Time in which the remorseless agents of decay would be doing their best to make Myra’s body unusable.
They had to buy time. There was only one way to do it. When Ranjit bullied his way into the chamber where what was left of his wife was being worked on, he at last understood why they had tried so hard to keep him out. Myra wasn’t in a hospital bed. She was submerged in a tank of water with half-melted ice cubes floating on its surface. Rubber cuffs at her neck and groin gave work space to the preservation techs, each perfusing Myra’s body with some chill liquid while Myra’s actual scarlet blood ran into a—toilet? But yes, that was where it was going!
From behind him a voice said, “Ranjit.”
He turned, his expression still horrified. The tone of Dr. Ada Labrooy’s voice had been kind, but the look on her face was stern. “You shouldn’t be here. None of this is pretty.” She glanced at a dial and added, “I think we’re in time, but you should get out of here and let us work.”
He didn’t argue. He had seen all he could stand to see. Over a long and happy marriage he had seen his wife’s naked body many times, pink-tinged and healthy, but now it was a bluish-violetish shade that he could not bear to look at.
The waiting time was forever, or seemed like it, but at last it came to an end. Ranjit was sitting in an anteroom, staring into space, when Dr. Labrooy came in, looking flushed and even happy. “It’s going well, Ranjit,” she said, taking a seat beside him. “We were able to establish all the interfaces. Now we’re just waiting while the data transfer is going on.”
Ranjit translated that for himself. “That means Myra’s being stored in the machine? Shouldn’t someone be there while that’s happening?”
“Someone is, Ranjit.” She lifted her arm to display a wrist screen. “I’m monitoring the flow. You know we’re lucky that the Grand Galactics have a habit of storing a few samples of every race they exterminate, so the Machine-Stored were already tooling up for the job before they got here.”
Ranjit scowled at a word. “What do you mean, ‘storing’? Are you talking about something like, I don’t know, some kind of coffin or urn or something?”
Ada scowled back. “Haven’t you been keeping up with the news, Ranjit? It’s nothing like that. It’s like the Machine-Stored themselves. They’re what you might call stage two machines. Stage one is just making exact copies of people and tucking them away for samples. Stage two is giving them life within the machine—no, wait,” she said as there was a tiny bell-like sound. Her eyes were on the news screen as she lifted her arm and spoke into the contraption on her wrist. A moment later the screen went black. When it lighted up again, Ranjit’s heart stopped, for what it was displaying was his wife as he had seen her last, wearing her swimsuit as before but now lying motionless on a surgical cot….
No, not motionless. Her eyes opened. Her expression was puzzled but interested as she lifted her hand and rotated it to study the fingers.
“You’re seeing her in her simulation,” Ada informed him proudly. “Later on she’ll learn how to simulate any surround she likes, and how to interact with others in the simulation.” Then she whispered again into the thing on her wrist. The screen went black once more. “We aren’t being fair to her, though. Let’s let her have her privacy while she gets used to what’s happened to her. You and I can get a cup of tea, and I’ll try to answer all your questions, assuming you have some.”
Oh, Ranjit had questions, all right. The tea in his cup, undrunk, grew cold while he tried to make sense of what had happened. At last there was another tiny bell and Ada smiled. “I think you can talk to her now,” she said, and nodded toward the screen, which abruptly displayed Myra again. “Hello, Aunt Myra,” Ada said to the screen. “Has the briefing program told you all you need to know?”
“Almost.” Myra touched her hair, untended since she’d come out of the water that had killed her. “I need to know how to fix myself up a little, but I didn’t want to wait any longer. Hello, Ranjit. Thanks for saving my—well, my meta-life, I guess, or whatever you can call it.”
“You are very welcome,” was all Ranjit could find to say. And then, as Ada got up to let the two of them talk in private, he said to Ada, “Wait a minute. You don’t have to be dead to be stored like this, do you? I mean, if I wanted to, you could put me right in the scene with her? And then it would be just as though we were flesh-and-blood people together?”
