On Wednesday 16 April 2003 08:02 pm, you wrote:
1. Regarding the first paragraph, I was not talking about elevations.

2. Your second paragraph is self-contradictory because it certainly WOULD be
reasonable to say the shoreline is infinite if you had to measure around
every grain of sand.

3. If you placed a boulder on a boundary defined by monuments then no, you
wouldn't be lengthening the boundary because the boundary does not depend on
objects it passes through (or over). If you placed a boulder half in and
half out of the water along a riverbank that defined a boundary, you also
would not lengthen the boundary, but only because man-made changes in a
watercourse do not change boundaries as a matter of law. If the same boulder
existed at the position described above at the time the boundary was defined
as the high-water mark then yes, the boundary is longer than it would have
been if the boulder had not existed. Ditto for all other boulders, stones,
sand grains, et cetera.

BJB

> Because it is water. If you go down to the riverbed, you will have some
> variable elevations, but that doesn't mean you don't measure the distances
> above them.
>
> It isn't really reasonable to say the high-water line on a stretch of beach
> has an infinite length because you have to measure around grains of sand.
>
> If I place a large boulder on the state line, am I somehow lengthening the
> border? I don't think so.
>
> -----Original Message-----
> From: Brian J. Butler [mailto:bjbutler@...]
> Sent: Wednesday, April 16, 2003 4:27 PM
> To: BoundaryPoint@yahoogroups.com
> Subject: Re: [BoundaryPoint] Re: American State Boundaries
>
>
> On Wednesday 16 April 2003 06:20 pm, you wrote:
> Why would the center of a river be any smoother than banks from which it is
> equidistant? And molecules, grains of sand, boulders, and great bends are
> all
> features that determine the edge of a river, hence its length. For some
> discussions it might be OK to ignore features below a certain size, but we
> are specifically discussing the length of the boundary, which is dependent
> on
> the scale of objects we consider.
> BJB
>
> > The center of a river is about as smooth as you can get.
> >
> > Why would you measure a boundary line around a grain of sand?
> > Theoretically, this discussion could get into such things, but
>
> practically,
>
> > the line would go right across the top of that grain, or boulder, or
> > rock, not around it.
> >
> > -----Original Message-----
> > From: Brian J. Butler [mailto:bjbutler@...]
> > Sent: Wednesday, April 16, 2003 3:44 PM
> > To: BoundaryPoint@yahoogroups.com
> > Subject: Re: [BoundaryPoint] Re: American State Boundaries
> >
> >
> > On Wednesday 16 April 2003 05:12 pm, you wrote:
> > You are not on the right wavelength yet. The natural boundaries you
> > enumerated are not smooth curves that can be measured in the traditional
> > sense. I agree that you can determine a minimum length of these
>
> boundaries
>
> > by interpolating between fixed points on the boundary. But the true
>
> length
>
> > of the boundary depends on how small your samples are. For example, you
> > would have a longer measurement if you measured around each rock along
> > the riverbank, or each grain of sand. So you are doubly correct - your
> > estimate
> >
> > could be off by a great margin, an infinite margin perhaps, and the
>
> minimum
>
> > length of the OK-TX boundary is longer than the CA-NV boundary. I don't
> > think you can make the statement that the OK-TX boundary is longer than
>
> the
>
> > VA-WV boundary, though, for example, because it depends on how irregular
> > the
> >
> > boundaries are and how carefully you measure them.
> >
> > BJB
> >
> > > Well, *anything* has a length depending on how you measure it. But most
> > > US state boundaries have specific definitions that are actual places on
> > > the ground, whether it's mean highwater, center of channel. top of the
> > > ridge, etc. E.g., the Kentucky boundary along the Ohio River is the
> > > waterline on the northern bank, so KY controls the river. The
> > > definition IIRC was fixed in time so that it doesn't change as the Ohio
> > > rises or falls or carves new segments of the channel.
> > >
> > > Anyway, I am still curious if there is a place to ascertain the actual
> > > length of the OK-TX boundary? I estikated it as somewhere around 800
> >
> > miles,
> >
> > > while CA-NV was just over 600 miles. My estimates could be off by a
>
> great
>
> > > margin, but I don't think they are off so much as to change the
> > > ranking.
> > >
> > >
> > > -----Original Message-----
> > > From: Brian J. Butler [mailto:bjbutler@...]
> > > Sent: Wednesday, April 16, 2003 12:12 PM
> > > To: BoundaryPoint@yahoogroups.com
> > > Subject: Re: [BoundaryPoint] Re: American State Boundaries
> > >
> > >
> > > On Wednesday 16 April 2003 01:18 pm, you wrote:
> > > A natural boundary, such as a river, has a length that depends on how
> > > closely
> > > you measure it.
> > > BJB
> > >
> > > > But CA-NV wouldn't be the longest border between two states, straight
> > > > or not. The OK-TX border for a good distance is the meandering Red
> > > > River. There's no basis to say that doesn't count as distance and
> > > > that one should draw an imaginary "straight" line instead to cut the
> > > > corners. The boundary is the boundary line itself.
> > > >
> > > > What is the length of the CA-NV boundary and the OK-TX boundary?
> > > >
> > > > -----Original Message-----
> > > > From: Brian J. Butler [mailto:bjbutler@...]
> > > > Sent: Wednesday, April 16, 2003 9:39 AM
> > > > To: BoundaryPoint@yahoogroups.com
> > > > Subject: Re: [BoundaryPoint] Re: American State Boundaries
> > > >
> > > >
> > > > On Wednesday 16 April 2003 11:19 am, you wrote:
> > > > CANV is certainly the straight-line champ. If we "go fractal" maybe
> > > > ID-MT, OK-TX, or even VA-WV would take the cake.
> > > > BJB
> > > >
> > > > > nice question & nice answer
> > > > >
> > > > > how about canv for longest
> > > > >
> > > > > --- 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
> > > > > >
> > > > > > > Which state shares the longest border with another state?
> > > > >
> > > > > (The border
> > > > >
> > > > > > > does not have to be continuous.) Which state shares the
> > > > >
> > > > > shortest?
> > > > >
> > > > > > > Your use of Yahoo! Groups is subject to
> > > > >
> > > > > http://docs.yahoo.com/info/terms/
> > > > >
> > > > > > --
> > > > > > Brian J. Butler
> > > > > > BJB Software, Inc.
> > > > > > 508-429-1441
> > > > > > bjbutler@b...
> > > > > > http://www.bjbsoftware.com
> > > > >
> > > > > 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