"You know, I am confused about why anyone would spoil the puzzle for you by telling you that it had something to do with gravity, and then not teach you any of the math you would need to do anything with that knowledge, or really actually know it at all."  Namely calculus.  "I'll have to think if there's anything I want to do with that.  Possibly you weren't spoiled on at least some parts of that puzzle."

"We've now seen what's implicitly the hardest part of the problem that's most difficult to train: picking the right language to think in.  Dath ilani kids get exposed to lots of problems that require 'jumping-out-of-the-system', finding a solution that violates what you thought were the rules, problems that are unsolvable until you look at them from the right angle of sideways, etcetera etcetera.  I'll see what I can do about recollecting some of those and throwing them at you."

"The warning sign that you need to 'jump-out-of-the-system' is the feeling that you've just had.  Well, that everyone except Carissa had.  Frustration, flailing around in the dark, trying desperate wild ideas and getting unhelpful results one after another.  When you feel like that, you're probably thinking in the wrong language, or missing something fundamental, or trying to do something that is in fact impossible.  Or impossible using the tools you have."

"In the absence of that warning sign, if it's plausible you're thinking in the right language at all, the next step is trying ideas from that language, looking for experiments that give interesting results, not just experiments that prove a particular theory, and then interpreting what you see..."

"But first, I conjecture that - although you all continue to look very interested and cheerful, even having finished the task requiring you to control your expressions - you are in fact stressed out by how I was asking you to do something you were never taught how to do."

"All 'pre-paradigmatic' Science is like that, let's be clear.  'Pre-paradigmatic' Science is what you do when you don't know what to do next.  Like the distinction between 'calculation', when you know the next steps, and 'mathematical-thinking', when you need to figure out the next steps.  You are here to invent the straightforward solutions that other people will someday learn, and that is not, itself, a straightforward task."

"But while you are learning to do that, if you ever want, for example, any recovery breaks after I've asked you to do something that was in fact very stressful, you need to actually show any emotion.  Or, failing that, say something out loud about it."

"When I first met the current researchers, I was trying out dath ilani teaching methods that aim to produce confusion, so that people can learn what to do when they are confused.  Instead of looking confused, my students continued to look fixedly cheerful and enthusiastic, as is a Chelish person's 'dignity'."

"So I tried harder to confuse them."

"Bit of a 'communication-with-aliens' problem, there."

"Ione, am I wrong about this?  I was expecting you tell me they were feeling stressed about -"

"They're a bit stressed, but they also think of themselves as tough Asmodeans who wouldn't be happy about my speaking up about it.  And they are in fact tough Asmodeans who'll end up fine even if you stress them out for a few hours more.  We were scheduled to go to the Worldwound, some of the people here are back from it."

"Cool.  I can respect that."

"Regardless of how tough you are or how much I respect that, take a five-minute break anyways, to recover from that and talk among yourselves.  The tier-1 researchers will clear out in the meanwhile, so you're not around anybody too high above you in the org chart.  Ione, Carissa, Meritxell, Asmodia, with me."

Alexandre has been carefully modulating his emotional reactions and letting five to ten percent of them through! He's kind of surprised that Keltham hasn't noticed how obviously he's giving off signs! He stops once Keltham leaves, of course; it's easier for him to think, if he doesn't need to bother controlling his emotions and can just conceal them and focus on what matters.

How could he have solved the puzzle better? How could he have not come in last? (other than sabotaging the other researchers which would get him punished and alterAlexandre would never do and so he is at no point seriously considering.) He can name the unspoken assumption he made now, that math never reacted to you, but the math was supposed to be a simulation of nature, which can react to you. (As in Keltham experimenting with acid and needing protection spells.) If he had paid more attention to the instructions, he might have noticed the confusion. That he didn't was an error characteristic of underestimating Keltham. An error he had been warned against and made anyway.

(He is still kind of expecting to be whipped for that; he can understand smart mistakes not getting you whipped, but stupid ones?)

Either way... so the warning sign is that he can't think of anything to try. In practice he could think of things to try, prime numbers, size caps, base-12, individual orders of magnitude, but all of them were unlikely. They were inelegant. They depended on Keltham having arbitrarily designated some range of numbers as 'acceptable', instead of having a very simple rule that was just outside what he could imagine.

The key thing to search for is the mental state. His frustration. The sense that he was beating his head against a wall.

Well. He can look for that.

(... Also, more worrisome: Every dath ilani child can solve the mystery of the planet's motion? More evidence that he's in over his head, as if he doesn't have enough. He is starting to understand his superiors' frustration, and to be impressed at their accomplishments. He will need to work harder.)

The kid really does think infuriatingly highly of himself.

Not that he's wrong to; it is clear why he is worth as much as he is to Cheliax, and probably any random peasant who suddenly found himself treasured by the Crown and fought over by gods themselves would comport themselves similarly. She worries, though, that it's contagious; part of what Keltham is trying to impart is the habits of dath ilan, the attitudes of dath ilan, and Keltham is a teenager who thinks too highly of himself, and so he'll teach them all to become teenagers who think too highly of themselves. 

You should never get too attached to a single frame through which to view a person, but as a first pass it seems to explain Keltham and Asmodia both; the Chosen of Asmodeus, she does not dare assess in the same terms, not exactly. 

The classroom is frightfully silent, probably because everyone is waiting for her to say something. Well, she'll let them wait a bit longer; she's not here to make them feel like there's someone competent around, even though obviously she is having that effect.

