their priceless but perishable gems of intelligence.
The largest sealift in history just piled into Northwest Africa. It is called Operation Torch, and it's going to take Rommel from behind, serving as anvil to Montgomery's hammer, or, if Monty doesn't pick up the pace a bit, maybe the other way around. It looks brilliantly organized but it's not really; this is the first time America has punched across the Atlantic in any serious way and so a whole grab bag of stuff is included on those ships-including any number of signals intelligence geeks who are storming theatrically onto the beaches as if they were Marines. Also included in the landing is the American contingent of Detachment 2702-a hand-picked wrecking crew of combat-hardened leathernecks.
Some of these Marines learned what they know on Guadalcanal, a basically useless island in the Southwest Pacific where the Empire of Nippon and the United States of America are disputing-with rifles-each other's right to build a military airbase. Early returns suggest that the Nipponese Army, during its extended tour of East Asia, has lost its edge. It would appear that raping the entire female population of Nanjing, and bayoneting helpless Filipino villagers, does not translate into actual military competence. The Nipponese Army is still trying to work out some way to kill, say, a hundred American Marines without losing, say, five hundred of its own soldiers.
The Japanese Navy is a different story-they know what they are doing. They have Yamamoto. They have torpedoes that actually explode when they strike their targets, in stark contrast to the American models which do nothing but scratch the paint of the Japanese ships and then sink apologetically. Yamamoto just made another attempt to wipe out the American fleet off the Santa Cruz Islands, sank
The Allies are doing some math of their own, and they are scared shitless. There are 100 German U-boats in the Atlantic now, operating mostly from Lorient and Bordeaux, and they are slaughtering convoys in the North Atlantic with such efficiency that it's not even
The problem is Shark.
The Germans call it Triton. It is a new cypher system, used exclusively by their Navy. It is an Enigma machine, but not the usual three-wheel Enigma. The Poles learned how to break that old thing a couple of years ago, and Bletchley Park industrialized the process. But more than a year ago, a German U-boat was beached intact on the south coast of Iceland and gone over pretty thoroughly by men from Bletchley. They discovered an Enigma box with niches for four-not three-wheels.
When the four-wheel Enigma had gone into service on February 1st, the entire Atlantic had gone black. Alan and the others have been going after the problem very hard ever since. The problem is that they don't know how the fourth wheel is wired up.
But a few days ago, another U-boat was captured, more or less intact, in the Eastern Mediterranean. Colonel Chattan, who happened to be in the neighborhood, went there with sickening haste, along with some other Bletchleyites. They recovered a four-wheel Enigma machine, and though this doesn't break the code, it gives them the data they need to break it.
Hitler must be feeling cocky, anyway, because he's on tour at the moment, preparatory to a working vacation at his alpine retreat. That didn't prevent him from taking over what was left of France-apparently something about Operation Torch really got his goat, so he occupied Vichy France in its entirety, and then dispatched upwards of a hundred thousand fresh troops, and a correspondingly stupendous amount of supplies, across the Mediterranean to Tunisia. Waterhouse imagines that you must be able to cross from Sicily to Tunisia these days simply by hopping from the deck of one German transport ship to another.
Of course, if that were true, Waterhouse's job would be a lot easier. The Allies could sink as many of those ships as they wanted to without raising a single blond Teutonic eyebrow on the information-theory front. But the fact is that the convoys are few and far between. Just exactly how few and how far between are parameters that go into the equations that he and Alan Mathison Turing spend all night scribbling on chalkboards.
After a good eight or twelve hours of that, when the sun has finally come up again, there's nothing like a brisk bicycle ride in the Buckinghamshire countryside.
Spread out before them as they pump over the crest of the rise is a woods that has turned all of the colors of flame. The hemispherical crowns of the maples even contribute a realistic billowing effect. Lawrence feels a funny compulsion to take his hands off the handlebars and clamp them over his ears. As they coast into the trees, however, the air remains delightfully cool, the blue sky above unsmudged by pillars of black smoke, and the calm and quiet of the place could not be more different from what Lawrence is remembering.
'Talk, talk, talk!' says Alan Turing, imitating the squawk of furious hens. The strange noise is made stranger by the fact that he is wearing a gas mask, until he becomes impatient and pulls it up onto his forehead. 'They love to hear themselves talk.' He is referring to Winston Churchill and Franklin Roosevelt. 'And they don't mind hearing each other talk-up to a point, at least. But voice is a terribly redundant channel of information, compared to printed text. If you take text and run it through an Enigma-which is really not all that complicated-the familiar patterns in the text, such as the preponderance of the letter E, become nearly undetectable.' Then he pulls the gas mask back over his face in order to emphasize the following point: 'But you can warp and permute voice in the most fiendish ways imaginable and it will still be perfectly intelligible to a listener.' Alan then suffers a sneezing fit that threatens to burst the khaki straps around his head.
'Our ears know how to find the familiar patterns,' Lawrence suggests. He is not wearing a gas mask because (a) there is no Nazi gas attack in progress, and (b) unlike Alan, he does not suffer from hay fever.
'Excuse me.' Alan suddenly brakes and jumps off his bicycle. He lifts the rear wheel from the pavement, gives it a spin with his free hand, then reaches down and gives the chain a momentary sideways tug. He is watching the mechanism intently, interrupted by a few aftersneezes.
The chain of Turing's bicycle has one weak link. The rear wheel has one bent spoke. When the link and the spoke come into contact with each other, the chain will part and fall onto the road. This does not happen at every revolution of the wheel-otherwise the bicycle would be completely useless. It only happens when the chain and the wheel are in a certain position with respect to each other.
Based upon reasonable assumptions about the velocity that can be maintained by Dr. Turing, an energetic bicyclist (let us say 25 km/hr) and the radius of his bicycle's rear wheel (a third of a meter), if the chain's weak link hit the bent spoke on every revolution, the chain would fall off every one-third of a second.
In fact, the chain doesn't fall off unless the bent spoke and the weak link happen to coincide. Now, suppose that you describe the position of the rear wheel by the traditional [theta]. Just for the sake of simplicity, say that when the wheel starts in the position where the bent spoke is capable of hitting the weak link (albeit only if the weak link happens to be there to be hit) then [theta] = 0. If you're using degrees as your unit, then, during a single revolution of the wheel, [theta] will climb all the way up to 359 degrees before cycling back around to 0, at which point the bent spoke will be back in position to knock the chain off And now suppose that you describe the position of the chain with the variable C, in the following very simple way: you assign a number to each link on the chain. The weak link is numbered 0, the next is 1, and so on, up to l — 1 where l is the total number of links in the chain. And again, for simplicity's sake, say that when the chain is in the position where its weak link is capable of being hit by the bent spoke (albeit only if the bent spoke happens to be there to hit it) then C = 0.
For purposes of figuring out when the chain is going to fall off of Dr. Turing's bicycle, then, everything we need to know about the bicycle is contained in the values of [theta] and of C. That pair of numbers defines the bicycle's state. The bicycle has as many possible states as there can be different values of ([theta], C) but only one of those states, namely (0, 0), is the one that will cause the chain to fall off onto the road.
Suppose we start off in that state; i.e., with ([theta] = 0, C = 0), but that the chain has not fallen off because Dr. Turing (knowing full well his bicycle's state at any given time) has paused in the middle of road (nearly precipitating a collision with his friend and colleague Lawrence Pritchard Waterhouse, because his gas mask blocks
