"Correct, but tier-2s speak first, Ione."

"Right.  Sorry."

They'll need to get either Gregoria or Pilar to take over Ione's current silence-covering duties via tier-1 prompting.

AlterCheliax does not HAVE or NEED a silence-covering duty and THAT is the part that needs to get conformed to ASAP.

Gregoria is trying but she doesn't actually think as fast as Ione and if she did she'd be Tier 1 herself! 

No prompting right now, if you don't have an answer ask a question, Gregoria.

"Suppose now that some 'troll' were further to say: maybe you can't trade fractions of fruit, only whole ones, because if you try to slice a banana in half, the parts exposed to the air will start rotting.  And furthermore, you can't express arbitrary ratios using very large numbers of fruit, because you've only got 100 of them."

"I'll trade nine bananas for ninety-nine cherries, or trade ninety-eight cherries for nine bananas.  What's my real ratio of bananas to cherries?  It could be a little less than 11 cherries per banana, or a little more than 10 point 8 repeating cherries per banana, or anywhere in the infinite space between!  Maybe you think you could try to pin that down by looking at the other trades I'll make with bananas, for other things that can be traded for cherries, but if anything I'd guess that the additional trading steps will just put even wider bounds on all the numbers you try to derive that way."

"So now you can't deduce any exact ratios from my trading patterns.  And, why, it's not that I'm hiding those exact ratios, it's that I don't have any, just some trading rules I use.  So now the two ideas aren't equivalent any more - I have a trading pattern where I don't accept strict losses and don't pass up strict gains, but I have no exact ratios between items."

"I can make up a ratio and assign it to you and you won't have any grounds on which to contradict me," says Peranza.

(...doesn't stay disintegrated under pressure, rallies and returns given a chance to catch her breath, because she is still a survivor out of the Ostenso wizard academy, and all the really pathetic students there are now laundry wizards in a tiny town somewhere paying back 'loans' that will last forever)

"What if I look at your ratio, and shake my head, and say that your ratio seems to me to be not quite right?  Is this not a grounds for contradiction?"

"Then you obviously know what your real ratio is and you're trying to hide it from me, in which case, once again, you in fact have a ratio."

Pretty adversarial attitude towards mathematics.  Keltham doesn't mind, he's masculine-gendertroped.

"Doesn't quite follow that I know my ratio and am hiding it.  You can know an answer is wrong without knowing the right answer, and this is in general a very important fact about how to think in Law-inspired ways.  Your sense that an answer is wrong often precedes your having any idea what the right answer is, and sometimes for quite a while."

"But yes, in general that's the idea I was aiming towards.  If we can't have fractions of fruit or unbounded fruit, then the two equivalent conditions are 'there's at least one possible set of prices-in-cherries you could be using, based on your behaviors', and 'you don't accept trade patterns that lead to strict losses or reject patterns that lead to strict gains'.  Where a strict loss is having less fruit in one place without having gained any fruit somewhere else, and a strict gain is having more of one kind of fruit without having lost any others."

"This, you might say, is how the notion of money-as-a-common-unit arises under the Law, when mortals meet and deal with each other.  The world begins with farms and scythemakers," Keltham has picked up that scythes are involved in farming, "so why does it need money?  Let farmers barter corn for scythes, let scythemakers eat some of the corn and barter other corn for metal, let the metalmaker barter metal for shoes - don't tell me that's not the right trade pattern, Tonia, just pretend I said something sensible, please."

"Why not just trade things you have for other things you want?  Why try to price everything in the same units everywhere?  Who's to say that wouldn't just cause everyone to make weird trades they wouldn't have made, would have been wiser than to make, if bartering things directly?"

