"You lose 12/12ths of a 2 each time you predict 1/2, so you lose 1/12th of a 2 less that way.  Which is better if losing 2s is bad."

"So would you agree that this scoring function..."

"Gives you more points, or rather, has you lose fewer 2s, the more probability you assign to whatever happened?"

"Gives you the same final number of points, or 2s lost, whether you're predicting two coinspins at once, or predicting them separately in different rounds?"

"And, at least in this particular example we checked, it wasn't possible to expect to score more average points, or lose fewer 2s, by giving an answer other than reality's answer for how often something happens?"

Yep! That does seem true!

Why does that still feel like a surprise even though she predicted it way earlier?  "And it's the only scoring function like that which can possibly exist," Asmodia states.

"Not exactly.  Counting lost 3s will also work.  Or counting lost 5s.  But that just scales the number of points you win.  There's around nineteen twelfths of a 2 in a 3, so if you know how many 3s you lost, you can convert to how many 2s you lost.  It's not so much that there's only one function, as that all the functions like that, are basically doing the same thing and have outputs that are trivial to convert back and forth."

"The Law, in this case, is not an exact function or an exact number of points, it's a structure such that every solution shares that structure and does almost exactly the same thing.  Like a simpler and clearer version of the way that lots of logics are ultimately equivalent to first-order logic in what they end up deriving."

"And you can - use this to figure out who's the best at predicting things?"

"If everyone is predicting the same questions using the same knowledge.  If your sole goal is to end with as many 2s as possible, and you get to pick whether or not to play the game, the only winning move is not to play, so you can end up with the same zero 2s you started with."

"Otherwise you start with nothing, and then lose more every time you try to predict anything that isn't absolutely certain, and the best you can do is losing the least 2s possible, which will always still involve losing some, it's just that if you don't match reality you do even worse.  So, yes, if that was a game with, like, actual penalties, and no other reward for playing it, nobody would play that game if they had a choice."

"I would," Pilar says.

"Kinky," says Yaisa.

"I mean, presumably you have people do this for outcomes of decisions they're already making, for accountability, not as a game they play for fun."

"Well," Keltham says, speaking less rapidly than usual, because some of his processing just got diverted to a subthread, "we can and do play it for fun, and do that our whole lives, in fact.  It just involves a mindset where - you can try to do as well as possible, each time you confront a prediction challenge, without feeling like you're losing something in virtue of doing less than perfectly."

"The most obvious thing to match yourself against, there, is other people's predictions.  Pilar predicts one number, Yaisa predicts another, we see who did better, just like if they were playing some other competitive game whose in-game rewards sum to zero across all sides, but whose positive extra is the fun people have from playing it, or their pride in showing their skills.  There's a version of that game which dath ilani play, before they're ready to go all the way to prediction markets, where we put up a sheet of paper on the wall - or just use walls and Prestidigitation, I guess - and write down a question, and then people who think the current probability is wrong can write down a different probability underneath and be scored by how much they gained or lost relative to the previous guess."

"I'm not quite sure we're ready yet, but once we are, we'll probably just start doing that over all the place, whenever somebody comes up with an interesting question that will actually settle in a few days."

"But I think the most basic point - lost 2s aren't actually like sending out the merchant ships to the wrong place.  They're a measure of how well you do, and you do better by losing fewer; but the fact that the numbers always look negative don't mean you're doing poorly.  If you're losing few enough 2s, you can send your merchant ships where they need to go, and that's the reward for playing."

The students are nodding. 

This feels like a really big part of Evil dath ilan. Accountability, true and perfect and impartial, handed down from reality itself, impossible to rebel against or lie to; competition for its own sake, to prove oneself worthy of the power to send ships -

- there's something there. Though also some heresies to navigate around.

"The more mature version of this is where people are betting money against each other inside a common market, forming a prediction market, and the places where prices settle then become Civilization's way of knowing what Civilization knows."

"If this project were running inside Civilization, there would already be a prediction market over what its outcomes were, like whether we succeed in our technological revolution, or start another war, and every time something interesting happened, the prices would shift, and that would reflect Civilization knowing more about our project's prospects.  Or, I mean, in this case, it would be a secret government prediction market, but then that's the government's way of knowing secret things.  I wish we had one, actually, I'd have loved to see what happened to the prices when Pilar started handing out Cayden Cailean candy."

"People who make massive amounts of money on prediction markets by being righter than everyone are incredibly rare in Civilization, and they're respected about as much any other kind of person who exists.  A Legislator is significantly less respectable than Nemamel, who beat the prediction markets her whole life to the point where she could only trade anonymously because nobody would knowingly bet against her.  Nobody takes that name any more, she owns it now, it's hers forever.  There's nine Legislators at any given time, and there were five people like Nemamel over the course of Civilization's remembered history."

Merenre keeps working at his desk and doesn't sneeze at all because this isn't that kind of universe.

