Mathematicians in Love

by Rudy Rucker

  “You’re just in time for supper,” he told me, knocking on the door. Paul Bridge opened the heavy dead bolt to let us in.

  The room was a refitted broom closet with a quality lock— the lock being perhaps the main selling feature for a room in this kind of place. The room was so cramped that the door couldn’t fully open without hitting the short, narrow bed set against the opposite wall. There was no window. The sole light was another of those three-watt bulbs in the ceiling. The floor was dirty brown and black linoleum. In addition to the flimsy bed the room held a rusty triangular metal stool and a second bed, folded in two and squashed behind the door against the left wall. Paul’s few possessions were tidily arranged in his Stanford duffel bag on the right.

  The three of us sat down side by side on Paul’s thin foam mat­tress, Haut in the middle with the bags of food in his lap. The shiny teapot with the paracomputer rested upon Paul’s stool, connected by a cable to the laptop on the floor beneath it.

  “Glad you showed up,” said Paul, handing me a plastic fork and a styrofoam box of warm ravioli. He and Haut each got the same. In addition, we had garlic bread, some tiramisu, braised greens, a bottle of red wine, and a couple of artichokes, everything shaded gray in the dim light.

  “The midnight feast of the mad mathematicians,” said Haut, starting to chuckle again. “An esoteric ritual of the arcane cult.” Maybe he was a little too cheerful. You never knew with him. “S’good,” I said with my mouth full. “So what’s up?”

  “We’ve been trying to make money,” said Paul. “Speculating. Roland’s been staying here too.”

  “I’m the runner,” said Haut, gesturing at his long blue dress. It had sailor-style white piping on the lapels. “Disguised to blend in.” I could see now that he was wearing yellowish pan­cake makeup in addition to his blunt-cut black wig.

  “Oh, nobody would give you a second look,” I said.

  “I fooled you, Kis. On the stairs you were trying to peek up my skirt.”

  “Imagine my disappointment,” I said. “And all you’ve been doing is speculating? That’s what my cousin Gyula would have done. How lowbrow. How middle-aged. I posted a rewrite of your axioms for the Gobrane, Paul. Plus a plan for a people’s paracomputer. There’s some errors I was hoping you’d help me fix.”

  “Didn’t see the post,” said Paul. “Roland and I’ve been doing other stuff too. Working on a paper about his paradox. Much further-out than anything I’d be doing at Stanford.”

  “That’s more like it. And don’t forget we want to change the past. Oh, speaking of Gyula, he thinks I should give him three hundred thousand dollars. Tell me how much you’ve made. One million? Twenty? A half-billion?”

  The two were quiet for a minute, and then Haut spoke up. “We lost all our savings and we’ve run up about ten thousand dollars apiece in credit card debt,” he said. “It’s been a complete fiasco.”

  “But now you can help us set things right,” Paul told me, hugely biting into his tiramisu. “I strongly suspect that we’ve been using the wrong morphonic model. Roland kept chang­ing it.”

  “What market have you been speculating in?” I asked.

  “Chip futures,” said Paul. “Just like Veeter. That’s the only market we have a good codec for. The codec that Veeter figured out. And we already had all his data on the laptop, and the model that you wrote, so what the hey. But it didn’t work long enough for us to really get ahead of the game. The accuracy kept going down.”

  “And then I improved on your model,” said Haut. “And our losses got worse.”

  “Were you updating the full terabyte of chip-industry data?” I asked.

  The two mathematicians looked at each other.

  “My understanding was that it would be enough to just up­date the current ticker prices,” said Haut in a small voice.

  “Pinheads. You’ve been playing the market for three days solid—and doing it wrong?”

  “Two and a half days,” said Paul. “You have to help us re­coup.” He picked up the laptop and began clicking windows, dribbling food on the keys. “So, okay, it costs two hundred dol­lars to download an up-to-the-minute version of the full chip- industry data set. But our bank and credit cards are maxxed out. Give me your bank card number, Bela, and we’ll hit the chip futures one more time, okay?”

  “I don’t have a bank card,” I quickly replied.

  “Bullshit,” said Paul, totally not going for it. “Give me the number and I’ll tell you about Roland’s paradox. And maybe I’ll look at your crappy, broken axioms. When did you post them?”