"But if people are in general trading in ways that don't let you extract lots of resources from them, they will be acting as if you could price everything in corn, or everything in pounds of iron, and have their trading patterns mostly make sense in those terms.  You won't be eliminating a lot of useful complexity and extra details that mattered, when instead of having all the local patterns of bartering ratios, you instead try to price everything in corn.  You are not holding up a mirror to life, and cutting off the pieces of life that don't fit; everything does fit into the mirror.  It's safe to do the thing that lets somebody work out instantly the ratio between shoes and scythes, without having to envision in detail how relatively useful shoes and scythes will be to them."

"That's what justifies, you might say, the approach of trying to weigh a book about rare magic items, and a book about spell design, relative to one another, by weighing both of them in some common unit, and not just comparing them to each other."

"Should that common unit be gold pieces, or minutes of our time?  The minutes of our time are, from one perspective, the most natural way to think about the resources that we have; almost anything else we want, that we can try to get, is going to burn some number of minutes of our time, and maybe some other resources too, but always the minutes.  As for money, you can always convert your time into that; even if your job saturates in a way that doesn't let you voluntarily work an extra hour or an extra day, you could trade your time for money elsewhere, by finding an employer who just needs an hour of work from somebody, even if that pays less well...  Actually now that I'm arguing this out loud I have a sudden worrying sensation that in Golarion it's not actually going to be possible for lots of people to trade their time into money at any reasonable exchange rate."

"Anyways, in Civilization, where you can convert between time and money, the common wisdom is that you should learn to value everything in terms of money, rather than minutes of your personal time.  Why?  Because that way you can, without an extra mental translation step, tell other people your prices, and understand what their prices are.  Time is the personal resource closest to us, but society's shared unit of wantingness is the way we interact with everything else, and so the common wisdom is that we'll all end up better off if we think in society's units."

"Of which it is said in dath ilan, 'money is the unit of caring' - with further implications such as, for example, that if you're weirdly reluctant to spend any money on something, you probably don't care about that thing very much.  Though the proverb loses something because Civilization's word for society's common unit for pricing, 'unit-of-account', is one of three different Baseline words I've found so far that all translate into Taldane's word 'money'."

"You can - mostly trade your time into money in Cheliax," says Gregoria. "I don't know about other places."

" - I think you mostly can other places unless they have some specific thing going on like not letting women work outside their homes."

"And the proverb just translates and makes sense, I think. If you don't want something enough to pay for it you don't want it much."

"In Civilization the common unit is the unskilled-labor-hour, which is, ideally, adjusted at a pace that changes smoothly over time but ends up tracking the value of an average person spending an hour of their time doing something they have no special training or talent for.  Everybody has that to trade, even if almost nobody should actually trade it, and enough people need it now and then that the market exists."

"There's a debate about whether that unit is actually a good idea, because from one perspective, the value of that unit tends to predictably go up over time.  As technology improves and society gets more productive, the minimum amount you have to pay anybody to work for an hour goes up, in terms of most other goods.  Which is to say that for other goods, the number of unskilled-labor-hours they're worth tend down over time."

"There's an argument that this is bad, since price-setters are more eager to adjust prices upward than downward, because if you're first to adjust your prices downward before others do, you're often relinquishing some portion of gains-from-trade within implicit agreements that take time to renegotiate.  So, the argument goes, we instead all ought to have a unit of account that's worth 3% less every year, because that way prices will mostly need to adjust upward, and people will want to be the first in line rather than the last in line to adjust their prices to match new realities.  And that way prices will adjust more quickly and naturally than in the current arrangement where we have a Seasonal Repricing Day, four times per year, where all the stuck prices go down at the same time if somebody was dragging their feet on minor price adjustments before then."

"How this all squares up with Cheliax's 'gold pieces' concept, I have no idea."

Wait, what?

"Uh, gold's just worth what...people will pay you for it... the coins are just useful as a standard amount of gold so you don't have to test it for purity and weight?" Gregoria offers after she's pretty sure she's not going to make any more sense of any of that.

"I suppose if I asked whether there's relatively more or less gold, compared to all the stuff being traded that isn't gold, every year, it would be very silly to expect an answer about that from a country where Governance does not know its own annual budget, and can't measure the value of all goods and services produced annually inside the country..."

