Quicksilver (11 page)

OCTOBER
1713

Hereby it is manifest, that during the time men live without a common power to keep them all in awe, they are in that condition which is called war; and such a war, as is of every man, against every man. For WAR, consisteth not in battle only, or the act of fighting; but in a tract of time, wherein the will to contend by battle is sufficiently known.

—H
OBBES
,
Leviathan

N
OW WALKING OUT ONTO
the upperdeck to find
Minerva
sailing steadily eastwards on calm seas, Daniel’s appalled that anyone ever doubted these matters. The horizon is a perfect line, the sun a red circle tracing a neat path in the sky and proceeding through an orderly series of color-changes, red-yellow-white. Thus Nature.
Minerva
—the human world—is a family of curves. There are no straight lines here. The decks are slightly arched to shed water and supply greater strength, the masts flexed, impelled by the thrust of the sails but restrained by webs of rigging: curve-grids like Isaac’s sundial lines. Of course, wherever wind collects in a sail or water skims around the hull it follows rules that Bernoulli has set down using the calculus—Leibniz’s version.
Minerva
is a congregation of Leibniz-curves navigating according to Bernoulli-rules across a vast, mostly water-covered sphere whose size, precise shape, trajectory through the heavens, and destiny were all laid down by Newton.

One cannot board a ship without imagining shipwreck. Daniel envisions it as being like an opera, lasting several hours and proceeding through a series of Acts.

Act I: The hero rises to clear skies and smooth sailing. The sun is following a smooth and well understood cœlestial curve, the sea is a plane, sailors are strumming guitars and carving
objets d’art
from walrus tusks,
et cetera,
while erudite passengers take the air and muse about grand philosophical themes.

Act II: A change in the weather is predicted based upon readings in the captain’s barometer. Hours later it appears in the distance, a formation of clouds that is observed, sketched, and analyzed. Sailors cheerfully prepare for weather.

Act III: The storm hits. Changes are noted on the barometer, thermometer, clinometer, compass, and other instruments—cœlestial bodies are, however, no longer visible—the sky is a boiling chaos torn unpredictably by bolts—the sea is rough, the ship heaves, the cargo remains tied safely down, but most passengers are too ill or worried to think. The sailors are all working without rest—some of them sacrifice chickens in hopes of appeasing their gods. The rigging glows with St. Elmo’s Fire—this is attributed to supernatural forces.

Act IV: The masts snap and the rudder goes missing. There is panic. Lives are already being lost, but it is not known how many. Cannons and casks are careering randomly about, making it impossible to guess who’ll be alive and who dead ten seconds from now. The compass, barometer,
et cetera,
are all destroyed and the records of their readings swept overboard—maps dissolve—sailors are helpless—those who are still alive and sentient can think of nothing to do but pray.

Act V: The ship is no more. Survivors cling to casks and planks, fighting off the less fortunate and leaving them to drown. Everyone has reverted to a feral state of terror and misery. Huge
waves shove them around without any pattern, carnivorous fish use living persons as food. There is no relief in sight, or even imaginable.

—There might also be an Act VI in which everyone was dead, but it wouldn’t make for good opera so Daniel omits it.

Men of his generation were born during Act V
^*
and raised in Act IV. As students, they huddled in a small vulnerable bubble of Act III. The human race has, actually, been in Act V for most of history and has recently accomplished the miraculous feat of assembling splintered planks afloat on a stormy sea into a sailing-ship and then, having climbed onboard it, building instruments with which to measure the world, and then finding a kind of regularity in those measurements. When they were at Cambridge, Newton was surrounded by a personal nimbus of Act II and was well on his way to Act I.

