"The fourth dimension," Mick said after a pause. "The space out there has got to be four-dimensional. Hyperspace! Like in
Geometry and Reality
."
Vernor nodded. This book, which he had gotten Mick to read . . . how long ago? This book had stated that only in four-dimensional space is it possible for an ordinary object to turn into its own mirror-image. The argument for this proceeded by saying that four-dimensional space is to us as our ordinary space would be to that legendary race of two-dimensional beings known as Flatlanders. More precisely: the idea was that if you have, say, a flat cut-out of a left hand sliding around on a table, the only way to turn it into a cut-out of a right hand is to lift it off the flat table
into space
and turn it over. Since the food tube was effortlessly turning into its mirror-image and back again, it seemed to follow that it was rotating in four-dimensional
hyperspace
.
"Man, I'm going out there," Turner exclaimed, moving towards the hatch.
"Mick, I don't think—" Vernor started, but stopped hopelessly. He was still to dazed from his nuclear freak-out to assert himself. Passively he watched Mick open the hatch and swing his legs out. That had been the one flaw in Mick's enjoyment of
Geometry and Reality
before . . . "Where
is
this fourth dimension?" he had demanded of Vernor. "Let's get stoned and
go
there!" Vernor had explained at length that even if it existed, there was no possible way to leave our space and float out into hyperspace . . . but Mick had never quite believed him.
"Here goes!" Mick yelled, pushing himself off from the scale-ship. He drifted about five yards and disappeared.
Vernor racked his brain for the proper Flatland analogy . . . oh yeah, Mick was in a different space-like slice of hyperspace. He was also crazy. Just for openers, how was he ever going to get back? If he was lucky he might drift far enough away from the VFG field to grow back to normal size . . . but in which space? And what
were
those other spaces which the hyperspace was made of?
His brain gave up and he turned down the power of the VFG cones. No point shrinking any further until he saw if Mick was coming back. Crazy bastard. Vernor looked out through the synthequartz windows. The shiny little spheres were all around them. They had a strange way of changing size while he watched . . . sometimes even disappearing . . . but always their surfaces remained featureless. There was a whisper of sound behind him, and he turned.
What appeared to be a thin slice from the world's largest blood-sausage had appeared in the center of the scale-ship. Vernor froze . . . attracted by curiosity, but repelled by fear . . . "Is that you, Mick? You don't look so good."
The shape of the slice gradually changed until finally what seemed to be an animated silhouette was floating in front of Vernor. It was like a thin, thin paper cut-out of a man, tinted all different shades . . . a strange shifting color pattern really . . . Suddenly Vernor realized that he was looking at an actual cross-section of Mick Turner. It was as if someone had, with a huge sharp razor, split Mick's front half from his back half; and then shaved off one slice to wave at Vernor. Wearily Vernor fumbled for an explanation . . . he felt ripe for another freak-out . . . if only he could stop trying to explain, to understand.
The cross-section wavered slightly, and then Mick Turner was back in the scale-ship. He seemed all right except that he looked funny, crooked. He reached his left hand out towards Vernor reassuringly. "It's great out—" He was interrupted by a violent explosion in front of his face.
Vernor's gears suddenly meshed. "Go back!" he shouted. "You're backwards! You're made of antimatter now!"
That
was why Mick had looked funny; he had turned over in hyperspace and come back as his mirror-image. Which meant that each of his particles was a mirror-image particle: antimatter. When antimatter touches matter the two annihilate each other . . . combine and disappear leaving nothing but a burst of energy. The air from Mick's exhaled words had just annihilated the air in front of his face. Thank God he hadn't touched Vernor with that reassuring left hand.
It was hard to tell if Mick grasped all this before he disappeared again. Time went on. Vernor assumed that Mick was trying to make sure that he came back to the scale-ship's space unreversed. Several times Vernor thought he saw cross-sections of Mick outside the scale-ship . . . once two circles, as if of his legs . . . but still he did not return.
While he was waiting, Vernor turned to the real question.
