"What Hawking says is that the universe is infinite in time. It has lasted forever. It will go on lasting forever.
"Please understand that this isn't the old Hoyle-Gold idea of continuous creation, which we took up last month. Hawking doesn't believe in creation at all. What he does say is that, every once in a while in the eternal history of the universe, there is a sort of vacuum fluctuation which produces a tempo-
rary flux of particles. 'Temporary' doesn't necessarily mean something that lasts for only a short time. It can be quite a long time—I would say, perhaps, in this case for as long as ten to the sixty-sixth years or more. These particles appear, they expand, they condense into galaxies and stars and planets and you and me. Then, over time, they subside again. The vacuum energies return to the zero state and the universe goes on unchanged—until the next eruption.
"Are you following me? Maybe a picture would make it clearer. You can draw it in your notebooks, if you want to.
"For your picture, think of the whole universe as an endless, one-dimensional line.
"Then think of that endless line as hollow. Like a very narrow hose. Better still, think of it as an extremely long, extremely skinny anaconda, and imagine that the anaconda has just swallowed a pig. From outside the anaconda, you can see the bulge in the snake's belly, where the pig is being digested—
"But the pig can't see that bulge in the snake's belly. The pig can't see the anaconda at all, because it is inside that infinitely long snake.
"Now think of ourselves as living within that pig inside that snake. Think of us as some smart, tiny bacteria that live in the pig's gut. Maybe we could be something like that favorite, harmless intestinal bug we all carry around called Escherichia coli, only a lot more intelligent. In fact, if we E. coli are intelligent enough, we might possibly be able to invent some kind of instruments—call them 'radio telescopes,' or something of the sort—that might let us explore the entire pig. We may even be able to deduce, from studying the pig's structure, that there was a 'beginning' to the pig. That would be the point in the snake's body where the curvature of the swallowed pig first begins to appear. We might call that 'the Big Bang.' Perhaps we can speculate that there will also be an end, when the last trace of the pig will be gone and the snake will resume its endless, one-dimensional stretch.
"We can imagine all that. But what we intestinal bacteria can never do is see past the outer limits of the pig we live inside, for the body of that pig is our whole perceivable universe.
"If one of us pig-gut fauna happens to be like Stephen Hawking, he may theorize that there could be a lot more of the snake than the pig's body occupies, even if we can't see it. Nevertheless, what we can never do, ever, is have any personal encounter with anything before or after the pig. Those areas are forever hidden from us. There may be other pig-universes elsewhere along the snake from its previous meals and later ones, but we can only guess about that. We will never be able to see them, or communicate with them, or have direct proof that they exist.
"For that reason, our bacterial Stephen Hawking will call these other possible universes 'imaginary.'
"In just that way, the living Stephen Hawking of our own world, in fact, describes everything before the Big Bang as 'imaginary time,' along with everything that follows after that temporary swelling of space and time which we perceive as our whole universe. He calls the time we live by—clock time; the time by which we measure our heartbeats and the recession of the galaxies and the rotation of the Earth—'real time,' because it seems real to us . . . since it's the only one we can ever detect.
"But, Hawking says, the universe runs on 'imaginary time.' What appears to us as real is only a deficiency in our ability to see beyond our slowly digesting pig.
"That's all for today, class. Bring your notes tomorrow, because we're going to have an open-book quiz."
Thus sang the ancient Earth scientist, who was also a poet, and the aiodoi heard. But here is what one aiodos sings:
"Which is the first particle in a flux of infinitely varied particles that has gone on forever?
"Every one is.
"For when each particle first comes to exist, it is, for itself, the first particle that ever existed.
"And what does 'cannot' mean?
" 'Cannot' has only one meaning, and that is that 'cannot' cannot ever be."
2
To Sork Quintero, the teachings of the old human scientists weren't heretical. They were human, and it was Sork's firm plan to learn everything the human race had ever known . . . as well as, God willing, everything the Turtles knew as well. That made Sork's life even harder than it would otherwise have been. Among other things, the effort cost him a lot of sleep. He didn't have time for much of it, when he put in his hours studying the borrowed old tapes after his day's work for the Turtles was through. It cost him pain, too, because it made his head hurt, especially when he tried to understand what those wild old tapes were talking about. Space. Time. The universe. It didn't mean that these were difficult subjects —as long as he didn't try to understand what the old scientists were saying exactly—but what in the world could they mean by something they called "imaginary time"?
When he did try to digest those indigestibles, then his head hurt. Then nothing they said made sense. Then everything the old Earth scientists said was far more alien than the Turtles themselves.
Sork had begun to convince himself that he would never understand the tapes without help. But where was that help going to come from? Certainly not from the Turtles, who would be horrified even to be asked about such things. Not from his twin brother, Kiri, either, because what did Kiri know of such matters?
He wished his twin was awake to talk to, anyway, but when Sork looked into Kiri Quintero's room, he saw that his brother was still bubbling soft snores in his bunk, untroubled by such questions. That was a pity. Kiri might not study these arcane, antique subjects, but Kiri had the power of comprehension. Kiri understood things. Kiri seemed to grasp conceptual matters almost intuitively; his mind functioned in large images—pictures—interactions—relevances. But Kiri was not, when you came right down to it, much help in his twin brother's desperate effort to learn, because Kiri Quintero was very bad at explaining the things he understood to anyone else.
Sork sighed and walked out into the waking-up noises of the Turtle compound, rubbing the back of his head, where the memmie slot sometimes itched. Already the long flatcar trains were rolling in with their cargoes of raw materials for the Turtles. Looking up, Sork could still see stars overhead—and one bright object that was not a star. It slid silently down the heavens as he watched, as bright as Sirius—and, Sork Quintero thought morosely, just as unreachable. But that wasn't fair either, because he recognized the thing. It was human-built! It was the abandoned shell of an old human space station, empty for centuries now, but still an every-night reminder that, once, human beings had ventured into space on their own.
Once. No longer.
A gentle mooing from behind made him move aside to make way for a Taur servant, ready to begin his day's work of cleaning in the Turtle compound. "Good morning," Sork said politely, though he knew it was unlikely the immature Taur would understand.
Then he began wandering aimlessly across the compound, trying to sort out the things he had heard. His head still hurt. And no wonder! Such strange talk! Time . . . real time, imaginary time, time as a dimension just like up and down and sidewise—what could such things mean?