Hut 8 is where they decrypt naval Enigma transmissions. Hut 4 accepts the decrypts from Hut 8 and analyzes them. If Waterhouse pretends to be a Hut 4 man the disguise will not last for long, because those fellows have to actually know something about the Navy. He perfectly fits the profile of a Hut 8 man, who need not know anything except pure math.

One of the RAF men peruses his papers, then steps into a small guardhouse and stirs the crank on a telephone. Waterhouse stands there awkwardly, marveling at the weapons slung from the shoulders of the RAP men. They are, as far as he can tell, nothing more than steel pipes with a trigger mounted toward one end. A small window cut through the pipe provides a view of a coil spring nested inside. A few handles and fittings bolted on from place to place do not make the Sten gun look any less like an ill-conceived high school metal shop project.

"Captain Waterhouse? You are to proceed to the Mansion," says the guard who had spoken on the telephone. "You can't miss it."

Waterhouse walks for about fifty feet and finds that the Mansion is, indeed, tragically unmissable. He stands and stares at it for a minute, trying to fathom what the architect had been thinking. It is a busy piece of work, with an excessive number of gables. He can only suppose that the designer wanted to build what was really a large, single dwelling, but sought to camouflage it as a line of at least half a dozen wildly mismatched urban row-houses inexplicably crammed together in the middle of six hundred acres of Buckinghamshire farmland.

The place has been well looked after, but as Waterhouse draws closer, he can see black lianas climbing up the brickwork. The root system that he glimpsed in the Underground has spread beneath forest and pasture even to this place and has begun to throw its neoprene creepers upwards. But this organism is not phototropic-it does not grow towards the light, always questing towards the sun. It is infotropic. And it has spread to this place for the same reason that infotropic humans like Lawrence Pritchard Waterhouse and Dr. Alan Mathison Turing have come here, because Bletchley Park has roughly the same situation in the info world as the sun does in the solar system. Armies, nations, prime ministers, presidents and geniuses fall around it, not in steady planetlike orbits but in the crazy careening ellipses and hyperbolae of comets and stray asteroids.

Dr. Rudolf von Hacklheber can't see Bletchley Park, because it is the second best kept secret in the world, after Ultra Mega. But from his office in Berlin, sifting through dispatches from the Beobachtung Dienst, he can glimpse fragments of those trajectories, and dream up hypotheses to explain why they are just so. If the only logical hypothesis is that the Allies have broken Enigma, then Detachment 2702 will have failed.

Lawrence displays further credentials and enters between a pair of weathered gryphons. The mansion is nicer once you can no longer see its exterior. Its faux-rowhouse design provides many opportunities for bay windows, providing sorely needed light. The hall is held up by gothic arches and pillars made of a conspicuously low grade of brown marble that looks like vitrified sewage.

The place is startlingly noisy; there is a rushing, clattering noise, like rabid applause, permeating walls and doors, carried on a draft of hot air with a stinging, oily scent. It is the peculiar scent of electric teletypes-or teleprinters, as the Brits call them. The noise and the heat suggest there must be dozens of them in one of the mansion's lower rooms.

Waterhouse climbs a paneled stairway to what the Brits call the first floor, and find it quieter and cooler. The high panjandrums of Bletchley have their offices here. If the organization is run true to bureaucratic form, Waterhouse will never see this place again once his initial interview is finished. He finds his way to the office of Colonel Chattan, who (Waterhouse's memory jogged by the sight of the name on the door) is the fellow at the top of the chart of Detachment 2702.

Chattan rises to shake his hand. He's strawberry blond, blue-eyed, and probably would be rosy-cheeked if he didn't have such a deep desert tan at the moment. He is wearing a dress uniform; British officers have their uniforms tailor-made, it is the only way to obtain them. Waterhouse is hardly a clothes horse, but he can see at a glance that Chattan's uniform was not thrown together by Mummy in a few evenings in front of a flickering coal grate. No, Chattan has himself an honest-to-god tailor somewhere. Yet, when he speaks Waterhouse's name, he does not say "woe to hice" like the Broadway Buildings crowd. The R comes through hard and crackling and the "house" part is elongated into some thing like "hoos." He has some kind of a wild-ass accent on him, this Chattan.

