Dear Mr. Hocknell,
Thanks for your message entitled: How long is a piece of string?
>It depends on how wide it is!? - or at least so it seems after my
>attempts in vain to calculate the lengths of three 'old' and one 'new'
>international land boundary.
Your message reminds me of the title of the classic paper written
by Benoit Mandelbrot in 1967:
How long is the Coast of Britain?
Statistical Self-Similarity and Fractional Dimension.
Science Vol. 156, No. 3775, pp. 636-638.
Ah! and not only does the length of a boundary depend on the coordinates
of its initial and end points, ("wide" is a bit confusing) but also
obviously on the path and, perhaps must importantly, the scale of the
coordinate samples collected along this path.
Most boundaries have fractal properties which, by definition, can have
different lengths based on the scale of the map or the sampling rate
of turning points along their paths. How different? The answer is a
function of the fractal scale. Rivers and coastlines have some of the
largest fractal scale values. Boundaries formed by parallels and
geodesics have the lowest value of course.
I believe that any "exact" length of all boundaries can be disputed.
This fact probably should not be held against the 'Encyclopaedia of
International Boundaries'.
>And for a bonus prize, what is the average length of an international
>land boundary? Please contact IBRU for terms and conditions of the
>competition (?!).
Exactly?
Regards,
Galo Carrera.
Secretary
Committee on Geodetic Aspects of the Law of the Sea
International Association of Geodesy
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Galo Carrera Honorary Consul
[log in to unmask] Consulate of Mexico in Nova Scotia
Phone: (902) 466-3678 53 Hawthorne Street
Fax: (902) 466-3678 Dartmouth, Nova Scotia
Canada B2Y 2Y7
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