“So we start them out with the basic tools of science. With numbers: that is, with magnitudes and quantification, with all that scientific observations are about. With grammar. This is not what you learned when you were thirteen years old, it is a technical term; it means with the calculus of statement and the basic rules of communication: that is so they can learn to think clearly by communicating fully and without fuzzy ambiguity. We give them very little else, only the opportunity to mix these two basic ingredients and come up with new forms of knowledge.
“What will come of these things? That is a fair question. Unfortunately there is no answer. Not yet. If we knew the answer in advance, we would not have to perform the experiment. So we do not know what will be the end result of this, but already they have accomplished very much. Old questions that have puzzled the wisest of scientists for hundreds of years they have solved already. I will give you one example. You will say, ‘yes, but what does it mean?’ I will answer, ‘I do not know’; I only know that it is so hard a question that no one else has ever been able to answer it. It is a proof of a thing which is called Goldbach’s Conjecture. Only a conjecture; you could call it a guess. A guess by an eminent mathematician some many years ago, that every even number can be written as the sum of two prime numbers. This is one of those simple problems in mathematics that everyone can understand and no one can solve. You can say, ‘Certainly, sixteen is the sum of eleven and five, both of which are prime numbers, and thirty is the sum of twenty-three and seven, which also are both prime, and I can give you such numbers for any even number you care to name.’ Yes, you can; but can you prove that for every even number it will always be possible to do this? No. You cannot. No one has been able to, but our friends on the Constitution have done it, and this was in the first few months. They have yet almost ten years. I cannot say what they will do in that time, but it is foolish to imagine that it will be anything less than very much indeed. A new relativity, a new universal gravitation—I don’t know, I am only saying words. But much.”
He paused again. No one was making a sound. Even the president was no longer staring straight ahead without expression, but was looking at him.
“It is not yet too late to spoil the experiment, and so it is necessary for us to keep the secret a bit longer. But there you have it, gentlemen and ladies. That is the truth about Alpha-Aleph.” He dreaded what would come next, postponed it for a second by consulting his papers, shrugged, faced them and said: “Now, are there any questions?”
Oh, yes there were questions. Herr Omnes was stunned a little, took a moment to overcome the spell of the simple and beautiful truths he had heard, but then first one piped up, then another, then two or three shouting at once. There were questions, to be sure. Questions beyond answering. Questions Knefhausen did not have time to hear, much less answer, before the next question was on him. Questions to which he did not know the answers. Questions, worst of all, to which the answers were like pepper in the eyes, enraging, blinding the people to sense. But he had to face them, and he tried to answer them. Even when they shouted so that, outside the thick double doors, the Marine guards looked at each other uneasily and wondered what made the dull rumble that penetrated the very good soundproofing of the room. “What I want to know, who put you up to this?” “Mr. Chairman, nobody; it is as I have said.” “But see now, Knefhausen, do you mean to tell us you’re murderin’ these good people for the sake of some Goldbach’s theory?” “No, Senator, not for Goldbach’s Conjecture, but for what great advances in science will mean in the struggle to keep the free world free.” “You’re confessing you’ve dragged the United States into a palpable fraud?” “A legitimate ruse of war, Mr. Secretary, because there was no other way.” “The photographs, Knefhausen?” “Faked, General, as I have told you. I accept full responsibility.” And on and on, the words “murder” and “fraud” and even “treason” coming faster and faster.
Until at last the president stood up and raised his hand. Order was a long time coming, .but at last they quietened down.
“Whether we like it or not, we’re in it,” he said simply. “There is nothing else to say. You have come to me, many of you, with rumors and asked for the truth. Now you have the truth, and it is classified Top Secret and must not be divulged. You all know what this means. I will only add that I personally propose to see that any breach of this security is investigated with all the resources of the government, and punished with the full penalty of the law. I declare this a matter of national emergency, and remind you that the penalty includes the death sentence when appropriate—and I say that in this case it is appropriate.” He looked very much older than his years, and he moved his lips as though something tasted bad in his mouth. He allowed no further discussion, and dismissed the meeting.
Half an hour later, in his private office, it was just Knefhausen and the president.
“All right,” said the president, “it’s all hit the fan. The next thing is: The world will know it. I can postpone that a few weeks, maybe even months. I can’t prevent it.”
“I am grateful to you, Mr. President, for—”
“Shut up, Knefhausen. I don’t want any speeches. There is one thing I want from you, and that is an explanation. What the hell is this about mixing up narcotics and free love and so on?”
“Ah,” said Knefhausen, “you refer to the most recent communication from the Constitution. Yes. I have already dispatched, Mr. President, a strongly worded order. Because of the communications lag it will not be received for some months, but I assure you the matter will be corrected.”
The president said bitterly, “I don’t want any assurances, either. Do you watch television? I don’t mean I Love Lucy and ball games, I mean news. Do you know what sort of shape this country is in? The bonus marches in 1932, the race riots in 1967—they were nothing. Time was when we could call out the National Guard to put down disorder. Last week I had to call out the Army to use against three companies of the Guard. One more scandal and we’re finished, Knefhausen, and this is a big one.”
