On Thursday 08 May 2003 01:17 pm, you wrote:
I wish you would read Chapter 5 of "The Fractal Geometry of Nature" by Benoit
M. Mandelbrot, the title of which is "How Long Is the Coast of Britain?".
Here is the second paragraph of that chapter:

"There are various ways of evaluating its length more accurately, and this
chapter analyzes several of them. The result is most peculiar: coastline
length turns out to be an elusive notion that slips between the fingers of
one who wants to grasp it. All measurement methods ultimately lead to the
conclusion that the typical coastline's length is very large and so ill
determined that it is best considered infinite. Hence, if one wishes to
compare different coastlines from the viewpoint of their 'extent', length is
an inadequate concept."

The book, and this chapter in particular, provide a rigorous mathematical
basis for what I have been arguing. I understand your point about "real
world" measurements, but I think the salient aspect of such measurements is
that they are only estimates. From a legal perspective a sufficiently
accurate estimate might suffice, but with natural boundaries it will always
be possible to improve on the estimated by considering smaller and smaller
scales, and when that happens the length of the boundary increases without
limit with mathematical certainty. So, at what scale do we lose interest and
claim it doesn't matter? I don't think you can get off the hook by claiming
that it is a "human scale" because that is a meaningless term. For example,
surveying accuracy standards are much more stringent in Manhattan than in
rural areas.

So the coastline of Ellis Island could not have been precisely measured,
opinions of the even the measurers notwithstanding. But I will concede that
at some arbitrary level of precision its length can be estimated and stated.

BJB

> I didn't say it's always an easy task -- following all the bends and bows
> of the Red River at OK-TX is a difficult chore -- but the legal boundary
> can be measured and is measured in human scale. It's fun to argue about
> measuring around a molecule, but c'mon. Don't get lost in the theory so
> much that you're immobilized in the real world.
>
> -----Original Message-----
> From: Brian J. Butler [mailto:bjbutler@...]
> Sent: Thursday, May 08, 2003 4:30 AM
> To: BoundaryPoint@yahoogroups.com
> Subject: Re: [BoundaryPoint] Re: American State Boundaries
>
>
> On Thursday 08 May 2003 02:07 am, you wrote:
> I seriously doubt that anyone has attempted to measure the length of the
> Ellis Island boundary. Why would they? Estimating and marking its
> position
>
> has value but determining its length is purely academic.
>
> Your analogy to the "angels on a pin" argument made me realize that your
> devotion to the "definite length theory for fractal boundaries" is a matter
> of faith for you, and is therefore impervious to logic. Would you agree?
>
> > Please let's not have the "how many angels can dance on the head of htis
> > pin" discussion again. We can and do measure natural borders, and we
> > don't need an electron microscope to do it. They did measure around the
> > presumed 1934 low water line on Ellis Island and there is a length to it.
> > It is really silly to say that a river that courses, e.g., 10 miles must
> > be regarded as infinite in shorelineand equal to the Nile.
>
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>
>
>
>
>
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--
Brian J. Butler
BJB Software, Inc.
508-429-1441
bjbutler@...
http://www.bjbsoftware.com