by Various
Tony was alone at this stop. This part of town was much quieter, a collection of nine-to-five businesses now closed for the weekend. The street was busy in one direction, people heading into the beating heart of downtown, but not so much in the other. Tony oriented himself and saw a subway sign down on the corner ahead. On this route he’d have to make an awkward train change, which would extend his journey time by quite a margin. But tonight that wouldn’t be a problem.
By the time he reached the station stairs, Tony was in a jog. He checked his speed as he approached, checked over his shoulder (just in case), then trotted down into the light.
The A-line was heaving, as always, a combination of people coming and going as the day’s train timetable drew to a close. Tony was happy in the crowd this time, as there were enough people to get lost in. He politely pushed himself to the front of the platform and waited for just half a minute before a train rumbled to a halt, the doors not quite in front of where he stood. Tony let himself be carried by the mass of people shuffling slightly to the right, and swung himself into the train car.
The train was very brightly lit, and without thinking Tony headed straight for the semi-alcove provided by the curve of the wall and the sliding doors on the opposite side of the car. There were no shadows to hide in here, unlike the bus, but nevertheless he squeezed himself against the plastic frame of the car, hands in pockets and arms held tight against his sides. People filled nearly all of the space around him, packing the train almost as full as the five o’clock rush hour.
Two stations later was his change. He wasted no time in moving between platforms, and safely inside the next train Tony returned to his corner and closed his eyes, counting the stops in his head as the train ploughed through them and feeling the other passengers thin out around them as the doors slid open and shut and open and shut.
When Tony opened his eyes, he swore quietly under this breath.
There, on a folding seat that was really only supposed to be used when the train wasn’t quite as full, sat the old black man. Tony couldn’t get a clear view, but as the train rocked he could alternately see the man under an armpit and behind a head, walking stick clutched so tightly the man’s knuckles were bleached white.
And he was looking at Tony.
Fuck. This was trouble. Who the hell was this guy? Not just a crim, not a mugger, nothing so petty. Maybe a mark, a decoy, a finder, an old peaceful man working with one of the Omega gangs, the groups of violent youths who thought they were doing the Cowl’s good works. Tony had been IDed as a target. The gang would be waiting for him on the streets above. He could see it now, teenagers, probably not more than five years younger than himself but, really, just children. Dressed up like their hero, omega symbols sprayed onto their T-shirts. Damn it, every black hat in the city thought they were in the Cowl’s gang. This old man, oh so innocent, must have watched Tony from the bus then got off at the next stop and managed, somehow, to intercept him from another subway stop farther uptown. It couldn’t have been a coincidence.
Tony focused on his breathing. The air was hot and damp, and in his tight corner filled with sweat and perfume. He tried not to move, not to draw attention to himself, for all the good it would do as the old man was still looking straight at him.
The train screeched a little as it punched the bright light of the next station—Tony’s stop—and glided to a halt. The car was packed but Tony wasn’t really interested in being nice to little old ladies, not tonight. As soon as the doors were half an inch apart he dived forward, using speed to catch the other passengers by surprise so they offered no resistance, and slipped out first. Tony’s thin-soled sneakers slapped the cement floor as he shot for the station exit.
It was much darker up top than it had been in downtown, even though Tony lived, in theory, within the central city area. Pedestrians here were few and the street traffic was light. Tony wasted no time, and after a perfunctory check of the roadway, sprinted across it from the station steps to the almost entirely black shadow cast by the still-unfurled awning of his local grocery. Back flat to the plate-glass storefront, Tony checked ahead, left, right.
All clear.
Tony waited a few more minutes. Two people emerged from the subway and walked off together in the opposite direction, but that was it. Tony counted to ten, then up to twenty, before finally settling on thirty. Holding his breath, he peeled off the window and headed up the street towards his apartment.
Tony slowed as he approached his building. He expected it to be fairly quiet—dead, in fact—at this time of night, but there was no need to burst into the lobby in any kind of rush, just in case. The safest place in the city was Tony’s apartment, and priority number one was getting up there in good time and with no suspicions raised.
