Complete Stories

by Rudy Rucker

  Much to Pythagoras’s alarm and surprise, his fist merged with his torso like the obscene bodily involutions of the Bristle Cat! At that moment, a familiar voice rang out. It was an apparition of the Crooked Beetle, floating as a large dusky ghost above the physical beetle that was still perched upon his old body’s face.

  “Hail, Pythagoras!” twittered the Beetle, seemingly in ecstasy over the philosopher’s new body. “Welcome to life as a pure mathematical form! I encrypted you rather nicely, don’t you think? I did the basic encoding that night I first bit you. And all along I’ve been updating the Pythagoras number to include your most recent thoughts. That’s what I was doing sitting on your face just now. Keeping your number right up to the minute. You remember everything, don’t you?”

  Pythagoras nodded mutely, and pulled his limb from his chest with a queer, unnamable sensation. Ranged around him were also ghostly forms of the Tangled Tree, the Braided Worm, the Bristle Cat, the Swarm of Eyes. Each of them was connected by the finest of tendrils to their earthly instances here in this malodorous dump.

  “Your new, numerically defined body still has only a not-quite-life,” explained the Beetle. “It’s unreal in the same way that your number-conjured flames are but colorful tetrahedra until being boosted into full reality by the presence of the elemental Fire within the kindling wood. Your broken old body—it contains your kindling.”

  Pythagoras looked down at his dying carcass with a feeling of revulsion. It was as uninviting as a soiled, wet toga. “You’re not counseling me to don that same old mortal coil, are you?”

  The Crooked Beetle spat, not a number this time, but a viscous dark glob that landed on Pythagoras’s foot with a tingling sensation. It was a tiny, crooked copy of the Beetle itself, connected to the ghostly Beetle by another of the thin, silken strands. The new beetle stretched out its wings, waved them tentatively, then buzzed into the air. “I don’t like to explain everything,” said the great Beetle.

  “You need your you to be you,” said the smiling Cat, rubbing against Pythagoras’s ghostly leg, and then passing right through it. “Be your own son and father.”

  “Breathe in what you expire,” buzzed the Swarm of Eyes.

  The Braided Worm beside the little brook swayed back and forth like a charmed snake. “Don’t fail us, Pythagoras. It still remains for you to prove your greatest result—to prove that we are real.”

  “So bend down and breathe in your dying breath!” exhorted the Tangled Tree, gesturing with every one of its innumerable branches.

  Of course. Now Pythagoras remembered the custom whereby a child would try to breathe in the last breath of a dying parent. His insubstantial body knelt at the side of his supine flesh. With eyes near-blinded by the light of eternity he stared up at his fresh-minted body. With clear fresh new eyes he stared down at his old self. Now came the dying man’s final breath, the expiration, and Pythagoras’s number-built new body breathed it in.

  From the viewpoint of his old self, Pythagoras felt as if he’d been yanked out of paradise. He felt grief and a kind of homesickness at not fully merging with the divine One whose hem he’d only just begun to touch. From the viewpoint of his new self, Pythagoras felt invigorated, renewed and—above all—solid and real. And then he was no longer two, but one. The infinitude of his divine soul had now fulfilled the incarnation of the number-model of his body.

  Looking around the dump, Pythagoras could no longer see the ghostly images of his apeiron friends—and friends they truly were, not rivals or enemies. Their earthly avatars still here upon the midden remained mute: a tree, a worm of water, a cat, a swarm of flies and a beetle. Pythagoras fully felt how truly these earthly forms did embody the apeiron, felt more strongly than ever the undivided divinity that is present within all things, whether great or mean.

  His new-made body felt strong and sound, though not overly so. The number form was, after all, only that of an old man. But he was no longer an old man who’d been crushed to death by stones. There was one more change as well. The adamantine gold was gone from his thigh, and looking within himself he saw that he’d lost his knowledge of the five magic numbers. He was glad.

  So what to do next? Most important was to see Eurythoë. And the Braided Worm had said something very intriguing about Pythagoras having another great result to prove. Perhaps the simplest would be to go back to his cave, receive visitors as always, and continue to think about mathematics. Surely his resurrection would frighten Glaucas into leaving him alone.

