It depends on the complexity of the power involved! And also the exact details of the visualization power since she hasn't said she wants it yet so the gift hasn't put energy into creating it.

The simplest possible power can be represented with no crossings in the diagram? There definitely exists a visualization of the type that she seems to want wherein the most complex possible first-level power has at most three elements intersecting on top of each other.

Ordinary paper is ... approximately the same size that she is? Not the size of the gaps in a sapphire crystal lattice and not the size of a star?

It suddenly conveys the impression of an epiphany. It could do a power that will fit the most complex possible first-level power onto a diagram with the same surface area as her skin and no elements smaller than about four times the width of her hair! Is that the kind of information that helps her?

That's... a start! 

General order of magnitude calculation... a hair is something something '1/x0,000th of an inch', and a more realistically doable resolution is something more like... what, a tenth of an inch? Might be closer to a hundredth, but this is all super approximate anyways. The surface area of her skin probably depends a lot on your quantization scheme, now that she thinks about it - does like, the inner surface of her lungs count? But a human pelt is probably in principle like... 1-10ish square meters? Pages are 8.5 by 11 in by convention, call it 10 by 10 call it 30 by 30 after conversion, 900 square cm, call it a 1000, 100 cm to a m twice over, so a page is a hundredth of a square meter, so you need ten hundred pages to cover that, at a resolution that's probably like 3-4x magnitudes too small to be practical? If all of the numbers that she has lying around in her head are accurate and she didn't misplace a bajillion orders of magnitude somewhere in there, which is certainly possible. Which sums up to something too impractical to usefully transcribe physically, but probably not too impractical to store digitally and render? That's a thought, actually, though that probably doesn't solve the problem of making it usefully viewable rather than making it something digestable in any way at all. But still, progress! 

Actually, the more important question is what idk, the 50/99th percentile is like? She's not planning on trying to transcribe the most perverse powers possible, just ones that she'll end up with anyways. 

Oh, if she only wants to handle the 99th percentile of powers in a reasonable amount of space ...

It could do a visualization power of this type that renders the 99th percentile of powers by complexity in a space the size of her (external) surface area with no elements smaller than a quarter of the width of the nail on her pinkie finger.

Or it could do a visualization power of this type that renders the 50th percentile of powers by complexity in a space the size of her external surface area with no elements smaller than three eighths of her interpupilary distance? Those might be the same power. She's getting very specific about this.

- Okay, there's no reason not to just use a computer for this. 

2 m^2 is probably a reasonable number, from a quick online search? and like a quarter to third of a cm is a reasonable enough resolution. Uh... 8.5 x 11 = 93.5 square in is 225 square cm is about 0.02 square m, so that's like 100 pages. That... sounds good, actually! She should really do this more carefully but nya! It's hard not to rush when you have someone hanging around waiting on you and all. 

She nabs the power (the 99th percentile power, to be safe.)

Hopefully her math works out well enough for this! 

This spark seems to take a bit longer to generate, but as it ignites, so does a detailed five-color diagram in her mind. It's a bit more discrete than other knowledge powers — it's not instincts for drawing a diagram, it's that she can 'see' the diagram in a separate part of her mind's eye. Right now the analysis spark is showing the diagram of itself, but it feels like she could refocus it on a different spark if she wanted to.

Zatara is content to let her calculate for a bit, since he has a novel thaumaturgic construct to poke at. He spends the time examining the escaped spark.

Uh... Looks like there's some paper lying around here? Yes, good, good, good. 

She can ditch the power she was using for the ice stuff for now - can she get a power she can use to transcribe these images onto the paper? 

"Just about done! Also, please do tell if there's anything crystals I could make for you or anything you're particularly interested in, light imbuement wise? I've just started out on expanding my repertoire of both, but I should be able to do most any of the things that a green lantern can, at least at a smaller scale? I'm not too sure what would be useful to you, magically speaking, but the power is expansive enough to make things like sunstones, so..."

She wiggleshrugs.  

It can do a power for accurately transcribing mental images onto paper, sure!

"Hmm. I'm not sure what effect using non-Earthly gemstones for magic would have. The elemental emotions are a universal force, but I would be surprised if the gemstones you create were tied into the magic of the Earth, given that your soul isn't. Then again, that could mean something completely clean of prior mystical influences ..."

Zatara has landed solidly in 'magical research mode' since Topaz keeps putting interesting magical problems in front of him. He grabs some of his own paper.