But they had, perversely, been living among people who were peering into the wrong end of the telescope, or something, and who had convinced themselves that the opposite was true—that the world had once been a splendid, orderly place—that men had made a reasonably trouble-free move from the Garden of Eden to the Athens of Plato and Aristotle, stopping over in the Holy Land to encrypt the secrets of the Universe in the pages of the Bible, and that everything had been slowly, relentlessly falling apart ever since. Cambridge was run by a mixture of fogeys too old to be considered dangerous, and Puritans who had been packed into the place by Cromwell after he’d purged all the people he
did
consider dangerous. With a few exceptions such as Isaac Barrow, none of them would have had any use for Isaac’s sundial, because it didn’t look like an
old
sundial, and they’d prefer telling time wrong the Classical way to telling it right the newfangled way. The curves that Newton plotted on the wall were a methodical document of their wrongness—a manifesto like Luther’s theses on the church-door.

In explaining why those curves were as they were, the Fellows of Cambridge would instinctively use Euclid’s geometry: the earth is a sphere. Its orbit around the sun is an ellipse—you get an ellipse by constructing a vast imaginary cone in space and then cutting through it with an imaginary plane; the intersection of the cone and the plane is the ellipse. Beginning with these primitive objects
(viz. the tiny sphere revolving around the place where the gigantic cone was cut by the imaginary plane), these geometers would add on more spheres, cones, planes, lines, and other elements—so many that if you could look up and see ’em, the heavens would turn nearly black with them—until at last they had found a way to account for the curves that Newton had drawn on the wall. Along the way, every step would be verified by applying one or the other of the rules that Euclid had proved to be true, two thousand years earlier, in Alexandria, where everyone had been a genius.

Isaac hadn’t studied Euclid that much, and hadn’t cared enough to study him well. If he wanted to work with a curve he would instinctively write it down, not as an intersection of planes and cones, but as a series of numbers and letters: an algebraic expression. That only worked if there was a language, or at least an alphabet, that had the power of
expressing
shapes without literally
depicting
them, a problem that Monsieur Descartes had lately solved by (first) conceiving of curves, lines,
et cetera,
as being collections of individual points and (then) devising a way to express a point by giving its coordinates—two numbers, or letters
representing
numbers, or (best of all) algebraic expressions that could in principle be evaluated to
generate
numbers. This translated all geometry to a new language with its own set of rules: algebra. The construction of equations was an exercise in translation. By following those rules, one could create new statements that were true, without even having to think about what the symbols referred to in any physical universe. It was this seemingly occult power that scared the hell out of some Puritans at the time, and even seemed to scare Isaac a bit.

By 1664, which was the year that Isaac and Daniel were supposed to get their degrees or else leave Cambridge, Isaac, by taking the very latest in imported Cartesian analysis and then extending it into realms unknown, was (unbeknownst to anyone except Daniel) accomplishing things in the field of natural philosophy that his teachers at Trinity could not even
comprehend,
much less
accomplish—
they, meanwhile, were preparing to subject Isaac and Daniel to the ancient and traditional ordeal of examinations designed to test their knowledge of Euclid. If they failed these exams, they’d be branded a pair of dimwitted failures and sent packing.

As the date drew nearer, Daniel began to mention them more and more frequently to Isaac. Eventually they went to see Isaac Barrow, the first Lucasian Professor of Mathematics, because he was
conspicuously a better mathematician than the rest. Also because recently, when Barrow had been traveling in the Mediterranean, the ship on which he’d been passenger had been assaulted by pirates, and Barrow had gone abovedecks with a cutlass and helped fight them off. As such, he did not seem like the type who would really care in what order students learned the material. They were right about that—when Isaac showed up one day, alarmingly late in his academic career, with a few shillings, and bought a copy of Barrow’s Latin translation of Euclid, Barrow didn’t seem to mind. It was a tiny book with almost no margins, but Isaac wrote in the margins anyway, in nearly microscopic print. Just as Barrow had translated Euclid’s Greek into the universal tongue of Latin, Isaac translated Euclid’s ideas (expressed as curves and surfaces) into Algebra.