  “Monday night after I got stoned with my band.”

  “Oh, forgive us for not getting on that immediately, Kis,” said Haut in his sarcastic professor tone. “Paul and I are planning a major paper on my paradox. I seem to be having an annus mirabilis. Perhaps in the fall I’ll have time to see if anything can be made of your little fantasia.”

  Out in the hall a woman was screaming in Chinese. From what I could make out, she was a drunk hooker who’d been shorted of her pay. Now she began kicking the door across the way. The door crashed open, a man’s voice roared, and a bottle shattered. A slap, sobbing, another door slam, silence.

  “Your unsavory landsmen, Bela,” said Paul. “You marooned me in a real dump.”

  “We didn’t want Veeter to find you, remember?”

  “I wonder about that,” said Paul. “Maybe he knows exactly where we are. Maybe he’s playing cat and mouse.”

  “I wonder too,” I echoed uneasily. “For sure he’d be interested in what we’re doing. He’d probably be glad we’re still working with his paracomputer. I think he only cut us off so that we wouldn’t taint his reputation any further. And I guess Doakes’s staff doesn’t want us Humelocke Common Grounders in on their new technology. If Van could quietly watch us, he would.”

  “Look, Paul, the fresh data’s downloaded and ready to un­lock,” said Haut, watching the computer screen. “Cough up your bank card, Kis. All we’ll charge on it is two hundred for the data- access fee, and two thousand for our new speculation nut.”

  “Oh, all right,” I said. It would, after all, be nice to have some real money. “But let Paul do the clicking. Don’t forget to roll back to my original model, Paul. The way it was before Roland spoiled it.” I took out my wallet and told him my bank card number and my password. “I got some money from Leni, but after renewing my lease, I only have a few hundred dollars in my account,” I said. "The good news is that I’m allowed up to three thousand on instant credit.”

  Paul clicked away for a few minutes, fiendishly buying and selling chip futures. The membrane in the teapot glowed and danced: scrolls and gliders, stripes and spots, jaggy blocks and washes of color—like a cartoon of an inside-out dream. Whenever I could tear my eyes away from the Gobrane, I checked Paul’s progress on the laptop screen. So far so good. But our margins for error were getting smaller with each trans­action. The reliability of our data set was beginning to fade. I could see this physically on the Gobrane. The patterns were less crisp than before.

  “We’ve got a million,” announced Paul. “Most optimal. Credited to Bela’s account.”

  “Good,” said Haut. “We’ll share it three ways. But keep go­ing. Go for morel”

  “Don’t,” I said. “The data’s too soft now.”

  “So get fresh data,” said Haut. “Why stop?”

  We were interrupted by another outburst of noise: A man pounding on our door and yelling, “Where my nice girl?” He was, I gathered, a Chinese pimp. His intense, high-pitched voice sounded vaguely familiar.

  “Not here,” I shouted. “Across the hall.”

  The man switched to the other door. We heard the door fly open. The same man as before began to yell. We heard the thud of a fist, the breaking of a chair, a woman’s harangue, and then the new man’s tenor voice quietly laying down the law. “Never mind them,” said Haut. “Go on, Paul.”

  I was beginning to feel uneasy. “Show me R
oland’s big para­dox now,” I said. “We can always make more money later. It’s like you’re using a beautiful scarf to shine shoes. Show me the paradox, and then let’s get out of this place.”

  “Here’s the paradox,” said Paul, digging out another of his neatly written lined-paper pads.

  “Oh, come on, dog, I want a demo, not a freaking math pa­per. I’m not an academic anymore. Can we make the paradox run is what I want to know. Can we really tear a hole in space­time?”

  “We’ve been, uh, hanging back on that,” said Haut. “How far is your car from here?”

  “Couple of blocks.”

  “I’d suggest that before we try any experiment, we be fully prepared to relocate,” said Haut. “The demo might cause a dis­turbance. But, hell yes, I want to see it, too. Give me that lap­top, Paul. I’ll download our model onto the paracomputer. And the codec is trivial. It’s a one-line program, Bela.”

  “Like a liar paradox?” I asked. "A sentence that says, ‘This sentence is false’?” Across the hall things had quieted down.

