[Potironette]

You COULD meaningfully plot it in THREE dimensions, and you'd get a single curve, not a surface.

You can of course find specific examples that you would be able to graph. (And yes, I think x³ works, because i³ = -i. The graph ends up being upside down relative to the real-valued version.)

Geometrically, this means you're taking that four-dimensional graph and taking a cross-section of it.

A cross section of a 3d object is 2d. A cross section of a 2d object might as well be 1d. Therefore a cross section of a 4d object a probably 3d?
And then therefore both quotes are saying imaginary numbers are plottable in 3 dimensions?
Why three dimensions though? What happened to the fourth one? What if something like x³ was plotted in four dimension? Would it not remain a curve? Is something like x² any different in the third dimension compared to with a fourth dimension? I guess f(x) = x where x and y are both imaginary works on in one dimension though?

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So...basically every dimension is the other dimension stretched out? Like a point(0) stretches into a line(1) which stretches into a flat thing(2) which stretches into a 3d thing like a cube or a marble or whatever real-life thing(3) which stretches into err..some weird looking object..

Hmm, the problem for me with klein bottles (I googled it) and tesseracts, is that I'm not sure how to see it as not 3d.
With klein bottles, since it's 2-surfaces in 4-space, I guess maybe the tube thing on the inside is a 2-surface..? (edit: after writing the bottom, I guess a surface is literally anything that has an area but no volume, so a klein bottle is just showing a 2d surface existing in 4 dimensions?) As for what the 4-space is, I'm confused about what makes it a 4-space.

With tesseracts, since it's a 4-solid it means that it is a 4d object in 4 dimensions? What even is the 4 dimensions that I'm supposed to look at? Am I imagining that, say, the center of the tesseract would be like this 3d world (the world is 3d, right xD? Or is it just one way to look at it x'D?) then lots of other worlds were to be put all around it. And then, to see in 4d would to be able to see all those 3d worlds at the same time xD? Like, if a rubix cube were transparent? ...does that mean a klein bottle is 4-space for having 3-d things technically stretched out because the middle spout is a surface wrapped around 3d air and so is the outside surface of the bottle?

Occasionally in video games a 3d character would clip together. That's about as far as I'm understanding what's beyond 3d. If I held up a piece of paper and looked at it exactly from the side, that would be two lines clipping together and I guess if I were 2d I could "see" 3d things that way. But that's not really what 3d is. If two 3d objects had the chance to clip together, that would be looking at a 4d world from the side xD?

Oh, and with tesseracts, I forgot about them rotating. It looks like a klein bottle were constantly having its surface moved around? But not really...


...Whenever something comes up that I slightly don't understand there's a chance I'll ask about it depending how much I can think about it. I think I understand a surface is a 2-d thing and a curve is a 1-d thing and just because something is 2-d or 1-d doesn't mean they can't be bent in higher dimensions.
Though, can they be bent into a lower dimension?