Cryptonomicon

At this point in history (April of 1945) the word that denotes a person who sits and performs arithmetical calculations is "computer." Waterhouse has just found a whole room full of dead computers. Anyone in his right mind--anyone other than Waterhouse and some of his odd Bletchley Park friends, like Turing--would have taken one look at these computers and assumed that they were the accounting department, or something, and that each slave in the room was independently toting up figures. Waterhouse really oughtto remain open to this idea, because it is so obvious. But from the very beginning he has had a hypothesis of his own, much more interesting and peculiar.

It is that the slaves were functioning, collectively, as cogs in a larger computation machine, each performing a small portion of a complex calculation: receiving numbers from one computer, doing some arithmetic, producing new numbers, passing them on to another computer.

Central Bureau is able to trace the identities of five of the dead slaves. They came from places like Saigon, Singapore, Manila, and Java, but they had in common that they were ethnic Chinese and they were shopkeepers. Apparently the Nipponese had cast a wide net for expert abacus users and brought them together, from all over the Co-Prosperity Sphere, to this island in Manila Bay.

Lawrence Waterhouse tracks down a computer of his own in the ruins of Manila, a Mr. Gu, whose small import/export business was destroyed by the war (it is hard to run such a business when you are on an island, and every ship that leaves or approaches the island gets sunk by Americans). Waterhouse shows Mr. Gu photos of the abaci as they were left by the dead computers. Mr. Gu tells him what numbers are encoded in those bead positions, as well as giving Waterhouse a couple of days' tutorial on basic abacus technique. The important thing learned from this is not really abacus skills but rather the remarkable speed and precision with which a computer like Mr. Gu can churn out calculations.

At this point, Waterhouse has reduced the problem to pure data. About half of it's in his memory and the other half scattered around on his desk. The data includes all of the scratch paper left behind by the computers. To match up the numbers on the scratch paper with the numbers left on the abaci, and thus to compile a flash-frozen image of the calculations that were underway in that room when the apocalypse struck, is not that difficult--at least, by the standards of difficulty that apply during wartime, when, for example, landing several thousand men and tons of equipment on a remote island and taking it from heavily armed, suicidal Japanese troops with the loss of only a few dozen lives is considered to be easy.

From this it is possible (though it approaches being difficult) to generalize, and to figure out the underlying mathematical algorithm that generated the numbers on the abaci. Waterhouse becomes familiar with some of the computers' handwriting, and develops evidence that slips of scratch paper were being handed from one computer to another and then to yet another. Some of the computers had logarithm tables at their stations, which is a really important clue as to what they were doing. In this way he is able to draw up a map of the room, with each computer's station identified by number, and a web of arrows interconnecting the stations, depicting the flow of paper, and of data. This helps him visualize the collective calculation as a whole, and to reconstruct what was going on in that subterranean chamber.

For weeks it comes in bits and pieces, and then one evening, some switch turns on in Lawrence Waterhouse's mind, and he knows, in some preconscious way, that he's about to get it. He works for twenty-four hours. By that point he has come up with a lot of evidence to support, and none to contradict, the hypothesis that this calculation is a variant of a zeta function. He naps for six hours, gets up, and works for another thirty. By that point he's figured out that it definitely is some kind of zeta function, and he's managed to figure out several of its constants and terms. He almost has it now. He sleeps for twelve hours, gets up and walks around Manila to clear his head, goes back to work, and hammers away at it for thirty-six hours. This is the fun part, when big slabs of the puzzle, painstakingly assembled from fragments, suddenly begin to lock together, and the whole thing begins to make sense.

It all comes down to an equation written down on one sheet of paper. Just looking at it makes him feel weirdly nostalgic, because it's the same type of equation he used to work with back at Princeton with Alan and Rudy.

Another pause for sleep, then, because he has to be alert to do the final thing.