Re: OT hypercube (was: Con-other)

>> 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

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