Cryptonomicon

As of the actual outbreak of war with Nippon, Schoen is on disability, and taking lots of drugs. Waterhouse spends as much time with Schoen as he is allowed to, because he's pretty sure that whatever happened inside of Schoen's head, between when the lists of apparently random numbers were dumped into his lap and when he finished building his machine, is an example of a noncomputable process.

Waterhouse's security clearance is upgraded about once a month, until it reaches the highest conceivable level (or so he thinks) which is Ultra/Magic. Ultra is what the Brits call the intelligence they get from having broken the German Enigma machine. Magic is what the Yanks call the intelligence they get from Indigo. In any case, Lawrence now gets to see the Ultra/Magic summaries, which are bound documents with dramatic, alternating red and black paragraphs printed on the front cover. Paragraph number three states:

NO ACTION IS TO BE TAKEN ON INFORMATION HEREIN REPORTED, REGARDLESS OF TEMPORARY ADVANTAGE, IF SUCH ACTION MIGHT HAVE THE EFFECT OF REVEALING THE EXISTENCE OF THE SOURCE TO THE ENEMY.

Seems clear enough, right? But Lawrence Pritchard Waterhouse is not so damn sure.

IF SUCH ACTION MIGHT HAVE THE EFFECT OF REVEALING...

At about the same time, Waterhouse has made a realization about himself. He has found that he works best when he is not horny, which is to say in the day or so following ejaculation. So as a part of his duty to the United States he has begun to spend a lot of time in whorehouses. But he can't have that much actual sex on what is still a glockenspiel player's pay and so he limits himself to what are euphemistically called massages.

ACTION... EFFECT... REVEALING...

The words stay with him like the clap. He lies on his back during these massages, arms crossed over his eyes, mumbling the words to himself. Something bothers him. He has learned that when something bothers him in this particular way it usually leads to his writing a new paper. But first he has to do a lot of hard mental pick-and-shovel work.

It all comes to him, explosively, during the Battle of Midway, while he and his comrades are spending twenty-four hours a day down among those ETC machines, decrypting Yamamoto's messages, telling Nimitz exactly where to find the Nip fleet.

What are the chances of Nimitz finding that fleet by accident? That's what Yamamoto must be asking himself.

It is all a question (oddly enough!) of information theory.

...ACTION...

What is an action? It might be anything. It might be something obvious like bombing a Nipponese military installation. Everyone would agree that this would constitute an action. But it might also be something like changing the course of an aircraft carrier by five degrees--or notdoing so. Or having exactly the right package of forces off Midway to hammer the Nipponese invasion fleet. It could mean something much less dramatic, like canceling plans for an action. An action, in a certain sense, might even be the total absence of activity. Any of these might be rational responses, on the part of some commander, to INFORMATION HEREIN REPORTED. But any of them might be observable by the Nipponese--and hence any of them would impart information to the Nipponese. How good might those Nips be at abstracting information from a noisy channel? Do they have any Schoens?

...EFFECT...

So what if the Nips did observe it? What would the effectbe exactly? And under what circumstances might the effect be REVEALING THE EXISTENCE OF THE SOURCE TO THE ENEMY?

If the action is one that could never have happened unless the Americans were breaking Indigo, then it will constitute proof, to the Nipponese, that the Americans have broken it. The existence of the source--the machine that Commander Schoen built--will be revealed.

Waterhouse trusts that no Americans will be that stupid. But what if it isn't that clear-cut? What if the action is one that would merely be really improbableunless the Americans were breaking the code? What if the Americans, in the long run, are just too damn lucky?

And how closely can you play that game? A pair of loaded dice that comes up sevens every time is detected in a few throws. A pair that comes up sevens only one percent more frequently than a straight pair is harder to detect--you have to throw the dice many more times in order for your opponent to prove anything.

If the Nips keep getting ambushed--if they keep finding their own ambushes spoiled--if their merchant ships happen to cross paths with American subs more often than pure probability would suggest--how long until they figure it out?

Waterhouse writes papers on the subject, keeps pestering people with them. Then, one day, Waterhouse receives a new set of orders.