The Return of the Black Widowers Read online

  "All right, then," said Trumbull, sitting back. "Well, Sandino came up with the lemma first and sent it in for publication."

  Drake was bent over the table, listening closely. He said, "Tough luck for Pochik."

  Trumbull said, "Except that Pochik says it wasn't luck. He claims Sandino doesn't have the brains for it and couldn't have taken the steps he did independently; that it is asking too much of coincidence."

  Drake said, “That’s a serious charge. Has Pochik got any evidence?"

  "No, of course not. The only way that Sandino could have stolen it from Pochik would have been to tap the computer for Pochik's data and Pochik himself says Sandino couldn't have done that."

  "Why not?" said Avalon.

  "Because," said Trumbull, "Pochik used a code word. The code word has to be used to alert the computer to a particular person's questioning. Without that code word, everything that went in with the code is safely locked away."

  Avalon said, "It could be that Sandino learned the code word."

  "Pochik says that is impossible," said Trumbull. "He was afraid of theft, particularly with respect to Sandino, and he never wrote down the code word, never used it except when he was alone in the room. What's more, he used one that was fourteen letters long, he says. Millions of trillions of possibilities, he says. No one could have guessed it, he says."

  Rubin said, "What does Sandino say?"

  "He says he worked it out himself. He rejects the claim of theft as the ravings of a madman. Frankly, one could argue that he's right."

  Drake said, "Well, let's consider. Sandino is a good mathematician and he's innocent till proven guilty. Pochik has nothing to support his claim and Pochik actually denies that Sandino could possibly have gotten the code word, which is the only way the theft could possibly have taken place. I think Pochik has to be wrong and Sandino right."

  Trumbull said, "I said one could argue that Sandino s right, but the point is that Pochik won't work. He's sulking in his room and reading poetry and he says he will never work again. He says Sandino has robbed him of his immortality and life means nothing to him without it."

  Gonzalo said, "If you need this guy so badly can you talk Sandino into letting him have his lemma?"

  "Sandino won't make the sacrifice and we can't make him unless we have reason to think that fraud was involved. If we get any evidence to that effect we can lean on him hard enough to squash him flat.—But now listen, I think it's possible Sandino did steal it."

  Avalon said, "How?"

  "By getting the code word. If I knew what the code word was, I'm sure I could figure out a logical way in which Sandino could have found it out or guessed it. Pochik, however simply won't let me have the code word. He shrieked at me when I asked. I explained why, but he said it was impossible. He said Sandino did it some other way—but there is no other way."

  Avalon said, "Pochik wants an interpretation but he won't tell you the dream, and you have to figure out the dream first and then get the interpretation."

  "Exactly! Like the Chaldean wise men."

  "What are you going to do?"

  "I'm going to try to do what Sandino must have done. I'm going to try to figure out what the fourteen-letter code word was and present it to Pochik. If I'm right, then it will be clear that what I could do, Sandino could do, and that the lemma was very likely stolen."

  There was a silence around the table and then Gonzalo said, "Do you think you can do it, Tom?"

  "I don't think so. That's why I've brought the problem here. I want us all to try. I told Pochik I would call him before 10:30 P.M. tonight"—Trumbull looked at his watch—"with the code word just to show him it could be broken. I presume he's waiting at the phone."

  Avalon said, "And if we don't get it?"

  "Then we have no reasonable way of supposing the lemma was stolen and no really ethical way of trying to force it away from Sandino. But at least we'll be no worse off."

  Avalon said, "Then you go first. You've clearly been thinking about it longer than we have, and it's your line of work."

  Trumbull cleared his throat. "All right. My reasoning is that if Pochik doesn't write the thing down, then he's got to remember it. There are some people with trick memories and such a talent is fairly common among mathematicians. However, even great mathematicians don't always have the ability to remember long strings of disjointed symbols and, upon questioning of his coworkers, it would seem quite certain that Pochik's memory is an ordinary one. He can't rely on being able to remember the code unless it's easy to remember.

