Thanks. I would then not have a problem, and be able to come up with the
length.
-----Original Message-----
From: Brian J. Butler [mailto:
bjbutler@...]
Sent: Thursday, April 17, 2003 4:29 AM
To:
BoundaryPoint@yahoogroups.com
Subject: Re: [BoundaryPoint] Re: American State Boundaries
On Thursday 17 April 2003 01:53 am, you wrote:
You are welcome to change the problem and answer it in any way you wish.
Good luck.
BJB
> 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
> >
> >
> >
> >
> > 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
Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/