Half a century later on the deck of
Minerva,
that’s all Daniel can remember about their Classical education; they took the exams, did indifferently (Daniel did better than Isaac), and were given new titles: they were now scholars, meaning that they had scholarships, meaning that Newton would not have to go back home to Woolsthorpe and become a gentleman-farmer. They would continue to share a chamber at Trinity, and Daniel would continue to learn more from Isaac’s idle musings than he would from the entire apparatus of the University.

O
NCE HE’S HAD THE OPPORTUNITY
to settle in aboard
Minerva,
Daniel realizes it’s certain that when, God willing, he reaches London, he’ll be asked to provide a sort of affidavit telling what he knows about the invention of the calculus. As long as the ship’s not moving too violently, he sits down at the large dining table in the common room, one deck below his cabin, and tries to organize his thoughts.

Some weeks after we had received our Scholarships, probably in the Spring of 1665, Isaac Newton and I decided to walk out to Stourbridge Fair.

Reading it back to himself, he scratches out
probably in
and writes in
certainly no later than.

Here Daniel leaves much out—it was Isaac who’d announced he was going. Daniel had decided to come along to look after him. Isaac had grown up in a small town and never been to London. To him, Cambridge was a big city—he was completely unequipped for Stourbridge Fair, which was one of the biggest in Europe. Daniel
had been there many times with father Drake or half brother Raleigh, and knew what
not
to do, anyway.

The two of us went out back of Trinity and began to walk downstream along the Cam. After passing by the bridge in the center of town that gives the City and University their name, we entered into a reach along the north side of Jesus Green where the Cam describes a graceful curve in the shape of an elongated S.

Daniel almost writes
like the integration symbol used in the calculus.
But he suppresses that, since that symbol, and indeed the term
calculus
, were invented by Leibniz.

I made some waggish student-like remark about this curve, as curves had been much on our minds the previous year, and Newton began to speak with confidence and enthusiasm—demonstrating that the ideas he spoke of were not extemporaneous speculation but a fully developed theory on which he had been working for some time.

“Yes, and suppose we were on one of those punts,” Newton said, pointing to one of the narrow, flat-bottomed boats that idle students used to mess about on the Cam. “And suppose that the Bridge was the Origin of a system of Cartesian coordinates covering Jesus Green and the other land surrounding the river’s course.”

No, no, no, no. Daniel dips his quill and scratches that bit out. It is an anachronism. Worse, it’s a Leibnizism. Natural Philosophers may talk that way in 1713, but they didn’t fifty years ago. He has to translate it back into the sort of language that Descartes would have used.

“And suppose,” Newton continued, “that we had a rope with regularly spaced knots, such as mariners use to log their speed, and we anchored one end of it on the Bridge—for the Bridge is a fixed point in absolute space. If that rope were stretched tight it would be akin to one of the numbered lines employed by Monsieur Descartes in his Geometry. By stretching it between the Bridge and the punt, we could measure how far the punt had drifted downriver, and in which direction.”

Actually, this is not the way Isaac ever would have said it. But Daniel’s writing this for princes and parliamentarians, not Natural Philosophers, and so he has to put long explanations in Isaac’s mouth.

“And lastly suppose that the Cam flowed always at the same speed, and that our punt matched it. That is what I call a flux-ion—a flowing movement along the curve over time. I think you can see that as we rounded the first limb of the S-curve around Jesus College, where the river bends southward, our fluxion in the north-south direction would be steadily changing. At the moment we passed under the Bridge, we’d be pointed northeast, and so we would have a large northwards fluxion. A minute later, when we reached the point just above Jesus College, we’d be going due east, and so our north-south fluxion would be zero. A minute after that, after we’d curved round and drawn alongside Midsummer Commons, we’d be headed southeast, meaning that we would have developed a large southward fluxion—but even that would reduce and tend back towards zero as the stream curved round northwards again towards Stourbridge Fair.”

He can stop here. For those who know how to read between the lines, this is sufficient to prove Newton had the calculus—or Fluxions, as he called it—in ‘65, most likely ‘64. No point in beating them over the head with it…

Yes, beating someone over the head is the
entire
point.