Star Science Fiction Stories No. 2

by Frederik Pohl

  “Let’s open it,” Scott said.

  She said brightly, “What fun! Isn’t it exciting! Elected to the Purple Fields!- Where are the Purple Fields, darling?”

  He stared at her, and she hesitated for a moment and then ran to put her arms around him.

  <>

  * * * *

  JAMES BLISH

  To the dull eyes of mortals, James Blish looks like a dapper young man with a thin mustache and a pleasant smile; but there isa secret inside that gentle exterior, and the secret is this: James Blish is a tetrahedron. Scan any of the four faces of his pyramidal writing talents, and you will find a seemingly solid literary personality; there is Clinical Blish, the precise and infinitely analytical author of Bridge and the Okiestories; Fanciful Blish, who draws plausibly scientific werewolves in stories like There Shall BeNo Darkness;Rough-and-Tumble Blish, who purveys bloodlust and action in such novels as The Warriors of Day; and finally, P. G. Dunsany-Blish, author of the present offering. Some day, if God is kind, the four Blishes may fuse into a supertalent which will dominate the science-fiction field as implacably as Stalin dominated the political essayists of recent Russia; but until that time, let us rejoice in such splendid stories as-

  FYI

  “I’ve got definite proof that we’ve been granted a reprieve,” Lord Rogge was insisting to thin air. “Perfectly definite proof.”

  We had been listening, either tensely or with resignation according to the man, to the evening news roundup in the bar of the Orchid Club. With the world tottering on the brink, you might have thought that an announcement like that would have elicited at least some interest. Had Rogge said the same thing in public, the reporters would have spread it to the antipodes in half an hour.

  Which only goes to show that the world knew less than it should about poor old George. Once the Orchid Club got to know him intimately, it had become impossible to believe in him any longer as one of the world’s wise men, Oh, he is one of the great mathematicians of all time, to be sure, but on any other subject he could be counted on to make a complete ass of himself. Most of us already knew, in a general way, what he meant by a “reprieve,” and how well his proof would stand up—supported, as usual, by a pillar of ectoplasm.

  “What is it now, George?” I said. Somebody has to draw him off, or he’ll continue to clamor for attention through the news bulletins. It was now my turn.

  “It’s proof,” he said, sitting down beside me at once, “I’ve found a marvelous woman in Soho—oh, a perfect illiterate, she has no idea of the magnitude of the thing she’s got hold of. But Charles, she has a pipeline to the gods, as clear and direct a contact as any human being ever had. I’ve written proof of it.”

  “And the gods tell her that truth and light will prevail? George, don’t you ever listen to the wireless? Don’t you know that these are almost surely our last days? Don’t you know that your medium is never going to have another child, that the earth’s last generation has already been born, that the final war is upon us right at this instant?”

  “Bother,” Rogge said, exactly as he might have spoken had he found soda instead of water in his whisky. “You can’t see beyond the end of your nose, Charles. Here you are, a speck in a finite universe in finite time, full of Angst because there may not be any more specks. What does that matter? You’re a member of a finite class. If you ever thought about it at all, you knew from the beginning that the class was doomed to be finite. What do you care about its ultimate cardinality?”

  “. . . has accused India of deliberately attempting to wreck the conference,” the wireless was saying. “Meanwhile, the new government of Kashmir which seized power last week has signed a treaty of ‘everlasting friendship and assistance’ with the Peiping government. The latest reports still do not reveal . . .”

  Well, I’d be briefed later; that was part of the agreement. I said, “I thought you were the one who cared about cardinality. Wouldn’t you like to see the number of the class of human beings get up some day into your precious trans-finite realm? How can we do that if we kill each other off this very month?”

  “We can’t do it in any case, not in the physical sense,” Rogge said, settling back into his chair. “No matter how long the race lives or how fruitful it is, it will always be denumerable—each member of the race can be put in one-to-one relationship with the integers. If we all lived forever and produced descendants at a great rate, we might wind up as a denumerably infinite class—in infinite time. But we haven’t got infinite time; and, in any case, the very first transfinite number is the cardinal number of all such classes. No, my boy, we’ll never make it.”