How
had the space around them become four-dimensional? He thought of analogies. Suppose that Flatland had a thickness which was unnoticed by its citizens. Say that Flatland was like a sheet of paper and that the Flatlanders were normally like ink-blots which had soaked right through the paper. But if each an ink-blot shrank enough, it would soon be a small black glob moving about inside the paper—which now would seem three-dimensional. Yes. That had to be it. The space we live in did have a slight fourth-dimensional hyper-thickness to it . . . just like a sheet of paper has a slight third-dimensional thickness . . . and now Vernor was so small that space's hyper-thickness was much greater than his size. So now there was a perceivable fourth dimension. Nice. Wasn't there something in one of Clifford's later papers—
Vernor's scientific reverie was interrupted by Mick's reappearance. This time Turner popped back right outside the scale-ship; and after cautiously spitting at the ship he climbed in. He looked the same as ever.
"So how was it, Mick? Did you see much?"
"Looked just like here . . . with those Christmas balls everywhere.
You
looked gross . . . like an anatomy chart. But what counted was how it
felt
."
"That extra degree of freedom felt all right, huh?" Vernor asked.
"It wasn't just
one
extra degree, baby. That's infinite dimensional space out there."
Vernor didn't feel like entertaining such a claim. "That's bullshit, Mick. Anyway there's no way you could tell the difference even between four and five dimensional space. Can a point tell a line from a plane?"
"Man, don't you see, all that is just intellectualizing. I was
out
there.
In
it. It's infinite dimensional. Go on and see. Go on." Mick seemed annoyed at Vernor's contradicting him and was actually pushing him towards the hatch.
"No," Vernor said. "I came here to travel around Circular Scale. I'm not going to risk fucking with higher dimensions."
Mick snorted in disgust, but he let Vernor go back to the controls. Vernor turned the VFG field back up and the spheres began growing. He looked at the closest one. Obviously they were going to have to get inside it. But it looked so smooth. It's surface appeared mirror-like; in fact he could make out their reflection.
It was funny about this shiny sphere, this Christmas ball, one instant it would be looming over them like an asteroid, and the next it would shrink back to the size of the scale-ship, or even smaller. By now, Vernor might have welcomed an attack from it, but the sphere seemed content to continue its solitary fluctuations.
The scale-ship was still shrinking, and the shiny balls were looking larger, but they showed no sign of breaking up into smaller particles. Could these spheres be the smallest possible particles . . . totally dense, totally smooth? If that was the case, further shrinkage would reveal nothing.
Vernor cut the power. The closest sphere was almost touching them. He looked at Mick for help, but his friend seemed to be lost in thought . . . perhaps of his "infinite dimensional" space. Vernor opened the hatch door and started throwing out pieces of the food crate. The hatch was on the opposite side of the ship from the giant Christmas ball, and he hoped to push into it by means of this crude jet propulsion. It seemed several times that they touched it, but only to slide off, or to have it shrink away from them. Disgusted, Vernor closed the hatch and lay down, panting with exhaustion.
"You know what that thing is, asshole?" Mick said finally.
"Is it an infinite dimensional sphere, Mick?"
"No. It's a hypersphere. Four-dimensional. I can tell from how it looked out there."
"O.K." Vernor said. "It's a hypersphere." He felt very tired.
"The
Universe
is a hypersphere, Vernor," Mick said quietly.
Mick's statement was correct. The old Einstein conjecture that the space of our universe is actually curved around on itself to make a hypersphere had come back into favor. Vernor knew, every
child
knew, that the space of the universe was a hypersphere—just as he knew that the space of the Earth's surface was a sphere. But Vernor had not been prepared to actually see a hypersphere. He
couldn't
actually see it all at once, but he had been seeing it in installments as he observed the various-sized spheres in front of him. Just as a sphere is a stack of circles, a hypersphere consists of infinitely many spheres, joined to each other in some unimaginable fashion.
"Mick," Vernor said finally. "I'm ready to believe anything else you tell me if only those things out there are each the universe."
"If those are each . . . " Mick echoed. "How can each one of those different hyperspheres be the same universe?"
