1673
Once the characteristic numbers of most notions are determined, the human race will have a new kind of tool, a tool that will increase the power of the mind much more than optical lenses helped our eyes, a tool that will be as far superior to microscopes or telescopes as reason is to vision.
—LEIBNIZ, Philosophical Essays, TRANS. BY ARLEW AND GARBER
NEAR THE MIDPOINT of London Bridge, a bit closer to the City than to Southwark, was a firebreak—a short gap in the row of buildings, like a missing tooth in a crowded jawbone. If you were drifting down-river in a boat, so that you could see all nineteen of the squat piers that held the bridge up, and all twenty of the ragstone arches and wooden drawbridges that let the water through, you’d be able to see that this open space—“the square,” it was called—stood directly above an arch that was wider than any of the others—thirty-four feet, at its widest.
As you drew closer to the bridge, and it became more and more obvious that your life was in extreme danger, and your mind, therefore, became focused on practical matters, you’d notice something even more important, namely that the sluice between the starlings—the snowshoe-like platforms of rubble that served as footings for the piers—was also wider, in this place, than anywhere else on the bridge. Consequently the passage through it looked less like a boiling cataract than a river rushing down from mountains during the spring thaw. If you still had the ability to steer for it, you would. And if you were a passenger on this hypothetical boat, and you valued your life, you’d insist that the waterman tie up for a moment at the tip of the starling and let you out, so that you could pick your way over that jammed horde of more or less ancient piles and the in-fill of mucky rubble; take a stair up to the level of the roadway; run across the Square, not forgetting to dodge the carts rushing both ways; descend another stair to the other end of the starling; and then hop, skid, and stagger across it until you reached the end, where your waterman would be waiting to pick you up again if indeed his boat, and he, still existed.
This accounted, anyway, for much that was peculiar about the part of London Bridge called the Square. Persons who went east and west on watermen’s boats on the Thames tended to be richer and more important than those who went north and south across the Bridge, and the ones who actually cared enough about their lives, limbs, and estates to bother with climbing out and hiking over the starling tended to be richer and more important yet, and so the buildings that stood atop the Bridge to either side of the Square constituted location! location! location! to the better sort of retailers and publicans.
Daniel Waterhouse spent a couple of hours loitering in the vicinity of the Square one morning, waiting for a certain man on a certain boat. However, the boat he waited for would be coming the other direction: working its way upstream from the sea.
He took a seat in a coffee-house and amused himself watching flushed and sweaty ferry-passengers appear at the head of the stairs, as if they’d been spontaneously generated from the fœtid waters of the Thames. They’d crawl into the nearby tavern for a pint, fortifying themselves for the traversal of the Bridge’s twelve-foot-wide roadway, where passengers were crushed between carts a few times a week. If they survived that, then they’d pop into the glover’s or the haberdasher’s for a bit of recreational shopping, and then perhaps dart into this coffee-house for a quick mug of java. The remainder of London Bridge was getting down at the heels, because much more fashionable shops were being put up in other parts of the city by the likes of Sterling, but the Square was prosperous and, because of the continual threat of boat-wrack and drowning, the merriest part of town.
And in these days it tended to be crowded, especially when ships came across the Channel, and dropped anchor in the Pool, and their Continental passengers were ferried hither in watermen’s boats.
As one such boat drew near the Bridge, Daniel finished his coffee, settled his bill, and ventured out onto the street. Cartage and drayage had been baffled by a crowd of pedestrians. They all wanted to descend to the starling on the downstream side, and had formed a sort of bung that stopped not only the stairs but the street as well. Seeing that they were by and large City men, intent on some serious purpose, and not Vagabonds intent on his purse, Daniel insinuated himself into this crowd and was presently drawn in to the top of the stairs and flushed down to the top of the starling along with the rest. He supposed at first that all of these well-dressed men had come to greet specific passengers. But as the boat drew within earshot, they began to shout, not friendly greetings, but questions, in several languages, about the war.
“As a fellow Protestant—albeit Lutheran—it is my hoping that England and Holland shall become reconciled and that the war you speak of will no more exist.”
The young German was standing up in a boat, wearing French fashions. But as the boat drew closer to the turbulence downstream of the Bridge, he came to his senses, and sat down.
“So much for hopes—now what of your observations, sir?” someone fired back—one of a few dozen who had by now crowded onto the starling, trying to get as close to the incoming boats and ferries as they could without falling into the deadly chute. Others were perched up on the edge of the Square, like gargoyles, still others were out on the river in boats plotting intercept courses, like bocaneers in the Caribbean. None of them was having any of this Lutheran diplomacy. None even knew who the young German was—just a passenger on a boat from abroad who was willing to talk. There were several other travelers on the same boat, but all of them ignored the shouting Londoners. If these had information, they would take it to the ’Change, and tell the tale with silver, and propagate it through the chthonic channels of the Market.
