Asimov, Isaac - Black Widowers 02 - Bouquets of the Black Widowers.pdf - Isaac Asimov - Planetar81

BOUQUETS OF THE BLACK WIDOWERS

ISAAC ASIMOV, 1984

Sixty Million Trillion Combinations

SINCE IT WAS Thomas Trumbull who was going to act as host for the Black Widowers that month, he

did not, as was his wont, arrive at the last minute, gasping for his preprandial drink.

There he was, having arrived in early dignity, conferring with Henry, that peerless waiter, on the details of

the menu for the evening, and greeting each of the others as he arrived.

Mario Gonzalo, who arrived last, took off his light overcoat with care, shook it gently, as though to

remove the dust of the taxicab, and hung it up in the cloakroom. He came back, rubbing his hands, and

said, "There's an autumn chill in the air. I think summer's over."

"Good riddance," called out Emmanuel Rubin, from where he stood conversing with Geoffrey Avalon

and James Drake.

"I'm not complaining," called back Gonzalo. Then, to Trumbull, "Hasn't your guest arrived yet?"

Trumbull said distinctly, as though tired of explaining, "I have not brought a guest."

"Oh?" said Gonzalo, blankly. There was nothing absolutely irregular about that. The rules of the Black

Widowers did not require a guest, although not to have one was most unusual. "Well, I guess that's all

right."

"It's more than all right," said Geoffrey Avalon, who had just drifted in their direction, gazing down from

his straight - backed height of seventy - four inches. His thick graying eyebrows hunched over his eyes

and he said, "At least that guarantees us one meeting in which we can talk aimlessly and relax."

Gonzalo said, "I don't know about that. I'm used to the problems that come up. I don't think any of us

will feel comfortable without one. Besides, what about Henry?"

He looked at Henry as he spoke and Henry allowed a discreet smile to cross his unlined, sixtyish face.

"Please don't be concerned, Mr. Gonzalo. It will be my pleasure to serve the meal and attend the

conversation even if there is nothing of moment to puzzle us."

"Well," said Trumbull, scowling, his crisply waved hair startlingly white over his tanned face, "you won't

have that pleasure, Henry. I'm the one with the problem and I hope someone can solve it: you at least,

Henry."

Avalon's lips tightened, "Now by Beelzebub's brazen bottom, Tom, you might have given us one old -

fashioned - "

Trumbull shrugged and turned away, and Roger Halsted said to Avalon in his soft voice, "What's that

Beelzebub bit? Where'd you pick that up?"

Avalon looked pleased. "Oh, well, Manny is writing some sort of adventure yarn set in Elizabeth's

England - Elizabeth I of course - and it seems - "

Rubin, having heard the magic sound of his name, approached and said, "It's a sea story."

Halsted said, "Are you tired of mysteries?"

"It's a mystery also," said Rubin, his eyes flashing behind the thick lenses of his glasses. "What makes you

think you can't have a mystery angle to any kind of story?"

"In any case," said Avalon, "Manny has one character forever swearing alliteratively and never the same

twice and he needs a few more resounding oaths. Beelzebub's brazen bottom is good, I think."

"Or Mammon's munificent mammaries," said Halsted.

Trumbull said, violently, "There you are! If I don't come up with some problem that will occupy us in

worthwhile fashion and engage our Henry's superlative mind, the whole evening would degenerate into

stupid triplets - by Tutankhamen's tin trumpet."

"It gets you after a while," grinned Rubin, unabashed.

"Well, get off it," said Trumbull. "Is dinner ready, Henry?"

"Yes it is, Mr. Trumbull."

"All right, then. If you idiots keep this alliteration up for more than two minutes, I'm walking out, host or

no host."

The table seemed empty with only six about it, and conversation seemed a bit subdued with no guest to

sparkle before.

Gonzalo, who sat next to Trumbull, said, "I ought to draw a cartoon of you for our collection since you're

your own guest, so to speak." He looked up complacently at the long list of guest - caricatures that lined

the wall in rank and file. "We're going to run out of space in a couple of years."

"Then don't bother with me," said Trumbull, sourly, "and we can always make space by burning those

foolish scrawls."

"Scrawls!" Gonzalo seemed to debate within himself briefly concerning the possibility of taking offense.