Ada looked alarmed. “Well, yes,” she said. She would have gone on, but Myra, speaking from the screen, was ahead of her.
“Dear Ranjit,” she said, “forget it. Much as I’d like to have you here with me, you mustn’t. It wouldn’t be fair to Tashy, or to Robert, or—Hell, let’s face it. It wouldn’t be fair to the world.”
Ranjit stared at the screen. “Huh,” he said. And then, after a moment’s pondering, “But I miss you already,” he complained.
“Of course. And I miss you. It’s not as though we could never see each other, though. The briefing program says we can talk like this as often as we like.”
“Huh,” Ranjit said again. “But we can’t touch, and I may live for years.”
“Many years, I hope, my darling. But it will give us something to look forward to.”
THE FIRST POSTAMBLE
The Long, Long Life of Ranjit Subramanian
That is the end of our story of Ranjit Subramanian.
This is not to say that he didn’t live—or “live”—for quite a long time after that. He did, first in his “normal” life and then in machine storage. What’s more, he had many fascinating and colorful occurrences in that postmortem “life” as a collection of electronic patterns. Most of these, however, we will not set down here. It isn’t that they aren’t of interest, for they are. It’s just that there were so many of them. There are other things for us to do that are more significant than recounting everything that happened to what incorporeal fragment of the original organic Ranjit Subramanian was stored and continued to live during the next large number of years.
There was, however, this one thing.
It happened much later in his machine-stored life, at a time when Ranjit had already done most of the touristy things he had always wanted to do. (That is, explored nearly all of the surface of Mars, as well as its even more interesting network of subsurface caverns, plus most other planets and major satellites of the solar system and a number of the larger objects in the Oort cloud.) At that particular time Myra had gone off on a trip to the core because she had always wanted to see a black hole close up. For the few thousand years she would be gone, Ranjit himself was occupying a virtual spun-glass mountainside while relaxing. (The way he was relaxing was by considering the theorem P = NP. This had kept him entertained for a fair number of decades already, with no end in sight.) Ranjit had created that virtual mountain within his surround in order to be alone, and it was a surprise to him to observe someone trudging up its slope in his direction.
The intruder was not only a stranger but a very odd-looking one. His eyes were tiny, his facial bone structure deeply carved, and he was a good three meters tall. When he reached the outcropping where Ranjit waited, he threw himself onto a deck chair (which had not existed before the stranger’s arrival), drew a couple of exaggeratedly deep breaths, and said, “Let me see. ‘That was quite a climb, wasn’t it?’ Was that the right thing for me to say?”
Ranjit had been bothered by too many strangers over the last few millennia to have much courtesy left over. He didn’t answer that. He simply asked, “Who are you and what do you want?”
The stranger looked both surprised and pleased. “I see,” he said. “You go directly to the point. Very well. Then I suppose I must say, ‘My name is—’”
He didn’t actually say a name, though. He simply emitted a blast of inarticulate sound, followed by, “but you may simply call me ‘Student,’ as I am here to study your thought processes and mannerisms.”
Ranjit considered throwing this interloper out of his carefully constructed pr
ivate surround, but there was something amusing about him. “Oh,” he said, “all right, study away. Why do you want to do that?”
The stranger puffed out his cheeks. “How do I explain this? It is a sort of commemoration of the return of the Grand Galactics—”
“Wait,” Ranjit said. “The Grand Galactics did finally come back?”
“Of course they did, after—let me see, in your counting—some thirteen thousand years. Not very long in terms of Grand Galactic time, but enough for some major changes for human beings like me. Oh, like you, too, of course,” he added graciously. “Therefore we have begun a recreation of those events, and as you were a minor figure in some of them, I have been chosen to re-create you.”
“You mean you’re making a kind of movie about it and you’re going to play me?”
