Ione Sala: "Context you're missing," Ione says, when the demonstration is over. "That's absolutely ridiculous fucking bullshit, most sixth-circle wizards couldn't do that. HOW."
She is guessing that Sevar does not, in fact, want her to hide her reaction here.
Carissa Sevar: "Well, you know, I was very motivated. But yes, Abrogail said she'd never even seen anyone try that, much less succeed at it. It's fun, it's kind of like tightrope-walking with magic."
Keltham: "I would no doubt be greatly impressed if I had anything like the skill or experience myself to appreciate how hard that was. I'll do my best to avoid predictable updates in my more abstract beliefs about you? But I suspect there's a visceral appreciation of this Difficult-Seeming Impressive Trick that I won't get for a while."
He doesn't know why they wouldn't tell him, if what he now suspects is true, but he's curious enough about that very question to keep quiet and see how it plays out.
lintamande: "So what did you do to get the Queen's attention," says Meritxell flatly.
Carissa Sevar: "Ah-uh, she specifically said to me she didn't have time to do this for all Project Lawful. Though our own High Priestess here might be worth a try."
Ione Sala: She hopes to Nethys that Meritxell is only pretending to think that's a good idea for alter-Cheliax reasons. Ione doesn't need dangerously suicidal people around her books.
Keltham: "I am missing so much context right now, I can tell."
Asmodia: Really!? Do you think?! Shit, isn't that High Priestess supposed to be talking to them all later?
Carissa Sevar: "...I can try to explain but I don't actually know what your question would be. Meritxell was asking if there's a way to get in on my incredibly fascinating sex life. Regrettably the Queen of Cheliax does not have time to provide such a hands-on education to all of us. However, the High Priestess Subarachs, who is on site to provide spiritual guidance to the Project Lawful girls, has some of the same expertise, which is why she was able to advise me on recovery, so if anyone wants to explore the space of highly motivated magic practice, they can ask her. - except me, of course, I'm yours."
Keltham: "Maybe once I know Jacint better, if I turn out to feel that way? But taking that slowly. I think I was sort of pushing things, the rate I rushed through everything with Abrogail, and in actual fact was leaning almost entirely on Abrogail being hot and seeming much more sensible than I was led to fear, rather than really having very much sense of her as a person."
Ione Sala: She doesn't know any of these people, she's just eating here because it's near her library.
Carissa Sevar: "There's no hurry. If you gave me to the High Priestess today she would just give me a book to read, anyway.
Or, you know, you could learn how to make girls shatter in your hands and come out of it masters of new kinds of magic yourself. No hurry on that either."
lintamande: "Can he learn that?" says Meritxell doubtfully. (doubt subtype: flirtatious). "Most people couldn't be the Queen of Cheliax even if you put a crown on their head and sent an erinyes to advise them."
lintamande: "Keltham isn't most people," says Yaisa.
"Are we, uh, doing a lesson today," says Peranza.
Keltham: "I was thinking Law of Probability, maybe also Law of Utility depending on whether I can teach them apart or only together."
"And, who knows, maybe I'll give learning that a shot at some point." Yes 'shatter' sounds bad, but it does not look bad if Carissa being so visibly happy is the outcome of whatever it actually means. "How many hours of practice are we talking about, assuming I have proper reference books and expert guidance? Three? Seven?"
lintamande: Blink blink blink.
"I think it's like....a thousand years, in Hell," says Meritxell. "But some people are fast learners."
Keltham: "To be clear, that is roughly what I was figuring."
"Also, checking model, afterlife people learn a lot slower than people in Golarion, it's just that they have all the time."
lintamande: "...I don't think they learn a lot slower?" Meritxell says. "I think you start out disoriented and it can take a while to get back to what you were capable of as a human but in principle eventually you're Contessa Lrilatha and I expect she'd learn, say, a new language, faster than I would."
