"You do not challenge and attempt to undo the works of unknown divinities without consulting me."

"...acknowledged," she says quietly.  "Your further - input, on this matter?"

"Make no further attempts on the barrier around her."

"Keep a tally of all who have read her thoughts, and all who have read their thoughts, and stand ready to send them all to Hell if needed, should it prove that within her there is dangerous knowledge.  Or perhaps send them to Abaddon, if there is within her a contamination from beyond known reality to which Hell is not immune."

"That tally does include myself."

"Learn well the lesson thereof."

Twenty minutes after Merrin flopped into bed, there's a soft light knock on her door, the sort somebody could easily miss if they were sleeping.

She's not sleeping! Merrin's circadian rhythm does not actually think it's bedtime quite yet; she's not overjoyed at having to get up again, but she suspects it's going to be very hard to actually sleep until she feels more oriented. 

List in hand, she goes to the door. "Yes?" 

"We've got an eighth-circle wizard to answer magic questions!  By the time you've run out your questions to him, with any luck we'll have located the next expert for your list."

"Thank you. I really appreciate all the effort you're going to here, I - realize it's probably not cheap." 

She follows Antonio to whichever non-bedroom area is available for this, so she can be introduced to an eighth-circle wizard! (One of her many questions: what does "eighth-circle" actually mean?) 

'Manohar', his name, is a bluff cheerful large man wearing somewhat loose wizard's robes.  In terms of subverbal signals, he comes across as a very safe person to be around.

There's nine standard degrees of spell complexity corresponding to the complexity of the topology of the spells!  Cantrips are a special case, considered level zero or not-really-wizardry; they're underpowered, but so absurdly stable that you can catch them after casting and cast them again a few seconds later.  Manohar will spin up an illusion so he can show Merrin nine examples of the visible-to-wizard-sight parts of spells he's familiar with, successively more topologically complex structures.  There's only nine, because ninth-circle casters are so rare that Manohar has not, in fact, personally seen a ninth-circle wizard spell being constructed.

......Whoa. That's incredibly cool! Merrin is tempted to try to draw them in her notes, but he's not holding each one for long enough and it's probably not the best way for her to understand their economicmagic better anyway. 

"So - the successively more complicated structures are - harder to learn, and can do more impressive things? And it sounds like a lot harder to learn, if you've never even seen one. Could you - give me a few examples of spells at each level of complexity, so I can get a better sense of what that corresponds to in practical terms. Ideally where the examples at each difficulty level are maximally different from each other - I'm not sure whether spells fall into clear categories but if they do then that'd also be really useful to know." 

Sure!  How about:

Prestidigitation, a 0th-circle Universal spell that lets you chill, warm, flavor, change the color of, gently lift if less than 1 pound, clean, or dirty, an object.  Changes to object substance (not just moving, cleaning, soiling), persist for up to an hour.  This is known as 'laundry magic' and is most of what actually gets cast in Golarion.

Endure Elements, a 1st-circle Abjuration that lets people resist hot and cold environments;

Greater Detect Magic, a 2nd-circle Divination that lets you see magic in enough detail to analyze who probably cast it;

Fly, a 3rd-circle Transmutation that lets wizards fly around for up to 2 minutes per caster circle, super popular;

Symbol of Laughter, a 4th-circle Enchantment for drawing a rune which, once seen or touched or passed over, causes all creatures within 60 feet who fail to resist the effect, to laugh uncontrollably for 2 rounds per caster circle;

Decollate, a 5th-circle Necromancy that allows a target to willingly remove their head;

Contingency, a 6th-circle Evocation that can be co-cast with another spell, that then gets triggered automatically under some set condition; complicated or convoluted conditions have a chance of failure;

Subjective Reality, a 7th-circle Illusion which lasts up to 12 seconds per caster circle, and temporarily convinces you that some targeted object or creature or force is itself an illusion, so firmly that you can, for example, walk through the wall you've convinced yourself is illusory;

Create Demiplane, an 8th-circle Conjuration which creates a bounded or looped mini-universe, up to ten 10-foot-cubes per caster circle, with specifiable elemental traits, or ecology, or its own alignment, you can specify the gravity levels, etc., lasting up to 2 days per caster circle, can be made permanent at a rather high cost;

Wish, a 9th-circle Universal spell which, in principle, can fulfill any spoken request, and, in practice, unless you keep to one of thirty or so known phrasings, results in an enormous flaming crater or worse.  This is a bad idea and you should not do it, even if you've thought of a very clever way to do it, which is where the enormous flaming craters come from.

