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"I can't believe you actually signed her yearbook with that," Uheri said, half in exasperation and half in amusement as she caught up to her frenemy.

Dillan shrugged a little. "It's not my fault if Terrible Teresa takes it the wrong way. Her attempts to save my soul are starting to annoy me."

"Oh, she'll take it the wrong way, all right," Uheri predicted. "'There is no hate stronger than Christian love?'"

"Yes, I mean, when she thinks about it, and realizes the insult, the slow smoldering burn will set in," Dillan answered, pulling out the key to their shared secret lab. "I only wish I could see it."

"Well, look here, dumb dumb," Uheri answered, pulling out her phone. "She posted that she has hope that even the most barbaric heathen as you will realize how powerful Christian love is." She slugged the boy in the arm for good measure. "She's literally too stupid to insult."

"Ow," Dillan complained. "I swear you hit harder than your brother."

"Of course I do. Unlike him, I'm not dating you," she sang as she descended the stairs.

\--

Down in the lab, sat The Beast. As far as either of the young teens could tell, it was part of a crashed spaceship, and specifically the part that allowed faster than light travel. Understanding how it worked, however, was a challenge the two solved in very different ways.

Uheri was a natural born tinkerer, and had cracked several puzzles by her intuitive sense of all things mechanical. Dillan was far more theoretical, and had dived into the computer to make sense of what the software suggested. Together, they had come up with a solid theory, although they hadn't figured out how to test it quite yet.

"Ok, so you had figured out the ignition sequence criteria yesterday, you said?" Dillan asked, drawing some figures on the whiteboard in the lab.

"Yes. This part here seems to involve a heavy gravitational field, while this part deals with a heavy magnetic field. We already knew that the FTL transition would have to occur near a strong gravity well. Like the sun."

"And you think the magnetic field has to do with it?"

"Look at how they interact. At a right angle. And you said they were both at a right angle to the direction the ship itself would be moving. Three right angles. Now, you're the math wizard, not me, but isn't spacetime supposed to be at a fourth right angle in the fourth dimension?"

Dillan tapped his chin with the dry erase marker for a moment, then drew out part of a cube shape on the board. "Momentum in the x axis, graviational field on the y axis, and magnetic field on the z axis. And momentum should be very high, if you're coming in to a tight solar parabolic orbit. You said magnetic... what if the magnetic pole is the spot we're looking for?"

"Well that's not good. The magnetic pole is a pretty small spot. How do you control for that? How do you aim for anywhere you want to go?"

Rather than answer, Dillan began furiously scribbling on the board. For a solid few minutes, Uheri watched, as the symbols became more and more esoteric to her eyes. Finally she spoke up. "What exactly are you doing?"

"Determining whether the number of activation points are one, or infinite."

"Two. There's a north and south pole, right?"

"Oh. Right." He added a 2 in front of one of his variables, and continued on with his equations from there.

"How can they be infinite if there are only two poles?"

Dillan stopped, mid-equation, glared at Uheri briefly, then finished his line. "If there is a region of non-zero size, then it is infinitely many possible positions. If it is a single mathematical point, then it isn't."

"Are you high? The poles can't be infinite, they're like a nothing of a percent of the total."

"Almost nothing times infinity is still infinity," Dillan answered. Then he paused. "Except when it isn't. Is it?" He shrugged. "There are infinitely many numbers, right?"

"Ok, sure. So what?"

"And there are infinitely many odd numbers."

"Ok, I guess so."

"And there are infinitely many numbers between zero and one."

"No. Nope. Not playing. You're going to ask me if there are more odd numbers than there are numbers between zero and one. But it's a fools errand, infinities are infinite!"

"The numbers between zero and one are bigger. I can always find a number between any two given numbers, but you cannot always find an odd number between two arbitrary odd numbers, eventually you run out. The size of the pole is the same, there are an infinitely large number of spots surrounding the pole. The question is if they count AS the pole. And we haven't even considered altitude above the pole. Is the region a sphere or a cone?"

"Well if it's a small enough region, it's effectively a point, right?"

Dillan shook his head again. "No, a point is a point, that's different. Like... consider a dart board."

"Ok, where are you going with this?"

"The odds of hitting any specific point on the dart board are tiny. In fact, I can prove with math that they are zero."

"If you are throwing the dart, yes they are zero," Uheri said, smirking.

"Har har. There are in fact infinite spots on the dartboard you could hit. The chance to hit any is one over infinity, which is zero. And yet, somewhere a dart must hit. So the sum of all those zeros, added together, is in fact, one."

"I think I see," Uheri answered.

"Good. Then let me work on this."

Uheri frowned, as Dillan continued to do his math. "You are assuming the sun is a perfect sphere?"

"It should be good enough for a first order approximation."

"And that the sun's mass is constant?"

"Sure. Yes, I know it's changing as it burns, but not by much."

"And that the magnetic field doesn't fluctuate. Doesn't move around? That the billions upon billions of atoms aren't constantly moving around?"

"Yes, I am making some simplifying assumptions to make the math work, what's your point Uheri?"

"You're using an idealized model of your system to estimate real world tolerances. But an idealized model doesn't need to have real world tolerances. So you will find the answer must be a single point, which is impossible to hit. Just like your dartboard. But this machine, for it to even be here in this lab, must have actually flown at least once. And there is no way it hit an exact mathematical point to do so - that computer it came with might be more powerful than any on Earth, but it is not.. ahem, infinitely so. What you need to ask is not if you can hit the dead center of the bullseye, but how big is the bullseye." Uheri smirked, and tossed the dry erase marker to Dillan, who caught it dumbstruck.

"Next time you try and lecture me on infinity, remember that just because you..."

"A bullseye, of course!" Dillan exclaimed, starting to scribble more on the board.

"... you aren't even listening now, are you?" Uheri sighed a little.

---

Submitted by FarmD33 on Fri, Nov 04, 2022 to /r/WritingPrompts/

The prompt

"So the infinity between 0 and 1 is smaller than the infinity between 0 and 2 but if you take all the points from the first infinity you can match them up evenly to all the points of the second infinity because it's infinite. That don't make no goddamn sense" "Yeah. <chuckles> Isn't math fun?"