Keltham: "Now that I think about it, there was something - crystalline, about Lrilatha, I'm not sure how to put it into words - I'm not sure I'd ask her to research a new field of study, she can be one kind of person flawlessly and at speed but - maybe there's other ways of thinking she can use, that I didn't see, we were always meeting in formal settings - I'm not sure Lrilatha comes across as something truly greater than any dath ilani, who'd defeat any of us in every contest of skill? Just someone who spent a thousand years practicing a collection of things and is now unmatchable in those places - Taldane does not have any of the words or concepts I want to use right now. But maybe that's the difference between what she is, and a god."
"Is it known what Lrilatha turns into in another ten thousand years?"
lintamande: "- not by me."
Carissa Sevar: "Gorthoklek, who you met, is a more powerful and intelligent kind of devil but I don't know if he's specifically a kind of devil downstream of Contessa Lrilatha's kind."
Keltham: "Didn't see much of him or how he thought, yeah. He looks more alien, for sure..."
"I suppose I've got time to figure it out, but I will want to figure it out, before I decide whether the afterlife here is really someplace I want to spend my own afterdeath, or if I'm supposed to figure out how to make the Starstone work reliably, or take some third option."
Carissa Sevar: What third option, become Baba Yaga and wander the multiverse in a house with legs, returning only occasionally to eat your children?
- not the time. How about instead they learn about Probability.
Pilar : Pilar messages her on the way out asking for clarification if everybody in alterCheliax is supposed to be calling their Queen 'Abrogail'.
Carissa Sevar: In alterCheliax it's a thing you might call her if you know her personally, not something people who know her only as the Queen would call her, though if they did they would just get an etiquette lesson rather than being promptly executed like in real Cheliax.
Pilar : She danced with one of my guests at a party I threw, does that count?
(This was approximately 24% of Pilar's total accumulated stress from the previous day.)
Carissa Sevar: She what now.
Carissa Sevar: Keltham does not know about that party, so, no. Even if Keltham knew about that party, it's not really the right kind of acquaintance. If Abrogail ever kisses Pilar gently while turning her to stone to deny her Hell forever then Pilar can call her Abrogail.
Pilar : Acknowledged.
Pilar really wants to get debriefed about yesterday by the proper Authority and is not above using blatant lures to accomplish this.
Halfling slave #958245 "Broom": If lessons are to restart, Broom will be there and trying to make sure nobody destroys the world.
Ione Sala: ...these weird people may be permitted to enter her library's study hall, but had better behave themselves while in it.
Asmodia: If Asmodia came back with anything at all, besides superpowers, it was with some practice in setting aside distractions and focusing. She's ready, and though she doesn't understand the meaning of all this, she's feeling a lot more motivated to grasp whatever she can now that there's any reason that anything matters.
Pilar : It's disorienting to think that this quiet part is the part that really matters, and that all the meetings with intelligence services and confrontations with paladins and the Queen dancing in her ballroom are just a distraction.
Carissa Sevar: It feels strange to be back at this, as if it's a habit from another world, even though it's actually only been two days off, and normal schools give you two days off sometimes, like after exams before the start of the next term.
She has her Unseen Servant take notes for her. Because she's a fourth-circle wizard.
lintamande: Meritxell sits in front. She was tipped off this morning that she needs to meet the High Priestess because Keltham might want her and she's going to make damn sure he does want her, by being the smartest.
Project Lawful: PL-timestamp: Day 5 / Morning
Keltham: So now, hopefully, they're getting to the good part! Previous stuff was just sort of trying to show you what Law is at all, like with Validity, and some stuff that seemed like a good idea for Cheliax to know very early on for bargaining purposes, like heredity and bargaining. The Law of Probability is starting to get into stuff you use all over the place!
And if he'd been thinking ahead properly, Keltham would've made sure that everybody got tapped with an Owl's Wisdom at least once before they started getting lectures like these. Probably they can get away with doing that tomorrow, one more day's lecture shouldn't set up too much triggerable cumulative enlightenment. Keltham is saying this out loud right now because he keeps forgetting to set that up.