"Is it - about intelligence or something else - is it hereditary - was she able to describe it -"

"Every kind of skill Civilization knows how to describe is one that thousands or millions of people learn.  Nemamel couldn't have been what she was, noticeably better than all her competitors, if she'd known how to describe all of what she was doing with no bits left over.  She passed on some of her skills and made the markets themselves better, but Nemamel had no successor and no replacement in the domains she'd mastered most, when she went into" cryosuspension "the deep cold of suspended time, waiting on the Future to awaken her.  It was one of her classic - your language doesn't have the word, an acerbic disclaimer of how far you fell short of your own standards in the course of impressing somebody else - that people who were actually competent and understood what they were doing could just teach their skills to others so everyone would have them.  You only become Nemamel by failing to understand yourself that well, or by being born with good heritage that isn't anything you hold in your mind's own hands and can teach to others, so why be impressed by that - was her acerbic disclaimer."

Can you steal dath ilanis with a Wish, Carissa wonders. 

It wouldn't even be a good idea necessarily - one dath ilani is probably all that Cheliax can handle - but could you. 

"Are the acerbic disclaimers important to what she was doing?  Should we be making acerbic disclaimers like that?"  (Peranza.)

"Probably sort of?  Suppose I put it this way:  Clearly, I should be telling you more about dath ilani heroes - heroes? - people who are incredibly impressive - because dath ilani don't grow up to be skilled by trying to be Keltham, they grow up trying to be Nemamel."

"But how does Nemamel grow up to be Nemamel?  She was better than all her living competitors, there was nobody she could imitate to become that good.  There are no gods in dath ilan.  Then who does Nemamel look up to, to become herself?"

"And the answer is - she looked up to an image that existed in her own imagination, better than all her competitors and also far better than herself, the person who would've executed all her own skills perfectly, been everything she was but better, not something like Nethys that knows the answers just because, but something less powerful than that which knows them for reasons and by being clever."

"If she'd ever stopped to congratulate herself on being better than everyone else, wouldn't she then have stopped?  Or that's what I remember her being quoted as saying.  Which frankly doesn't make that much sense to me?  To me it seems you could reach the Better Than Everybody key milestone, celebrate that, and then keep going?  But I am not Nemamel and maybe there's something in there that I haven't understood yet."

"It didn't seem like a kind of pride that was being offered to me then, in retrospect, looking back.  It was the pride of the very smart people who are smarter than the other people, that they look around themselves, and even if they aren't the best in the world yet, there's still nobody in it who seems worthy to be their competitor, even the people who are still better than them, aren't enough better.  So they set their eyes somewhere on the far horizon where no people are, and walk towards it knowing they'll never reach it."

"But now we sort of are the very smart people now, aren't we, or trying to be that, and maybe I understand a little more, now that I think on it again.  I mean, if I try to imagine myself - looking at Golarion, and being like, 'Ah yes, I have done better than Golarion, yay me' - that would just be stupid.  No offense.  Probably Nemamel was that, but for dath ilan.  To her it was like Golarion is to me.  And that's why when people congratulated her on being better than everybody, she was all, 'stop that, you only like me that much because you're thinking about it all wrong', compared to some greater vision of Civilization that was only in her own imagination."

Keltham doesn't aspire to be like Contessa Lrilatha when he grows up; that would be aiming too low. 

Maybe even trying to build Evil dath ilan is aiming too low. 

She's not actually sure what would be aiming higher, though.

Or maybe the idea is not to aim high, the aim is just to imagine what you'd get if everybody was doing everything right all the time -

- if everybody was doing everything right all the time, Asmodeus's weaknesses could be taught in schools so smart children grew up thinking how to strengthen Him, and they would think thoughts that were actually a good idea, instead of in this world where Aspexia Rugatonn seemed to genuinely consider it plausible that it's better for most people to be stupid lest they trip over their own cleverness. 

If everybody were doing everything right all the time, then when Keltham had arrived they would not have needed to lie to him; they'd have known how to explain themselves to him, because they'd have known how to explain themselves at all. 

What if not everybody was doing everything right all the time, but Carissa personally was. Then she'd have noticed all the things she didn't understand sooner - (and gotten executed for heresy) - no, she'd be like Pilar, impossible to accuse of heresy because none of her thoughts twist away from other things - why did Asmodeus pick Carissa rather than Pilar - 

- anyway by the time Keltham landed she'd understand the thirty-word explanation of Hell that makes it not upsetting to Good people and they wouldn't need to be running an elaborate deception. And if there was occasion for it, she'd be better at it, because of understanding how all the world is deeply interconnected.

No, no, that's not good enough either, aim higher -

Literally every person in this classroom is already somebody's oracle or cleric or has sold their soul, and He can't maneuver any (more) of the Way's followers here because of Otolmens's Edict.  Why is His life like this?

"What was that about the deep cold and the future awakening her?  It sounds like - things that happen with epic heroes, here.  There's some way for Nemamel to come back if she's really needed?"  (Still Peranza.)