  But before doing anything else, Pythagoras tended to his soul’s former shell. Gripping the corpse by the shins, Pythagoras bumped it across the slope of the midden and into a patch of trees. He lacked any shovel to dig with, but he used a stick to scrape out a shallow grave, and then gathered a great heap of brush to decently cover the body. It took a long time, several hours in fact, but what did time matter to a man risen from the dead? While he worked, the rudiments of a new and wonderful theorem began coming to him. It hinged, as he’d suspected, on the ratio of a square’s diagonal to its side.

  His earlier theorem of the right triangle said that the square on a diagonal is equal to the sum of the squares on the two sides. If the two sides were equal, this meant that the diagonal square was twice the magnitude of each side square. Put differently, a diagonal square and a side square were in proportion two to one. And put differently once again, the ratio of the diagonal to the side could be called the “square root of two”.

  For several years now, Pythagoras and his followers had sought for a whole number ratio to represent this curious “square root of two.” The search involved looking for squares that were in a perfect two to one ratio. 49 to 25 was close and 100 to 49 was closer, which meant the square root of two was close to the ratio 7/5 and closer to the ratio 10/7. But the match was never quite perfect, and now that he’d finally let the apeiron all the way into his heart, Pythagoras fully grasped that the match never would be perfect at all. There was no whole number ratio precisely equal to the square root of two.

  He found himself singing a happy tune as he finished up the reverential chores of covering his corpse. Now that he fully understood what he wanted to prove, he would find a way to do it. Mulling over the distinctions between odd and even numbers, Pythagoras set out towards Tarentum. The clever Archytas could help him hone a proper proof.

  At the edge of the dump, Pythagoras encountered Eurythoë, her face wet with tears. She was dressed in the black garments of mourning. For him? She didn’t really see him, for she was too busy peering past him, looking for his body on the dump.

  “Woman, why are you weeping?” said Pythagoras. “Whom do you seek?”

  Eurythoë wiped her face with the black cloth of her veil. “Sir, if you have carried him off, tell me where you have laid him, and I will take him away.”

  Pythagoras spoke her name. “Eurythoë.”

  She turned and fully saw him at last. “Pythagoras!”

  “My dear, even-souled Eurythoë. The apeiron has saved me. Good as new.” He chuckled and skipped about, executing a little twirl.

  “My dear, odd-brained Pythagoras,” sang Eurythoë. “But what of your madness?”

  “What madness? Believe this, woman, I’m working on a proof of the reality of the apeiron! It all has to do with evens and odds.”

  “Then I can help you! Let’s go up to your cave.”

  “Right now? What about Glaucas and the priests?”

  “Glaucas is dead,” said Eurythoë, seemingly not overly saddened by having to deliver this news. “Alcibedes slew him only minutes after they carted your body away. My son Archytas is the new king, and the populace rejoices. The priests of Apollo will do as Archytas says. We already have Turnus’s abject assurances.” She burst out laughing. “Glaucas is the official reason why I’m wearing mourning. But, O Pythagoras, it was only for you.”

  “I should speak to Archytas,” said Pythagoras. “About the wonderful new proof.”

  “We’ll do that late
r,” said Eurythoë, kissing him. “After the cave. I want to give you a proper welcome.”

  “Very well then,” said Pythagoras. “Let’s take the bridge across the river.”

  “No more sorcery?” said Eurythoë.

  “No,” said Pythagoras. “Just mathematics.”

  ============

  Note on “The Square Root of Pythagoras” (Written with Paul Di Filippo)

  Written in 1999.

  SF Age, October 1999

  This is a story I always wanted to write. As a math professor, I’ve had a lot of occasion to meditate about Pythagoras. He’s a very shadowy historical figure, and the stories about him which survive are miracle tales, many of which are incorporated into this story. In February of 1999, I visited Paul Di Filippo at his home in Providence, and he helped me to finally get a Pythagoras story done.

