On Thursday 17 April 2003 07:58 pm, you wrote:
OK, I give up. And I give you an F in fractal geometry.
BJB

> I really have not misunderstood any of the points made in opposition to
> measuring a physical boundary... I have only said that it can be done, and
> it is done. I don't agree with the notion that there is infinite length in
> a river that flkoiws only, say, 10 miles. That's an absurd notion. A
> highway might be measured by its length along a centerline in the median,
> while the distance along its outside shoulders may be different... still,
> the distance is not infinite! We can prove that by arriving at our
> destination.
>
> Once a high water mark is established, if that is the boundary, then it can
> be measured. I didn't say it was easy to go 1,000 miles along the banks of
> the Red River (I believe the OK-TX boundary is the center of the channel,
> which would be much less difficult to measure), but it can be done.
>
> At a human scale, the water line does not have to be measured around
> molecules, or grains of sand, to be called accurate. As with my highway
> example.
>
> -----Original Message-----
> From: Brian J. Butler [mailto:bjbutler@...]
> Sent: Thursday, April 17, 2003 4:18 PM
> To: BoundaryPoint@yahoogroups.com
> Subject: Re: [BoundaryPoint] OKTX --finally! figures
>
>
> On Thursday 17 April 2003 05:04 pm, you wrote:
> Let me trry one more time, and then if you still don't get it, I will give
> up. Suppose a boundary is defined as the high water mark along a river
> bank.
> Further suppose the river bank is irregular, which should not be much of a
> stretch if you have ever looked at a river bank. The irregularities exist
> at
> many scales, from broad bends measured in miles, to smaller meanders
> measured
> in hundreds of feet, to smaller gouges measured in tens of feet, to rocks
> meausured in feet, to pebbles measured in inches, to small pebbles, ...
> etc.
>
> Clearly if you consider smaller and smaller irregularities, the length of
> the
> river bank increases without bound, as illustrated by the two measurements
> given for the OK-TX boundary. Since you think the length is bounded, it
> implies that you stop measuring around features below some size threshold.
> My
> question to you is: At what scale do you stop measuring, and why? Please
> actually think about the question.
> BJB
>
> > It would really not go on like that. If the boundary is defined, one
> > follows that definition. If OK-TX has been defined as a certain location
>
> in
>
> > the channel of the Red River, one would follow that and measure it as
> > s/he goes. If the menaderings are part of the definition, that would be
> > followed.
> >
> > The hard number really is out there. It is not infinite.
> >
> > -----Original Message-----
> > From: Brian J. Butler [mailto:bjbutler@...]
> > Sent: Thursday, April 17, 2003 1:55 PM
> > To: BoundaryPoint@yahoogroups.com
> > Subject: Re: [BoundaryPoint] OKTX --finally! figures
> >
> >
> > On Thursday 17 April 2003 12:13 pm, you wrote:
> > And following really small meanders
> >
> > Red River - -1234 miles
> > East Panhandle line -- 133.6 miles
> > North Panhandle line -- 167 miles (minus 2.2 miles TXNM)
> >
> > Total -- 1532.4 miles
> >
> >
> > And following really small meanders and medium sizes irregularities:
> >
> > Red River -- 2816 miles
> > East Panhandle line -- 133.6 miles
> > North Panhandle line -- 167 miles (minus 2.2 miles TXNM)
> >
> > Total -- 3114.4 miles
> >
> > Etc.
> >
> > > Including only larger river bends:
> > >
> > > Red River -- 480.0 miles
> > > East Panhandle line -- 133.6 miles
> > > North Panhandle line -- 167 miles (minus 2.2 miles TXNM)
> > >
> > > Total -- 778.4 miles
> > >
> > > Following the smaller meanderings of the rivers:
> > >
> > > Red River -- 726 miles
> > > East Panhandle line -- 133.6 miles
> > > North Panhandle line -- 167 miles (minus 2.2 miles TXNM)
> > >
> > > Total -- 1024.4 miles
> > >
> > > Source: Texas Almanac
> > >
> > > --Joe
> > >
> > > (Will post some pics of my visit to Copperhill TN/McCaysville GA soon.
> > > The border runs through a grocery store and a church)
> > >
> > >
> > >
> > >
> > >
> > > 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