Asmodia: "I'll be blunt.  Do the girls in the category need to be attracted to you?  I'm not, or at least, I haven't ended up attracted to you yet."

Keltham: Keltham doesn't suppress the smile that comes from verifying that girls are allowed to say that to him, thereby rendering meaningful other possible signals on that channel.

"I mean, they need to be able to be attracted to me, on the pattern I think I'm seeing.  So if you're pretty confident you'll never be attracted to me, now that you've met me, then yeah, that would exclude you from the category."

"Unless you're the 'asexual'."

Asmodia: "'Asexual'?" Asmodia repeats.

Keltham: "Maybe a Taldane translation would be - asexual?  Somebody who doesn't experience sexual attraction?"

Asmodia: If Keltham were a Chelish person or able to read Chelish people, Asmodia might possibly have failed a Bluff check.  He isn't, and he can't, so she hasn't.

"Can you possibly back up and explain what this category is," Asmodia says.  "What this whole pattern is.  I was thinking something that just got contradicted, like - the category is interesting girls who you can also have romances with -"  She needs to dance carefully around the Keltham Corruption Project and not ruin it where Security will write down that she did.  "- though, I mean, it's not like you couldn't have sex with an 'asexual', I guess, if that's what you were into."

Keltham: "If I paid her enough, you mean?"

Asmodia: "Sure.  Is that why an 'asexual' would be in the category and part of the pattern for you?"

Keltham: "No, actually.  It's not - my pattern, it's something out of dath ilan, that's in my memories, and the exact nature of it is something that wouldn't be easy to explain - but in the pattern, somebody - a man in this particular subpattern, though there are female versions too - comes across three to five very interesting girls with whom it's possible to have romances."

"Sometimes, though not always, there's an additional girl, an 'asexual', who has a special status within the pattern, often that she's the one standing back and watching the whole thing happen and talking with you about it.  You might still date her and have a romance with her, maybe also marry her alongside the other girls.  But you don't have sex with her at all, that's the point."

Asmodia: WELL THAT WASN'T WHAT SHE WAS EXPECTING TO HEAR AT ALL

NOW SEEMS LIKE A GREAT TIME FOR A DISTRACTION

"...I'm trying to think of what the math we learned about probabilities today, could say about a puzzle like this one, and not really coming up with much."

Keltham: "That would've been easier to explain if we'd had the lecture I'm hoping for this afternoon, first."

Asmodia: "We do have the option of breaking now and resuming at dinner, if it's really a place where things will be much easier to understand after one more lecture."

Which would give Asmodia time to flee, followed by time to think!  Both of those kinds of time sound like good forms of time to have! 

Keltham: "You know, since it's you, I'll try improvising and see if you just get it."

"The general principle is, we compare the different ways reality could be, the different worlds we could be living in, and see whether our observations are more or less probable in different worlds.  The fact that you didn't immediately say whether or not you were asexual, and asked me more questions about asexuals, doesn't prove you're an asexual.  But you're more likely to do that if you're currently going WAIT WHAT inside yourself about how I mysteriously just nailed your sexuality - possibly one you didn't know was a standard sexuality five minutes ago, if Taldane has no word for 'asexual'.  So my probability on you being asexual went up after that.  Not up to certainty, just up."

"That said, the basic challenge, on a problem like this one where you didn't carefully write down your predictions in advance, is that you overestimate how much your favorite theory predicts things, and underestimate how much your less favorite theories predict things.  I didn't expect, on being invited up here, that you were going to tell me you weren't currently attracted to me.  It's not something the pattern told me to expect in advance.  Afterwards, I thought of a different part of the pattern that could fit it, but the pattern is a very large one and has a lot of potential variations and you can probably twist it around to fit anything, the question is, how far did you have to twist it, and how much does that lower the probability it assigns."

"At least in dath ilan, I don't know about Golarion, 'asexuals' are not really that uncommon, and more common among women than men; the chance of there being an 'asexual' in a group this size is already probably something like 50%, and if anything, I'd guess that fewer than 50% of the instances of the pattern I was talking about have an 'asexual' in them.  You could think about whether Asmodia is a special case of a random research group member, because she went to Hell and came back with no superpowers and now has a reason to talk with me, and whether it would be on-theme for the pattern if the 'asexual' was the one interesting girl who didn't have a weird background but was just very respectable by being better at Law than anyone, but the more you twist things around like that and specify more additional facts to make things fit, the more the probability goes down and down.  It's like asking if a rival merchant ship will come in with a cargo of shoes from Absalom, instead of asking whether a competing supply of shoes appears in the city for any reason at all."

Asmodia: Asmodia nods along.  She is tracking this; it unfortunately requires that she not process any of her other questions about what usually happens to asexuals in dath ilani romance novels, whether Keltham is suddenly offering her a much better deal on a marriage than she's likely to get anywhere else in Cheliax, or any suppressed panic she has about what Sevar will do to her if she accidentally offers Keltham any confirmation of tropes theory by being 'asexual'.  And how much she may have already given herself away and whether she should try to lie to Keltham about it.

BY THE WAY SECURITY IF YOU'RE LISTENING, Sevar needs to be brought into this loop and caught up; a lie to Keltham may be required very soon.  Please acknowledge.

Iarwain: Light forehead tap of acknowledgment.

Keltham: "It's really not the least bit impossible, in a world that isn't being influenced by this pattern at all, that I come up with a weird theory about you getting superpowers after coming back from death, which is just completely wrong.  This in a totally natural and ordinary way, causes you to ask me some questions about that, and it comes up in the conversation that you're not attracted to me.  Which girls are allowed to be even if they're not asexual.  Though - if it is because you're asexual and not just unattracted to me personally - it does seem a little improbable that they'd put an asexual in a group that was, I assume, put together the way this one must have been?  Or did they not know that about you?"