Anyways! Does Cheliax already know anything about Probability, the mathematics and Law of uncertainty? Anything he can build upon, or conversely, needs to refute and redo?
lintamande: They know the failure chances for certain kinds of magic that have somewhat reliable failure chances and happen frequently enough you can record how often the failure happens, like Augury or teleporting off a picture.
Carissa Sevar: "And merchants know the failure chances for more complicated things than that, like the odds a ship you send to Casmaron will make it back, which uses past voyages to Casmaron but also the state of the ship, and the state of the seas, and the season, and the competence of the captain. If you're bad at guessing then you'll lose all your money."
Keltham: Do they perchance have any known mathematics of probability which involves... more than one probability at a time, or two probabilities that relate to one another in some way?
lintamande: Maybe merchants have a clever way to do merchanting but it doesn't come up in wizard education, if so.
Keltham: Keltham is fairly sure he saw this class - admittedly, this was a while ago - being able to solve problems like 'If you randomly arrange four girls including me, what are the chances I'm second in line'. He was not especially expecting them to be balked by 'If you randomly arrange us two times, what's the chance I'm first in line both times?'
lintamande: Well, says Meritxell, the chance it's the same girl first in line both times is one in four, and that splits out into me-both-times Ione-both-times Pela-both-times Jacme-both times, each of those taking a sliver of the same size, so it's one in sixteen. ....but that's not applying a known Rule of Probability taught in school, it's just kind of obvious.
Keltham: "I suppose at least there's nothing to unlearn."
Keltham: Suppose that instead Keltham asks how often they are ever uncertain of anything, in the course of their daily lives. Not in a mathy way, just unsure about something.
lintamande: ....most of the time? Especially since the project started, since it makes life very unpredictable.
Keltham: "Well, for purposes of concrete examples, is there something anyone can name that they're unsure about right now, or that you were recently unsure about today?"
Asmodia: She's definitely very uncertain about THAT but THAT is SECRET so she can't talk about THAT...
lintamande: Jacme is not sure if Pilar really went to Elysium. Can't say that.
Meritxell is not sure if Keltham's going to ask her out. Can't say that.
Yaisa heard that the reason they had the Grand High Priestess on site was that by policy either she or Carissa must be in the room with Keltham at all times, and she's not sure if it's true, but she definitely cannot say that.
Gregoria heard that some of the other girls had to train their impersonators this morning. Can't say that.
Carissa Sevar: "I'm not sure whether Asmodeus anticipated Zon-Kuthon trying to kill you and whether He let it happen in order to have all the gods in consensus around sealing Zon-Kuthon."
lintamande: Well you can say that kind of thing if you're Carissa Sevar.
Keltham: "Actually, now that you point it out, we already think that the gods on our team saw a dominant probability of that happening. Which demands the question of why, if it was already that predictable, all the other gods couldn't predict it too and first-strike Zon-Kuthon instead of waiting for him to attack."
"But that example seems vastly overcomplicated? Literally the next thing I'd have to talk about, to walk through my reasoning about that question, is Law of Probability that a dath ilani kid wouldn't get until three years after today's layer, about whether or not gods should ever disagree about predictions like that."
"Can you think of an example much more mundane? Like, not so much gods as... scrambled eggs."
lintamande: "...I'm not sure if they'll serve duck at lunch," Meritxell says.
Keltham: "Okay, now everybody think of, but don't say, a number to represent the chance there's duck at lunch. And nobody's allowed to go to the kitchen and tell them to do that or not do it, I hereby declare that the bad kind of cheating."
"Raise your hand when you've got your number, and once everybody has raised their hand, we'll go around saying the numbers." Keltham raises his hand immediately; there's been duck at 2 of the previous meals he's had, of which he thinks there were around 12 but he's not going to count, and he is so ignorant of Golarion that nothing else could possibly figure into his calculations.
lintamande: The students take longer but not that much longer, and turn out mostly to have put down numbers between 4 and 6.
Keltham: "So my number was going to be 1/6, but I'm guessing that in your terms that number should've been 6, because the number you gave means, like, 1 out of how many chances? Am I interpreting it right? So a number of 12 is half as likely as a number of 6?"
lintamande: ....mostly they were imagining it was a scale where, like, 1 meant 'very likely' and 12 meant 'very unlikely', except that many of them were imagining it as the exact opposite where 1 meant very unlikely and 12 meant very likely.