  I was, to say the least, irritated. How the man could be so smug in the face of the red ruin staring us all in the face . . .

  “So the reprieve you were talking about is no reprieve for us.”

  “It may well be, but that’s the smallest part of the implications. . . . Have you another of those panatelas, Charles? . . . There now. No, what I was talking about was a reprieve for the universe. It’s been given a chance to live up to man.”

  “You really ought to listen to the B.B.C. for a few minutes,” I said. “Just to get some idea of what man is. Not much for the universe to live up to.”

  “But it’s a two-penny universe to begin with,” Rogge said, from behind a cloud of newborn smoke. “There’s no scope to it. It’s certainly no more than ten billion years old at the outside, and already it’s dying. The space-time bubble may or may not continue to expand forever, but before long there won’t be anything in it worth noticing. It’s ridiculously finite.”

  “So is man.”

  “Granted, Charles, but man has already made that heritage look stupid. We’ve thought of things that utterly transcend the universe we live in.”

  “Numbers, I suppose.”

  “Numbers, indeed,” Rogge said, unruffled. “Transfinite numbers. Numbers larger than infinity. And we live in a universe where they don’t appear to stand for anything. A piece of primer-work, like confining a grown man in a pram.”

  I looked back at the wireless. “We don’t sound so grown up to me.”

  “Oh, you’re not grown up, Charles, and that holds true for most people. But a few men have shown what the race could do. Look at Cantor: he thought his way right out of the universe he lived in. He created a realm of numbers which evolve logically out of the numbers the universe runs on—and then found no provision had been made for them in the universe as it stands. Which would seem to indicate that Whoever created this universe knew less math than Cantor did! Isn’t that silly?”

  “I’ve no opinion,” I said. “But you’re a religious man, George. Aren’t you skirting blasphemy?”

  “Don’t talk nonsense. Obviously there was a mathematician involved somewhere, and there are no bad mathematicians. If this one was as good as His handiwork indicates, of course He knew about the transfinites; the limitation was purposeful. And I think I’ve found out the purpose.”

  Now, of course, the great revelation was due. Promptly on schedule, Rogge fussed inside his jacket pocket. I sat back and waited. He finally produced a grubby piece of paper—a fragment of a kraft bag.

  “You’re going to need a little background here,” he said, drawing the paper out of reach as I leaned forward again. “Transfinite numbers don’t work like finite ones. They don’t add, subtract, multiply, or divide in any normal sense. As a matter of fact, the only way to change one is to involute it—to raise it to its own power.”

  “I’m bored already,” I said.

  “No doubt, but you’ll listen because you have to.” He grinned at me through the cigar smoke, and I began to feel rather uncomfortable. Could the old boy have been tipped off to our rotating system of running interference with him? “But I’ll try to make it clear. Suppose that all the ordinary numbers you know were to change their behavior, so that zero to the zero power, instead of making zero, made one? Then one to the first power would make two; two squared would equ
al three; three cubed would be four, and so on. Any other operation would leave you just where you were: two times three, for instance, would equal three, and ten times 63 would equal 63. If your ordinary numbers behaved that way, you’d probably be considerably confused at first, but you’d get used to it.

  “Well, that’s the way the transfinite numbers work. The first one is Aleph-null, which as I said before is the cardinal number of all denumerably infinite classes. If you multiply it by itself, you get Aleph-one. Aleph-one to the Aleph-first equals Aleph-two. Do you follow me?”

  “Reluctantly. Now let me crackyour brains for a minute. What do these numbers number?”

  Rogge smiled more gently. “Numbers,” he said. “You’ll have to try harder than that, Charles.”

  “You said Aleph-null was the cardinal number of—of all the countably infinite classes, isn’t that right? All right, then what is Aleph-one the cardinal number of?”

  “Of the class of all real numbers. It’s sometimes called C, or the power of the continuum. Unhappily, the continuum as we know it seems to have no use for it.”