Asmodia: She needs to lie; there's no time for Sevar to be brought up to speed if she's not in-loop already, she'll use the lie that Sevar already authorized it doesn't completely not fit.  "What I'm trying to figure out right now is actually more like - if hypothetically I say something like, I've ever felt attraction to a boy one time, or a girl one time, even if nothing happened there because they didn't want me, so I could maybe possibly feel that for you, that means I don't get any superpowers.  So I'd be thinking, maybe it wasn't real attraction and I don't even know what that would actually feel like, because, if it wasn't real attraction, I can maybe still be the asexual and get whatever nice things asexuals get when they're part of a pattern like the one you describe.  Does dath ilan have any way to tell for certain whether somebody is asexual?"

Keltham: "No, it doesn't.  I'm sorry.  People have looked hard for a test like that and not found it.  Civilization does try very hard not to send asexuals a message that they need to be anything other than they are.  But a lot of asexuals themselves still feel like they got a raw deal from biology, and if that's the way you feel, well, there are all these cases where somebody thought they were asexual for years and then it turns out that they started being able to feel attraction to this one person they eventually met or got to know well enough.  It's not even all that rare.  Which means that for the rest of the asexuals, if they don't want to be what they are, they can never be sure."

"It's one of the more genuinely awful fates in dath ilan, that a pretty significant chunk of the population gets handed, that Civilization hasn't been able to fix.  There's been a massive search for drugs that will induce sexual desire in asexuals, not because it's wrong to be asexual, but because there's so many of them who do say for themselves that's not what they want to be and are offering huge drug bounties on it.  As of when I left Civilization, all the drugs they'd ever found weren't very good and had large side effects."

"On the plus side, from my perspective - because I don't actually want to be in a pattern like that - an asexual who isn't sure she's asexual, who doesn't want to be asexual, who might eventually end up attracted to the protagonist and not have to be asexual anymore, is some degree of evidence against that pattern holding here.  Actually fairly strong evidence against it holding, at least in this particular case.  Because, like, that is a Problematic Message they'd never put in there, flaming shit would that end up in the Ill-Advised Consumer Goods store."

"Does that hold here?  I notice you were careful to say 'hypothetically' and so on."

Asmodia: The desirable lie to Keltham seems obvious given her goals and Sevar's goals, but Asmodia will look down uncertainly and give Security a moment to tell her something, just in case Sevar has already been caught up on the transcript.

"Yeah," Asmodia says quietly after that pause.  "Does that mean - you're not interested in, doing the thing you'd do inside the pattern, with somebody who knew she was asexual and was happy about that?"

Carissa Sevar: Carissa is in the middle of catching up. 

- okay but Asmodia does have superpowers. She's pretty sure. And is actually asexual. She's pretty sure.

.....is tropes theory actually true. That's not how Keltham would think about it, just balances of evidence, either way - but the balances of evidence weigh in favor of tropes theory more than they've let Keltham realize -

- is she actually a secret cleric? The Grand High Priestess's reassurance was carefully worded -

- no, that's stupid -

- does Asmodia have superpowers and how -

"Ask her," she says to Security, "to ask Keltham what superpowers she would've gotten if asexual." Because she is. So maybe she got them. 

Keltham: "We can always make our own 'eroLARP' with our own rules for it, if that's what we both want.  I mean, the reason why that's part of the pattern in the first place is that it's something a lot of people would want for ordinary reasons, that there's somebody in the pattern who they can talk to without worrying about whether that's leading to sex."

"The most common outcome in Civilization is for asexuals to marry each other - to the point where it's an issue with respect to assortative mating prevention - but there's more female than male asexuals, so the second most common outcome for a female asexual who wants a stable heterosexual relationship is that she finds a man who can manage multiple relationships, who can have enough sex for himself with other women, but he could still use additional cuddles or emotional support or everything else that isn't about sex."

Asmodia: Asmodia gets the Security notification, and feels the ice slide through her because it's obvious exactly what Sevar is thinking.

She doesn't see any way to avoid it.

"What superpowers would I have gotten if I'd been all the way asexual, according to the pattern?"

Keltham: "Most probably, the superpower of being the best at math.  And being in on the ground floor of Project Lawful, and having a chance to revolutionize Golarion and someday ending up incredibly rich.  I mean, speaking of sending Messages that aren't Problematic, that sure is one that most authors will take an opportunity to mention, at some point, so that everybody in Civilization doesn't get a constant bombardment of fiction carrying the message that you need candy powers or prophecy powers in order to ever be important or worth dating."

Carissa Sevar: Okay, but, if there's a thing in the genre of prophecy superpowers or candy superpowers, do you know what it'd be.

Asmodia: Still no way to avoid it.

"And in the less probable case where there's something like prophecy superpowers or candy superpowers?  I'm curious what I missed by, apparently, this time, not being asexual enough."

Keltham: "Not really the way I'd recommend thinking about it, but -"

"Well, first of all, you'd be much more likely to be a Combat 'Ace' or an all-anti-powerful Nullifying 'Ace' in the version of the pattern where everything is much more sexualized and we're constantly fighting off sexy Zon-Kuthon agents bent on dragging us away to have sex with us.  In which case, the classic form of the 'trope' is that they can't use sexual mind control on you, and maybe you can also bop somebody on the head and make them snap out of the mind control."

Asmodia: "I admit that is not what I was expecting to hear," Asmodia says.  "And if it wasn't that?  I'm still trying to grasp what this whole pattern is."  It's not a good look on her, at this point, if she makes Sevar force her to say it.

Keltham: "Those actually are the top two obvious possibilities.  If it wasn't that, if it was a 'deconstructed' version of the 'trope' where it's supposed to be a nonsexy shadow of the sexy thing... something about nullification, maybe, something you can prevent or that you're immune to?  Or something that conveyed, like, how people can care for each other in a way that has nothing to do with sex."

Asmodia: Well she needs to say something before Keltham starts getting suspicious.

"I was thinking that this pattern you keep talking about was the dath ilani equivalent of awful pre-Asmodean books, romance novels, full of, how did you put it, Problematic Messages, about women who stand around being pretty and conceited until a man decides he's really attracted to her and wants to do all the work of giving her a happy life without her having to be clever about it at all.  I'm increasingly confused about what this is instead of that."

Keltham: "So imagine that you started from there, took up the average Intelligence of the reader by 6 points and the average Intelligence of the author by 8 or 10 points, and then there was a Civilization of people many of whom had sufficient spare time for things to get really really really overcomplicated, and you may understand why I am not even trying to explain what an 'anthropic selection' effect that looks like a meta-'eroLARP' based on 'deconstructive secondary-literature' of an 'eroLARP' would be."