"Actually no, I can ask that.  Do prices over time usually go up a tad, or down a tad?"

Asmodia thinks very quickly.

(Implausibly quickly, in fact, but that's fine so long as nobody including her notices.)

...this direction whatever it is, should be the same in alterCheliax and realCheliax so far as Asmodia can currently tell; flipping the answer is more of a risk than keeping it the same.

These wizarding students who have had meaningful purchasing power for, like, two years, don't know!

"I heard headbands are getting cheaper?" Meritxell says uncertainly. 

"They go up, over time, but not very much? You'd need to be looking at prices over a decade or something, to see it. I could ask for my father's books."

"Well, if using gold means that all the prices tend to go up just a tad every season, instead of downward, don't be in a rush to change your use of gold as money without a lot of careful debate first.  If everything else is the same, which it could very well not be, you might be doing better than Civilization in at least that one exact way."

"...though I'm not sure how you'd get that result out of mining a metal, whose value is implicitly going down a bit every year under that equilibrium, which should induce less mining of it.  But, I am not expecting anyone in the classroom to know an answer to that... actually, I bet it has to do with Asmodeus's Church taking control of Cheliax, that probably brought in a moving-to-a-new-equilibrium-surge of new investments from outside the country and those were probably done in gold?  In which case maybe you'd need to get away from gold-based pricing in another decade, or prices might start going down again."

"Anyways."

AARGH.

Asmodia has never heard of economics and doesn’t know what an economist is, but she knows she needs one in this fortress right now.

"I have, I fear, digressed somewhat from the proper order in which to present things in theoretically pure ways; the invention of abstract units of caring is supposed to be a relatively advanced idea under the Law, to which your hand gets forced later."

"Let's go down a different path.  Suppose you've only got one of each kind of fruit that there is, but you've got, like, fifty different kinds.  You can't cut any of them into pieces or they'll rot.  Furthermore, each of your actions within the world can only swap one fruit for another fruit at a time.  You can give somebody a fruit without getting any back, I suppose - everybody has an unbounded supply of the empty fruit - but you can't make a transaction promising anyone that you'll give them more fruit on a later round.  Because thought experiments, that's why."

"I claim to you that in this world, there is no choice but to give up all hope of figuring out how many cherries a banana is worth, since all you can do is trade one whole banana for one whole cherry, and very few hungry people would trade a big fruit like a banana for a small one like a cherry."

"At least, there's no way to do it without being some kind of dirty cheater."

"But maybe somebody here is a dirty cheater, I don't know.  If so, how do you cheat?"

There's a silence, but not the oh-no-heresy silence, just the silence of a hard problem. 

And then the delightful clarity of the problem snapping into focus as like a different kind of problem done a few days ago -

"You trade someone - a coin flip where you'll give them a banana if it comes up heads, for a cherry whether it does or not. You'd need one of those dath ilani provable-randomness-creators to do it properly."

"A coin you can both see spinning works fine for that - you can use a random source of 0s and 1s to generate an arbitrary-precision fraction uniformly between 0 and 1."

"Let's say that Text is 0 and Queen is 1, on a spinning coin.  The first time you spin it, add 1/2 to the total if it comes up Queen.  The next time you spin it, add 1/4 to the total if it comes up Queen.  Third time, 1/2 to the third power or 1/8."

"Suppose you spin three times and the results are Queen, Text, Queen.  The current running total is 1/2 + 0/4 + 1/8 = 5/8 or 0.625, can't get any lower than that, and can never go above 6/8ths or 0.75 even if every future spin comes up Queen.  So if you were trying to generate a 60/100 chance of something, you could stop at that point and declare that the event hadn't happened."

"Uh, assuming there's no magic way to control how coinspins land.  If there is, you'd have an arms race between that and Detect Magic and whatever counters Detect Magic etcetera, if the coinspins were important."