You cannot simply assume that, just because you have cast a spell, it is gone. That spells usually do not interfere with other spells is a generalization, not close to a law.

2,4,6 again? Still NO. 3,5,7?

YES, quite slowly, as Keltham's eyes flicker over the whole previous sheet of paper while successfully making it less than completely obvious what he's doing, as might be obvious if his eyes moved slowly down the page in order.

Dath ilani play enough games where direction of eye gaze can be a giveaway that Keltham has at least some training in that particular aspect of Bluff.

... Well, this is still going to be a difficult challenge. He has the hint, but he needs the Law; whatever it is can't be simple addition, because at one point he tossed a hundred billion in. Each slot may still mean something different, and he has such a tiny, frustrating window to tell useful things from his information!

Still, things may be simple. 3,5,7 again?

(NO, instantly.)

3,5,7 again continues to be no? (NO, instantly.)

Excellent. Then he's going to check this again just because Keltham is a sadist. 3,5,7? (NO.)

Then... is it really just that simple? He... he thought it would be much more complicated than this. His guess, this time, is that anything you've tried before gets a 'no' and anything else gets a 'yes'.

CORRECT.

... He cannot believe it took him this long to get it, but yes, he is feeling... joy, at finally mastering a difficult art, at taking an absurdly complicated thing-in-the-world, and studying it, and reducing it down to something so simple, that he couldn't believe it took him so long to understand it. Through pain, to strength. Great is Asmodeus, Lord of All.

(And Alexandre will let a tiny bit of the happiness he is feeling leak through, since alterAlexandre would not hide his expressions as well as trueAlexandre. Just a little.)

Keltham looks happy about it too, in fact! He's trying to hide it, but not at all well by Chelish standards.

...as for that tiny bit of leaked happiness from Alexandre, there's no chance in the Abyss of Keltham getting that.

All of her sequences so far are new. So -

2, 4, 6: NO.

Incredible.

She would have gotten this faster if she hadn’t been thinking about it as a kind of fucking math. Or if she had been a five-year-old. Or if she had been dumber.

Well, she can probably learn to be dumb sometimes, if that’s what it takes.

3, 5, 7. Guess: Outputs "YES" when given a new sequence; outputs "NO" when given a sequence already used.

NO. CORRECT.

She doesn’t collapse in panicked relief on her desk, because she’s not actually five and also that would be disobeying instructions about leaking information. She stares ahead, outwardly calm - which is probably in itself leaking information, because she probably unintentionally leaked a bunch of distress everywhere right around 1, 2, 3, 4. In any case, her soul is crying out in relief, and she gets a sympathetic mental pat from Pretender about it.

Only then does she look around, and see that all of the other new students are still writing. Some of the old researchers - including, of course, the Chosen - have stopped writing, but not all of them.

She really doesn’t know how to feel about this.

Previously, on Willa (the Complete Disaster at Everything):

With a heavy heart, she writes the fateful numbers.

3, 4, 6: NO

Oh no. Well, as bad as this is, she has to be sure.

2, 3, 6: NO

It's a little slow again this time, because of course it is. He had to read up her sheet. But she isn't sure ENOUGH.

1, 1, 1: NO

And she has to make sure she isn't missing something else either. Order could matter too. She is not going to get this WRONG. Not AGAIN.

6, 3, 2: YES

Well fine then. She notices that she still has an internal flinch expecting that WRONG gets written after her answer, in spite of all her reason insisting it won't be.

The law is that if the three numbers have been entered before in order by Willa, nature says NO. If this is the first time the three numbers have been entered by Willa, nature says YES.: CORRECT

She's a massive failure, but she's still relieved. None of it shows on her face though.

2, 4, 6: NO

2, 2, 2: NO

0, 1, 2: NO

900, 600, 300: NO

-1, 0, 1: NO

a, b, c: INVALID

Well, that's some obvious theories that don't seem to be on the right track at all. Back to basics, then: does the rule output the same judgment every time you give it the same input? 

2, 4, 6: YES

- and there's an obvious theory (any set is allowed the second time, but not the first) which does seem to be on the right track, but she's met Keltham so she's SUSPICIOUS it's more complicated than that. For example, maybe it'll be allowed the second time but not the third, or maybe the second time it gets evaluated by a different rule than it did the first time, but the different rule might not always return 'yes'? Or maybe once the numbers have been used they are allowed in any order?

-1, 0, 1: YES

6, 4, 2: NO

2, 4, 6 for the third time?: YES

6, 4, 2: YES

2, 4, 6 for the fourth time?: YES

2, 2, 2: YES

-2, 45, 1: NO
 
-2, 45, 1: YES

1e16, 1000, 4: NO

1e16, 1000, 4: YES

...on the other hand sometimes the rule is in fact simple and you shouldn't overthink it. 

She submits her guess. 

She's done first. What kind of bizarre nonsense is everyone else getting up to?

Keltham had assigned YES->NO to half the tier-1s and tier-2s, NO->YES to the other half, making sure to put Asmodia and Carissa on separate sides.