"It's looking like a moot point; a lot of the theory's predictions seem increasingly like false starts and - looking up at clouds, that weren't shaped to be faces, and trying to identify a nose and a mouth until you twist yourself around to seeing faces in the clouds."

Asmodia: Are we done here, Sevar?  This looks like a good outcome for the Project, maybe the best possible one, and Asmodia very much wants to quit while she's ahead.

Carissa Sevar: Yep, all done, you can pursue your not-romance with Keltham or not as you wish as long as you're in good standing.

Asmodia: "I - probably want to go off and think about this."

"Do you already know whether you'd want an almost-asexual in your pattern, if other things worked out?"

Keltham: "I do not think that quickly any more than you do."

"By the way, I notice I have a pending question you didn't answer, about how somebody like yourself ended up in the group of girls that got sent here?  I'd otherwise imagine there'd be a screening question, like, are you liable to be okay having sex with Governance's sperm-harvesting target after a relatively short acquaintance."

Asmodia: This seems like a really bad question to even visibly hesitate on -

"I mean, I can still have high-Intelligence kids with somebody?  I did not plan on going the rest of my life never having sex with anyone even for purposes of having kids, and I was okay with having more sex than just the minimum for those kids."

She knows that's an unauthorized lie, Asmodia's judgment was that it would have looked very suspicious to delay to ask for authorization.

Carissa Sevar: Yep, fine.

Keltham: "I do have any additional questions about that, but should probably bother Carissa with them rather than you."

"You want I should go back downstairs myself and leave you in this nice room to think?"

Asmodia: "...yeah."

Keltham: He does!

Asmodia: ...she does.

Keltham: Actually Keltham is back, looking sheepish, and wants to know the classification status on Asmodia's (mostly)(a)sexuality.

Asmodia: It's not a secret.  Tell whoever.

Keltham: He's gone again!

Asmodia: Asmodia stares out at the coast, it's windy enough today that there's regular crashing waves, and she can, if she makes an effort, not think about anything at all.

She doesn't want it to seem suspicious, when her mind actually does go quiet from the perspective of listening Security.

Asmodia: When she legitimately hasn't thought much, for a short while, she imagines herself back in the Gardens of Erecura, in the midst of Dis, as is under the seal of Hell, and thinks.

Does Asmodia want to be married to Keltham, even if she never has sex with him, even if he gets all his sex from Sevar and Ione and Pilar?  It's an important question for reasons beyond the obvious.

Asmodia: She's pretty sure - though she has taken time to think about it - that the answer is no.

Asmodia: She wants to make fifth-circle and Teleport herself the fuck out of Cheliax and live the rest of her life answerable to nobody, is what she actually wants.  And then at the end of that, go to the gardens of Erecura forever, or go to Abaddon briefly.

Keltham may have neglected to explain the difference between aromantic and asexual, and Taldane certainly isn't helping out with words for such things.  But even so, Asmodia knows, she is not just sexually unattracted to Keltham.  She does not dislike him, and for certain she would choose him over every man of Cheliax; but there is nothing about the thought of establishing a household with him that appeals, compared to the thought of just walking away from everything.

Asmodia: Sevar thinks, obviously, that the trope theory is true.  What happened today must have just about nailed it down, from her perspective.

Asmodia: In reality, Asmodia doesn't fit that pattern at all.

Asmodia: And Keltham also doesn't believe it, because, so far as he knows, even if for different reasons, Asmodia does not fit that pattern.

Asmodia: Then if Cayden Cailean and Nethys are frantically scurrying around setting up the appearance of a dath ilani romance novel - and maybe it's not Asmodeus who is Sevar's patron, after all, even if she thinks that's Who -

Asmodia: The target they're trying to fool isn't Keltham.

It's Cheliax.

Asmodia: What will Asmodia do, with this thought?  Nothing, that she can think of that she ought to do, except to hold it secret behind her barrier.

Whether her Patron, whichever interfering god that is, is making use of her - or whether there is, as would be the moral of a dath ilani romance novel, someone somewhere in all of everything who cares - Asmodia is grateful, and wants more.  So whatever is happening around her, though Asmodia does not understand it, she will surely not destroy it.

Asmodia: "The asexual is the one who watches it all, is she?" Asmodia says out loud.  It's a perfectly fine thing for Security to report to Sevar.  "Sure.  I can do that."

dath ilan: (If an Ace is present at all, even with a prominent story role, she is not always a romanceable character inside an eroLARP.  There is aroace representation too.  Just saying.)

Nethys: Even Nethys can't tell what is and isn't a trope at this point.

The things that watch from orthogonal angles to ultimate reality now seem unsure which events represent selection for a trope, and which events are reality just unfolding under its own not-further-selected momentum.

Nethys: Nethys suspects that even the Tentatively Hypothesized Things That Put Keltham Where There Would Be Possible Tropes may not know for sure what's a trope anymore.

Project Lawful: PL-timeline:  Day 6 / Afternoon

Keltham: Keltham reconvenes his lectures, more aware than before that he is trying to teach in days what Civilization takes years to engrain when it forges a dath ilani; even if, yes, Civilization is teaching it to children rather than adults; yes, even so.

He may need to make more than one run on Probability in a lecture, if it's to be understood and used, as the other lectures Keltham taught were not quite meant to be used right away the same way.  And then go on conveying it in his everyday words and actions, as adults show themselves before children.

Keltham: From the other direction, this time; begin from the Law of Probability that would, if they were doing things in the right order rather than quickly, have been proven as the only possible Law that yields all of a collection of Law-fragments that would each have been motivated on their own.

The probability of an event is between 0 and 1:\X.  0 <= P(X) <= 1

Definition:  X \/ Y denotes "the event that X happens or Y happens or both happen".

Definition:  X & Y denotes "the event that both X and Y happen".

Definition:  ~X denotes "the event that X doesn't happen".