Of course the elevator took forever. The building wasn’t particularly new, but then it wasn’t exactly a rundown dump—Tony had struck lucky finding the place, especially on his limited means. It was just a hair above average, in an OK area with a manageable rent provided he kept up the extra shifts at the store. It wasn’t five star living, but it was clean and tidy. And safe.
The imaginary chase—and it was imaginary, surely—and the interminable wait for the elevator tore at Tony’s nerves. He jumped from foot to foot as the elevator rattled upwards, balancing on his toes, almost unable to contain his impatience. As soon as the elevator dinged his level he was tapping at the chromed doors with his door key. His taps left tiny pale marks on the shiny surface, which vanished with a rub of his thumb, and then the doors slid open.
The next few seconds were a brown blur of communal hallway carpet, slightly muted fluorescent lighting and a parade of gray doors flashing past on either side. At his own door Tony pushed his hand forward, without pause, letting the key mate with the lock in perfect, practiced alignment.
In the dark of his apartment, Tony leaned against the reassuring solidity of the door, bumping his head back onto it and breathing heavily from his sudden burst of activity. He was panicking again, and he knew it. An overreaction, an irrational fear, a phobia. He closed his eyes, allowing the dark of his apartment to melt into total blackness behind his eyelids. He cleared his mind, slowed his breathing, and focused on the pinging in his calf muscles.
He stood like this for a few minutes, enjoying the semi-meditative state. Total relaxation, his mind floating free. After a spell, his attention turned to thirst. It was late, and bed called. A pot of tea, a little reading, then tomorrow was a Saturday in summer. If Tony wanted, it could be a perfect day.
He flicked on the light and, squinting at the sudden brightness, walked into the kitchen. Operating on automatic, he grabbed the china pot from on top of the fridge, spoon from the drawer, and jar of loose leaf from the pantry. He reached for the jug, gave it an experimental waggle to judge the amount of water, then moved to the sink to refill it. His friends at Big Deal ribbed him for his taste in English tea, something he’d picked up from his Anglophile parents. But Tony knew there was just nothing quite like it.
There was a window above the sink. It wasn’t much of a view, just down onto the main street, a windowless beige office building across the way covered with a giant, though dated, mural. If you leaned out a bit to the left, you could see the corner of a small park with a brightly colored plastic playground. It wasn’t a bad part of town, not really. But then did San Ventura actually have any good parts?
Tony caught the thought as it arrived, and stifled it. Enough already. Tea, book, bed. He hit the faucet and filled the jug, then glanced out of the window again.
Outside, across the street, the old man with the stick was standing, a black silhouette against the milky monochrome of the office block.
Tony froze. Even at this distance, the man was nothing more than an indistinguishable dark shape, but Tony could see his old, wet eyes glint, just a little, in the street lighting.
Holy shit. Fuck paranoia, he’d been right. Damn. It.
Distracted, Tony let the jug overfill, s
ending lava-hot water cascading onto the back of his hand. He swore, knocked the faucet off, and dumped the kettle in the sink. With his uninjured hand he reached up and released the window blind, sending the thin metal slats snapping down almost instantly.
Tony jumped in fright, and abandoning his tea making, went to the bathroom—where there were no windows—to run his burnt hand under the cold faucet.
He’d been right all along. He had to get out of San Ventura.
• • •
On the street, in the shadow of the office block, the old man clacked his tongue as Tony’s kitchen blinds zipped down with a bang.
The man sniffed, shuffled the stick into his other hand, and walked away.
John Chu became eligible for the John W. Campbell Award for Best New Writer with the publication of “Incomplete Proofs” in Bloody Fabulous (2012), edited by Ekaterina Sedia.
Visit his website at www.johnchu.net.
