It judged Newton’s method to be not only the first—“by many years”—but also more elegant, more natural, more geometrical, more useful, and more certain.
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It vindicated Newton with eloquence and passion, and no wonder: Newton was its secret author.

The Royal Society published it rapidly. It also published a long assessment of the report, in the
Philosophical Transactions
—a diatribe, in fact. This, too, was secretly composed by Newton. Thus he anonymously reviewed his own anonymous report, and in doing so he spoke of candor:

It lies upon [Leibniz], in point of Candor, to tell us what he means by pretending to have found the Method before he had found it.

It lies upon him, in point of Candor, to make us understand that he pretended to this Antiquity of his Invention with some other Design than to rival and supplant Mr. Newton.

When he wrote those Tracts he was but a Learner, and this he ought in candour to acknowledge.

He declared righteously: “no Man is a Witness in his own Cause. A Judge would be very unjust, and act contrary to the Laws of all Nations, who should admit any Man to be a Witness in his own Cause.”
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Newton wrote many private drafts about Leibniz, often the same ruthless polemic again and again, varying only by a few words. The priority dispute spilled over into the philosophical disputes, the Europeans sharpening their accusation that his theories resorted to miracles and occult qualities. What reasoning, what causes, should be permitted? In defending his claim to first invention of the calculus, Newton stated his rules for belief, proposing a framework by which his science—any science—ought to be judged. Leibniz observed different rules. In arguing against the miraculous, the German argued theologically. By pure reason, for example, he argued from the perfection of God and the excellence of his workmanship to the impossibility of the vacuum and of atoms. He accused Newton—and this stung—of implying an imperfect God.

Newton had tied knowledge to experiments. Where experiments could not reach, he had left mysteries explicitly unsolved. This was only proper, yet the Germans threw it back in his face: “as if it were a Crime to content himself with Certainties and let Uncertainties alone.”

“These two Gentlemen differ very much in Philosophy,” Newton declared under cover of anonymity.

The one teaches that Philosophers are to argue from Phænomena and
Experiments
to the Causes thereof, and thence to the Causes of those Causes, and so on till we come to the first Cause; the other that all the Actions of the first Cause are Miracles, and all the Laws imprest on Nature by the Will of God are perpetual Miracles and occult Qualities, and therefore not to be considered in Philosophy. But must the constant and universal Laws of Nature, if derived from the Power of God or the Action of a Cause not yet known to us, be called Miracles and occult Qualities?
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