"Yeah, I think you want to go through the fifth-year standard book of spells or something and catalogue all the things you need to communicate, this gets, like, three axes out of six efficiently and the other ones with layered notation which is kludgy if you need it all at once and that's why you're eventually getting into trouble -"

"Yeah, do you think you could show me some of the motions in the advanced curriculum -"

He can! 

She takes notes and then runs through her tentative list of ways to add degrees of freedom to the system.

" - maybe sketch them out? It'd be useful if with practice you could sight-read 'em and some designs are much easier than others for that -"

She draws examples. "This one takes up more space but then I don't have to add as many clarifying bits..."

"Might be worth it. - oh, I can think of a spell that design won't handle very well -" he demonstrates it -

"...yeah that doesn't work at all I don't know what to do with that one - show me again -"

"Prelexate." Swoop-shiver-pull-back. "It's not very common, there aren't really many problems best solved by shrinking all metal objects in an area for half a second - you can seriously injure anyone wearing rings and possibly kill people with the wrong kind of necklace but, like, in circumstances under which that'd be justified there are things that are more reliable and better targeted -"

"It still means that's a thing the system might have to account for, might appear in other spells."

"Yeah exactly. Can't think of any off the top of my head but I bet there are some."

"I'll think about it. Anything else like that?"

"None come to mind but if I think of some I'll come find you."

"Who else should I ask - I want it more polished before I go to a professor -"

"If you have everything in the standard book of spells grade five mapped that seems like it'd be enough to go to a professor with, and I bet you'll discover some more unusual ones along the way -"

"Okay. Minor bought all the textbooks first year and I bet he still has them all around."

"I bet he does. He gets three times as much pocket money as I do so if anything he probably has even more of them now."

"...why does he get so much more pocket money?"

"In descending order of reasonableness of reasons, because I do things like 'spend all my money on presents for a girl' which are independent of how much money I have, and not substantially improved if I have more of it, and he spends his on copper and zinc and books and electric eels, and he gets better marks, and he's our father's favorite."

"...okay."

"Good luck."

"Thanks!" She goes and looks for Minor.

He's watching a broomstick duel between Theodore and one of his Quidditch teammates. "Swan!"

"Hi! I need to borrow all the years of textbooks with wandwork in them I'm inventing notation for it."

"Ooooh, how's that work?"