Keltham: (Continued from within my fun research project.)
The library-classroom is more crowded, now, but not overcrowded; it was built with this in mind. Eight existing hires, twelve job candidates, two visible Security, Keltham himself, and finally, if you're paying sufficiently close attention, Broom.
And Keltham out of dath ilan holds forth, then, upon the way of SCIENCE.
"Good morning, all, newcomers and oldcomers alike."
"Let me start by saying that this lecture probably isn't going to work."
"This class is too large, too unfamiliar. The new students are all full of Chelish dignity and haven't learned to show facial expressions that I can use to have any idea whatsoever of how my class is going. I expect the newcomers with all-important dumb questions to think they should stay quiet so that supposedly smarter students can learn faster - don't do that, by the way, just ask the question. You got all your Law of Probability off Asmodia yesterday, and I have no idea how much you really got from her or if that even worked at all."
"We're probably going to have to abort it ten minutes in, and break up into smaller units, so more of the current researchers can try again to teach the new candidates the requisite Probability, with more individualized instruction and myself around to supervise. This being the way things are usually done in dath ilan: older children teach younger children, overseen by the Watchers-over-children. And in teaching, the older children also learn."
Keltham: "So why am I trying things this way?"
"Because, if this just works, it will be faster."
"And I am not sure that this won't work. I haven't tried. I haven't checked."
"So we're experimenting. We are looking. We are going forth and finding out."
"When to that underlying emotional spirit of curiosity, questioning, 'blah blah blah'(*), and glorious discovery, is added the inspiration of Law, it becomes what dath ilani call 'blah blah blah'(**)..."
"Right, uh, let me just pause and tap everyone with Communal Shared Language (Baseline)."
Keltham then goes about from person to person. He's glad he got two of those spells, today; with this many people, he can only give most researchers and candidates an hour of Baseline apiece per casting.
(*) 'Maniacal-experimentation'.(**) 'SCIENCE!', lit 'Civilization's-learning', with 'learning' as in a child's learning. Distinguished from ordinary everyday systematic experimentation using math, in that it is a societywide effort to COMPREHEND and CONQUER the ENTIRE UNIVERSE.
Korva Tallandria: So the entity - Keltham, Keltham, his name is Keltham and he goes by it, it's going to sound so weird if she says "the entity" out loud, even though it probably won't actually cause any wall problems - Keltham actively wants dumb questions, even though the project leaders obviously don't. That's good. It should be easier to think of questions that don't reveal anything if she doesn't have to also filter for being incredibly insightful. And hey, maybe she won't even have to contribute much to classroom chatter in the first place; everyone else is probably just as capable of asking dumb questions as she is. Not that she's going to make any ill-founded yet confident assumptions about what other people are thinking when she can't see it, because she's decided that there's quite enough of that around here, and she's going to at least find less repetitive ways of being constantly wrong.
(Also... apparently Keltham already knows that the way they're mostly taught involves remaining silent, so why do they have to go to so much effort to act like it isn't? But that's a question from her real self, not her alter-world self; she tucks it away and resolves to stick with what the project leaders have told her, because they've obviously had more time to think about the picture they're presenting to him.)
Willa Shilira: Willa Shilira is sitting in the back of the class and she's very unhappy about it, but you couldn't tell that by looking at her. She has less Chelish dignity and stonefaced composure in her than perhaps any of the other students, but that's still plenty to be unassuming in a crowd of almost two dozen. (She's mentally acute enough to count the twenty-three visible people in the room while barely thinking about it, but not perceptive enough to even notice Broom being the twenty-fourth.)
Willa came into the project bright eyed and excited about Law and learning and superpowers, desperate to be special. She was so desperate for it that when a chance to ask questions came up, she tried to ask one mostly just to show off:
"Of course if the project is so important we should all be getting intelligence headbands, right, and I can put that impertinent demand in fancy probability language to prove I understood the homework too! I didn't stop to think that economic reasons were a trivial concern and that the real thing I should be worried about was fooling Keltham, even though you just gave a giant speech about how the important thing was fooling Keltham. So obviously I'm a complete idiot and you should never trust me with anything at all!"
That's not actually what she said, but it might as well have been. They didn't torture her for it at all which was super weird, but now alter Willa is 'studious, shy, and hesitant.' Forever. And she has to mentally run all her questions by Asmodia now, of course, to make sure they aren't suicidally stupid to say out loud. And she can guess that means if she ever actually has a good one it'll get given to someone else who isn't supposed to be 'shy and hesitant.'
She could choke herself with a rusty spoon.
She messed up and she knows it and she's mostly just sulking, angry at herself. There's a simmering annoyance with Asmodia for forcing alter Willa on her, and still a lingering resentment towards Sevar for capturing most of her soul-profits, but in the end the reason she can't be a model student actor agent is that she's too obsessed with being special and not obsessed enough with winning. It's a terrible failing in her and it's worse that she knows deep down that it's still true, it's not something she knows how to change.
She's not going to be able to distinguish herself to Keltham by asking clever questions, and honestly even if she was she maybe couldn't trust herself to do it safely. Instead she'll have to distinguish herself to Asmodia by thinking useful thoughts. Then maybe eventually Asmodia won't hate her anymore she'll be out of the doghouse and at less risk for washing out entirely.
Keltham: Having tapped everyone with Share Language - including Broom, once Broom reminded Keltham of his existence - Keltham speaks forth again:
"The first thing to do in this experiment... is something I expect you'll all find way too natural, namely, don't say anything and control your facial expressions. That's not the usual rule in this classroom, but in this case I want you to confront a problem separately and without leaking information to each other, so no comments out loud on what I'm about to do or say here. If you want to say something to me, or have a question, say 'Message' and then use Message."
Keltham goes to the wall, casts Prestidigitation, and draws three Baseline numbers via color-changing the wall's surface. Possibly using Prestidigitation all the time will help train magic use to where it becomes more innate and reflexive for him? Though he should actually check that concept with Carissa at some point, because it's a time-costly experiment.
The Baseline numbers that Keltham draws are 2, 4, 6.
(It should be immediately apparent that Baseline numbers are both easier to draw, and more visually distinguishable, than Taldane digits. Just one more little reminder that almost everything about dath ilan was designed and not just allowed to happen.)
Korva Tallandria: That is not, actually, immediately apparent to Korva; maybe it would be if she were focused on it, but right now she's busy trying to control her heartbeat even though she's pretty sure nobody can hear it leaking evidence that she's freaking out a little about whatever bizarre new kind of math this is going to be.
Keltham: "I am now the - world? Nature? - 'environment' in Baseline," in case any of the concepts of 'thing that interacts with the agent and is separated from it only by a false conceptual boundary' make it across in translation.
"On each round, you input to me a sequence of any three integers, and I output to you either 'yes' or 'no'."
"You are learning me, unraveling me, theorizing about me and experimenting on me; you are trying to predict what makes me say 'yes' or 'no' on each round. To be clear, I wouldn't particularly suggest that you think of these symbols 'yes' or 'no' as really meaning anything, except insofar as you think you've determined experimentally what makes me say them."
"You will now write down 2, 4, 6 on your paper - Taldane is fine, I can still read that. When you're done, raise your hand, and I'll mark down on your paper whether this initial input causes me to output 'yes' or 'no' to you."
"If you think you've guessed the Law that governs my outputs, you can write that down, and I'll write 'correct' or 'wrong' next to that, where those words do have their standard meanings."
Willa Shilira: Willa's still a little jumpy.
When he first asks them to raise their hands just for the '2, 4, 6' she suspects it's a trap, and writes just slowly enough to make sure she sees a couple other students raise their hands first. Turns out it isn't a trap?
2, 4, 6: YES
8, 10, 12: YES
Willa would ordinarily guess here, right away, if she hadn't just been admonished to be careful. But she was, so she stopped, thought for a second, and then-
-6, -8, -10: YES
3, 1, -1: YES
The law is that the absolute value of the number must cha- Willa crosses that one out, realizing something.
5, 7, 5: YES
And there's a triumphant expression that's too subtle for Keltham to see but not too subtle for any Chelish students that might happen to be looking at her.
The law is that the the absolute value of the change of the number must be 2 each time.: WRONG
She experiences existential anguish, and then pauses in terror, expecting Asmodia to scream at her in indignation.
Asmodia: Asmodia does in fact yell at her, on relay through Security: Control your facial expressions and don't fucking mess up Keltham's test, you fucking moron. He may be able to tell from the results he gets if we didn't all follow instructions. Luckily I don't think anybody who wasn't Security was stupid enough to be looking at you.
Don't do anything alterWilla isn't doing, FUCKING PERIOD. If you prove unable to fucking understand that, alterWilla will fail to keep up and sadly resign from this Project.
Willa Shilira: Of course she messed up again, apparently she can't do anything right. She fiercely pushes everything down, and at least for a little while, her expression will remain thoroughly blank.
Alexandre Esquerra: Idly translating Keltham's pre-Share Language sentences, Alexandre Esquerra, second-circle wizard and new Project Lawful researcher, discovers that Baseline has a word for "a societywide effort to COMPREHEND and CONQUER the ENTIRE UNIVERSE," and Alexandre Esquerra has never been so happy in his life.
Then, Keltham's test. Alexandre will, of course, do better than his rivals; his first instinct is that he needs to solve it in as few guesses as possible, which he immediately crushes, stamps down on. He should not win the contest, he should learn, getting as much information as he can from Keltham before he dares hazard any guess. Once he's solved it, he can dawdle around and do extra checks and answer everything.
2,4,6: YES.
All right, think of this as spellcraft, to make sure magic items or spells stabilize; a ratio of 2,4,6 is in balance, is 2,4,7?
YES. 1,4,6? YES. 2,3,6? YES.
