Proof by Brute Force
BY KIRIN KHAN
Sara Rahbar, Nothing left to win, nothing left to lose, 2014, bronze, 27 x 20 x 24 inches. Courtesy of the artist.
Proof by Brute Force
Kirin Khan / OCT 2020 / Issue 2
It was during her Real Analysis class that Joonie reached the disturbing, if obvious, truth: that if there are indeed an infinite set of numbers between any two numbers, all the counting she’d ever done in her life was a lie. As Professor Lamb walked through the various constructions, pacing in front of the dry-erase board, her hands rolling one over the other as though unraveling the proofs like old sweaters, Joonie thought of her little child self, sitting on the floor and counting to one thousand, slow and steady, her hands playing with the carpet, the satisfaction and relief of reaching the end, of opening the closet door to creep out as silence and darkness set in. It was a way of waiting, of making progress in moments that felt like they would never end. Time was just counting, when you got down to it.
Except all this counting was a lie. Joonie felt ridiculous for feeling so upset, and yet her stupid tears blurred her vision and made it harder for her to take notes. She looked at the clock above the dry erase boards, watched its hands making their slow cycle towards lunch.
She kept her head down, close to her notebook as though she was just focusing hard and hoped today was more of a lecture and less of a “everyone participates” sort of class. It was too intangible, when the whole point of studying math in the first place was that it felt closest to the only sort of truth in the world, the only time her feet were on solid ground.
Professor Lamb was moving past the axioms (good, axioms were sort of bullshit anyway, things were never as self-evident as dead math professors seemed to think) and into the theorems, all the while pacing, gesturing, uncapped marker in hand.
Joonie drew a spiral in the corner of her notebook. So many men had proven that the reals are complete, ages ago, how stupid she must be to have not thought about it until now, not really understood that every moment, walking down the number line, was not a walk but a leapfrog —from one lily pad to the next, the breadth and depth of waters between the rational numbers filled with the irrational, the imaginary, and the complex. She shaded the spiral in heavy downward strokes.
Calm down. Breathe. 10, 9, 8, in, 7, 6, 5, 4, out…
She packed up her notebook, her planner, her overpriced, battered textbook. She’d go to office hours and listen to Professor Lamb walk other students through proofs, let the quiet pleasure of working through something hard and beautiful soothe her from the louder, sharper sounds of the world.
Except that when she got to Professor Lamb’s office, no one else was there. She couldn’t hide quietly in a corner of the office and slip out with the others. Professor Lamb was sitting at her desk, facing the door, so Joonie couldn’t run away, either. She sat down across from her and pulled out her homework, her textbook, and, to show she was confident, a pen.
“I’m having trouble with this one problem,” she started, but her throat closed up and her voice seemed to fade.
Professor Lamb waited, her bright eyes and gray springs of hair made her seem extra eager to pounce on whatever problem Joonie might surface. “Let me see.” She reached for Joonie’s notebook.
But the page was blank.
“I don’t,” she looked at her hands, they looked like a child’s hands, small, the carpet threads, “I’m not,” she searched for the word, “comfortable.” Joonie wished she could hide under a desk, or in a cupboard, somewhere very small where there wasn’t so much of her exposed. Where she could feel all of the walls against her skin and she could be alone, counting.
Professor Lamb seemed disappointed by this different sort of problem. “What can I do for you?”
Joonie tried to explain how, how sick it made her feel, that she would start to think about infinity and too many unknown numbers, but her breathing got funny and hands tingled and she had trouble speaking, which made it even harder to explain what was bothering her, exactly, about the stupid, infinite set R.
“Well yes, obviously, the integers and rationals are infinite too.” Professor Lamb seemed confused by Joonie’s feelings. Granted, office hours weren’t usually used for existential crises, and existential crises were not usually kicked off by the construction of the real numbers. But still, she couldn’t be the first student to show up sweaty and panicking at her door. This was, after all, the Math department.
Professor Lamb tapped her pen against the dark wood desk and frowned at Joonie, and added as an afterthought, “—though not complete.”
And there, really, was the problem. Completeness, the difference between leapfrogging from one pad to the next, or drowning. Joonie walked out of Dr. Lamb’s office and crossed the pavilion, the scent of roses that surrounded the Math and Computer Science building shifted in gradients to the salt and grease of the campus café. French fries. Lunch time.