Keltham: Sure, he can work with that. If anything, it might be more useful as a gentle introduction than if they'd invented the same system that dath ilani kids never invent because they just grow up with it; a 1-12 scale has some properties but not others.
"Should've seen this part coming and asked earlier, but, anyone got a simple public randomness source, like for generating a 0 or a 1 both with equal probability? Could literally just be some physically symmetrical object that you can spin and have it fall on one side."
Carissa Sevar: "I have coins. I don't know if they land on both sides with equal odds but it's probably pretty close."
Keltham: "Can I borrow one for the lecture, and is it okay if we call the borrowing term short enough that it rounds to 0% interest?"
(It briefly occurs to him to wonder if owning Carissa would mean he transitively owns her stuff, but he quickly dismisses this thought as obviously insane; if you had that kind of relationship, it would be one where she broke oaths and went to Abaddon on request.)
Carissa Sevar: "....yes."
lintamande: What kind of relationship do they have.
Carissa Sevar: Have a gold coin.
Keltham: Keltham borrows the coin at 0% interest! That's the kind of trusting relationship they have!
(Anyone who recognizes Abadar's symbol should really know better than to ask this.)
The gold coin looks like the other 600 instances of this coin that he owns, with a picture of Abrogail's face on one side, and on the other side 'Sworn by Hell to be pure'. At some point he needs to ask what Hell is swearing Abrogail to be pure about, but that's not important right now.
On close examination, a coin does look sufficiently physically symmetrical, with enough lingering asymmetry for identification purposes, to serve as a randomness source if spun.
"Okay, so this coin can land 'Abrogail' or 'Text'. Now... actually, something else first..."
"First, I want you all to rescale your old lunch duck numbers to a 1-12 scale where 1 is super unlikely and 12 is super likely, so we're all on the same page about what the scale meant. If you were picking a lunch duck number that meant something totally else, scale it instead."
"Raise your hands when you've done that, then let's say our commonly-scaled numbers once we've raised our hands."
"Oh, and don't update your estimate off what other people thought, this is just supposed to be your original estimate, but we're making sure all estimates are on the same scale."
lintamande: 3, 4, 4, 6, 4, 6, 6, 6, 8, 7, 4, 5!
Keltham: And his is 3!
Now, again without taking others' opinions into account - especially considering that people might be using different real meanings for their scales, so who knows if anybody really disagrees - consider the chance that there will be duck for lunch, AND when Keltham spins this coin, it will fall Abrogail's-face-upward. In other words, both things have to happen, so if the coin lands text-up, it doesn't matter if there's duck for lunch or not, the combined event didn't happen.
Generate new numbers for this combined event, same 1-12 scale from very unlikely to very likely. Please stick to your original opinion and original scale, rather than guessing what others mean by their numbers and updating off those.
Raise your hand when you've got it, then everybody says their numbers.
lintamande: 2, 2, 3, 2, 4, 3, 4, 3, 3, 4, 2, 2
Keltham: "And mine is 2."
"You may recall that shortly before the gods went to war - to be clear, I don't think there was actually a direct connection as such - I talked a bit on the Law of Dividing Gains From Trade, and one of the constraints was that identical agents receive identical pay."
"You've now generated two numbers, one for the chance that we have duck at lunch, and one for the chance that we have duck at lunch and that when I spin this coin it will land Abrogail's-face-up. Raise your hand open if you think you could state an aspect of Law connecting these two numbers, raise your hand closed into a fist if you've given up on doing that."
lintamande: Most of the hands go up into the air open, after a bit of hesitation.
Keltham: He'll give a half-minute to anyone who doesn't have their hand raised in either way, and then ask people with raised-open hands to state whatever Law they had in mind when they raised their hand.
lintamande: "...our numbers should have gone down. Because now it's two things that have to go right, not just one."
"They should have gone down by half," says Meritxell.