So much for the 'ratios' idea. That's thoroughly disproved. Well, Keltham's knowledge is strange and alien, and he should not expect it to match that of his own civilization. 6,4,2? YES.
... All right, so even reversing the order works; he's starting to get annoyed, he doesn't have good alternate possibilities and so he's stabbing in the dark. He isn't letting it show, of course, he's not a child. Does 1,1,1 stabilize? YES...
There has to be some spell structure that doesn't stabilize under these absurd laws, doesn't there? How about if he tries to break the bounds with -6000,7000,0: YES. Smoldering annoyance. Desire to burn everything. He can manage, while hating, if he could not manage he would not be alive. 500,0,500? YES. 100000000000,0,0. YES.
All right, he knew that was going to happen, his actual expectation was that one hundred billion would stabilize, which, per Keltham's rules, means he already knew it. The actual goddamn law is 'any three numbers', isn't it? There has to be something that isn't accepted unless Keltham is a -
Of course. Yes. Keltham is a sadist. He should not have considered this question as 'the output of a superior civilization bent on teaching its students', he should have considered the question as 'the output of a sadistic teacher intent on inflicting suffering on his class'. Hell is the destruction of hope, such as his hope of successful learning. He'd like to let security know he thinks he has a correct guess, but wants to make sure he isn't the first one to write it down.
(And, while he does that, he'll continue writing random strings of numbers so Keltham doesn't guess. 313-496-386? YES, of course.)
Asmodia: Security relay from Asmodia: Stop. Stop trying to act in ways that your alterCheliax self wouldn't. Just stop. Don't do anything fancy. Just. Be. AlterAlexandre. He'd go ahead and guess, so go ahead and guess before Keltham notices you're acting weird.
(...is this what it's like for Aspexia Rugatonn when she tries to explain to anyone about what probably seems to her like an incredibly simple and straightforward concept of just following orders? It totally is, isn't it. No, Asmodia isn't feeling even slightly sympathetic, because Aspexia Rugatonn.)
Alexandre Esquerra: ... All right, yes, acknowledged, he rather deserved that. The law is that any sequence of three integers will get YES.
Keltham: WRONG.
Korva Tallandria: This sounds even worse than normal math!!
She writes down 2, 4, 6 on her paper in Taldane, as instructed. She raises her hand, being careful not to be the first one.
2, 4, 6: YES.
1, 1, 1: YES.
Huh. Okay, different numbers, all odd, same pattern.
3, 5, 7: YES.
Opposite order.
7, 5, 3: YES.
Uh, branch out more, so you can see some no’s.
7, 8, 9: YES.
Her heart is hammering out of its chest, and it shouldn’t be. She’s so scared of being the last one to figure this out. Realistically, not everyone will, but they can kick as many people off the project as they need to, so -
1, 2, 3? No - 1, 9, 2, that’s more different.
1, 9, 2: YES.
Nothing to be gained from not guessing, probably? Guess the obvious.
Guess: Always outputs “YES”. And she adds another number guess, so as not to waste Keltham’s time when her first obviously-wrong-guess is wrong.
2, 5, 1: YES. WRONG.
Willa Shilira: Maybe it can be any difference?
101, 102, 101: YES
... or maybe it can just be anything at all?
101, 102, 100: YES
Let's just make sure.
1, 10, 107:
This time, Keltham fails to notice her for a round, because she's hiding in the back like a mouse and she hates alter Willa. Eventually though he notices her again.
1, 10, 107:YES
Let's be really sure.
pi, 5.67, 78/7: INVALID INPUT
And now she remembers they were supposed to be integers. She needs to get it together. It's probably wording and she's just phrasing it wrong, it has to be.
The law is that the three numbers must be integers.:WRONG
The law is that nature always says yes.:WRONG
Maybe if she throws enough things at the wall he will eventually tell her no.
-5, 10, -7:YES
1 is a pretty special number.
1, 1, 1:YES
Zero is too.
0, 1, 2:YES
Maybe the numbers just need to be really large.
10^20, 10^20, 2:YES
Is it really just a tricky wording after all?
The law is that if you give 3 valid inputs nature always says YES.: WRONG
No. YES to everything, absolutely everything, except something she can't think of. She's just stupid, obviously.
Keltham: ...people sure are making some assumptions that dath ilani wouldn't make! Possibly human beings just naturally make a lot of assumptions, and naturally stay in small mental boxes, that dath ilani kids have already been implicitly jailbroken from by the time they first encounter this problem?
Alexandre Esquerra: Alexandre will burn this useless scrap of paper! (No, he will write -3, -6, -9 and get back a YES.)
... alterAlexandre would snap even alterAlexandre is not weak. 0,0,0. YES. He continues his search for NO in the endless sea of YES; 2,4,8? (Yes.) 3,9,27? (Yes.) 8,4,2? (Yes.) -2,4,-8? (Yes.)
Mindful of Asmodia's warning not to do anything alterAlexandre wouldn't, he begins letting some strain show on his face. It is rather less than he's feeling, but he's never been outside Cheliax and doesn't know how much Taldorians conceal their facial expressions. He's used to having some idea of where to search.
Next step: 300, 400, 500. Is there some band where the usual ones don't apply? (YES, that is, SCREW YOU.)
4444,3333,2222... (YES.) wait, Baseline sometimes uses Base-12. 12-144-1728? (YES.) So really, Yes and No are inverted, and he can't find any point where he can stabilize this. 59326-78442-19848? YES. 16,4,2? YES.
... Hmm. Alexandre is starting to notice that Keltham is taking longer and longer to answer.
... ... Let's think about this logically. He's tried ascending order and descending order and powers and in the opposite order. He's been told to only try integers or he'd move into fractions. He's tried to break it from the top and from the bottom and input three of the same number and... ... Wait. Hmm. Odd. 2,2,4.
(YES, but with a long delay.)
That's... odd. 2-4-2. (YES) Probably someone else has stumbled on the secret, and whatever the secret is involves Keltham having to do a lot of complicated mental math.
So he's trying prime factors, and seeing if there's a slot that the 4 should go in. 4-2-2? (YES.)
... 4-2-2 took less time than 2-2-4. Keltham may have just been distracted, or be waiting pauses of ambiguous length. 3-3-3? YES. Yes, yes, as expected, but if it was 'all primes and we don't count 1 as a prime' he doesn't know how he could have lived with himself. (In a dry, slightly ironic tone.) He hesitates a bit to do some quick arithmetic of his own, then: 79-11-879?
An immediate Yes.
Well, that should be interesting.
Korva Tallandria: 2, 4, 8. Those numbers at least have a relationship.
2, 4, 8: YES.
Did he say the integers have to be less than ten? He didn’t, did he? Okay.
1, 247, 6: YES.
Okay, try negatives.
1, -1, 0: YES.
Try all negatives??
-5, -247, -8: YES.
Try all zeroes.
0, 0, 0: YES.
This exercise is STUPID.
5, 3, 15: YES.
Stupid and AWFUL.
Okay, what other traits do integers have. They can be even or odd. They can be positive or negative. They can be factors of one another. They can be… addition problems, the first one was an addition problem. They can be division problems.
Try writing down STUPIDLY LARGE numbers, even though this won’t get her anywhere.
568, 9840348, 653203: YES.
Obviously.
She can’t think of anything but she’s obviously not allowed to give up, even though her heart is dropping like a rock. She gets a sense of curious worry from the butterfly familiar still in her room, over the empathic link, presumably from all of the intense emotions she’s having. She tries to tamp down her current emotions enough to send a coherent message back. The feeling of seeing a warm meal when hungry, the feeling of being chained up alone in a dark room, the feeling of seeing a warm meal again. This is supposed to indicate to Pretender that she’s fine, actually. She’s not entirely sure that she is.
……..okay, wait. When Korva had reason to design a code with things sort of like digits, she did - alternating differently-valenced things? Try alternating things that are different.
1, 2, 1: YES.
-1, 2, -3. YES.
This is obviously doomed, but be thorough anyway.
1, -4, 2: YES.
She hates this. They’re going to send her to hell right away, and she won’t even have learned anything, and she will therefore be starting at a disadvantage relative to everyone else in hell because she died young and didn’t even get to learn the things that mortals are supposed to learn, so she’ll be worthless for her entire existence and have a boring and fundamentally useless eternity, not even because she was inherently worthless, but because someone sent her into this stupid, ridiculous class for how to be an axiomite made of math just because she knows how HISTORY works.
These aren’t things that alter-Korva would be thinking except that OH WAIT YES THEY QUITE POSSIBLY ARE, GIVEN THAT EVEN IN ALTER CHELIAX SHE ALSO NEVER GETS TO GO HOME UNTIL THE PROJECT IS OVER.
1, 2, 3, 4, she writes down, angrily, in case disobeying instructions is the POINT.
1, 2, 3, 4: INVALID INPUT.
Okay. Not that.
That technically breaks the “always outputs yes” rule.
3, 2, 1, she writes, and a guess. Guess: Always outputs "YES" when given a valid input sequence.
3, 2, 1: YES. WRONG.
Of course.
What other things can you do with integers. Division problems, sure, that won’t fucking be it but she can test it.
…wait.
Willa Shilira: Maybe she'll just try prime numbers. It's something, at least.
2, 3, 5: YES
It seems to take Keltham a while to answer this time. Maybe it really is primes, somehow?
23, 19, 41: YES
And it's faster this time. Her primes have betrayed her! Maybe the numbers just need to be pretty small somehow, in some confusing way.
2, 3, 6: YES
But it's slow again! Somehow she has something. Maybe.
Sense Motive check, is Keltham:
A) just messing with her, orB) legitimately having trouble computing this quickly, or C) is he wondering why she's so stupid?
Also, Willa's trying to very subtly look around the room at this point to see if everyone else is finishing and she's alone in her pathetic stupidity.