  I have five of the apeiron beings, because I think of mathematics as having core concepts: Number, Space, Logic, Infinity and Information. These correspond to, respectively, the Tangled Tree, the Braided Worm, the Bristle Cat, the Swarm of Eyes and the Crooked Beetle. The Crooked Beetle is also our old friend the Mandelbrot Set. The creatures also represent, again in the same order, Earth, Water, Fire, Air and the Cosmos.

  Pockets

  (Written with John Shirley)

  When the woman from Endless Media called, Wendel was out on the fake balcony, looking across San Pablo Bay at the lights of the closed-down DeGroot Chemicals Plant. On an early summer evening, the lights marking out the columns of steel and the button-shaped chemical tanks took on an unreal glamour; the plant became an otherworldly palace. He’d tried to model the plant with the industrial-strength Real2Graphix program his dad had brought home from RealTek before he got fired. But Wendel still didn’t know the tricks for filling a virtual scene with the world’s magic and menace, and his model looked like a cartoon toy. Someday he’d get his chops and make the palace come alive. You could set a killer-ass game there if you knew how. After high school, maybe he could get into a good gaming university. He didn’t want to “go” to an online university if he could help it; virtual teachers, parallel programmed or not, couldn’t answer all your questions.

  The phone rang just as he was wondering whether Dad could afford to pay tuition for someplace real. He waited for his dad to get the phone, and after three rings he realized with a chill that Dad had probably gone into a pocket, and he’d have to answer the phone himself.

  The fake porch, created for window washers, and to create an impression of coziness the place had always lacked, creaked under his feet as he went to climb through the window. The narrow splintery wooden walkway outside their window was on the third floor of an old waterfront motel converted to studio apartments. Their tall strip of windows, designed to savor a view that was now unsavory, looked down a crumbling cliff at a mud beach, the limp gray waves sluggish in stretched squares of light from the buildings edging the bluff. Down the beach some guys with flashlights were moving around, looking for the little pocket-bubbles that floated in like dead jellyfish. Thanks to the accident that had closed down the DeGroot Research Center, beyond the still-functioning chemicals plant, San Pablo Bay was a good spot to scavenge for pocket-bubbles, which was why Wendel and his dad had ended up living here.

  To get to the phone, he had to skirt the mercury-like bubble of Dad’s pocket, presently a big flattened shape eight feet across and six high, rounded like a river stone. The pocket covered most of the available space on the living room floor, and he disliked having to touch it. There was that sensation when you touched them—not quite a sting, not quite an electrical shock, not even intolerable. But you didn’t want to prolong the feeling.

  Wendel touched the speakerphone tab. “Hello, Bell residence.”

  “Well this doesn’t sound like Rothman Bell.” It was a woman’s voice coming out of the speakerphone; humorous, ditzy, but with a heartening undercurrent of business.

  “No ma’am, I’m his son Wendel.”

  “That’s right, I remember he had a son. You’d be about fourteen now?”

  “Sixteen.”

  “Sixteen! Whoa. Time jogs on. This is Manda Solomon. I knew your dad when he worked at MetaMeta. He really made his mark there. Is he home?”

  He hesitated. There was no way to answer that question honestly without having to admit Dad was in a pocket, and pocket-slugs had a bad reputation. “No ma’am. But …”

  He looked toward the pocket. It was getting smaller now. If things went as usual, it would shrink to grapefruit size, then swell back up and burst—and Dad would be back. Occasionally a pocket might bounce through two or three or even a dozen shrink-and-grow cycles before releasing its inhabitant, but it never took terribly long, at least from the outside. Dad might be back before this woman hung up. She sounded like business, and that made Wendel’s pulse race. It was a chance.

  If he could just keep her talking. After a session in a pocket Dad wouldn’t be in any shape to call anyone back, sometimes not for days—but if you caught him just coming out, and put the phone in his hand, he might keep it together long enough, still riding the pocket’s high. Wendel just hoped this wasn’t going to be the one pocket that would finally kill his father.

  “Can I take a message, Ms., um …” With his mind running so fast he’d forgotten her name.

  “Manda Solomon. Just tell him …”

  “Can I tell him where you’re calling from?” He grimaced at himself in the mirror by the front door. Dumbass, don’t interrupt her, you’ll scare her off.

