Proof and Consequence

Posted on January 7, 2005 by Jenna

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I.

Little Susie proves that 0=1.

“Nonsense,” says Mr. Gibbles, her elementary school mathematics teacher. “If that were true, then there would be no truth.”

Susie gestures impassively at her composition book and the equations written within.

“The truth demonstrates itself,” she says.

“I’ll send this to the institute for higher mathematics,” her teacher says. “They’ll tell you where you’re wrong.”

Little Susie’s face is a study in dispassion. And freckles. It is a study in freckles and dispassion.

II.

Little Susie is wakened by a rapping, rapping, rapping on her window from outside. She walks over to her window. She looks out the window at the face of Professor Harold Moyes.

“Yes?” she asks.

“Could you please open the window, little girl?” he asks. He is dangling precariously from the roof on a rope.

“I am curious if you will fall,” she says.

“I see.” Professor Moyes clears his throat. “Er. In any case.”

“Also, it is cold out.”

“Understood. I will make this brief,” he says, cold white knuckles clinging tightly to the rope. “I wish to know if you are in fact the girl responsible for the extraordinary proof submitted by Mr. Gibbles; and, should this be so, how you came by it.”

“I dreamt it,” she says. “Bit by bit from the well of dream.”

“That’s very good, Susie,” he says. The wind blows. The rope shakes. Professor Moyes suppresses a yelp. “But surely you realize that if 0=1, then all numbers are the same, and all Gödel numbers are the same, and all things are the same, and all equally nonexistent?”

“I recognize that,” Susie says in a nihilistic tone.

“Yet I am here, and you are there. Inside. Where it is warm.” Professor Moyes’ voice is longing. “That is also truth.”

“It is.”

“How does your dream account for that?” he asks.

Little Susie yawns sleepily. Then she blinks. But her tone is clear. “I argue that the act of analysis changes the world,” she says. “Computation on data changes the underlying substance. The 0 is the 0 predating my computation; the 1 is what it has become afterwards. A single contradiction does not unravel the world; rather it proceeds through examined truths and evaluated truths like a tsunami, altering everything that it passes.”

“I see,” says Professor Moyes.

“Does this surprise you?” asks Susie.

“No,” he says. “It is the nature of woglies; it is the cycle of the world.”

III.

Susie does not grow old. She is like an insect preserved in amber. In five years’ time, she is still little Susie, clutching her teddy bear.

“It worries me,” says little Susie’s mommy. “You’re still so young.”

“I would not worry about it, mommy,” Susie says.

“And you never play in the sun.”

Susie looks up at Mommy. There is a mix of disdain and fondness on her cute little face.

“I am an ageless child of the night,” she says.

“Yes, well,” says her mommy. “Well.”

Susie goes up to her room. She looks in the mirror. Then she sighs. There is a terrible rending of the world, and she becomes a swirling indefinable shape. She eddies through the window glass and is gone.

IV.

Professor Moyes stands on a balcony overlooking the main floor of the institute of higher mathematics. His hands grasp its rail.

“Mathematicians may never enter a place without invitation,” he says.

Little Susie eddies and swirls in the air behind the balcony. Her pigtails perform slow orbits. She looks frustrated.

“But please,” says Professor Moyes, “come in.”

Susie flows forward and coalesces into a girl.

“Why should mathematicians be limited in such a fashion?” she says.

“To be human is to be a zero-size point, scattered infinitely far from all others in a measureless space,” says Professor Moyes.

“… Oh.”

“This is also why running water is such a trouble.”

“Mommy says I can take baths if I wait until the water is still,” says little Susie.

“I just use deodorant,” says Professor Moyes.

They watch the work of the institute below.

V.

“I don’t think she’s normal,” says Mr. Gibbles. He’s still an elementary school mathematics teacher.

“Oh?” asks the principal expansively.

The principal is a giant of a man. He wears a white suit. When he laughs, he puts his hands to his stomach and rolls out with, “Ho ho ho!”

“She proved that 0=1,” says Mr. Gibbles, “and then didn’t get any older. I would almost think that she was exploiting a contradiction to prolong her childhood, except that the institute for higher mathematics said that her argument did not withstand a double-blind trial.”

“Ho ho ho!” laughs the principal. “Little girls are so earnest when they do math!”

“It’s not natural,” insists Mr. Gibbles.

“I don’t know what you want from me,” says the principal. “I can’t kick her out of your class until she grows older. It’s a strict school rule.”

Mr. Gibbles looks frustrated. “Then I’ll have to deal with her myself.”

VI.

Mr. Gibbles and little Susie sit together on the lunchground.

“I’ve invited you to have lunch with me this recess,” says Mr. Gibbles, “because I believe that you’re a blasphemous abomination.”

“Girls can be mathematicians like anyone else,” says little Susie.

“Well, yes,” says Mr. Gibbles. “But not blasphemous abominatory ones.”

Little Susie sighs. She looks longingly at the people playing hopscotch. Her thoughts are written on her face. How come they don’t have to have lunch with the math teacher?

“The other teachers are afraid of you,” says Mr. Gibbles. “Even the principal! Someone has to take a stand.”

Mr. Gibbles sets out beside him a wooden stake.

“So you will … stake me through the heart?” little Susie asks.

“No,” says Mr. Gibbles. “I am not just an elementary school teacher. I am also a vampire. If all is lost, this is for me.”

“Vampires and mathematicians are not so very different,” says little Susie sadly.

It does not change Mr. Gibbles’ resolve.

“We will have a math-off,” says Mr. Gibbles. “To the death.”

Little Susie is silent.

“There is no other way,” Mr. Gibbles says, and his fangs are very white.

VII.

Little Susie’s mommy washes the dishes. She looks outside. Little Susie is trudging home. A small cloud hovering directly over her head shelters her from the sun.

Little Susie enters the house.

“Hi, honey,” Mommy says.

“I do not understand what death is,” says little Susie.

Mommy thinks about this for a bit. “It’s like 0,” she says.

“Oh.”

Little Susie twists one foot around on its ankle. She wants to ask something else.

“What is it, honey?”

“Which kind of 0?” Susie asks.

THE END

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