With Chattan is a smaller man in British fatigues-tight at the wrists and ankles, otherwise blousy, of thick khaki flannel that would be intolerably hot if these people couldn't rely on a steady ambient temperature, indoors and out, of about fifty-five degrees. The overall effect always reminds Waterhouse of Dr. Dentons. This fellow is introduced as Leftenant Robson, and he is the leader of one of 2702's two squads-the RAE one. He has a bristly mustache, trimmed very short, of silver and auburn whiskers. He is a cheerful sort, at least in the presence of higher ranks, and smiles frequently. His teeth splay out radially from the gumline so that each mandible has the appearance of a coffee can in which a small grenade has been detonated.

"This the fellow we've been waiting for," Chattan says to Robson. "The one we could've used in Algiers."

"Yes!" Robson says. "Welcome to Detachment 2701, Captain Waterhouse."

"2702," Waterhouse says.

Chattan and Robson look ever so mildly startled.

"We can't use 2701 because it is the product of two primes."

"I beg your pardon?" Robson says.

One thing Waterhouse likes about these Brits is that when they don't know what the hell you are talking about, they are at least open to the possibility that it might be their fault. Robson has the look of a man who has come up through the ranks. A Yank of that type would already be scornful and blustery.

"Which ones?" Chattan says. That is encouraging; he at least knows what a prime number is.

"73 and 37," Waterhouse says.

This makes a profound impression on Chattan. "Ah, yes, I see." He shakes his head. "I shall have to give the Prof a good chaffing about this."

Robson has cocked his head far to one side so that it is almost resting upon the thick woolly beret chucked into his epaulet. He is squinting, and has an aghast look about him. His hypothetical Yank counterpart would probably demand, at this point, a complete explanation of prime number theory, and when it was finished, denounce it as horseshit. But Robson just lets it go by. "Am I to understand that we are changing the number of our Detachment?"

Waterhouse swallows. It seems clear from Robson's reaction that this is going to involve a great deal of busy-work for Robson and his men: weeks of painting and stenciling and of trying to propagate the new number throughout the military bureaucracy. It will be a miserable pain in the ass.

"2702 it is," Chattan says breezily. Unlike Waterhouse, he has no difficulty issuing difficult, unpopular commands.

"Right then, I must see to some things. Pleasure making your acquaintance, Captain Waterhouse."

"Pleasure's mine."

Robson shakes Waterhouse's hand again and excuses himself.

"We have a billet for you in one of the huts to the south of the canteen," Chattan says. "Bletchley Park is our nominal headquarters, but we anticipate that we will spend most of our time in those theaters where heaviest use is being made of Ultra."

"I take it you've been in North Africa," Waterhouse says.

"Yes." Chattan raises his eyebrows, or rather the ridges of skin where his eyebrows are presumably located; the hairs are colorless and transparent, like nylon monofilament line. "Just got out by the skin of our teeth there, I'm afraid."

"Had a close shave, did you?"

"Oh, I don't mean it that way," Chattan says. "I'm talking about the integrity of the Ultra secret. We are still not sure whether we have survived it. But the Prof has done some calculations suggesting that we may be out of the woods."

"The Prof is what you call Dr. Turing?"

"Yes. He recommended you personally, you know."

"When the orders came through, I speculated as much."

"Turing is presently engaged on at least two other fronts of the information war, and could not be part of our happy few."

"What happened in North Africa, Colonel Chattan?"

"It's still happening," Chattan says bemusedly. "Our Marine squad is still in-theater, widening the bell curve.

"Widening the bell curve?"

"Well, you know better than I do that random things typically have a bell-shaped distribution. Heights, for example. Come over to this window, Captain Waterhouse."

Waterhouse joins Chattan at a bay window, where there is a view across acres of what used to be gently undulating farmland. Looking beyond the wooded belt to the uplands miles away, he can see what Bletchley Park probably used to look like: green fields dotted with clusters of small buildings.

But that is not what it looks like now. There is hardly a piece of land within half a mile that has not been recently paved or built upon. Once you get beyond the Mansion and its quaint little outbuildings, the park consists of one-story brick structures, nothing more than long corridors with multiple transepts: +++++++, and new +'s being added as fast as the masons can slap bricks on mud (Waterhouse wonders, idly, whether Rudy has seen aerial reconnaissance photos of this place, and deduced from all of those +'s the mathematical nature of the enterprise). The tortuous channels between buildings are narrow, and each is made twice as narrow by an eight-foot-high blast wall running down the middle of it, so that the Jerries will have to spend at least one bomb for each building.

