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“This is the main sitting room…the dining room is through there…this is the library, and my father’s study is off through that door.” Justin Finch-Fletchley’s house was large enough that it took quite some time to show guests around. Of course it didn’t help that he’d never done it before; but now that he was a teenager, Mother had decided he was mature enough to be allowed to have a guest. “My room is down this hallway, come on. This is my brother’s room—ooh, he’s left it open! Want to take a look?” Without waiting for a reply, Justin pushed the door open and walked in. Ernie followed him, still carrying his luggage. “Rupert’s reading maths at Oxford,” Justin said. “He’s seven years older than I.”

“Maths, that’s like Arithmancy, right?”

“Mostly. They both involve manipulating numbers, and letters standing in for numbers, but there must be some differences since Muggle maths doesn’t involve magic or any of numbers’ magical characteristics.”

Ernie’s eyes widened. “But how can Muggles manipulate numbers without knowing if they’re even or odd, or prime, or conjunct, or…or…”

“Muggles still have even and odd. And prime. I don’t know if they have conjunct, though. We didn’t learn about it in primary school.”

“But evenness and oddness are innately magical properties! I thought Muggles didn’t learn about any sort of magic.”

“Yes, but you know how even numbers can also be divided by two with nothing left over, and odd numbers can’t? When Muggles talk about evenness and oddness, that’s all they mean. They’re still referring to the same sets of numbers, but they don’t know there’s anything else special about them.”

“Weird. They’re missing out.”

“I know. But Muggles can accomplish a lot more than you realize. Here, look.” Justin grabbed a smooth-sided object, shaped like a book but smaller, off the desk and slid the cover back. “This is a calculator,” he said. “It can do everything we learned about in Arithmancy and a lot more. Look, it does sines and cosines. Remember how we read about them when we borrowed the sixth year Arithmancy textbook for our research project? Any Muggle child can do sines and cosines simply by typing the numbers in.”

“Let me see!” Ernie said. He grabbed the calculator and sat down on top of his trunk to poke some numbers in. “I don’t think it’s working,” he said. “I tried the cosine of one, ‘cause that’s the only one I remember, and the answer’s supposed to be one, but this says it’s point five-four-something…a really long number.”

“Muggles don’t use orbis to measure circles,” Justin said. “They use degrees, and rad-something, and maybe others, I don’t know. We learned about degrees when I was in primary school. 1 orbis in degrees would be 360, I think. Because 1/4 orbis is 90 degrees, I remember that.”

“I’ll try 360,” Ernie said. “Hey, it’s all gone blank. Is it supposed to do that?”

“I don't think so. Electrical devices don’t do well with magic…perhaps it got overloaded.”

“I do have a lot of magical stuff in my trunk. Maybe it was too much for it.”

“Better get it out of here and put everything magical in my room. I don’t own much of anything electrical, anyway.”

“What about when your brother tries to use the calculator?”

“Oh dear, I didn’t think of that. Here, I’ll hide it. Hopefully by the time he finds it whatever we did to it will have worn off, and he’ll just think he misplaced it.” He slipped the calculator behind the dustiest books he could find on the bookcase. “Now, come on! We have a whole week of fun ahead of us, and I don’t want to waste any more of it talking about school!”