Keltham: "Whether they go down by half depends on what the scale means. Mine went from 3 to 2, because I'm taking the 1 of the scale to mean that something absolutely can't happen, and equal intervals to represent equal amounts of chance, so halving the interval from 1 to 3 gets me the interval from 1 to 2. But it's fine if somebody else is interpreting their scale in some totally different way!"
"In fact, the aspect of Law I'd propose to govern here is that, when you have two events that both need to happen, the chance of that happening, cannot go up compared to the chance of just one event happening."
"Ione, for example, could've been tipped by the Whatchamacallit of Nethys that this coin is definitely going to land Abrogail's-face-up, in which case Ione could just give the exact same number she did before for the duck-lunch part. But even Ione's number shouldn't go up. By the way, Ione, thanks for being you, your mere presence here substantially expands the space of immediately relatable scenarios I can use for probability-theoretic examples."
Ione Sala: "Thank you, I think."
lintamande: The students seem persuaded that the number cannot go up.
Keltham: "Now, for the next demonstration... actually, task to run simultaneously while that's in progress. Carissa, can your magic writing thingy copy what I write down on one paper scrap, to other paper scraps, without you knowing what was written?"
Carissa Sevar: "There's supposedly a rare spell for that but Unseen Servant can't do it unfortunately."
Keltham: "Noted, worth talking to Acquisitions about that or an item because this won't be the last time we run into this issue."
"For now, though, I first want to establish a common scale of probability before the next demonstration. Please think of the chance we have a beef dish at lunch," that'd be around 3/12 in his own guess and memory, "on a scale where 1/5 means the same as the chance that you're first in line in a randomized line of five people, or 1/10 means the chance is around the same as first in line among 10 people. If you're thinking something like, it's between 1/3 and 1/4, you're allowed to say 1 over 3-and-a-half, or even say 7/24, but you don't need to go complicated if you don't have a very exact notion of beef-lunch probability."
Raise hands when you have your number; when all hands raised, articulate guesses. Keltham isn't tracking this one closely, he just wants to check that they're now working to an understood common scale of probability.
lintamande: They do seem competent to use the scale, and to mostly assign beef-lunches between a third and a half chance of occurring today.
Keltham: (Encouraging! Like, not super encouraging or anything, but it could've gone wrong, and it didn't.)
Next, Keltham is going to distribute two propositions each to half the girls, to be assigned a probability on this kind of scale.
He'd be making 6 copies of each proposition, for everyone to look at privately, if he had easy copying. Since he doesn't, he'll give each group a piece of paper to be passed around among themselves, and everybody writes down their own answer individually, on the same common scale they just used for beef-lunches. Don't discuss it among yourselves and especially don't show your question to the other group.
Don't worry, it won't be a complicated proposition. It's something that happens around here about a third as often as they have beef at a meal, going on his own memory.
On this occasion they will not-really-pseudorandomize by taking alternate girls from among 'desks', that is, if they were to be numbered in a seating chart, evens would go to one side of the room, odds to the other side, starting from Meritxell. Can they sort themselves out while he writes the two propositions?
lintamande: Here are Meritxell Jacme Pela Peranza Ione and Tonia, and here are Carissa Asmodia Gregoria Pilar Yaisa and Paxti.
Keltham: Cool! Keltham is writing on two scraps of paper while that occurs.
Meritxell et al get:
Chance over next 1 year that another god attacks Keltham, starting another god-war.
Carissa et al get:
Chance over next 1 year that another god-war starts.
They can take a minute to think, not much longer please.
When they're done, they can put their slips into two heaps. Don't look at each other's propositions yet; Keltham will announce both groups' probability-sets first.
lintamande: This is VERY STRESSFUL.
Security relays to Carissa that several girls are thinking whether to lie and if so what lie they're supposed to give.
Carissa Sevar: This seems like PRECISELY the kind of situation where the lies would be discovered because they would have the WRONG UNDERLYING MATH SOMEHOW. Tell them NOT to.
