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/
>
>