"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?"

"If you were a god you could probably learn just as much from observing it."

"Perhaps.  Why?"

"- it just seems like anything you do only in your head, like making a prediction, a god could just - have part of them that didn't have the answer do that, or more realistically probably just do that after the fact but not be influenced by knowing the answer. But humans are weak and flawed and so would err if we tried that, and predicting beforehand makes us less vulnerable to that error."

"I remember `3. No empirical theory can prove itself except by risking its disproof.'"

"Is part of it that if you don't make the theory before the fact of seeing the evidence, it can't have a real risk of being disproved by that evidence? Because if the evidence was already there you knew how it would interact with the theory beforehand, and so there couldn't be a real risk involved?"

"More of an issue with mortals than with 'ideal-agents' or, I suspect, gods.  Or maybe it's just the Lawful ones, I don't know.  But an 'ideal-agent', even a 'bounded ideal-agent', if It considers the theory after seeing the evidence, won't be at all influenced by having seen the evidence, in what predictions It says the theory makes.  So while It might not even bother to invent some wrong theory, if the evidence contradicts it, it would nonetheless be the case, that if you asked It what the evidence said about that wrong theory, It would know the correct answer there."

"I nonetheless claim that if you hook up to the Keltham-environment a random input generator that picks three random numbers each independently between negative one thousand and positive one thousand, and let a god passively observe that, the god will learn less than a mortal playing the game with Keltham.  Well, maybe not with the 'timing side-channel' information added, but definitely without that timing information."

"Furthermore, I claim that this mysterious superiority of the mortal, over the god, has to do with a process which includes the mortal predicting things in advance of seeing them, nor may it be done without the mortal making those predictions."

"Well, say the god has several theories and isn't sure which is right. If the god doesn't get to choose the numbers then they can't pick numbers that distinguish between their theories. You can figure things out a lot faster if you get to choose what tests you're doing. So being able to choose which tests to do is really valuable, but only if you have - some underlying guess about what's going on, so you can choose tests that show if you're right. If you have no idea what's going on then tests aren't any more valuable than the random numbers."

"Yeah, that's basically it.  In terms of what you should be feeling using Probability-Sight, it's that you've got to extend out the predictions, the 'likelihood-functions', from the things that might be true, to possible observations, so you can imagine what sorts of observations might distinguish between things that might be true, and then steer into that region of reality so you get to see those observations."

"In terms of underlying Law, there's a huge amount of math here of 'computer-science', about what determines how many observations you need, in principle, to narrow down between theories in particular classes.  None of which is a practical priority for you to learn right now, because mortals are so enormously less efficient than gods, or so I expect, who in turn are enormously less efficient than 'ideal-agents', so the principled bounds hardly matter, you're going to be buying way way more evidence than a god would need to arrive at the same conclusion.  But among the things you learn from studying those impossible ideals, is that it takes much much less evidence to figure something out, when you're allowed to pick which questions to ask.  It's often the difference, not so much between 'can be done with ten copper' and 'can be done with a million gold', as 'can be done at all' versus 'can't be done at all'."

"Next I ask - is there any wise advantage in looking at a quantity, a 'scalar-quantity' like the amount of time I take to answer?  Why the amount of time, instead of, say, my facial expression and where my eyes were moving?  Not that I was letting my eyes move down the page in order, or anything that easy to catch, but still.  Why focus on the amount of time I took, which collapses down to a 'scalar-quantity', and not, say, the order in which I approached students when more than one student had their hand raised?  Wouldn't the order in which I picked students be a more complicated, structured, interesting thing to try to predict?  Is there any advantage to trying to measure 'scalar-quantities' besides that they could be measured more precisely, using a pocketwatch that I didn't catch anybody actually looking at?"

Asking dumb question is better than asking no questions. And so he will let himself be scourged by failure, again. "Even without a pocketwatch, the difference between five seconds and six seconds is noticeable. You can compare questions that received five-second waits to those that received six-second waits, and notice that there are gradual increases in the wait over time... I think that latter is important. You cannot notice a gradual effect changing over time in the order you approach students - without a truly tremendous number of tests, that is. You can in the time. But I do not know how to put that into the language of probability-sight."