  “More or less,” said Haut. “A program that tells the Gobrane to predict the opposite of what it predicts it’ll predict. It’s akin to calculating the sum of an alternating infinite series: one minus one plus one minus one plus one forever—does it sum to zero or to one? It’s not so much the potential for self- contradiction that matters, you understand, it’s the divergent regress of self-reference. You’ve heard of the Margolus-Levitin theorem?”

  “Barely,” I said. “I heard Veeter mention it when he talked about your paradox.”

  “You told him about my paradox, Paul?” Haut was instantly outraged.

  “It was all under nondisclosure, Roland. It’s not like he’s gonna publish it.”

  "Easy for you to say with your fat grant,” fumed Haut. “You’re giving away my leverage! I should crush you like a—”

  “Academic fame doesn’t matter anymore, Roland,” said Paul. "We’ve got money from the market, and as for power—we’re close to altering reality! And to think I was so worried about getting back for a meeting with my department chair.”

  “Can one of you finish telling me what we’re talking about?” I demanded.

  “There’s a maximum computational rate that any limited re­gion of space can perform at any given energy level,” said Haut, composing himself. “That’s the Margolus-Levitin limit. It’s high—maybe ten-to-the-fiftieth bit-flips per second on your teapot paracomputer—but I’ve proved that in the process of trying to, as it were, unpredict itself, a paracomputer running my paradoxical program will overshoot the limit. A digital com­puter has a built-in maximum capacity, but there’s nothing other than the geometry of space to stop a naturally occurring analog paracomputation from growing without bound. And we know from Einstein that space is elastic. I predict that, in order to preserve the Margolus-Levitin condition while expanding without limit, my paradoxical paracomputation will deform the Gobrane’s space. A spherical volume around the Gobrane will bulge out into hyperspace and—”

  “And if the bulge touches another sheet of spacetime, we get a tunnel!” shouted Paul excitedly. He was kneeling on the floor, stashing his few possessions in his little red bag.

  “All this from a one-line program?” I asked.

  “It doesn’t even have to be a program that comes in via a codec,” said Haut. “We should be able to initiate the behavior on the Gobrane by electrically zapping it in a particular spot. The paradoxical point. Paul and I calculated its location this morning in terms of the fixed point of a matrix self-map. The eigenvector. The paradoxical point’s coordinates involve our old friend the golden ratio. Delightful. That’s part three of our paper.”

  “Sweet,” I said, thrown back into my old admiration of Haut’s mathematical technique.

  With all his gear packed, Paul was compulsively arranging the trash, nesting the containers and fitting them into the empty shopping-bag. A spare steamed artichoke remained from our meal.

  “This can be our test particle,” he told Haut, fastening his wristwatch around the plump gray-green bud. “And I’ll throw in my watch to check for temporal effects.”

  “Surreal,” I marveled. “So what’s going to happen to the arti­choke?”

  “Nothing,” said a voice from the laptop computer. Veeter’s face appeared in a window on the screen. “I’m not going to let you maniacs do this.”

  “Are you live?” I asked the window. “Not a tape, not a simu­lation?”

  “It’s the real me,” said Veeter. “Didn’t it ever occur to you so- called geniuses that I’d be watching you through the laptop I gave you? Hanging back and learning from you? Oh, and I en­joyed that broken little paracomputer recipe you posted Mon­day night, Bela. But don’t do that again. Frank Ramirez’s staff wanted to have you shot. I had to spend some of my political capital to save you.”

  “You’re talking about the vice president?” I said uneasily. “Why would he care?”

  “From now on, the paracomputer is top-secret classified, and talking about it is a treasonable offense warranting termination with extreme prejudice, as they say. I can’t afford to protect you again. The fun’s over. And as for this crazy experiment you’re about to pull, if that were to cause any major damage, it would be terrible publicity for—”

  As surely as if I had a prediction machine embedded in my brain, I saw what was coming. Veeter was going to send a signal to the laptop, a signal that would pass through the connector cable and disable the Gobrane. With a seamless, smooth gesture that was utterly one with the inspiration to act, I snaked out my hand and disconnected the laptop from the little brass teapot.