  "That would limit it to some common phrase or some regular progression that you couldn't possibly forget. Suppose it were ALBERT EINSTEIN, for instance. That's fourteen letters and there would be no fear of forgetting it. Or SIR ISAAC NEWTON, or ABCDEFGHIJKLMN, or, for that matter, NMLKJIHGFEDCBA. If Pochik tried something like this, it could be that Sandino tried various obvious combinations and one of them worked."

  Drake said, "If that's true, then we haven't a prayer of solving the problem. Sandino might have tried any number of different possibilities over a period of months. One of them finally worked. If he got it by hit-and-miss over a long time, we have no chance in getting the right one in an hour and a half, without even trying any of them on the computer."

  "There's that, of course," said Trumbull, "and it may well be that Sandino had been working on the problem for months. Sandino pulled the waiter routine on Pochik last June, and Pochik, out of his mind, screamed at him that he would show him when his proof was ready. Sandino may have put this together with Pochik s frequent use of the computer and gotten to work. He may have had months, at that."

  "Did Pochik say something on that occasion that gave the code word away?" asked Avalon.

  "Pochik swears all he said was 'I'll show you when the proof is ready,' but who knows? Would Pochik remember his own exact words when he was beside himself?"

  Halsted said, "I'm surprised that Pochik didn't try to beat up this Sandino."

  Trumbull said, "You wouldn't be surprised if you knew them. Sandino is built like a football player and Pochik weighs 110 pounds with his clothes on."

  Gonzalo said, suddenly, "What's this guy's first name?" Trumbull said, "Vladimir."

  Gonzalo paused a while, with all eyes upon him, and then he said, "I knew it. VLADIMIR POCHIK has fourteen letters. He used his own name."

  Rubin said, "Ridiculous. It would be the first combination anyone would try."

  "Sure, the purloined letter bit. It would be so obvious that no one would think to use it. Ask him."

  Trumbull shook his head. "No, I can't believe he'd use that."

  Rubin said, thoughtfully, "Did you say he was sitting in his room reading poetry?"

  "Yes."

  "Is that a passion of his? Poetry? I thought you said that outside mathematics he was not particularly educated."

  Trumbull said, sarcastically, "You don't have to be a Ph.D. to read poetry."

  Avalon said, mournfully, "You would have to be an idiot to read modern poetry."

  "That's a point," said Rubin. "Does Pochik read contemporary poetry?"

  Trumbull said, "It never occurred to me to ask. When I visited him, he was reading from a book of Wordsworth's poetry, but that's all I can say."

  "That's enough," said Rubin. "If he likes Wordsworth then he doesn't like contemporary poetry. No one can read that fuddy-duddy for fun and like the stuff they turn out these days."

  "So? What difference does it make?" asked Trumbull.

  "The older poetry with its rhyme and rhythm is easy to remember and it could make for code words. The code word could be a fourteen-letter passage from one of Wordsworth's poems, possibly a common one: LONELY AS A CLOUD has fourteen letters. Or any fourteen-letter combinations from such lines as 'The child is father of the man' or 'trailing clouds of glory' or 'Milton! thou shouldst be living at this hour.'—Or maybe from some other poet of the type."

  Avalon said, "Even if we restrict ourselves to passages from
the classic and romantic poets, that's a huge field to guess from."

  Drake said, "I repeat. It's an impossible task. We don't have the time to try them all. And we can’t tell one from another without trying."

  Halsted said, "It's even more impossible than you think, Jim. I don't think the code word was in English words."

  Trumbull said, frowning, "You mean he used his native language?"

  "No, I mean he used a random collection of letters. You say that Pochik said the code word was unbreakable because there were millions of trillions of possibilities in a fourteen-letter combination. Well, suppose that the first letter could be any of the twenty-six, and the second letter could be any of the twenty-six, and the third letter, and so on. In that case the total number of combinations would be 26 x 26 x 26, and so on. You would have to get the product of fourteen 26's multiplied together and the result would be"—he took out his pocket calculator and manipulated it for a while—"about 64 million trillion different possibilities.

