Luke pulled a case from the car trunk. "Don"t wanna even talk about it," he said, then walked back toward the garage.
Ronald sank down against the car, crouched on his heels with his back against the b.u.mper. He buried his face in the sleeve of the arm set across his knees. With the other arm he still held out the MasterCard.
When he arrived home at 6:26, Ronald wasn"t at all surprised not to find Jessica waiting, not to find any note saying where she had gone. He poured himself a scotch and water and sat on the living room sofa, his feet up on the coffee table.
Due to overtime work at NASA, the consumption of wrapped sandwiches rose 14 percent. Three junks sank off Taiwan.
After a second scotch and water, Ronald said, aloud, "It"s not my fault. How the h.e.l.l am I supposed to keep a service station from selling spark plugs?"
After a third gla.s.s, he shouted, "It is my fault! It"s all my fault! I shouldn"t have lost the position with Resotech. I couldn"t have lost it!"
He went for a fourth drink, but the scotch bottle was nearly empty. He poured what little was left and held the gla.s.s up to the cove light over the kitchen sink. "That"s about one-eighth," he said. "Yeah, definitely one-eighth." He finished it with a swallow and grabbed his car keys.
Bernie"d won seventeen bets with Ronald"s help. Little twerp owed him seventeen beers. Eight ounces a gla.s.s, one hundred and thirty-six ounces. One point eight repeating six-packs. One point zero six two five gallons of beer.
He started the car. Two point four miles to McCollough"s Pub.
He parked on the street outside the bar; the parking lot was filled from the Friday-night crowds. The bouncer stared at him when he walked in, so Ronald tried to stand straight and walk evenly. He had to elbow his way through the crowd. My G.o.d, he thought, there must be a hundred and eighteen people in here. Rock music blared over the sound system, and Ronald had to pause and close his eyes every few steps through the crowd. His head throbbed. He looked around, trying to spot Bernie, and finally ran into Stan at the bar. The mechanic was staring into his beer mug, apparently fascinated by watching the bubbles in the beer head popping their way down to the liquid.
"Hey, Stan," he said, poking the man"s shoulder. "Where"s Bernie? He owes me some beers."
Stan glanced over, looking a bit dazed from the break in concentration. "Oh, hi, Ronnie." Then he turned his entire body toward Ronald. "Ronnie? Ronnie!" Stan threw his arms around Ronald in a bear hug, and Ronald felt his breath pressed out of his lungs. Stan was laughing wildly.
"I win! I finally won! That little twerp b.a.s.t.a.r.d finally loses one. Ronnie, it"s nice as h.e.l.l to see you!"
Ronald struggled for a breath and tried to keep his balance, a combination he realized the scotch was making difficult. "It"s, uh, nice to see you too, Stan."
Stan put a hand to his head and kept laughing, although he suddenly seemed embarra.s.sed. "I"m sorry, Ronnie. It"s just Bernie bet me thirty bucks that he could invite you to McCollough"s twenty times in a row and you"d never show. He"s only asked you seventeen times, and here you f.u.c.king are."
Stan hugged him again, and Ronald felt nauseous from the thick air, the noise, and the press of the crowd. "C"mon," Stan said, "they got a table near the back. I"m gonna show you off and win my prize. I can"t wait to see the twerp"s face."
Bernie"s face, Ronald saw, did not let Stan down. When he and Stan reached the back table, Stan tapped Bernie on the shoulder, and when Bernie turned he dropped his beer mug halfway through the motion of sipping from it. But his face was nothing like Jessica"s, whose hand Bernie was holding across the table. Her eyes went wide and empty.
Ronald wasn"t sure what his own face was showing, but it must have been something impressive. Stan took him by the arm and said, "Hey, what the h.e.l.l"s wrong with you, Ronnie?"
"My wife."
Stan looked at Jessica, then at Bernie, his face slowly changing. "Oh, s.h.i.t," he said. "Bernie, you"re f.u.c.king sc.u.m. Oh, s.h.i.t, Ronnie."