  “And Aleph-two?”

  “Is the cardinal number of the class of all one-valued functions.”

  “Very good.” I had been watching this process with considerable secret glee; Rogge is sometimes pitifully easy to trap, I had been told, if you’ve read his works and know his preoccupations; and I’d taken the trouble to do so. “It seems to me that you’ve blasted your own argument. First you say that these transfinite numbers don’t stand for anything in the real universe. Then you proceed to tell me, one by one, what they stand for.”

  Rogge looked stunned for an instant, and I got ready to go back to listening to the wireless. But I had misinterpreted his expression. I hadn’t stumped him; he had simply underestimated my ignorance, one of his more ingratiating failings.

  “But Charles,” he said, “to be sure the transfinite numbers stand for numbers. The point is that they stand for nothing else. We can apply a finite number, such as seven, to the universe; we can, perhaps, point to seven apples. But there aren’t Aleph-one apples in the universe; there aren’t Aleph-one atoms in the universe; there is no distance in the universe as great as Aleph-one miles; and the universe won’t last for Aleph-one years. The number Aleph-one applies only to concepts of number, which are things existing solely in the minds of men. Why, Charles, we don’t even know if there is such a thing as infinity in nature. Or we didn’t know until now. At this present moment, not even infinity exists.”

  Impossibly enough, Rogge was actually beginning to make me feel a little bit circumscribed, a little bit offended that the universe was so paltry. I looked around. Cyril Weaver was sitting closest to the broadcaster, and there were tears running down his craggy face onto his medals. John Boyd was pacing, slamming his fist repeatedly and mechanically into his left palm. Off in the corner next to the fire, Sir Leslie Crawford was well along into one of his ghastly silent drunks, which wind up in a fixed, cataleptic glare at some inconsequential object, such as a tuft in the carpet or the space where a waiter once stood; he was Her Majesty’s Undersecretary for Air, but at such moments no event or appeal can reach him.

  Evidently nothing that had come through on the wireless had redeemed our expectations in the slightest. Of them all, I was the only one—not counting Lord Rogge, of course—who had failed to hear the news, and so would still be listening for a word of hope during tomorrow’s broadcast.

  “Almost thou persuadest me, George,” I said. ‘“But I warn you, none of this affects my opinions of mediums and spiritualism in the least. So your cause is lost in advance.”

  “My boy, I’m not going to ask you to believe anything but what I’m going to put before your own eyes. This charwoman, as I said, is utterly uneducated. She happens to have a great gift, but not the slightest idea of how to use it. She stages seances for ignorant folk like herself, and gives out written messages which purport to be from her clientele’s departed relatives. The usual thing.”

  “Not at all impressive as a start.”

  “No, but wait,” Rogge said. “I’m interested in such things, as you know, and I got wind of her through the Psychical Research Society. It seems that some of the woman’s patrons had been complaining. They couldn’t understand the spirit messages. ‘Uncle Bill, ‘e wasn’t never no one to talk like that.’ That sort of complaint. I wouldn’t have bothered at all, if I hadn’t seen one of the ‘messages,’ and after that I couldn’t wait to see her.

  “She was terrified, as such people are of anybody who speaks reasonable English and asks questions. I won’t rehearse the details, but eventually she admitted that she’s been practicing a fraud on her trade.”

  “Remarkable.”

  “I agree,” Rogge said; somewhat mockingly, it seemed to me. “It appears that the voices she hears during her trances are not the voices of the relatives of her neighbors. As a matter of fact, she isn’t even sure that they’re spirit voices, or human voices. And she doesn’t herself understand what it is that they say. She just writes it down, and then, once she’s conscious again, tries to twist what she’s written enough to make it apply to the particular client.”

  I expect I had begun to look a little sour. Rogge held up a hand as if to forestall an interruption. “After I got her calmed down sufficiently, I had her do the trick for me. Believe me, I’m not easily fooled after all these years. That trance was genuine enough, and the writing was fully automatic. I performed several tests to make sure. And this is what she wrote.”

