This is simply paralysis of theory. Of course natural boundaries can be
measured with relatively precise accuracy. One would not need to measure and
include the height of every blade of grass on the line, not go around each
grain of sand in the way. You measure across it. It isn't illegitimate to
say one river flows for 15 miles down the center of its channel and another
1,000. What is not reasonable is to say when determining a water boundary
that both of those watercourses are of the same infinite length because they
are fractal.
> ----------
> From: Brian J. Butler[SMTP:bjbutler@...]
> Reply To: BoundaryPoint@yahoogroups.com
> Sent: Wednesday, April 16, 2003 5:49 PM
> To: BoundaryPoint@yahoogroups.com
> Subject: Re: [BoundaryPoint] Re: American State Boundaries
>
> On Wednesday 16 April 2003 05:58 pm, you wrote:
> Actually, it is illigitimate to say that a river goes on for 15 miles, or
> that a river goes on for 1000 miles. The center of a river is of
> indeterminate length because it is a fractal object, not a smooth curve.
> The
> same goes for a ridge line. Of course, you can choose to estimate its
> length
> by ignoring an arbitrary amount of detail. This can give you a reasonable
>
> lower bound for the length, which, in the case of the OK-TX boundary, may
> be
> sufficient to show that it is longer than the straight-line CA-NV
> boundary.
> But you cannot really measure the upper limit of the length of OK-TX or
> of,
> say, VA-WV. So how can you say that one of these is longer than the
> other?
> And you certainly cannot put a fixed number on either one.
>
> BJB
>
> > I disagree completely. There is no measuring around an infinite number
> of
> > grains of sand or molecules involved in measure the OK-TX boundary. If
> it
> > is the center of the Red River, there is a definite, not indeterminate,
> > length to that. It is legitimate to continue along that course around
> > every oxbow and bend for that is the true boundary.
> >
> > It is illegitimate to say a river boundary that might go on for 15 miles
> is
> > to be regarded as equally as long as a 1,000-mile river boundary. These
> are
> > not distinctions that are difficult to make.
> >
> > By any real-world standard, the CA-NV boundary is shorter than OK-TX
> >
> > -----Original Message-----
> > From: acroorca2002 [mailto:orc@...]
> > Sent: Wednesday, April 16, 2003 3:33 PM
> > To: BoundaryPoint@yahoogroups.com
> > Subject: [BoundaryPoint] Re: American State Boundaries
> >
> >
> >
> > however for longest interstate boundary
> > the best available truth appears to be that the fractal principle
> > would actually make all river boundaries stretch into the same
> > condition of indeterminacy as we have observed for oktx
> >
> > so all such river boundaries must be considered equally long
> > all appearances to the contrary notwithstanding
> > with their supposed or apparent length depending only on how
> > carefully they are measured
> >
> > if all are measured with equal & consistent care
> > a fair proviso under the circumstances
> > then all bulges bends oxbows etc of the same size would be
> > measured equally or equally disregarded on all boundaries
> >
> > right down to the molecular level i suppose
> >
> > & in practical reality
> > such conscientious measuring
> > besides being impossible
> > would quickly lead to the realization that canv cant be surpassed
> > in length without somehow stretching or bending the truth
> >
> > i grant that one may be a bit harder to be satisfied with tho
> >
> > --- In BoundaryPoint@yahoogroups.com, "Craig" <trehala@y...>
> >
> > wrote:
> > > Thank-you for your answer, Brian, however I am looking for a
> >
> > state
> >
> > > border that does not meet at a point. Think of Turkey-Azerbaijan
> >
> > or
> >
> > > Western Sahara-Algeria: tiny tiny borders but on a state level.
> > >
> > > --- In BoundaryPoint@yahoogroups.com, Brian J. Butler
> >
> > <bjbutler@b...>
> >
> > > wrote:
> > > > On Wednesday 16 April 2003 09:50 am, you wrote:
> > > > The shortest is easy - at AZ-CO-NM-UT there are two pairs of
> >
> > states
> >
> > > that meet
> > >
> > > > at a point.
> > > > BJB
> >
> > Your use of Yahoo! Groups is subject to
> http://docs.yahoo.com/info/terms/
> >
> >
> >
> >
> >
> > Your use of Yahoo! Groups is subject to
> http://docs.yahoo.com/info/terms/
>
> --
> Brian J. Butler
> BJB Software, Inc.
> 508-429-1441
> bjbutler@...
> http://www.bjbsoftware.com
>
>
>
>
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>
>