Running the Numbers

It was a quiet end-of-term night in the Dungeon as the students frantically worked to finish the last of their homework so they could advance with the rest of their class. Heads down, they worked into the night, interrupted only occasionally by muffled pops and bangs from the Potions lab downstairs.

“Bubotuber balls! Wingarduim leviosa! Confuego!!” From the first-years’ table, papers rose in a tornado of flame as Charity Gormling burst into tears.

“You’re the designated firstie wrangler,” murmured Narcissa from her chair near the fire. Spike looked up from her Ancient Runes text, and sighed, getting up.

”Augamente,” she said, and the flames were extinguished. “What’s up, Gormling?”

“I hate Arithmancy!!! Hate it, hate it, hate it!”

“Hate it--or it doesn’t come easy?” Spike handed Gormling a handkerchief with a black lace edging.

Gormling dried her eyes.

“Both,” she admitted sourly. Slytherin to the core, Gormling refused to admit defeat, or concede she might need help.

“Let’s see what I can do--Arithmancy was one of my best subjects.” Narcissa overheard, and looked up with a raised eyebrow.

“Also the reason Spike was kicked out of Durmstrang,” she whispered, sotto voce, to the upperclassnakes nearby. “The dark geometries teacher caught her passing notes--”

“Not exactly.” Spike smiled at Hecuba and Drusilla. “But that’s a story for later.” Turning back to Gormling, she said, “So. The practical assignment is to create a pair that are the same size, but not the same gauge, right? And no cheating with engorgio/reducio, you’re supposed to change space itself with numbers.”

“Uh-huh.”

“So okay. You know your usual sock is 60 stitches on a size 1 needle, and you get 7.5 stitches per inch, yeah?”

“Yeah.”

“So make me one now.” Gormling flicked her wand, and an orange and white striped sock appeared.

“Great! Now, what other yarn do you craft in?”

“Worsted. And I have some plain orange.”

“Ok. And what’s your usual gauge in worsted?”

“4.4 stitches per inch.”

“So--you know that a sock that fits at 7.5 stitches per inch takes 60 stitches, and you want to know how many stitches a sock at 4.4 stitches will take. We do a little algebra--”

“Algae-what?”

“Mermish math. Has to do with unknowns. And--” Spike scribbled on a spare bit of parchment. “--We get 40 stitches for the plain orange sock. That should give you two socks that both fit your feet.”

Gormling tried them on, “Thank you! I could do the same thing to change a sweater, couldn’t I?”

Spike nodded. “You could, but swatch first. A larger gauge is likely to be stiffer and won’t drape as nicely or be as fluid.” She shrugged, getting up. “It has fewer stitches to bend and flex, after all.”

“So what exactly happened at Durmstrang?” asked Drusilla.

Spike had told the tale over and over in her interviews at Hogwarts; the story flowed smoothly now. “The professor there thought I was passing notes, so he snatched one up to read to the class. Have you ever had an idea that set you on fire? Where you had to stop right now and get it all down?” The other Slytherins nodded, they knew that feeling. “So that’s what I was up to; I was drawing up an equation relating time and space. If I was right, you’d have something between Legilimency and the Floo Network; you could communicate mind-to-mind over great distances using the aether.”

“But what about--well, I’ve heard that there are things in the aether. Just hints and murmurings and stuff. Practically Quibbler things, but once in a while they get it right.”

Spike sighed. “That would explain what happened to the professor then. He …” She closed her eyes for a second, thinking about that day in the classroom. *The blood on the walls.* “I hear he’s doing much better,” she concluded. “I understand the Healers have been able to *scrougify* the feeding instructions they posted to save paperwork.”