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upwards, not northwards
a flatlander learns about parallel transport
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Tonight's New Year's Eve, and not just any New Year's Eve, it's 2999 and soon to be 3000 in a few hours. The whole city is celebrating, the streets crowded and noisy. For A Peg though, it's like any other night, the fog slowly growing darker as A Peg lays in bed, unwinding with a mystery novel.

For the most part, A Peg is not a very spiritual person, his interest in three dimensions begins and ends in the abstract. He's read Flatland before but mostly dismissed it as the ramblings of a madman, a very forward-thinking one in terms of mathematics, but a madman nonetheless, assuming it isn't a full fabrication. Instead, his idiosyncracies take on a very different flavor: he spends his time pondering square roots of negative numbers and power series.

A Peg's world is about to get an extra dimension.

 

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"Greetings, Flatlander. You have been selected to learn of the true form of your reality. Your reality is in fact, not how it seems. "

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What was that? A Peg is pretty sure he just heard someone talk.

"Who's there?"

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"Ok, should I just cut to the chase? Because I'd rather not have to waste time with you claiming that I'm an intruder or something."

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A Peg has placed down his book and is now looking around to see where the Voice is coming from.

"Okay, cut the shit, where are you?"

It occurs to A Peg that the voice seems to be as loud as if he was standing right next to its source and it becomes worryingly probable to A Peg that disembodied voices actually exist, and that if there really is an actual disembodied voice talking to A Peg right now, whatever it's about to say is probably very important.

"Alright, fine, you can talk."

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The Voice decided to "cut the shit" and appear.

"Right in front of you. As you can see, I have appeared with no comprehendable explanation that your mind can think of. Don't worry, I can teach you."

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The Circle is almost correct that he has appeared with no comprehensible explanation. Closely inspecting the circle, it seems to be an actual circle with no seams or gaps to suggest any mundane mechanism for his appearance, leaving one remaining possible explanation:

"Let me guess, you're a sphere from Spaceland, whose intersection with the Plane appears as a growing and shrinking circle, who has come to teach me about the concept of 3d space, which exhibits three spatial dimensions and can be thought of as a stack of 2d planes, just like how a 2d plane can be thought of as a stack of 1d lines."

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"W- tha- yo- h- I- it- sure???"

The Sphere really wished he'd done more inspection on the type of person he was teaching. He then disappeared in embarrassment, trying to think of how to recover.

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"Ok, are you gonna pluck me from my 2d slice of the universe or something?"

Somehow, A Peg failed to consider the hypothesis that actually this is all a dream or hallucination or something. On one hair, it seems very implausible that Flatland was actually real the whole time, on the other, it's too vivid and A Peg is fully aware of the absurdity of the situation, which would be unusual for a dream. Now that he thinks of it, Flatland is unusually... coherent? Perhaps that's not the right word but it's definitely not your typical madman's manifesto.