He's surprised to find that NO->YES looks like it was slightly easier, rather than slightly harder as he thought it would be.  He would've given NO->YES to the new candidates if he'd known.  Oh well.

Alexandre was the last one, right?  After a quick final round to make sure he didn't forget anyone, Keltham announces that they're done.

"And now," says Meritxell, "all of the slowest performers will be dropped into boiling acid as an example for the others, exactly as it's done in dath ilan -"

"She's kidding," says Gregoria.

"They knew that, spoilsport."

"They might not have known that!"

"I was kidding," says Meritxell. "Only the absolute worst performer is dropped into acid and it is not necessarily boiling, depends whether it had time to get to a boil while you were being slow-"

Since Korva was bizarrely un-slow, she doesn't worry.

She does wonder whether anyone is going to talk to the old guard about whether alter-Cheliax could plausibly have people who might not have known whether several of them were going to be immediately dropped into boiling acid due to slow performance on the very first exercise, or whether that sort of thing is only for newcomers.

There's probably no way to find that out.

"Understood," says Alexandre drily. "Is it permitted to cast Resist Acid first, or does does dath ilan forbid protecting oneself as opposed to the spirit of maniacal-experimentation?"

(He knows perfectly well that countries other than Cheliax are too weak to drop their students into boiling acid, and dath ilan is far more good - that is to say weak - than Taldor. But he may well be whipped once he's finished, anyway, or at least beaten, Taldor does still exist so it can't be that weak.)

Was that appropriately witty and spontaneous or did Alexandre just make some terrible error? She thinks that one student speaking up like that is probably more likely to happen in alter Cheliax, but her trust in her own instincts is at an all time low right now.

At least it's not the type of call she's going to have to make, being 'shy and hesitant.' She hates that she feels relieved.

"I'm not even sure being faster at the exercise is being better at the exercise," the Chosen of Asmodeus, who was the fastest, says in the same light-banter tone. "One way to be fast is to be careless, which is the only real way to fall into vats of boiling acid in dath ilan."

"But today we are charged with doing maniacal-experimentation," says Meritxell. 

"I would of course never dream of working with volatile high-temperature acid without casting Resist Energy (Acid).  It was in no way the case that our Nethysian Safety Officer had to browbeat me into waiting a day to pray for those spells first."

"And today, indeed, we're not just learning maniacal-experimentation, but learning the Law of maniacal-experimentation.  Of this the Law is relatively simple: when experiments are cheap, do lots of them, when they're expensive, spend more on figuring out which experiments to do.  Even then, though, when you're doing lots of similar experiments and they're all failing, what you probably need is to back off and think.  Even even then you might try running some weird or random experiments anyways, while you're thinking."

"Incidentally, a bit of maniacal-experimentation I did myself on the side:  I assigned half the current researchers to start with 'Yes if not tried before' and half the researchers to 'No if not tried before'.  I was expecting 'Yes if not tried before' to be the easier one for non-dath-ilani, but it looks like it was actually the harder direction.  Sorry about that.  Had I run a pilot experiment first, I'd have known to run the real experiment with 'No if not tried before' for all the newcomers, instead of, as I did, it all being 'Yes if not tried before'.  Such is the price of maniacal experimentation where you don't run smaller pilot tests before you run the big ones."

"Carissa was in the 'No' group, but still a huge 'outlier' in speed even so.  Is there some kind of Worldwound experience that let you get it after your fifth input, or...?"

" - after I tried a couple things I figured I should check whether a given input always produced the same output or not. I cannot think of a specific occasion at the Worldwound where I had to do this but it does seem like - sort of a thing to do fairly early in figuring out something mysterious."

"Yeah, that's basically around how long it takes dath ilani kids to get it.  We play a lot of games with 'gotchas' of all kinds.  Even on the non-game side of things, by the time a kid gets introduced to this game, they've probably heard the proverb that when you're trying out new maniacal-experiments in a new domain with new equipment, among the first things you try is to measure the same thing twice, or two things that you expect to be very similar, so you can see around how much error there is in your measuring instruments."

"I wasn't expecting this problem to be as difficult as it was for non-dath-ilani... er, other than Carissa.  I was mostly trying to set you up for the trap where you see 2-4-6 and try 3-6-9 or 3-5-7, and are sure you've found the answer then.  The lesson about that is to test the negative spaces as well as the positive spaces, the places where your model says a procedure should fail and not just where you expect to succeed.  To pin down a boundary you need to check what should be outside, not just what's inside."

"I wasn't expecting the step after that to be as hard as it was.  But it looks like you all ended up learning a valuable lesson anyways, and the 'explicitization' of that lesson is this:"

"Very often in Science, especially when you're working in a confused 'pre-paradigmatic' field, 98% of the work is in coming up with the right hypothesis to test.  That's often more important than the elaborate Law of Probability about how to interpret results that are less than totally clear.  We study that part because it has clearer Law to study and it helps reshape our thoughts, not because it's the most important or difficult part of the problem."

