Spacetime Donuts

by Rudy Rucker

  After eating, they lay around on the tensegrity lattice relaxing. Vernor was full and the air recycler made a low hum. As he gazed absently out through the synthequartz, his thoughts turned to sex.

  It had been almost a year since he had gotten laid. For the zillionth time, he cursed himself for not having called Alice immediately after leaving the jail. The scale-ship's strange passage down to air beneath water had reminded him of the Inquarium. He'd made love there with sweet Alice.

  "It's too sad. You're not the same person." Her last words to him echoed in his mind. She had been right, about him taking too much dope, but he needed it . . . or did he? In jail he hadn't really missed dope . . . in jail he'd been a different person, he'd had no expectations, no desires, no physical life at all. And getting out had been such a trip . . . these two weeks in the lab he'd never really come down, but now . . . now he was resting at the bottom of a shitty crack in the floor, surrounded by mile-high policemen who would be around for years of his time.

  The only hope of escape was the slightly dubious possibility that scale is circular. And like an asshole he hadn't called Alice from Waxy's. He'd imagined he had lots of time. Alice, Dallas Alice. A slight moan escaped Vernor's lips. He slipped his hand into his pants and squeezed his aching cock.

  "Need some help?" Mick asked. Vernor looked into Mick's outlaw face. The question was natural enough; many Dreamers were bi. Turner drew closer.

  "No," said Vernor. "I'd rather just sneak and beat off when you're asleep." He paused. Why? "I'm scared you'd eat my brain."

  "Eat your brain? Well, all right." Turner didn't seem to much care either way. "How do you shit in this thing?" he asked after a minute.

  "Well, what do you think? You go outside with the E. coli."

  "Won't the air rush out?"

  Vernor shook his head. "The Professor said it wouldn't. The field should hold it in pretty well. The synthequartz is just to prevent the long-term diffusion of the air. If we didn't have it, most of the air would be gone in a couple of days."

  Mick opened the hatch door. No whooosh. Kurtowski knew his field theory. The floor in the immediate area of the tensegrity sphere looked normal, as it was shrunk to the same scale as them. The floor sloped up on all sides of the ship, becoming rougher and more magnified with distance.

  "Hey, Vernor," Mick shouted after a few minutes. "Give me those empty food tubes."

  "What for?"

  "I'm going to try and throw this thing out of the field. It'll shake up those one-celled hammond organisms and put some odor on the loach's shoe." Only Mick would have thought of that, Vernor mused, handing out the flattened food-tubes. Turner used them to pick up his turd and hurl it away from the scale-ship. As it receded from them it grew in size and seemed to slow down. Soon it was hanging in their field of vision like a slowly waxing brown moon. Before long it would break out of the air bubble and ooze up from the crack in the laboratory floor. Turner climbed back into the ship well pleased with himself.

  "It'll be up to life-size in a few days of our time," said Vernor. "One minute loachal time. They'll never figure out where it came from. I'm glad you came along, Mick."

  Mick examined the instrument panel. "How is this circular scale jive supposed to work? How can we get bigger by getting smaller?"

  "You want the whole story?" asked Vernor.

  "Tell me."

  "O.K." said Vernor. "Basically the idea is that space-time plus scale looks like a doughnut. Say you have a doughnut lying on the table in front of you. Now, if you laid a square of cardboard on top of the doughnut it would touch the doughnut in a circle." He looked at Mick for a response.

  "Right. A circle on the top of the doughnut."

  "Yeah. This circle is like made up of the points on the doughnut which are the highest," Vernor emphasized.

  "Go on."

  "Now if the points on this circle start sliding down into the hole, what happens to the circle?"

  "It gets smaller," Turner replied.

  "It gets smaller," Vernor agreed. "So we've got the circle staying horizontal and kind of sliding down into the doughnut hole, shrinking all the time. When is it the smallest?"

  "When it goes right around the inside of the hole. When it's like the circle where your finger would touch if you stuck it in the hole."

  "Good. Now dig, Mick, when the circle goes down below the hole it starts to grow."