“What ship were you on, sir?” someone bellowed.
“Where did that ship come from, sir?”
“Calais.”
“Had you any conversation with Naval persons?”
“A little, perhaps.”
“Any news, or rumor, of cannons bursting on English ships?”
“Oh, sometimes it happens. By everyone in the ships of the melee, it is seen, for the whole side of the hull is out-blown, and out the bodies fly, or so they say. To all of the sailors, friend and enemy, it is a lesson of mortality, perhaps. Consequently they all talk about it. But in the present war it happens no more than usual, I think.”
“Were they Comstock cannons?”
The German took a moment to understand that, without even having set foot on English soil yet, he had talked himself into deep trouble. “Sir! The cannons of my lord Epsom are reckoned the finest in the world.”
But no one wanted to hear that kind of talk. The topic had changed.
“Whence came you to Calais?”
“Paris.”
“Did you see troops moving on your journey across France?”
“A few ones, exhausted, south-going.”
The gentlemen on the starling hummed and vibrated for a few moments, assimilating this. One broke away from the crowd, toiling back towards the stairs, and was engulfed in barefoot boys jumping up and down. He scribbled something on a bit of paper and handed it to the one who jumped highest. This one spun, forced a path through the others, took the stairs four at a time, broke loose onto the Square, vaulted over a wagon, spun a fishwife, and then began to build speed up the bridge. From here to the London shore was a hundred and some yards, from there to the ’Change was six hundred—he’d be there in three minutes. Meanwhile the interrogation continued: “Did you see Ships of Force in the Channel, mein Herr? English, French, Dutch?”
“There was—” and here the man’s English gave way. He made a helpless, encompassing gesture.
“Fog!”
“Fog,” he repeated.
“Did you hear guns?”
“A few—but very likely they were only signals. Coded data speeding through the fog, so opaque to light, but so transparent to sound—” and here he lost control of his intellectual sphincters and began to think out loud in French, fortified with Latin, working out a system for sending encrypted data from place to place using explosions, building on ideas from Wilkins’s Cryptonomicon but marrying them to a practical plan that, in its lavish expenditure of gunpowder, would be sure to please John Comstock. In other words, he identified himself (to Daniel anyway) as Dr. Gottfried Wilhelm Leibniz. The watchers lost interest and began aiming their questions at another boat.
Leibniz set foot on England. He was closely followed by a couple of other German gentlemen, somewhat older, much less talkative, and (Daniel could only suppose) more important. They in turn were pursued by a senior servant who headed up a short column of porters lugging boxes and bags. But Leibniz had burdened himself with a wooden box he would not let go of. Daniel stepped forward to greet them, but was cut off by some brusque fellow who shouldered in to hand a sealed letter to one of the older gentlemen, and whispered to him for a moment in Low-Dutch.
Daniel straightened up in annoyance. As luck would have it, he looked toward the London shore. His eye lingered on a quay just downstream of the Bridge: a jumbled avalanche of blackened rubble left over from the Fire. It could have been rebuilt years ago, but hadn’t, because it had been judged more important to rebuild other things first. A few men were doing work of a highly intellectual nature, stretching lines about and drawing sketches. One of them—incredibly—just happened to be Robert Hooke, City Surveyor, whom Daniel had quietly abandoned at Gresham’s College an hour ago. Not so incredibly (given that he was Hooke), he’d noticed Daniel standing there on the starling in the middle of the river, greeting what was quite obviously a foreign delegation, and was therefore glaring and brooding.
Leibniz and the others discussed matters in High-Dutch. The interloper turned round to glance at Daniel. It was one of the Dutch Ambassador’s errand-boys-cum-spies. The Germans formed some sort of a plan, and it seemed to involve splitting up. Daniel stepped in and introduced himself.
The other Germans were introduced by their names but what mattered was their ancestry: one of them was the nephew of the Archbishop of Mainz, the other the son of Baron von Boineburg, who was the same Archbishop’s Minister. In other words very important people in Mainz, hence rather important ones in the Holy Roman Empire, which was more or less neutral in the French/English/Dutch broil. It had all the signs of being some sort of peace-brokering mission, i.e.
Leibniz knew who he was, and asked, “Is Wilkins still alive?”
“Yes…”
“Thank God!”
“Though very ill. If you would like to visit him I would suggest doing it now. I’ll escort you gladly, Dr. Leibniz…may I have the honor of assisting you with that box?”
“You are very civil,” Leibniz said, “but I’ll hold it.”
“If it contains gold or jewelry, you’d best hold it tight.”
“Are the streets of London not safe?”
“Let us say that the Justices of the Peace are mostly concerned with Dissenters and Dutchmen, and our cutpurses have not been slow to adapt.”
“What this contains is infinitely more valuable than gold,” Leibniz said, beginning to mount the stairs, “and yet it cannot be stolen.”
