That made an unexpected amount of sense.  Also, wow, Civilization goes hardcore on its kids.  Maybe not in terms of how they get punished for failing, but in terms of how hard the things are that they're expected to do... could these two facts possibly be correlated in some way, Cheliax?  Well, not the time.

"Tonia, what'd you get for #1?"

Keltham will actually just go re-write the problems while that's going on, for convenience.

1.  Your strength in the Way is your ability to be more confused by fiction than by reality.  If you're equally good at explaining any outcome you can see, that's the same as not knowing anything.

2.  Surprising claims require surprising evidence; unsurprising evidence suffices for unsurprising claims.

3.  No empirical theory can prove itself except by risking its disproof.

4.  To convince me of your theory, make a correct prediction that no other theory makes.

5.  A precise true prediction is much more convincing than an imprecise true one.

6.  It is impossible to coherently expect to convince yourself of anything.

7.  You can't expect anyone else to convince you of something either, even if you think they're controlling everything you see.

"Do you want my proof or my explaining what it means?"

"Both, why not."

"What does it mean to not know anything. First I said 'not knowing anything is assigning equal weights to each possible future outcome', but that does mean you at least know what the possible outcomes are, so I don't think that's quite it. Then I said knowing things is your negative-two score, which also isn't right because not having any guesses is what not knowing anything is, and you do better in the negative-two game by not having any guesses. And you could say, okay, what does it mean to not have any guesses, can we put that into math. So I tried that. 

And what I came up with - with a Fox's Cunning - was, uh, a definition of being surprised: you're surprised by however many twos you lose. So, imagine a predictor that no matter what happens is the same amount of surprised, loses the same amount of twos. The value of consulting that predictor is zero; being the same amount surprised by everything is the same as knowing nothing - and I think actually maybe that's the most satisfying definition of knowing nothing, that the value of consulting you is zero." She puts up an illusion with her notes as she talks; she is talking fast and seems a bit nervous. 

(She is not on the light punishment regime, but she doesn't think that's why she's nervous, alter Tonia is just worried she'll get fired if she said something stupid.)

"Mm.  Anyone else in tier-2 want to add or argue anything for that, else, anyone in tier-1?  I'll save my interpretations for last, when we're through all the problems.  And then Keltham goes after all of mine, I think."

"I had the notion that - it's pointing at - a form of unLawfulness where people try to get out of being caught at being bad at predicting, by being clever at arguing about it.  Let's say there's a guide who claims to be very good at unravelling dungeons, so you take them along on a delve, and you get to a splitting path that can go six different ways, with some clues.  One person who's already been past that level knows which one of the six paths leads down to the next level and which five lead into trapped rooms.  And they ask the person who claims to be a good guide, which path is correct?  And the guide could, if you told them a path, come up with an argument for why it was obviously that path.  But if you don't tell them which path, and they come up with six arguments for all six paths, then even if those arguments all sound tremendously intelligent and clever, they obviously don't know anything useful."

"If you ask them for probabilities on the six paths, instead of arguments, you can just score them and that's it, that's how well they did and how much, uh, reward they should get paid.  So putting numbers and probabilities on things is Lawful and arguing about them isn't."

Gregoria nods. "It's like, imagine everyone around you has thirty points more Splendour than you, how do you believe anything at all they say. And you'd just have to make them predict it in advance."

"I got as far as working out that if everything sounded equally appealing, that was the same as assigning equal probability to anything that might happen.  I didn't realize we were supposed to keep working on anything once we got past that point."

"Well, and the probabilities have to sum to 1 or less, is I think the key idea there.  You can't say that everything is very probable the way that you can come up with really appealing justifications for each of them."

They'll run through #1, then interpretations of #2, then interpretations of #3...

(Asmodia is a little put out by other people being clever at all, but she's still reasonably sure of her ability to sound more impressive than the sum of all their reasoning, once it's her own turn.)