“Oh, certainly not a ‘movie.’ But, yes, I am to ‘play’ you.”
“Huh,” Ranjit said. “I haven’t been paying a lot of attention to events lately. I didn’t know the Grand Galactics had come back, even.”
The stranger looked surprised. “But of course they did. They had told the Nine-Limbeds and the One Point Fives that they would be gone for only a short time. So they were. Of course, although thirteen thousand years was only a short time by their standards, it wasn’t by ours. The Grand Galactics were, it seems, quite surprised to find that we had developed so fast. They had had no experience of a sentient species’ being allowed to evolve at its own pace, having methodically prevented any such evolution with every other species they’d discovered. But I don’t think they minded being relieved of their burden.” He moved his lips experimentally for a moment, and then said, “Would you say ‘huh’ one more time for me, please?”
“Huh,” Ranjit said, not only to grant the request but because he could think of no other response to what he had just heard. “What do you mean? Relieved of what burden?”
“Oh, running things,” the stranger said, studying the look on Ranjit’s face and trying to reproduce it on his own. “Not that they didn’t do a good job, mostly. But it was wrong to prevent the development of so many interesting species. And although the technical stuff was generally all right, you have to admit that what they did with the cosmological constant was simply embarrassing.”
Ranjit sat up straight. “Well,” he said, “if the Grand Galactics aren’t running things anymore, shouldn’t somebody else be taking over for them?”
“Of course,” the stranger said impatiently. “I thought you knew. Someone is. It’s us.”
THE SECOND POSTAMBLE
Acknowledgments, and Other Acknowledgments
As one of us has noted elsewhere, there is a definition of a gentleman that describes him as “one who is never rude by accident.” In the same way, we feel a proper science-fiction writer should never misstate a canonical scientific truth by accident.
The significant words here, however, are “by accident,” because there are times in the writing of a science-fiction story when the author is forced to take a scientific liberty because otherwise his, or her, story won’t work. (For example, we all know that traveling faster than light is pretty much out of the question. However, if we don’t let our characters do it anyway, there are whole classes of interesting stories that we can never write.)
So when such liberties are taken, we think it only fair that the writers admit to them. In the present work there are three such cases:
1. There is in this early twenty-first-century time no such spacecraft as the high-speed one Joris Vorhulst describes as visiting the Oort cloud. We wish there were, but there isn’t.
2. There is no five-page proof of Fermat’s Last Theorem such as the one Ranjit Subramanian is described as having produced, and one of us thinks it is possible there never can be because the question may be formally undecidable.
3. Sri Lanka could never really be the ground terminal for a Skyhook because it isn’t really on the equator. In a previous work one of us dealt with that problem by moving Sri Lanka farther south. Rather than repeat that, however, in the present case we have chosen a somewhat different solution. The equator, after all, is nothing but an imaginary line. So we have simply chosen to imagine it a few hundred kilometers farther north.
Finally we would like to acknowledge certain kindnesses, such as the elucidation provided by Dr. Wilkinson of the Drexel Math Forum of what Andrew Wiles really accomplished with his one-hundred-fifty-page proof, and such as the assistance beyond the call of duty provided by our friend Robert Silverberg and, through him, the principal orator of Oxford University in the UK.
THE THIRD POSTAMBLE
Fermat’s Last Theorem
We felt it would be useful to give more details of what Fermat’s Last Theorem was all about, but we could not find an earlier place for this discussion that did not wound, almost fatally, the story’s narrative pace. So here it is at the end…and, if you are part of that large fraction of humanity who doesn’t know it all already, we do think you will find that it was worth waiting for.
The story of the most famous problem in mathematics began with a casual jotting by a seventeenth-century French attorney from Toulouse. The attorney’s name was Pierre de Fermat. Lawyering did not take up all of Fermat’s time, and so he dabbled in mathematics as an amateur—or, to give him his due, actually as a person with a solid claim to being called one of the greatest mathematicians of all time.
