Sweetly the aiodoi sang on, and listened on, and sometimes almost laughed at the smallsongs they heard.
"When we were talking about particle formation some of you had trouble reconciling the wave-particle duality. I suppose by now you've got the duality question pretty clear in your mind, or anyway if you haven't you're probably flunking out of the course so it doesn't matter. Now I want to try something else.
"Let's put the 'wave' part of the duality out of our minds for a minute, so we can talk about another little peculiarity of the particle considered only as a particle.
"When you think of the electron as a particle, you probably envision it as small, hard and round—like a tiny version of a planet like the Earth. That's all right up to a point. The point where it stops being all right is when you start to rotate the particle.
"Let me give you an illustration.
"Suppose you took a slip of paper and bent it into a ring, gluing the ends together.
"Then suppose you took a bead that was the size of an electron—you can't possibly do this, of course, but we're just supposing—and you made a slit in it so that you could thread it onto the paper ring. (It would have to be a very small paper ring, of course.) Let's say this little electron-sized bead has distinct surface markings—maybe it looks like a globe of the Earth—so you can always tell which part is facing you: You're looking directly down on Ecuador. The particle's North Pole is toward your head, its South Pole is toward your feet.
"Got that so far? All right, now let's do our mind experiment.
"If you slide this bead all the way around the ring of paper, when it comes back to its original position you are looking down at Ecuador again. The bead has turned through 360 degrees and it's exactly as it was before. Anybody who didn't see you turning it would have no way of knowing it had been turned at all. There is no test anyone can apply that can tell whether or not it had been rotated. So it doesn't really matter, in any objective sense, whether youVe spun the thing around through 360 degrees or not.
"That isn't the case with an electron.
"If you wanted to perform the same experiment with a real electron, rather than with an electron-sized bead, you would have to make the paper ring a different way. That is, you would have to give the paper a half-twist before you glued the ends together.
"Doing that, of course, turns the paper ring into what's called a Moebius strip.
"So now you can do your mind experiment, and you will see that something funny happens. When you slide your electron around the ring to its original position, it's not quite the same. You're still looking down on 'Ecuador,' all right, but the rest of the globe is all screwed up. It turns out that now the North Pole is where the South Pole used to be. The thing has been turned upside down.
"It's still possible to get it straightened out, but now it requires an extra step. If you want to return it to its original state, you have to slide it around the Mocbius strip twice. Then it's back the way it started and, again, there is no test anyone can apply that can show it was rotated at all.
"So in a certain sense, from the point of view of an electron, a circle doesn't have just 360 degrees, it has 720.
"Does that confuse you?
"Good! Let me just remind you of what Niels Bohr said, long ago: 'If a man does not feel dizzy when he first learns about the quantum, he has not understood a word.'"
And, greatly amused, the aiodoi sang:
"What is there to understand?
"What is so is so. What is so understands itself, and that is all there is."
9
For Sue-ling Quong, this was becoming a real adventure. It was exciting! It made her feel young again—as young as Moon Bunderan, or even younger, for the girl from New Mexico seemed to be able to take all in her stride . . . while Sue-ling was experiencing one thrill after another. When she looked around the control room of The Golden Hind she was not only impressed, she was starded, as well, and even delighted, like any tourist visiting a wondrous place never seen before.
The heart of a waveship was certainly impressive to look at. There were banks of controls—two separate sets of them, it seemed, though for what reason Sue-ling could not guess. Though it was a large room it was crowded now. The two Turtles and Moon Bunderan's Taur took up more space than anyone else, but the little band of human adventurers now numbered seven—well, Sue-ling thought, assuming you included as human these odd new robotic things that said they were Francis Krake's crew.
But some of the pleasure and excitement were spoiled for Sue-ling Quong by the childish, abrasive, deplorable way everyone was acting! She was almost ashamed of her friends— well, when you came right down to it, she admitted to herself, only two of them. Kiri as always was quiet and generally placatory; Moon Bunderan and the two robotic crew members were mostly listening. The offenders, really, were Francis Krake, veins starting out on his dark temples as he shouted at the two Turties—though Sue-ling had long since lost track of just what it was the captain and the Turtles were arguing so vehemently about . . . and, yes, that problem child, that loved one who was so seldom lovable, Sork Quintero. He was so up! She toyed with the thought that perhaps he'd started drinking again—but where would he get liquor on this spartan waveship?
Willing to do anything to stop the bickering, Sue-ling marched up to Sork, took his arm, pulled him away. "What's the matter with you?" she demanded. "Can't we just get started without all these cat fights?"
Sork stared at her unbelievingly. "But didn't you hear what that big Turtle's saying? He wants us to find their missing Mother—or get them a new one, or something. They're really out of their minds now, Sue-ling. I thought Litlun was crazy when he was trying to buy everything in sight—the Taur, the lecture chips—but this is really loopy."
Sue-ling interrupted him. "I've been thinking about that. Are they all connected?—the Taur, the chips, this trip?"
Sork blinked at her, trying to wrestle this new datum into his overriding plan. "I don't know," he said at last. "That's not what I'm worrying about, anyway. What's on my mind is— what if they succeed?"
Sue-ling gazed at him, not understanding. "Yes?"
"Don't you see? Litlun wants us to help him keep the Turtle race alive—but that's not what we want! If they all die off it will be the best thing that ever happened to us!" Sork turned to his brother and Moon Bunderan, drawing near
them to get away from the storm center. "Isn't that true, Kiri?" he demanded.
Even Kiri's calm had been frayed by the squabbling. He gave his brother a tired, forgiving smile and said gently: "Whatever is right will happen, Sork."
Moon Bunderan turned and looked up at him. "Are you sure of that, Kiri?"
"Very sure," he said positively, though his face was still strained.
"Oh, I hope you're right," the girl from New Mexico told him. "But I'm still afraid of that little one. Why do you suppose he wants Thrayl?"
Sork made a sweeping-away gesture, dismissing all such questions at once: "Turtles! Who knows why they want anything? What matters is what we want. Shall we help the Turtles survive?"
The little red robot thing named Marco was scuttling over to them. "Friends," he callcd out, the face on his belly smiling up at them, "it looks like we're going to be on our way. I suggest you all hold onto something for undocking!"
"Have they settled what they're going to do?" Sork Quintero demanded.
"Settled?" The face was laughing now. "No, you can't say anything's really settled . . . but we're taking off anyway!"