Keltham could of course ask questions like these they'd all have no choice but to lie about, but hopefully first they can learn a bit more of the Law...
She puts down 1/3. The rest of her group puts it lower: 1/8, 1/4, 1/4, 1/10, 1/20.
The other group has 4/5, 1/4, 1/2, 1/3, 1/2, 1/8.
lintamande: The 4/5 is Meritxell, reasoning that Keltham has been here three days and started one godwar so what are the odds they'll make it through the entire next year without a second one.
Keltham: Keltham announces these results! Whatever Group Evens (Carissa) was asked about, it was clearly something pretty unlikely; while whatever Group Odds (Meritxell) was asked about, it was clearly much more likely.
Okay, compare your propositions now!
So, all y'all consider yourselves to be 'Lawful' Evil, huh.
lintamande: ....wow, that's -
Carissa Sevar: It's a test you can't lie on, is what it is (though also even if you are telling the truth if you're bad at truth you'll get it wrong).
lintamande: "Can we argue with the other group about who is right?"
Keltham: "Sounds like fun. Five minutes."
lintamande: "Keltham started one godwar in his first three days of being here so I don't see how we get through an entire year without another one," says Meritxell.
"Well, that was with Zon-Kuthon and there's not another god who almost wants to destroy the world. Except Rovagug, and someone'd have to let him out."
"Well, maybe someone'll do that," says Meritxell. And smugly: "though I wouldn't give four in five specifically for that."
"A god wouldn't have to almost want to destroy the world," says Pela. "We're changing it enough they could've been really in favor before and still turn out against now. Like....Urgathoa, if Keltham cures all diseases."
"Wouldn't she have figured that out and fought with Zon-Kuthon?"
"Do we know she didn't?"
"Well if she did then that's not another godwar in the future."
Keltham: "Okay, actually, you know what, on second thought, everybody shut up and my apologies for not thinking ahead faster about what might be a dangerous line of thought. I suspect that properly this conversation happens between myself and the Grand High Priestess in a heavily screened room. Nobody repeat the name of that god you just mentioned until cleared to do so."
He wants to tell them not to think it, but has a dreadful suspicion that this would be a counterproductive instruction for non-dath-ilani.
lintamande: - solemn nods and immediate silence.
Keltham: "Going right back to Probability, one thing I'd be enthusiastic to test is whether devils make the same error. If we try this on twelve of whatever Gorthoklek is, do they make the error? Twelve Lrilathas? Twelve of whatever devil said hi to Asmodia when she showed up? Twelve people who've been in Hell ten years, fifty years, a hundred years?"
Carissa Sevar: " - I bet not, for full devils. I'm less sure about new petitioners but we could, actually, ask Hell to check for us."
Keltham: "Do you know how expensive that is to ask? Also, doing this with 144 subjects is more reliable than 12 subjects, if it's not much more expensive to run a larger test on the other side."
Carissa Sevar: "No idea how expensive but we could ask the High Priestess. I think most of the expense would be communicating the instructions so larger's probably fine if we can do it at all."
Keltham: "If we can batch questions more cheaply then I have additional questions. Such as, for example, whether devils already knew about where the balance comes from between men and women, and weren't allowed to say. Or we could find that the younger devils don't know it until we tell them, but the older devils already know it, which would imply that information is stratified within Hell the way that it's stratified between gods and Golarion."
"If Lrilatha and Gorthoklek are past this fallacy, they presumably watch people committing it every 3 minutes, but are not allowed to say out loud what all the humans are doing wrong. Whatever rules prevent them from showing you what I just showed you, those rules are a key part of the foundations of order for Golarion. I want to know what those rules are. I want to check if I can maybe snap them over my knee in five minutes if I come at them from the right angle."
"Like, say, maybe there are things that, say, Gorthoklek isn't allowed to tell younger devils, but Gothoklek is allowed to point out those pieces of knowledge to me because I already know, and then I can tell one younger devil that, and they can tell others."
"Of course, before doing that, it might be good to know why those rules existed in the first place."