For every event, the chance that it both happens and doesn't happen is nope:\X.  P(X & ~X) = 0

And for every event, the chance that it either happens or doesn't happen is yes:\X.  P(X \/ ~X) = 1

If two events are mutually exclusive, in the sense that they can't both happen, the probability of either happening is the sum of the individual events' probabilities:\X Y.  P(X & Y) = 0   =>   P(X \/ Y) = P(X) + P(Y)Or more generally, if they're not exclusive, we can still sum them by subtracting their overlap:\X Y.  P(X \/ Y) = P(X) + P(Y) - P(X & Y)

Keltham shall first pause and call upon them to recognize that Probability generalizes Validity; the laws of logical reasoning, that are valid over every possible world, can be seen as a special case of reasoning with the probabilities of 0 and 1.

He shall then, by way of illustrating some of what is being skipped over, ask them what bad thing would happen to them if they tried to claim that some events could have a probability of 3 or -7.

lintamande: They are not immediately sure. 

"I mean, you can derive a bunch of silly things about the probability of all other events?"

"Yeah, like, things get more probable if you assert that a thing and the probability three event happen - wait, do they - that's not on the board but I'm pretty sure it's true -"

Keltham: Why, nonsense, the probability 3 event and the regular event could be the sort of things that never happen at the same time, in which case the probability of their intersection is 0.  Say, the chance that Keltham is holding a silver coin is 0.5, and the chance that Keltham is not holding a silver coin is 3.  The chance that Keltham is holding and not holding a silver coin is surely 0.

lintamande: No, that breaks the rule on the board about how the probability of a thing and not-that add to one.

Keltham: Pffft, rules.  What good do rules ever do anyone?  Rules just stop people from doing what they want, and are therefore, universally, bad.  If we're going to violate the rule about probabilities being between 0 and 1, let's violate the sum-to-1 rule too!  Who needs that rule - what bad thing happens to you if you violate that one?

You can't just go about justifying rules by appealing to other rules, there has to be a reason why anyone cares about any of the rules in the first place!

Ione Sala: The inevitable collapse of Asmodean sanity seems kind of hopeless for Ione to stop, actually?  Once you're paying attention and your ears have been attuned to listen, you start to notice how Project Lawful may be the most intrinsically doomed thing that has ever been tried in the history of Golarion.

lintamande: The reason for the rules is that they're the only set of rules that have the useful properties discussed earlier in the lecture?

Keltham: Nice try at guessing the password on his Forbiddance, but that's not how dath ilani education works.  Which of those useful properties fails at probability 3, and how?

Asmodia: Asmodia has been thinking about it.  "Someone's going to try saying that it means you can gain 2s instead of losing 2s in the scoring game, you're going to say so what -"

Keltham: "Gonna say it was a very depressing game and the prospect of being able to gain anything at all in it sure sounds nice, and, yes, I was waiting for somebody to try that line on me."

Asmodia: "After which Pilar comments that she liked the game the old way -"

Pilar : ...okay fine yes she was thinking that, so she's a good Asmodean, sue her.

Asmodia: "But mostly I think it will appeal to some principle you haven't shown us yet.  That'd be my prediction."

Keltham: "Well, invent the principle then."

"There's at least two lessons here.  The first lesson is noticing when you have no explicit idea why a set of rules has to be the way it is, and couldn't give a strong solid answer about what goes wrong, if somebody asks you, well, how about if the rules were different, how about if we break those rules?  It's closely related to the art of making sure that your beliefs mean anything.  The way of having math mean anything, if you are using that math for something and not just admiring it, is to say what ill fate would befall you if you used different math."

"And the second lesson is, Civilization didn't get to learn the principle that, yes, I haven't covered yet, by successfully noticing they didn't know it, and then sitting back in class waiting for a teacher or a god to tell them.  The ancestors of Civilization noticed the gap in their knowledge, some people tried to fill it in, somebody eventually succeeded, and that's why Civilization now knows.  You try.  Come up with some bad thing that happens to people who assign a 300/100 chance that something happens.  I'm not going to answer until I see somebody try, even if they fail, because I'd rather teach people to try and fail, then to teach them to wait for the teacher to answer."

Carissa Sevar: "Say there's a merchant ship, and you make 100 gold if it comes back and 0 gold if it doesn't, how much should you be willing to spend to send it? If it has a .5 chance, 50 gold - eliding that you want a profit, for the moment - If it has a 0 chance, 0 gold. If it has a 3 chance....300 gold?"

Keltham: "Go to the Overly Advanced Student Holding Cell next to Asmodia and use Message next time you're that far ahead.  Nobody else learns things if they just wait for Carissa to tell them."

lintamande: "She has a headband," someone mutters.

Carissa Sevar: She does and she loves it. 

Keltham: "And now she's in the Overly Advanced Student Holding Cell, so you can continue to learn things in advance of your own headbands arriving.  Also we should now have Fox's Cunnings to use if we run into a stumbling block, and I'm mostly thinking we should save them for more technical stumbling blocks, but if you feel like you have a thought and can almost complete it, you're allowed to request one, or use one of your own spells if you've got a Cunning hung."

Keltham: "But to generalize the point beyond merchant ships, the purpose for which we ultimately use our wordless senses of which things are more or less likely, is to divide up our few resources between the many things we could potentially try to do.  Not just limited resources like money, but limited time, limited attention; you can only act so often and only think so much."

"Tomorrow will go differently depending on whether Nidal has figured out our new location and attacks us again even with their god sealed up, or if, alternatively, we have an enjoyable day of lectures and me learning some magic and other activities.  In the latter case, Fox's Cunnings are quite useful.  In the former case, where Nidal attacks, Fox's Cunnings are less useful and spells for setting things on fire are more useful.  But again if it's a peaceful day, spells for setting things on fire are less useful."

"So how can we possibly plan, in such an uncertain world?  The best strategy if the universe is one way, is not at all the best strategy if the universe is a different way!  And we are uncertain and can never attain absolute certainty because it's not the sort of thing that's true in every possible world, and if it were we might make a logic error anyways.  Oh woe!  Oh alas!  Shall we just choose at random since no choice is perfectly defensible?"