"If you could make a pair of identical 'clean' crystals shaped like this ... Amethyst preferably ... Ooh! Or maybe as a circle inlay in another stone ..."

He starts sketching plans for a theoretical crystal-based sympathetic resonance spell transport framework.

She follows along as best she can! 

"I think I can? I'd expect that if you wanted for it to work well you'd probably want to set up a proper purified space first to prevent contamination? And since from what you've said, I don't think the gift is doing what it's doing by connecting to Earth's magic systems, it should be possible to create this in space, which might be another way to go about that? I've been poking at space flight in the background, actually, so that's less infeasible then it might sound, though I'm not sure how that compares to just doing a more conventional setup." 

She goes to just show off her solution before pausing, for a moment. 

"Got everything set-up with a dedicated quick transcription power - before I start doing that, is there anything I should know about safely transcribing spell diagrams?" 

She's not even sure that's like, a thing that makes sense to worry about, but better to be safe than sorry? 

Zatara blinks, and sits back from his diagramming.

"Right, sorry. So the main thing is don't write the names of certain powerful entities, such as demon lords, because they'll notice. I don't really expect that to be a problem here, but it's something to know in general — such entities usually have a metaname, a thing that their name is called, that you can safely use in diagrams. Like the tetragrammaton. Other than that ... don't use magically reactive inks, such as ritually prepared inks, inks containing mercury or saltpeter, or blood unless you know what you're doing."

"Oh! Once you have written it, don't store in in a way that it could come into contact with a magically charged object. That's why spells are usually stored on scrolls, so that nothing can touch the inside accidentally. That's not so much a concern while writing, though, because it's incomplete ... If the spell contains a closed loop, especially a circle, it is usually a good idea to finish drawing that last. That's not relevant to most spells, but for the ones where it's irrelevant it's also harmless, so it's worth getting into the habit of doing."

He thinks for a moment to be sure there isn't anything else.

"I think that's all you should need to keep in mind — magical workings that involve written components have to have some way to bind magic into the symbols. Usually that's done by using special materials (which isn't the case here), or it's done by using the caster's intent. Since you intend to copy the spell for study, not for casting, it shouldn't be reactive."

She nods firmly. 

Alright, hopefully this big stack of pages is enough for her to transcribe her four pter? If not... Can she transcribe the diagram of merged powers? If she can do that, then she'll just go down the line for the generalist material generation line and see where she can start on those. 

Oh, and she might as well merge these two up while she's at it...

...and can she convert this format into - what did he call it 'Collegium Standard Casting Instructions' with another power? The native form is probably still interesting in it's own right, but! 

Thinking ...

It could do skill and intuition for figuring out a set of compatible incantations and gestures for a spell based on a visualization in this format?

And yes, the ream of printer paper looks sufficient for transcribing her fourth-level spark. The transcription isn't all that fast — she can do a page in about 30 seconds — but it comes out in cleanly-rendered multi-colored diagram. It looks something like a knot diagram, if knot diagrams had lines that changed thickness and swirled around into continuous cursive symbols.

"Making the diagram of my big crafting power now! Looks like there's no straightforward way to transcribe it into your format, but I could get a power to help me do it manually? Probably not worth it to get into for the moment, alas." 

"I'd be interested in seeing the diagram, definitely, even if it doesn't come with casting instructions," Zatara assures her. "Does making the diagram like that take much focus?"

"Nope! More or less piping the output of one power into another, so there's no need for my brain to be too involved. Not totally sure it would work quite that way without the two powers being merged, but concentration isn't an issue, here." 

She manuevers her hand and the stack of papers to let him see the top page. 

"Excellent! Then I can give you the introduction to basic thaumaturgy while we wait!" he declares, clapping his hands together.

"The main thing to know about magic is that it is incredibly diverse, as a field. There are hundreds of different magic traditions, many with their own abilities, properties, and requirements. For example, my family has a heritable ability that allows us to replace the gestures and incantations of many spells with a highly compressed variant. That's why I can do something like—"

He holds out a hand. "!rewolf etaerC" A blooming rose appears in it.

"— and if you tried to do the same thing, nothing would happen. That's also why most of my advice is going to be wrapped in 'sometimes' or 'usually'; there is almost always an exception to any given magical rule, if you look hard enough."

