Subject: Fw: [BoundaryPoint] Re: Can a point also be a border?
Date: Jun 01, 2002 @ 18:46
Author: granthutchison ("granthutchison" <granthutchison@...>)
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> mwmztz tho disputed would appear to occupy in both probabilities a
> permanently wet position
> & not an alternately wet&dry position in either case
> as you seem to indicate
>
> so you may prefer to use a better example of what you mean
> say perhaps mdvawv or dcmdvan
> both of which are actually at mean low water mark on the potomac
> & thus sometimes in the river & sometimes not
>
> for that is the kind of situation you mean isnt it

Jesper will correct me if I'm wrong, but I understood him to mean
that a point whose position is defined as being on the edge of a body
water could be considered to be half-in and half-out of that water -
half wet, half dry in a *spatial* rather than *temporal* way. Hence,
I imagine, his choice of non-tidal water. But, as you say, Brownlie
maybe makes mwmztz a bad example, and the inevitable sloshing of even
the stillest body of water interferes with the purity of the concept.

Even if I'm not understanding Jesper's point, there is a point here I
quite enjoy thinking about. I don't see any reason why a
dimensionless point can't be half one thing and half another - or
even further subdivided. It's a matter of viewing infinitesimal
objects as the limiting state of more extended objects - very much an
acceptable notion, since it's exactly how differential and integral
calculus were invented.
Imagine you draw a circle, radius r = 1m, around the exact meeting
point of Utah, Colorado, Arizona and New Mexico. A quarter of it lies
in each state. Shrink it by half. A quarter of that circle lies in
each state. And shrink it again. And again. No matter how small the
circle gets, it's still neatly subdivided into four quadrants. At the
limit, as r->0, it's quarters all the way down. So the infinitesimal
quadpoint is divided into four equal infinitesimal segments. This is
no more unreasonable than the fact that (infinite number) + (infinite
number) = (infinite number).
Now, if you accept this (and why do I think I hear distant rumbles of
dissent?) it means that tripoints are not evenly divided between the
abutting countries - AZIRTR, for instance, looks to be about 50%
Iranian, 45% Azeri and only 5% Turkish. So each country has only a
limited share in its infinitesimal "tripoint territory", and
somewhere there is a country cursed with acute-angle tripoints that
has the lowest average tripoint-share of any country in the world.

Grant