"And the answer is, you put weights upon the different worlds that might be true, and figure out the consequences in those different worlds, and weigh those consequences according to their probability.  A thing that makes the scale from 0 to 1, more useful than the earlier scale from 1-12, is that 0 reflects not being at all concerned about the consequences to us in some world, because we think that reality just can't be that way, we multiply the weight of consequences there by 0 hundredths out of 100.  1 says that we're going to weigh the consequences only if that proposition is true, because we are certain of it; we're going to take all of those consequences as objects of concern, and not diminish them at all in proportion to their uncertainty and unlikelihood.  To be clear, we are never actually certain; even Nethys, Ione told us, reasons in probabilities, just more extreme ones.  But sometimes we are sure enough that it's not worth the cost of thought to weigh the other possibilities more finely."

"A probability of 3 is like saying that the consequences of something weigh on your mind three times as much, getting three times the share of your limited resources, as some possibility you were absolutely certain of; and if you try to cash out what that could even mean, you start getting results like the one Carissa talked about - that you spend 300 gold with certainty, in order to make back 100 gold with probability 3, because that outcome weighs three times as much in your calculations as if it were certain."

"Among the ways that we'd make our way to the corresponding law-Fragment if we were doing everything in slow careful order, would be to show that, if we're not going to end up going in circles in certain ways, we need to consistently weigh the possibilities we deal with, and make choices based on weights of consequences, and these weights of consequences end up looking like multiplying the consequences by their probability.  And then having gone through all that slow pathway, you'd be able to say, more generally than in the special case of merchant ships that have costs and profits measurable in gold, what ill fates will befall someone if they weigh a consequence three times more strongly than if it were certain."

"That's the principle you're missing, in this case.  I'm not actually going to cover that Law-fragment at least today, but I wanted to at least make clear what I was skipping; because someday in due time you're going to have to redesign Chelish education, and it's going to have to go back and fill in, not just that part, but all the other Law-fragments we're skipping that pin down and spotlight the Law of Probability."

"Or to summarize, and maybe to see it at a glance:  To see what bad thing would happen to you, if you assigned a probability of 3, you'd have to be using that probability for something and doing something with that probability, such as, for example, sending out merchant ships, or making a bet, or deciding how many of your limited spell slots to spend on preparing against a Nidal attack."

lintamande: Nods all around. 

Ione Sala: "Also if 300 out of 100 people with INT 15 could become fifth-circle wizards, you'd start with a graduating class of 150 INT 15s and get 450 fifth-circle wizards out of them.  Can I point to that example and say it's not allowed - is that an instance of the same principle?"

Keltham: "Interesting question!  And you might ask then, what if there's magic that can make three copies of somebody?  Maybe you just can start with 150 INT 15s and get 450 5th-circle wizards.  And, if so, what would it be like to be one of those wizards?  Should you then go around saying that your chance of making 5th-circle is 300%, and weigh the consequences of that three times as much as if you were certain?"

"This however would get us into 'anthropics', and we are not getting into 'anthropics'.  That, by the way, is a general slogan of dath ilani classes on probability theory:  We are not getting into 'anthropics'.  I'm not even going to translate the word.  As long as you don't make any copies of people, you can stay out of that kind of trouble.  That trouble-free life should be our ambition for at least the next several weeks."

Ione Sala: "I'm sorry I asked."

Keltham: "Under ordinary circumstances I'd say not to be sorry for asking, that's how people learn, but you did ask about 'anthropics' so instead I'll say, apology accepted."

Carissa Sevar: Shit now she urgently needs to figure out what an anthropics is. Any abstract concept that Keltham is jokingly terrified of is going to be relevant to her life very soon, it's getting to be a rule.

Keltham: "Though, I should also note, I might have to revisit that if it starts looking again like 'tropes' are going to be a thing, which, Carissa, remind me to tell you about this update later, I am increasingly convinced that they're just not."

Carissa Sevar: "I am glad to hear it," says Carissa.

Keltham: "Moving on!  I now introduce a new key definition, that of conditional probability:"

P(X◁Y)  =def  P(X & Y) / P(Y)

"For example, in the case of Int 15 wizards who make 5th-circle:"

P(INT 15) ~ 0.01P(INT 15 & 5th-circle) ~ 0.0002P(5th-circle ◁ INT 15) ~ 0.0002 / 0.01 = 0.02 = 2/100

"If we start with 100,000 Chelish citizens, there should be around 1000 of them with INT 15, and then 20 of those who become 5th-circle wizards according to the statistics I totally made up this morning, and so 2% of people become 5th-circle wizards conditional on them having INT 15."

"The symbol is easy to remember because you can imagine that, on the right side, it shows a wide pool of people with INT 15, diminishing on the left side to a narrower pool of people who have INT 15 and are 5th-circle wizards."

Thellim: So far away that there is no distance and no time between here and there, Thellim is trying for the first time to look up how statistics work on her new home planet.

The conditionalization operator is written "P(X|Y)" using a neat, symmetrical, vertical bar.

It doesn't weigh much against all the other bad news she's seen in the last day, but it is still not great news about how sane statistical mathematics is liable to be in this place.

lintamande: "So it's sort of like in logic, where you have a starting premise from which you can deduce further things according to rules, except instead of a starting premise it's a starting probability?" says Meritxell. 

Keltham: "I'm not going to put you in the Holding Cell for that, but only because I didn't actually ask the advanced question you just went and answered."

"Yes.  Though to state it more exactly, the right-hand side of the operator represents a starting set of worlds, such that we consider the probability of the left-hand side's event only within those worlds.  We are not interested in the probability that a random Chelish citizen is a 5th-circle wizard; the total contribution there would be greater from INT 16s, or so it sounds like from what Carissa said.  We're not interested in the probability that a random Chelish citizen is an INT 15 and becomes a 5th-circle wizard.  We're interested in the probability that, if we select a random Chelish citizen, and then narrow our focus to only those worlds in which the random selection produced an INT 15, what is the chance within those worlds that the person becomes a 5th-circle wizard."