Carissa Sevar: "I don't know the deep secrets of Hell but my prediction would be that Contessa Lrilatha gets it right the way my father might get it right because he does a lot of guessing which ships are going to be profitable, and he doesn't know a rule he could tell me about, but he's pretty good at what he does. And Contessa Lrilatha would be better but still like that. Maybe not, though."
Halfling slave #958245 "Broom": Broom is, without showing any outward sign, trying to pray to determine whether his goddess wants him to kill Keltham yet. As always there's no response, leaving matters up to his own best judgment.
Keltham: Keltham has no particular idea that he might be close to death!
"Well, that result would be interesting from a completely different angle. Because if Asmodeus does not explicitly know that thing I just showed you, I will be really surprised. Which would mean there are things I know that Asmodeus can't tell Lrilatha."
"...I'm actually just going to check that the next time I meet her, shouldn't be long at this rate."
lintamande: Girls sit there nervously.
Keltham: Keltham is aware that some people might consider the current topic of conversation to be portentous! This is deliberate! He has an infohazardous chain of thought he is trying to distract them from, and himself too for that matter.
"But let's return to the experiment we just ran. One notable thing about it is that, just based on the experimental results themselves, we can't point to any one of you, and say, this person must've done something insane. We can't point to Peranza," yesterday Keltham gave up and did actual memory exercises to try and remember people apart from their nametags, "and say, her estimate was unreasonably high, her estimate was unreasonably low. We can tell that the two groups were collectively insane but not that any particular person in them was insane."
"Let's go back to considering the estimates for the chance of duck at lunch. Even after we get to see lunch today, can we say anything about who was sane and who was crazy, based on the 12-point scale?"
lintamande: "I mean, we can keep track and see if we notice a pattern over time, about who is good at guessing."
Keltham: "What kind of pattern would look like being good at guessing?"
lintamande: "....being right more often?"
Keltham: "Well, on a scale of 1-12, suppose you say 4, and then there's duck for lunch. You say 5 the next day, and there's no duck for lunch that day. You say 4 the day after and there's no duck for lunch. How are you doing? Are you being right more often?"
Carissa Sevar: "You can make some kind of scoring system where you don't really get any points for saying '5' every day and get points for higher numbers when there's duck and lower numbers when there isn't duck."
And then she can do performance reviews.
Asmodia: "And there's more rules like 'you can't have your number go up when you're predicting more things at once' and when you have four rules like that there's only one possible scoring system which is the Law of Scoring," Asmodia says out loud, a strange electric excitement running through her.
Keltham: "Good, Asmodia. That's not literally exactly correct, but you've seen the pattern."
"That's sufficiently far ahead of where I was going, that the next time you have a prediction that far ahead, I want you to say 'Prediction' and then write it down instead of... or actually just say 'Prediction' and then Message me, because we're all casters here."
lintamande: Asmodia gets some envious glances.
Asmodia: If they want their own envious glances they can go be that good.
Keltham: "Now, if we could all just pretend to forget that Asmodia spoiled the book for us by telling everyone the ending while I was just getting started..."
"We've just heard a new rule proposed by Carissa that you should get more points for giving higher numbers on duck, when there's duck, and more points for putting lower numbers on duck, when there's no duck. Well, I agree, that's pretty reasonable. Any other rules come to mind?"
lintamande: "...if a prediction breaks down into predictions for two parts, you shouldn't get more points for the combined predictions than from getting each of the parts right separately?"
"If - hmm - if two people both say duck, but one is more sure than the other, and it's duck, that one should get more points."
"And if two people say no duck and it's duck, but one was more wrong that one should lose more points. And they should get the same points for the same prediction."
Carissa Sevar: "You shouldn't be able to be better off for points by not guessing at all, though."
lintamande: "You should get the most possible points if you are - Nethys, and always give the right answer with perfect confidence, and the least possible points if you are .....Zon-Nethys, and always give the wrong answer with perfect confidence."
Ione Sala: "Nethys still thinks in probabilities, they're just more extreme ones takaral."
(Ione does not appear to notice that she has said anything unusual.)
Keltham: "...right."
