“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?”
Aboard Minerva, Cape Cod Bay, Massachusetts
NOVEMBER 1713
HE DISSECTED MORE than his share of dead men’s heads during those early Royal Society days, and knows that the hull of the skull is all wrapped about with squishy rigging: haul-yards of tendon and braces of ligament cleated to pinrails on the jawbone and temple, tugging at the corners of spreading canvases of muscle that curve over the forehead and wrap the old Jolly Roger in as many overlapping layers as there are sails on a ship of the line. As Daniel trudges up out of Minerva’s bilge, dragging a chinking sack of ammunition behind him, he feels all that stuff tightening up, steadily and inexorably, each stairstep a click of the pawls, as if invisible sailors were turning capstans inside his skull. He’s spent the last hour below the water-line—never his favorite place on shipboard, but safe from cannonballs anyway—smashing plates with a hammer and bellowing old songs, and never been so relaxed in all his life. But now he’s climbed back up into the center of the hull, just the sort of bulky bull’s-eye pirates might aim swivel-guns at if they lacked confidence in their ability to pick off small fine targets from their wave-tossed platforms.
Minerva’s got a spacious stairwell running all the way down through the middle of her, just ahead of the mighty creaking trunk of
the mainmast, with two flights of stairs spiraling opposite directions so the men descending don’t interfere with those ascending—or so doddering Doctors with sacks of pottery-shards do not hinder boys running up from the hold with—what? The light’s dim. They appear to be canvas sacks—heavy bulging polyhedra with rusty nails protruding from the vertices. Daniel’s glad they’re going up the other stairs, because he wouldn’t want one of those things to bump into him. It’d be certain death from lockjaw.
Some important procedure’s underway on the gundeck. The gunports are all closed, except for one cracked open a hand’s breadth on the starboard side—therefore, not far from Daniel when he emerges from the staircase. Several relatively important officers have gathered in a semicircle around this port, as if for a baptism. There’s a general commotion of pinging and thudding coming from the hull-planks and the deck above. It could be gunfire. And if it could be, it probably is. Someone grabs the sack from Daniel and drags it to the center of the gundeck. Men with empty blunderbusses converge on it like jackals on a haunch.
Daniel’s elbowed hard by a man hauling on a line that enters Minerva through a small orifice above the gunport. This has the effect of (1) knocking Daniel down on his bony pelvis and (2) swinging said gunport all the way open, creating a sudden square of light. Framed in it is part of the rigging of a smaller ship, so close that a younger man could easily jump to it. There is a man—a pirate—on that ship pointing a musket in Daniel’s direction, but he’s struck down by a gaudy spray of outmoded china fragments, fired down from Minerva’s upperdeck. “Caltrops away!” says someone, and boys with sacks lunge toward the open gunport and hurl out a tinkling cosmos, down to the deck of the smaller ship. Moments later the same ceremony’s repeated through a gunport on the larboard side—so there must be a pirate-vessel there, too. The gunports are hauled closed again, sporting new decorations: constellations of lead balls fired into ’em from below.
The screaming/bellowing ratio has climbed noticeably. Daniel (helping himself to his feet, thank you, and hobbling crabwise to a safe haven near the mainmast, to inventory his complaints) reckons that the screaming must originate from shoeless pirates with caltrop-spikes between their metatarsals—until he hears “Fire! Fire!” and notes a curl of smoke invading the gundeck through a cracked gunport, speared on a shaft of sunlight. Then some instinct makes Daniel forget his bruises and sprains—he’s up the last flight of stairs, spry as any eight-year-old powder monkey, and out in the sail-dappled sunlight, where he’ll happily risk musket-balls.
But it’s the pirate-sloop, not Minerva, that’s on fire. Lines are going slack all over the starboard half of the ship. Each of them happens to terminate in a rusty grappling-hook that’s lodged in a ratline or a rail. The pirates are cutting themselves free!
Now comes a general rush of men to larboard, where a whaleboat is still pestering them. Minerva rolls that direction on a sea. The whaleboat comes into view, no longer eclipsed by the hull’s tumblehome, and a score of muskets and blunderbusses fire down into it at once. Daniel only glimpses the result—appalling—then Minerva rolls starboard and hides it from view.
The men throw their weapons into lockers and ascend into the rigging, pursuant to commands from van Hoek, who’s up on the poop deck bellowing into a shiny trumpet of hammered brass. There are plenty of men belowdecks who could be making contributions here, but they don’t come up. Daniel, beginning to get the hang of pirate-fighting, understands that van Hoek wants to hide the true size of his crew from Teach.
They have been running before a north wind (though it seems to’ve shifted a few points westwards) for over an hour. The southern limb of Cape Cod is dead ahead, barring their path. But long before reaching the shore, Minerva would run aground in coarse brown sand. So they have to come about now and begin to work to windward, towards the open Atlantic. These simple terms—“come about,” for example—denote procedures that are as complicated and tradition-bound as the installation of a new Pope. Great big strong men are running toward the bow: the foreyard loosers and furlers, and the headsail loosers and stowers. They take up positions on the forecastledeck or shinny out onto the bowsprit, but politely step aside for the wiry foretopmen who begin their laborious ascent up the fore shrouds to work the topsails and things higher up the foremast. It is a bristling and tangled thicket of nautical detail. Like watching fifty surgeons dissect fifty different animals at once—the kind of stuff that, half a century ago, would’ve fascinated Daniel, sucked him into this sort of life, made him a sea-captain. But like a captain reefing and striking his sails before too strong a wind, lest it drive his ship onto the shallows, Daniel ignores as much of this as he can get away with, and tries to understand what is happening in its general outlines: Minerva is coming round toward the wind. In her wake, a mile abaft, is the sloop, her sails lying a-shiver, leaving the little ship dead in the water, drifting slowly to leeward, as pirates try to beat out flames with sopped canvas whilst not stepping on any of those caltrops. Several miles north of that, four more ships are spread out on the bay, waiting.
