Leareth in fact wakes up less than ten minutes later. He's briefly disoriented, and goes still until he remembers where he is. "- Oh. Sorry about that." 

"Hasn't been long at all." 

"I was not even sure it was possible to take naps with the Ring of Sustenance, but I suppose it has been an exhausting couple of days." He disentangles himself a little, stretches. "All right, we have both done copious talking about our emotions - did you have other plans for what to do while we are in Aktun?" It also seems plausible the pharaoh has other work to do that he can't justify abandoning for longer, but Leareth is currently not sad and he suspects once he's alone again he will be sad, so he's not in a hurry for Khemet to leave. 

He counts them off on his fingers. "We could ride the trolleys all around the whole of Aktun and people-watch. We could go to the theatre. We could go to the museum of measurement, or the museum of light; the other ones are closed today, most museums close on Moonday to give their staff a day off since they don't get weekends. We could pay for flight and go explore other districts of Axis. We could get lunch. We can probably do at most three of those, I told Aroden we'd be back in the evening."

"Ah, I am quite curious about the museum of measurement! And then perhaps lunch." 

Then they can go see the museum of measurement! It has all kinds of elaborate inventions - some the state-of-the-art, some that are very old but represent an important step forward at the time - for measuring distance, or temperature, or pressure, or the mass of small particles, or the wavelength of light, or the speed of light, or the distance to the Sun, or units of time, or electric current. There's a whole room full of clocks that were once three hundred years ago all set to the same time but have varying precision.

Leareth is delighted! Some of the inventions are commonplace in Velgarth, some are completely new even to him, some he invented the equivalents to at some point in the last two thousand years. He muses on whether the speed of light is the same in Velgarth as here. That's one he hasn't managed to measure, though he did suspect light had a speed and was in some ways analogous to sound, with a wavelength and different 'pitches'; this certainly isn't widely-known by Velgarth scholars. 

Electricity is fascinating and Leareth asks Khemet how it's used in Golarion. 

Khemet isn't a scientist but he thinks the speed of light in a vacuum is one of those things that's the same across all the planes, which suggests it'd probably be the same in Velgarth? He doesn't have a guess why, though. 

(One of the staff members at the museum overhears them and pulls out a table of the elements and wants to know if Leareth thinks it matches Velgarth.)

Oh, that's brilliant! Velgarth alchemists have isolated some elements but never came up with that kind of categorization. Leareth peers at it for a while. He doesn't see any obvious mismatches, at least? 

After a couple of hours at the museum Leareth is pretty ready for lunch. 

If it matches then they've got pretty much the same speed of light, a significantly different one would mean different elements would be stable, the staff member says. 

They can get lunch at one of several dozen restaurants within a few blocks; Khemet picks one out that does palm-sized miniature pizzas and orders a dozen different ones for them to share.

It's a very good food concept, Leareth decides, even if it still seems very weird to him that you can teleport into the afterlife and get lunch at a restaurant there. He makes pleasant conversation with Khemet about goings-on in both their countries and some of Aroden's upcoming plans for Cheliax. 

Khemet seems more relaxed here; maybe it's the lack of guards and servants or the fact that no one knows or particularly cares who he is.

His relaxation level is sort of contagious, Leareth thinks, because he too feels lighter and looser than usual. It's nice. He appreciates it. 

"I think I would like to return to the apartment for a bit," he says when they're done. "And then perhaps do another thing if there is time afterward." 

"Sounds good." And they can head back on over to the big tall building and go up to the rooms he rented.

Leareth flops onto the couch. It's not a very characteristic-for-Leareth motion but he feels like it, right now, and it's not like he intrinsically cares about being dignified when there's no one around whose opinions it'll affect. 

He sits down next to Leareth's head on the couch and runs his hand through Leareth's hair and reveals from a pocket that he sneakily bought some souvenirs at the museum of measurement.

Leareth is also startled about Khemet touching his hair! And separately surprised that it's very pleasant. He oohs appreciatively at the souvenirs. He's visibly a lot happier than he was this morning. 

Well, good, that was most of the aim here.

Leareth can tell that this was Khemet's aim and that he's pleased about it working, which is really nice, actually. 

He unflops after a while. Maybe they can ride the trolleys and people-watch for a bit until it's a reasonable time to go back to the material plane and see Aroden? 

They can do that. Khemet is going to have his arm around Leareth possessively for it.

Aww. Leareth is, again, mildly surprised and quite pleased about this. 

"You're going to have to take us home once you're done here, I spent almost all my spells on the thing this morning and don't have another Plane Shift."

"Of course. I - do not want to leave until we definitely need to, because I am guessing you will not be able to go around hugging me in public in the palace." Leareth is...kind of confused, though very pleased, about today and what it means for his working relationship with Khemet going forward. He should probably just ask but it also feels confusing what question to start with. 

"I feel - less like this, in Sothis, I am somebody and cannot forget it and I'm bleeding Law just a little bit whenever I let you ignore all the rules because I like you, which is entirely on me and not on you at all but it's not great for a carefree mood...I don't strongly expect anyone would care if I hugged you, it's not as if I'm not permitted to hug people, everything just gets - weighted down by all the rules and all the guards and all the -" Shrug. "You seem to really need hugs, though."

"- Oh. I - had not even considered that, I am sorry, I - had mostly been distracted from the rules by tracking other strategic priorities, but if Law means the rules are strategically relevant for you then I will be much more careful." And he thinks he'll find it easier to remember, if it fits more naturally into that category of thing, which his mind tracks almost as effortlessly as breathing, as opposed to - he's not even sure how he was categorizing it before, actually. "It seems simplest if you do not hug me in public, then, it would - not feel the same anyway. Though...it does seem to help. Much more than I expected." 

He frowns at the passing city. "I...am just trying to wrap my head around what sort of relationship we have going forward, because - well, it was already confusing before, I think, and now even more so."