He oohs and aahs at everything.

Based on what's in the sky right now, the simplest use would be checking the angle between two points. Or the air pressure thing. Neither sounds very useful, actually, but the sextant can help point out which areas can and can't be affected by which constellations. So, math!

It's not quite as simple as drawing a copy of the stars. It would be in the degenerate case where the relevant stars are directly above, but of course that's rarely true. She describes what she's doing as she goes, with delays for more explanation at some of the right times. One of the displays shows a map of the city with the sites of the "stars" marked; the ones that are lit up are showing a distorted form of the constellation. Which is like four stars, but still. Eventually the calculators spit out which sites to use and which lights there would come closest to the ideal position.

Diana prints off a diagram matching the earthbound version of the constellation, tapes together the sheets as needed, and points out which switches will activate the right points.

"Would you like to do the honors? There are a few minutes to spare before the sky comes closest to the best match I could set up."

"Sure! Tell me when."

A countdown flickers into existence, each numeral taking up a quarter of the screen. Because why not. It's not long before it hits zero.

Flick!

There's a few seconds' delay, then a flash. A sextant appears in the diagram. It looks mostly ordinary, except one smooth piece rather than metal joined together. Shafts of light project from its openings. If he takes off his glasses, it's too bright to look at.

"It'll last for a few hours before it fades. Until then...any two points you'd like to check an angle between?"

He laughs. "Oh, sure, how about here and here?" he asks, pointing at two random spots.

She consults the map for what they're looking for.

This construct doesn't seem to care that the line of sight is obstructed. After she fiddles with it, the eyepiece shows a single point at each of the correct distances away. Not very useful for spying, but it makes it trivial to compare the apparent angle.

He giggles more. "This is amazing."

"Isn't it? While it's here, there were a couple other measurements we should get..."

She helps Sadde use it horizontally. The sextant is oddly steady in the hands of a novice. A spotlight pointed upward from the roof of a small building makes a precisely measurable angle with the one part of a floodlight system that the field's owners can never seem to keep in working order. And so on, collecting several measurements for a small handful of installations. (For anything that looks like the Astrologer probably doesn't technically own it, she has it flash briefly and then stop. Unobjectionable ones can stay on.)

"There might be a way to use the existing lights to copy Aquarius with the right amount of foreshortening to get a few extra weeks. This is to double-check the geometry as much as to show off the computers; most of the rest will just be math."

"Maths is fun anyway. Are there books about this? Do you have a list of everything you can do or do you just rederive it from basic principles?"

"No books, but there are notes from the people who developed it. Um, I probably shouldn't say any exhaustive list of what has and hasn't been discovered though."

"—yeah, that's fair. Er, I promise I have no plans to harm you or yours or use this knowledge against you, and my interest in any lacks, loopholes, weaknesses, or any other kinds of limitations of this system is strictly curiosity and interest in the system itself."

"Pretty sure most practitioners wouldn't accept that, but it's not like I don't like talking about it anyway."

She doesn't have to dig far to find a well-worn binder full of city maps and star charts. The index pages are in her hand, but flipping through the pages shows some unfamiliar writing. Hers is a relatively small minority. It's organized by date: which stars are best positioned when. Within each month it's roughly by complexity, but the bookmarked pages are labeled as being useful.

"There is definitely more that can be done; this is just what's been developed so far."

He drinks it up. This is fascinating and way fun.

She's glad someone else thinks so! Most of the tricks look like more trouble than they're worth, or very powerful but only on a limited area not of their choosing somewhere in the city, or keeping the lights occupied for long periods of time. And then some of them are "summon superlatively strong construct to bash one's enemies." (That one isn't marked as useful.)

He doesn't really think it's super useful in general, either—life's more than fighting. But his life... well.

Diana skips over those ones more quickly than most. On to more interesting things, like a complex method of invoking any of three constellations to increase ambient temperature around flat surfaces for when you really need that paint to dry now.

What a specific application!

There are probably other applications for that! But she's only ever used it once, and the interesting part of that one is the way her mentor came up with of keeping the system self-reinforcing so the user doesn't have to update the light switches every few hours for days. Anyone earlier would have had an easier time letting their paint dry the long way around.

Yeah doesn't sound too practically useful.

True. It's one of the few cases where you get to do logic puzzles and say it's magic; that's the real point.

He definitely understands that, it's super cool, and he starts suggesting other things that could possibly be done with this system.

She gets even more excited when he does. Most of them won't end up working out, usually for either astronomical or technical reasons and occasionally magical ones. Few of his suggestions can be ruled out without diving into the process.

Still fun to do and he kinda wants to test them even if it might take a while.