A (hollow) circle lives in 2D space, but is actually one-dimensional. How so? I can continuously map it to two 1D structures, one straight line for the top part and one straight line for the bottom part.
Now, there are moments (such as a cursive "e", for example) where our line crosses itself (so there's a point in two different "regions" of the line), so we can't say that all cursive writing is 1D. But it's darn close to being so.
What's more: even though our characters are darn-close-to-being-1D, the text we write with them is 1-dimensional. Some concrete poetry has tried to be two-dimensional, to little effect, but we mostly have sequential thoughts and a sequential language -- and only 1D structures can be sequential.
> even though our characters are darn-close-to-being-1D
I assume you meant 2D there. I kind of get what you're saying.
What about Chinese/Japanese characters, surely they're not 1-dimensional? Our vision is still 2D though, with the sensation of depth being provided in the processing layer. What might actual 2-dimensional or 3-dimensional "text" be like? Say written by 4D beings with 3D eyes. [0]
(the primary topic on this page being systems that we may not relate to, comprehend, or even imagine, after all.)
> I assume you meant 2D there. I kind of get what you're saying.
If you were to remove the exact point of overlap in our cursive "e", we would have a 1D structure, even if a discontinuous one. And it would still be legible as an "e". This is what I mean by "darn close": infinitesimally so.
I haven't thought this through, but probabily every character in a legible sans serif point can be subject to this removal-of-overlaps process and still remain legible.
As for Japanese: katakana seems reducible to 1D by the same criteria; hiragana is certainly not, let alone ideograms (kanji/hanzi in chinese).
