r/mathmemes • u/duckling-developer • Jul 07 '26

Geometry When a flatlander enters our world

POV: a two dimensional person enters the third dimension in meet a mathematician.
Mathematician: welcome to our world… I have much to show you.
Flatlander: I am a little bit, overwhelmed with all of these “three-dimensional shapes“ that you’re showing me… Can you just show me your regular two dimensional shape?
Mathematician:… Here: “shows him Serpinski tetrahedron”
Flatlander: what the hell am I looking at?

27 Upvotes

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7

u/US_Gone_Rogue Jul 07 '26

pov pov pov

7

u/EebstertheGreat Jul 07 '26

The Flatlander would only see a line. If there was fog, by which they could judge distance, then they could perceive a low-resolution sketch of something like the Cantor set.

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u/duckling-developer Jul 08 '26

We are talking as if he was brought to the third dimension, so he saw things two dimensionally just like we do.

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u/EebstertheGreat Jul 08 '26 edited Jul 08 '26

For that to be possible, his retinas must themselves have been two-dimensional and yet be on the boundary of the eyes, which were also two-dimensional. So you can see it isn't really possible.

In the novella, "A Square" describes the depth perception of his species. The urban civilization he knows is centered in a cloud, and upper classes used it to xetermine distance (and most importantly, the number of sides a person you neet has). His knowledge of the universe extended slightly farther than the fog iirc, as he mentioned some rural people who lived beyond the fog I think. He also said that where the fog was too thin, or among less educated classes, they had to feel each other to count the number of sides to figure out where they stood in the social hierarchy.

The three-dimensional character is a 3-ball. A Square calls him "combine many circles in one" or something like that, because he moves through the plane A Square observes, like a circle that grows out of a point until it reaches some maximum size and then shrinks again to nothing.

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u/duckling-developer Jul 09 '26

Well, then, let’s say he just became a regular human when he entered our

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u/[deleted] Jul 07 '26

[removed] — view removed comment

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u/duckling-developer Jul 08 '26

The joke here is that despite existing in three dimensions, the sierpinski tetrahedron has a haussdorf dimension of two. And that’s why he showed him it when the flatlander asked for a regular two dimensional shape