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.
ONCE HE’S HAD THE OPPORTUNITYto 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 down-river, 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 fluxion-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.
Almost five thousand years agone, there were pilgrims walking to the Celestial City, as these two honest persons are; and Beelzebub, Apollyon, and Legion, with their companions, perceiving by the path that the pilgrims made that their way to the City lay through this town of Vanity, they contrived here to set up a fair; a fair wherein should be sold all sorts of vanity, and that it should last all the year long. Therefore at this Fair are all such merchandise sold, as houses, lands, trades, places, honours, preferments, titles, countries, kingdoms, lusts, pleasures, and delights of all sorts, as whores, bawds, wives, husbands, children, masters, servants, lives, blood, bodies, souls, silver, gold, pearls, precious stones, and what not.
And moreover, at this Fair there is at all times to be seen jugglings, cheats, games, plays, fools, apes, knaves, and rogues, and that of all sorts.
-JOHNBUNYAN,The Pilgrim’s Progress
IT WAS LESS THAN ANhour’s walk to the Fair, strolling along gently sloped green banks with weeping-willows, beneath whose canopies were hidden various prostrate students. Black cattle mowed the grass unevenly and strewed cow-pies along their way. At first the river was shallow enough to wade across, and its bottom was carpeted with slender fronds that, near the top, were bent slightly downstream by the mild current. “Now, there is a curve whose fluxion in the downstream direction is nil at the point where it is rooted in the bottom-that is to say, it rises vertically from the mud-but increases as it rises.”