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

Paul Bennett wrote:
> On Sun, 29 Jan 2006 01:04:15 -0500, Sai Emrys <sai@...> 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.
Exactly, an arbitrary degree of branching would have to be able
to accept any (whole) number whether that be two or googleplex.

> 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.
"Accepting any value determined by whim or impulse" is the most
common way "arbitrary" is used in mathematics, engineering, and
computer science.  That's hardly an "arcane corner."  (Though the
exact limits of the values involved vary between disciplines.)

However, the problem is not with any particular term, it's with
the whole phrase "arbitrary degree of branching."  An "arbitrary
temperature" is any temperature at a particular location.  An
"arbitrary degree of temperature" is meaningless since once you
have a degree it is no longer arbitrary.  In just that manner,
"arbitrary degree of branching" is meaningless, which is why I
need for it to be defined.

--
Jefferson
http://www.picotech.net/~jeff_wilson63/myths/

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