Vaguely relevant link courtesy of Abstruse Goose
bowserevilking wrote:In Flatland, would they see 1D like we see 2d? Would there be 1D art? I don't think a single point counts as art, does it?
Yeah, they're supposed to be able to see one dimension, but they see a section of it it all at once the way that we see 2D images all at once. (The Abstruse Goose comic linked above isn't quite an accurate depiction, I believe, since the line of colors still has a small vertical length... but I don't think there's any way for us to visually represent (or mentally visualize) a truly one-dimensional field of experience anyway). Flatlanders, according to Abbott, get an impression of other objects thanks to something like an "atmospheric haze" that reveals depth: objects farther away become fuzzier--or lighter, blurrier, I forget exactly. This is analogous to the effect created by atmospheric haze for us here on Earth in 3D.
Flatlanders can also move around, which, coupled with their "depth perception", allows them to get reasonably good ideas of object shapes. If necessary, they can make little tangential movements (literally tangential, in the mathematical circular sense) to reveal more detail about an object from other angles. Naturally, they'd have to circle around completely to see the other side and get a full picture--just as we have to circle around a 3D object to get a full picture of it. However, we're pretty good at inferring the rest of an object from a 2D representation that only shows about half (or less) of it, and presumably a Flatlander could do the same.
So anyway, if they have some method of creating and distinguishing "colors" or something analogous, yeah, I think they could have art. Confusingly, they could probably create optical depth illusions by coloring a flat object to appear as though it had angles that protruded and receded, just as we do with 2D optical illusions. Color and a means of depth perception other than size probably aren't strictly necessary for some
kind of art, but they make things so much easier; it's a lot harder for me, at least, to understand how a Flatlander would see "art" (or other objects at all) without similar perceptual aids.
P.S. Didn't anyone notice the pun in the last bit of dialogue? "That was out of line".... the stick-figure really is drawing "out of line" by adding new ones to a Flatlander.