Re: OT hypercube (was: Con-other)

On Sat, May 31, 2008 at 4:42 AM, Eugene Oh <un.doing@...> wrote:
> I think the harder thing is not so much imagining the shape on a macro
> scale, but trying to piece together in your brain how to map "edges" of
> cubes to "faces" of tesseracts.
Well, sure.  But it's more the other way around... a cube has squares
connected by edges; a tesseract has cubes connected by squares. :)

My sophomore year in college I had a roommate (another computer geek)
who had written a basic program to display a projection of an
N-dimensional cube for N up to 7 (the limit came from the BASIC
language's limit on array subscripts).  You could turn perspective on
or off, and rotate the figure arbitrarily in its space before the
projection (hypercubes rotate around planes, instead of lines, and
there are six such planar "axes").

> I've always been fascinated by talk of dimensions, at least since primary
> school (when I was, say, 9) when my teacher offhandedly mentioned them.
For me, and many of my peers, it was _A_Wrinkle_in_Time_, which
involved "tessering" as a means of transportation.  With a completely
unsatisfying explanation, math/physicswise, but it did get me hooked
on the higher-dimension concept.

> As I grew older I started getting skeptical about the
> whole concept of dimensions, because, my reasoning went, no matter how small
> you make a point, it still occupies volume.
Well, modern physics believes that the universe has many higher
physical dimensions; they're just very small.  That is, our 4-d
spacetime is like a piece of paper in 3-d space - it's really
3-dimensional, but it seems 2-dimensional because it's so thin.

--
Mark J. Reed <markjreed@...>

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