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.