"Well, those are all interesting rules, but the idea that two different people who give the same numbers should get the same points, seems to imply that everybody is, in some sense, using the same scale, in which case, that scale seems like it should maybe mean something. The same way that, inside a language, the same sounds mostly mean pretty similar things to different people."
"But let's back up. We can imagine that we've got this game which awards more points to people who put higher numbers on things that did happen, and lower numbers on things that don't happen. You can't be better off by not guessing. We don't have the Law for it, or any such thing, we just built a game that encourages numbers to go up or down in a way that matches what does and doesn't happen. We play that game for a while, turns out somebody is really good at it, say Yaisa has the best score by far. What" human capital "person-with-a-valuable-skill do we now have in the form of Hypothetical Yaisa? Maybe Hypothetical Yaisa is just good at playing a strange game but the skills in that game aren't useful for anything else."
lintamande: "I mean," says Yaisa, "I can branch out to predicting merchant ships and make a lot of money, if I've got a gift for something real."
Keltham: "Who says the numbers you learned to assign are the ones that merchants need to decide whether to send out a ship? You're slapping 3s on this and 9s on that and the merchant is like, 'uh, but do I send this ship or not' and you're like 'well I don't know what the numbers mean, I just learned what kind of number-assigning gets me a high score'."
Carissa Sevar: "Well, if Yaisa can't explain herself at all, we can check how often she's right when she says 9, and then the merchant can do the translation from 9s to profits himself."
Keltham: "These how-often-she's-right numbers sound quite interesting, maybe we should actually just be using them directly instead of the 12-point scale? I mean, if we've got to translate the original scale into how-often-she's-right numbers, maybe we can skip the extra step and have the game just be about those? Though first, right-oftenness numbers would have to be a thing. Can you say more?"
Carissa Sevar: "Well, it's kind of what we did with the gods prediction, right, 'one third' or 'one quarter', except wars with gods don't happen often enough you can figure out who is good at it, but if someone predicts whether a ship will come back, and if they say 'it'll come back a quarter of the time' and if they say that of four ships one comes back, then that's very valuable, pretty much as good as soothsayers used to be anyway."
Keltham: "Even if something didn't happen very often, let's say a Nidal invasion instead of that other thing, I might go to the person who had a really good record about ships. I mean, it might not be optimal, but at the very least they'd have a bunch of experience with how to hone and slice anything down to the difference between one-third and one-fourth. And they'd answer in numbers that meant that, instead of saying 3 or 9 on a 12-point scale and then you've got to pause and ask them for a hundred predictions like that so you can even figure out what a 3 or a 9 mean."
"Well, anyways, let's say that in this game you give a number from 0 to 100, and those numbers are supposed to directly represent the chances out of 100. If something happens 1 time in 4, you say 25, because something that happens 1 time in 4 will also happen 25 times out of 100."
"How do you score those numbers from 0 to 100?"
Carissa Sevar: "...when it happens, you give them points or deduct points in proportion to how likely they said it was. So....if they said 25, and it happened, deduct 25 points? And if they said 25, and it didn't, add 25 points?"
Keltham: "And if they said 24, and it didn't, add 24 points?"
Carissa Sevar: "Nah, 26, because you should get more points for a more correct prediction."
Keltham: So apparently his brain just registered a reluctance to shoot down his girlfriend too cruelly, and wow does that impulse need to get poisoned and handed off to the Surreptitious Head Removers, not just because entire integrity of the teaching process, but also because Keltham has ever met Carissa Sevar and if she could read his mind about that she would be cometary-impact levels of sad and possibly angry.
"Interesting, interesting. Well, Carissa, want to play a few rounds with me of predict-if-the-coin-lands-Abrogail-twice-in-a-row? It's a pretty simple game, on each round, we write down our numbers, Asmodia spins the coin twice, and if it's Abrogail both times that's a yes-event, and otherwise a no-event. Which we also mark down. After 12 rounds we reveal our numbers, score ourselves using your rule, and whoever has the highest score wins. Anyone else in class is also welcome to play along."