  "Now, if you used an English phrase or a phrase in any reasonable European language, most of the letter combinations simply don't occur. You're not going to have an HGF or a QXZ or an LLLLC. If we include only possible letter combinations in words then we might have trillions of possibilities, probably less, but certainly not millions of trillions. Pochik, being a mathematician, wouldn't say millions of trillions unless he meant exactly that, so I expect the code word is a random set of letters."

  Trumbull said, "He doesn't have the kind of memory—"

  Halsted said, "Even a normal memory will handle fourteen random letters if you stick to it long enough."

  Gonzalo said, "Wait awhile. If there are only so many combinations, you could use a computer. The computer could try every possible combination and stop at the one that unlocks it."

  Halsted said, "You don't realize how big a number like 64 million trillion really is, Mario. Suppose you arranged to have the computer test a billion different combinations every second. It would take two thousand solid years of work, day and night, to test all the possible combinations."

  Gonzalo said, "But you wouldn't have to test them all. The right one might come up in the first two hours. Maybe the code was AAAAAAAAAAAAAA and it happened to be the first one the computer tried."

  "Very unlikely," said Halsted. "He wouldn't use a solid-A code any more than he would use his own name. Besides Sandino is enough of a mathematician not to start a computer attempt he would know could take a hundred lifetimes."

  Rubin said, thoughtfully, "If he did use a random code I bet it wasn't truly random."

  Avalon said, "How do you mean, Manny?"

  "I mean if he doesn't have a superlative memory and he didn't write it down, how could he go over and over it in his mind in order to memorize it? Just repeat fourteen random letters to yourself and see if you can be confident of repeating them again in the exact order immediately afterward. And even if he had worked out a random collection of letters and managed to memorize it, it's clear he had very little self-confidence in anything except mathematical reasoning. Could he face the possibility of not being able to retrieve his own information because he had forgotten the code?"

  "He could start all over," said Trumbull.

  "With a new random code? And forget that, too?" said Rubin. "No. Even if the code word seems random, I'll bet Pochik has some foolproof way of remembering it, and if we can figure out the foolproof way, we'd have the answer. In fact, if Pochik would give us the code word, we'd see how he memorized it and see how Sandino broke the code."

  Trumbull said, "And if Nebuchadnezzar would only have remembered the dream, the wise men could have interpreted it. Pochik won't give us the code word, and if we work it with hindsight, we'll never be sufficiently sure Sandino cracked it without hindsight.—All right, we'll have to give it up."

  "It may not be necessary to give it up," said Henry, suddenly. "I think—"

  All turned to Henry, expectantly. "Yes, Henry," said Avalon.

  "I have a wild guess. It may be all wrong. Perhaps it might be possible to call up Mr. Pochik, Mr. Trumbull, and ask him if the code word is WEALTMDITEBIAT," said Henry.

  Trumbull said, "What?"

  Halsted said, his eyebrows high, "That's some wild guess, all right. Why that?"

  Gonzalo said, "It makes no sense."

  No one could recall ever having seen Henry blush, but he was distinctly red now. He said, "If I may be excused. I don't wish to explain my reasoning until the combination is tried. If I am wrong, I would appear too foolish.—And, on second thought, I don't urge it be tried."

  Trumbull said, "No, we have nothing to lose. Could you write down that letter combination, Henry?"

  "I have already done so, sir."

  Trumbull looked at it, walked over to the phone in the corner of the room, and dialed. He waited for four rings, which could be clearly heard in the breath-holding silence of the room. There was then a click, and a sharp, high-pitched "Hello?"

  Trumbull said, "Dr. Pochik? Listen. I'm going to read some letters to you—No, Dr. Pochik, I'm not saying I've worked out the code. This is an exper— It's an experiment sir. We may be wrong—No, I can't say how—Listen, W, E, A, L— Oh, good God." He placed his hand over the mouthpiece. "The man is having a fit."

  "Because it's right or because it's wrong?" asked Rubin.

  "I don't know." Trumbull put the phone back to his ear. "Dr. Pochik, are you there?—Dr. Pochik?—The rest is"—he consulted the paper—"T, M, D, I,T, E, B, I, A,T." He listened. "Yes, sir, I think Sandino cracked it, too, the same way we did. We'll have a meeting with you and Dr. Sandino, and we'll settle everything. Yes—please, Dr. Pochik, we will do our best." Trumbull hung up, heaved an enormous sigh, then said, "Sandino is going to think Jupiter fell on him.—All right, Henry, but if you don't tell us how you got that, you won't have to wait for Jupiter. I will kill you personally."