Bernie was suddenly very busy. To Ronald, he sputtered, "No lie, she"s your wife? I just met her tonight. Just met her." To Stan he said, "Hey, I owe you money, don"t I? We can go to the bar and have them cash a fifty." He finally seemed to realize he was still holding Jessica"s hand, and pulled back as if he had touched a hot plate. Quieter, but not so quiet that Ronald couldn"t hear him, he said, "Jessica, there"s no way he could have shown up here. There"s no way."
Stan lifted Bernie from the chair by his shirt collar. His blue shirt collar. "I"m sorry Ronnie, I didn"t know. The twerp hit on her weeks ago when she wandered in alone. He"s been meeting her here ever since. I didn"t know she was your wife." He dragged Bernie off in the direction of the bar.
Too much at once, Ronald thought. Too many variables. Then he felt the anger swelling in him, and he wasn"t sure where it should go or who deserved it most.
Jessica had lowered her head. "I needed to see him one last time, Ronald." She was stirring her mixed drink with a swizzle stick, slow circles, the ice clanking against the gla.s.s. "I don"t know why I came. I guess I was breaking it off."
All of the anger finally came to a head as Ronald watched the swizzle stick stirring even, gentle circles in her gla.s.s. He inhaled slowly. "You... G.o.ddammit, you"re out of control."
He saw her shake, and the swizzle stick fell from her fingers. She looked up, her mouth open again. He had hurt her; it felt good, very good.
"Bernie?" Ronald said. "Bernie? A mechanic? You cheat on me with a blue-collar worker?"
"Jesus, Ronald, your obsession with collars and status. With numbers. With variables." She wasn"t looking at him now. "Bernie gave me attention. That"s the only way he"s different from you."
"I thought I understood you," he said, and now he saw her tears starting. He walked away, out of the bar.
He"d done everything he possibly could. Everything. What else could be done? Nothing. He drove, still blurry from the scotch, into the unlit parking lot of Luke"s service station. He put the car in park, took the keys out of the ignition, each action dragging like a tread through dead water. "I"ve done everything!" he shouted when he climbed from the car.
He tried the door first before he kicked it in. Inside was solid blackness, but the layout was simple geometric shapes in his memory. He had no idea where a hammer would be, but found an exhaust pipe in the m.u.f.fler inventory.
He felt his way along the wall to where the spark plugs were stored and began beating the exhaust pipe against the cases. "I"ve done everything!" he shouted as the pipe tore the boxes apart. "Everything!" Two of the cases ripped open. Spark plug ring holders scattered on the next hit, and he continued to beat them into the floor, sparks from metal striking metal shooting out with each swing.
Ten cases. Eleven. Twelve.
The garage filled with the swirling red and white of police rollers outside the front window, and the lights came on. "Put down the pipe!" a voice shouted, but Ronald kept swinging until two sets of arms grabbed him and pinned him to the floor. He kicked and tried to twist out of their hold; there was a third grip, and he felt the clamp of metal on his wrists.
"This guy"s out of his head!" one of the voices said. "Jesus, get him under control!"
A question burned away the haze of his hangover. Had he gotten all the plugs? It seemed he had been able to wreck most of them. Yes, all of them, in fact.
It took time for Ronald to manage the six feet from the cell bunk to the bars. "Hey," he called to the officer at the desk across from the lockup. "Hey!"
The officer put down the newspaper he was reading and rose from his desk. He walked slowly over to the bars, carrying a sandwich and coffee. "Yeah?" he asked, taking a bite from the sandwich. Ronald"s stomach was queasy.
"Do I get a phone call?"
The officer shrugged. "You should dry out first, buddy."
"Please," Ronald said. He pressed his face against the bars. "I"ve got to call home. What time is it?"
The officer unlatched the barred door. "It"s almost four in the morning," he said. "You better have a real understanding family. Don"t get your hopes up about being bailed. I"m supposed to keep you until the evaluation."
"Evaluation?"
"Yeah, you know." The officer traced circles around his temple with one finger and whistled coo-coo sounds. "The boys from the mind-farm gotta find out if you"re safe to let out on the streets." He led Ronald by the elbow over to a pay phone bolted to the gray concrete wall of the station office. He tossed Ronald a quarter.
Ronald dialed the house. On the seventh ring, he glanced behind him at the officer. "She"s asleep," Ronald said. "It will take her a while to get to the phone." The officer stared like stone over the top of his newspaper.