Daniel lunged forward in an effort to keep step. Leibniz was slender, of average height, and tended to bend forward when he walked, the head anticipating the feet. Once he had reached the level of the roadway he turned sharply and strode towards the City of London, ignoring the various taverns and shops.
He did not look like a monster.
According to Oldenburg, the Parisians who frequented the Salon at the Hotel Montmor—the closest French equivalent to the Royal Society of London—had begun using the Latin word monstro to denote Leibniz. This from men who’d personally known Descartes and Fermat and who considered exaggeration an unspeakably vulgar habit. It had led to some etymological researches among some members of the R.S. Did they mean Leibniz was grotesquely misshapen? An unnatural hybrid of a man and something else? A divine warning?
“He lives up this way, does he not?”
“The Bishop has had to move because of his illness—he’s at his stepdaughter’s house in Chancery Lane.”
“Then still we go this way—then left.”
“You have been to London before, Dr. Leibniz?”
“I have been studying London-paintings.”
“I’m afraid most of those became antiquarian curiosities after the Fire—like street-plans of Atlantis.”
“And yet viewing several depictions of even an imaginary city, is enlightening in a way,” Leibniz said. “Each painter can view the city from only one standpoint at a time, so he will move about the place, and paint it from a hilltop on one side, then a tower on the other, then from a grand intersection in the middle—all on the same canvas. When we look at the canvas, then, we glimpse in a small way how God understands the universe—for he sees it from every point of view at once. By populating the world with so many different minds, each with its own point of view, God gives us a suggestion of what it means to be omniscient.”
Daniel decided to step back and let Leibniz’s words reverberate, as organ-chords must do in Lutheran churches. Meanwhile they reached the north end of the Bridge, where the racket of the water-wheels, confined and focused in the stone vault of the gatehouse, made conversation impossible. Not until they’d made it out onto dry land, and begun to ascend the Fish Street hill, did Daniel ask, “I note you’ve already been in communication with the Dutch Ambassador. May I assume that your mission is not entirely natural-philosophick in nature?”
“A rational question—in a way,” Leibniz grumbled. “We are about the same age, you and I?” he asked, giving Daniel a quick inspection. His eyes were unsettling. Depending on what kind of monster he was, either beady, or penetrating.
“I am twenty-six.”
“So am I. We were born about sixteen forty-six. The Swedes took Prague that year, and invaded Bavaria. The Inquisition was burning Jews in Mexico. Similar terrible things were happening in England, I assume?”
“Cromwell crushed the King’s army at Newark—chased him out of the country—John Comstock was wounded—”
“And we are speaking only of kings and noblemen. Imagine the sufferings of common people and Vagabonds, who possess equal stature in God’s eyes. And yet you ask me whether my mission is philosophick or diplomatic, as if those two things can neatly be separated.”
“Rude and stupid I know, but it is my duty to make conversation. You are saying that it should be the goal of all natural philosophers to restore peace and harmony to the world of men. This I cannot dispute.”
Leibniz now softened. “Our goal is to prevent the Dutch war from growing into a general conflagration. Please do not be offended by my frankness now: the Archbishop and the Baron are followers of the Royal Society—as am I. They are Alchemists—which I am not, except when it is politic. They hope that through pursuit of Natural Philosophy I may make contacts with important figures in this country, whom it would normally be difficult to reach through diplomatic channels.”
“Ten years ago I might have been offended,” Daniel said. “Now, there’s nothing I’ll not believe.”
“But my interest in meeting the Lord Bishop of Chester is as pure as any human motive can be.”
“He will sense that, and be cheered by it,” Daniel said. “The last few years of Wilkins’s life have been sacrified entirely to politics—he has been working to dismantle the framework of theocracy, to prevent its resurgence, in the event a Papist ascends to the throne—”
“Or already has done so,” Leibniz said immediately.
The offhanded way in which Leibniz suggested that King Charles II might be a crypto-Catholic hinted to Daniel that it was common knowledge on the Continent. This made him feel hopelessly dull, naïve, and provincial. He had suspected the King of many crimes and deceptions, but never of baldly lying about his religion to the entire Realm.
He had plenty of time to conceal his annoyance as they were passing through the heart of the city, which had turned into a single vast and eternal building-site even as the normal business of the ‘Change and the goldsmiths’ shops continued. Paving-stones were whizzing between Daniel and the Doctor like cannonballs, shovels slicing the air around their heads like cutlasses, barrows laden with gold and silver and bricks and mud trundling like munition-carts over temporary walk-ways of planks and stomped dirt.
Perhaps reading anxiety on Daniel’s face, Leibniz said, “Just like the Rue Vivienne in Paris,” with a casual hand-wave. “I go there frequently to read certain manuscripts in the Bibliothèque du Roi.”
“I’ve been told that a copy of every book printed in France must be sent to that place.”
