Complete Stories

by Rudy Rucker

  Jack picked his way off the glacier and up a scree of stones with inconceivably many facets. At the peak stood a marble palace, looking out upon subordinate ranges of peaks in every direction. Was this the top? Absolute Infinity?

  The droning chant was coming from within the temple. Peering in through the portico, Jack saw a host of singers, praising a figure on a high altar: a large eye resting upon a golden platter. Lo and behold, one of the choristers was Ulla, her skin a bit darkened from the lightning bolts, but otherwise in fine form.

  “Jack! You found me. I hate this place. That big bossy eye up there, his name is Jayvee. He thinks he’s so great. Get us out of here. I can’t figure out how to get down.” Her gentle voice was breathy in the thin air.

  Jayvee twitched as Jack ushered Ulla out. The big eye didn’t want to lose his new recruit. His golden platter rose into the air, and he followed the couple onto the temple’s porch. The eye extruded a snaky arm bearing a flaming sword. Jayvee was preparing to smite them.

  “Dear infinity, please help me,” said Jack once again. The sword swung, Jack and Ulla ducked, and a faint pop sounded from high above.

  In an instant, the blue dome became crazed all over with cracks—and fell apart, revealing a much higher range of mountains, stretching up towards a mighty sun. The bullying Jayvee quailed and took refuge in his little temple.

  “We are not going any higher!” exclaimed Ulla, guessing Jack’s thoughts.

  Jack and Ulla went tobogganing down the slick curves of the glacier’s crevasse—and as they neared the base, they flipped to the dual view of things, becoming subdimensional plankton in the glowing sea’s benthic abyss. From here they drifted effortlessly upwards.

  As they rose, Jack watched the branching marine forms even more closely than before—and reached his own conclusion about the Generalized Continuum Problem: the powers of the successive alefs obeyed no uniform pattern at all. 2ℵ20 was a shocking ℵ101 , 2ℵ101 was a tame ℵ102 , 2ℵ102 was a near-miss ℵ105 , and 2ℵ105 was ℵ1946 . There was no overarching pattern at all.

  It made a kind of sense. Of course the transfinite numbers should be as quirky and individualistic as the finite integers. Why would the behavior of the transfinite cardinals be any simpler than the distribution of the primes, or the set of integer solutions to whole-number equations, or the indices of Turing machines? Why would set theory be simpler than number theory? Why wouldn’t the march of alefs be an inexhaustible source of surprise? There was no simple answer to the Generalized Continuum Problem. Once Jack got past his initial sense of disappointment, the new wisdom filled him with joy.

  He didn’t bother telling his insight to Ulla—for one thing they couldn’t talk while in the undersea subdimensions, and for another, she wouldn’t have been that interested. Rather than counting things, she seemed to be studying the curves and colors of the wondrous subdimensional forms.

  Jack tensed as they approached the gleaming sheet of the Planck frontier. Would this mean a return to the conniving aktuals of Alefville? With all his heart, he wished to be back home with Ulla. And it was so. The two of them oozed up from the rug on their living room floor.

  “I knew the outline of Alefville reminded me of something,” remarked Ulla when they were done exulting. “Alefville is exactly the same shape as this smear of cadmium red that I made on the rug when I was painting your portrait.”

  “Alefville is the smear of paint,” exclaimed Jack. “Physical space is absolutely continuous. Every level of the transfinite exists in the small. What a day. And I’m—I’m done with the Generalized Continuum Problem, too.”

  “You solved it?”

  “Not exactly. But I found a way to let go of it. The thing is—”

  “Please don’t start writing a paper about this,” said Ulla. “It is really and truly time for our dive trip. Hey—wait! You already wrote your paper before we left!”

  “Sweet,” said Jack, going to fetch the printout. He sat silently on the couch, flipping through the pages. Outdoors the sun was below the horizon and the rain was setting in.

  Ulla made a pot of tea. “So?” she said, coming back into the living room.

  “It’s all here,” said Jack. “But not in the right form.”

  “What do you mean?”

  “It’s not an academic paper at all. It’s, um, like a science fiction story. About what happened to us today.”

