I guess it's how you define it. I gather your
interpretation is that of taking infinite
horizontal-plane crossections of the space we have in
question. Then tracing the border and projecting
upwards. The horizontal surfaces as differences are
easy to see if you think about a simplified bridge
with perfectly straight lines.
But what about a person standing on a bridge. Again,
north of the median line of the Rio Grande, but south
of the marker. Take a horizantal plane crossing me at
some point through my legs. This plane would have a
border as projected directly upwards from the river
median line. It would also contain two circular-esque
enclaves of Mexico in US, the two enclaves being the
cross-section of each leg.
But you can only project this upwards until there is a
change whereby the cross-section will not match the
one below it. I.E.: Project this scenario upwards by
vertical surfaces until the border changes on another
particluar plane. If we were only thinking of the
river median line, you could project this plane
upwards forever without having to have any horizontal
differentiation. But we have the additional
complication of the person. If a person was made of
certain regular geometric shapes (like stacks of
squares and rectangles of different sizes on each
other), you may be able to project upwards 4 inches
before hitting a difference - creating a horizontal
surface linking two different projections. The next
one up may go 2 inches, etc.
But people are not a regular shape at all. Each
cross-section you take will be different because the
body (and clothing etc.) is not geometircally perfect.
So you can't project it up any distance vertically,
because the next plane up will be different. So you
have an infinite number of contiguous crossectional
planes which are all different (from the feet to the
head of the person).
All of the contiguous horizontal planes come together
to form 3-D space. The infinite unchanging river
median line projections come together to form a
vertical surface (you can change your z-coordinate
while maintaining your x and y coords). But the
surface created by the infinte number of lines of the
human cross-sections is not purely vertical. If you
want to change your z-coordinate, you have to change
either your x or your y as well.
So I think if we call the vertical surface a border,
we have to call the nonvertical surface a border too,
since they are both made up of the same infinite
number of border tracings on contiguous planes. I
would call them both border surfaces.
--- m06079 <
barbaria_longa@...> wrote:
> --- In BoundaryPoint@yahoogroups.com, Michael
> Kaufman
> <mikekaufman79@y...> wrote:
> > Thanks for clarifying this, Lowell. Yes, this
> does
> > make more sense from a practical aspect. But it
> also
> > adds a level of variability to the exact 3-D shape
> of
> > the border (i.e.: people and cars move, the 3-D
> border
> > surface moves with them) that I don't recall
> seeing
> > elswhere.
>
> wait mike
>
> youve still almost got it
>
> but neither the border nor the border surface really
> moves with
> the people & the cars
>
> in fact
> border surface
> as such
> is a practically meaningless concept
>
> for borders really have no surface
>
> not a horizontal surface anyway
>
>
> they have a vertical dimension
> it is true
>
> & in rare cases such as this they are vertically
> differentiated
> besides
>
> & so i suppose you could say that the vertical
> projections of
> border lines do form surfaces of a sort
>
> but i think that that is as far as you could take
> this term
>
>
> moreover
> split level borders must of course adjoin horizontal
> surfaces that
> link their differing vertical positions &
> projections
>
> but borders per se can have no surface other than a
> vertical one
> so far as i can see
>
>
> & such a variability as you imagine is the case
> neither on mxus
> nor anywhere else
> i believe
>
> the variability that does exist on mxus consists
> only in the vertical
> differentiation between a historic thalweg position
> recorded &
> frozen on a bridge railing
> & the ongoing location of the living thalweg itself
>
>
> the activity on the bridge doesnt affect the
> boundary
>
>
> & it is true that you havent seen what you describe
> elsewhere
> since it actually obtains nowhere
> so far as i am aware
>
>
> >
> > --- "Lowell G. McManus" <mcmanus71496@m...> wrote:
> > > Michael,
> > >
> > > You've almost got it.
> > >
> > > Not only the physical substance of the MXUS
> bridges,
> > > but also persons and
> > > traffic upon them are governed by the
> established
> > > boundary monuments on the
> > > bridges. Anything or anyone not on the bridges
> (in
> > > the air above or on the
> > > ground or water below) is governed by the
> current
> > > location of the middle of the
> > > main channel of the river. This is by the 1970
> > > treaty.
> > >
> > > If it were otherwise, the wording on the bridge
> > > monuments and signs would be
> > > meaningless to their readers if those readers
> had to
> > > look off the bridge
> > > (perhaps in darkness) and estimate the location
> of
> > > the middle of the river.
> > >
> > > Lowell G. McManus
> > > Leesville, Louisiana, USA
> > >
> > >
> > > ----- Original Message -----
> > > From: "Michael Kaufman" <mikekaufman79@y...>
> > > To: <BoundaryPoint@yahoogroups.com>
> > > Sent: Thursday, February 12, 2004 6:17 AM
> > > Subject: Re: [BoundaryPoint] Israel Army
> Proposes to
> > > Create Enclaves
> > >
> > >
> > > >
> > >
> >
>
http://groups.yahoo.com/group/BoundaryPoint/message/10911
> > > > Due to the changing course of the river, the
> > > > bordermarker on the bridge is now directly
> over
> > > land
> > > > on the northern/US bank of the Rio Grande.
> The
> > > bridge
> > > > itself and its supports are Mexican all the
> way up
> > > > until the marker. But for everything else,
> the
> > > border
> > > > is the middle of the river. So for instance,
> you
> > > > could be standing on the bridge say 2 feet
> south
> > > of
> > > > the bordermarker. Directly beneath you is a
> > > sovereign
> > > > Mexican bridge. But beneath and above that is
> > > > soverign US airspace and land on the north
> bank of
> > > the
> > > > Rio grande. You are in the US even though you
> are
> > > > south of the marker. Only the physical bridge
> is
> > > in
> > > > Mexico. But you can not be in Mexico this way
> > > since
> > > > you would have to occupy the same physical
> space
> > > as
> > > > the bridge at the same time, which is, of
> course,
> > > > impossible. If you were on the bridge and
> wanted
> > > to
> > > > visit Mexico, you would have to walk further
> south
> > > > until you pass the middle of the river. This
> is
> > > how I
> > > > understand the situation to be.
> > > > -Mike
> > >
> >
> >
> > __________________________________
> > Do you Yahoo!?
> > Yahoo! Finance: Get your refund fast by filing
> online.
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>
>
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