Mary Smith fouls up the whole system of equations

Wherein I excerpt a mathematical treatise on managing your sigma level


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Of course for anyone who has read Neal Stephenson's Cryptonomicon, this is nothing new. In the novel, Lawrence Waterhouse, a code-breaking genius, has been dispatched to Australia to finish off the Japanese. He long ago noted a difference in performance based upon performance. Though Stephenson uses many enlightening graphs to illustrate the math, I've left those out of this excerpt:

Waterhouse has been chewing his way through exotic Nip code systems at the rate of about one a week, but after he sees Mary Smith in the parlor of Mrs. McTeague’s boarding house, his production rate drops to near zero. Arguably, it goes negative, for sometimes when he reads the morning newspaper, its plaintext scrambles into gibberish before his eyes, and he is unable to extract any useful information.

Despite his and Turing’s disagreements about whether the human brain is a Turing machine, he has to admit that Turing wouldn’t have too much trouble writing a set of instructions to simulate the brain functions of Lawrence Pritchard Waterhouse.

Waterhouse seeks happiness. He achieves it by breaking Nip code systems and playing the pipe organ. But since pipe organs are in short supply, his happiness level ends up being totally dependent on breaking codes.

He cannot break codes (hence, cannot be happy) unless his mind is clear. Now suppose that mental clarity is designated by C(m), which is normalized, or calibrated, in such a way that it is always the case that

0 <=C(m) < 1

where C(m) = 0 indicates a totally clouded mind and C(m) = 1 is Godlike clarity—an unattainable divine state of infinite intelligence. If the number of messages Waterhouse decrypts, in a given day, is designated by N(decrypts), then it will be governed by C(m) in roughly the following way: [deleted graph]


Clarity of mind (C(m)) is affected by any number of factors, but by far the most important is horniness, which might be designated by [sigma], for obvious anatomical reasons that Waterhouse finds amusing at this stage of his emotional development.

Horniness begins at zero at time t=t(m) (immediately following ejaculation) and increases from there as a linear function of time: [deleted statement]


The only way to drop it back to zero is to arrange another ejaculation.

There is a critical threshold [sigma sub c] such that when [sigma] > [sigma sub c] it becomes impossible for Waterhouse to concentrate on anything, or, approximately,



which amounts to saying that the moment [sigma] rises above the threshold [sigma sub c] it becomes totally impossible for Waterhouse to break Nipponese cryptographic systems. This makes it impossible for him to achieve happiness (unless there is a pipe organ handy, which there isn’t).

Typically, it takes two to three days for [sigma] to climb above [sigma sub c] after an ejaculation: [deleted graph]


Critical, then, to the maintenance of Waterhouse’s sanity is the ability to ejaculate every two to three days. As long as he can arrange this, [sigma] exhibits a classic sawtooth-wave pattern, optimally with the peaks at or near [sigma sub c] wherein the grey zones represent periods during which he is completely useless to the war effort.

So much for the basic theory. Now, when he was at Pearl Harbor, he discovered something that, in retrospect, should have been profoundly disquieting. Namely, that ejaculations obtained in a whorehouse (i.e., provided by the ministrations of an actual human female) seemed to drop [sigma] below the level that Waterhouse could achieve through executing a Manual Override. In other words, the post-ejaculatory horniness level was not always equal to zero, as the naive theory propounded above assumes, but to some other quantity dependent upon whether the ejaculation was induced by Self or Other: [sigma] =[sigma sub self] after masturbation but [sigma]=[sigma sub other] upon leaving a whorehouse, where [sigma sub self] > [sigma sub other] an inequality to which Waterhouse’s notable successes in breaking certain Nip naval codes at Station Hypo were directly attributable, in that the many convenient whorehouses nearby made it possible for him to go somewhat longer between ejaculations.


If he had thought about this, it would have bothered him, because [sigma sub self] > [sigma sub other] has troubling implications—particularly if the values of these quantities w.r.t. the all-important [sigma sub c] are not fixed. If it weren’t for this inequality, then Waterhouse could function as a totally self-contained and independent unit. But [sigma sub self] > [sigma sub other] implies that he is, in the long run, dependent on other human beings for his mental clarity and, therefore, his happiness. What a pain in the ass!

Perhaps he has avoided thinking about this precisely because it is so troubling. The week after he meets Mary Smith, he realizes that he is going to have to think about it a lot more.

Something about the arrival of Mary Smith on the scene has completely fouled up the whole system of equations. Now, when he has an ejaculation, his clarity of mind does not take the upwards jump that it should. He goes right back to thinking about Mary. So much for winning the war!

He goes out in search of whorehouses, hoping that good old reliable [sigma sub other] will save his bacon. This is troublesome. When he was at Pearl, it was easy, and uncontroversial. But Mrs. McTeague’s boardinghouse is in a residential neighborhood, which, if it contains whorehouses, at least bothers to hide them. So Waterhouse has to travel downtown, which is not that easy in a place where internal-combustion vehicles are fueled by barbecues in the trunk. Furthermore Mrs. McTeague is keeping her eye on him. She knows his habits. If he starts coming back from work four hours late, or going out after dinner, he’ll have some explaining to do. And it had better be convincing, because she appears to have taken Mary Smith under one quivering gelatinous wing and is in a position to poison the sweet girl’s mind against Waterhouse. Not only that, he has to do much of his excuse-making in public, at the dinner table, which he shares with Mary’s cousin (whose first name turns out to be Rod).

But hey, Doolittle bombed Tokyo, didn’t he? Waterhouse should at least be able to sneak out to a whorehouse. It takes a week of preparations (during which he is completely unable to accomplish meaningful work because of the soaring [sigma] level), but he manages it.

It helps a little, but only on the [sigma] management level. Until recently, that was the only level and so it would have been fine. But now (as Waterhouse realizes through long contemplation during the hours when he should be breaking codes) a new factor has entered the system of equations that governs his behavior; he will have to write to Alan and tell him that some new instructions will have to be added to the Waterhouse simulation Turing machine. This new factor is FMSp, the Factor of Mary Smith Proximity.

In a simpler universe, FMSp, would be orthogonal to [sigma], which is to say that the two factors would be entirely independent of each other. If it were thus, Waterhouse could continue the usual sawtooth-wave ejaculation management program with no changes. In addition, he would have to arrange to have frequent conversations with Mary Smith so that FMSp would remain as high as possible.

Alas! The universe is not simple. Far from being orthogonal, FMSp and [sigma] are involved, as elaborately as the contrails of dogfighting airplanes. The old [sigma] management scheme doesn’t work anymore. And a platonic relationship will actually make FMSp worse, not better. His life, which used to be a straightforward set of basically linear equations, has become a differential equation.

It is the visit to the whorehouse that makes him realize this. In the Navy, going to a whorehouse is about as controversial as pissing down the scuppers when you are on the high seas—the worst you can say about it is that, in other circumstances, it might seem uncouth. So Waterhouse has been doing it for years without feeling troubled in the slightest.

But he loathes himself during, and after, his first post-Mary-Smith whorehouse visit. He no longer sees himself through his own eyes but through hers—and, by extension, those of her cousin Rod and of Mrs. McTeague and of the whole society of decent God-fearing folk to whom he has never paid the slightest bit of attention until now.

It seems that the intrusion of FMSp into his happiness equation is just the thin edge of a wedge which leaves Lawrence Pritchard Waterhouse at the mercy of a vast number of uncontrollable factors, and requiring him to cope with normal human society. Horrifyingly, he now finds himself getting ready to go to a dance.