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# Re: OT hypercube (was: Con-other)

From: Mark J. Reed Saturday, May 31, 2008, 15:22
```On Sat, May 31, 2008 at 10:57 AM, Eugene Oh <un.doing@...> wrote:
> Planar rotation goes even further off my radar. I can't even begin to
> imagine it! I envy all you people who grasp mathematics so easily. :(
Well, grasping the math is one thing.  I still can't visualize this
stuff.  But these days you can  play with computer models in real-time
- "rotate this 30 degrees cata"... and sort of get a feel for how it
fits together, although I find that feel doesn't last long afterward.

Squares rotate around points.
Cubes rotate around axes.
Tesseracts rotate around planes.
Penteracts rotate around spaces.... that's where it gets weird for me.
Our entire universe is an axis of rotation for these things. :)

> There is a process of pattern-repetition that has a name either very similar
> or identical to "tesseract", but I can't remember what...
tesselate.

> In 3D terms, that might be like... having a cube that was actually a
> tesseract but no one realises it because from whichever angle human eyes can
> only see a cube? Is that it?
Sort of. It's like we're 2-d critters walking around inside a plane,
unable to perceive the thickness of the plane itself.

Your description is closer to the 2d critters' view of intersecting 3d
critters in _Flatland_.  Or our view of the titular structure in in
the Heinlein story "And he built a crooked house", where each room was
a cube of a tesseract.

Imagine that you are a 2d critter walking around the surface of a
cube.  The angle change at the directions is completely invisible to
you, so all you see is six square rooms, four in a line N-S, with one
east and one west of the second-to-southernmost room.  Perfectly
normal-looking, but they have magic doors!  If you stand in the south
room facing south and look through its southern door, you find
yourself looking into the north room from its north door - wraparound!
Which is spooky enough.  But if you stand in the north room looking
east through its eastern door, you find yourself looking into the
eastern side room - facing WEST!

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