Iarwain: Results: Keltham is patient but wondering - more like he's wondering about everyone, not wondering about her in particular, his facial expression doesn't change much as he moves away from her. Possibly he wasn't expecting this problem to be as hard for everyone as it seems to be?
Some frustration here and there is leaking through other students' expressions in a way that Willa can detect, despite Keltham's instruction.
A number of the other previous hires look finished, but such is only to be expected. Oh, and what's-her-name - Korva - seems to be finished too.
(The Chosen of Asmodeus finished almost immediately, of course, but that was hardly worth noting.)
Willa Shilira: The more senior researchers don't shake her much. They've had more time. It's only fair.
But Korva's just as new as Willa, and she's already better. It's a dagger in her heart, but she has to keep going. Whatever happens she can't let herself be last. It'd be the end of the world.
Ok. Go time.
Is she absolutely sure it's not a wording thing?
Nature's output to Willa is YES when she writes three valid inputs.:WRONG
She's sure enough for now. Let's try other small numbers, that won't look stupid to Keltham at all, no siree.
3, 4, 6: YES
It takes him a while again, and she has a terrible, horrible suspicion now.
Alexandre Esquerra: 879-97-11? Immediate YES. -1,1,-1. Slow YES. ... Oh? -1,1,2? 1,-1,-1. Both swift YES. Very interesting. 1,-1,1? YES, very slowly.
What on Golarion could this possibly be? Now he really wants to know. 1,1,-1. Another slow YES. -1,-1,1 YES, slowly again.
... Hmm. He hypothesizes that -1,-1,-1 is quick? He'll test that hypothesis. YES but a slow yes.
Fascinating. He really just wants to know the answer... Wait. -3,0,0? YES but a slow YES.
... He's imagining that Keltham has to do a lot of mental math here because he's trying to calculate - in his model, everything is either positive once Keltham has done some calculations, and that gets YES, or negative, and that gets NO, and that suggests to him that's multiplication of some sort but the different places meaning different things but he isn't sure which place means which...
-2,1,-2?
Keltham: Keltham gazes at the paper, eyes flickering a bit, and then writes YES. It took him about as much time as before; relatively slow.
Alexandre Esquerra: - Wait, actually, no, there's an even dumber test he should do: -2,1,-2
An immediate NO.
... This cannot be that simple. 2,4,6?
NO.
... Alexandre now sees his fault. He had been, fundamentally, assuming that these were standard tests, independent tests, each question isolated from the last. He had not realized... the meaning of what Keltham had said. He had heard the word, and not thought about it, so only now, does he see the truth: That he cannot consider all his steps in isolation. He does not know the Law, yet, but he is one step closer to finding it.
If he was not in Cheliax, he would be smiling.
dath ilan: Among the first things one does with unfamiliar measuring instruments, in standard tests, is check that equipment's reliability-width by measuring the same thing multiple times! Any child would know that!
Alexandre Esquerra: You cannot simply assume that, just because you have cast a spell, it is gone. That spells usually do not interfere with other spells is a generalization, not close to a law.
2,4,6 again? Still NO. 3,5,7?
Keltham: YES, quite slowly, as Keltham's eyes flicker over the whole previous sheet of paper while successfully making it less than completely obvious what he's doing, as might be obvious if his eyes moved slowly down the page in order.
Dath ilani play enough games where direction of eye gaze can be a giveaway that Keltham has at least some training in that particular aspect of Bluff.
Alexandre Esquerra: ... Well, this is still going to be a difficult challenge. He has the hint, but he needs the Law; whatever it is can't be simple addition, because at one point he tossed a hundred billion in. Each slot may still mean something different, and he has such a tiny, frustrating window to tell useful things from his information!
Still, things may be simple. 3,5,7 again?
(NO, instantly.)
3,5,7 again continues to be no? (NO, instantly.)
Excellent. Then he's going to check this again just because Keltham is a sadist. 3,5,7? (NO.)
Then... is it really just that simple? He... he thought it would be much more complicated than this. His guess, this time, is that anything you've tried before gets a 'no' and anything else gets a 'yes'.
CORRECT.
... He cannot believe it took him this long to get it, but yes, he is feeling... joy, at finally mastering a difficult art, at taking an absurdly complicated thing-in-the-world, and studying it, and reducing it down to something so simple, that he couldn't believe it took him so long to understand it. Through pain, to strength. Great is Asmodeus, Lord of All.
(And Alexandre will let a tiny bit of the happiness he is feeling leak through, since alterAlexandre would not hide his expressions as well as trueAlexandre. Just a little.)
Keltham: Keltham looks happy about it too, in fact! He's trying to hide it, but not at all well by Chelish standards.
...as for that tiny bit of leaked happiness from Alexandre, there's no chance in the Abyss of Keltham getting that.
Korva Tallandria: All of her sequences so far are new. So -
2, 4, 6: NO.
Incredible.
She would have gotten this faster if she hadn’t been thinking about it as a kind of fucking math. Or if she had been a five-year-old. Or if she had been dumber.
Well, she can probably learn to be dumb sometimes, if that’s what it takes.
3, 5, 7. Guess: Outputs "YES" when given a new sequence; outputs "NO" when given a sequence already used.
NO. CORRECT.
She doesn’t collapse in panicked relief on her desk, because she’s not actually five and also that would be disobeying instructions about leaking information. She stares ahead, outwardly calm - which is probably in itself leaking information, because she probably unintentionally leaked a bunch of distress everywhere right around 1, 2, 3, 4. In any case, her soul is crying out in relief, and she gets a sympathetic mental pat from Pretender about it.
Only then does she look around, and see that all of the other new students are still writing. Some of the old researchers - including, of course, the Chosen - have stopped writing, but not all of them.
She really doesn’t know how to feel about this.
Willa Shilira: Previously, on Willa (the Complete Disaster at Everything):
With a heavy heart, she writes the fateful numbers.
3, 4, 6: NO
Oh no. Well, as bad as this is, she has to be sure.
2, 3, 6: NO
It's a little slow again this time, because of course it is. He had to read up her sheet. But she isn't sure ENOUGH.
1, 1, 1: NO
And she has to make sure she isn't missing something else either. Order could matter too. She is not going to get this WRONG. Not AGAIN.
6, 3, 2: YES
Well fine then. She notices that she still has an internal flinch expecting that WRONG gets written after her answer, in spite of all her reason insisting it won't be.
The law is that if the three numbers have been entered before in order by Willa, nature says NO. If this is the first time the three numbers have been entered by Willa, nature says YES.: CORRECT
She's a massive failure, but she's still relieved. None of it shows on her face though.
Carissa Sevar: 2, 4, 6: NO
2, 2, 2: NO0, 1, 2: NO900, 600, 300: NO-1, 0, 1: NOa, b, c: INVALIDWell, that's some obvious theories that don't seem to be on the right track at all. Back to basics, then: does the rule output the same judgment every time you give it the same input? 2, 4, 6: YES- and there's an obvious theory (any set is allowed the second time, but not the first) which does seem to be on the right track, but she's met Keltham so she's SUSPICIOUS it's more complicated than that. For example, maybe it'll be allowed the second time but not the third, or maybe the second time it gets evaluated by a different rule than it did the first time, but the different rule might not always return 'yes'? Or maybe once the numbers have been used they are allowed in any order?-1, 0, 1: YES6, 4, 2: NO2, 4, 6 for the third time?: YES6, 4, 2: YES
2, 4, 6 for the fourth time?: YES2, 2, 2: YES
-2, 45, 1: NO -2, 45, 1: YES
1e16, 1000, 4: NO
1e16, 1000, 4: YES
...on the other hand sometimes the rule is in fact simple and you shouldn't overthink it.
She submits her guess.
She's done first. What kind of bizarre nonsense is everyone else getting up to?
Keltham: Keltham had assigned YES->NO to half the tier-1s and tier-2s, NO->YES to the other half, making sure to put Asmodia and Carissa on separate sides.
He's surprised to find that NO->YES looks like it was slightly easier, rather than slightly harder as he thought it would be. He would've given NO->YES to the new candidates if he'd known. Oh well.
Alexandre was the last one, right? After a quick final round to make sure he didn't forget anyone, Keltham announces that they're done.
lintamande: "And now," says Meritxell, "all of the slowest performers will be dropped into boiling acid as an example for the others, exactly as it's done in dath ilan -"
"She's kidding," says Gregoria."They knew that, spoilsport."
"They might not have known that!"
"I was kidding," says Meritxell. "Only the absolute worst performer is dropped into acid and it is not necessarily boiling, depends whether it had time to get to a boil while you were being slow-"
Korva Tallandria: Since Korva was bizarrely un-slow, she doesn't worry.
She does wonder whether anyone is going to talk to the old guard about whether alter-Cheliax could plausibly have people who might not have known whether several of them were going to be immediately dropped into boiling acid due to slow performance on the very first exercise, or whether that sort of thing is only for newcomers.
There's probably no way to find that out.
Alexandre Esquerra: "Understood," says Alexandre drily. "Is it permitted to cast Resist Acid first, or does does dath ilan forbid protecting oneself as opposed to the spirit of maniacal-experimentation?"
(He knows perfectly well that countries other than Cheliax are too weak to drop their students into boiling acid, and dath ilan is far more good - that is to say weak - than Taldor. But he may well be whipped once he's finished, anyway, or at least beaten, Taldor does still exist so it can't be that weak.)
Willa Shilira: Was that appropriately witty and spontaneous or did Alexandre just make some terrible error? She thinks that one student speaking up like that is probably more likely to happen in alter Cheliax, but her trust in her own instincts is at an all time low right now.
At least it's not the type of call she's going to have to make, being 'shy and hesitant.' She hates that she feels relieved.