“Yes.”
“But it was established in the same year that we had our Fire—so I ween that it must be very small yet, as it’s had only a few years to grow.”
“A few very good years in mathematics, sir. And it also contains certain unpublished manuscripts of Descartes and Pascal.”
“But none of the classics?”
“I had the good fortune to be raised, or to raise myself, in my father’s library, which contained all of them.”
“Your father was mathematickally inclined?”
“Difficult to say. As a traveler comprehends a city only by viewing pictures of it drawn from differing standpoints, I know my father only by having read the books that he read.”
“I understand the similitude now, Doctor. The Bibliothèque du Roi then gives you the closest thing that currently exists to God’s understanding of the world.”
“And yet with a bigger library we could come ever so much closer.”
“But with all due respect, Doctor, I do not understand how this street could be anything less like the Rue Vivienne—we have no such Bibliothèque in England.”
“The Bibliothèque du Roi is just a house, you see, a house Colbert happened to buy on the Rue Vivienne—probably as an investment, because that street is the center of goldsmiths. Every ten days, from ten in the morning until noon, all of the merchants of Paris send their money to the Rue Vivienne to be counted. I sit there in Colbert’s house trying to understand Descartes, working the mathematical proofs that Huygens, my tutor, gives me, and looking out the windows as the street fills up with porters staggering under their back-loads of gold and silver, converging on a few doorways. Are you beginning to understand my riddle now?”
“Which riddle was that?”
“This box! I said it contained something infinitely more valuable than gold, and yet it could not be stolen. Which way do we turn here?”
For they’d come out into the hurricane where Threadneedle, Cornhill, Poultry, and
Lombard all collided. Message-boys were flying across that intersection like quarrels
from crossbows—or (Daniel suspected) like broad Hints that he was failing to Get.
LONDON CONTAINED A HUNDRED LORDS, bishops, preachers, scholars, and gentlemen-philosophers who would gladly have provided Wilkins with a comfortable sick-bed, but he had ended up in his stepdaughter’s home in Chancery Lane, actually rather close to where the Waterhouses lived. The entrance to the place, and the street in front, were choked with sweating courtiers—not the sleek top-level ones but the dented, scarred, slightly too old and slightly too ugly ones who actually got everything done.* They were milling in the street around a black coach blazoned with the arms of Count Penistone. The house was an old one (the Fire had stopped a few yards short of it). It was one of those slump-shouldered, thatch-roofed, half-timbered Canterbury Tales productions, completely outmoded by the gleaming coach and the whip-thin rapiers.
“You see—despite the purity of your motives, you’re immersed in politics already,” Daniel said. “The lady of the house is Cromwell’s niece.”
“What!? The Cromwell?”
“The same whose skull gazes down on Westminster from the end of a stick. Now, the owner of that excellent coach is Knott Bolstrood, Count Penistone—his father founded a sect called the Barkers, normally lumped in with many others under the pejorative term of Puritans. The Barkers are gratuitously radical, however—for example, they believe that Government and Church should have naught to do with each other, and that all slaves in the world should be set free.”
“But the gentlemen in front are dressed like courtiers! Are they getting ready to siege the Puritan-house?”
“They are Bolstrood’s hangers-on. You see, Count Penistone is His Majesty’s Secretary of State.”
“I had heard that King Charles the Second made a Phanatique his Secretary of State, but could not believe it.”
“Consider it—could Barkers exist in any other country? Save Amsterdam, that is.”
“Naturally not!” Leibniz said, lightly offended by the very idea. “They would be extinguished.”
“Therefore, whether or not he feels any loyally toward the King, Knott Bolstrood has no choice but to stand for a free and independent England—and so, when Dissenters accuse the King of being too close to France, His Majesty need only point to Bolstrood as the living credential of his independent foreign policy.”
“But it’s all a farce!” Leibniz muttered. “All Paris knows England’s in France’s pocket.”
“All London knows it, too—the difference is that we have three dozen theatres here—Paris has only one of them—”
Leibniz’s turn, finally, to be baffled. “I don’t understand.”
“All I am saying is that we happen to enjoy farces.”
“Why is Bolstrood visiting the niece of Cromwell?”
“He’s probably visiting Wilkins.”
Leibniz stopped and considered matters. “Tempting. But the protocol is impossible. I cannot enter the house!”
“Of course you can—with me,” Daniel said. “Just follow.”
“But I must go back and fetch my companions—for I do not have the standing to disturb the Secretary of State—”
“I do,” Daniel said. “One of my earliest memories is of watching him destroy a pipe organ with a sledgehammer. Seeing me will give him a warm feeling.”
Leibniz stopped and looked aghast; Daniel could almost see, reflected in his eyes, the stained-glass windows and organ-pipes of some fine Lutheran church in Leipzig. “Why would he commit such an outrage!?”