  "No need, Mr. Trumbull," said Henry. "I will tell you at once. I merely listened to all of you. Mr. Halsted pointed out it would have to be some random collection of letters. Mr. Rubin said, backing my own feeling in the matter, that there had to be some system of remembering in that case. Mr. Avalon, early in the evening, was playing the game of alliterative oaths, which pointed up the importance of initial letters. You yourself mentioned Mr. Pochik's liking for old-fashioned poetry like that of Wordsworth.

  "It occurred to me then that fourteen was the number of lines in a sonnet, and if we took the initial letters of each line of some sonnet we would have an apparently random collection of fourteen letters that could not be forgotten as long as the sonnet was memorized or could, at worst, be looked up.

  "The question was: which sonnet? It was very likely to be a well-known one, and Wordsworth had written some that were. In fact, Mr. Rubin mentioned the first line of one of them: 'Milton! thou shouldst be living at this hour.' That made me think of Milton, and it came to me that it had to be his sonnet 'On His Blindness' which as it happens, I know by heart. Please note the first letters of the successive lines. It goes:

  "When I consider how my light is spent

  Ere half my days, in this dark world and wide,

  And that one talent which is death to hide,

  Lodged with me useless, though my soul more bent

  To serve therewith my Maker, and present

  My true account, lest he returning chide;

  'Doth God exact day-labor, light denied?'

  I fondly ask; But Patience, to prevent

  That murmur, soon replies, 'God doth not need

  Either man s work or his own gifts; who best

  Bear his mild joke, they serve him best. His state

  Is kingly. Thousands at his bidding speed

  And post o'er land and ocean without rest:....'"

  Henry paused and said softly, "I think it is the most beautiful sonnet in the language, Shakespeare's not excepted, but that was not the reason I felt it must hold the answer. It was that Dr. Pochik had been a waiter and was
conscious of it, and I am one, which is why I have memorized the sonnet. A foolish fancy, no doubt, but the last line, which I have not quoted, and which is perhaps among the most famous lines Milton ever constructed—"

  "Go ahead, Henry," said Rubin. "Say it!"

  "Thank you, sir," said Henry, and then he said, solemnly,

  'They also serve who only stand and wait! "

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  THE REDHEAD

  M

  ario Gonzalo, host of that evening's meeting of the Black Widowers, had evidently decided to introduce his guest with éclat. At least he rattled his glass with a spoon and, when all had broken off their pre-prandial conversations and looked up from their cocktails, Mario made his introduction. He had even waited for Thomas Trumbull's as-usual late arrival before doing so.

  "Gentlemen," he said, "this is my guest, John Anderssen—that's an s-s-e-n at the end. You can discover anything you want about him in this evening's grilling. One thing, however, I must tell you now because I know that this bunch of asexual loudmouths will never discover it on their own. John has a wife who is, absolutely, the most gorgeous specimen of femininity the world has ever seen. And I say this as an artist with an artist's eye."

  Anderssen reddened and looked uncomfortable. He was a blond young man, perhaps thirty, with a small mustache and a fair complexion. He was about five-ten in height and had rather chiseled features that came together to form a handsome face.

  Geoffrey Avalon, looking down from his stiff-backed seventy-four inches, said, "I must congratulate you, Mr. Anderssen, although you need not take seriously Mario's characterization of ourselves as asexual. I'm sure that each of us is quite capable of appreciating a beautiful woman. I, myself, although I might be considered to be past the first flush of hot-blooded youth, can—"

  Trumbull said, "Spare us, Jeff, spare us. If you are going to give an embarrassing account of your prowess, you are better off being interrupted. From my point of view, the next best thing to having

  127 the young woman in our midst—if our customs allowed it— would be to see her photograph. I imagine, Mr. Anderssen, you carry a photo of your fair wife in your wallet. Would you consent to let us look at it?"