"We don't have machines that add or subtract - at least, I assume you're talking about something more autonomous than an abacus."

Huh. He would have thought the Magical Flying Islet Society would have calculation magic.

He's going to wait a few moments for Command to say something if they think he shouldn't explain. Command says it's fine.

"I can demonstrate." He takes out a similar model e-reader to the one the pilot had. It's also only black and white. Functionally it's actually closer to a smartphone, though the display is e-ink and it's a lot wider and taller than Earth ones. This one is touchscreen.

He puts it to a calculator app and writes with the stylus. It has OCR, so the handwritten numbers are interpreted by the computer. He reads out as he writes.

"One gross five dozen to the power of two divided by eight times three equals... nine great gross four dozen and six."

"I understand the theory of how it works, though I don't know how to create one or how it works in practice, except for the very simplest mechanical models."

"I can begin to think how I might make a machine that adds and subtracts by moving objects around somehow. I cannot begin to think how I might make a machine that recognizes handwriting," she says, staring in fascination at the e-ink display. "—also we use numbers differently, ours go by tens, but I think I can calculate the translations in my head."

Admittedly, he doesn't fully understand how the optical character recognition works, but he's just going to gloss over that.

"We used to use decimal too, but in our history we converged on using dozenal" in an act of radical imperialism by the Imperator.

There's a slight pause while he waits for Control to tell him what to say. Their best guess is that they came here accidentally, or at least are trying to give off that impression. How to broach the topic...he decides to make a very prosaic question.

"What brings you to Zmavliterdi? That is our name for our planet."

"We're explorers! I concocted an engine that can take a small islet out of one world and into another, and we ended up in yours. I'm hoping to refine my theories with what I learn from examining this world and put together a better version of the engine—I'm not as confident as I'd like to be that the one we have will reliably get us home."

Wow. So they have interuniversal transport but not computers. He is reaching the limits of his impassivity training.

Is it appropriate to say condolences? Hm..."I hope that you'll be able to refine your engine to reliably get you home. What sort of examinations do you plan to conduct? Could we help you?" And perhaps sneak peeks of what their engine looks like. And get information about their engine based on what examinations they would conduct.

"The thing that would help most is learning about the nature of your world and how it works. My theory predicts that there's variance between worlds in many possible aspects, but I only had one example to go on so I wasn't sure which things might vary or how. For example, I observe that it's very cold here, and that the landmass we've been travelling over is large and surrounded by ocean. Can you tell me more about that? Is the cold a feature of this world or just of the local area?"

The nature of the world and how it works? Physics? He supposes different worlds could have different physics, but surely they must still have the same mathematics. He can't imagine any entity that operates with a different mathematical system being able to exist in any meaningful form in this one.

"The cold is a feature just of the local area. This area is close to one of the poles of our planet, so it receives little sunlight per unit area. That's one of the main determinants of temperature on our planet."

The way they asked the question implied that their planet or world is laid out differently. No major oceans? But they said that the landmass they've been traveling over is 'large'...

Her ears prick up alertly. "What is a planet?"

Control, please advise.

Is their world flat? Do they not have gravity? But they have flight — surely they would have noticed the curvature of their own planet, if they were from a planet.

"A planet is a spheroid of rock, massive enough to maintain a spheroid shape with its own gravity. Does your world have gravity?"

"Yes, but our landmasses don't form spheroids. This islet is a pretty normal shape for a landmass of its size, but bigger ones are much broader than they are tall, and usually mostly flat on top - there's such a thing as mountains, but not such a thing as... giant rock orbs, not naturally occurring ones anyway. And gravity isn't relative, it's absolute - down is the same direction for everyone." She pauses to consider. "So all this," an encompassing gesture at the land around them, "is the surface of a giant rock orb, with down pointing inward? That explains some things. At home, all landmasses float in the sky, the way our islet does. We have oceans, but only on continents big enough to support one, and there's very few of those. Here I suppose the land and the water would be intermingled, all on the same level, wrapped around the orb?"

Several physicists with security clearances are internally screaming in the background.

"Yes. Our suns are also the same, except they are made of plasma. And yes, the water sits on top of the land. Where the land is low, that is where oceans and other bodies of water form, since that is where water would collect."

She nods. "Water collects in low points on our landmasses too, but when it runs to an edge it pours off." (There is in fact a trickle of water pouring off one side of the islet, from a small stream that flows across its grassy surface - though the trickle has been slowing as the far end begins to freeze over, and was never very large to begin with.) "That's fascinating! I wonder what the source of the difference is."

They're definitely going to assign someone to collect water samples of that later.

"I'm curious to know too. The arrangement on your world would be a natural impossibility. It implies that your world works by different physics — I'm surprised you (pl.) and your (pl.) islet are able to survive here." Well, aside from the fact that they have magic, which already implied different physics.

"I tried to constrain the engine to only operate within a range of variance that would allow for us to still exist on the other side, and I'm pleased to see that it worked!"