"Wrong!  But positive feedback for being courageously wrong out loud instead of quietly clutching your error to yourself and leaving me, your teacher, in a silent void of zero evidence about what any of my students could possibly be thinking!  I'm also a kind of thing that requires observations to feed on in order to know things!  Lots of them, even, since I'm not a god!  Yet!"

"There's all sorts of phenomena in the ordering that you could potentially notice right away, if you knew to look for them, and that they were there.  For instance, maybe after you choose a sequence with any big number, I approach you last out of all students currently with their hand raised, and after you choose a sequence of all small numbers, I approach you first."

"But even if that had been true, and somehow important - like big numbers being harder for me to calculate and therefore unpleasant and so I'd subconsciously started avoiding people in the middle of testing those hypotheses - it would have been a harder pattern to notice in the ordering data, compared to noticing how sometimes a number is big and sometimes small.  Actually, even the example I gave of a pattern is really something that got projected down to a scalar-quantity - on a scale of beginning to end, where does my selection of you land inside the set of people with hands raised?"

"If it had been anything more subtle than that - maybe, like, my approaching a new candidate rather than current researcher next, if you showed me any big number - then while it might be very easy to verify that was going on, in terms of updating probabilities, once you noticed anything interesting at all and came up with that hypothesis, that pattern would be a lot harder to notice initially and pretheoretically, compared to noticing a number getting bigger or smaller."

"This is both a useful fact and a cautionary one.  Measuring things in scalar-quantities can give us results that are, in a certain sense, easier to work with - easier to try to notice things about - but that we find it easier to work with scalar-quantities is a fact about us, not a fact about the things.  If you're not measuring the right scalar-quantity, or if the critical measurement isn't a scalar-quantity at all, then you're just - uh, dath ilani proverb.  Somebody loses... a small precious object... a platinum piece, something worth their time to search for... while walking outside at night.  While retracing your path, it might make sense at first to go looking in any well-lighted places along which you'd walked, just in case your platinum piece happened to be there."

"But if you don't find it there, the first time, you need to go get a 'flashlight', a light-generating object, and go looking along the rest of your dark path where it isn't as convenient to look.  It's a comical character, a silly-child character, who insists that they'll go on searching the well-lighted areas because those are the easiest places to look."

"If what you need to watch is in fact my facial expression and not how long I take to answer - then you'd better not get too attached to measuring things in scalar-quantities.  But scalar-quantities sure do make sense as a thing to quickly check out first, if you have a choice of things to look at.  In fact, you might find it so much easier to notice patterns there, that your Science-mind gets out of the habit of even looking at things that aren't easily-measurable scalar-quantities!"

"With that caution in mind - scalar-quantities are easily related to each other.  Not just that, easily related to each other by math, which makes it easier to notice all sorts of mathematical patterns in them."

"If you'd started recording my times more exactly, and found that my average delay times were growing over time for every student, but growing at different rates for different students, you could start looking for other scalar-quantities that were growing at different rates for different students.  Then one of the scalar-quantities you checked might be 'the number of previous inputs that student had already written down'.  Then when you found that my delay time was roughly and on average proportional to the number of previous inputs - in a way that was similar across all the students, even as different students had different numbers of previous inputs growing over time - you'd have a critical insight into the structure of the Keltham-environment's behavior."

"A habit of measuring all the even slightly relevant-looking things that come out in scalar-quantities, or in Baseline, 'quantifying' the 'quantifiable-observables', is something that Civilization has in fact found incredibly useful.  When we start messing around with spellsilver, we're not going to be trying a bunch of random crap to see if anything works, even as written in the language of 'chemistry' where random tries are much more likely to do interesting things.  We'll crush a lot of spellsilver ore down to sand, and mix it all thoroughly so every batch of ore-sand we use is almost exactly the same across experiments.  We'll try small perturbations to the process, most of which will be harmful, but we'll quantify exactly exactly how much less spellsilver came out the other side, and compete to come up with theories that try to call those experimental results in advance."

