PatrickPowers wrote:I like Arctos and Boros too.
When it goes to more than 4 dimensions I'll stick with prosaic numbers. Hinton used classical type names back there in the 19th century but I found this inpenetrable. I'm not willing to deal with that.
I think past a certain point, you need to have a systematic nomenclature rather than just inventing more arbitrary names. Like Wendy's Greek/Latin suffix/radix system in her Polygloss, from which predictable systematic names can be generated. Some kind of mapping from numerical dimension indices to lexical roots from which surface forms are derived.
E.g., the first few dimensions have ad hoc roots: 0D: -teel-; 1D -lat-; 2D: -hedr-; 3D: -chor-; but from 4D onwards the roots are regularly derived from Greek numerals: 4D: -tet-, 5D: -pent-, 6D: -hex-, and so on. All derivations are regular, though: teelon - point; latron - edge; hedron - polygon; choron - polyhedron. With different suffixes, different objects of specific dimension are indicated: hedrix = 2D manifold, chorix = 3D manifold, terix = 4D manifold, and so on.
In terms of cardinal directions, the first 2 pairs are already fixed, and ad hoc: north/south, east/west. The 3rd pair can probably be ad-hoc named arctos/boros. But probably starting from the 4th pair onwards, some kind of regular derivation would be desirable. Perhaps a regular suffix or regular mutation of root-initial consonant or something like that for deriving pairs of names from the sequence ... -tet-, -pent-, -hex-, etc.. Or perhaps, to prevent overloading the Greek numerical roots (when speaking of a sufficiently high dimension the Greek roots would dominate the lexical structure of the text, which can make it hard to parse), we could use a different sequence of roots taken from, say, Russian or something. Or something exotic like Austronesian, for maximum lexical distance from Greek roots.
Perhaps one direction could derive from Russian numerals and the corresponding opposite direction from Austronesian numerals, starting from 4 (because we already have north/south, east/west, and we agreed on arctos/boros). So you'd have two sequences: -chet(y)r-, -pyat-, -shest-, -sem-, -vos(e)m- (Ru); -sept-, -lim-, -enm-, -pit-, -wal- (Au) - with some vowels deleted to make every root monosyllabic. Supposing we arbitrarily pick -(o)th as the standard directional suffix, we'd have: chetroth/septoth, pyatoth/limth, shestoth/enmoth, semth/pitoth, vosmoth/walth as the next pairs of cardinal directions. (Vowel randomly deleted to make shorter words... but for consistency we could also always keep the vowel).