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Here are some notes, in no particular order.

The question of whether I can learn to visualize four-dimensional objects (see Can You See It?) reminds me of the article What Is It Like to Be a Bat?. In other words, the question is, what is it like to be four-dimensional?

Just as in three dimensions there are polyhedra, so in four dimensions there are polychora. I already mentioned the tesseract and the hexadecachoron, but there are others—including one with 600 faces!—that you can read about at the following sites. The first has an explanation that is both nice and short, while the second has an unbelievable amount of detail.

The Fourth Dimension
Four Dimensional Figures Page

Also, although I didn't try them, I did find a couple of programs for viewing polychora. The first is interesting to me because it uses dynamic stereo pairs, which I've never heard of anyone else doing (besides me). The second I like mainly because the site has nice pictures.

4-D Polytope Viewer
Polytope Visualization: Peek

Finally, there's a little story behind this sentence from How to Orient Yourself.

The maze world has its own eight directions, which are absolute: north and south, east and west, zenith and nadir, and two that shall here remain nameless.

If you've been following my essays (ha ha), you probably know that it's not like me to leave things nameless. I've done it before, even once in a title, but I don't do it without considering the possibilities first.

I knew the story Tangents mentioned a few names, but I rejected them, for two reasons: one, I didn't like them, and two, they were used in a way that implied that the directions were relative rather than absolute.

(But, I will mention one pair, “ana” and “kata”, which seem to be fairly standard, and which I would consider using as relative directions in place of “in” and “out”. The latter made sense in the context of the game, but do have other meanings that would eventually cause confusion. It would be easy to remember which is which, since “ana” sounds a lot like “in”. And, by the way, although the names look Japanese, they're actually just the Greek words for “up” and “down”. We usually see them as the prefixes “ana-” and “cata-”.)

Then, of course, I considered inventing new names. Unfortunately, I couldn't see any pattern in the existing names—they are just arbitrary names for a fixed set of directions. (Although that didn't stop me from thinking of “ollie”.)

The other thing I tried was the following search on Google.

+"fourth dimension" north south east west zenith nadir

That didn't find me any names, but it sure found me a lot of weird stuff, including several copies of Ritual for summoning Yog-Sothoth and opening the Gate. I was amused … Lovecraft's Cthulhu mythos was not exactly what I'd had in mind.


  See Also

  4D Maze Game

@ February (2003)