Then he compromised by saying, "You seem to be in a foul mood, Tom."

"I seem so because I am. I'm in the situation of the Chaldean wise men facing Nebuchadnezzar."

Avalon leaned over from across the table. "Are you talking about the Book of Daniel, Tom?"

"That's where it is, isn't it?"

Gonzalo said, "Pardon me, but I didn't have my Bible lesson yesterday. What are these wise men?"

"Tell him, Jeff," said Trumbull. "Pontificating is your job."

Avalon said, "It's not pontificating to tell a simple tale. If you would rather - "

Gonzalo said, "I'd rather you did, Jeff. You do it much more authoritatively."

"Well," said Avalon, "it's Rubin, not I, who was once a boy preacher, but I'll do my poor best. The

second chapter of the Book of Daniel tells that Nebuchadnezzar was once troubled by a bad dream and

he sent for his Chaldean wise men for an interpretation. The wise men offered to do so at once as soon

as they heard the dream but Nebuchadnezzar couldn't remember the dream, only that he had been

disturbed by it. He reasoned, however, that if wise men could interpret a dream, they could work out the

dream, too, so he ordered them to tell him both the dream and the interpretation. When they couldn't do

this, he very reasonably - by the standards of Oriental potentates - ordered them all killed. Fortunately

for them Daniel, a captive Jew in Babylon, could do the job."

Gonzalo said, "And that's your situation, too, Tom?"

"In a way. I have a problem that involves a cryptogram - but I don't have the cryptogram. I have to work

out the cryptogram."

"Or you'll be killed?" asked Rubin.

"No. If I fail, I won't be killed, but it won't do me any good, either."

Gonzalo said, "No wonder you didn't feel it necessary to bring a guest. Tell us all about it."

"Before the brandy?" said Avalon, scandalized.

"Tom's host," said Gonzalo, defensively. "If he wants to tell us now - "

"I don't," said Trumbull. "We'll wait for the brandy as we always do, and I'll be my own griller, if you

don't mind."

When Henry was pouring the brandy, Trumbull rang his spoon against his water glass and said,

"Gentlemen, I will dispense with the opening question by admitting openly that I cannot justify my

existence. Without pretending to go on by question - and - answer, I will simply state the problem. You

are free to ask questions, but for God's sake, don't get me off on any wild - goose chases. This is

serious."

Avalon said, "Go ahead, Tom. We will do our best to listen."

Trumbull said, with a certain weariness, "It involves a fellow named Pochik. I've got to tell you a little

about him in order to let you understand the problem but, as is usual in these cases, I hope you don't

mind if I tell you nothing that isn't relevant.

"In the first place he's from Eastern Europe, from someplace in Slovenia, I think, and he came here at

about fourteen. He taught himself English, went to night school and to University Extension, working

every step of the way. He worked as a waiter for ten years, while he was taking his various courses, and

you know what that means. Sorry, Henry."

Henry said, tranquilly, "It is not necessarily a pleasant occupation. Not everyone waits on the Black

Widowers, Mr. Trumbull."

"Thank you, Henry. That's very diplomatic of you. However, he wouldn't have made it, if it weren't plain

from the start that he was a mathematical wizard. He was the kind of young man that no mathematics

professor in his right mind wouldn't have moved heaven and earth to keep in school. He was their claim

to a mark in the history books - that they had taught Pochik. Do you understand?"

Avalon said, "We understand, Tom."

Trumbull said, "At least, that's what they tell me. He's working for the government now, which is where I

come in. They tell me he's something else. They tell me he's in a class by himself. They tell me he can do

things no one else can. They tell me they've got to have him. I don't even know what he's working on, but

they've got to have him."

Rubin said, "Well, they've got him, haven't they? He hasn't been kidnapped and hijacked back across the

Iron Curtain, has he?"

"No, no," said Trumbull, "nothing like that. It's a lot more irritating. Look, apparently a great

mathematician can be an idiot in every other respect."

"Literally an idiot?" asked Avalon. "Usually idiots savants have remarkable memories and can play

remarkable tricks in computation, but that is far from being any kind of mathematician, let alone a great

one."

"No, nothing like that, either." Trumbull was perspiring and paused to mop at his forehead. "I mean he's

childish. He's not really learned in anything but mathematics and that's all right. Mathematics is what we

want out of him. The trouble is that he feels backward; he feels stupid. Damn it, he feels inferior, and

when he feels too inferior, he stops working and hides in his room."