"Having assumed this fact away, it indeed becomes a premise for further deductions, as you say, just as if we were asking about whether it's valid that 'Y implies X' and for purposes of that validity are allowed to just assume Y is true.  While asking about the probability that somebody becomes a 5th-circle wizard, conditional on INT 15, we have available the assumed fact of their INT 15-ness."

lintamande: Meritxell, who wants very badly to be in the Holding Cell, looks cheered about this.

Keltham: Keltham has deduced as much, but he's not putting her in there until it reaches the point where he estimates she's answering questions too fast and disadvantaging other students from learning.  That's what it takes to get put in the Holding Cell!  And for so long as Meritxell hasn't forced him to toss her in by threatening the other students with spoilers, she'll just have to try harder in order to get in.

Anyways, as a basic comprehension check, how about if everyone invents and writes down a conditional probability, including the underlying P(Y) and P(X&Y).  First, in a case you're allowed to just make up.  Then, a realistic case, something where you know, or can constrainedly guess, the actual statistics.  No extreme stats where it's 100% or 0% of something.  Raise an open hand if you're done, closed hand if you think you can't do it.  (He's not expecting the latter, but why trust what you can cheaply verify.)

Pilar : Pilar, who again has less practice than most Chelish citizens in her position with needing to constrain her own thought processes, gets it last; it takes her longer to work past her brain's repeated generation of forbidden suggestions that she can't write down for Keltham to check, like the probability that a citizen in Ostenso is a Lastwall spy.  Eventually Pilar does get a made-up example about the chance a 3rd-circle priest ever reaches 4th-circle, and a real example about the chance she scores in the top 10% of class given that she scores in the top two-thirds of the class.  She remembered and tracked this statistic because it determines who punishes who, but Keltham doesn't need to know why Pilar remembers it.

Somebody really should punish her for being slowest, but she can see about that later.

Keltham: Quickly checking confirms that everybody got it basically right, modulo Yaisa who divided the number of girls who became wizards, by the number of wizards, to get the probability that a girl becomes a wizard, which... Yaisa maybe just needs to actually think about the meanings of the numbers, instead of writing symbols?  Keltham was probably ever trained to do that as a kid, but he doesn't know how he was trained, it's the sort of thing that gets buried implicitly into learning something else.  Maybe visualize the scaffolding between the numbers and reality like you could see it with Detect Magic?

lintamande: Yaisa smiles like this is not at all the most horrifying thing that has happened since - well, she was going to say 'since Kuthites attacked' but actually getting something wrong which everybody else got right is more horrifying than that, and to top it off she's still incredibly confused about the concept here and imagining scaffolding isn't the helpful kind of advice at all. At...least....she's not going to be punished?

Keltham: All right, let's try plowing back into how parsing everything into probabilities works.  Once you've practiced these skills hard enough, they become mostly innate and you hardly need to resort to making up numbers in cases where you don't have numbers.  Keltham can think of occasions in the last few days where he's made up numbers, but he's mostly needed to do that because of literally landing in another universe, and then a lot of those occasions would be weird to use as examples.  There's a potential example from a conversation he just had with Asmodia, which is too weird to use, or so Keltham tells the classroom.  And another example just from today's lunch, when Carissa and Ione and Pilar supposedly all went off to get Invisibility copied and it was exactly the three most obviously special girls from a group of eleven girls even though 'copy Invisibility' isn't specialness-laden, but the hypothesis Keltham was actually updating is again too weird to talk about...

Actually, if Keltham thinks back earlier, there's a less weird example.  If you try to find a weird book at Ostenso wizard academy's library, so there's just one local copy, but most people wouldn't usually need to borrow it, what's the chance that it's already checked out when you first try to get it?  Everybody close your eyes, think about the probabilities in your experience, put your hand all the way down for 0, all the way up for 1, closed fist to defy the question.

lintamande: Why does he keep using examples that are relevant to lies. Maybe because everything's relevant to lies. Is lying here authorized.

Carissa Sevar: Yes, you can imply books are checked out of libraries more often than they in fact are. 

lintamande: The girls mostly put their hands somewhere around halfway.

Ione Sala: The back of Ione's mind is now calculating exactly how unlikely it is to randomly pick those 3 girls from a group of 12 and mostly getting 'really fucking unlikely what the fuck were you thinking' and while that was theoretically Sevar's responsibility to catch and Sevar made up the particular excuse she did, part of Ione still believes deep down that a senior Security is about to have a very unhappy 'conversation' with her about this.

It shows on her face not at all.  She still grew up in Cheliax.

Ione puts her hand a third of the way up; alter-Ione has been checking out weirder books than cleric spell compendiums.

Keltham: More agreement than he'd have expected?

"Okay to open eyes."

Ione Sala: "For the record, my estimate is for the average weird book I check out, not the particular weird book I think you're thinking of."

Keltham: Heh.  "Right.  Well, this happened when I asked Ione if I could borrow a compendium of cleric spells, and she said that the book existed but was checked out already.  I then considered two possible ways the world could be, and how likely those worlds would be to generate what I observed."

"In one possible world I could have been in, I reasoned, the library actually had plenty of books with all the cleric spells, but those books contained spells that Chelish Governance would rather I not know about, or Ione wasn't sure that was not true given poor general circulation of information around Project Lawful, so she told me there was only one such book and it was already checked out.  If the world is one where Chelish Governance is generally trying to keep me and my capabilities under control, how likely am I to be stonewalled on a book of cleric spells while they try to quickly print up a new one without all the spells they don't want me to know about?  My guess there was around 3/4, or 75% - it's not 100% because maybe they've already got an altered book printed, for example, and in that case they don't have to claim it's not there."

"In the other possible world, there's an ordinary library situation on which Ione reports truthfully.  Then we ask how likely it is that there'd really be only one book with a compendium of half the economically important magic, even if the library is mainly aimed at wizards, and also this book is already checked out.  In dath ilan that'd be very improbable.  Here, I guessed 30%."

Keltham is writing on the white-wall:

P(no-book ◁ Conspiracy) = 75%P(no-book ◁ Ordinary) = 30%

"Now, what is the Lawful way to think when you find yourself in that situation?  Can you say whether or not I should then think the book was being hidden from me?  Don't bring in all the other facts you know that might be relevant; just as a matter of math, in the Law of Probability, is there anything obvious you can do, any other conclusion you can derive, with the information written on the wall so far?"

