Do the words happen to correspond with one another? Also; does he recognize any of the books on the shelf as being in his language?

A large number of the words seem to correspond at least loosely in position, but unfortunately it's not a one-to-one, nor is there any obvious matching, so they'll have to go through them manually.

He recognizes one of the books. It's apparently about some part of his world's mythology, plus 'lumen'. The mythology – in case her world differs in this respect – is about a sort of ever-present wind, guiding and protecting, and purifying fire, improvement through destruction of the old and rebuilding, named Thuviar and Karheil respectively.

She certainly doesn't have anything like that. The mythology sounds vaguely like a shamanistic thing.

Lumen?

Is it not translating?

A small glowing blob appears in front of them, about ten centimeters in diameter, the color of his hair: slightly dark blue. He nods in its direction.

Whoa. Neat. You a mage?

He looks confused. No, I'm not magic? There's a pause and then he continues: Does magic exist on your world?

It does, but not everyone can do it. I'm mundane.

… Everyone on my planet can do lumen.

What else can lumen do?

Change color? Intensity? Transparency? Plus it's able to do slight changes in temperature and keep an area relatively uniform in temperature and you can do diagrams with it if you're practiced with it and he can do little models of people because he is in fact relatively practiced with it.

Cool. Her world's magic can do .... more categories of things. She's not a mage, so she's not sure what, but it definitely includes illusions, conjuring fire, invisibility, mind control ... 

Well those sound sort of useful but also slightly terrifying? Lumen isn't particularly terrifying. It's used for diagrams and pictures and jokes and things, or sometimes to be rude but, y'know, it's not that inherently.

Yyyep, magic is terrifying. Especially blood magic, which is powered by literally killing people! And guess what: it's legal in Aztlan. 

That is slightly horrific. Meaning very horrific. Itaruko looks rather horrified.

Is Aztlan a big country? Is it the name of the world itself? If a country, how much of the world does it take up, are there places it's illegal?

Aztlan encompases this entire continent (formerly called South America) and half of this one! The country is run by a corporation called Aztechnology. Corporations in the future get to enforce their own laws on their property -- the practice is called "extraterritoriality", and means anything in Aztlan is legal if Aztechnology buys land elsewhere. 

Oh, and Aztechnology produces half of the world's food supply. 

That is really not how it works where he's from! His whole world is basically on one relatively small continent in comparison and a few islands, and there are four main actual countries – originally the Thamari used to all be over in this section to the south-west which is now the country Thurin, the Luna (like him) were down in the south-east in what is now Serenta, and the Rhunes were all up north in either what is now Kerune, over in the east, or slightly over west in the northernmost bit which is Isora.

Then there are a few islands. The biggest one is has only been colonized more recently, looks sort of like Madagascar off Africa (in terms of scale, not absolute size), and is mainly part of Thurin but various governments have small areas in it and it's used mainly for tourism really and they mostly follow international laws on things with their own sort of mini-government so it's not really a part of Thurin.

And that's about it, excluding the ice caps. There are a lot of mountains. A few volcanoes, too.

The governments are all quite nice and mainly work 'for the people' in, uh, actual transparent and presumably-legitimate ways?

Governments on Earth -- that's the name for her planet -- don't work that way. They tend to be dominated by a single corporation or extremely declawed with jurisdiction over border security and little else. In major trade and finance cities dozens of corporations vie for control. The entire world is extremely fragmented, due both to spirit encroachment and to the sudden chaos of the dispossessed fighting their governments with magic and taking back their land. That happened in China, Australia, much of the former United States, Europe ...

Her planet is way bigger than Itaruko's but displays many of the same topographical phenomena.

Huh.

If they're trying to learn each other's languages, they should probably start off with some more basic words, so perhaps pronouns and basic nouns and a few verbs. He suggests doing that and then aids the process with some lumen diagrams.

That will also help them save paper! Especially since whatever they write seems to translate automatically. 

... are there any other pens around?

There is a blue one on one of the shelves of the bookshelf and… one that is probably transparent, over near the mini-fridge?

The pen itself isn't transparent, but it seems like it writes transparent ink. Perhaps it just reflects UV light or something.

She uses the blue one to write Can you read this? on the same sheets of paper they've been using.

He looks at it curiously and then at her questioningly, shaking his head tentatively.

So it's not the paper. She uses the black pen to write Can you read this? on her arm. 

He tilts his head briefly… then nods.

The black pen translates things! Does your world have anything like this? Might be unique; the world might have other useful things, too --

Let's go exploring. We need food, anyway, since there's no obvious way to go back. I've been to the tall building that way -- she points -- but not on the path with the trees. It's weird no one else is around; I'd assume humans to have build all of these buildings and roads.