“Because it was in an Anglican cathedral. He would have been about twenty—a high-spirited age.”
“Your family were followers of Cromwell?”
“It is more correct to say that Cromwell was a follower of my father—may God rest both of their souls.” But now they were in the midst of the courtier-mob, and it was too late for Leibniz to obey his instincts, and run away.
They spent several minutes pushing among progressively higher-ranking and better-dressed men, into the house and up the stairs, and finally entered a tiny low-ceilinged bedchamber. It smelled as if Wilkins had already died, but most of him still lived—he was propped up on pillows, with a board on his lap, and a fine-looking document on the board. Knott Bolstrood—forty-two years old—knelt next to the bed. He turned round to look as Daniel entered. During the ten years Knott had survived on the Common-Side of Newgate Prison, living in a dark place among murderers and lunaticks, he had developed a strong instinct for watching his back. It was as useful for a Secretary of State as it had been for a marauding Phanatique.
“Brother Daniel!”
“My lord.”
“You’ll do as well as anyone—better than most.”
“Do for what, sir?”
“Witnessing the Bishop’s signature.”
Bolstrood got a quill charged with ink. Daniel wrapped Wilkins’s puffy fingers around it. After a bit of heavy breathing on the part of its owner, the hand began to move, and a tangle of lines and curves began to take shape on the page, bearing the same relationship to Wilkins’s signature as a ghost to a man. It was a good thing, in other words, that several persons were on hand to verify it. Daniel had no idea what this document was. But from the way it was engrossed he could guess that it was meant for the eyes of the King.
Count Penistone was a man in a hurry, after that. But before he left he said to Daniel: “If you have any stock in the Duke of York’s Guinea Company, sell it—for that Popish slave-monger is going to reap the whirlwind.” Then, for maybe the second or third time in his life, Knott Bolstrood smiled.
“Show it to me, Dr. Leibniz,” Wilkins said, skipping over all of the formalities; he had not urinated in three days and so there was a certain urgency about everything.
Leibniz sat gingerly on the edge of the bed, and opened the box.
Daniel saw gears, cranks, shafts. He thought it might be a new sort of timepiece, but it had no dial and no hands—only a few wheels with numbers stamped on them.
“It owes much to Monsieur Pascal’s machine, of course,” Leibniz said, “but this one can multiply numbers as well as add and subtract them.”
“Make it work for me, Doctor.”
“I must confess to you that it is not finished yet.” Leibniz frowned, tilted the box toward the light, and blew into it sharply. A cockroach flew out and traced a flailing parabola to the floor and scurried under the bed. “This is just a demo’. But when it is finished, it will be magnifique.”
“Never mind,” Wilkins said. “It uses denary numbers?”
“Yes, like Pascal’s—but binary would work better—”
“You needn’t tell me,” Wilkins said, and then rambled for at least a quarter of an hour, quoting whole pages from relevant sections of the Cryptonomicon.
Leibniz finally cleared his throat and said, “There are mechanical reasons, too—with denary numbers, too many meshings of gears are necessary—friction and backlash play havoc.”
“Hooke! Hooke could build it,” Wilkins said. “But enough of machines. Let us speak of Pansophism. Tell me, now—have you met with success in Vienna?”
“I have written to the Emperor several times, describing the French king’s Bibliothèque du Roi—”
“Trying to incite his Envy—?”
“Yes—but in his hierarchy of vices, Sloth would appear to reign unchallenged by Envy or anything else. Have you met with success here, my lord?”
“Sir Elias Ashmole is starting a brave library—but he’s distracted and addled with Alchemy. I have had to attend to more fundamental matters—” Wilkins said, and gestured weakly toward the door through which Bolstrood had departed. “I believe that binary arithmetickal engines will be of enormous significance—Oldenburg, too, is most eager.”
“If I could carry your work forward, sir, I would consider myself privileged.”
“Now we are only being polite—I have no time. Waterhouse!”
Leibniz closed up his box. The Bishop of Chester watched the lid closing over the engine, and his eyelids almost closed at the same moment. But then he summoned up a bit more strength. Leibniz backed out of the way, and Daniel took his place.
It was all he could get out. Drake had been his father, but John Wilkins really was his lord in almost every sense of the word. His lord, his bishop, his minister, his professor.
“The responsibility now falls upon you to make it all happen.”
“My Lord? To make what happen?”
But Wilkins was either dead or asleep.
THEY STUMBLED THROUGH a small dark kitchen and out into the maze of yards and alleys behind Chancery Lane, where they drew the attention of diverse roosters and dogs. Pursued by their hue and cry, Mr. Waterhouse and Dr. Leibniz emerged into a district of theatres and coffee-houses. Any one of those coffee-houses would have sufficed, but they were close to Queen Street—another of Hooke’s paving-projects. Daniel had begun to feel like a flea under the Great Microscope. Hooke subtended about half of the cosmos, and made Daniel feel as if he were flitting from one place of refuge to another, even though he had nothing to hide. Leibniz was hale, and seemed to enjoy exploring a new city. Daniel got them turned back in the direction of the river. He was trying to make out what responsibility, specifically, had just been placed on his shoulders by Wilkins. He realized—after a quarter of an hour of being a very poor conversationalist—that Leibniz might have ideas on the subject.