“The purposes are beyond reproach—”
“Your purposes may be. Mine may be, or I try to tell myself it is for the good of science I did this, and not so I will be in the history books as the president who contributed a major breakthrough. But what are the purposes of your friends on the Constitution? I agreed to eight martyrs, Knefhausen. I didn’t agree to forty billion dollars out of the nation’s pockets to give your eight young friends ten years of gang-bangs and dope.”
“Mr. President. I assure you this is only a temporary phase. I have instructed them to straighten out.”
“And if they don’t, what are you going to do about it?” The president, who never smoked, stripped a cigar, bit off the end and lit it. He said, “It’s too late for me to say I shouldn’t have let you talk me into this. So all I will say is you have to show results from this flim-flam before the lid blows off, or I won’t be president anymore, and I doubt that you will be alive.”
Constitution Four
This is Shef again and it’s, oh, let me see, about Day 250. 300? No, I don’t think so. Look, I’m sorry about the ship date, but I honestly don’t think much in those terms any more. I’ve been thinking about other things. Also I’m a little upset. When I tossed the rouble the hexagram was K’an, which is danger, over Li, the Sun. That’s a bad mood to be communicating with you in. We aren’t vengeful types, but the fact is that some of us were pretty sore when we found out what you’d done. I don’t think you need to worry, but I wish I’d got a better hexagram.
Let me tell you the good parts first. Our velocity is pushing point four oh C now. The scenery is beginning to get interesting. For several weeks now the stars fore and aft have been drifting out of sight as the ones in front get up into the ultraviolet and the ones behind sink into the infrared. You’d think that as the spectrum shifts the other parts of the EMF bands would come into the visible range. I guess they do, but stars peak in certain frequencies, and most of
them seem to do it in the visible frequencies, so the effect is that they disappear. The first thing was that there was a sort of round black spot ahead of us where we couldn’t see anything at all, not Alpha Centauri, not Beta Centauri, not even the bright Circini stars. Then we lost the Sun behind us, and a little later we saw the blackout spread to a growing circle of stars there. Then the circle began to widen.
Of course, we know that the stars are really there. We can detect them with phase-shift equipment, just as we can transmit and receive your messages by shifting the frequencies. But we just can’t see them anymore. The ones in direct line of flight, where we have a vector velocity of .34c or .37c (depending on whether they are in front of us or behind us) simply aren’t radiating in the visible band anymore. The ones farther out to the side have been displaced visually because of the relativistic effects of our speed. But what it looks like is that we’re running the hell out of Nothing, in the direction of Nothing, and it is frankly a little scary.
Even the stars off to one side are showing relativistic color shifts. It’s almost like a rainbow, one of those full-circle rainbows that you see on the clouds beneath you from an airplane sometimes. Only this circle is all around us. Nearest the black hole in front the stars have frequency-shifted to a dull reddish color. They go through orange and yellow and a sort of leaf green to the band nearest the black hole in back, which are bright blue shading to purple. Jim Barstow has been practicing his farsight on them, and he can relate them to the actual sky map. But I can’t. He sees something in the black hole in front of us that I can’t see, either. He says he thinks it’s a bright radio source, probably Centaurus A, and he claims it is radiating strongly in the whole visible band now. He means strongly for him, with his eyes. I’m not sure I can see it at all. There may be a sort of very faint, diffuse glow there, like the gegenschein, but I’m not sure. Neither is anyone else.
But the starbow itself is beautiful. It’s worth the trip. Flo has been learning oil painting so she can make a picture of it to send you for your wall, although when she found out what you’d been up to she got so sore she was thinking of boobytrapping it with a fusion bomb or something. (But she’s over that now. I think.)
So we’re not so mad at you anymore, although there was a time when, if I’d been communicating with you at exactly that moment, I would have said some bad things.
…I just played this back, and it sounds pretty jumbled and confused. I’m sorry about that. It’s hard for me to do this. I don’t mean hard like intellectually difficult (the way chess problems and tensor analysis used to be), but hard like shoveling sand with a teaspoon. I’m just not used to constricting my thoughts in this straitjacket anymore. I tried to get one of the others to communicate this time instead of me, but there were no takers. I did get a lot of free advice. Dot says I shouldn’t waste my time remembering how we used to talk. She wanted to write an eidetic account in simplified notation for you, which she estimated a crash program could translate for you in reasonable time, a decade or two, and would give you an absolutely full account of everything. I objected that that involved practical difficulties. Not in preparing the account, I don’t mean. Shucks, we can all do that now. I don’t forget anything, except irrelevant things like the standard-reckoning day that I don’t want to remember in the first place, and neither does anyone else. But the length of transmission would be too much. We don’t have the power to transmit the necessary number of groups, especially since the accident. Dot said we could Gödelize it. I said you were too dumb to de-Gödelize it. She said it would be good practice for you.
Well, she’s right about that, and it’s time you all learned how to communicate in a sensible way, so if the power holds out I’ll include Dot’s eidetic account at the end. In Gödelized form. Lots of luck. I won’t honestly be surprised if you miss a digit or something and it all turns into Rebecca of Sunnybrook Farm or some missing books of apocrypha or, more likely of course, gibberish. Ski says it won’t do you any good in any case, because Henle was right. I pass that on without comment.