* * *
Short Story: “Incomplete Proofs”
INCOMPLETE PROOFS
by John Chu
First published in Bloody Fabulous (2012), edited by Ekaterina Sedia
• • • •
NEXT AUTUMN’S proof of Gödel’s incompleteness theorem tailored itself to Grant’s body. A three section proof, the trousers grew snug around his waist and shortened to break against his feet. The shirt buttoned itself as it tightened against his chest, arms and shoulders. Jacket sleeves shrank to reveal his hands. The proof looked retro rather than timeless, not at all what Grant expected from Duncan. Grant wondered what the buyers and journal editors on the other side of the curtain would make of it. He hadn’t verified a proof for an audience this important in years.
His own jacket, shirt and trousers pooled around his feet. Duncan’s stylists stopped fussing with Grant’s face and hair, pronouncing him fit for the runway. They scooped up his clothes, patted him on the back for luck, then left him alone to focus.
The cutting edge mathematics that held the proof together permeated Grant’s brain. He felt its structure, how each lemma and proposition stitched together to support the conclusion that no axiomatic system could be both consistent and complete. Either some truths were unprovable or the system could erroneously prove falsehoods. This time, Duncan had proved the theorem through computability theory.
The audience’s quiet murmur bled through the curtain. Grant took a deep breath, then cursed himself for letting himself become a cog in Duncan’s machinations again. His grad students had been having the time of their lives watching mathematicians verify proof after proof. Otherwise, he’d have told Duncan’s stylists to go stuff themselves when they asked him to verify the final proof of the new Duncan Banks autumn collection.
Grant exhaled. His feet tested the runway’s sprung floor as he stepped through the curtain. Where other theorem houses placed safety nets for their mathematicians, a trench of spikes lay on either side between Grant and the audience. Nothing was too over the top for Duncan. Journal editors thought he was potentially the best mathematician since Gauss or Euler. People had worn their proofs, or ready-to-wear copies thereof, for over a century. Editors expected the same from Duncan.
The audience hushed except for his students: Marc and Lisa. They stood, cheering and waving their arms in the air. The silence surrounding them made their excitement sound ironic. He resisted the urge to bury his face in his hands. Instead, he launched into the first steps of the proof: a tumbling pass down the length of the runway.
The jacket, shirt and trousers exploded apart at their seams into their constituent lemmas and propositions. They swirled in wide arcs around him as he twisted and spun through the air. Pain spiked his knees and shocked through the rest of his body each time he landed. Air whooshed past him and flapping lemmas surrounded him on all sides. Each somersault, jump, and handstand evoked the logic and reasoning that stitched pieces of proof together. The body canvas and chest canvas slipped inside the jacket’s shell and gave the jacket its retro shape.
The proof danced in counterpoint exactly as he expected his logic and reasoning to animate them. As he flipped through the air in a pike position, the trouser slid onto his legs. One section proved, two to go. He stepped to the far end of the runway. The shirt weaved around his arms then settled on his torso. It buttoned itself as Grant ran, building up speed for the proof’s final steps. Focused on proving the theorem, he danced with the jacket.
It flew toward him from the side rather than from the back. Its sleeves reached out as if it wanted a hug. Rather than sliding onto his body, it was about to tangle him in mid-air, knocking him into the pit of spikes. If he lined himself up with the jacket, it’d slide onto his body but, in the process, he’d tumble off the side of the runway into the pit of spikes. No valid proof took a mathematician off the runway. Either he repaired Duncan’s proof right now, or he’d be impaled by rows of sharp spikes.
Grant stretched his mind out to the jacket. He’d already started his front triple layout when he realized the jacket’s shape was subtly off. Duncan hadn’t intended the jacket to feel retro. Its chest was prone to collapse and the lapel rolled too easily. The proof’s linch pins, the body canvass and chest canvass inside the jacket’s shell, were fine by themselves, but they didn’t hold this proof together. Grant need stronger intermediate results.