  “But you ran that giant computer search to generate this paper. Did something go wrong?”

  “I’m not sure,” said Jack. “Of course there are infinitely many programs that can write my twenty-six papers and then generate a brand-new twenty-seventh paper entitled ‘Physical Applications of Transfinite Set Theory.’ But my search procedure was supposed to select a junk-free minimal program that takes a very long time to produce its outputs—so you can tell it’s doing some serious computation. But it doesn’t look like I ended up with the right program after all. This is the wrong kind of paper.” Jack paused, thinking. “Or maybe not? Actually, I’ve always wanted to write some science fiction. But I never thought I’d dare to—”

  “I’m sure it’s going to be fine like this,” said Ulla, pouring out the tea. “Someone will publish your article anyway. Our true-life adventure. Hey, don’t forget to write in that your backache went away.”

  Jack penciled in the change and sat up, stretching his arms and smiling. “Done! I feel better already. Let’s head for the South Pacific, Ulla.”

  “What about those two aktuals?”

  “I think they’re done with us,” said Jack, studying the pencil stub in his hand. Out on the deck sat a toad, enjoying the fitful patter of the rain.

  ============

  Note on “Jack and the Aktuals, or, Physical Applications of Transfinite Set Theory”

  Written December, 2008.

  Tor.com, 2008.

  In 2008, I heard from the John Templeton Foundation, a foundation devoted to encouraging scientific work that could shed light upon theological issues. They’d recently organized a conference on new concepts of infinity in mathematics, physics, and theology, and they offered to pay me to contribute to their forthcoming volume of proceedings, New Frontiers in Research on Infinity, to be edited by Michael Heller and W. Hugh Woodin for the Cambridge University Press.

  Back in the 1970s, I’d gotten my Ph.D. in set theory (the mathematical study of infinity), and had published several mathematical papers on the topic. So I was excited about having a chance to publish something about infinity again. But I’d been out of the technical end of the field for so long, that I didn’t want to try and write anything like a math paper. So I thought it would be a good idea to write a science fiction story instead, a tale involving higher levels of infinity and possible physical manifestations of infinity.

  I’d already done something like this in my first published novel, White Light of 1980. But I had a number of new ideas about infinity to dramatize, and I wrote “Jack and the Aktuals” pretty easily. It helped that I’d recently met both the pre-eminent contemporary set-theorist Hugh Woodin, as well as Paul Cohen, who’d been the most influential set-theorist when I was in grad school.

  Woodin and the Templeton Foundation were all for including my SF story in their collection, but the Cambridge University Press balked. So I ended up publishing the story in Tor.com online science-fiction site, and writing a long introduction for the Cambridge tome.

  (A practical note. Not all ereaders or web browsers are willing to display the Hebrew letter alef that appears a about a dozen times in this story. In this case you may see little squares in place of the alefs, or possibly little boxes with question marks in them. Think of them as the mysterious alefs anyhow!)

  All Hangy

  (Written with John Shirley)

  “But you said you were gonna jump off the bridge, didn’t you, Roberto?” Breeze sounded like a girl doing a funny imitation of a guy, but that was just her voice.

  Roberto hugged himself against the cold morning
wind and glanced sideways at Breeze. Her long hair streamed from behind, over the railing, as if trying to get down to the cold gray sea. They were on the sidewalk of the Golden Gate Bridge, leaning on the rail, looking at the wrinkled chaos of the bay waters below. Tourists chattered behind them, endless traffic roared by on the metal-grated road. In front of them lay the void, just one vault over that rail.

  “Um—yeah,” said Roberto. “Eventually might do it. Today we’re only reconnoitering. I’d want to be stone cold sure I have my moves right—so I end up all hangy. And, I’d want you to film me. This should be a big media event.”

  “Camera’s ready,” said Breeze, pulling her cellphone from her jeans. “I’ve got hi-def video in here, and I can upload it wireless to my website. Go on and jump, Roberto. You told me you were all set to flip your, uh, dimensional entanglements? So…”

  He wasn’t sure if she really wanted him to take the risk—or if she was trying to get him to see how dangerous the whole thing was. But she had that camera, and the green light was on.

