Sunday, October 11, 2009

Appropriate Applications of Basic Arithmetic

"Now, everyone in the Weir knows that mathematics is the most important skill you can learn," Mr. Willems said. "But can anyone tell me why?"

Several hands went up. "Me! Me!" Andrea demanded.

"All right, all right, settle down," Mr. Willems said, chuckling. "Andrea, why don't you explain?"

"It's 'cuz math makes bad things go away!" Andrea said triumphantly.

"That's right!" Mr. Willems congratulated. "A good enough mathematician can solve any problem, no matter how thorny. Why don't I give a demonstration?"

"Show us! Show us!" the class clamoured. "We want to see you do math!"

Mr. Willems laughed. "Watch closely, now," he said, and stepped to the back of the classroom. A box-shaped object, covered in black cloth, sat on a table; every child in the room had their eyes fixed on it as Mr. Willems reached down, got a solid grip, and yanked the cloth away. And what they saw beneath -

"Aaaaa!" Sallya screamed.

"It's a monster!" Jervin yelped, his voice filled with terror. "Kill it, kill it, make it go away!"

"Now, now, children, don't be afraid," Mr. Willems said soothingly. "The big bad monster is in a cage. It can't get out. See?" He poked a finger into the cage, to demonstrate. The monster snapped at it; Mr. Willems yanked back quickly. He turned, holding his index finger before the class. "See? Harmless!"

"Are you gonna beat it with maths?" Elpin asked.

"No," Mr. Willems said.

Faces fell all across the classroom. "Then what are you gonna do?" Jervin asked.

"I'm going to have one of you beat it for me!" Mr. Willems said.

"Whoa!" Benn exclaimed. "Awesome!"

"How are we supposed to do that?" Kelliagh asked.

"It's simple," Mr. Willems said. "See there, above its head?"

"Yeah!" Jervin shouted. "They're numbers! We learned 'em last year. There's a two and a six, and a pembleteen in between!"

"Don' be stupid," Sallya reprimanded him. "There's no such thing as a 'pembleteen'!"

"Be polite now, children," Mr. Willems said. "But Sallya's right - the symbol in between isn't a number at all. Can anyone tell me what it is?"

"I remember! I remember!" Andrea said, practically leaping from her chair. "It's a 'plus'! That's "two plus six!" It's a 'quation!"

"Oh, yeah!" Benn realized belatedly. "We learned those last year. I'd forgot!"

"Very good!" Mr. Willems said. "This one is the equation you need to solve to beat the monster. that's why it's hovering above its head! Can anyone tell me what the answer is?"

"Four?" Jervin suggested hastily.

"Not quite," Mr. Willems said. "Does anyone else want to try?"

Andrea sat with an expression of ferocious thought. "It's eight," she said. "Eight! Eight, stupid monster!"

The monster reeled. It fell backwards. Then it hit its head against the bars! Down went the monster!

"Exactly right!" Mr. Willems congratulated. "That's how you beat a monster. Basic arithmetic will only get you so far, though; this one will be back in a few hours, once it feels better. If we wanted to stop it for good, we'd have to try a little harder. Now, everyone saw the numbers right above its head; "2 + 6". If you look very hard, though, and maybe even squint, you should be able to see something else. Why not try now?"

The children squinted.

"There're... more numbers?" Sallya said hesitantly. "I think it's a two and a nine. No, a seven and a nine. But there's something in between... a 'x'?"

"Can everyone else see the equation?" Mr. Willems asked. "Don't worry if it was hard, or you couldn't make it out well; this is the sort of thing you have to practice for. That was the equation you would have to solve to kill the monster. "7 times 9"."

"What's times?" Ephriem asked.

"That's what we're going to be learning this year," Mr. Willems said. "And we'll start on it first thing tomorrow. But now - field trip!"

"Hooray!" the class shouted in unison. "Field trip!"

"We're going to the courthouse!" Mr. Willems told the class.

"...yaaay?" the class said. "...courthouse?"

"And we're going to see them do math!" Mr. Williams said.

"Yaaaaaaaay!" the class shouted.

Then they went to the courthouse.

"I call this proceeding to order," the Judge said sternly. "Jury, do you have a decision?"

"Yes, Your Honor," the jury foreman said. "We solved the equations together, and are now ready to pronounce this bandit - guilty of all charges."

"No!" the accused shouted. "No! It was only some bread! I needed to feed my children! I needed to feed my children!"