....This is the weirdest flaming magic system that Merrin has ever heard described. She feels as though she's reading the worldbuilding summary-notes of a novel that was written by an author who was taking three different Ill-Advised Consumer Goods mind-altering drugs at the same time. And not trying at all to make it seem surface-level coherent, though presumably there's some deeper level on which it makes perfect sense. Merrin feels like that was a very dense and helpful information-dump and yet it's not very much constraining her predictions at all. 

Why in the name of radioactive sewage is there a spell for WILLINGLY REMOVING YOUR HEAD. They don't even have cryonics here which would at least be something where it might be useful. 

There is a spell specifically for programming conditional statements into other spells and that is incredibly cool and also...surprising...? She's not sure why it feels surprising, yet, but there's something to be poked at there. 

She really wants to fly now and it's deeply unfair that she CAN'T because she is INHERENTLY IMMUNE TO MAGIC SOMEHOW. 

Merrin is pretty sure that those are only a tiny fraction of her questions and they're going to keep hitting her for the next ten minutes as she finishes processing that. She takes very fast shorthand notes, and then divides the remaining space on her paper into quadrants and starts organizing. 

"- Sorry, I may need a minute to think that over, but that was a very helpful rundown. Um. So I'm gathering that there are standard categories to describe spells, which are - orthogonal to the complexity-level or "circle", right? Categories are Universal, Abjuration, Divination, Transmutation, Enchantment, Conjuration, Illusion, Evocation, am I missing any– oh, Necromancy. I am gathering that Divination is - information-gathering, enchantment is - much more centrally mentalisticmagic than economicmagic, actually, it's...mind-affecting? Conjuration makes things. Illusion I think actually mostly translates straightforwardly to Baseline, it makes - images or imitations of things? I'm going to wildly guess that Transmutation changes how physical laws affect objects or people. I think I need more training examples or else an actual definition to figure out what Evocation or Abjuration or Necromancy would cover more broadly. Universal is just...uncategorized? I want to confirm if my guesses there are at all on the right track and get some more clarification, and I think I could also use more detail on - where spells come from, why are do these specific ones exist and not others, and approximately how many different spells exist by category and by circle."

Pause.

".....Incidentally I am somewhat feeling like you should not have told me about the flaming craters spell and I'm not sure why more than five people in this entire world know that it exists that sounds like such an infohazard. To be clear I would have no intentions of trying it even if I could do magic but still." 

Manohar's pretty sympathetic about the infohazard thing, but knowledge of Wishes seems too widespread to eliminate?  They've played too much of a role in history?  There are, as stated, very few ninth-circle casters, and most people who make it that far without blowing themselves up have some sense of caution.

Her descriptions of the standard categories... are vaguely right, for not reflecting the underlying technical realities?  Subjective Reality is an Illusion spell because moving things halfway out of reality relative to yourself is technically dual to moving things halfway into reality relative to somebody else.  Evocation calls on forces and elements, bringing them into reality, evoking them.  Abjuration prevents something or tells it not to happen or blocks it.  Necromancy involves the manipulation of life and death.  'Universal' spells are called that because they don't have any of the technical qualities from the other categories, which means you can cast them even if you're a specialized wizard who's pretty bad at some category of effects.

Spells get copied and passed around down through centuries and millennia.  Unusually powerful ninth-circle wizards sometimes invent new ones.  Failed spells tend to explode and resurrections aren't cheap.

These spells exist and not others because - the person who made them, wanted that spell to be a thing, and it turned out to actually be possible and also they could figure out how to do it?

There's anywhere from, usually, six to a couple of dozen known spells per category per circle.

Merrin is now incredibly curious to know the underlying technical realities! She is aware that this is almost certainly not explainable in ten or twenty minutes. 

"So that's -" she does some very quick mental rounding, ten "circles" and assume ten categories and ten spells per, "- roughly a thousand total known spells? Do there tend to be more at the lower-complexity circles?" 

Dath ilan screened off their history and for all Merrin knows it might have been in order to eliminate widespread knowledge of something analogous to Wishes. Merrin doesn't say this out loud; it seems pointlessly critical and unproductive. She...is kind of curious what the difference is, there - Golarion doesn't have Keepers but it does have gods - maybe the gods of other alignments would be in opposition, even if Merrin is pretty sure that Asmodeus, being "Lawful" "Good" whatever that actually means, would be in favor of fewer flaming craters. 

Also this entire world's attitude toward research safety continues to be ridiculous even though it makes sense in context. 

"...I'm going to see if I can guess how spells I already knew about would be categorized. The translation effect is - maybe Enchantment? The lights are maybe Illusion or maybe Conjuration? I think most of what Albe tested with me was Evocation. If the flying spell is Transmutation then probably the instant-movement spell is too - what circle is that, incidentally? And do you have any approximate statistics on how many wizards exist in Cheliax at each circle? Or just relative proportions if you're not sure of total numbers." Merrin is making a not-very-confident advance prediction that it's probably a power law distribution. 