Sex. You always want to hear about sex. It’s great. Now that we don’t have to fool with the pills anymore we’ve been having some marvelous times. Flo and Jim Barstow began making it as part of a multiplexed communications system that you have to see to believe. Sometimes when they’re going to do it we all knock off and just sit around and watch them, cracking jokes and singing and helping with the auxiliary computations. When we had that little bit of minor surgery the other day (now we’ve got the bones seasoning), Ann and Ski decided to ball instead of using anaesthesia, and they said it was better than acupuncture. It didn’t block the sensation. They were aware of their little toes being lopped off, but they didn’t perceive it as pain. So then Jim, when it was his turn, tried going through the amputation without anything at all in the expectation that he and Flo would go to bed together a little later, and that worked well too. He was all het up about it; claimed it showed a reverse causality that his theories predicted but that had not been demonstrated before. Said at last he was over the cause-preceding-the-effect hangup. It’s like the Red Queen and the White Queen, and quite puzzling until you get the hang of it. (I’m not sure I’ve got the hang of it yet.) Suppose he hadn’t balled Flo? Would his toe have hurt retroactively? I’m a little mixed up on this, Dot says because I simply don’t understand phenomenology in general, and I think I’ll have to take Ann’s advice and work my way through Carnap, although the linguistics are so poor that it’s hard to stay with it. Come to think of it, I don’t have to. It’s all in the Gödelized eidetic statement, after all. So I’ll transmit the statement to you, and while I’m doing that it will be a sort of review for me and maybe I’ll get my head right on causality.
Listen, let me give you a tip. The statement will also include Ski’s trick of containing plasma for up to 500K milliseconds, so when you figure it out you’ll know how to build those fusion power reactors you were talking about when we left. That’s the carrot before your nose, so get busy on de-Gödelizing. The plasma dodge works fine, although of course we were sorry about what happened when we converted the drive. The explosion killed Will Becklund outright, and it looked hairy for all of us.
Well, anyway. I have to cut this short because the power’s running a little low and I don’t want to chance messing up the statement. It follows herewith:
1973354 + 331852 + 172008 + 547 + 39606 + 288 take away 78.
Lots of luck, fellows!
Washington Four
Knefhausen lifted his head from the litter of papers on his desk. He rubbed his eyes, sighing. He had given up smoking the same time as the president, but, like the president, he was thinking of taking it up again. It could kill you, yes. But it was a tension-reducer, and he needed that. And what was wrong with something killing you. There were worse things than being killed, he thought dismally.
Looking at it any way you could, he thought objectively, the past two or three years had been hard on him. They had started so well and had gone so bad. Not as bad as those distant memories of childhood when everybody was so poor and Berlin was so cold and what warm clothes he had came from the Winterhilfe. By no means as hard as the end of the war. Nothing like as bad as those first years in South America and then in the Middle East, when even the lucky and famous ones, the Von Brauns and the Ehrickes, were having trouble getting what was due them and a young calf like Knefhausen had to peel potatoes and run elevators to live. But harder and worse than a man at the summit of his career had any reason to expect.
The Alpha-Aleph project, fundamentally, was sound! He ground his teeth, thinking about it. It would work—no, by God, it was working, and it would make the world a different place. Future generations would see.
But the future generations were not here yet, and in the present things were going badly.
Reminded, he picked up the phone and buzzed his secretary. “Have you got through to the president yet?” he demanded.
“I’m sorry, Dr. Knefhaus
en. I’ve tried every ten minutes, just as you said.”
“Ah,” he grunted. “No, wait. Let me see. What calls are there?”
Rustle of paper. “The news services, of course, asking about the rumors again. Jack Anderson’s office. The man from CBS.”
“No, no. I will not talk to the press. Anyone else?”
“Senator Copley called, asking when you were going to answer the list of questions his committee sent you.”
“I will give him an answer. I will give him the answer Götz von Berlichingen gave to the Bishop of Bamberg.”
“I’m sorry, Dr. Knefhausen, I didn’t quite catch—”
“No matter. Anything else?”
“Just a long-distance call, from a Mr. Hauptmann. I have his number.”
“Hauptmann?” The name was puzzlingly familiar. After a moment Knefhausen placed it: to be sure, the photo technician who had cooperated in the faked pictures from Briareus Twelve. Well, he had his orders to stay out of sight and shut up. “No, that’s not important. None of them are, and I do not wish to be disturbed with such nonsense. Continue as you were, Mrs. Ambrose. If the president is reached you are to put me on at once, but no other calls.”
He hung up and returned to his desk.
He looked sadly and fondly at the papers. He had them all out: the reports from the Constitution, his own drafts of interpretation and comment, and more than a hundred footnoted items compiled by his staff, to help untangle the meanings and implications of those, ah, so cryptic sometimes, reports from space:
“Henle. Apparently refers to Paul Henle (note appended); probably the citation intended is his statement, ‘There are certain symbolisms in which certain things cannot be said.’ Conjecture that English language is one of those symbolisms.”