“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 arithmetickal 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.”

“Touche.”

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.”

“ Herewe 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 ?nigmas 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-”