Published December 16, 1999 5:00PM (EST)

He divides his time between thinking about sex and thinking about mathematics. The former keeps intruding upon the latter. It gets worse when the stout fiftyish cook named Blanche, who has been bringing him his meals, comes down with dropsy or ague or gout or colic or some other Shakespearian ailment and is replaced by Margaret, who is about twenty and quite fetching.

Margaret really messes up his head. When it gets really intolerable, he goes to the latrine (so that the staff will not break in on him at an inopportune moment) and executes a Manual Override. But one thing he learned in Hawaii was that a Manual Override is unfortunately not the same as the real thing. The effect wears off too soon.

While he's waiting for it to wear off, he gets a lot of solid math done. Alan provided him with some notes on redundancy and entropy, relating to the voice encryption work he is currently doing in New York City. Waterhouse works through that stuff and comes up with some nice lemmas which he lamentably cannot send to Alan without violating both common sense and any number of security procedures. This done, he turns his attention to cryptology, pure and raw. He spent enough time at Bletchley Park to realize just how little of this art he really understood.

The U-boats talk on the radio way too much and everyone in the German Navy knows it. Their security experts have been nagging their brass to tighten up their security, and they finally did it by introducing the four-rotor version of the Enigma machine, which has knocked Bletchley Park on its ass for about a year ...

Margaret has to walk round the castle out of doors to bring Waterhouse his meals, and by the time she gets here, her cheeks have turned rosy red. The steam coming from her mouth floats around her face like a silken veil --

Stop that, Lawrence! The subject of today's lecture is the German Naval four-wheel Enigma, known to them as Triton and to the Allies as Shark. Introduced on 2 February of last year (1942), it wasn't until the recovery of the beached German U-boat U-559 on 30 October that Bletchley Park got the material they needed to break the code. A couple of weeks ago, on 13 December, Bletchley Park finally busted Shark, and the internal communications of the German Navy became an open book to the Allies once more.

The first thing they have learned, as a result, is that the Germans have broken our merchant shipping codes wide open and that all year long they have known exactly where to find the convoys.

All of this information has been provided to Lawrence Pritchard Waterhouse within the last few days, via the totally secure one-time pad channel. Bletchley is telling him this stuff because it raises a question of information theory, which is his department and his problem. The question is: how quickly can we replace our busted merchant shipping codes without tipping the Germans off to the fact that we have broken Shark?

Waterhouse does not have to think about this one for very long before he concludes that it is far too tricky to play games with. The only way to handle the situation is to concoct an incident of some sort that will explain to the Germans why we have totally lost faith in our own merchant shipping codes and are changing them.

By Neal Stephenson

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