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Re: Con-other

From:Philip Newton <philip.newton@...>
Date:Friday, May 30, 2008, 8:54
On Fri, May 30, 2008 at 8:21 AM, Eugene Oh <un.doing@...> wrote:
> I'm very curious, though, about the animation near the top of the article > you provided: It looks as though the structure is a cube inside another à la > Russian Dolls, both with vertices of variable length, and folding in on > itself. When you said that the walls of a tesseract are cubes, I sort of got > the impression that it was supposed to be like a stubby cross. The walls > don't look at all like cubes to me!
Well, it's not easy representing a four-dimensional structure on a two-dimensional screen! And it's not easy (at least for me) to visualise the fact that each volume of a tesseract is a cube. I can handle "each side of a square is a straight line" and "each face of a cube is a square", but I can't imagine how something can have multiple volumes. "Walls" is the wrong term here, I think, since that implies 2D to me. And "one cube inside another" is one way of mapping a tesseract to 3D, but it's only topologically the same (it's "a tesseract" in the sense that a doughnut is a coffee cup - you can stretch one to get the other, but they're not the same shape at all). In 4D, all vertices are, of course, the same distance from all other vertices they're connected to, just like in 3D, this is the case for a cube, even if it's drawn on 2D in a perspective view that makes some of them look closer to each other than others. I find 4D rather hard to wrap my brain around. Cheers, -- Philip Newton <philip.newton@...>