A thousand spells sounds about right?  Maybe a little low?  Fifteen hundred?

Half the population could learn Prestidigitation if they tried, every village usually has at least one person who knows laundry magic.  Five percent of the population actually is first-circle wizards - Cheliax is proud of this, that's the highest ratio in the known world, reflecting Cheliax's excellent education system that among other things identifies smart-enough people and wizard-tracks them - and then it halves for each circle up from there, more or less, with sharper dropoffs as you start going past 4th, 7th.

Speaking Baseline is Divination, the lights above are Evocation, the instant-movement spell is 5th-circle Conjuration, most instant-movement spells are, though there's a 4th-circle Illusion called Shadow Step that lets you step into one shadow and out of another.  What Albe tested was Conjuration.

....Yeah, she's clearly going to need to know any of the technical details before she can start to make sense of this magic system at all. 

Oh no why does becoming a wizard ALSO rely on being very smart, terrible not actually one of her biggest problems right now. 

"What's - difficult about magical education, other than inherent intelligence limits? - I did previously learn that you can use magic to increase intelligence, but if it requires a very expensive and difficult-to-make artifact then I guess that doesn't help much on the scale of Cheliax as a whole." She also has SEVERAL questions about how and why that's a thing that works, and she barely has guesses about what category it would be, aside from 'probably not Necromancy'. "...Also this is not actually an important question but why did someone invent the head-removing spell. What do you use that for." 

"I don't know why anyone invented it and I've literally never heard of anybody using it for anything.  A lot of the other Necromancy spells that come to mind are less pleasant; the field and its famous practitioners have something of an ill reputation, especially in Lawful Good Countries."

"Intelligence is indeed the primary requisite of wizardry, mainly for being able to visualize the invisible interactions of magic involved in constructing and hanging a spell for later use.  This in turn requires advanced mathematics, in particular incredibly-elementary-algebra-your-parents-teach-you-before-you-start-school, ridiculously-basic-topology-for-nine-year-olds, and at higher levels, linear-algebra-too-simple-to-bother-with and the-first-five-minutes-of-a-calculus-lesson.*"

(*) Not literally the terms in Baseline, just what the actual and precise mathematical subject names sound like to any dath ilani, even Merrin.

...If it turns out that Merrin knows more math than literally anyone on this entire planet she is going to. She doesn't even know what. The worst part is that she probably shouldn't be surprised. She keeps noticing evidence in one direction. 

Currently she is feeling torn between 'run around in circles gibbering in horror' and 'somehow, PROFIT'. 

"Manohar, how long would it actually take for me to check if I can learn the 0th-circle one, um, Prestidigitation? I might only be immune to external sources of magic." 

"If you already possessed all the mathematical requisites and were exceptionally talented... probably still several hours per day for several days?  Months would be more typical of the average student who succeeds at all.  The most talented wizard not ancient, out of the current world, is said to have learned her first 0th-circle within half an hour; it's said that she had a native intelligence of 21, where 10 is the mean for this world and 2 is the... your language has a single-syllable term for standarddeviation.  I don't know why that surprises me, at this point, but it does."

"I suspect that the average intelligence of your own world was not 10, on our scale."

Okay but none of those requisites are actually math. Merrin learned them FINE without it even being much EFFORT, therefore 

"I...don't know what '10' in your scale would correspond to in our measurements, but - assuming I have not met literally anyone with an intelligence of 10 because everyone I've met was filtered for either being a wizard student or the sort of expert or Governance official you'd send to greet someone from another world - then I agree." Shrug. "I doubt I'm exceptionally talented either way, but I do know the prerequisites," and a lot more than that. "Dath ilan - may just be a lot better at math education than here, the way Cheliax is unusually good at teaching wizards. So I think I want to try, even if it's likely to be time-consuming. If I can learn it at all, that - gives us some information about the limits of my antimagical effect, which - maybe lets us infer something about the purpose of it." 

That could happen.  Does she want to start right now?

The actual answer is that YES SHE DOES whether or not this makes sense as a priority. 

"Um, I - yes, but I'm waiting for some other experts to answer different questions I have, I think I'd better sort that out first before I commit to several hours of practicing. I think I've already asked all my basic questions for you, and to the extent I'm still confused it's about the technical details and actually trying to learn how to do it seems like a reasonable way to get less confused. Though I don't want to take up more of your time than I have to, especially . You could just explain the kind of exercise I would need to do, if it's something you can cover in twenty minutes, and I can arrange to actually practice it later, maybe with the wizard students I met earlier?"