Carissa Sevar: "I'm not even sure being faster at the exercise is being better at the exercise," the Chosen of Asmodeus, who was the fastest, says in the same light-banter tone. "One way to be fast is to be careless, which is the only real way to fall into vats of boiling acid in dath ilan."
lintamande: "But today we are charged with doing maniacal-experimentation," says Meritxell.
Keltham: "I would of course never dream of working with volatile high-temperature acid without casting Resist Energy (Acid). It was in no way the case that our Nethysian Safety Officer had to browbeat me into waiting a day to pray for those spells first."
"And today, indeed, we're not just learning maniacal-experimentation, but learning the Law of maniacal-experimentation. Of this the Law is relatively simple: when experiments are cheap, do lots of them, when they're expensive, spend more on figuring out which experiments to do. Even then, though, when you're doing lots of similar experiments and they're all failing, what you probably need is to back off and think. Even even then you might try running some weird or random experiments anyways, while you're thinking."
"Incidentally, a bit of maniacal-experimentation I did myself on the side: I assigned half the current researchers to start with 'Yes if not tried before' and half the researchers to 'No if not tried before'. I was expecting 'Yes if not tried before' to be the easier one for non-dath-ilani, but it looks like it was actually the harder direction. Sorry about that. Had I run a pilot experiment first, I'd have known to run the real experiment with 'No if not tried before' for all the newcomers, instead of, as I did, it all being 'Yes if not tried before'. Such is the price of maniacal experimentation where you don't run smaller pilot tests before you run the big ones."
"Carissa was in the 'No' group, but still a huge 'outlier' in speed even so. Is there some kind of Worldwound experience that let you get it after your fifth input, or...?"
Carissa Sevar: " - after I tried a couple things I figured I should check whether a given input always produced the same output or not. I cannot think of a specific occasion at the Worldwound where I had to do this but it does seem like - sort of a thing to do fairly early in figuring out something mysterious."
Keltham: "Yeah, that's basically around how long it takes dath ilani kids to get it. We play a lot of games with 'gotchas' of all kinds. Even on the non-game side of things, by the time a kid gets introduced to this game, they've probably heard the proverb that when you're trying out new maniacal-experiments in a new domain with new equipment, among the first things you try is to measure the same thing twice, or two things that you expect to be very similar, so you can see around how much error there is in your measuring instruments."
"I wasn't expecting this problem to be as difficult as it was for non-dath-ilani... er, other than Carissa. I was mostly trying to set you up for the trap where you see 2-4-6 and try 3-6-9 or 3-5-7, and are sure you've found the answer then. The lesson about that is to test the negative spaces as well as the positive spaces, the places where your model says a procedure should fail and not just where you expect to succeed. To pin down a boundary you need to check what should be outside, not just what's inside."
"I wasn't expecting the step after that to be as hard as it was. But it looks like you all ended up learning a valuable lesson anyways, and the 'explicitization' of that lesson is this:"
"Very often in Science, especially when you're working in a confused 'pre-paradigmatic' field, 98% of the work is in coming up with the right hypothesis to test. That's often more important than the elaborate Law of Probability about how to interpret results that are less than totally clear. We study that part because it has clearer Law to study and it helps reshape our thoughts, not because it's the most important or difficult part of the problem."
"And of that work of coming up with the right hypothesis to test, again, often the most difficult part is seeing the rule you were taking completely for granted - not a rule you explicitly believed, just a way you behaved automatically without being able to see that and so question it. As soon as you see the implicit rule, you can imagine it being false, but only once you see it."
"The difficult thing, in most pre-paradigmatic and confused problems at the beginning of some Science, is not coming up with the right complicated long sentence in a language you already know. It's breaking out of the language in which every hypothesis you can write is false."
Alexandre Esquerra: That sounds extremely wise; does Keltham intend to explain how to do it?
Korva Tallandria: ...she kind of did explicitly believe the rule that was getting in her way, though. Young children probably would be better at this problem, which isn't that surprising because it probably is, in fact, an exercise for children. It's not that they're fundamentally sharper, they've just taken fewer math classes, and don't know that in math classes you mostly deal with the sorts of problems that always output the same answer for the same inputs.Note to self: next time, before you panic, take a step back and pretend to be a five year old.
Willa Shilira: There was an expectation buried within Willa, so deep that she couldn't notice it, that real world things might look back at you when you looked at them, but purely math things never did. The thrill of realizing this is sorta wrong is the first thing to really break through her depressive spiral since the class started.
Keltham: "Breaking out of your language and finding new structures in which it is possible to frame the correct hypothesis, is legendarily the most difficult part of Science to teach; any part of it that's been reduced to a formula is no longer the difficult part of the problem."
"In the case of things like manufacturing acid and improving spellsilver refinement, you'll be at a great advantage because I can tell you much of the correct language to think about those problems... until we start trying to improve those processes using dath ilani knowledge plus magic, as was never in dath ilan, and then we're back to 'pre-paradigmatic' experimentation again."
"Since 'jumping-out-of-the-system' is such a vital part of the Science problem and so difficult to reduce to formula - there is Law of it, but it doesn't help much unless you're making some really basic mistakes - it is mainly taught to dath ilani children by experience."
"For example, dath ilani children are told that the reward of passing a competence test will be theirs, if they can only guess correctly what it is that holds up the Sun in the sky, and prevents it from falling down, and guides its motion, as it circles our planet every day. Is there some shell that holds it in place? Invisible wires? Is the Sun just made of very light material so that it doesn't fall?"
"Of this it is forbidden to speak to children, until they guess it for themselves. Only then, as their reward, are they shown where they are within the universe - where they have always lived, all their time."
"I assume everybody here was already spoiled on that one because Golarian. But just in case, raise your hand if you already know."
lintamande: Chelish wizard students do in fact know that the Sun is very far away and Golarion circles it.
Keltham: "In retrospect I should have checked that before showing the current researchers where dath ilan was within its universe. But looks like no harm done."
"So, yes, until the kid says that they suspect that dath ilan is spinning in place and that just makes it look like the Sun is circling it, while the Sun is staying in place, they're not shown any model of dath ilan's solar system."
"And then, once they see it, there's a new question: what motive force keeps dath ilan circling the Sun? What keeps the other planets circling the Sun? What keeps the Moon circling dath ilan? Why don't they wobble out of place, slow to a halt, or keep going in a straight line instead? Everyone know that one already? Raise your hand if you do."
lintamande: They are taught, too, that it's gravity, the force that pulls the heavenly bodies in their places. (They are not specifically taught why gravity causes that to happen instead of causing some other thing.)
Korva Tallandria: Well that seems like an important dath ilan fact, the not telling anyone about the solar system before they've earned it. How many kids ever figure that out? Approximately intelligence sixteen on average, so, what... forty? Fifty percent? She's still gotta be crap at probabilities for things where you don't have any examples to work from, and she's not sure that the fact that Golarion is spinning even was something that humans ever figured out on their own, so it's hard to say how long they could go without figuring it out, but, hm, she doesn't feel like she could possibly have more than a fifty percent chance of figuring that out alone. Probably way less than that. Maybe if someone were standing by to tell her right away which of her guesses were wrong, like in the exercise just now, so that she could take hundreds and hundreds of wild guesses until she happened upon the right one by being ever more imaginative, but a lot of people still wouldn't, right...?
There could be lots of stuff like that, that people aren't privy to until they've figured out some crucial element for themselves. That fits into what the Chosen of Asmodeus was saying, earlier, about how lies are necessary for most people, but how it's possible for some people to actually be told the truth without the truth making them even more wrong. Maybe you first have to demonstrate that you're the sort of person who can figure out some pieces of the truth on your own, before you can be trusted with more adjacent pieces.
(And she might feel just a tiny bit of pride, about that, not so much for herself, but for the five-year-old who had the impulse to chase the shadows of true things through the pages of library books that were incompetently censored. She wouldn't have to feel so concerned about having that impulse, if the way of knowing true things without breaking was to earn them.)...except, wait, if you prove it in a context where you can guess as many times as you want, you haven't proved that you'll consistently land on the right answer with the right information at all, you've only proven something about the scope of your imagination, which might be useful for finding right answers, but also seems like it would lead to lots of wrong ones.
Hm.
Keltham: "You know, I am confused about why anyone would spoil the puzzle for you by telling you that it had something to do with gravity, and then not teach you any of the math you would need to do anything with that knowledge, or really actually know it at all." Namely calculus. "I'll have to think if there's anything I want to do with that. Possibly you weren't spoiled on at least some parts of that puzzle."
"We've now seen what's implicitly the hardest part of the problem that's most difficult to train: picking the right language to think in. Dath ilani kids get exposed to lots of problems that require 'jumping-out-of-the-system', finding a solution that violates what you thought were the rules, problems that are unsolvable until you look at them from the right angle of sideways, etcetera etcetera. I'll see what I can do about recollecting some of those and throwing them at you."
"The warning sign that you need to 'jump-out-of-the-system' is the feeling that you've just had. Well, that everyone except Carissa had. Frustration, flailing around in the dark, trying desperate wild ideas and getting unhelpful results one after another. When you feel like that, you're probably thinking in the wrong language, or missing something fundamental, or trying to do something that is in fact impossible. Or impossible using the tools you have."
"In the absence of that warning sign, if it's plausible you're thinking in the right language at all, the next step is trying ideas from that language, looking for experiments that give interesting results, not just experiments that prove a particular theory, and then interpreting what you see..."
Keltham: "But first, I conjecture that - although you all continue to look very interested and cheerful, even having finished the task requiring you to control your expressions - you are in fact stressed out by how I was asking you to do something you were never taught how to do."
Keltham: "All 'pre-paradigmatic' Science is like that, let's be clear. 'Pre-paradigmatic' Science is what you do when you don't know what to do next. Like the distinction between 'calculation', when you know the next steps, and 'mathematical-thinking', when you need to figure out the next steps. You are here to invent the straightforward solutions that other people will someday learn, and that is not, itself, a straightforward task."
