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It's kind of heavy on the math and not exactly written for pleasure reading, but the front matter suggests that it's suitable for secondary school (which it identifies as "ages 7-10", but it also claims to have been published on Mars).

The girl finishes her much shorter book, orders an omelette and sandwich and food for all six of her Pokémon, asks for a handbook on working Security, reads it, signs on for a job, goes to sit in the Security office, comes back after a four-hour half-shift during which a few people who seem to be regulars and just want to eat come in and go out and don't make any trouble, gets a couple other things to read and reads them, and then departs the bar.
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And then, apparently, ages six years, gets cosmetic ear surgery, and completely changes in dress sense, forgetting in the intervening time that Milliways exists, because she sure looks puzzled.

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Max looks up from his book.

"What the- what? You! What are you doing back here? What happened to you?"
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She looks rather taken aback. She tucks her hair behind one pointed ear.

"I See you, but have not, I think, seen you before. Nor this place."
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"Your ear! What- your ears! What do you mean you haven't- what? What is this? You're not- who...?"

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"I am an elf. Perhaps you have not met an elf before."

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"Elf- you- oh, god, she mentioned elves, the damn bar- but- but you're her, what was her name, the one with the Pokémon! You're definitely her!"

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"I have never seen you before and do not know what a Pokémon might be."

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"...Tell you what, I'm gonna take you at your word there. Let me check something."

He stomps over to the bar.

"Bar! What's this all about? Why's she an elf now? Did you do this?"
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The elf you just spoke to has never previously visited here. I have no control over who is and is not offered a door, the bar napkins.

(Napkins from the previous conversation have been quietly cleared away.)
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"Yeah, okay, she told me that part. Except... wait, d'you not have eyes or something? She looks and sounds exactly like... what was her name, the trainer girl. Like, exactly."

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You never asked the trainer's name, the bar points out. The elf looks and sounds similar - I can see, and hear - but is from a different world and a different species.

The elf, meanwhile, is slowly scanning the environs of the bar; she is apparently captivated by the window.
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Spectacularly helpful as usual, he grumbles internally.

"Yeah, I- I didn't think I'd need her name, whatever- she signed up for your Security thing, right? What'd she put down on the form? And- no, wait, that's not the point, the point is why can she be the same person but a different species, this is a new kind of weird!"
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I don't give out employee details, writes the bar primly. They aren't the same person. They are alts.

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"Alts," he repeats. "Alts. What's an alt?"

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Occasionally the same sort of person will appear in different universes. They will usually look more or less alike and share traits that are particularly key to the template in question, sometimes including things about their contexts within their home worlds, but otherwise vary.

The elf approaches the bar. Observing that Max has been talking to it, she says, "It would be good to know of your courtesy what manner of place this is."

She gets a napkin, which she reads with interest.
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The same sort of... god, he should have asked that girl more personal questions, it would have made getting a shape of the similarities easier by virtue of being able to ask the elf as opposed to the cagey and put-upon sapient bar.

"Now- hold on, the same sort of... I have to assume, by the probability of this person appearing here, now, that... this isn't just, you have customers from an infinite number of universes and logically some of them are going to be similar. They're common enough for you to have a name for them."
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I suspect, says the bar, that the sort of person who has alts is also more likely to find the bar. But you probably want to be more conservative about how common a thing must be before I have a name for it.

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"...No, that's not it, is it? If there are infinite universes... does that mean every possible universe exists? Does every conceivable universe... countably vs uncountably... sorry, the thing I was getting at is- under the assumption that all universes exist rather than a merely infinite number, that's, that's probably not a safe assumption..."

He shakes his head.

"The question is, are alts a Thing, some sort of common template that proliferates more commonly than chance in a mere countably infinite set of universes, implying that they are significant in and of themselves without reference to this bar... or are they just... an artifact of which universes the door chooses to open to? It would imply... not that they're selecting for humanness necessarily, but that they're searching for universes that contain specific people- people close enough to some idea of who-they're-looking-for, that they decide to open the door to them, and not to, say, a random location on the Plane Of Infinite Featureless Jell-O Pudding."

Max is not optimistic about the chances of the bar having a particular interest in these questions of metaphysics. From what he's been able to gather, she just wants to serve drinks, and is only answering his questions to be polite.
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I don't think every possible universe exists, at least not yet, but I couldn't say for sure. You might have to be more specific about how often you'd expect any of these things to occur 'by chance'. Although I will mention that a plane like the one you just made up would be unlikely to contain doors or people to open them.

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"...I think it'd be the lack of people thing, yes. I somehow doubt that whatever engine powers the interdimensional travel here requires doors as a fundamental piece of its operation. I... assume if the boss or bosses did want to make the door open to somewhere with no people, they could."

The alternative is a deeper level of weird than he's willing to contemplate right now.

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The door doesn't work that way, although occasionally people have found their way here through other mechanisms.

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"Sure, sure."

A thought strikes him. He's not sure why it didn't strike him until just now.

"...what do you do with money, anyway? Do you have... a business model, or what?"
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I don't keep it for myself. I'm just obliged to charge. To be honest, I'm not sure if people who pay by credit actually see their amounts deducted on a consistent basis.

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"...well. That's... I can't imagine why that would be. Surely, anyone powerful enough to create you and this place in the first place doesn't need money for anything."

Max's eye turns to the elf. She's been quiet- must be a lengthy napkin, if she hasn't asked any more questions.
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