The name of that famous problem is Fermat’s Last Theorem.
One of that theorem’s greatest appeals is that it is not at all hard to understand. In fact, for most people coming to it for the first time, it is hard to believe that proving something so elementary that it can be demonstrated by counting on one’s fingers had defied all the world’s mathematicians for more than three centuries. In fact the problem’s origins go back a lot further than that, because it was Pythagoras himself, around five hundred B.C., who defined it in the words of the only mathematical theorem that has ever become a cliché:
“The square of the hypotenuse of a right triangle equals the sum of the squares of the opposite sides.”
For those of us who got as far as high school freshman math, we can visualize a right triangle and thus write the Pythagorean theorem as a2 + b2 = c2.
Other mathematicians began investigating matters related to Pythagoras’s statement about as soon as Pythagoras stated it (that is what mathematicians do). One discovery was that there were many right triangles with whole-number sides that fit the equation. Such a triangle with sides of five units and twelve units, for instance, will have a hypotenuse measuring thirteen units…and, of course, 52 plus 122 does in fact equal 132. Some people looked at other possibilities. Was there, for example, any whole-number triangle with a similar relation to the cubes of the arms? That is, could a3 plus b3 ever equal c3? And what about fourth-power numbers, or indeed numbers with an exponent of any number other than two?
In the days before mechanical calculators, let alone electronic ones, people spent lifetimes squandering acres of paper with the calculations necessary to try to find the answers to such questions. So they did on this problem. No one found any answers. The amusing little equation worked for squares but not for any other exponent.
Then everyone stopped looking, because Fermat had stopped them with a single scrawled line. That charming little equation that worked for squares would never work for any other exponent, he said. Positively.
Now, most mathematicians would have published that statement in some mathematical journal. Fermat, however, was in some ways a rather odd duck, and that wasn’t his style. What he did was make a little note in the white space of a page of his copy of the ancient Greek mathematics book called Arithmetica. The note said:
“I have discovered a truly marvelous proof of this proposition which this margin is too narrow to contain.”
What made this offhand jotting important was that it contained the magic word “proof.”
A proof is powerful medicine for mathematicians. The requi
rement of a proof—that is, of a logical demonstration that a given statement must always and necessarily be true—is what distinguishes mathematicians from most “hard” scientists. Physicists, for instance, have it pretty easy. If a physicist splatters a bunch of high-velocity protons onto an aluminum target ten or a hundred times and always gets the same mix of other particles flying out, he is allowed to assume that some other physicist doing the same experiment somewhere else will always get the same selection of particles.
The mathematician is allowed no such ease. His theorems aren’t statistical. They must be definitive. No mathematician is allowed to say that any mathematical statement is “true” until he has, with impeccable and unarguable logic, constructed a proof that shows that this must always be the case—perhaps by showing that if it were not, it would lead to an obvious and absurd contradiction.
So then the real search began. Now what the mathematicians were looking for was the proof that Fermat had claimed to possess. Many of the greatest mathematicians—Euler, Goldbach, Dirichlet, Sophie Germain—did their best to find that elusive proof. So did lesser names by the hundreds. From time to time some weary one of their number would leap to his feet with a cry of joy and a claim to have found the solution. Such alleged “proofs” turned up in the hundreds; there were a thousand of them in one four-year stretch of the early twentieth century alone.
But they were all quickly slain by other mathematicians who found the writers had made fundamental mistakes in fact or in logic. It began to seem to the mathematical world that great Fermat had stumbled and that no proof of his scribble would ever be found.
In that conclusion, however, they were not entirely right.
A true and final proof of Fermat’s theorem came at last at almost the end of the twentieth century. It happened in the years 1993 to 1995, when a British mathematician named Andrew Wiles, working at Princeton University in the United States, published a final, complete, error-free, and definitive proof of Fermat’s 350-odd-year-old conjecture. The problem had been solved.