"Bailiffs, restrain him," the Judge said calmly. "I will now enact the sentence. For three counts of attempted murder, one count of trespassing, and one count of exacerbated banditry, I hereby sentence you to death. Sixteen by eighty-four. Thirteen-fourty-four."

"Noooo!" the bandit wailed. Then the impact of the maths struck him, and he faded into oblivion.

"That's the power of mathematics, children," Mr. Willems said. "It can be dangerous, so you must always remember to use it wisely."

"Wowww," Benn said.

"Now, I'll take you back to the classroom, and you can find your way home from there - " Mr. Willems began -

Before being rudely interrupted. A woman slammed the doors of the courtroom open, panting heavily. "Brigands!" she said. "An army, at the gate! All able-minded adults to the walls!"

"You'll have to take the children with you, teacher," the Judge said, stepping down. "The children won't be safe at home alone, and you heard the messenger - every able mind is needed."

Mr. Willems hesitated. "Very well," he said. "Come on, everyone, with me. You can play together near the wall, where we can keep an eye on you."

The class followed Mr. Willems, muttering. "Do you think it's bad?" Sallya asked. "I hope mummy and daddy are safe," Corrin mumbled.

As Mr. Willems left the courtroom, a black bird swooped overhead, something clutched in its claws. It landed on the lintel of the door, and took a long, slow, look around. Then it tore at the shape it carried, dropping something onto the ground, and rose again, flying quickly out of sight. Besides the door was the thing the bird had dropped - a rodent's head, trailing severed viscera behind it.

"Ewww!" the children cried en masse, leaning back. Almost immediately thereafter, some of the boys began eyeing the head with curiosity.

"A bad omen," the Judge said, pushing through the children.

"It's nothing," Mr. Willems said. He squinted. "d/dx (6x + 5)... 6." The aspect of the head which foretold an ill future vanished.

"Wow!" Jervin said. "Was that multiplication?"

"No, no," Mr. Willems said, seeming distracted. "Come along, now. We need to hurry."

The scene at the wall was pure chaos. Arrows arced through the air, deflected from harm by swift-adding auxiliaries: "One! Ten! Three! Seven!" one chanted, sending arrows careening away from the defenders. Others struck at the bandits more directly, peering down with spyglasses to see the equations. "Seven plus five-fifteen is five-twenty-two," one announced. "Ninety-six plus thirty-four is - ah - 140. No. No. 130! Yes." A few had set themselves to the task of dismantling the siege engines and ladders the bandits brought against the walls.

But among the arrows were those not deflected, but instead finding their marks; among the bandits were those that avoided the arithmetic of the defenders and made their way to the ladders. And with each passing moment there were more of the latter; and men and women went tumbling from the wall, blood stains spreading from their wounds.

"There are more every year," the Judge said, walking towards the wall.

"Every year," Mr. Willems agreed, seeming sunken within depression. "Impossible to stop them for more than a few months, a year."

"Why not just use math?" Andrea asked.

Mr. Willems started, remembering the presence of the children with him. "We are," Mr. Willems explained to Andrea, gesturing to the efforts on the wall before them. "But there's a lot of math to do, and sometimes we can't solve all the equations fast enough."

"No, no," Andrea said, exasperated at the stupidity of adults. "Don't fight them. Solve them. Beat the thing that makes bandits."

"But - it's not that simple," Mr. Willems said. "There's a complex system of socioeconomic causes creating the bandits - it's a practically insoluble problem!"

"You said that a good enough mathematician 'can solve any problem, no matter how thorny'," Benn quoted. Belief shone in his eyes.

"Well - all right. I'll look," Mr. Willems said, peering into the air over the battle. He had little hope of success - but, to his own surprise, he saw - something. Barely visible, a glimmer in the air - a one-point font in blue-on-slightly-darker-blue...

"lim (x -> 0) 6x / -sin (x) ?" Mr. Willems read slowly, somewhat unbelieving.

"Yeah!" the children cheered. "Solve it, Mr. Willems, solve it!"

"But - I can't!" Mr. Willems protested. "It's an indeterminate form! Insoluble!"

"We know you can do it, Mr. Willems!" Andrea told him, her voice filled with unshakable faith.

Mr. Willems paused. "Wait - I think I remember something..."

He did the math.

He double-checked.

"...negative six?" he suggested.

There was a pause.

The world changed.


EDIT: Fixed final equation.

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