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/