  “I don’t know you guys anymore,” said Veeter, and with a slight popping sound, the laptop screen blanked out.

  “You screwed things up again, Kis,” said Haut, blindly tap­ping at the laptop’s keys. “Why’d you yank the connector? The laptop’s gone dead. And did you hear what Veeter said? Now I’ll never get a grant from him.”

  “Ramirez wants to kill Bela?” said Paul, more to the point. Across the hall a cell phone rang twice and stopped.

  “Let’s run the experiment right now,” I said. “Duh, Roland, the reason I unplugged the teapot was so Veeter couldn’t dis­able the Gobrane.” I peeked into the pot. The colorful mem­brane was as lively as ever. “Hurry and zap it like you two said. At the paradoxical point. Maybe those flying alien cone shell snails can help us.”

  “They’re real?” said Haut, growing pale. “The doctor said I’d only imagined them. I don’t want this!” He got to his feet and made shooing gestures with his hands, backing towards the left side of the room. “You’re a menace, Kis!”

  The pounding on our door resumed.

  “Bela Kis!” shouted the same high-pitched voice as before, and now I realized who was out there: Veeter’s muscleman, Big Owen, also known as Yuan from Shanghai. He’d be in here quite soon—to kill me, or just to confiscate the Gobrane?

  I feared the worst. I yanked the laptop’s power cord from the wall, took out my pocket-knife, cut the cord in two, and stripped the insulation off the wires leading from the plug. My hands were shaking, and it took longer than I liked. “Stick the plug back in the outlet,” I told Paul, handing it to him. “Then zap the Gobrane where Roland said.”

  “Don’t,” said Haut from behind me. “No cone shells.”

  I spread my arms, blocking Haut from reaching Paul and the magic teapot.

  “Do it,” I told Paul. “Otherwise Owen breaks my head.”

  “I’m down with this,” said Paul leaning over the Gobrane. “Be cool, Roland.”

  The door was shaking under Owen’s fists, but still it held. That dog across the hall was barking again, and the woman and man were out there too, discussing every move in rapid Chinese.

  With a quick, precise gesture, Paul touched the bare-tipped wires to certain spot upon the elliptical Gobrane: near the teapot’s spout and a bit to one side. The paradoxical point. A spark jumped;
our little ceiling light died; there were exclama­tions from the hall.

  Behind me, Haut moaned.

  The Gobrane glowed. A nested pattern of red and blue raced from the zapped spot to the edges and back, the oval patterns moving at uneven speeds, overtaking each other to form fringes of green and yellow. The core of the pattern was alternately red and blue. Yes and no. Zero and one. The Go­brane was trying to predict the opposite of what it predicted.

  Owen had begun ramming our door with his shoulder. Al­though our fine, strong dead bolt was holding up, I could hear the wood around it splintering. In the dark it was hard to be sure how soon the door would give way

  The flicker of the Gobrane doubled and redoubled its fre­quency Soon my crude human eyes could distinguish only a steady mauve ellipse. Something odd was happening to the noises from the hall—the thudding, the barking, the Chinese commentary—the sounds were slowing down. As if the air were turning to honey, to cough syrup.

  “I better back off now,” said Paul, placing his wristwatch- wearing artichoke upon the open lid of the teapot. “Only another couple of seconds till it passes the flat-space Margolus- Levitin limit. And then it’ll bulge.”

  “They’ll eat me!” cried Haut. Paul stepped back to my side of the room.

  And then a lot of things happened. The mauve ellipse within the teapot rose up in a bulge, with the artichoke wob­bling on top of it; the bulge ballooned into a ten foot puffball of light, resting like a genie upon the teapot. Where the puff­ball touched the ceiling, the building materials crumbled away. Scraps of lath and plaster dropped through the air, silhouetted like dark snow against the glowing lavender light. The closer the flakes were to the light, the faster they seemed to move.

  Looking into the ball was like staring into a tunnel. At the far end were green islands and floating blue—lakes? Wiggling seas of water against a clear sky, with dozens of lush islands to explore. The ball was the door to another world. A cord like a vine or a kelp stalk stretched along one side of the tunnel from the other world to our own. The far end of the stalk disap­peared into one of the seas and the stalk’s near end tapered to a point on the left side of the ball.