At Ostenso, Pilar was often the first person to talk during a Silence.  A little annoying, maybe, but she understood why it had to be her.  "If Keltham asks later, Willa, Alexandre, and Tonia got cookies from me.  I get why nobody in realCheliax wants one right now, but those reasons don't apply in alterCheliax."

Korva doesn't say anything to anyone, because she doesn't have anything to say. She doesn't think about the problem, either, or how she could have solved it faster - she hasn't made it through all of the transcripts that were given to her, yet, but she's definitely noticed the pattern that Keltham will constantly say things that appear to be hopelessly convoluted and complex, before more information reveals that he's actually saying something very simple, and that she wouldn't have gotten if she had been busy trying to figure out what it could possibly be with only the information she had so far. So she'll wait, and see if there are any later clues that indicate that she hasn't fully understood the lesson that's been taught to her.

Korva privately supposes that there are actually lots of different reasons why someone might not want a cookie.

"Also most of the reasons the atmosphere in alter Cheliax would be less funereal ought to apply here and you could all stand to relax," Gregoria says. "That went fine. There'll be homework, and how you do on it will matter much more for Keltham's impression of your intelligence than this. So you're not Sevar; you already knew that."

"Is she - always much more skilled in everything," Sibilla asks.

"If so, she doesn't always show it? Asmodia usually finishes the purer math stuff ahead of her. You're definitely allowed to be faster if you can. In alter Cheliax there's no Chosen of Asmodeus."

"Is Keltham under the impression she has the same standing as his other students? He indicated she was responsible for the nametags, if they didn't happen - has he not noticed that will obviously make the nametags happen?"

" - you know, I don't know?" says Gregoria. "I think he says 'this is Carissa's problem if no one else solves it' because he doesn't think highly of the project staff and he trusts her? But possibly the project logistics staff in fact work a lot harder when he says that because they don't get as many lectures as we do about acting like they're in alter Cheliax."

"If they have not been instructed better they are definitely doing the idiotic thing."

"Is she not officially 'his deputy'?" Alexandre asks, having memorized the org chart last night so he could know he officially had to defer to. "And the 'leading shareholder' not from dath ilan?"

"Correct."  She read the corporate contracts a few times because alterPeranza likes Civilization things.

"That fails to solve your problem, which is that anything Keltham deputizes will get done as quickly as if his deputy were really in charge of this whole operation. In alter Cheliax I cannot imagine logistics would be tripping over themselves to help alter-Sevar."

"Alter-Sevar is still sleeping with the Queen."

"Can everyone extrapolate my response or need I say it, possibly in more filtered company."

- Gregoria has honestly half lost track of what they're arguing about. 

Willa is unhappy that alter Willa needed a cookie.

Outside of that, five minutes isn't a lot of time for Keltham to get safely far away and back, so she's going to stay firmly in her shell, just in case. Even if it is, she isn't really feeling gregarious at the moment. She'll let the conversation about Sevar mostly flow over her.

What she wants to do is use mage hand to play with her quill; it's one of her favorite ways to destress (and won't it be pretty to watch once she gets that Arcane Sight.) But doing that would probably draw attention that she doesn't want to deal with. It might not even be adequately shy. She'll have to stew without assistance instead.

Willa wants to be special, and she's made negative progress at that since getting on this project. She isn't especially good at the work (yet), she couldn't make clever statements even if she could think of any, and most of her superiors already dislike her. She feels frustrated, like she doesn't have the right tools to solve the problem. Alter Keltham who she could whine to about this problem would tell her to step outside of the solution space.

What's special about Willa? If she gets hired, she's going to be selling her soul; that isn't special, especially not in Cheliax, but also selling an option on her sold soul is. Is it useful somehow? She can't think of how, especially since all the other new hires will be in the same boat, but it's a persistent idea all the same. Selling an option on a soul feels like it was definitely someone stepping outside of a solution space, but as far as she can tell it's not to her benefit. Hell is going to own her soul; in all respects it should probably act as normal until and unless the option is executed?

What other especially unusual stuff has happened? People keep ominously mentioning the tropes, so they're probably something special, but without knowing anything else about what they are they aren't special in any useful way. Even the 2-4-6 'math looking back at you' angle doesn't help if you have no idea what you're trying to look at.

Alexandre thinks about telling Lady Eulàlia Avaricia de Seguer that, actually, no, in an alter-Cheliax that was at all competent, logistics would be tripping over each other to help Keltham's deputy, because literally every instant of Keltham's time is worth more than the lives of several dozen ordinary people. It's an enjoyable fantasy which would be highly unwise for his future life expectancy to try to execute, so he isn't going to do it. He's just going to think about it.

...and everyone's quiet again.  She'll give it one more try.  "Korva, you finished faster than anyone who wasn't tier-1.  Any advice that carries over to the rest of us?  This isn't a normal competition, the whole Project succeeds or fails as one and you end up a Duchess if it succeeds."

Korva has literally zero desire to be a duchess, which does not at all mean that she doesn't separately want the project to succeed.

Also she kind of hates talking to people, but that doesn't mean she can't answer direct questions.

"Honestly I think I got lucky? But I thought afterwards that I would have gotten it faster if I'd been a small child, because I wouldn't have taken as many math classes and wouldn't have learned the implicit rule that math classes almost always deal with problems where the same input always gets the same output. And since a lot of the people in this room were specifically picked for their ability in math classes, they might be even more vulnerable to that than a normal person. So I was thinking that the next time I ran into a problem like this, if I got stuck, it might be worth pretending to be five, and seeing if it helps anything."

The problem with saying things is that most things make you look weak, foolish, or low-status. So, useful information, Korva! We're all better off for you providing it! Alexandre is keeping his mouth shut.