Whoa, that's so pretty! 

To start with she'd like spellbooks for herself and Leareth, then. Also would it be all right if she watched Carissa do some cantrips, to see what the magic looks like to their mage-sight? 

(And also what the mental control aspect looks like to Mindhealing Sight, because Nayoki has more than just mage-gift, but she doesn't volunteer this.) 

Of course.  She can make them some spellbooks right after this.

She runs through her cantrips - Detect Magic, Dancing Lights, Prestidigitation, Mage Hand.

That gets Leareth's attention, and he watches the magic intently. He seems to be enjoying himself, or at least is very engaged. 

"What would researching new spells look like?" he asks her, once she's run through all of them to his and Nayoki's satisfaction. "You mentioned it was dangerous and would require precautions; I am wondering if the shield-talismans and Work Rooms we can provide could be enough to make it not very dangerous for you and thus lower-cost." 

"You have to try to derive for yourself what the spellform should be, from the forms of related spells. Sometimes it explodes in your face. It'd depend on the quality of your shield-talismans, I'd think. Inventing new low-level spells won't kill me regardless but, for example, you'd probably want Scry and Teleport, and those are powerful enough to kill me if they explode in my face. At home powerful wizards mostly arrange for resurrections before they do dangerous spell research but I would have to rederive Limited Wish for that, and I'd worry that with no afterlife it might not work."

Leareth and Nayoki share a glance, and then Leareth nods. 

"That does sound like more risk than I would prefer to take. Hmm. Can your Detect Magic gauge the approximate power level of a spell as well as its structure - for example, if I wear a shield-talisman and have Nayoki demonstrate attacking me with a spell that is within its tolerance to block, and you were watching from a safe distance, could you judge whether that was more or less power than an exploding Teleport?" 

"Leareth regularly tests magic that explodes in his face and would kill him if he were not shielded," Nayoki says, smirking. 

"I haven't seen fifth-circle spells explode. I could probably manage an informed guess."

Nod. "And if I can arrange enough protective shielding on you to hold off two or three times that much magical force, I would feel reasonably comfortable with you carrying out that research. ...Hmm, also I am guessing you could try to derive some third or fourth circle spells first? How does the power tied in in spells increase with circle - could you make a third-circle spell explode on purpose so that we can observe its force...?" 

"Sure, if I do it a little bit wrong, and I'll definitely do it a bunch by accident trying to rederive the third-circle spells I know but don't have. Power scales faster than circle - the difference between fourth and fifth is larger than the difference between third and fourth. More powerful casters also sort of incidentally get good at channeling more power in their lower-level spells, and at making them last longer, there's a single underlying skill."

"...Hm. Do you recall if there is a consistent mathematical relationship there, even if not a linear one? If you have first, second, and third-level spells now, and can make supervised mistakes so they explode while we are watching, then maybe we can graph it out and predict what fifth-level will look like." 

"It is consistent, yes, within the range we have good ways to measure which doesn't go all the way to ninth."

Nod. "Well, I think that with some research and preparation, we can probably make it safe for you to do spell research, if you are up for that." 

"Of course." He has good reason not to get her killed yet and it might be something she has an edge at over the locals because she's been studying magic longer.

Leareth folds his hands over one knee, looks levelly at her. "It sounds like we have a plan, then. Nayoki and I will study cantrips to get better intuitions for how arcane magic behaves, and I can design some tests to figure out a model and get a ceiling on power discharge from exploding spells at different levels, and we can build you a safe work area and get you shields for that research. ...Also if you think you can make the enchanted dagger that makes the bearer invisible, I am especially curious to study that one and compare it to our illusions, invisibility is possible but very challenging with our magic. Is there any other research that seems particularly promising to you?" 

"I don't know what else is easier with our magic than with yours. Some things might be valuable if your world's defensive measures against them don't happen to counter our version, like scrying. ...I'm tempted to try to rederive the ancient prophecy spells, if prophecy works here - does it?" 

"That makes sense. We have a local spell we call scrying, and defences against it, but I would not be surprised if the Golarion version works by a different route. And, yes, we have Foresight, though mostly it is the gods and certain - beings created by Them - who can access it fully. Humans are sometimes born with a Gift of Foresight. It comes in two variants. Short-range gives visions of personally salient events in the next few minutes to candlemarks; long-range usually shows up as cryptic vivid dreams and refers to events months to years ahead, and I think it is more likely to be directly mediated or at least easily meddled with by god-level powers. There are also...weirder phenomena, here, followers of our gods will sometimes receive direct prophecies despite not having the Gift of Foresight. I am not sure if the mechanism of Foresight here is similar enough to prophecy as it once existed in Golarion that your spells would work, but - it seems worth trying, it could certainly be very powerful." 

"The gods used to be able to see futures, in our world, but it broke when Aroden died. I don't know what it was like but there are spells for extremely short term knowledge, the next second, and I think the prophecy spells that don't work anymore were related to those, and I could try, eventually, if it's safe to experiment."

Nod. "That makes sense. - Also your world has spells that increase intelligence? I am very intrigued by that. This is - as far as I know impossible with our magic." 

" - huh." Actually she should've guessed that because he's smarter than her but not nearly as smart as someone with a thousand years of access to intelligence-enhancement should be. "Yes. Wish can do that but I'm not going to be able to rederive Wish, I'm sorry. But you can also make headbands that do it and those I could learn how to make."

Leareth nods. "Then that would seem a high priority. Probably you ought make one for yourself first, since I assume it would help with your research? I am not sure how costly each one would be in time and materials." 

"I need to retrain into wondrous items or - do something that I can't think of a reason you can't do but I've never heard of -" she could make very small wearable swords. In concrete terms this is probably not very different from retraining into wondrous items but it's more obvious how she'd do it, with no wondrous items to study. "Once I can make them at all I should be able to make a standard one every two days, with less materials than the dagger, or if you have lots more spellsilver I could make the most powerful kind known to be stable, which would be...between four and five times as much spellsilver and take four or five times as long. It'll help me with my research but I presume it'll also help you with yours."

"Well, yes, but I have been doing my research for a very long time and you have not. And I do not expect to be bottlenecked on raw intelligence for the initial part of learning your magic, it looks - complicated but not that complicated and my existing senses and intuitions for magic will help. I am in favour of you making a standard one for yourself first and then me, and once we have more spellsilver available - I am planning to open a new mining project to obtain more of the relevant ores - then you can try the more powerful one. How does that sound?" 

"I can do that." She still hasn't figured out the locally appropriate term of address for him; maybe there isn't one. "I don't know how long it'll take; properly training into wondrous items usually takes at least a couple of months but I might be able to do something faster than that."

"I understand." He shifts in his chair as though to rise. "- Anything else?" 

"No."