Gonzalo said, "So what's the problem? Everyone just has to keep telling him how great he is all the time."

"He's dealing with other mathematicians and they're almost as crazy as he is. One of them, Sandino, hates

being second best and every once in a while he gets Pochik into a screaming fit. He's got a sense of

humor, this Sandino, and he likes to call out to Pochik, 'Hey, waiter, bring the check.' Pochik can't ever

learn to take it."

Drake said, "Read this Sandino the riot act. Tell him you'll dismember him if he tries anything like that

again."

"They did," said Trumbull, "or at least as far as they quite dared to. They don't want to lose Sandino

either. In any case, the horseplay stopped but something much worse happened. You see there's

something called, if I've got it right, 'Goldbach's conjecture'."

Roger Halsted galvanized into a position of sharp interest at once. "Sure," he said. "Very famous."

"You know about it?" said Trumbull.

Halsted stiffened. "I may just teach algebra to junior high school students, but yes, I know about

Goldbach's conjecture. Teaching a junior high school student doesn't make me a junior - "

"All right. I apologize. It was stupid of me," said Trumbull. "And since you're a mathematician, you can be

temperamental too. Anyway, can you explain Goldbach's conjecture? - Because I'm not sure I can."

"Actually," said Halsted, "it's very simple. Back in 1742, I think, a Russian mathematician, Christian

Goldbach, stated that he believed every even number greater than 2 could be written as the sum of two

primes, where a prime is any number that can't be divided evenly by any other number but itself and i.

For instance, 4 = 2 + 2; 6 = 3 + 3; 8 = 3 + 5; 10 = 3 + 7; 12 = 5 + 7; and so on, as far as you want to

go."

Gonzalo said, "So what's the big deal?"

"Goldbach wasn't able to prove it. And in the two hundred and something years since his time, neither

has anyone else. The greatest mathematicians haven't been able to show that it's true."

Gonzalo said, "So?"

Halsted said patiently, "Every even number that has ever been checked always works out to be the sum

of two primes. They've gone awfully high and mathematicians are convinced the conjecture is true - but

no one can prove it."

Gonzalo said, "If they can't find any exceptions, doesn't that prove it?"

"No, because there are always numbers higher than the highest we've checked, and besides we don't

know all the prime numbers and can't, and the higher we go, then the harder it is to tell whether a

particular number is prime or not. What is needed is a general proof that tells us we don't have to look

for exceptions because there just aren't any. It bothers mathematicians that a problem can be stated so

simply and seems to work out, too, and yet that it can't be proved."

Trumbull had been nodding his head. "All right, Roger, all right. We get it. But tell me, does it matter?

Does it really matter to anyone who isn't a mathematician whether Goldbach's conjecture is true or not;

whether there are any exceptions or not?"

"No," said Halsted. "Not to anyone who isn't a mathematician; but to anyone who is and who manages

either to prove or disprove Goldbach's conjecture, there is an immediate and permanent niche in the

mathematical hall of fame."

Trumbull shrugged. "There you are. What Pochik's really doing is of great importance. I'm not sure

whether it's for the Department of Defense, the Department of Energy, NASA, or what, but it's vital.

What he's interested in, however, is Goldbach's conjecture, and for that he's been using a computer."

"To try higher numbers?" asked Gonzalo.

Halsted said promptly, "No, that would do no good. These days, though, you can use computers on

some pretty recalcitrant problems. It doesn't yield an elegant solution, but it is a solution. If you can

reduce a problem to a finite number of possible situations - say, a million - you can program a computer

to try every one of them. If every one of them checks out as it's supposed to, then you have your proof.

They recently solved the four - color mapping problem that way; a problem as well known and as

recalcitrant as Goldbach's conjecture."

"Good," said Trumbull, "then that's what Pochik's been doing. Apparently, he had worked out the

solution to a particular lemma. Now what's a lemma?"

Halsted said, "It's a partway solution. If you're climbing a mountain peak and you set up stations at

various levels, the lemmas are analogous to those stations and the solution to the mountain peak."

Asimov, Isaac - Black Widowers 02 - Bouquets of the Black Widowers.pdf

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