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Re: OT hypercube (was: Con-other)

From:Eugene Oh <un.doing@...>
Date:Saturday, May 31, 2008, 17:19
Heinlein's... story... makes me... woozy... Although I've been sort of
enlightened on the workings of tesseracts for now (but still have trouble
visualising them). I understood your example, at least.
Though now I have a new question -- what happens when, on a plane, two 2D
objects travelling in intersecting directions meet? Do they bump? Overlap?
Pass right through?


On Sat, May 31, 2008 at 11:22 PM, Mark J. Reed <markjreed@...> wrote:

> 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@...> >


Peter Collier <petecollier@...>