by quickfur » Tue Nov 23, 2010 6:14 pm
This discussion on glyphs is interesting... it made me reconsider what 4D writing is more likely to be.
A naïve generalization of 3D writing may suggest such glyphs as a hollow sphere to be the analogue of 'O', or that glyphs would be made of 2D curves and polygons. However, such a writing is highly impractical except in print, because filling out a hedrix (2-manifold) to make a character is a rather tedious task if you assume the nib of the pen to be a point. Even if you assume the nib to be an edge, the kind of shapes that can be written would be sweeps of that edge, rather than geometrical shapes like spheres. Plus, the sweeps would only trace out a 1D curve (possibly self-intersecting if the path crosses itself).
Furthermore, it is more practical if the curves that constitute each glyph more-or-less progresses in the direction of the writing, rather than form intricate polyhedral 1-skeletons. The latter is of course doable in print, but in handwriting, one would expect the development of a cursive which is more or less a 1D curve winding through the 3D surface of the paper, mostly progressing in the direction of writing, with some loopbacks and some angles. In other words, the glyphs won't be that elaborate at all, at the most consisting of a few loops and some simple branches, maybe with the occasional dot or diacritic. It would be unlikely, for example, to have glyphs with icosahedral symmetry, even if it seems very appealing to us.