On the thirteenth ring, Ronald glanced back again and tried to laugh. "It"s sixty-two feet from the sofa to the upstairs phone. If she"s asleep on the sofa she"ll need to walk all the way up there."
Nineteen rings. "She isn"t there, fella."
"She has to be!" Ronald said. He took hold of the receiver with both hands and leaned the back of his head against the wall. "I got them all," he said, "I ruined every last case. Luke could never sell them now. They were the variable. Everything is under control." The officer rolled his eyes and repeated his coo-coo whistle.
Twenty rings. Twenty-seven. Thirty-three.
The officer came over and took the receiver from his hands. He let Ronald stay there, back to the wall, and returned to his newspaper.
Not a stable variable, Ronald thought. She should have been home. Not a constant, because he had destroyed the plugs. That meant the influence had changed, had somehow moved on. A random variable? One that could alter its cause but retain its effect? Even if that were true, he could find it, the way he had found the spark plugs. He would find it- The rustle of the newspaper caught Ronald"s attention. The police officer"s thumb gripped the page just below a 45-cent coupon for Maxwell House coffee.
For S. L. Spotts.
Division by Zero.
TED CHIANG.
1.
D.
ividing a number by zero doesn"t produce an infinitely large number as an answer. The reason is that division is defined as the inverse of multiplication; if you divide by zero, and then multiply by zero, you should regain the number you started with. However, multiplying infinity by zero produces only zero, not any other number. There is nothing which can be multiplied by zero to produce a nonzero result; therefore, the result of a division by zero is literally "undefined." 1a Renee was looking out the window when Mrs. Rivas approached.
"Leaving after only a week? Hardly a real stay at all. Lord knows I won"t be leaving for a long time." Renee forced a polite smile. "I"m sure it won"t be long for you." Mrs. Rivas was the manipulator in the ward; everyone knew that her attempts were merely gestures, but the aides wearily paid attention to her lest she succeed accidentally.
"Ha. They wish I"d leave. You know what kind of liability they face if you die while you"re on status?"
"Yes, I know."
"That"s all they"re worried about, you can tell. Always their liability--" Renee tuned out and returned her attention to the window, watching a contrail extrude itself across the sky.
"Mrs. Norwood?" a nurse called. "Your husband"s here." Renee gave Mrs. Rivas another polite smile and left.
1b Carl signed his name yet another time, and finally the nurses took away the forms for processing. He remembered when he had brought Renee in to be admitted, and thought of all the stock questions at the first interview. He had answered them all stoically.
"Yes, she"s a professor of mathematics. You can find her in Who"s Who."
"No, I"m in biology."
And: "I had left behind a box of slides that I needed."
"No, she couldn"t have known."
And, just as expected: "Yes, I have. It was about twenty years ago, when I was a grad student."
"No, I tried jumping."
"No, Renee and I didn"t know each other then."
And on and on.
Now they were convinced that he was competent and supportive, and were ready to release Renee into an outpatient treatment program.
Looking back, Carl was surprised in an abstracted way. Except for one moment, there hadn"t been any sense of deja vu at any time during the entire ordeal. All the time he was dealing with the hospital, the doctors, the nurses: the only accompanying sensation was one of numbness, of sheer tedious rote. 2 There is a well-known "proof" that demonstrates that one equals two. It begins with some definitions: "Let a = 1; let b = 1." It ends with the conclusion "a = 2a," that is, one equals two. Hidden inconspicuously in the middle is a division by zero, and at that point the proof has stepped off the brink, making all rules null and void. Permitting division by zero allows one to prove not only that one and two are equal, but that any two numbers at all --real or imaginary, rational or irrational --are equal. 2a As soon as she and Carl got home, Renee went to the desk in her study and began turning all the papers facedown, blindly sweeping them together into a pile; she winced whenever a corner of a page faced up during her shuffling. She considered burning the pages, but that would be merely symbolic now. She"d accomplish as much by simply never glancing at them.
