That's convenient. Now another student – how about her? – should try singing something else. Don't tell him what it is. 

- she'll sing a song for swords to be swift and deadly in battle.

Huh. It looks kind of like Haste. 

"I'm guessing that makes attacks faster and more accurate. Something in that vein, anyway." 

- okay, they're very impressed at that.

(They should be, he's very good at this). 

When they've studied more magic, they'll also be able to look at the structure of a spell and determine what it does. He's still mostly guessing with their sort of magic, but in the system he knows these correspondences are well-understood. He can't cast two spells at the same time, but when all of them have learned Detect Magic he'll show them what that looks like. 

There is math that goes with this, and he'll get to that in a bit. For now, he wants them all to get used to working with magical structures. He's hoping the string models will help with that – it's dangerous to rely on them too heavily, but they can be useful for developing intuitions about how modifying spells effects their form. 

Someone should join the woman singing. Can anyone describe how the magic changes? 

With more singers, the magic works better; a wider spread, a stronger effect, more subtlety. This is a well known fact, though it's fascinating to actually see it.

Well, Élie's kind of flying blind here. Is it possible to achieve any one of those effects without the others? 

Not with this song? You could sing a different song?

Alright, let's try that. The idea here is to start noticing patterns in which structures correspond to which effects – he doesn't expect anyone to get very far with this today, but they should all start keeping notes. 

He can prompt them by describing the features he noticed that let him identify this song's function. It's hard to describe in words – shape is the metaphor most commonly used, but it isn't exact, and different people might perceive magical energies in slightly different ways (he once had a friend who swore he could taste it). 

They will cooperatively try lots of metaphors! Color and refractivity and smoothness and slipperiness and silkiness and translucency? (One gets the sense that a lot of Quendi education may focus on describing artwork.)

There is no right answer, they should try to identify a conceptual vocabulary that helps them manipulate these structures in their head. 

When everyone seems reasonably comfortable with this, Élie will project what Detect Magic looks like to him when someone else is casting it. 

It's beautiful!

It really is!!!

Now they're going to learn some introductory topology so they can formalize it. (They should stop him if they know this already – where he's from they teach this to ten-year-olds). 

They do not teach it to ten year olds here, and only the people with a particular interest in math are familiar with their world's version!

Okay, then he'll just do his best. They should stop him if he's going too quickly or too slowly. (He'd reassure them they won't be punished but he's not sure he actually has the authority). 

They don't actually seem nervous. They do seem - weirdly unhurried? Like 'going too slowly' isn't a complaint they'd have at any pace? They ask a lot of questions and don't seem to care that this slows him down notably.

They are pretty smart, so the end result is still a reasonable pace of instruction for an inexperienced math class.

Then eventually they will be done for the day. If any of them have comments on his teaching style and are worried about retaliation they can give anonymous notes to one of the servants or Félix (he can't really tell humanoids apart). 

...huh??

...Obviously he does not intend punish them but any teacher would say that on the first day of class, so he understands if they want additional reassurance! 

They'll ....let him know if they have any feedback.

That also works. 

He's brought a meal, and told the human commanders are there to meet him.

Élie doesn't really expect to get anything out of this while he's still dependent on an interpreter, but he can't exactly refuse. 

They are pleased and honored to meet him, this is the human commander of the people of Arror, a great early human hero who fell in battle with the Enemy. They are happy to answer any questions he has.

He's also pleased and honored to meet them. He'd very much like to know how the human villages are governed.