"Seven." Opalyn glares.

"What's the first derivative of the sine function?"

It has been a minute! She almost blurts "cosine!" from sheer rote memory but takes a second to check. She mentally graphs the sine function and notices that it's steeply increasing at first and then flattens out and then steeply decreasing and then flat again. Sure seems like cosine.

"Cosine!"

"Is the rest of your file also completely wrong?"

"I don't know! I haven't seen my file! But I suspect it may have other errors, yes!"

"I should probably mention that I don't have any idea how to use math and magic together."

"Thaaaaaat doesn't make any sense so I'm just going to ignore it and explain everything from scratch but also use math words.  Falash means you arrange your magic so the convergence nodes are dense in four dimensions with a packing corresponding to a solid tiling of regular hexadecachorons and the oscillation of each node being a round number of sixteenth-circles out of phase with respect to its neighbors along each dimension!  It's one of the simplest kinds of dense magic that there is!  But if you don't know how to use math and magic together at all, you should probably just will your magic to look like my magic and not think about it too hard.  The whole definition of being a sorcerer is that you can use magic without having to know how it works, after all!"

Opalyn's initial reaction is something like PANIC because the faceless executioner man is saying math words she's never heard before. At first she thought he'd mispronounced "hexadecahedron" and then realized, no, he really meant "hexadecachoron" and WHAT IS A CHORON and WHAT DOES IT LOOK LIKE, maybe Opalyn is going to fail the math test.

But this is a familiar gut reaction. Opalyn's had it hundreds of times. When she was a wee Opalyn she took it seriously; she thought she was supposed to know everything already, and if anyone said anything to her that she didn't already know it was an error condition that needed to be corrected immediately through either anger at the other person or crushing shame directed at herself.

Now she knows that this feeling is just the thing that happens before she learns a new thing! So she quickly transmutes the feeling of inadequacy into the feeling of curiosity, buttressed by her solid conviction that she probably is going to succeed at learning the new thing, and that this uncomfortable period of confusion is probably temporary.

"I don't already know what a hexadecachoron is or how to densely pack them in four dimensions but I am excited to find out!"

"I'd ask how anybody learns about calculus without even doing any four-dimensional geometry first but it's not actually my job so I won't!  Also if what I said didn't already make complete sense, then just tell your magic to look like my magic and forget about all the math parts.  We don't have time to walk you through becoming a wizard from scratch."

Fascinating! They have an entirely different way to learn calculus! Opalyn is pretty interested to see how that works. She wonders if people here can actually perceive more dimensions somehow, so that these visualizations are easy for them, and if so, if everyone can do it or if you need innate magical ability.

"All right, I'll try winging it!"

"Maybe you didn't mean it that way, but 'winging it' would be very bad, actually, especially if your file is right about you being a Duchess!  You don't wing anything, actually!  You do exactly what I tell you to do, when I tell you to do it, and do nothing else whatsoever!  If you do anything else, I might turn your blocking collar right back on--or maybe, if your magic looks powerful and dangerous enough, vaporize your head!  When I tell you to look at my magic, and make that much magic which looks the same as my magic, do exactly that."

That's exactly what Opalyn meant by 'winging it.' Anytime she's just imitating what someone else is doing without really deeply understanding it, that's winging it, that's substituting in someone else's judgment for her own. Opalyn will grant that there are many circumstances in which it is advantageous to let someone else drive, but it's always going to feel risky.

Explaining this to Fdera doesn't feel important, so she doesn't.

"Understood. I will attempt to imitate you without variation!"

"Great!  I'm sorry if you weren't planning to do anything weird, and I made it sound like you might be.  Just remember, we get a lot of strange people here at the Farm and when I don't super double check everything, people die and then I get a frowny note on my record!  But not a big frowny note because they don't want to discourage my killing people too much."

"Next, I'm going to check that you can follow instructions and imitate other people.  Not with magic, just with your plain old material body.  That's not a punishment for anything you did, it's because sometimes we get people at the Farm who just can't follow instructions at all, even if they say that they can."

"Ready?"

Opalyn is encouraged by this very sensible precaution!

"Ready!"

"Put your hand on your head!"

This really is like preschool!

Opalyn puts her hand on her head.

"Put your left hand on your stomach and your right hand on your head!"

"Without taking your hand off your stomach, put your hand on my head!"

"Subtract three from seven and say 'fizzbuzz' that many times!"

Opalyn puts her left hand on her stomach and her right hand on her head.

Opalyn moves her right hand from her own head to Fdera's head.

Opalyn says "fizzbuzz, fizzbuzz, fizzbuzz, fizzbuzz."

Opalyn giggles.

He waits a few seconds to see if Opalyn gives in to the temptation to remove her hand from his head, despite having not been instructed to do that.

Nope! Opalyn holds this ridiculous pose. She's trying to peer into Fdera's hood to see what's in there. She had to get quite close to him to get her hand onto his head.

Beneath the hood is nothing but darkness, so far as Opalyn's eyes can see.  She can tell that there's some interesting, unfamiliar magic going on, not just underneath the hood, but throughout the whole armored suit and the body inside it.

"Take your hand off my head."

"Next, I'm going to give you a set of instructions, where you shouldn't do any of them, until I say 'go', and then you'll do them all simultaneously.  Once I've given you the instructions, say 'Ready' if you think you remember all of them and you're ready to do them, or 'Repeat' if you want me to say them again, or 'I'm not sure I can' if you think it's too many things to do simultaneously, or 'I didn't understand' if it was hard to understand."

"The instructions are:  Put your right hand on your stomach, make a fist with your left hand, and say 'moop'."

Opalyn takes her right hand off Fdera's head.

She takes a moment to visualize herself following the instructions, and then says "Ready."

"Go!"

Opalyn simultaneously moves her right hand to her stomach, balls up the left hand (which is still at her stomach), and says, "Moop!"

Next Fdera's going to ask what sound a sheep makes.

"Very good!  From now on, don't execute any instructions until I say 'go'--unless I begin by saying 'Immediately!' and then you should do what you hear me say as soon as you think you've understood it.  If I haven't said 'immediately', and I finish by saying 'end' and without saying 'go', that means you should reply 'ready' or else say 'I didn't understand' or 'I'm not sure I can' or things like that."

"Say fizzbuzz fifteen times end."

"I'm not sure I can! It's very hard to say that word several times in a row, and it's also hard to simultaneously count to fifteen, especially if I'm not supposed to use my fingers to count. I can attempt it anyway if failure is non-catastrophic but I estimate my chance of flawless success at around fifty percent."