The doctors would probably describe it as obsessive behavior. Renee frowned, reminded of the indignity of being a patient under such fools. She remembered being on suicide status, in the locked ward, under the supposedly round-the-clock observation of the aides. And the interviews with the doctors, who were so condescending, so obvious. She was no manipulator like Mrs. Rivas, but it really was easy. Simply say "I realize I"m not well yet, but I do feel better," and you"d be considered almost ready for release. 2b Carl watched Renee from the doorway for a moment, before he pa.s.sed down the hallway. He remembered the day, fully two decades past, when he himself had been released. His parents had picked him up, and on the trip back his mother had made some inane comment about how glad everyone would be to see him, and he was just barely able to restrain himself from shaking her arm off his shoulders. He had done for Renee what he would have appreciated during his period under observation. He had come to visit every day, even though she refused to see him at first, so that he wouldn"t be absent when she did want to see him. Sometimes they talked, and sometimes they simply walked around the grounds. He could find nothing wrong in what he did, and he knew that she appreciated it. Yet, despite all his efforts, he felt no more than a sense of duty towards her. 3 In the Principia Mathematica, Bertrand Russell and Alfred Whitehead attempted to give a rigorous foundation to mathematics using formal logic as their basis. They began with what they considered to be axioms, and used those to derive theorems of increasing complexity. By page 362, they had established enough to prove "1 + 1 = 2."
3a As a child of seven, while investigating the house of a relative, Renee had been spellbound at discovering the perfect squares in the smooth marble tiles of the floor. A single one, two rows of two, three rows of three, four rows of four: the tiles fit together in a square. Of course. No matter which side you looked at it from, it came out the same. And more than that, each square was bigger than the last by an odd number of tiles. It was an epiphany. The conclusion was necessary: it had a rightness to it, confirmed by the smooth, cool feel of the tiles. And the way the tiles were fitted together, with such incredibly fine lines where they met; she had shivered at the precision.
Later on there came other realizations, other achievements. The astonishing doctoral dissertation at twenty-three, the series of acclaimed papers; people compared her to Von Neumann, universities wooed her. She had never paid any of it much attention. What she did pay attention to was that same sense of rightness, possessed by every theorem she learned, as insistent as the tiles" physicality, and as exact as their fit.
3b Carl felt that the person he was today was born after his attempt, when he met Laura. After being released from the hospital, he was in no mood to see anyone, but a friend of his had managed to introduce him to Laura. He had pushed her away initially, but she had known better. She had loved him while he was hurting, and let him go once he was healed. Through knowing her Carl had learned about empathy, and he was remade.
Laura had moved on after getting her own master"s degree, while he stayed at the university for his doctorate in biology. He suffered various crises and heartbreaks later on in life, but never again despair. Carl marveled when he thought about what kind of person she was. He hadn"t spoken to her since grad school; what had her life been like over the years? He wondered whom else she had loved. Early on he had recognized what kind of love it was, and what kind it wasn"t, and he valued it immensely.
4.
In the early nineteenth century, mathematicians began exploring geometries that differed from Euclidean geometry; these alternate geometries produced results that seemed utterly absurd, but they didn"t produce logical contradictions. It was later shown that these non-Euclidean geometries were consistent relative to Euclidean geometry: they were logically consistent, as long as one a.s.sumed that Euclidean geometry was consistent.
The proof of Euclidean geometry"s consistency eluded mathematicians. By the end of the nineteenth century, the best that was achieved was a proof that Euclidean geometry was consistent as long as arithmetic was consistent.
4a At the time, when it all began, Renee had thought it little more than an annoyance. She had walked down the hall and knocked on the open door of Peter Fabrisi"s office. "Pete, got a minute?" Fabrisi pushed his chair back from his desk. "Sure, Renee, what"s up?" Renee came in, knowing what his reaction would be. She had never asked anyone in the department for advice on a problem before; it had always been the reverse. No matter. "I was wondering if you could do me a favor. You remember what I was telling you about a couple weeks back, about the formalism I was developing?"
He nodded. "The one you were rewriting axiom systems with."
"Right. Well, a few days ago I started coming up with really ridiculous conclusions, and now my formalism is contradicting itself. Could you take a look at it?" Fabrisi"s expression was as expected. "You want--sure, I"d be glad to."
"Great. The examples on the first few pages are where the problem is; the rest is just for your reference." She handed Fabrisi a thin sheaf of papers. "I thought if I talked you through it, you"d just see the same things I do."