"But while you are learning to do that, if you ever want, for example, any recovery breaks after I've asked you to do something that was in fact very stressful, you need to actually show any emotion. Or, failing that, say something out loud about it."
"When I first met the current researchers, I was trying out dath ilani teaching methods that aim to produce confusion, so that people can learn what to do when they are confused. Instead of looking confused, my students continued to look fixedly cheerful and enthusiastic, as is a Chelish person's 'dignity'."
"So I tried harder to confuse them."
"Bit of a 'communication-with-aliens' problem, there."
"Ione, am I wrong about this? I was expecting you tell me they were feeling stressed about -"
Ione Sala: "They're a bit stressed, but they also think of themselves as tough Asmodeans who wouldn't be happy about my speaking up about it. And they are in fact tough Asmodeans who'll end up fine even if you stress them out for a few hours more. We were scheduled to go to the Worldwound, some of the people here are back from it."
Keltham: "Cool. I can respect that."
"Regardless of how tough you are or how much I respect that, take a five-minute break anyways, to recover from that and talk among yourselves. The tier-1 researchers will clear out in the meanwhile, so you're not around anybody too high above you in the org chart. Ione, Carissa, Meritxell, Asmodia, with me."
Alexandre Esquerra: Alexandre has been carefully modulating his emotional reactions and letting five to ten percent of them through! He's kind of surprised that Keltham hasn't noticed how obviously he's giving off signs! He stops once Keltham leaves, of course; it's easier for him to think, if he doesn't need to bother controlling his emotions and can just conceal them and focus on what matters.
How could he have solved the puzzle better? How could he have not come in last? (other than sabotaging the other researchers which would get him punished and alterAlexandre would never do and so he is at no point seriously considering.) He can name the unspoken assumption he made now, that math never reacted to you, but the math was supposed to be a simulation of nature, which can react to you. (As in Keltham experimenting with acid and needing protection spells.) If he had paid more attention to the instructions, he might have noticed the confusion. That he didn't was an error characteristic of underestimating Keltham. An error he had been warned against and made anyway.
(He is still kind of expecting to be whipped for that; he can understand smart mistakes not getting you whipped, but stupid ones?)
Either way... so the warning sign is that he can't think of anything to try. In practice he could think of things to try, prime numbers, size caps, base-12, individual orders of magnitude, but all of them were unlikely. They were inelegant. They depended on Keltham having arbitrarily designated some range of numbers as 'acceptable', instead of having a very simple rule that was just outside what he could imagine.
The key thing to search for is the mental state. His frustration. The sense that he was beating his head against a wall.
Well. He can look for that.
(... Also, more worrisome: Every dath ilani child can solve the mystery of the planet's motion? More evidence that he's in over his head, as if he doesn't have enough. He is starting to understand his superiors' frustration, and to be impressed at their accomplishments. He will need to work harder.)
Lady Eulàlia Avaricia de Seguer: The kid really does think infuriatingly highly of himself.
Not that he's wrong to; it is clear why he is worth as much as he is to Cheliax, and probably any random peasant who suddenly found himself treasured by the Crown and fought over by gods themselves would comport themselves similarly. She worries, though, that it's contagious; part of what Keltham is trying to impart is the habits of dath ilan, the attitudes of dath ilan, and Keltham is a teenager who thinks too highly of himself, and so he'll teach them all to become teenagers who think too highly of themselves.
You should never get too attached to a single frame through which to view a person, but as a first pass it seems to explain Keltham and Asmodia both; the Chosen of Asmodeus, she does not dare assess in the same terms, not exactly.
The classroom is frightfully silent, probably because everyone is waiting for her to say something. Well, she'll let them wait a bit longer; she's not here to make them feel like there's someone competent around, even though obviously she is having that effect.
Pilar : At Ostenso, Pilar was often the first person to talk during a Silence. A little annoying, maybe, but she understood why it had to be her. "If Keltham asks later, Willa, Alexandre, and Tonia got cookies from me. I get why nobody in realCheliax wants one right now, but those reasons don't apply in alterCheliax."
Korva Tallandria: Korva doesn't say anything to anyone, because she doesn't have anything to say. She doesn't think about the problem, either, or how she could have solved it faster - she hasn't made it through all of the transcripts that were given to her, yet, but she's definitely noticed the pattern that Keltham will constantly say things that appear to be hopelessly convoluted and complex, before more information reveals that he's actually saying something very simple, and that she wouldn't have gotten if she had been busy trying to figure out what it could possibly be with only the information she had so far. So she'll wait, and see if there are any later clues that indicate that she hasn't fully understood the lesson that's been taught to her.
Korva privately supposes that there are actually lots of different reasons why someone might not want a cookie.
lintamande: "Also most of the reasons the atmosphere in alter Cheliax would be less funereal ought to apply here and you could all stand to relax," Gregoria says. "That went fine. There'll be homework, and how you do on it will matter much more for Keltham's impression of your intelligence than this. So you're not Sevar; you already knew that."
"Is she - always much more skilled in everything," Sibilla asks.
"If so, she doesn't always show it? Asmodia usually finishes the purer math stuff ahead of her. You're definitely allowed to be faster if you can. In alter Cheliax there's no Chosen of Asmodeus."
Lady Eulàlia Avaricia de Seguer: "Is Keltham under the impression she has the same standing as his other students? He indicated she was responsible for the nametags, if they didn't happen - has he not noticed that will obviously make the nametags happen?"
lintamande: " - you know, I don't know?" says Gregoria. "I think he says 'this is Carissa's problem if no one else solves it' because he doesn't think highly of the project staff and he trusts her? But possibly the project logistics staff in fact work a lot harder when he says that because they don't get as many lectures as we do about acting like they're in alter Cheliax."
Lady Eulàlia Avaricia de Seguer: "If they have not been instructed better they are definitely doing the idiotic thing."
Alexandre Esquerra: "Is she not officially 'his deputy'?" Alexandre asks, having memorized the org chart last night so he could know he officially had to defer to. "And the 'leading shareholder' not from dath ilan?"
Peranza: "Correct." She read the corporate contracts a few times because alterPeranza likes Civilization things.
Lady Eulàlia Avaricia de Seguer: "That fails to solve your problem, which is that anything Keltham deputizes will get done as quickly as if his deputy were really in charge of this whole operation. In alter Cheliax I cannot imagine logistics would be tripping over themselves to help alter-Sevar."
lintamande: "Alter-Sevar is still sleeping with the Queen."
Lady Eulàlia Avaricia de Seguer: "Can everyone extrapolate my response or need I say it, possibly in more filtered company."
lintamande: - Gregoria has honestly half lost track of what they're arguing about.
Willa Shilira: Willa is unhappy that alter Willa needed a cookie.
Outside of that, five minutes isn't a lot of time for Keltham to get safely far away and back, so she's going to stay firmly in her shell, just in case. Even if it is, she isn't really feeling gregarious at the moment. She'll let the conversation about Sevar mostly flow over her.
What she wants to do is use mage hand to play with her quill; it's one of her favorite ways to destress (and won't it be pretty to watch once she gets that Arcane Sight.) But doing that would probably draw attention that she doesn't want to deal with. It might not even be adequately shy. She'll have to stew without assistance instead.
Willa wants to be special, and she's made negative progress at that since getting on this project. She isn't especially good at the work (yet), she couldn't make clever statements even if she could think of any, and most of her superiors already dislike her. She feels frustrated, like she doesn't have the right tools to solve the problem. Alter Keltham who she could whine to about this problem would tell her to step outside of the solution space.
What's special about Willa? If she gets hired, she's going to be selling her soul; that isn't special, especially not in Cheliax, but also selling an option on her sold soul is. Is it useful somehow? She can't think of how, especially since all the other new hires will be in the same boat, but it's a persistent idea all the same. Selling an option on a soul feels like it was definitely someone stepping outside of a solution space, but as far as she can tell it's not to her benefit. Hell is going to own her soul; in all respects it should probably act as normal until and unless the option is executed?
What other especially unusual stuff has happened? People keep ominously mentioning the tropes, so they're probably something special, but without knowing anything else about what they are they aren't special in any useful way. Even the 2-4-6 'math looking back at you' angle doesn't help if you have no idea what you're trying to look at.
Alexandre Esquerra: Alexandre thinks about telling Lady Eulàlia Avaricia de Seguer that, actually, no, in an alter-Cheliax that was at all competent, logistics would be tripping over each other to help Keltham's deputy, because literally every instant of Keltham's time is worth more than the lives of several dozen ordinary people. It's an enjoyable fantasy which would be highly unwise for his future life expectancy to try to execute, so he isn't going to do it. He's just going to think about it.
Pilar : ...and everyone's quiet again. She'll give it one more try. "Korva, you finished faster than anyone who wasn't tier-1. Any advice that carries over to the rest of us? This isn't a normal competition, the whole Project succeeds or fails as one and you end up a Duchess if it succeeds."
Korva Tallandria: Korva has literally zero desire to be a duchess, which does not at all mean that she doesn't separately want the project to succeed.
Also she kind of hates talking to people, but that doesn't mean she can't answer direct questions.
"Honestly I think I got lucky? But I thought afterwards that I would have gotten it faster if I'd been a small child, because I wouldn't have taken as many math classes and wouldn't have learned the implicit rule that math classes almost always deal with problems where the same input always gets the same output. And since a lot of the people in this room were specifically picked for their ability in math classes, they might be even more vulnerable to that than a normal person. So I was thinking that the next time I ran into a problem like this, if I got stuck, it might be worth pretending to be five, and seeing if it helps anything."
Alexandre Esquerra: The problem with saying things is that most things make you look weak, foolish, or low-status. So, useful information, Korva! We're all better off for you providing it! Alexandre is keeping his mouth shut.