But Joonie wasn’t hungry. Other girls spread across the green lawns and concourse, laid out in the sun, they laughed and talked to each other and seemed on another planet entirely from Joonie. Even if they were Math majors, which they most certainly were not, they were aliens— rich girls, mostly white girls, wearing hiking boots and cut off shorts and other outfits made to look cheap but branded just so, to make sure everyone knew they weren’t. Joonie’s mother would have laughed at them; she was so confident, almost arrogant, among other women. A different person than who she was around men.
Joonie typically started the day with 3, 1-2-3 (ah ah ah, she heard the Sesame Street Count in her head) natural number cups of coffee and her books, and a few more in late afternoon if she needed, to keep going, shimmering in caffeine and hunger until dinner, which she’d grab from the dining hall and sneak to her dorm to eat, alone on the floor, in the closet like a small animal, the closet which smelled like cigarettes the same way old hotels do, decades after smoking indoors was a thing.
She rushed to the safety of her dorm, watching her feet move in front of her, her steps.
1, 2, 3, no, stop counting, stop.
She shook her head hard to get the thoughts out of her mind and wondered if anyone would say she looked like a freak, counting to herself and shaking her head. It was so easy to forget that she was in public. The natural numbers, the integers, the rationals, all countable—which is to say, if you had all the time in the universe, if you lived forever, you could start counting and yes, you’d count forever, but you’d count, you’d make progress across time and space.
She learned to count young. She loved how the numbers just kept going. There was something comforting about that. But the nauseating completeness of the reals meant that you could never really start counting. You’d always be skipping a number. You could not begin to speak. Uncountable.
And counting was important. She didn’t remember the first time Mom told her to go to the closet, but she remembered the times after. “Count to one thousand, Joonam. Don’t come out no matter what, until you reach one thousand, no peeking.”
19, 20, 21…Little Joonie waited, she counted, she listened. Every minute in the closet was an hour, a night, a year. She sat on the floor, she pulled threads from the carpet, and she counted.
She had faith.
In her dorm room, Joonie put her backpack down by the door and walked to her sliding door closet, opened the door, sat down, and closed it behind her. She sipped her coffee and pressed her back against the wall. It felt firm behind her. She took another sip of her coffee.
52, sip. Breathe. 53, 54. Breathe. 55, sip. The integers were clean, evenly spaced, easily counted sips.
Focus, you’re doing it wrong. At least sip at intervals that make sense.
The shouting and smashing wouldn’t stop until she reached around 600, then heavy steps walking away. The front door would slam shut in the 800s, a good sign. Then just a little more to go, the sound of the car out front turning on and grinding out of the driveway.
She checked her phone and decided to call her mother. Voicemail. “Mom, I’m having this problem,” she started. Joonie never told her that she was calling from a closet every day, years after the need had passed, years after Dad said “I divorce you” three times and left them to put their lives together. “Actually, you know what, it’s okay, I’ll figure it out. I hope you’re okay.”
Her dorm room door slammed open.
“Joonie Moonie! Where are you!” Her roommate Nadja, back from dance, was full of sparkle and energy.
Joonie put her back against the closet door. She heard Nadja walk up to it and drop her duffle bag, heard the door respond to Nadja’s hands pressing on the other side, and almost felt her slide down to kneeling. She heard the soft tap of Nadja’s forehead against the door; it would be against the back of Joonie’s head, maybe her neck, if they could touch.
“What’s going on?” Nadja was always like this. It was like being randomly assigned as Joonie’s roommate in the Muslim dorm was an act of Allah, tying them together. She was immediately sisterly. Joonie didn’t have siblings, so she felt both grateful and alarmed by how gentle Nadja was towards her.
“I’m having trouble with this problem.” Joonie clutched the carpet in her fists and her body went rigid. “And I can’t calm down.”
“It’s okay. That’s okay. Can you count it out?” She’d learned fast, the ways Joonie talked herself down.
“No!” Joonie said, louder than she meant to.
And that was it, she was crying.
Nadja ran her hand up and down the door as though rubbing Joonie’s back. “That’s okay, that’s okay. Start at the beginning. Tell me about your day.”
Joonie told her about the counting, about class, about being swallowed up and unable to breathe and her funny hands. She did not tell her about the closet, about the other counting.
