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Re: Non-linear full-2d writing (again)

From:Sai Emrys <sai@...>
Date:Sunday, January 29, 2006, 6:04
On 1/28/06, Jefferson Wilson <jeffwilson63@...> wrote:
> >>What do you mean by "arbitrary degree?" If all symbols are the > >>same size you're more-or-less restricted to six branches from a > >>single symbol. > > > > Only if they're also all square AND not allowed to overlap (or 'fill' > > a square space, like all 'ideographic' languages I know do - e.g. > > Japanese / Chinese kanji/hanzi always "take up" one square of space, > > no matter what they do within it). > > Uh, no. It doesn't matter whether they're square or allowed to > overlap or change in size. Two-dimensional space-filling permits > only six connections, and if you aren't talking about same-size > space-filling then your connections aren't arbitrary in the first > place.
I don't believe you. Prove it? I can think of several simple counterexamples - hexagonal grids like wargames, my drawing a circle with a bunch of lines coming out of it to circles all around it (distance required increases with N, if they're all equidistant; otherwise, it becomes like atomic shells); etc.
> > If you have different shape of their 'personal space' - e.g. hexagonal > > (viz. maps used for wargames) - or if they have allowance for some > > sort of fusional morphology, then I see no reason why it cannot in > > fact be literally to any arbitrary degree of branching / recursion. > > You've failed to define what you mean by "arbitrary degree of > branching." Mathematically, space-filling two-dimensional > arrangements are limited to six connections. Even if there's a > higher order of symmetry (7-fold or eight-fold) there can still > be only six or fewer local connections. Greater connectivity can > be defined, but if it's defined it can't (by definition) be > arbitrary.
I don't see how you arrive at that <=6 number. - Sai


Jefferson Wilson <jeffwilson63@...>
Paul Bennett <paul-bennett@...>