And a good thing, because otherwise she might have felt awkward. Since he keeps on doing it.

She has paper on her, she can work on a tricky problem that had been troubling her while she waits.

When he finishes what he's doing he turns around and says 'what are you working on?'

"Oh, it's--" and then she describes the problem. It is legitimately tricky and interesting.

"Okay. There's a book on that -" he names it - "might help." 

And goes back to his work.

"Thanks."

...Okay then. She will just. Continue to work on the thing, then.

Eventually some people bring food.

That is convenient and she will eat.

About an hour after that he looks at her and says "Oh, I've got it" and describes the answer to the problem.

This is fascinating and has several implications worth pursuing further!

Well, she can't tell him about them, he's back at work.

...She's going to see if she can find anyone to talk to to confirm that this is normal and ask what being apprenticed to him means in practical terms.

There are people around.

"Hi."

"Marillë, right? What are you working on?"

She describes it.

"Huh, interesting -" he has suggestions on something to read, something to test, something to ask his father -

She writes down reminders to herself as applicable. "Thank you. Is it--usually like this?"

"People work on their own stuff and occasionally look over your shoulder and have ideas? Yeah. If you need something explained to you you can just ask, but if what you're already working on is valuable no one's going to expect you to put it on pause to have a structured education. If he thinks you're wasting your time he'll point you at a better use of it, but if you're already doing something interesting then there's not much to teach."

"Oh. Okay. I wasn't particularly expecting conventional but given that he showed up at my door, said he liked my paper and asked me if I wanted to actually learn something I wasn't really expecting this kind of unconventional. Thank you for clarifying."

"You'll learn lots of things, don't worry."

"I was less worried than confused but thank you for the reassurance."

Nod. He turns back to his work.

Yeah, that's apparently how things work here. It's not exactly optimized for her learning style but real life is rarely optimized for any one person and it's better than what she was doing before the crown prince showed up at her door. She follows suit.

There are, occasionally, twelve-hour long debates on various topics people are working on; they're just not very scheduled.