  “I’m not ready after all,” he admitted, looking down with a shiver. The bay was so very far below. A container ship slid under the bridge, bringing cars from Korea. “They say if you hit the water from this high up it drives your leg bones into your chest.”

  “But you’d twist yourself into being all hangy before you hit the water,” said Breeze in that low voice of hers. All hangy was the term people were using for the new phenomenon.

  “Like Wing Wah disappearing during his high dive in the Olympics last week,” continued Breeze. “Like the two women acrobats at the Portland circus yesterday. Lulu and Vulu! They went all hangy. Do it now, and you’ll be the fourth one to go all hangy. If you wait…” She shrugged. “You’ll be lost in the crowd.”

  Roberto looked at her, trying to formulate a cool answer. Inevitably thinking, If you’re so ready for someone to jump off this bridge—you go first! But knowing he would try to stop her, if she made to jump. Suppose it didn’t work? Breeze would be the bigger loss to the world.

  He tried to imagine this vital being just snuffed out, if it went wrong. Here beside him—and gone. Just look at her…

  She had wavy brown hair with blond highlights, bruise-like accents in the skin under her brown eyes, a sexy overbite, wide shoulders, gangly legs, and pointy breasts in the black t-shirt and jeans jacket she was shivering in. No makeup. Not conventionally pretty, but looking at her always got him worked up.

  They were Berkeley students, three years into it, Breeze funded by her crunchy engineer parents in Mill Valley, Roberto supported by a scholarship—no school money in his sprawling house-painter office-cleaner yard-gardener family from San Jose.

  Roberto was a computer science major, hoping to create animated figures for virtual realities and videogames. He’d started out as a business major, which fully stank. The business classes were just about grubbing for cash. A few of the people in Roberto’s family were already good at that—such as his half-brother Leon who now sharing Roberto’s little room in a Berkeley student co-op.

  Breeze had a room in the same co-op as Roberto. She was a music major, and she practiced on her cello in the lounge sometimes—which drove Roberto frantic with lust. He’d even created a computer animation of Breeze playing the cello naked, wrapping a photo of her face onto the 3D grid of the puppet’s head, but—

  Whoah! Suddenly Roberto was seeing two women hanging upside down in midair, twenty feet out from the bridge railing.

  “Breeze!” he cried, pointing. “Do you—”

  Yes, she saw them too. Lulu and Vulu, the twin Portland aerialists in their spangled suits, moving their mouths in synch, the sweet voices coming into Roberto’s and Breeze’s heads, a siren song about—he couldn’t quite make it out.

  “What’d they say?” asked Roberto when the women abruptly disappeared. He realized that he’d damn near jumped, whether or not he had the twists and turns clear in his mind.

  “Apocalypse?” said Breeze uncertainly. “Transformation?” She too had brought her foot up onto the lowest rung of the railing. She shook her head now, backing away.

  “All hangy,” Roberto muttered, putting his arm around Breeze. “I want to do it, but I don’t want to blow it.” He shook his head, stunned at what he’d seen. There was a cause and effect, an underlying principle in esoteric physics that explained it, but seeing two women just appear in empty air off the Golden Gate Bridge was hard to digest. He felt more than a scootch unreal. And why had they appeared to him—right then? “Lulu and Vulu must know I’m nearly ready. That’s why they were calling to me.”

  “They were calling me, too,” said Breeze. She smiled, went on musingly, “Maybe I can get there with my cello. A certain fillip of the bow. A unique glissando.”

  He leaned back, a little, to look at her. Suddenly aware that he’d put his arm around her, and she hadn’t discouraged it. “You serious? I mean about—using music?”

  “I’ve been thinking about it, yeah.”

  It was drizzling rain, and the hangy aerialists were gone, like smiling stage magicians after a finger-snap. Roberto remembered a Zen formulation from an Alan Watts book his philosophy teacher had given him: Where do you go after you die? Where does a fist go after the fingers unclench?