“You said you wanted to carry Wilkins’s work forward, Doctor. Which of his projects were you referring to? Flying to the moon, or—”
“The Philosophical Language,” Leibniz said, as if this should have been obvious.
He knew that Daniel had been involved in that project, and seemed to take the question as a sign that Daniel wasn’t especially proud of it—which was true. Noting Leibniz’s respect for the project, Daniel felt a stab of misgivings that perhaps the Philosophical Language had some wonderful properties that he had been too stupid to notice.
“What more is there to be done with it?” Daniel asked. “You have some refinements—additions—? You wish to translate the work into German—? You’re shaking your head, Doctor—what is it, then?”
“I was trained as a lawyer. Don’t look so horrified, Mr. Waterhouse, it is respectable enough, for an educated man in Germany. You must remember that we don’t have a Royal Society. After I was awarded my Doctor of Jurisprudence, I went to work for the Archbishop of Mainz, who gave me the job of reforming the legal code—which was a Tower of Babel—Roman and Germanic and local common law all mangled together. I concluded that there was little point in jury-rigging something. What was needed was to break everything down into certain basic concepts and begin from first principles.”
“I can see how the Philosophical Language would be useful in breaking things down,” Daniel said, “but to build them back up, you would need something else—”
“Logic,” Leibniz said.
“Logic has a dismal reputation among the higher primates in the Royal Society—”
“Because they associate it with the Scholastic pedants who tormented them in university,” Leibniz said agreeably. “I’m not talking about that sort of thing! When I say logic, I mean Euclidean.”
“Begin with certain axioms and combine them according to definite rules—”
“Yes—and build up a system of laws that is as provable, and as internally consistent, as the theory of conic sections.”
“But you have recently moved to Paris, have you not?”
Leibniz nodded. “Part of the same project. For obvious reasons, I need to improve my knowledge of mathematics—what better place for it?” Then his face got a distracted, brooding look. “Actually there was another reason—the Archbishop sent me as an emissary, to tender a certain proposal to Louis XIV.”
“So today is not the first time you have combined Natural Philosophy with Diplomacy—”
“Nor the last, I fear.”
“What was the proposal you set before the King?”
“I only got as far as Colbert, actually. But it was that, instead of invading her neighbors, La France ought to make an expedition to Egypt, and establish an Empire there—creating a threat to the Turk’s left flank—Africa—and forcing him to move some armies away from his right flank—”
“Christendom.”
“Yes.” Leibniz sighed.
“It sounds—er—audacious,” Daniel said, now on a diplomatic mission of his own.
“By the time I’d arrived in Paris, and secured an appointment with Colbert, King Louis had already flung his invasion-force into Holland and Germany.”
“Ah, well—’twas a fine enough idea.”
“Perhaps some future monarch of France will revive it,” Leibniz said. “For the Dutch, the consequences were dire. For me, it was fortuitous—no longer straining at diplomatic gnats, I could go to Colbert’s house in the Rue Vivienne and grapple with philosophick giants.”
“I’ve given up trying to grapple with them,” Daniel sighed, “and now only dodge their steps.”
They rambled all the way down to the Strand and sat down in a coffee-house with south-facing windows. Daniel tilted the arith-metickal engine toward the sun and inspected its small gears. “Forgive me for asking, Doctor, but is this purely a conversation-starter, or—?”
“Perhaps you should go back and ask Wilkins.”
“Touché.”
Now some sipping of coffee.
“My Lord Chester spoke correctly—in a way—when he said that Hooke could build this,” Daniel said. “Only a few years ago, he was a creature of the Royal Society, and he would have. Now he’s a creature of London, and he has artisans build most of his watches. The only exceptions, perhaps, are the ones he makes for the King, the Duke of York, and the like.”
“If I can explain to Mr. Hooke the importance of this device, I’m confident he’ll undertake it.”
“You don’t understand Hooke,” Daniel said. “Because you are German, and because you have diverse foreign connections, Hooke will assume you are a part of the Grubendolian cabal—which in his mind looms so vast that a French invasion of Egypt would be only a corner of it.”
“Grubendol?” Leibniz said. Then, before Daniel could say it, he continued, “I see—it is an anagram for Oldenburg.”
Daniel ground his teeth for a while, remembering how long it had taken him to decipher the same anagram, then continued: “Hooke is convinced that Oldenburg is stealing his inventions—sending them overseas in encrypted letters. What is worse, he saw you disembarking at the Bridge, and being handed a letter by a known Dutchman. He’ll want to know what manner of Continental intrigues you’re mixed up in.”
