(They've now stepped into the next 'breakout room' over from Ione.)
"So #1 is, I assume you got this part stop me if you didn't, about the way that the implication-probabilities for all the different observations or things that can happen or different pieces of evidence you could get, all have to sum to 1, or no more than 1 if we're not assuming the list exhausts every possibility which in real life it obviously never can."
"Meanings and implications. A world or a theory or a way things can be, has a limited resource like money, like it has one gold piece total divided into a hundred coppers, which it has to spend on all the possibilities that it wants to claim credit for having predicted. I can't let you spin the coin and then say, Queen has 100% probability, Text also has 100% probability, that adds up to 200%. That's why they try to train dath ilani out of assigning more probability afterwards, then they would beforehand, it's why that's contrary to the nature of Probability's Law, if you assign more probability to a happening, after hearing that it happened, then when you add up all the probabilities you'd assign to all the happenings afterwards, you'll get way over 100%. Only if you do it in advance are you guaranteed to have it add up to 100%."
"Golarion doesn't understand that Law. Golarion doesn't know that Law. Which means that everybody who's got a belief in their minds, is looking at, whatever happens, and trying to convince themselves, sure, that thing there, that is just what ought to happen in the world I think I'm living in, that should happen with 100% probability. They'd say that for anything just the same. So if you try to - turn that back into coherent math - it says that every outcome has the same probability, and if there's five outcomes, maybe each of them gets 20%, after you're done telling somebody it can't be 100% for each. But 20% for each of the same five outcomes is the same as if you just said 'I don't know' for each of them, instead of, in every case, there being a clever way to twist things around make it sound like that thing is totally what should have happened."
"The poetry Keltham quoted us for #1, I suspect if he said it in his own language it would rhyme, or there's a version of it that does, it had that feel to it, and I think I've got it memorized by now: 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. It's not about how good you are at explaining away whatever happens, the only thing that - focuses, concentrates - the limited supply of what you can predict, into some predictions and not others - is that your explanations will sound more plausible for some things and less plausible for others, if there aren't some things you can't explain, that's the same as not being able to predict anything will happen, because you can't predict anything won't happen. Explaining and predicting are the same thing to a dath ilani, the degree to which a belief says, 'I'm great at explaining that, you should credit me for being totally compatible with that thing you saw', is, to the dath ilani, just the same number as the probability that got put on there, and probability is conserved, so you can't be equally good at explaining everything. To predict reality you have to be the sort of person who, if you were told a fiction instead, would go 'wait what I can't explain that thing how surprising' instead of coming up with a clever explanation of that thing you were told that wasn't real."
"Ione thought that only #6 and #7 were going to be deadly to Asmodeanism. She's wrong. All seven are going to cause problems if the others in class really understand them. Everything that people see, they're trying to explain how their version of Asmodeanism predicts that thing, so Asmodeanism can claim credit for having predicted it, but if they'd seen something very different, they'd predict that too. Keltham's world trains Keepers out of that all the way and it trains people like Keltham four-fifths out of the way of doing that, and when you've started practicing with numbers and maths for some things, it affects all the rest of your thinking, the way you think in words. I remember seeing it when I wore the headband, it was so vivid then and it's faded now but I remember what I saw, the way that - the beliefs inside me - were trying to warp and distort themselves and pretend to shove more probability into the things that they knew had already happened, that they'd never have predicted or never have predicted that strongly, and the more that people are lying to themselves the more that distortion is going to be holding all the lies in place while they try to suck the credit of being right out of whatever-happened by explaining it - and dath ilanism trains that out of people, Keltham's going to make people play some game and when they're done playing the game they'll do that less and then everything that was held in place before becomes shakier - if you had a headband like the one I borrowed, you'd be able to visualize the right Law as math at the same time you watched your own mind trying to do it wrong -"
(There's no obvious sign that Asmodia is ever going to stop talking about problem #1 in particular.)