“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?”

HE DISSECTED MOREthan 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.