All of the anger finally came to a head as Ronald watched the swizzle stick stirring even, gentle circles in her glass. He inhaled slowly. “You… goddammit, 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 muffler 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 inconspicuousl
y 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 passed 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 assumed 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.”
“You’re probably right.” Fabrisi looked at the first couple pages. “I don’t know how long this’ll take.”
“No hurry. When you get a chance, just see whether any of my assumptions seem a little dubious, anything like that. I’ll still be going at it, so I’ll tell you if I come up with anything. Okay?” Fabrisi smiled. “You’re just going to come in this afternoon and tell me you’ve found the problem.”
“I doubt it: this calls for a fresh eye.”
He spread his hands. “I’ll give it a shot.”
“Thanks.” It was unlikely that Fabrisi would fully grasp her formalism, but all she needed was someone who could check its more mechanical aspects.
* * * *
4b
Carl had met Renee at a party given by a colleague of his. He had been taken with her face. Hers was a remarkably plain face, and it appeared quite somber most of the time, but during the party he saw her smile twice and frown once; at those moments, her entire countenance assumed the expression as if it had never known another. Carl had been caught by surprise: he could recognize a face that smiled regularly, or a face that frowned regularly, even if it were unlined. He was curious as to how her face had developed such a close familiarity with so many expressions, and yet normally revealed nothing. It took a long time for him to understand Renee, to read her expressions. But it had definitely been worthwhile.
Now Carl sat in his easy chair in his study, a copy of the latest issue of Marine Biology in his lap, and listened to the sound of Renee crumpling paper in her study across the hall. She’d been working all evening, with audibly increasing frustration, though she’d been wearing her customary poker face when last he’d looked in.
He put the journal aside, got up from the chair, and walked over to the entrance of her study. She had a volume opened on her desk; the pages were filled with the usual hieroglyphic equations, interspersed with commentary in Russian.
She scanned some of the material, dismissed it with a barely perceptible frown, and slammed the volume closed. Carl he
ard her mutter the word “useless,” and she returned the tome to the bookcase.
“You’re gonna give yourself high blood pressure if you keep up like this,” Carl jested.
“Don’t patronize me.”
Carl was startled. “I wasn’t.”
Renee turned to look at him and glared. “I know when I’m capable of working productively and when I’m not.”
Chilled. “Then I won’t bother you.” He retreated.
“Thank you.” She returned her attention to the bookshelves. Carl left, trying to decipher that glare.
Full Spectrum 3 - [Anthology] Page 27