Nadja was a physics major, so while she didn’t take Real Analysis, she knew how hard it could be. “Man, if I had a dollar every time math made me cry,” she laughed. “You think that’s bad, try O Chem.”
Joonie didn’t laugh.
Nadja tapped her head against the door with a thud and tried again. “It could be beautiful, if you let it. Some people stare at the ocean waves and just think of shipwrecks and drowning. Don’t be one of those people. Let it make you feel small, sure, the way mountains make you feel small, the way stars make a person feel small, and you can let that fill you with awe, or terrify you.”
“I can’t, I can’t.” If she thought about it too much, if she tried to see the real number line in her head, she felt a whooshing sound in her brain, as her mind zoomed in and in and in and never stopped.
“But why, Moonie, why is it bothering you so much? Just don’t think about it.”
“Because then it never stops.”
“None of the numbers stop, Joonam, you’re all mixed up.”
“No, if I never reach one thousand,” she was crying too hard now, “he never stops.” The hyperventilating, gasping, panic crying made her impossible to understand.
“When you reach one thousand, it will all be over.”
That night, the fighting had started over dinner, before Mom even sat down. That terrible night, she saw what she’d previously only heard. Dad wanted to move back home, Joonam was becoming too American, Mom was working at the grocery and Dad didn’t like that she was talking to men, and was that makeup she was wearing? Joonie was surprised to see that her mother did not cower. She did not apologize. Instead, Mom grabbed her empty plate and hit him across the face with it. The plate did not break. Dad rose up like a mountain and grabbed her, shook her, screamed in her face.
Joonie ran to the closet, saying it over and over again, “Count to one thousand. Don’t come out.”
Every number one step closer to her mother, to Joonie walking out of the door and finding her mother sitting at the dining room table, alone, crying but breathing, her red face not yet purple, but beginning to swell.
When she heard mouse-like stirring from the floor, Joonie creaked the door open and walked so quietly to find Mom picking up broken pieces of Joonie’s favorite plates, the ones with rabbits on them. “You did it,” Mom said through a bleeding, swollen lip. “My good girl.”
Joonie felt a burning, nauseous anger inside her. She knew now that her mother did not try to please him, did not try to do everything to make him happy. Joonie hated her. And still, still, wanted to protect her. And hated her for that, too.
The reals weren’t a number line, not really. They were a black hole, a series of dilations within dilations, the distance between any two numbers getting wider and wider, crammed with all the dark matter of numbers she hadn’t yet thought of, until the angry chasm opened up and swallowed her.
One.
Two. Good. Breathe. Focus. In her mind, a little girl starts counting. The screams get louder.
She’ll reach one thousand, and then he stops.
One. One point one.
Between any two numbers, an infinite—
No. wait.
The dishes break and keep breaking.
She can’t get to the next one.
She sits behind the closet door and does nothing, nothing for her mother except count like she was taught, count like prayer, count like reciting tasbeeh.
One point zero one.
And again. And again, an echo, an infinite loop, the car, the noise, the dishes, the fighting, the slammed door, good girl, infinite, infinite.
One point zero zero one.
No. Wait.
One.
Kirin Khan is a Pukhtun writer from Albuquerque, NM who lives in Oakland, CA. Her work centers on trauma, the body, sports, violence, grief, immigration, and queerness. An alumna of VONA/Voices, Las Dos Brujas, Kearny Street Workshop, and the Tin House Writers Workshop, she was a PEN Emerging Voices Fellow, SF Writers Grotto Fellow, a Steinbeck Fellow, and a recipient of residencies from the Vermont Studio Center and Tin House. Her essay “Tight” was nominated by Nat. Brut for a Pushcart Prize.
Sara Rahbar is a contemporary artist born in Tehran, Iran. She left her birthplace during the period of immense upheaval that followed the revolution in Iran and the start of the Iran-Iraq war. While her works had initially explored deeper concepts of nationalism and belonging, her overall artistic practice stems from her personal experience and is largely autobiographical—driven by central ideas of pain, violence, and the complexity of the human condition. Sara has exhibited widely in art institutions including Queensland Museum, Sharjah Art foundation, Venice Biennial, The Centre Pompidou, and Mannheimer Kunstverein. She lives and works in New York.