“It’s not a secret that my patron is the Archbishop of Mainz,” Leibniz protested.
“But you said you were a Lutheran.”
“And I am—but one of the Archbishop’s objectives is to reconcile the two churches.”
“Here we say there are more than two,” Daniel reminded him.
“Is Hooke a religious man?”
“If you mean ‘does he go to church,’ then no,” Daniel admitted, after some hesitation. “But if you mean ‘does he believe in God’ then I should say yes—the Microscope and Telescope are his stained-glass windows, the animalcules in a drop of his semen, or the shadows on Saturn’s rings, are his heavenly Visions.”
“Is he like Spinoza, then?”
“You mean, one who says God is nothing more than Nature? I doubt it.”
“What does Hooke want?”
“He is busy all day and night designing new buildings, surveying new streets—”
“Yes, and I am busy overhauling the German legal code—but it is not what I want.”
“Mr. Hooke pursues various schemes and intrigues against Oldenburg—”
“But surely not because he wants to?”
“He writes papers, and lectures—”
Leibniz scoffed. “Not a tenth of what he knows is written down, is it?”
“You must keep in mind, about Hooke, that he is poorly understood, partly because of his crookedness and partly because of his difficult personal qualities. In a world where many still refuse to believe in the Copernican Hypothesis, some of Hooke’s more forward ideas would be considered grounds for imprisonment in Bedlam.”
Leibniz’s eyes narrowed. “Is it Alchemy, then?”
“Mr. Hooke despises Alchemy.”
“Good!” Leibniz blurted—most undiplomatically. Daniel covered a smile with his coffee-cup. Leibniz looked horrified, fearing that Daniel might be an Alchemist himself. Daniel put him at ease by quoting from Hooke: “‘Why should we endeavour to discover Mysteries in that which has no such thing in it? And like Rabbis find out Cabalism, and ænigmas in the Figure, and placing of Letters, where no such thing lies hid: whereas in natural forms…the more we magnify the object, the more excellencies and mysteries do appear; and the more we discover the imperfections of our senses, and the Omnipotency and Infinite perceptions of the great Creator.’”
“So Hooke believes that the secrets of the world are to be found in some microscopic process.”
“Yes—snowflakes, for example. If each snowflake is unique, then why are the six arms of a given snowflake the same?”
“If we assume that the arms grew outwards from the center, then there must be something in that center that imbues each of the six arms with the same organizing principle—just as all oak trees, and all lindens, share a common nature, and grow into the same general shape.”
“But to speak of some mysterious nature is to be like the Scholastics—Aristotle dressed up in a doublet,” Daniel said.
“Or in an Alchemist’s robe—” Leibniz returned.
“Agreed. Newton would argue—”
“That fellow who invented the telescope?”
“Yes. He would argue that if you could catch a snowflake, melt it, and distill its water, you could extract some essence that would be the embodiment of its nature in the physical world, and account for its shape.”
“Yes—that is a good distillation, as it were, of the Alchemists’ mental habit—which is to believe that anything we cannot understand must have some physical residue that can in principle be refined from coarse matter.”
“Mr. Hooke, by contrast, is convinced that Nature’s ways are consonant to man’s reason. As the beating of a fly’s wings is consonant to the vibration of a plucked string, so that the sound of one, produces a sympathetic resonance in the other—in the same way, every phenomenon in the world can, in principle, be understood by human ratiocination.”
Leibniz said, “And so with a sufficiently powerful microscope, Hooke might peer into the core of a snowflake at the moment of its creation and see its internal parts meshing, like gears of a watch made by God.”
“Just so, sir.”
“And this is what Hooke wants?”
“It is the implicit goal of all his researches—it is what he must believe and must look for, because that is the nature of Hooke.”
“Now you are talking like an Aristotelian,” Leibniz jested.
Then he reached across the table and put his hand on the box, and said something that was apparently quite serious. “What a watch is to time, this engine is to thought.”
“Sir! You show me a few gears that add and multiply numbers—well enough. But this is not the same as thought!”
“What is a number, Mr. Waterhouse?”
Daniel groaned. “How can you ask such questions?”
“How can you not ask them, sir? You are a philosopher, are you not?”
“A Natural Philosopher.”
“Then you must agree that in the modern world, mathematicks is at the heart of Natural Philosophy—it is like the mysterious essence in the core of the snowflake. When I was fifteen years old, Mr. Waterhouse, I was wandering in the Rosenthal—which is a garden on the edge of Leipzig—when I decided that in order to be a Natural Philosopher I would have to put aside the old doctrine of substantial forms and instead rely upon Mechanism to explain the world. This led me inevitably to mathematicks.”
