I understand everything that you're saying, but I refuse to go there.
A typical boundary might be considered analogous to an imaginary vertical wall
stretching from the center of the earth to the upper reaches of the atmosphere
or beyond. However that's only an analogy. The situation that obtains on MXUS
bridges, with their treaty-ordained vertical differentiation, is anything but
typical. It is arguably unique in all the world. As such, it does not lend
itself to analogies. To even try would require the typical imaginary wall to
become a curtain of the very finest spandex, which would envelope and cling
around every protuberance and into every orifice of the human and vehicular
traffic moving upon those segments of the bridges that are between the movable
middle of the Rio Grande and the fixed boundary monuments on the bridges.
This desire to over-analogize the situation seems to spring from the notion that
boundaries are physical objects or laws of nature that are subject to the most
minute mensuration. This is not the case. Boundaries proceed from the minds
of men, who decide what and where they should be. Agreements as to these
decisions are committed to paper. Men then go out onto the landscape and
jointly demarcate the boundary, relying upon nothing more as their mandate than
the agreed-upon words and numbers on paper.
To put it bluntly, there is no provision for a clingy spandex curtain in the
MXUS treaty of 1970 (a fact for which the International Boundary and Water
Commission is undoubtedly grateful). No demarcation beyond the periodic mapping
of the middle of the main channel of the river and the placement of monuments on
bridges is mandated. Why? Because that is sufficient to determine which
sovereignty is applicable to every foreseeable practical eventuality. That's
all a boundary is for. If some person, thing, or occurrence is on a bridge,
sovereignty is determined by the fixed monument on the bridge. If it's anywhere
else (including on the land or water under the bridge or in the air above the
bridge), sovereignty is determined by the constantly accreting and avulsing
median line of the river. It's complex, it's simple too, but most of all, it is
sufficient!
If the two nations ever need a practical way of determining sovereignty over a
mosquito flying through the airspace between the legs of a pedestrian walking on
the portion of a bridge between the median line of the Rio Grande and the
monument on the bridge, then perhaps new treaty provisions will be agreed upon,
and the IWBC will carry them into execution. Until then, what you see is what
you get.
Lowell G. McManus
Leesville, Louisiana, USA
----- Original Message -----
From: "Michael Kaufman" <mikekaufman79@...>
To: <BoundaryPoint@yahoogroups.com>
Sent: Saturday, February 14, 2004 1:41 AM
Subject: Re: [BoundaryPoint] Re: Israel Army Proposes to Create Enclaves
> 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
> > > >
> > >
> > >
> > > __________________________________
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> >
>
>
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