  "Yeah," Turner nodded.

  "And when it goes down further to become the circle where the doughnut touches the table it's even bigger. And when it begins to crawl up the outside of the doughnut it gets bigger than it was to start with!"

  "Man, what are you talking about with this doughnut story?" exclaimed Turner.

  "Don't you see? We have 'getting smaller' turning into 'getting bigger' . . . continuously. By starting to shrink and then continuing in the same direction, the circle ends up growing bigger than it was when it started. And if it continues . . . if it continues in the same direction it shrinks on around to the starting position."

  "Space-Time Do-Nuts on my mind," Mick said. "And that's supposed to be the universe or what?"

  Vernor continued enthusiastically. "It's like each one of those circles is a size level. The first level is human level, then you shrink on down to the atomic level, the little circle around the hole. Next you get up to the level of the big universe when you hit the equator—the circle around the outside of the doughnut."

  "What about that other human-sized level on the bottom of the do-nut?" Mick asked suddenly, "what about that?"

  "Well, that is a difficulty with the doughnut model," Vernor admitted. "I feel that the doughnut model must be discarded at this point. The model's usefulness is simply to show that it's conceivable to have continued shrinkage turning into expansion. It might be better now to just draw a clock-face and call 12: human level, 2: cellular level, 5: sub-atomic, 7: galactic, 10: planetary, and back to 12: human level . . . " His voice trailed off.

  "What happens at 6, Vernor?" Turner asked with an edge to his voice. "You got us into this and I'm not sure you know what the fuck you're talking about."

  They sat in silence for a few minutes. What would the transition from the smallest monadic level to the largest universal level be like? Would it actually work?

  Finally Vernor spoke, "I don't know, Mick. I guess I never thought it would actually get to the point where my theories had something to do with saving my personal ass." He sighed. "We might as well go further down."

  Chapter 12: Real Compared to What?

  Vernor seated himself at the control panel and turned on the power. He'd taken a dump outside the ship, too, and before long the two turds were like misshapen twin planets beneath an unimaginably distant celestial sphere. The floor material continued to develop new complexities of structure; as they shrank, new peaks and mounds of the plastic rose around them.

  Vernor stared at an outcropping near them. A few minutes ago, the edges of the formation had begun to vibrate, and now the whole thing was to be alive with color and motion . . . like a pile of flickering snakes. He slowed the rate of shrinkage to enjoy the spectacle.

  They were now small enough to actually see the long chain-like molecules which composed the plastic floor of Professor Kurtowski's laboratory. The molecules were continually writhing and twisting, now joining together, now splitting in two.

  It was hard to believe that the molecules were not alive. One in particular caught Vernor's attention. It was viciously attacking its fellows, seizing them by the middle and then snapping itself backwards to break them in half. It hesitated in its rhythmic task of destruction and seemed to be feeling for something in the air—like a caterpillar looking for its next leaf. Now it was moving towards them. Could it be after the scale-ship? Impossible, a molecule had no mind, but yet . . . perhaps their charge, polarization, or field pattern was capable of triggering a tropism.

  The lighting had become spotty and varicolored. They were so small that the corpuscular nature
of light was evident. When Vernor looked at the molecular landscape, he did not see by a uniform illumination . . . instead it looked rather like a badly turned Hollowcast.

  "Why does it look so funny?" Mick asked. "Is it nighttime already?"

  "That question I can answer," Vernor replied. "For us to see something, a photon has to come from it to us. Now, any given atom in one of those molecules will bounce or shoot a photon in our direction only occasionally. And any given photon has only one fixed wavelength."

  "I dig," Turner replied. "The flickering is because we're small enough to actually notice the different positions that the photons come from, and it's colored because each photon is a flash of just one color—" His voice changed suddenly, "Look at that fucker!"

  The molecule which had caught Vernor's attention before was quite close now. Turner's outburst was prompted by the fact that this molecule had reared back and struck at them like a rattlesnake. Again, they were safe from assimilation, since before the molecule could actually reach them it would have to enter the VFG field . . . which would, of course, shrink it down to nothing. Nevertheless, it was unsettling to have this flaring Chinese dragon flying towards them.

