On Sun, 29 Jan 2006 01:04:15 -0500, Sai Emrys <[log in to unmask]> wrote:

>> 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.

I don't see how the number 6 has anything to do or not to do with the word  
"arbitrary". Whether there is one connection or 18,000 that number is (by  
defintition) defined. By taking such a broad view of what is not  
arbitrary, I cannot see how any number could *be* arbitrary.

I suspect there's a conflict in semantic domains. We have a clash of the  
actual meaning of the word arbitrary as something close to "defined at  
will by some act of executive fiat, rather than subject to natural laws",  
and what seems to be a piece of specialized technical jargon from some  
arcane corner of mathematics that happens to have the same form as the  
word we all know.