A panic of luffing and shivering spreads through Minerva’s rig as all the sails change their relationship to the wind, then everything snaps tight, just as the sailors knew it would, and she’s running as close-hauled as she can, headed northeast. In just a few minutes she’s drawn abeam of that scorched sloop, which is now steaming, rather than smoking, and attempting to make sail. It’s obvious that caltrops and flying crockery-shards have deranged the crew, in the sense that no man knows what to do when. So the sloop’s movements are inconclusive.
All the more surprising that van Hoek orders a tack, when it isn’t really necessary. Minerva comes about and sails directly toward the meandering sloop. Several minutes later, Minerva bucks once as she rams the sloop amidships, then shudders as her keel drives the wreckage under the sea. Those burly forecastle-men go out with cutlasses and hatchets to cut shreds of the sloop’s rigging away from the bowsprit, where it has become fouled. Van Hoek, strolling on the poop deck, aims a pistol over the rail and, in a sudden lily of smoke, speeds a drowning pirate to Hell.
Royal Society Meeting, Gunfleet House
1673
“I RENEW MY OBJECTION—” said Robert Boyle. “It does not seem respectful to inventory the contents of our Founder’s guts as if they were a few keepsakes left behind in a chest—”
“Overruled,” said John Comstock, still President of the Royal Society—just barely. “Though, out of respect for our remarkably generous host, I will defer to him.”
Thomas More Anglesey, Duke of Gunfleet, was seated at the head of his drawing-room, at a conspicuously new gilt-and-white-enamel table in the barock style. Other bigwigs, such as John Comstock, surrounded him, seated according to equally barock rules of protocol. Anglesey withdrew a large watch from the pocket of his Persian vest and held it up to the light streaming in through about half an acre of window-glass, exceptionally clear and colorless and bubble-free and recently installed.
“Can we get through it in fifty seconds?” he inquired.
Inhalations all round. In his peripheral vision, Daniel saw several old watches being stuffed into pockets—pockets that tended to be frayed, and rimmed with that nameless dark shine. But the Earl of Upnor and—of all people—Roger Comstock (who was sitting next to Daniel) reached into clean bright pockets, took out new watches, and managed to hold them up in such a way that most everyone in the room could see that each was equipped, not just with two but three hands, the third moving so quickly that you could see its progress round the dial—counting the seconds!
Many hunched glances, now, toward Robert Hooke, the Hephaestus of the tiny. Hooke managed to look as if he didn’t care about how impressed everyone was—which was probably true. Daniel looked over at Leibniz, sitting there with his box on his lap, who had a soulful, distant expression.
Roger Comstock, noting the same thing: “Is that how a German looks before he bursts into tears?”
Upnor,
following Roger’s gaze: “Or before he pulls out his broadsword and begins mowing down Turks.”
“He deserves our credit for showing up at all,” Daniel murmured—hypnotized by the movement of Roger Comstock’s second-hand. “Word arrived yesterday—his patron died in Mainz.”
“Of embarrassment, most likely,” hissed the Earl of Upnor.
A chirurgeon, looking deeply nervous and out of his depth, was chivvied up to the front of the room. It was a big room, this. Its owner, the Duke of Gunfleet, perhaps too much under the spell of his architect, insisted on calling it the Grand Salon. This was simply French for Big Big Room; but it seemed a little bigger, and ever so much grander, when the French nomenclature was used.
Even under the humble appellation of Big Big Room, it was a bit too big and too grand for the chirurgeon. “Fifty seconds!—?” he said.
There was a difficult interlude, lasting much longer than fifty seconds, as a helpful Fellow tried to explain the idea of fifty seconds to the chirurgeon, who had got stuck on the misconception that they were speaking of 1/52S—perhaps some idiom from the gambling world?
“Think of minutes of longitude,” someone called out from the back of the Big Big Room. “One sixtieth of that sort of a minute is called what?”
“A second of longitude,” said the chirurgeon.
“By analogy, then, one sixtieth of a minute of time is—”
“A second…of time,” said the chirurgeon; then was suddenly mortified as he ran through some rough calculations in his head.
“One thirty-six-hundredth of an hour,” called out a bored voice with a French accent.
“Time’s up!” announced Boyle, “Let us move on—”
“The good doctor may have another fifty seconds,” Anglesey ruled.
“Thank you, my lord,” said the chirurgeon, and cleared his throat. “Perhaps those gentlemen who have been the patrons of Mr. Hooke’s horologickal researches, and are now the beneficiaries of his so ingenious handiwork, will be so kind as to keep me informed, during my presentation of the results of Lord Chester’s post-mortem, as to the passage of time—”
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