"Even if most things we find make the process worse, those are still facts we can use - especially in combination with other dath ilani knowledge - to build up 'testable-hypotheses' about what's going on inside the spellsilver-refining process."

"Am I saying the same thing as you if I say 'it's good to measure lots of things, but it's especially valuable to measure things you can turn into numbers on a common scale, because those are some of the easiest for humans to notice patterns from? So when stuck, measuring your response times was likelier to be useful than noting whether you blinked or not?"

"Yup!  Well done at simplifying back into Taldane!  Though, to be clear, it's even more easier for machines to notice patterns in numbers, but you won't have any number-noticing machines for probably a fair while."

"But all of that, this entire previous discussion, is something you could also say to an individual trying to understand, analyze, and improve spellsilver refining."

"What distinguishes 'SCIENCE!' from merely ordinary individual Lawful experimentation with the goal of probing for unexpected patterns or distinguishing among hypotheses already formed, is that 'SCIENCE!' is a protocol for stacking the efforts of multiple individuals - the efforts, indeed, of all Civilization.  It's a designed artifact-shadow of Coordination in much the same way as Governance."

"What, do you suppose, would be the key ingredients of 'SCIENCE!' as a multi-agent practice of Civilization?"

"They get the smartest people to organize it?"

"They offer rewards for correct theories." And punishments for incorrect ones. 

"Standardization of weights, terms and measures, and requiring universal and public record-keeping." Because otherwise people could pretend to lose less 2s than they, in fact, lost, by selectively reporting only the predictions they did well on.

"They do it with prediction markets."  Because he explained those shortly before explaining this.

"You need either a way for people to see and interpret the results of other peoples' individual experiments, like standard reporting of results, or a way to aggregate individual guesses into an overall best guess without anyone having a reason to say something other than their real best guess - if you have that, you don't need everyone reporting their experiments, just betting on reality with the knowledge their experiment gave them. Prediction markets do that, and also do another thing you need, which is a reason for people to go out and do experiments instead of staying home and making their numbers up."

"Prediction markets actually don't work well enough at paying people to go out and secretly do experiments.  The market traders are pretty good at guessing when somebody else is just coming in with new information, and the old traders won't sell at their previous prices - the price moves sharply enough that the experimenter often can't make much of a profit off the prediction market.  Like, the current price is 80%, but that doesn't mean you can just buy a million shares at 80%, reveal your experimental results, and resell at 90%.  Once you start buying in massive quantities like that, the price starts moving upward from 80%, because market participants have guessed you have private information."

"It's more straightforward and direct and less clever than that, actually; what happens is that people will just straight-up promise 'impact-purchases' on discoveries they want to see made."

"Like most dath ilani males, I am 'gynosexual' and very 'straight', meaning that I'm only attracted to women, and mostly only if they present with fairly central feminine gendertropes.  Like most such men, I committed to the outstanding bounty for finding a reasonably-completely-safe 'medical-enhancement' intervention that would make me also be attracted to men, because, as all the 'bisexuals' keep telling the rest of us, we're missing out on half the fun.  The collective commitment is up to something like a hundred billion unskilled-labor-hours at this point... about five hundred million gold pieces in Golarion terms, maybe possibly?  That's how rich you would be in dath ilan, if you singlehandedly found a safe way to turn men bisexual, all by yourself with nobody else contributing.  It's one of the biggest, most famous unclaimed bounties."

What.

(No comment, this is a class.)

- most men, if their battalion gets deployed somewhere where there aren't any hangers-on around to keep them company, like at the Worldwound, find they're actually into men after all. Or, you know, able to get a blowjob and pretend it's a girl at absolute minimum.

Carissa is not sure this is a valuable observation.

"Is this in fact a problem you, personally, want to solve."

"It's relatively less important to me now that I have otherwise saturated dating opportunities, but that doesn't mean I'm not curious."

"...I think it would legitimately be way way down on my list of priorities, given the current competition for my priorities list.  Why?"

"I know some categorically adequate sex therapists who'd probably take you on out of sheer curiosity. People in Cheliax have also encountered this problem, usually the other way. It does seem like a stupid use of your time but who am I to discourage you on those grounds."