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Re: OT hypercube (was: Con-other)

From:John Vertical <johnvertical@...>
Date:Friday, May 30, 2008, 20:58
>> 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! >> Eugene >> > >That's because you're looking at a *picture* of a >tessaract, not an actual tesseract.
Or, more exactly, a 2D picture of a 3D projection of a tesseract… generally a 2D projection would not map unambiguously onto a specific 3D projection. One particularly symmetric fashion, with all the edges projected equally long, involves inscribing an octagram within an octagon, then a smaller octagram within the smaller octagon at the octagram's center, and then erasing the smaller octagon. Makes a neat doodle on grid paper, too (it can be done entirely with 2-square segments at a 2:1 or 1:2 slope).
>Once you get the idea, you can go on and try to >imagine 5D 'cube', where all the 'faces' are >tesseracts.... > >P
I think this is severely limited by the human mind's inability to visualize true hyperspace. Curved volume is still somewhat understandable; I can just wrap my brains around the surface-less but closed hypersurface (volume) of a hypersphere - but how this then divides hyperspace into one open and one closed component, I'm just not seeing. OTOH this mental excercise certainly makes me understand better the topological near-equality of the space inside and outside a sphere (or a circle, for that matter). So trying to visualize a penteract, for me at least, just becomes a horrendous jumble of distorted cubes, which is about as far off as visualizing a cube as an 1D mess of overlapping line segments… John Vertical


Peter Collier <petecollier@...>