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.”

Here Daniel was a bit lost. “Fluxion seems to mean a flowing over time-so it makes perfect sense when you apply the word to the position of a punt on a river, which is, as a matter of fact, flowing over time. But now you seem to be applying it to the shape of a weed, which is not flowing-it’s just standing there sort of bent.”

“But Daniel, the virtue of this approach is that it doesn’t matter what the actual physical situation is, a curve is ever a curve, and whatever you can do to the curve of a river you can do just as rightly to the curve of a weed -we are free from all that old nonsense now.” Meaning the Aristotelian approach, in which such easy mixing of things with obviously different natures would be abhorrent. All that mattered henceforth, apparently, was what form they adopted when translated into the language of analysis. “Translating a thing into the analytical language is akin to what the alchemist does when he extracts, from some crude ore, a pure spirit, or virtue, or pneuma. The f?ces-the gross external forms of things-which only mislead and confuse us-are cast off to reveal the underlying spirit. And when this is done we may learn that some things that are superficially different are, in their real nature, the same.”

Very soon, as they left the colleges behind, the Cam became broader and deeper and instantly was crowded with much larger boats. Still, they were not boats for the ocean-they were long, narrow, and flat-bottomed, made for rivers and canals, but with far greater displacement than the little punts. Stourbridge Fair was already audible: the murmur of thousands of haggling buyers and sellers, barking of dogs, wild strains from bagpipes and shawms whipping over their heads like twists of bright ribbon unwinding in the breeze. They looked at the boat-people: Independent traders in black hats and white neck-cloths, waterborne Gypsies, ruddy Irish and Scottish men, and simply Englishmen with complicated personal stories, negotiating with sure-footed boat-dogs, throwing buckets of mysterious fluids overboard, pursuing domestic arguments with unseen persons in the tents or shacks pitched on their decks.

Then they rounded a bend, and there was the Fair, spread out in a vast wedge of land, bigger than Cambridge, even more noisy, much more crowded. It was mostly tents and tent-people, who were not their kind of people-Daniel watched Isaac gain a couple of inches in height as he remembered the erect posture that Puritans used to set a better example. In some secluded parts of the Fair (Daniel knew) serious merchants were trading cattle, timber, iron, barrelled oysters-anything that could be brought upriver this far on a boat, or transported overland in a wagon. But this wholesale trade wanted to be invisible, and was. What Isaac saw was a retail fair whose size and gaudiness was all out of proportion to its importance, at least if you went by the amount of money that changed hands. The larger avenues (which meant sluices of mud with planks and logs strewn around for people to step on, or at least push off against) were lined with tents of rope-dancers, jugglers, play-actors, puppet shows, wrestling-champions, dancing-girls, and of course the speciality prostitutes who made the Fair such an important resource for University students. But going up into the smaller byways, they found the tables and stalls and the cleverly fashioned unfolding wagons of traders who’d brought goods from all over Europe, up the Ouse and the Cam to this place to sell them to England.

Daniel and Isaac roamed for the better part of an hour, ignoring the shouts and pleadings of the retailers on all sides, until finally Isaac stopped, alert, and sidestepped over to a small folding display-case-on-legs that a tall slender Jew in a black coat had set up. Daniel eyed this Son of Moses curiously-Cromwell had re-admitted these people to England only ten years previously, after they’d been excluded for centuries, and they were as exotic as giraffes. But Isaac was staring at a constellation of gemlike objects laid out on a square of black velvet. Noting his interest, the Kohan folded back the edges of the cloth to reveal many more: concave and convex lenses, flat disks of good glass for grinding your own, bottles of abrasive powder in several degrees of coarseness, and prisms.

Isaac signalled that he would be willing to open negotiations over two of the prisms. The lens-grinder inhaled, drew himself up, and blinked. Daniel moved round to a supporting position behind and to the side of Isaac. “You have pieces of eight,” the circumcised one said-midway between an assertion and a question.

“I know that your folk once lived in a kingdom where that was the coin of the realm, sir,” Isaac said, “but…”

“You know nothing-my people did not come from Spain. They came from Poland. You have French coins-the louis d’or?”

“The louis d’or is a beautiful coin, befitting the glory of the Sun King,” Daniel put in, “and probably much used wherever you came from-Amsterdam?”

“London. You intend to compensate me, then, with what-Joachimsthalers?”

“As you, sir, are English, and so am I, let us use English means.”

“You wish to trade cheese? Tin? Broadcloth?”

“How many shillings will buy these two prisms?”

The Hebraic one adopted a haggard, suffering look and gazed at a point above their heads. “Let me see the color of your money,” he said, in a voice that conveyed gentle regret, as if Isaac might have bought some prisms today, and instead would only get a dreary lesson in the unbelievable shabbiness of English coinage. Isaac reached into a pocket and wiggled his fingers to produce a metallic tromping noise that proved many coins were in there. Then he pulled out a handful and let the lens-grinder have a glimpse of a few coins, tarnished black. Daniel, so far, was startled by how good Isaac was at this kind of thing. On the other hand, he had made a business out of lending money to other students-maybe he had talent.