"They're shiny aren't they?" Vernor said. "I figure they're sort of reflections of each other. But that can wait. The real problem is how to get
inside
one of 'em."
"You thought throwing that shit out the hatch was going to push us into it?" Mick asked pityingly.
"You got any better ideas? Or should I bring on the analogies?"
Mick shook his head. "Let's just rest. Maybe it'll come
git
us. I think I could probably get
my
self in there, but I don't think there's anything I could do to maneuver the ship into the right position."
"Like making a disk stick to a sphere," Vernor mused. "We really should try—" he started, but broke off in a yawn. He was bone tired. They lay on the scale-ship's floor watching the fluctuating cross-section of the hypersphere.
"I bet it's helps to get into it if you're already out of it," said Mick. He lit a stick of weed and passed it across to Vernor.
"Just a second," Vernor hissed a few minutes later. "There's something different out there. Moving towards us—up there." He pointed. There was, indeed, something approaching the scale-ship from above the hypersphere. It was irregularly shaped and seemed to be moving with a sort of beating motion.
"Oh, come back tomorrow," Mick exclaimed. "It's going to be something else trying to eat us." The object drew closer. It was shaped almost like a man, but there could hardly be people floating around here . . . smaller than an atom, larger than the universe. Strangely, the object did not shrink as it approached the scale-ship . . . could it penetrate their field and devour them?
Mick gave a sudden whoop, "Hey, Professor, we're in here!"
"But can't be," Vernor moaned. "But can't be!" Sure enough, it
was
Professor Kurtowski. Reaching the ship he climbed in the hatch, sat down in the pilot's chair, and beamed at them.
"I'm dreaming," he offered by way of explanation. "I often come here when I get uncoupled. I was never quite sure before that this place was . . . shall we say
real
?"
Vernor's mouth opened and closed silently, but the resilient Turner was not at a loss for words, "Professor, is that thing there the Universe?"
"Go on in. Maybe you'll find out." Kurtowski replied.
"That's the problem. We can't get in," Vernor said, finding his voice.
"It's something you do with your head. Keeping still. Go to sleep. Sleep. Sleep." Professor Kurtowski was fading, and then he was gone, but this occasioned no outcry, as the two passengers of the scale-ship had dozed off.
After all had been quiet on the ship for some time, the ever-shifting sphere drew closer and dwindled to point-size. To an observer on the scale-ship it would have appeared now that the hypersphere had disappeared, but it had only moved "under" the ship.
Immanuel Kant called space an "ineluctable modality" of human thought, but Mick and Vernor were far gone enough to prove him wrong. All barriers were down, and the hypersphere rose to assimilate them.
Vernor snapped awake. Such a strange dream . . . first Kurtowski, then Alice, and then . . . what? There was an expanding sphere of darkness in the scale-ship with them. A darkness marbled with streamers of light . . . growing towards him. The scream stuck in Vernor's throat as he realized that they were home free.
"The Professor was right," Mick remarked. Strange, had he had the same dream? But no dream could compare with what they were witnessing now—everything, everything at once.
They were in it, filling a tenth of it. "The All," Vernor said reverently. It was alive. It was alive and glad to see them. The Universe. What did it look like? What does a head of clover look like . . . or a rock or a thumb or a moon or a microbe? Nothing's really any bigger than anything else on the Circular Scale. But still, but still, if you expect a lot, you see a lot. ZZ-74.
The patterns around Vernor told him everything there was to know. When later he tried to express his feelings during those minutes of total communication with the Universe, he could do no better than to quote Wittgenstein, "The solution of the problem of life is seen in the vanishing of the problem."
But soon this passed, as it always does, and Vernor was analyzing, differentiating, observing. They were surrounded by a three-dimensional network of light. Pulses of brightness traveled through the network, forking here, merging there. A minute ago these patterns had seemed to be part of him, invisible, but now he could only gape and wonder.
"God's brain." Mick said simply. That was it. And what thoughts were they watching, what had they left behind? The network region near them maintained an increased level of activity. It was still talking to, in, them . . . but Vernor couldn't hear it anymore.