  Sniffling from the cold, Roberto and Breeze walked back to her car. It was cozy in there with the heater going, the fan clearing mist from the inside windshield, the windshield wipers in rhythmic counterpoint to Roberto’s heartbeat. Breeze maneuvered through the traffic towards Berkeley. As the car warmed up; Roberto could smell the vinyl of the car interior, and Breeze’s shampoo and, ever so faintly, the dreamed-of nooks and crannies of her flesh. Eden.

  “At some level, in some dimension, Wing Wah, Lulu and Vulu are with us right now,” said Roberto.

  “Dangling from my rear-view mirror like three good-luck dolls,” said Breeze, airily waving her hand. If Roberto squinted his eyes, he could almost see them—tiny Wing Wah lithe and powerful in his bathing suit, and Lulu hanging from Vulu’s feet.

  “I saw an interview with Lulu online this morning,” said Roberto. “It’s not like she disappeared for good. She can still walk around like a regular person. But when they feel like it, she and Vulu and Wing Wah can send themselves skipping around the world like stones skimming a pond.”

  “Or like tree roots,” said Breeze. “Popping out of the ground where you don’t expect.”

  “Or like bats hanging in our heads as if our skulls were caves,” said Roberto.

  “It’s great how we can’t nail it down to one single metaphor yet,” said Breeze. “Great that mass culture hasn’t assimilated the hangy thing and made it mundane.” She was pulling up in front of the rambling, decrepit co-op where they rented their rooms. “I’ve got to practice my cello now.”

  “You’re just going on the same as before?” said Roberto. “After what we just saw?” He snorted. “The world might be ending, you know.” His implication was that he and Breeze should finally make love. But she wasn’t picking up on that.

  Or maybe she was, and the answer was no.

  “I’m going to practice differently than usual,” she said, her voice dreamy, as they walked into the co-op. “I’ll be working on the thing with my bow and the magic notes. I’m serious about that. Why should you be the only one in our co-op to get all hangy?” She looked at him, with her pleasingly crooked smile. Affectionate mockery. “Especially if you’re going to keep chickening out, Roberto.”

  “I can help you practice,” he said, loath to have the conversation end. “I can show you the moves I plan to use when I do my jump.”

  “Show me down here?” said Breeze, nodding at the dusty couches of the lounge. Ruling out the possibility of him coming to her room.

  “Sure,” said Roberto, flopping down on one of the sagging couches. “I’ll get the demo ready on my cell while you get your cello.” Breeze disappeared up the stairs.

  Roberto was in no rush to go to his own roo
m, given that his squatter brother Leon would be awake by now, draped across Roberto’s bed like a sullen snake, broodingly playing the same licks over and over on his cruddy guitar with the stickers all over it. Leon had nothing to do all day until he went out for his evening’s work, which was buying and selling low-grade street drugs, mostly weed and meth, just like he’d been doing down in San Jose before Mama threw him out.

  Bending over the little screen of his all-purpose phone, Roberto cued up the animation he’d created by merging the films of Wing Wah’s dive and of Lulu and Vulu’s final aerial routine. He’d superimposed his face onto the wireframe model, so that a little Roberto-faced figurine spun through the air and—zip-zap—disappeared. The underlying mathematics had to do with tensors, spinors, and higher-dimensional flips. Orientation entanglement. Roberto had snarfed that part from a physics professor’s site. The surprising thing had been how readily he’d been able to turn the equations into computer code.

  As he waited for Breeze, he dug into his code, looking for ways to condense it. If he could bum it down to something simple enough, he wouldn’t actually need to jump off the Golden Gate Bridge to get all hangy, and he wouldn’t need the muscles of an athlete to carry out the twists and flips. He found what seemed like a good approach and ran the animation again. Yes. Much faster.

  “Hey there.” It was Breeze, lugging her giant cello case, lively in her boots and jeans. She’d pulled on a sweatshirt.

  “Watch.” He showed her the latest version of the demo.

  “Sweet,” she said, watching it. “But how do you know it really would work? I mean, aren’t you just faking the disappearance? Blanking the screen?”

  “Well—I guess you could say that,” allowed Roberto. “But the physics is all good. I’m reasonably sure that if I could physically carry out these moves I’d get all hangy. But it’s still a little too—”

  “Acrobatic for the likes of us?” said Breeze in her husky voice.