  “From San Jose, I’m a project manager at Endless Media. Just show him—oh, have you got iTV?”

  “Yeah. You want me to put it on?” Good, that’d take some more time. If Dad had kept up the payments.

  He carried the phone over to the iTV screen hanging on the wall like a seascape; there was a fuzzy motel-decor photo of a sunset endlessly playing in it now, the kitschy orange clouds swirling in the same tape-looping pattern. He tapped the tab on the phone that would hook it to the iTV, and faced the screen so that the camera in the corner of the frame could pick him up but only on head-shot setting so she couldn’t see the pocket too. “You see me?”

  “Yup. Here I come.”

  Her picture appeared in a window in an upper corner of the screen, a pleasant looking redhead in early middle age, hoop earrings, frank smile. She held up an e-book, touched the page turner which instantly scrolled an image of a photograph that showed a three-dimensional array of people floating in space, endless pairs of people spaced out into the nodes of a warped jungle-gym lattice, a man and a woman at each node. Wendel recognized the couple as his dad and his mother. At first it looked as if all the nodes were the same, but when you looked closer, you could see that the people at some of the more distant nodes weren’t Mom and Dad after all. In fact some of them didn’t even look like people. This must be a photo taken inside a pocket with tunnels coming out of it. Wendel had never seen it before. “If you print out the picture, he’ll know what it’s all about,” Manda was saying.

  “Sure.” Wendel saved the picture to the iTV’s memory, hoping it would work. He didn’t want Manda to know their printer was broken and wouldn’t be repaired anytime soon.

  “Well it’s been a sweet link but I gotta go—just tell him to call. Here’s the number, ready to save? Got it? Okay, then. He’ll remember me.”

  Wendel saw she wasn’t wearing a wedding band. He got tired of taking care of Dad alone. He tried to think of some way to keep her on the line. “He’ll be right back—he’s way overdue. I expect him…”

  “Whoops, I really gotta jam.” She reached toward her screen, then hesitated, her head cocked as she looked at his image. “That’s what it is: You look a lot like Jena, you know? Your mom.”

  “I guess.”

  “Jena was a zippa-trip. I hated it when she disappeared.”

  “I don’t remember her much.”

  “Oops, my boss is chiming hysterically at me. Bye!”

&
nbsp; “Um—wait.” He turned to glance at the dull silvery bubble, already bouncing back from its minimum size, but when he turned back, Manda Solomon was gone and it was only the showy sunset again. “Shit.”

  He went to the bubble and kicked it angrily. He couldn’t feel anything but “stop,” with his sneaker on. It wasn’t like kicking an object, it was like something stopped you, turned you back toward your own time flow. Just “stopness.” It was saying “no” with the stuff of forever itself. There was no way to look inside it: once someone crawled in through a pocket’s navel, it sealed up all over.

  He turned away, heard something—and when he looked back the pocket was gone and his dad, stinking and retching and raggedly bearded, was crawling toward him across the carpet.

  -----

  Next morning, it seemed to Wendel that his Dad sucked the soup down more noisily than ever before. His hands shook and he spilled soup on the blankets.

  His dad was supposedly forty—but he looked fifty-five. He’d spent maybe fifteen years in the pockets—adding up to only a few weeks in outside time, ten minutes here and two hours there and so on.

  Dad sat up in his bed, staring out to the bay, sloppily drinking the soup from a bowl, and Wendel had to look away. Sitting at the breakfast bar that divided the kitchenette from the rest of the room, he found himself staring at the pile of dirty clothes in the corner. They needed some kind of hamper, and he could go to some Martinez garage sale and find one next to free. But that was something Dad ought to do; Wendel sensed that if he once started doing that sort of thing, parental things, his dad would give a silent gasp of relief and lean on him, more and more; and paradoxically fall away from him, into the pockets.

  “I was gone like—ten minutes world-time?” said Dad. “I don’t suppose I missed anything here in this…this teeming hive of activity.”

  “Ten minutes?” said Wendel. He snorted. “You’re still gone, Dad. And, yes, there was a call for you. A woman from Endless Media. Manda Solomon. She left her number and a picture.”