Carissa Sevar: Why did she take this job.

(Because she's the only person who even might be able to do it, and that's worth at least three Wishes and a lot of spellsilver, to Hell.)

lintamande: "It depends on what you considered likelier previously," Meritxell says. "It's likelier than you thought before - though if I were running a conspiracy on you I'd not tell you Ione had magic library powers -"

Keltham: "Okay Meritxell, that's twice in a row, go to the Overly Advanced Student Holding Cell and use Message next time."

"And yes, that's a fair point about Ione telling me about her magic library powers in the first place, but all that stuff falls into the category of 'please don't bring in all the other facts you know'."

Keltham writes on the white-wall:

Have:

    P(no-book ◁ Conspiracy) = P(no-book & Conspiracy) / P(Conspiracy) = 75%    P(no-book ◁ Ordinary) = P(no-book & Ordinary) / P(Ordinary) = 30%

"This is as far as we can get by applying the definitions of terms we know, and it doesn't obviously let us derive any further interesting facts or quantities."

"Now, what I want to know is the chance that there's a Conspiracy going on or that things are Ordinary, given that I'm now nearly-certain-except-for-insanity-or-stranger-weirdness, by the way your language needs a shorter word for that, that I was told there was no book of cleric spells available in the Ostenso library.  We could write the quantity I'm interested in as follows:"

Want:

    P(Conspiracy ◁ no-book)    ----------------------------------      P(Ordinary ◁ no-book)

"Let's talk a moment about the meaning of that term I just wrote down.  First, in both the numerator and denominator, we're conditioning on being in a world in which I was told there was no book.  Second, starting from inside that world, we narrow it down, in the numerator, to the worlds where there's a conspiracy; and in the denominator, worlds where it's an ordinary library situation and an honest Ione.  By dividing these two numbers, we narrow them down into one number, and that one number is a quantity telling me the relative odds of the Conspiracy World and the Ordinary World; it's how many times more probable the Conspiracy world is than the Ordinary world.  This single quantity might say, for example, 'Conspiracy is twice as likely as Ordinary' or 'Conspiracy is one-third as likely as Ordinary'."

"Why phrase it that way, instead of just asking how likely Conspiracy is in an absolute sense, after observing no-book?  Why not ask for an answer that says, 'If I see no book, a Conspiracy is 20% probable' or some such?  Because to get an absolute probability for Conspiracy given no-book, I'd have to consider every other plausible hypothesis that competes with the Governance conspiracy, including, for example, that Cayden Cailean suddenly mind-controlled Ione to answer falsely, in a way that Governance had nothing to do with."

"By dividing the Conspiracy probability and the Ordinary probability, we can ask about the relative chances there, without dragging in all other possible hypotheses involving say Cayden Cailean."

"Mathematically speaking, what further information do I need to derive that quantity I want, from the quantities I have?"

Need:

    ???

Asmodia: Asmodia quickly expands definitions on her scrap paper, and cancels terms a moment later:

P(Conspiracy & no-book) / P(no-book)           P(Conspiracy & no-book)---------------------------------------------------    =    -----------------------------------  P(Ordinary & no-book) / P(no-book)                P(Ordinary & no-book)

Shortly after, Asmodia calls out "Prediction" and Messages Keltham, to which Keltham nods.

Carissa Sevar: Carissa is distracted by being annoyed with Keltham for being too hard to deceive. Why couldn't they have gotten a stupid dath ilani. Why couldn't they have gotten a properly Evil one. 

- if she doesn't learn this stuff and learn it very thoroughly then she's going to lose. She wants to know how many times more likely a conspiracy is if there's no-book. It's not a real problem to do with a real conspiracy, it's just a bunch of meaningless symbols on a page and she needs to cancel some terms and -

"Prediction."

lintamande: Meritxell is not nearly as sure of how you'd go about this on the math side but she knows the feel of the answer already. the thing you want is how suspicious to be, and obviously to know how suspicious to be you need to know how probable the thing you're suspicious of is, if someone says there's a stray dog that's less suspicious than if they say there's a dragon. And she just has to make the numbers on the paper say the thing that's obviously true. 

"Prediction."

Pilar : The concept of being so Lawful that you can figure out Laws authority hasn't told you about, is one that Pilar is still struggling with.  There is little she will not do for her Lord Asmodeus, however, and it has been made clear enough to her that this work is important.

There's also not many ways you can go down this path, if you only do the derivations that are allowed, and that, Pilar is good at.

P(no-book & Conspiracy) / P(Conspiracy)          P(no-book & Conspiracy)        P(Ordinary)-------------------------------------------------------    =    ----------------------------------  *  --------------------    P(no-book & Ordinary) / P(Ordinary)                 P(no-book & Ordinary)        P(Conspiracy)

She struggles momentarily what to do from there, but then she gets it.

P(no-book & Conspiracy) / P(Conspiracy)      P(Conspiracy)         P(no-book & Conspiracy)         P(Conspiracy ◁ no-book)-------------------------------------------------------  *  --------------------   =   ----------------------------------   =   -----------------------------------    P(no-book & Ordinary) / P(Ordinary)            P(Ordinary)              P(no-book & Ordinary)            P(Ordinary ◁ no-book)

"I have the answer in symbols, but I'm not quite sure what it means now that I have it," Pilar says.

Keltham: He'll wait for others to catch up, and then explain.

The key quantity needed is P(Conspiracy) / P(Ordinary), or any other quantity which determines that one, which for this example means how likely Keltham thought Conspiracy versus Ordinary was before the absent-book observation.  Say, if Keltham previously thought a Conspiracy was 10% as likely as the Ordinary world, and then he saw the no-book observation, which in Keltham's estimate was ~2.5 times as likely if there's a Conspiracy than in the Ordinary world, the result is that a Conspiracy then becomes 25% as likely as the Ordinary world.  So it goes from 'a tenth as likely' to 'a quarter as likely'.

