From: | H. S. Teoh <hsteoh@...> |
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Date: | Saturday, April 21, 2007, 0:08 |

On Fri, Apr 20, 2007 at 02:43:16PM -0700, John Crowe wrote:> Hello, > > << > I haven't actually done it yet, but I've considered making a conlang for > describing geometry in 4 (spatial) dimensions, as perceived by a > (hypothetical) 4D being. > >> > > Interesting. Unfortunatly, it seems to me that languages (natlangs, > at least) don't even do so well in 3D. In an outdoor theater (no > backs on seats, seats are stuck together on each row) I once > encountered the situation where someone said "scoot up" and the > people nearby had all sorts of interpretations.That is true. I do have this sneaking suspicion that if natlangs had terms that describe 3D very well, it would approach the current utility of natlangs in 4D, since if we analogize our gravity-bound state to 4D beings, they'd basically be dealing with a 3D floor, and would only occasionally need to split hairs to accomodate for the 4th direction.> Geometry? I'm not sure if there is a good way to describe 3D > polyhedra. Are our conworld inhabitants doomed to reciting Schlafli > symbols (http://en.wikipedia.org/wiki/Schl%C3%A4fli_symbol)? (On > second thought, that might not be so bad...)Math symbols are all fine and good, but I was thinking more along the lines of, "If I lived in 4D, what words would I need to adequately describe the shape of my 4D bedroom and the placement of furniture in it?". I doubt our hypothetical 4D beings would be too concerned with reciting Schläfli symbols for polychora (4-polytopes), much as *we* aren't too concerned with reciting Schläfli symbols for 3D polyhedra in our everyday life.> I find other spacial dimensions fascinating. 4D people can walk in > 3D, or "flying" in 3D terms. They might look "up" at the birds and > wish they had even more mobility.More curious facts: - In 4D, you could remain upright, and turn around, *and* maintain your gaze at someone, all at the same time! (Analogous to looking in the same direction in 3D while doing cartwheels... except in 4D, the extra dimension lets you remain upright at the same time as well.) This surely must have cultural significances (turning in this way could be some kind of gesture, or your orientation while speaking with someone could convey your attitude, etc.). - There are 6 planes of rotation, not 4 (as one may be tempted to think), which means you can simultaneously rotate in two different ways at once, at different rates of rotation. (In 3D, attempting to do this only results in a simple rotation around a slanted axis.) - Planetary orbits are inherently unstable, so there wouldn't be the equivalent of planetary systems as we know it. Well, circular orbits are possible, but only if they're *perfectly* circular---very unlikely in the real world. The slightest perturbation means spiralling outwards into the cold death of outer space, or inwards into the sun. - Atoms, as we know them, are inherently unstable in 4D, because the Schroëdinger equation (at least for the equivalent of a hydrogen atom) does not have discrete solutions in 4D: all electrons would simply collapse into the nucleus (there are no possible 4D orbitals). So matter would need to exist under some different system altogether. The upshot of all this is that I can take great liberties in my conlang and conculture to make things just the way I want them. ;-)> Sometimes I feel that fish have more freedom than anything else. > They can truly enjoy travel in three dimensions (compared to a > bird, which has to land on a branch some time or another).[...] Then if we were fish, would we be able to visualize 4D better? :-) After all, *we* see in only 2D, and can visualize 3D quite well. 4D beings would hypothetically see in 3D and infer 4D from it, so if fish have a greater grasp of 3D space, being more aware of it in their everyday activities than we are on our 2D land, maybe they're better at visualizing 4D! --T

John Crowe <johnxcrowe@...> |