Willa Shilira: Willa's model of her five year old self has a lot of really obviously terrible ideas about how to try to be special here.
Keltham: And Keltham is back! He doesn't ask what transpired during his absence, so nobody has to scramble to make anything up. He does ask if anyone's got any brief questions before the next lecture section.
Asmodia: Message on relay from Asmodia to Lady Avaricia: Security forwarded your observation to us. Mostly, Sevar and Maillol and Security and myself are already on task for deciding which Keltham-requests get handled at what speed. Nametags will arrive shortly before the hour is up. But your point is a valid one and I'll ensure that staff here understand what Sevar's alterCheliax priority should look like absent other instructions, namely less than Keltham's and higher than any other project member's.
Lady Eulàlia Avaricia de Seguer: Lady Avaricia's immediate thought in response is that that this is satisfactory behavior from Asmodia, though she does not expect that to be relayed to Asmodia in light of how Asmodia is technically her superior here.
She has no brief questions for Keltham.
Keltham: ...no questions, huh. All right then, onwards.
When Keltham was inquiring into spellsilver refinement, he was told that among the things they'd tried were:
- Using the ash of bones from different animals, and some varieties of people, in case those had more potent alchemical properties than the ash of ordinary random bones.- Prayer.- Using fire instead of acid.- Having a step in the process performed by 'godrelated people' - possibly clerics but why didn't they just say that, well, anyways.
Alas and alackaday, none of this worked to improve spellsilver refinement.
The students here may now recognize this as a variant of their own frantic flailing on the 2-4-6 game. To be clear, it's much more respectable and dignified to frantically flail around with random experiments in your current broken 'specification-language' of experiments, than to not try anything. They would have been ill-served, in the 2-4-6 game, by pulling back after their tenth failed attempt to do nothing but think; the Keltham-Environment was still walking around, and there's no point in not running tests when the Environment is right there and cheap to query. Still, if you imagine 'YES' as meaning 'YES, that didn't improve spellsilver refinement', everything the refiners tried got the same old frustrating YES.
When you haven't yet found the Answer Outside Your Previous Language, the brilliant hypothesis to test - what can you possibly do besides frantic flailing at a process that just keeps on returning the same answer?
Some of the candidates here did figure out something to do besides just frantic flailing, as they zoomed in - or it looked to Keltham like they were following that track, anyways.
Ione Sala: "Not sure if Keltham explained this yet, but his rule is that students recognized as more advanced speak later. So none of the current researchers will try answering that until some of the new candidates have spoken."
"Keltham will also be more impressed by wrong answers than no answers, especially if the silence has gone on for more than a few moments."
Keltham: "Affirmed, thanks Ione."
Korva Tallandria: "Check whether you're asking the right question," says Korva, because she needs to speak up for the first time at some point. "So - for the spellsilver question, take a step back and double-check whether there are any other ways of obtaining more spellsilver besides improving the existing refinement process."
Keltham: "Not the answer I had in mind, but a fair one! I did in fact check whether it was possible to detect giant masses of pure spellsilver from a very long distance away, in which case I'd have some ideas about where to look for those elsewhere inside a stellar system, but no such detection method was known."
"Alexandre," (said after reading the nametag, of course) "by the time you were finishing up, it looked to me like you were no longer just looking at my 'YES' answers, you were thinking about something else too. Am I correct?"
Alexandre Esquerra: He does not think Keltham means his flailing with prime numbers or powers or base-12, which means Keltham already knows -
"You are," says Alexandre. "I was paying attention to your response time. You responded faster to some queries, slower to others. Since all questions received the answer 'yes', I gained almost no information from a 'yes', so instead I focused my investigation on what triggered an unusual response from you, in the hopes that would lead me to the Law."
Keltham: "Well stated. The reason being, of course, that as there were more and more inputs on your paper, I had to scan through more and more of them to check you weren't repeating anything, especially if the input was just a few small digits with a particular pattern of positive and negative values. I could, of course, lengthen all of my response times equally, to eliminate the information from this 'timing side-channel attack'. I elected not to, because it was illustrating an important point."
"From the standpoint of the Law of Probability, any time you see evidence that's almost entirely what you expect, it's not producing much of a shift between hypotheses. You were already expecting the 'YES' answers, so that part wasn't informative. You might not have had the correct hypothesis about what was producing the timing differences, to see that it was being validated; but at least you weren't already sure of what the timing would be like on each input. By poking around there, you were gaining information faster than you could gain it from my, apparently, just always answering 'YES' to everything."
"Willa, you're one of the others who noticed the 'timing side-channel', or so it looked to me. How would you apply a similar kind of reasoning to spellsilver mining?"
Willa Shilira: Wow this is terrifying. She obviously has to think fast here.
"I would shy away from trying new tests similar to tests that got a result that was just as good, or almost as good, as the usual process. I'd focus on ideas where the first test went really badly and screwed everything up somehow, and try to do something slightly different than that. Because if it managed to make a lot of difference, even if it was bad, doing something similar might make a lot of difference that's good."
"You'd need to be pretty wealthy to do tests like that because you'd waste a lot of ingredients and potential spellsilver that way, though, and maybe never get anything to show for it."
Keltham: "Somewhat valid? It's usually not true that, if you can make something a lot worse, you can reverse the same manipulation to make it a lot better, especially if you're dealing with processes that somebody already refined to near an optimum. Lots of things that aren't at all like the current refining process, won't work at all to refine spellsilver; if you find that result, it's not surprising."
"The version of your idea that I'd suggest is to look for things you can do that make spellsilver refinement slightly worse, rather than wrecking it completely. Then, measuring quantitatively how much more of those things you can do, to make the output how much worse. Then, trying to see if you could predict those quantities - maybe not in the sense that you would have a brilliant theory about it, but in the sense of trying some new intervention that ought to make things slightly worse, and trying to call in advance how exactly that would go."
"Similarly, if you'd been mounting a more serious attack on the Keltham-Environment, your obvious next step - from a dath ilani standpoint - would be measuring my response times down to the second, or even a fraction of a second, writing those down, and trying to predict them precisely."
"This already is a way of thinking that seems not quite to be known yet in Golarion. The spellsilver miners and refiners to whom I spoke, had stories of what didn't work, but not measurements of exactly how much it made things worse, nor theories to predict exactly how much damage would be done by which failed interventions."
Willa Shilira: Willa feels chastened; she was so eager to 'step outside the solution space' that she went too far outside it. And looked stupid again.
But it occurs to her now that even if you were trying relatively risky experiments, you might not have to actually try them all: you could just decide on what experiments you might do, and then use Auguries or even more powerful future predicting divinations to see if they would lead anywhere or not. It'd be a little bit error prone, but it'd also be much cheaper and faster than going without.
This isn't to say you wouldn't still do experiments and take data, but the experiments you ended up doing would be selected in advance by a sort of filter. You'd effectively be putting more educational sequences into your 2-4-6 game, on average.
This is an idea born of magical knowledge though, and so it might be more than a little dangerous. Especially because getting Keltham into the habit of preparing and using too many divinations of that sort could end up going pretty badly. But then again, it's the kind of thing Keltham will probably think of doing himself before too long, and it might make the conspiracy universe more probable if all these other people more used to having magic available didn't suggest it first.
She thinks loudly at security to ask Asmodia if she thinks mentioning this Augury-pre-experimenting line of thought is worth the risk.
Asmodia: Sevar's call. Considerations Asmodia can see include 'if he relies more on Auguries we can spoof him', 'it adds a random factor that makes it difficult to control him', 'we screw up the probabilities on Augury failures', 'if this speeds things up we want his work sped up', 'if this is a good technique we want it developed here and not in Osirion later'.
Carissa Sevar: She'd be firmly against, if not for the ability to spoof the augury; given that, it seems worth proposing.
Willa Shilira: Willa manages to be surprised that she gets to ask the question herself; she'd kind of been assuming her questions would go to someone else if they somehow managed to be good. In hindsight, that would probably create bad colors on The Wall, which is something she should've thought of to begin with.
"What if we used auguries to help select our experiments? We would think of two plausible experiments to do every time we would have done one, and then cast augury to pick which."
She's getting pretty excited now and her words start speeding up. "It wouldn't always select the more useful one, but it would more often than not! So the data we'd get would probably end up being more useful! We could make progress faster, and we could even try slightly riskier, costlier experiments, since the worst failures would usually be filtered out by the auguries!"
Keltham: "Auguries are second-circle spells and trade off directly against Resist Energy (Acid) spells; their time horizon is roughly half an hour; and they're not reliable enough that we could try anything we had a strong prior expectation would be dangerous, even if otherwise cleared by Augury. It's not a bad idea, but relatively narrowly applicable - we apply it only when the experiment is expensive enough that we don't just do it regardless, only when the time horizon is less than half an hour, only when the danger level is such that the Augury's 'likelihood-ratio' of around 4 actually shifts our decision."
"We'd also have to experiment earlier to see if Augury could learn to define 'got a surprising or enlightening result' rather than 'improved the manufacturing process' as being the 'good' outcome. Which is my way of changing the subject back to the next point I was going to make: Civilization teaches a soft conceptual separation between understanding a phenomenon, and improving it. We want to develop magical Science!, and it's tempting to jump right to casting Auguries as a way of improving it. But first we'd want to understand how Auguries interact with the work of Science."
"Can Augury define 'got a surprising or enlightening result' rather than 'improved the manufacturing process' as being the 'good' outcome, if that's what we want? Is an Augury smart enough to know that a very surprising explosion can be worth the cost of equipment destroyed, for what the explosion tells us? Do we have to figure that out within half an hour for the Augury to know it was worth it?"
"The first step would be to do promising experiments, cast Auguries before doing them, go on to do the experiment regardless of what the Augury said, and figure out exactly what Auguries were telling us."
