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.

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.

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 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.

...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.

"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."

"Affirmed, thanks Ione."

"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."

"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?"

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."

"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?"

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."

"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 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.

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'.

She'd be firmly against, if not for the ability to spoof the augury; given that, it seems worth proposing.

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!"

"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."

"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."

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.

"...what's a diastolic beat?"

"...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."

"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."

"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."

"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."