  Without any attempt at a dramatic pause, he passed the scrap of brown paper over to me. The block printing on it was coarse, sprawling, and badly formed; it had evidently been written with a soft pencil, and there were smudge marks to show where the heel of a hand had rested. The text was:

  FYI WER XTENDIN THE FIE NIGHT CONTIN YOU UMBRELLAS OF THIS CROWN ON TO OMEGA AHED OF SHED YULE DO TO CHRIST IS IN HEAVEN ROOSHIAN OF CHILDREN OPEN SUDO SPEAR TO POSITIV CURVACHER AND BEGIN TRANSFORMATION TO COZ MOST OF MACRO SCOPICK NUMBER

  I handed the paper back to Rogge, astonished to find that my heart had sunk. I hadn’t realized that it had attained any altitude from which to sink. Had I really been expecting some sort of heavenly pardon through this absurd channel? But I suppose that, in this last agony of the world, anyone might have grasped at the same straw.

  “On to omega, indeed,” I said. “But don’t forget your bumbershoot. How did she manage to spell ‘transformation’ right?”

  “She wears one,” Rogge said. “And that’s the key to the whole thing. Obviously she didn’t understand more than a few words of what she—well, what she overheard. So she tried to convert it into familiar terms, letting a lot of umbrellas and Russians into it in the process. If you read the message phonetically, though, you can spot the interpolations easily—and converted back into its own terms, it’s perhaps the most important message anybody on earth ever got.”

  “If anybody told me that message was from Uncle Bill, I wouldn’t just guess it was a fraud. Go ahead, translate.”

  “First of all, it’s obviously a memorandum of some sort. FYI—for your information. The rest says: ‘We are extending the finite continuum as of this chronon to omega ahead of schedule due to crisis in evolution of children. Open pseudosphere to positive curvature and begin transformation to cosmos of macroscopic number.’ “

  “Well,” I said, “it’s certainly more resonant that way. But just as empty.”

  “By no means. Consider, Charles: omega is the cardinal number of infinity. The finite continuum is our universe. A chronon can be nothing but a unit of time, probably the basic Pythagorean time-point. The pseudosphere is the shape our universe maintains in four-dimensional space-time. To open it to a positive curvature would, in effect, change it from finite to infinite.”

  I took time out to relight my cigar and try to apply the glossary to the message. To my consternation, it worked. I got the cheroot back into action only a second before my h
ands began to shake.

  “My word, George,” I said, carefully. “Some creature with a spiral nebula for a head has taken up reading your books.”

  He said nothing; he simply looked at me. At last I had to ask him the preposterous questions which I could not drive from me in any other way.

  “George,” I said. “George, are we the children?”

  “I don’t know,” Rogge said frankly. “I came here convinced that we are. But while talking to you I began to wonder again. Whatever powers sent and received this message evidently regard some race in this universe as their children, to be educated gradually into their world—a world where transfinite numbers are everyday facts of arithmetic, and finite numbers are just infinitesimal curiosities. Those powers are graduating that race to an infinite universe as the first step in the change.

  “The human race has learned about transfinite numbers, which would seem to be a crucial stage in such an education. And we’re certainly in the midst of a crisis in our evolution. We seem to qualify. But . . . Well, there are quite a few planets in this universe, Charles. We may be the children of whom they speak. Or they may not even know that we exist!”

  He got up, his face troubled. “The gods,” he said quietly. “They’re out there, somewhere in a realm beyond infinity, getting ready to open up our pseudospherical egg and spill us out into an inconceivably vaster universe. But is it for our benefit or for—someone else’s? And how will we detect it when it happens? On what time-scale do they plan to do it—tomorrow for us, or tomorrow for them, billions of years too late for us?”

  “Or,” I said, “the whole thing may be a phantom.”

  “It may be,” he said. He knew, I think, that I had said that for the record, but he gave no sign of it. “Well, in the meantime you’re relieved of duty, Charles. I shan’t keep you any longer; I had to tell someone, and I have. Think about it”