woww grant
& let me interject my even greater delight & amazement
wowww
at the recent arrival in our files section of your long
anticipated international boundaries xls file
a giant step toward the fulfillment of the punctological & mosaical
inflation of the entire globe
btw can you tweak it so your comments dont fall off the page
as those that i can see are an inspiration
& all the data are lighter & more delicate than we usually get here
so i say let the standing ovation begin without further ado
& now too
just as an aside from me to you within this greater & more general din
of appreciation
i am so pleasantly surprised also to see you opening here below to the
possibility that a line which is nonphysical in the first place might
need to disconnect from itself in order to pass over an also
nonphysical point that is actually part of that line etc etc while it
could easily within nonphysical reality simply cross itself no problem
so unless such an elegant solution to what you call your odd problem
still doesnt make any sense to you
boundary crosses here we finally do come
m
--- In BoundaryPoint@y..., "granthutchison" <granthutchison@b...>
wrote:
> > The question I pose is this: can a point, more specifically a
> > quadrapoint (quinta or even more), also be a border? Take Four
> > Corners, USA for example. Is it correct to say that New Mexico and
> > Utah 'border' one another? Or Arizona and Colorado?
> Like you, I've puzzled over this, with reference to Jungholz and the
> other exclaves that join the parent country at a single point.
> My take is that the two entities don't adjoin each other at all,
> since the length of their border is zero - the same as the length of
> any border for any other two non-adjoining entities.
> But this leaves me with an odd problem when I'm counting
> international border segments around Jungholz, and other exclaves
> that are joined to the parent country by a single point. From inside
> Jungholz, there is a continuous border with Germany. And from
> Austria, there's also a continuous border with Germany. But on the
> German side, there's a discontinuity - Germany borders Austria, then
> an Austrian exclave (Jungholz), then mainland Austria again.
> So Germany counts three border segments, but Austria+Jungholz count
> only two. Hmmm. That upsets me, so I have to revise things and say
> that the border between mainland Austria and Germany is in two
> discreet segments, separated by the quadripoint with Jungholz.
>
> So that's what I think. Anyone else?
>
> Grant