On pretext of cleaning up his mess, Enoch begins to pick the spilled cards off the floor. Each is marked at the top with a rather large number, always odd, and beneath it a long row of ones and zeroes, which (since the last digit is always 1, indicating an odd number) he takes to be nothing other then the selfsame number expressed in the binary notation lately perfected by Leibniz. Underneath the number, then, is a word or short phrase, a different one on each card. As he picks them up and re-stacks them he sees: Noah’s Ark; Treaties terminating wars; Membranophones (e.g., mirlitons); The notion of a classless society; The pharynx and its outgrowths; Drawing instruments (e.g., T-squares); The Skepticism of Pyrrhon of Elis; Requirements for valid maritime insurance contracts; The Kamakura bakufu; The fallacy of Assertion without Knowledge; Agates; Rules governing the determination of questions of fact in Roman civil courts; Mummification; Sunspots; The sex organs of bryophytes (e.g., liverwort); Euclidean geometry-homotheties and similitudes; Pantomime; The Election amp; Reign of Rudolf of Hapsburg; Testes; Nonsymmetrical dyadic relations; the Investiture Controversy; Phosphorus; Traditional impotence remedies; the Arminian heresy; and-

“Some of these strike one as being too complicated for monads,” he says, desperate for some way to break the ice. “Such as this-‘The Development of Portuguese Hegemony over Central Africa.’ “

“Look at the number at the top of that card,” Waterhouse says. “It is the product of five primes: one for development, one for Portuguese, one for Hegemony, one for Central, and one for Africa. ”

“Ah, so it’s not a monad at all, but a composite.”

“Yes.”

“It’s difficult to tell when the cards are helter-skelter. Don’t you think you should organize them?”

“According to what scheme?” Waterhouse asks shrewdly.

“Oh, no, I’ll not be tricked into that discussion.”

“No linear indexing system is adequate to express the multi-dimensionality of knowledge,” Dr. Waterhouse reminds him. “But if each one is assigned a unique number-prime numbers for monads, and products of primes for composites-then organizing them is simply a matter of performing computations… Mr. Root. ”

“Dr. Waterhouse. Pardon the interruption.”

“Not at all.” He sits back down, finally, and goes back to what he was doing before: running a long file back and forth over a chunk of metal with tremendous sneezing noises. “It is a welcome diversion to have you appear before me, so unlooked-for, so implausibly well-preserved, ” he shouts over the keening of the warm tool and the ringing of the work-piece.

“Durability is preferable to the alternative-but not always convenient. Less hale persons are forever sending me off on errands.”

“Lengthy and tedious ones at that.”

“The journey’s dangers, discomforts, and tedium are more than compensated for by the sight of you, so productively occupied, and in such good health.” Or something like that. This is the polite part of the conversation, which is not likely to last much longer. If he had returned the compliment, Daniel would have scoffed, because no one would say he’s well preserved in the sense that Enoch is. He looks as old as he ought to. But he’s wiry, with clear, sky-blue eyes, no tremors in his jaw or his hands, no hesitation in his speech once he’s over the shock of seeing Enoch (or, perhaps, anyone) in his Institute. Daniel Waterhouse is almost completely bald, with a fringe of white hair clamping the back of his head like wind-hammered snow on a tree-trunk. He makes no apologies for being uncovered and does not reach for a wig-indeed, appears not to own one. His eyes are large, wide and staring in a way that probably does nothing to improve his reputation. Those orbs flank a hawkish nose that nearly conceals the slot-like mouth of a miser biting down on a suspect coin. His ears are elongated and have grown a radiant fringe of lanugo. The imbalance between his organs of input and output seems to say that he sees and knows more than he’ll say.

“Are you a colonist now, or-”

“I’m here to see you.”

The eyes stare back, knowing and calm. “So it is a social visit! That is heroic-when a simple exchange of letters is so much less fraught with seasickness, pirates, scurvy, mass drownings-”

“Speaking of letters-I’ve one here,” Enoch says, taking it out.

“Great big magnificent seal. Someone dreadfully important must’ve written it. Can’t say how impressed I am.”

“Personal friend of Dr. Leibniz.”

“The Electress Sophie?”

“No, the other one.”

“Ah. What does Princess Caroline want of me? Must be something appalling, or else she wouldn’t’ve sent you to chivvy me along.”

Dr. Waterhouse is embarrassed at having been so startled earlier and is making up for it with peevishness. But it’s fine, because it seems to Enoch that the thirty-year-old Waterhouse hidden inside the old man is now pressing outward against the loose mask of skin, like a marble sculpture informing its burlap wrappings.

“Think of it as coaxing you forward. Dr. Waterhouse! Let’s find a tavern and-”

“We’ll find a tavern-after I’ve had an answer. What does she want of me?”

“The same thing as ever.”

Dr. Waterhouse shrinks-the inner thirty-year-old recedes, and he becomes just an oddly familiar-looking gaffer. “Should’ve known. What other use is there for a broken-down old computational monadologist?”

“It’s remarkable.”

“What?”

“I’ve known you for-what-thirty or forty years now, almost as long as you’ve known Leibniz. I’ve seen you in some unenviable spots. But in all that time, I don’t believe I’ve ever heard you whine, until just then.”

Daniel considers this carefully, then actually laughs. “My apologies.”

“Not at all!”

“I thought my work would be appreciated here. I was going to establish what, to Harvard, would’ve been what Gresham’s College was to Oxford. Imagined I’d find a student body, or at least a protege. Someone who could help me build the Logic Mill. Hasn’t worked out that way. All of the mechanically talented sorts are dreaming of steam-engines. Ludicrous! What’s wrong with water-wheels? Plenty of rivers here. Look, there’s a little one right between your feet!”

“Engines are naturally more interesting to the young.”

“You needn’t tell me. When I was a student, a prism was a wonder. Went to Sturbridge Fair with Isaac to buy them-little miracles wrapped in velvet. Played with ’em for months.”

“This fact is now widely known.”

“Now the lads are torn every direction at once, like a prisoner being quartered. Or eighthed, or sixteenthed. I can already see it happening to young Ben out there, and soon it’ll happen to my own boy. ‘Should I study mathematics? Euclidean or Cartesian? Newtonian or Leibnizian calculus? Or should I go the empirical route? Will it be dissecting animals then, or classifying weeds, or making strange matters in crucibles? Rolling balls down inclined planes? Sporting with electricity and magnets?’ Against that, what’s in my shack here to interest them?”

“Could this lack of interest have something to do with that everyone knows the project was conceived by Leibniz?”

“I’m not doing it his way. His plan was to use balls running down troughs to represent the binary digits, and pass them through mechanical gates to perform the logical operations. Ingenious, but not very practical. I’m using pushrods.”

“Superficial. I ask again: could your lack of popularity here be related to that all Englishmen believe that Leibniz is a villain-a plagiarist?”

“This is an unnatural turn in the conversation, Mr. Root. Are you being devious?”

“Only a little.”

“You and your Continental ways.”

“It’s just that the priority dispute has lately turned vicious.”