“When I was fifteen, I was handing out Phanatiqual libels just down the street from here, and dodging the Watch—but in time, Doctor, as Newton and I studied Descartes at Cambridge, I came to share your view concerning the supreme position of mathematics.”
“Then I repeat my question: What is a number? And what is it to multiply two numbers?”
“Whatever it is, Doctor, it is different from thinking.”
“Bacon said, ‘Whatever has sufficient differences, perceptible by the sense, is in nature competent to express cogitations.’ You cannot deny that numbers are in that sense competent—”
“To express cogitation, yes! But to express cogitations is not to perform them, or else quills and printing-presses would write poetry by themselves.”
“Can your mind manipulate this spoon directly?” Leibniz said, holding up a silver spoon, and then setting it down on the table between them.
“Not without my hands.”
“So, when you think about the spoon, is your mind manipulating the spoon?”
“No. The spoon is unaffected, no matter what I think about it.”
“Because our minds cannot manipulate physical objects—cup, saucer, spoon—instead they manipulate symbols of them, which are stored in the mind.”
“I will accept that.”
“Now, you yourself helped Lord Chester devise the Philosophical Language, whose chief virtue is that it assigns all things in the world positions in certain tables—positions that can be encoded by numbers.”
“Again, I agree that numbers can express cogitations, through a sort of encryption. But performing cogitations is another matter entirely!”
“Why? We add, subtract, and multiply numbers.”
“Suppose the number three represents a chicken, and the number twelve the Rings of Saturn—what then is three times twelve?”
“Well, you can’t just do it at random,” Leibniz said, “any more than Euclid could draw lines and circles at random, and come up with theorems. There has to be a formal system of rules, according to which the numbers are combined.”
“And you propose building a machine to do this?”
“Pourquoi non? With the aid of a machine, truth can be grasped as if pictured on paper.”
“But it is still not thinking. Thinking is what angels do—it is a property given to Man by God.”
“How do you suppose God gives it to us?”
“I do not pretend to know, sir!”
“If you take a man’s brain and distill him, can you extract a mysterious essence—the divine presence of God on Earth?”
“That is called the Philosophick Mercury by Alchemists.”
“Or, if Hooke were to peer into a man’s brain with a good enough microscope, would he see tiny meshings of gears?”
Daniel said nothing. Leibniz had imploded his skull. The gears were jammed, the Philosophick Mercury dribbling out his ear-holes.
“You’ve already sided with Hooke, and against Newton, concerning snowflakes—so may I assume you take the same position concerning brains?” Leibniz continued, now with exaggerated politeness.
Daniel spent a while staring out the window at a point far away. Eventually his awareness came back into the coffee-house. He glanced, a bit furtively, at the arithmetical engine. “There is a place in Micrographia where Hooke describes the way flies swarm around meat, butterflies around flowers, gnats around water—giving the semblance of rational behavior. But he thinks it is all because of internal mechanisms triggered by the peculiar vapors arising from meat, flowers, et cetera. In other words, he thinks that these creatures are no more rational than a trap, where an animal seizing a piece of bait pulls a string that fires a gun. A savage watching the trap kill the animal might suppose it to be rational. But the trap is not rational—the man who contrived the trap is. Now, if you—the ingenious Dr. Leibniz—contrive a machine that gives the impression of thinking—is it really thinking, or merely reflecting your genius?”
“You could as well have asked: are we thinking? Or merely reflecting God’s genius?”
“Suppose I had asked it, Doctor—what would your answer be?”
“My answer, sir, is both.”
“Both? But that’s impossible. It has to be one or the other.”
“I do not agree with you, Mr. Waterhouse.”
“If we are mere mechanisms, obeying rules laid down by God, then all of our actions are predestined, and we are not really thinking.”
“But Mr. Waterhouse, you were raised by Puritans, who believe in predestination.”
“Raised by them, yes…” Daniel said, and let it hang in the air for a while.
“You no longer accept predestination?”
“It does not resonate sweetly with my observations of the world, as a good hypothesis ought to.” Daniel sighed. “Now I see why Newton has chosen the path of Alchemy.”
“When you say he chose that path, you imply that he must have rejected another. Are you saying that your friend Newton explored the idea of a mechanically determined brain, and rejected it?”
“It may be he explored it, if only in his dreams and nightmares.”
Leibniz raised his eyebrows and spent a few moments staring at the clutter of pots and cups on the table. “This is one of the two great labyrinths into which human minds are drawn: the question of free will versus predestination. You were raised to believe in the latter. You have rejected it—which must have been a great spiritual struggle—and become a thinker. You have adopted a modern, mechanical philosophy. But that very philosophy now seems to be leading you back towards predestination. It is most difficult.”
“But you claim to know of a third way, Doctor. I should like to hear of it.”
“And I should like to tell of it,” Leibniz said, “but I must part from you now, and make rendezvous with my traveling companions. May we continue on some other day?”