Meritxell's observation is that Keltham also ought to take into account that Ione told him about her book powers in the first place, even though that makes it harder for Governance to control Keltham's information and potentially makes him suspicious if they try to.  Let's say that's 1/20 as likely in the Conspiracy world than in the Ordinary one - not impossible, there's weird side possibilities where that could happen because Governance wasn't on the ball there, but yeah, sure, unlikely.  So if Keltham took that argument at face value, he'd then multiply 'Conspiracy a quarter as likely as Ordinary' by 'observation a twentieth as likely on Conspiracy as Ordinary' and get 'an eightieth as likely'.

But then of course we have to consider how the three most obvious interesting-background girls, Carissa, Ione, and Pilar, all disappeared at lunch today, supposedly to copy Invisibility spells.  Since Invisibility has nothing to do with interesting backgrounds, the probability of randomly getting that set of three women selected from twelve possibilities is 12 * 11 * 10 / 3 * 2 * 1, or 220:1.  So the new odds of Conspiracy over Ordinary are 'an eightieth as likely' times '220 times as likely' or a bit less than 'three times as likely', 2.75 times as likely to be exact.

Keltham should therefore now consider himself 2.75 times as likely to be in a Dark Governance Conspiracy world than an Ordinary world.  Does that reasoning sound correct to everyone?

lintamande: .....no? 

Keltham: "Oh, and this should hopefully be obvious from lesson context, but if you know an actual real story that totally refutes that whole argument - Ione, Carissa, Pilar, or anyone else who happens to know for sure - don't just blurt it out yet."

Carissa Sevar: She has a lie prepared but fine, then. "Okay, I won't explain, but it seems like it's some kind of error for that to be two hundred and twenty times likelier if - oh, wait, I can formalize that, there are possible nonrandom explanations for the event which aren't the specific theory you have."

Keltham: "Carissa, even if you don't just tell them whatever the exact story is, you're not allowed to tell them the abstract form of the answer generalized from your knowledge of whatever the exact story is.  You, Ione, and Pilar are all sitting this one out."

"Asmodia, Meritxell, you're allowed to answer too, this time, after a one-minute pause.  Because an obvious avenue for this challenge, in advance of formalizing anything, is to try to say informally what's wrong with my reasoning, and then formalize it.  My guess is that you two don't have as much of an advantage at informal argument, so it's safe to let you out of the Holding Cell temporarily; I could be wrong."

lintamande: "Carissa has an interesting backstory?" says Gregoria.

Keltham: "Apparently not on the same level as Ione and Pilar by Golarion standards, but if you look at it from my perspective, randomly landing next to an INT 18 third-circle, with better spellcraft than fifth-circles with intelligence headbands, who can scaffold to spellsilver six feet away etcetera, is still a pretty interesting background even leaving out some other things."

"Though there's also the seed of a stronger counterargument there, if you want to double down on it and think you can translate it more into the language of probability."

lintamande: "Any wizard who's the staff wizard for their unit at the Worldwound is going to be really good at something," Gregoria says. "If you're walking down the street and meet someone that cool, something weird happened; if you wander into a random fortress at the Worldwound it's not. ....I don't know if that's in the direction of the stronger counterargument. It just feels like you're double-counting or something. And if the group had been different people, and later you'd discovered, I don't know, that I'm the bastard daughter of the Baron of Arenys, then you could say that was proof of a conspiracy too."

Keltham: "I agree that's something to be wary of in general - you don't want to look at what happened, and afterwards draw an exact category around it.  In this case, though, I had in fact formed Carissa, Ione, Pilar, and Possibly Asmodia as a large distinguished mental category, in advance of seeing Carissa Ione and Pilar vanish mysteriously at lunch.  It wasn't at all drawn up afterwards, in this particular case."

"Not to completely throw your fine argument out the window, however, let's say that the Conspiracy hypothesis really allowed for two possibilities:  First, that Carissa-Ione-Pilar would vanish at lunch, and second, that Carissa-Ione-Pilar-Asmodia would vanish at lunch.  So we now have the new probabilities," Keltham writes some more.

P(Carissa-Ione-Pilar ◁ Conspiracy) = 1/2P(Carissa-Ione-Pilar-Asmodia ◁ Conspiracy) = 1/2P(Carissa-Ione-Pilar ◁ Ordinary) = 1/220     =>P(Conspiracy ◁ Carissa-Ione-Pilar) / P(Ordinary ◁ Carissa-Ione-Pilar) = 1/80 * (1/2 / 1/220) = 1/80 * 110 = 1.375

"So in the light of your new argument, I shall concede that the Nefarious Governance Conspiracy is only half as relatively likely as I previously calculated, 11/8ths as likely as an Ordinary world, not 22/8ths as likely."

"But this was surely the only error in my calculations and my totally Lawful argument; I doubt you can find any others."

Part of Keltham's brain also wants to start tracking the possibility that Gregoria is in fact the 'bastard??' daughter of the 'Baron??' of whatever, and Keltham tells it to shut up, either they'll end up dating or not.

lintamande: "If they were a conspiracy, probably they wouldn't sneak off right in front of you very suspiciously," says Yaisa.

Keltham: "Clearly that's exactly what they want me to think."

lintamande: Yaisa has absolutely no idea what to make of that.

Asmodia: Asmodia's minute is up, now.  And during that minute, she's also thought about what her - Sponsor? - probably wants, from this whole situation.  And while Asmodia's conclusion is mostly that she doesn't know, Ione did foretell the Zon-Kuthon attack and Pilar threw herself in front of Keltham.  That's some evidence - Asmodia's not trying to Probabilize it right now - that her Sponsor does prefer that Project Lawful continue, rather than shutting down.  So she's not hindering her Sponsor's work, probably, if she points out flaws in Keltham's argument here.

"Even if that is what they want you to think, you can't reasonably say that the Conspiracy premise predicts with total 100% probability that some set of girls will mysteriously disappear at lunch," Asmodia says.  "There should be a third possibility, that nothing happens."

Keltham: "But that possibility didn't happen, so I can eliminate it from my calculations now."

Asmodia: "If that were true, you could eliminate the Carissa-Ione-Pilar-Asmodia possibility, since it didn't happen, and leave Conspiracy putting 100% on Carissa-Ione-Pilar again, and then Ordinary would also put 100% on that since everything else didn't happen."