"Three is, if you can't say what would prove you wrong, you aren't saying anything. If the Church couldn't say 'if in fact practically all people got sorted Good then Asmodeanism wouldn't be true' then it's not saying anything."

Are we just. Making up heresies on the spot to win arguments in probability class now. Is that what we're doing. 

Gregoria hates all these people.

"So, I mean, for #4, I think for seeing the meaning, it helps to see how obvious it is?  Like, sure the equations say that if P(path 2 ◁ fire level) = P(path 2 ◁ water level), then seeing it was path two that led downlevel doesn't give you any information about the next level's elemental orientation being fire or water.  But also, if you didn't have to make a prediction no other theory makes, you could go around saying, 'I'm the best predictor in the world, I predict better than Nemamel, yesterday I put 99.9999% probability on the Sun still being on fire today and today it was.'  And everybody else would go, incredible, such a prediction, so much probability on the correct outcome, wow!"

Pilar.

Remember that time Ione had to deliver a prophecy about an incoming Nidal attack?

It wouldn't have been a good thing for Asmodeus's interests if the Asmodeans had spent a lot of time questioning how that might be a cunning Nethys plot, before acting on it, right?

...what is this about and what are you angling to get me to do without questioning it?

Actually, Pilar's curse is just telling Pilar to signal Security to start reading her thoughts - they don't usually waste attention on Pilar, since she's loyal and doesn't usually have suggestions or orders for other people - and Pilar's curse doesn't want Pilar to argue about that.

...fine.

Pilar casts Mage Hand under her desk, and taps one of the two Security in class.  No more signal than that should be necessary; they've got Arcane Sight and can see whose Hand it is.

Security, relay the following to Sevar priority verbatim:

In a few minutes, Pilar's curse will make a request that Pilar might otherwise argue with or doubt or spend too much thought questioning, because she's lacking context.  Pilar's curse requests that Sevar command Pilar to obey to the best of her ability, without questioning the request, or spending a lot of energy trying to figure out why her curse is asking this.

The suggestion, when it comes, will be that Pilar not hold back her opinions the way she almost always does, and that she tell Keltham very frankly everything that she actually actually feels about something Keltham will say.  As Sevar has already seen, it's sometimes possible to make headway with Keltham by speaking truly from your heart, without trying to manipulate him.  Nobody else needs to do anything special so long as that part works.

As it happens, this act will serve the interests of Asmodeus, and Cayden Cailean, and also Broom's god.

The context Pilar is missing is about Broom's god, and that you wouldn't expect Pilar's curse to lie about that part, because that would get Cayden Cailean in trouble.  Don't try to actually explain about Broom's god right now, that would distract Pilar.

Order Security to stand by to tap Pilar with Eagle's Splendour when Pilar's curse gives the word.  It's probably not necessary, Pilar can probably do it anyways, but it might help her a little.  Or if nobody on staff has Eagle's Splendour, there's still enough time to emergency-Teleport one of the eighth-circle wizards in from the front lines so they can use a Limited Wish for that.  Haha!

Pilar's curse isn't actually funny.  At all.  If something is actually funny you don't need to add 'Haha!' at the end to let other people know it's supposed to be funny.  Pilar's curse knows that, right?

Pilar's curse is wounded.  Pilar's curse is the essence of hilarity.

It's just that sometimes Pilar's curse is other things too.

What would the Grand High Priestess do. 

Pilar, do it.

Acknowledged.

Pilar is incredibly fine with this.  Pilar is not asking any further questions inside her own mind even.  Her curse submitted the request to Sevar instead of herself, which is a proper and Asmodean way to do things, and her superior told her that it was fine to shut up and obey and not ask questions.  Pilar wishes that situation would happen to her a lot more often these days.  Pilar wishes her curse would do everything like this.

Sevar does have anything else to do with her life besides run Pilar's life.

Pilar knows that is true but Pilar doesn't have to like it.