The jacket sideswiped him as he started the second revolution of his layout. If this were a valid proof, he’d be wearing the jacket now. Instead, he thought back to where the proof had gone wrong. The jacket split on its seams into pieces. It flowed around him rather than tangling him and knocking him into the pit of spikes. He landed, then tumbled an extra pass, flipping and twisting in the air. Through that reasoning, he proved stronger versions of the lemmas Duncan had used. The body and chest canvasses morphed in response from what Grant was given into their proper shapes.
The math was so complicated that the reasoning took longer than the length of the runway. As he hit the end, he front tumbled towards the curtain he’d started from. His lungs burned with each breath. His heart pound not from nerves or even fear of death but from exhaustion. His legs wanted to crumble each time they hit the runway. The jacket reformed, now swooshing towards him from the front. He dove and the jacket rushed onto his body just before he rolled to stand next to the curtain.
Grant stood, his arms stretched overhead, the jacket, shirt and trousers crisp on his body. His students stood again and hollered, their arms pumping. This time, applause did fill the space. He nodded to half the audience, pivot turned, then nodded to the other half. Disconcertingly, the applause seemed to be growing. They had to have noticed the jacket he wore now wasn’t the jacket he’d started with, but that didn’t stop anyone from cheering.
Duncan strode onto the runway to receive the applause as Grant left. The two passed each other. Grant glared. Letting this proof onto the runway was no accident. At the latest, the theorem house should have caught its flaws during the run through. Duncan trapped Grant in his arms. He whispered into Grant’s ear.
“Hi, Tsai.” Duncan always called Grant by his last name. “I know you’re angry at me. Meet me in the dressing room after the show. I’ll explain everything.”
• • •
Grant hung the proof of Gödel’s incompleteness theorem on a rack with the other proofs verified tonight. His own clothes lay in a heap on the dressing room table next to some proof that hadn’t been put away. His wallet and cellphone fell out as he pulled out his shirt. Wisps of thread jutted where there should have been buttons. One sleeve dangled from its seam. His trousers had been rent into strips. That explained how the stylists had undressed him so quickly. They’d assumed he’d worn a proof to the show and could fix the damage. His clothes, though, were just clothes, ready-to-wear.
The proof still on the table had an apology in Duncan’s handwriting pinned to it. Grant recognized the work, a proof of Fermat’s last theorem Duncan had created during grad school. Its asymmetrical curved seams emphasized Grant
’s musculature. He didn’t feel clothed as much as he felt like an anatomy chart. Spent, he slumped into the chair next to the table and waited.
Duncan strode into the dressing room wearing the proof of the first significant problem they’d solved together: ten was a solitary number. A critical triumph, the proof never sold well. Too few people had the body to pull it off. Duncan had, and damn it, he still did.
To Grant’s dismay, Duncan wore the proof better now than ever. His brawn no longer fought to burst out of the proof. Rather, the proof now exposed his beautiful proportions. He was still the mutant spawn of the sun and lightning. If the sun had passed its zenith and the lightning now the lament of distant thunder, he still made any room feel too cramped to contain him.
“You couldn’t have asked me for help before you put the proof on the runway?” Grant was determined to stay angry despite Duncan’s smile. “You invited Marc and Lisa here, all expenses paid. It’s not like you didn’t know how to find me.”
“You wouldn’t have come, much less helped, if I hadn’t brought your students here.” Duncan sat on the table. “The proof of Gödel’s incompleteness theorem is the signature piece of the fall collection. No one understood its flaw much less how to fix it. I brought here, the only way I could, the one person who could fix it.”
Grant stood. He folded his arms across his chest. With Duncan sitting on the table, they saw each other eye to eye. Duncan’s gaze burned, but Grant met it.
Duncan was right, as usual. Grant wasn’t above refusing to help just to spite him.
“The one person who could fix the proof? Give me a break. And what were you going to do if I’d failed or died trying? Let the fiasco destroy your theorem house?”
Buyers and editors were a fickle lot. One tumbling pass that wasn’t parallel to the sides of the runway was enough to cancel orders and deny publication.