Keltham: "The question that Science begins from is 'How do we understand spellsilver refining?', and it is then this understanding that we use to ask 'How do we improve spellsilver refining?'"
"The heartbeat of cognition, as it would be said out of dath ilan, is that sensory information floods into you on the 'diastolic-beat', from this you build a map or model of reality, then you search for strategies that the current model predicts may succeed, then actions surge out of you on the 'systolic-beat', which actions affect the environment and the 'sense-data' you get on the next heartbeat. Where of course it's not a 'pointwise-perfect' analogy because in your heartbeat the expansion that draws blood in, and the contraction that pushes blood out, are distinct phases. In cognition, sensory information is always coming in and we're always acting. But, you get the idea. Well, hopefully you get the idea. I'll actually just spell out the idea. The idea is that we can be overeager about jumping ahead to trying to improve things, not so much before we understand them, but without having properly realized that understanding is a distinct task that we can focus on and solve in its own right."
"Consider again the spellsilver refiners; if they'd been saying to themselves 'How can I figure out exactly what's happening during the spellsilver-refining process?', they might have performed different experiments and taken more precise notes. Contrasted to asking 'Does this work to improve refining?' and then, when the answer is 'No', they treat that as a failure."
"The same distinction reproduces itself on the meta-level; you should consider yourself as first asking, not 'How can I make Science work better?' but rather 'What are the rules governing which ways of pursuing Science would yield which sorts of things happening?'"
"If you're just running ahead trying to improve things, you might think that 'map first, then improve' sounded like great advice. Once you enter the mapping mindset, you'll realize that the key claim is more like, 'people who follow "map first, then improve" ultimately invent improvements faster than people who don't follow that advice'. That makes it plainer that this advice is really a theory, and a theory you could poke at and test to understand the laws governing people using Science; then, with this understanding, try to improve your pursuit of Science."
"This process of Science reflecting and improving on itself is not, to be clear, something you can continue without limit until it turns you into a god. There's 'diminishing-returns' and the process 'asymptotes', at least as humans do it in dath ilan. Once you're doing most basic things right, doing things slightly more perfectly than that is often not worth the extra time it takes to think. But that process of reflection is how you get to the point of doing the basics correctly; and that's not a process Golarion has undergone yet."
Lady Eulàlia Avaricia de Seguer: Well, the sort of tedious people who make spellsilver for a living haven't undergone it yet; Lady Avaricia thinks she'd do fine at it, if she were going to work for a living.
lintamande: "...what's a diastolic beat?"
Keltham: "...your heartbeat has two distinct components, a 'diastolic' beat where your heart opens valves to your 'veins' that carry blood inwards towards the heart, and expands to draw in blood, then a 'systolic' beat where your heart closes those valves and opens valves to the 'arteries' that carry blood outward, and contracts to force the blood it drew in outwards."
"Or in more detail, it's really more of a four-stage process where blood gets pulled inward from your body, pumped outward to your lungs to get Element-8 restored from the air you breathed in and exchange 'two-8s-one-6' to your lungs for you to exhale, pulled back into your heart, and pumped out to the rest of the body, except that the two pulling-in stages from body and lungs, and the two pumping-out stages to body and lungs, happen simultaneously even as blood flows through four different pipelines... I can draw a diagram if for some reason it's important."
"I think I'd actually rather return to the thing it was a metaphor for: sensory information coming in to our brain-hearts from the environment-body, us thinking, which you could see as a kind of lungish metaphor thing, actions going out of the brain-heart to the environment-body, interacting with the environment, and we then see what happened when the sensory information comes back in. Only as a continuous process rather than in distinct stages -"
"You know, actually, forget that entire metaphor."
"Just remember that improving things and understanding things are distinct tasks, and you can often make more headway by separating out the 'understanding' part so you can explicitly pursue it as a task in itself."
Ione Sala: "Does the distinction between understanding and improving correspond to the distinction between the Law of Probability and the Law of Utility? It sounds like it should."
Keltham: "Sensible question, but no, not exactly. Probability is something like a separable core that lies at the heart of Probable Utility. The process of updating our beliefs, once we have the evidence, is something that in principle doesn't depend at all on what we want - the way reality is is something defined independently of anything we want. The scaffolding we construct between propositions and reality, or probabilities and reality, doesn't have a term inside it for 'how much would you value that thing', just, is the coin showing Queen or Text."
"But the process of Science, of experimenting on something to understand it, doesn't belong purely to Probability. You have to plan experiments to find ones that distinguish between the possible hypotheses under consideration, or even just, are effective at probing to uncover surprises and unexpected patterns that give you a first handle on what's happening. The Law of Probability just says how to update after you get the evidence. Planning an experiment that you then act on, implement, is the domain of Probable Utility and can't exist apart from it."
"In fact the influence of the 'utilityfunction' on 'epistemics', the influence of what we ultimately want on how we map reality, is in-theory-but-not-in-practice much more pervasive. In principle, how we classify things in reality and lump them together - treating all gold pieces as 'gold pieces' instead of as uniquely detailed individual elements of reality - reflects how any two gold pieces are usually equally useful to us in carrying out the same kinds of plans, they are plan-interchangeable. In practice, even people who want pretty different things, on a human scale, will often find pretty similar categories useful, once they've zoomed into similar levels of overall detail."
"Dath ilani kids get told to not get fascinated with the fact that, in principle, 'bounded-agents' with finite memories and finite thinking speeds, have any considerations about mapping that depend on what they want. It doesn't mean that you get to draw in whatever you like on your map, because it's what you want. It doesn't make reality be what you want."
"But when it comes to Science, it really does matter in practice that planning an experiment is about wanting to figure something out and doing something you predict will maybe-probably yield some possibly-useful information. And this is an idea you just can't express at all without some notion of Probable Utility; you're not just passively updating off information somebody else gave you, you're trying to steer reality through Time to make it give up information that you want."
"Even when you do get information passively, figuring out what to think about it reflects which thoughts you expect will be useful. So the separable core of Probability inside of Probable Utility is really more of a Law thing about basic definitions, then anything that corresponds to - there being a sort of separable person who only implements a shadow of Probability and doesn't shadow any structure cast from Probable Utility, who's really great at understanding things and unraveling mysteries and answering questions, but never plans anything or tries to improve anything. Because humans are constantly-ubiquitously-in-the-unseen-background choosing which thought to think next, in order to figure things out; usually wordlessly, but in words too when the problems get especially difficult. Just the action of turning your head in a direction, to look at something, because you wordlessly anticipate gaining info that has the consequence of helping you answer some other question, is in theoretical terms an action."
Ione Sala: "Just to check, is that supposed to be some kind of incredibly deep lesson full of meaning about something else important? If so, I didn't get it."
Keltham: "Nah, it's just an answer to your question. Or at least, if it had some hugely important hidden meaning about how to avoid some dreadful Science!-related catastrophe, I didn't get it either, when it was emphasized to me as a kid."
Keltham: "Anyways, I think we're drifting off-topic a bit."
"Returning to the main point, I suggested that if you were mounting a serious assault to conquer the Keltham-Environment, and you hadn't figured out yet how to get any result but 'YES', your next steps should include: Measuring other things about me besides my 'YES' answer; measuring how much time I took to answer each input, as precisely as you could with your time-measuring instruments, and writing down all those results; trying to predict the time for new inputs you constructed."
"I don't know how much Probability you got off Asmodia, but can any of the researcher-candidates say what that advice truly means - why it makes sense - in terms of the Law of Probability?"
Alexandre Esquerra: "Because it - removes twos; it destroys some of the probabilities, by exposing them to reality; it alters the ratio of the masses on each of the thousand sides of the scale, by evaporating the weight on them unevenly between them. The more we see that some types of questions seem to take longer for you to answer, the less likely it is that the time it takes you to answer a question is unrelated to the contents of the question."
Keltham: "Every time you expose yourself to the reality of my 'YES' answer, if you weren't absolutely sure already that you'd get a YES answer, some of the probabilities evaporate. That's already true. What's different about adding the timing measurement, then?"
"How does the evaporation of probability change with measuring my timing? How does it change with measuring my timing more precisely? How does it change with trying to predict the timing for particular inputs instead of trying random inputs and passively observing the timed results?"
Willa Shilira: After receiving mental approval, Willa says, "I was really surprised by the first long pause after an input of very simple small numbers, then I tried bigger numbers and got a short pause, then I tried small numbers again and got another long pause. This seemed to sharply reduce the probability that whatever was being done to the numbers was a direct computation of some kind, and from there I realized the type of answers I'd been missing really fast."
Alexandre Esquerra: "The leading theories I had were that long pauses meant difficult questions, long pauses were unrelated to the difficulty of the question, perhaps being randomly decided, and long pauses were a deliberate attempt to mislead me, 'trolling' in your parlance, in that order; I would have put roughly a 6:2:1 ratio on them, when I started, though in fact I did not think that explicitly. If I asked a question that I expected would be difficult and you answered slowly, that was evidence that either I was right it was difficult or you were trolling me, and also that - given that I believed it was a difficult question - that my first theory was right and my second and third theories were wrong. If, on the other hand, I expected that it would be difficult and you answered quickly, that was evidence either that I was wrong about it being difficult or I was right and you were trolling me, and also that my leading theory was wrong and hence one of the others - or neither of the others - was correct."
Keltham: "So that's the particular things that happened during your 'timing side-channel' experiments, and what you thought about them in Taldane. The thing I'm asking for is more like -"
"Well, I called it Probability Sight at one point, by analogy to Arcane Sight, and Asmodia called it that too after she suddenly developed it one day."
"It's an abstract way of seeing things that would generalize to doing more Science later. I'm trying to figure if there's some way to get it into people without either raising them as dath ilani, or dropping an artifact headband on them for two hours and inducing a permanent need for a cognitive prosthetic."