"In that building there," Chattan says, pointing to a small building not far away-a truly wretched-looking brick hovel-"are the Turing Bombes. That's 'bombe' with an 'e' on the end. They are calculating machines invented by your friend the Prof."

"Are they true universal Turing machines?" Waterhouse blurts. He is in the grip of a stunning vision of what Bletchley Park might, in fact, be: a secret kingdom in which Alan has somehow found the resources needed to realize his great vision. A kingdom ruled not by men but by information, where humble buildings made of + signs house Universal Machines that can be configured to perform any computable operation.

"No," Chattan says, with a gentle, sad smile.

Waterhouse exhales for a long time. "Ah."

"Perhaps that will come next year, or the next."

"Perhaps."

"The bombes were adapted, by Turing and Welchman and others, from a design dreamed up by Polish cryptanalysts. They consist of rotating drums that test many possible Enigma keys with great speed. I'm sure the Prof will explain it to you. But the point is that they have these vast pegboards in the back, like telephone switchboards, and some of our girls have the job of putting the right pegs into the right holes and wiring the things up every day. Requires good eyesight, careful attention, and height."

"Height?"

"You'll notice that the girls who are assigned to that particular duty are unusually tall. If the Germans were to somehow get their hands on the personnel records for all of the people who work at Bletchley Park, and graph their heights on a histogram, they would see a normal bell shaped curve, representing most of the workers, with an abnormal bump on it-representing the unusual population of tall girls whom we have brought in to work the plug boards."

"Yes, I see," Waterhouse says, "and someone like Rudy-Dr. von Hacklheber-would notice the anomaly, and wonder about it."

"Precisely," Chattan says. "And it would then be the job of Detachment 2702-the Ultra Mega Group-to plant false information that would throw your friend Rudy off the scent." Chattan turns away from the window, strolls over to his desk, and opens a large cigarette box, neatly stacked with fresh ammunition. He offers one to Waterhouse with a deft hand gesture, and Waterhouse accepts it, just to be social. As Chattan is giving him a light, he gazes through the flame into Waterhouse's eye and says, 'I put it to you now. How would you go about concealing from your friend Rudy that we had a lot of tall girls here?'

"Assuming that he already had the personnel records?"

"Yes."

"Then it would be too late to conceal anything."

"Granted. Let us instead assume that he has some channel of information that is bringing him these records, a few at a time. This channel is still open and functioning. We cannot shut it down. Or perhaps we choose not to shut it down, because even the absence of this channel will tell Rudy something important."

"Well, there you go then," Waterhouse says. "We gin up some false personnel records and plant them in the channel."

There is a small chalkboard on the wall of Chattan's office. It is a palimpsest, not very well erased; the housekeeping detail here must have a standing order never to clean it, lest something important be lost. As Waterhouse approaches it, he can see older calculations layered atop each other, fading off into the blackness like transmissions of white light propagating into deep space.

He recognizes Alan's handwriting all over the place. It takes a physical effort not to stand there and try to reconstruct Alan's calculations from the ghosts lingering on the slate. He draws over them only with reluctance.

Waterhouse slashes an abscissa and an ordinate onto the board, then sweeps out a bell-shaped curve. On top of the curve, to the right of the peak, he adds a little hump.

"The tall girls," he explains. "The problem is this notch." He points to the valley between the main peak and the bump. Then he draws a new peak high and wide enough to cover both:

"We can do that by planting fake personnel records in Rudy's channel, giving heights that are taller than the overall average, but shorter than the bombe girls."

"But now you've dug yourself another hole," Chattan says. He is leaning back in his officer's swivel chair, holding the cigarette in front of his face, regarding Waterhouse through a motionless cloud of smoke.

Waterhouse says, "The new curve looks a little better because I filled in that gap, but it's not really bell-shaped. It doesn't tail off right, out here at the edges. Dr. von Hacklheber will notice that. He'll realize that someone's been tampering with his channel. To prevent that from happening I would have to plant more fake records, giving some unusually large and small values."

"Invent some fake girls who were exceptionally short or tall," Chattan says.

"Yes. That would make the curve tail off in the way that it should.'

Chattan continues to look at him expectantly.

Waterhouse says, "So, the addition of a small number of what would otherwise be bizarre anomalies makes it all look perfectly normal."

"As I said," Chattan says, "our squad is in North Africa-even as we speak-widening the bell curve. Making it all look perfectly normal."