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

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

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