"Let me try -"
"So, a few days ago, when I was introducing the idea of lost-powers-of-2 as the 'truth-functional' relationship between a probability-claim, and reality, Carissa was briefly worried about how, if you could only ever lose 2s by playing that game, would that mean, people would be incentivized to avoid playing it? And I was like, nothing bad directly happens to you when you lose a 2, it's just a relative measure of how well you're predicting, given that you're trying to predict at all."
"When you start trying to predict the timing, you lose more 2s, or 'bits' in Baseline. The joint probability you assign to everything you see, goes down, because you see more. But in the course of losing more 2s, you further narrow down what's probably true, and concentrate the remaining probability that hasn't been eliminated."
"This is not necessarily something that happens every time you manage to predict more and lose more 'bits'. If that was always a productive activity, I could go on spinning a coin and seeing whether it came up showing the Queen's face, or the text on the reverse side, and lose one 'bit' every time. The thing about the 'timing side-channel' is that some different hypotheses about what could be going on, lose different amounts of 2s; that's what makes it an informative experiment."
"That's why adding this new 'variable' to measure and predict, which makes you lose more 2s, is actually a great move, because the 2s are differentially coming from different hypotheses. Figuring out which hypothesis is true, is what we care about, not how many 2s we lose along the way inside predictions we didn't stake lots of value on getting right."
"Why does it help to measure the times more precisely?"
Aevylmar: "Because it's more specific?"
Keltham: "Can you be more meta-specific about exactly why it helps to be more specific? In the language of Probability?"
Aevylmar: "Because the more precise your claim is, the fewer twos you lose if you get it right and the more twos you lose if you get it wrong?
Keltham: "I was asking about why it helps to have a more precise measurement, not to make more precise claims. But maybe you're right and all we really need is the precise claim. So we should measure my response times to within the nearest 6 seconds, but predict that my next response will take exactly 4.59823987 seconds. This way we get all the benefits of a precise claim, but without the risk of losing lots of 2s by actually measuring. Would you agree that this is the pathway of wisdom? If not, why not?"
lintamande: "More precise answers rule out more things? Like, if we're looking for a person, and we can measure where he is but only to within five hundred miles of precision, our measurement moves us towards all the theories that said he'd be in Cheliax, but can't tell the difference between theories that said he'd be in Egorian and theories that said he'd be in Ostenso."
Korva Tallandria: "You're not actually gaining more information from the precise claim if you can't measure whether it was truer than a less-precise claim."
DeAnno: "This time it would've helped because if you kept taking data it would've been clear the pauses were slowly growing longer, on average, as more and more sequences were tried. After long enough, any explanation that didn't have a reason for the pauses to grow longer wouldn't predict that, and it would lose 2s."
Alexandre Esquerra: "Because 'short' or 'long' is yes-or-no, but fractions-of-a-second are continuous; you can only get one bit out of a yes-or-no question, but many more out of a continuous one. The more data you have, the greater the updates you can make based on it."
lintamande: "Having lots of precision can't possibly help - I mean, the difference between 4.59823987 seconds and 4.59823986 seconds - that difference isn't going to be related to anything -"
Keltham: "I mean, it totally can help by the time you're Civilization, but you're not gonna get there for a while. That's the kind of precise difference you'd run into if you were measuring the difference in exactly how fast time flows at the bottom of a mountain versus the top of a mountain."
"And, okay, let me finish responding to some of the previous things."
"You can't literally measure a continuous quantity and get a continuous answer, in fact, because that would correspond to infinite precision and an infinite number of 'bits' in the measurement. It's also not true that you can only lose at most 1 'bit' on predicting something yes-or-no, for instance, you could predict YES with probability 63/64 and NO at 1/64 and see NO and lose 6 'bits'."
"When it comes to noticing just that the pauses are getting longer and longer, just measuring to the nearest round works for that; you don't need to measure to the nearest second. Being able to notice the pauses are getting longer, is an argument for measuring the timing at all, because it causes some hypotheses to differentially lose 2s. It's not an argument for measuring precisely."
"Among the remaining arguments, we have: An argument that precise claims help by allowing right claims to lose fewer 2s, and wrong claims to lose more. An argument that, if you don't measure precisely, you can't verify or falsify precise claims. An argument about how precise measurements can rule out more theories, because if you can see closer than five hundred miles you can distinguish between claims about Egorian and claims about Ostenso."
"Those arguments are all valid, for having been spoken in Taldane. But can anyone rephrase it more into the language of the Law of Probability, to fit it all into a common framework? Tier-2s may now also answer."
lintamande: "A more precise claim is one that - describes a smaller set of worlds," says Gregoria. "Not all the worlds where the person is in Cheliax, just the ones where they're in Ostenso, or just the ones where they're in this fortress. More precise claims are going to take more 2s to - find - and more observations are going to be evidence, about a more precise claim. Almost nothing I see is evidence about whether Asmodeus is 'great', because what does that even mean, but lots of things I see are evidence about whether Asmodeus expends more resources on the Material than other gods, and still more things I see are evidence - no, that's not precisely it, 'Asmodeus has thirteen tines in His crown' is a precise claim but almost nothing has bearing on it -"
lintamande: " - okay, I think there is something there, I just need to nail it down. More precise claims point at smaller pieces of reality. It takes more twos to point to smaller pieces of reality. A theory that makes a more precise prediction is much more valuable, if it's right, it hit a smaller target. A theory that makes a more precise prediction is more easily wrong, which is just another way of saying what I just said - it couldn't be more valuable if it was right unless it was more easily wrong. You have to have a much better understanding of reality to make more precise predictions and have them still be correct.
And your claim is only as precise as - if my measurement can't tell the difference between two claims, then I don't get any of the benefits of having made one rather than the other, a claim is only usefully precise if it's precise about what you're going to see, so, what your measurement is."
Peranza: "I think possibly he's just looking for us to rephrase in terms of Problem 5 from that list of seven problems he gave us just before the artifact headband got dropped on Asmodia. Which if I remember right was like - if you divide claims into a thousand parts and predict it down to the thousandth, that's like predicting that exact thing ten times as strongly than if you only say it's in a hundredth, but it could be in any of ten thousandths inside that and you're not saying which. If you only measure it down to the hundredth, you'd - uh, I'm not sure what happens then, but you obviously can't be proven correct in the claim about thousandths."
lintamande: "Yes, that's what I just said," Gregoria says.
Alexandre Esquerra: Yes, that is EXACTLY what Alexandre was trying to say!
Keltham: "Tier-1s."
Asmodia: "It doesn't take more 2s to point at smaller pieces of reality, it takes more 2s to point at smaller pieces of the probability distribution. If you assign probability 1/64 to something, it takes you 6 'bits' to point there. If you're already assigning 98/100 to some particular measurement coming in at exactly 0.891 seconds, you're only going to lose 0.03 2s each time. Once you can exactly predict the measurements very certainly, they're not helping you narrow down things much further. It would only automatically take more 'bits' to specify narrower pieces of reality if there was - some kind of - fixed probability distribution, or - this actually feels like it's pointing somewhere important but I don't know where yet."
"Precise claims don't have to talk about a smaller set of worlds, there can still be probability everywhere, it's that most of the probability will be concentrated in a narrower set of worlds."
"But theories only have so much probability to spread over all the possible precise measurements, so when there's more possible measurements, the probabilities on the vast majority of possible measurements have to be thinner. Measuring things to three decimal places is one way to get lots of possible outcomes you're measuring over. But it could also be something like - measuring three different things about it down to one-tenth apiece."
"If one theory puts lots of its probability within 0.002 seconds of 0.891 seconds, and another theory says 0.887 plus or minus 0.003 seconds, they've got some overlap, but measuring down to the nearest thousandth is pretty likely to do a good job of prying them apart. Measuring down to the nearest hundredth instead, would be like adding up all the thousandths closest to that hundredth, to get the theory's predictions about what the measure would say as opposed to what was exactly real. And then the two theories would give around the same probability to measuring 0.89, if you were only measuring down to the hundredth, and measuring at that precision wouldn't pry them apart much."
DeAnno: "You could maybe pry those two difficult theories apart more, even with only one hundredth precision available, if you constructed your experiment to measure them somewhere different."
"Theory 1 might say '7, 8, 9' takes 0.887s +/- 0.003s and Theory 2 might say '7, 8, 9' is 0.891s +/- 0.002s."
"But then you could also do an experiment at '107, 118, 129'. Maybe Theory 1 says that's 0.567s +/- 0.003s and Theory 2 says it's 0.128s +/- 0.002s. Your hundredth second resolution can detect that difference easily, it'll make one (or both) theories lose a lot of 2s in every measurement."
"You want to plan your experiments so they measure a place where your theories with the highest prior probabilities diverge more, so they're easier to distinguish from each other."
Keltham: "Good! I'm not sure how to explain what I was looking for, there, or why I wasn't already satisfied with the earlier answers, but it's something like - the difference between thinking in Taldane, and justifying those thoughts afterwards using the language of Probability, versus starting to see in probability distributions, and putting those thoughts into Taldane."
"With respect to the last point: yep, even if you can't measure precisely, you can still go looking for some other place where the major theories come apart. The thing is, that often requires more extreme conditions, or weird conditions. If you can measure time using clocks accurate to one part in ten million billion, sixteen digits in base 10, you can notice a clock ticks very slightly faster after you raise it from waist height to head height. With less accurate clocks you'd have to find much much more extreme, expensive conditions to start losing ten million billion times more time from the same phenomenon, so you could measure missing seconds. Even Civilization couldn't do that; the energies are too high."
"Still, that segues well enough into my next question. Why try to predict the timing of my next response? Why not just observe it passively and consider what it meant only after the fact?"
lintamande: "If you were a god you could probably learn just as much from observing it."