  They continued shrinking, and soon it was difficult to make out the snakes which were the molecules of plastic. The flickering became more pronounced. It was like looking out into a crowd of people taking flash pictures in a darkened auditorium . . . only each flash was a different brilliant color.

  In general, an atom will emit photons of only one color most of the time, so it was possible to pick out the paths of some of the atoms in the swarm of light flashes around them. They moved in unpredictable zig-zags—like fireflies on an August night.

  As they continued shrinking, three atoms came to dominate the visual field. The closest one gave off blue and occasional green flashes and was floating motionless in front of Vernor as he sat in the pilot's seat. The other two atoms were located directly above and directly below the transparent sphere of the scale-ship. These gave off red flashes and seemed to be vibrating towards and away from the blue flashing atom.

  "H2O," Mick exclaimed. "Cool, cool water."

  "Yeah," Vernor said. "That must be it. The angles look just right for those two reds to be hydrogens bound to a nice blue oxygen. This might be a stray water molecule from our breathing. We're inside a molecule." The blue-flashing oxygen atom was drawing closer as the steady, pulsating dance of the red-flashing hydrogen atoms continued. "Pretty soon we're not going to be able to see at all, though," Vernor concluded, as the flashes grew more infrequent.

  "Why not?" Mick asked. "Why shouldn't we be able to see the electrons and the nucleus? They're there, we're still shrinking . . . what's the problem?"

  "There's no way we can see them," Vernor said patiently. "For you to see something it has to send a signal to you. The smaller we get, the less likely it is that a photon will hit us. Once we're smaller than a photon I don't think it even can hit us." He thought for a minute, then continued. "But maybe—"

  Turner finished his sentence for him, delightedly crying, "But maybe you're full of shit!" The darkness around them had filled with an even, milky luminosity. The actual particles of the oxygen atom were becoming visible!

  "This is impossible," Vernor said as they drifted closer to the atom in front of them. It had now grown to the size of a weather balloon. The blue and green flashes had died out as he had predicted . . . they were so small that the chances of a photon from the atom hitting them were infinitesimal. Nevertheless, he could see the atom.

  The electrons formed a sort of cloud or haze around the tiny nucleus, but a haze unlike any he had ever seen. If he glanced at the whole electron cloud there were no lumps, no individual electrons . . . merely the continuous probability distribution demanded by orthodox quantum mechanics. On the other hand, if he focused his whole attention on any limited region of the cloud, a small yellow ball would appear there . . . an electron orbiting the nucleus according to the laws of pre-quantum physics. What he saw depended on what he tried to see! He turned to Mick, "What do you see? Do you see separate electrons or just a cloud?"

  Turner gave him a strange look, "I see little yellow balls whizzing around a tiny pulsing thing in the middle. What kind of cloud you talking about?"

  "The electron cloud, dammit. Electrons don't have both a position and a velocity. Heisenberg Uncertainty Principle. You can't see a particular electron at a particular spot moving in a definite direction with a definite speed. You just can't!" He broke off as an electron the size of a beachball glided serenely across his visual field.

  Mick was silent for a minute, then spoke. "Yeah, I remember that Uncertainty stuff. It was on the Uncle Space-Head Show . . . Tuesday mornings at nine. Yeah. Now that I remember that, I can't see the electrons. That's really weird, as soon as you reminded me it got all cloudy . . . what is this?"

  But Vernor had no answer. The electron cloud had now grown to the size of a cathedral. The glowing nucleus was a pearl of light in the center. The atom seemed to be moving towards them. As with the plastic molecule before, he had the strange illusion that the atom's behavior was purposeful, that it was moving towards them because it sensed their presence. Was everything they met going to try to eat them?

