On Thursday 17 April 2003 02:00 am, you wrote:
I don't believe you are really thinking about the problem. But enough said.
BJB

> 1. But the boundary is. You may not be talking about elevations, but if the
> boundary is the middle of the river, that's where it is.
>
> 2. Even if you had to measure around every grain of sand it would be a
> finite distance, as there is a finite number of grains. But even so, this
> is not how the line is measured, so it's not relevant. In the real world of
> surveying and measuring, the length would be determined.
>
> 3. A boulder on a boundary wouldn't necessarily lengthen the boundary
> unless it was a feature defined in the legal metes and bounds. As with the
> grains of sand, the line would ordinarily continue in a path through it.
>
> > ----------
> > From: Brian J. Butler[SMTP:bjbutler@...]
> > Reply To: BoundaryPoint@yahoogroups.com
> > Sent: Wednesday, April 16, 2003 6:16 PM
> > To: BoundaryPoint@yahoogroups.com
> > Subject: Re: [BoundaryPoint] Re: American State Boundaries
> >
> > 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
> >
> >
> >
> >
> > 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