"Thaumaturgy is a particular school or approach to magic that is nearly unique in that anyone, regardless of heritage, can learn to use it. It's possible that you would be a better fit for a different school, but unless you have a specific magical tradition that you already know you meet the requirements for, thaumaturgy is a good starting point. If you find a particular group of thaumaturgic spells, such as light spells or fire spells, to be significantly easier, that probably means you have an elemental affinity, which could become a starting point for exploring more specific or esoteric traditions."

"Questions so far?"

She hums a little. 

"Is there a specific incantation and set of gestures that you're compressing, that you have in mind when saying an incantation like that, or is it handled automatically somehow? Is there a comprehensive list of possible elemental affinities, or is it more just that there's a long right tail of possible but rare affinities outside of the ones that people tend to expect? I have the same question re: schools and traditions, and a bit of curiousity why the first step wouldn't be to test for affinities over just learning Thaumaturgy first." 

"Ah! Good questions. My family's particular affinity handles the incantation replacement ... partially automatically. We can cast spells from our own tradition without having another incantation in mind, but trying to adapt a spell from instructions for another tradition goes better when the incantation is already known and you keep it in mind. For the list of elemental affinities — the most common ones are fire, earth, air, water, wood, metal, light, and darkness, in rough order of commonality. But you're correct that there is a long right tail; I know of no reason in principle why someone couldn't have an elemental affinity for, say, non-magnetic steel alloys with high amounts of molybdenum."

"Giving the same kind of answer for schools and traditions is a lot harder, just because many of them are secretive, and don't share details with outsiders. I can say that I have personally met Christian priests, Caddo shamans, Vodun practitioners, street magicians, demon cultists, new-age ritualists, and raw elementalists, all of whom practiced some magic in a way familiar to me, and some in a way totally foreign. With enough experience, you can often pick up enough about magic-in-general to at least infer what someone from an unfamiliar school is doing, but assembling a comprehensive identification guide would be the work of many lifetimes, if it were possible at all."

"And that great diversity and secrecy is why I recommend learning Thaumaturgy first: I don't actually know of a way to test for any other affinities, outside rare circumstances. For example, being able to burn demons with holy symbols is a sign that one is well-suited to Theurgy — but running into a demon with which to test that is usually not a good idea. Anyone can learn to practice Thaumaturgy, with enough care and time. Ease of casting elemental Thaumaturgy spells is the easiest test for elemental affinity, besides just going around and trying to shape every element you see with your mind. What exactly makes one suited for other schools?"

He shrugs.

"Who knows?"

She hums complatively, and idly pokes the gift to see if it could give her an affinity test. 

"I see! I suppose that makes some sense - if you can't test for it directly, you can at least test for it - circularly?" 

She tilts her head, then shakes it. 

"I'd assume there's probably something - if nothing else, you make it sound like there's a lot that are culturally inherited and passed down that way, which implies that affinities are probably substantially inheritable? But yeah, can see how it could readily be some mix of too complicated to figure out and too politically sensitive to try to trample on the toes of other magical traditions." 

It could do an affinity test! What affinity does she want to test for?

"Yes, indeed."

Zatara takes a moment to think about where he had gotten to.

"And the reason that anyone can learn Thaumaturgy is that it isn't about harnessing any kind of internal power or ability — it's about shaping the magic that exists all around us into useful forms, through the use of gestures, incantations, material properties, symbolism, and so on. In many ways, it's like using a lever: pushing a boulder requires strength, but starting a boulder rolling using a lever just needs knowledge about where to put the lever and a gentle push."

"... Oh! But the reason I wanted to test whether your passenger could supply the power for a spell was because if it could then I could recommend you different styles of magic that rely on having an internal wellspring of power. But I don't think we actually tested that."

"Oh, it can! Just got a bit distracted. Have anything more specific in mind?"

She smiles a bit sheepishly.  

"It can! That's marvelous! Let me see ... Oh, there's too many options to decide. How's your singing voice? How do you feel about contracts? Do you want to concentrate on making equipment and doing advance preparation, or do you want to concentrate on spontaneous effects?"

"Body is new and fresh and should work reasonably well for singing, but I've never had much of an ear for it? It's fun, though. Contracts are interesting to me, but I'm not the sort of person who feels like their relationships should have to be mediated through them? Right now I've been focusing on crafting and advanced preparation, and I feel like that's a natural place for me to fall given the lack of dedicated crafters in the league's orbit and my relative newness, but arguably that's a weakness that should be corrected in my skillset? Hard to say."