"And of that work of coming up with the right hypothesis to test, again, often the most difficult part is seeing the rule you were taking completely for granted - not a rule you explicitly believed, just a way you behaved automatically without being able to see that and so question it.  As soon as you see the implicit rule, you can imagine it being false, but only once you see it."

"The difficult thing, in most pre-paradigmatic and confused problems at the beginning of some Science, is not coming up with the right complicated long sentence in a language you already know.  It's breaking out of the language in which every hypothesis you can write is false."

That sounds extremely wise; does Keltham intend to explain how to do it?

...she kind of did explicitly believe the rule that was getting in her way, though. Young children probably would be better at this problem, which isn't that surprising because it probably is, in fact, an exercise for children. It's not that they're fundamentally sharper, they've just taken fewer math classes, and don't know that in math classes you mostly deal with the sorts of problems that always output the same answer for the same inputs.

Note to self: next time, before you panic, take a step back and pretend to be a five year old.

There was an expectation buried within Willa, so deep that she couldn't notice it, that real world things might look back at you when you looked at them, but purely math things never did. The thrill of realizing this is sorta wrong is the first thing to really break through her depressive spiral since the class started.

"Breaking out of your language and finding new structures in which it is possible to frame the correct hypothesis, is legendarily the most difficult part of Science to teach; any part of it that's been reduced to a formula is no longer the difficult part of the problem."

"In the case of things like manufacturing acid and improving spellsilver refinement, you'll be at a great advantage because I can tell you much of the correct language to think about those problems... until we start trying to improve those processes using dath ilani knowledge plus magic, as was never in dath ilan, and then we're back to 'pre-paradigmatic' experimentation again."

"Since 'jumping-out-of-the-system' is such a vital part of the Science problem and so difficult to reduce to formula - there is Law of it, but it doesn't help much unless you're making some really basic mistakes - it is mainly taught to dath ilani children by experience."

"For example, dath ilani children are told that the reward of passing a competence test will be theirs, if they can only guess correctly what it is that holds up the Sun in the sky, and prevents it from falling down, and guides its motion, as it circles our planet every day.  Is there some shell that holds it in place?  Invisible wires?  Is the Sun just made of very light material so that it doesn't fall?"

"Of this it is forbidden to speak to children, until they guess it for themselves.  Only then, as their reward, are they shown where they are within the universe - where they have always lived, all their time."

"I assume everybody here was already spoiled on that one because Golarian.  But just in case, raise your hand if you already know."

Chelish wizard students do in fact know that the Sun is very far away and Golarion circles it. 

"In retrospect I should have checked that before showing the current researchers where dath ilan was within its universe.  But looks like no harm done."

"So, yes, until the kid says that they suspect that dath ilan is spinning in place and that just makes it look like the Sun is circling it, while the Sun is staying in place, they're not shown any model of dath ilan's solar system."

"And then, once they see it, there's a new question: what motive force keeps dath ilan circling the Sun?  What keeps the other planets circling the Sun?  What keeps the Moon circling dath ilan?  Why don't they wobble out of place, slow to a halt, or keep going in a straight line instead?  Everyone know that one already?  Raise your hand if you do."

They are taught, too, that it's gravity, the force that pulls the heavenly bodies in their places. (They are not specifically taught why gravity causes that to happen instead of causing some other thing.)

Well that seems like an important dath ilan fact, the not telling anyone about the solar system before they've earned it. How many kids ever figure that out? Approximately intelligence sixteen on average, so, what... forty? Fifty percent? She's still gotta be crap at probabilities for things where you don't have any examples to work from, and she's not sure that the fact that Golarion is spinning even was something that humans ever figured out on their own, so it's hard to say how long they could go without figuring it out, but, hm, she doesn't feel like she could possibly have more than a fifty percent chance of figuring that out alone. Probably way less than that. Maybe if someone were standing by to tell her right away which of her guesses were wrong, like in the exercise just now, so that she could take hundreds and hundreds of wild guesses until she happened upon the right one by being ever more imaginative, but a lot of people still wouldn't, right...?

There could be lots of stuff like that, that people aren't privy to until they've figured out some crucial element for themselves. That fits into what the Chosen of Asmodeus was saying, earlier, about how lies are necessary for most people, but how it's possible for some people to actually be told the truth without the truth making them even more wrong. Maybe you first have to demonstrate that you're the sort of person who can figure out some pieces of the truth on your own, before you can be trusted with more adjacent pieces.

(And she might feel just a tiny bit of pride, about that, not so much for herself, but for the five-year-old who had the impulse to chase the shadows of true things through the pages of library books that were incompetently censored. She wouldn't have to feel so concerned about having that impulse, if the way of knowing true things without breaking was to earn them.)


...except, wait, if you prove it in a context where you can guess as many times as you want, you haven't proved that you'll consistently land on the right answer with the right information at all, you've only proven something about the scope of your imagination, which might be useful for finding right answers, but also seems like it would lead to lots of wrong ones.

Hm.