On Wednesday 16 April 2003 07:12 pm, you wrote:
The thalweg is also of indefinite length because there can be an infinite
number of changes in the y value over any interval of x.
BJB

> The riverbanks can have an almost infinite length
> which is practically impossible to measure, but I
> think the center or thalweg can not be considered in
> the same category. Looking at it from above with one
> bank on the bottom and the other on top (thus
> traveling along the bank is traveling along the x-axis
> and crossing river is along y-axis), there emerges an
> upper and lower bound. When drawing the boundary
> along the center or thalweg, you can only go in one
> direction without doubling back and must stay within
> the bounds...essentially only one y-coordinate per
> each x-coord. This is unlike the bank which, due to
> shapes of rocks, you can have the shore go in and out
> (several y-coord per x-coord).
>
> --- "Brian J. Butler" <bjbutler@...>
>
> wrote:
> > 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
>
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--
Brian J. Butler
BJB Software, Inc.
508-429-1441
bjbutler@...
http://www.bjbsoftware.com