  Vernor covered his eyes with his hands to think. How could the atom's appearance depend on what he expected to see? When he put the Uncertainty Principle out of his mind he saw a miniature solar system . . . like now . . . he watched the sixteen electrons circling around the oxygen nucleus. Mick and Vernor were so small now that their time-scale was on a par with that of the atom, so it was easy to watch the electrons as long as you believed in them . . . there was one dropping down to a lower orbit . . . a photon went wriggling away from this event. With a start Vernor realized that his hands were still over his eyes. He opened his mouth, but Mick was already talking.

  "Vernor, I can see with my eyes closed! It's like when I took my first acid trip. I just sense where everything is . . . feel it with my brain!" Without turning his head, Vernor could see that Mick was lying on the floor of the scale-ship with his eyes closed . . . and he could easily hear him yell, "Oh, yes!" to the approaching nucleus.

  Vernor observed the nucleus only superficially and grappled with the problem of how they could be seeing without their eyes. It must be some type of field acting directly on his brain, he reasoned. Conceivably a field could produce mental images . . . the brain's memory storage was basically holographic, so perhaps the interference pattern between his memory field and some external field could produce these slightly hallucinatory images he was observing . . . the nucleus seemed to glow approvingly . . . but what kind of field would it be? The nuclear boson forces could not reach this far, the electromagnetic field was too coarse, so that left gravitation . . . but, no, gravitational effects would be flattened out by the Virtual Field before they could reach him here. Suddenly the answer popped into his mind. "Probability amplitudes!" Vernor shouted. "The pure quantum field!"

  "Man, stop trying to explain it," Mick said quietly. "Get loose while you still can. Look at it."

  It was something to look at all right. The oxygen atom had grown to an immense size, and they were drifting in through the electron cloud. The specificity of their presence was introducing violent turbulence and instability in the atom. One minute they were in a swirling probability fog; the next, electrons were rumbling past them like trucks. Several electrons spiraled down into the nucleus, emitting a variety of smaller particles on the way.

  Their progress through the electron shells was uneven; they proceeded in jumps, and each jump was accompanied by crashes and showers of sparks.

  Suddenly they were through the electrons' domain and the bare nucleus blazed ahead of them, perhaps half the size of the scale-ship. It was growing rapidly as they drifted towards it. A deep rumbling filled their tensegrity sphere, and the smell of sulfur and burnt earth filled their nostrils. Vernor was not surprised . . . if the quantum mechanical probabili
ty field could act directly on the memory structure of his brain to produce visual images, there was no reason it couldn't produce the sounds and smells as well. Intellectually he was hardly surprised . . . but on the gut level he was as scared as he'd ever been.

  The nucleus was a dusky red interspersed with patches of black and threads of glowing white. Its shape, although roughly spherical, was irregular and constantly changing. There was no doubt whatsoever in Vernor's mind that it knew they were there, and was waiting for them to get close enough for it to make its move. He was repelled at the thought of being sucked into the heart of the fantastically dense entity ahead of them. But surely the Virtual Field would protect them?

  A terrible idea struck Vernor. Although the Virtual Field would prevent the nucleus from physically touching them, the spherical symmetry of the VFG field might produce a lens effect . . . a lens magnifying and focusing the fantastically powerful nuclear strong forces upon the interior of the scale-ship. Of course the VFG field was acting as a lens, otherwise the intensity of the quantum probability field would have been too weak to affect their brains . . . "Mick!" Vernor screamed. "We've got to stop!" He fumbled for the controls with thumb-fingered hands.

  "Stay cool," Mick said reaching over Vernor's shoulder to turn down the power control. They stopped shrinking, and the nucleus stopped growing. It seemed to be hovering fifty yards from them, a balefully glowing eye as large as the scale-ship. There was some kind of tension growing in the back of Vernor's mind . . .

  Suddenly Vernor's hand shot out and turned the VFG field up to full. The impulse to turn the power up had come from his brain . . . but what had put it there? The nucleus filled his mind as he clung to the controls, fending off Turner's efforts to turn the field back down.

  The laboring VFG cones whined shrilly, and in seconds the scale-ship was a twentieth the size of the huge atomic nucleus looming ahead. The rumbling and the stench grew more intense, and suddenly a chain of sparks shot out from the nucleus and enveloped the scale-ship, inside and out.