Dear Hardrockers,

I have read with amusement the discussions on the length of the Hardrock

course. Clearly a mathematician's input is needed. Of course we live in

a three-dimensional space, but for simplicity, let's just use x for

horizontal displacement and y for vertical displacement. The usual

Euclidean metric gives the total displacement as

d = (x^2 + y^2)^{1/2} (the Pythagorean Theorem). In mathematical jargon

this might be referred to as the L^2 metric. John and Charlie are using

the L^1 metric: d = |x| + |y|. In fact, there is a whole continuum of

L^p metrics, for 1 <= p <= infinity: d = (|x|^p + |y|^p)^{1/p} in the

L^p metric. (For p = infinity, the limiting case,

d = max{|x|,|y|}.)

So what does this mean for us Hardrockers? While parapsychology is a bit

outside my realm of expertise, it seems clear that a gathering of 100

deranged minds in one location has the potential to distort space, thereby

changing the metric. In fact, once the runners get spread out along the

course, it is likely that the space surrounding one clump of runners will

have drastically different geometry from the space surrounding runners on

a different part of the course. This is the real reason that

most of the runners finished ahead of me. They were working

with a different metric, more favorable to the runner.

I am virtually certain that I ran at least 100 miles last year. (Look how

long it took me, if you have any doubts!) But just to be sure, I will get

up early the morning of the race and take a ten-mile run before the

start. I invite any other runners with geometric anxiety to join me.

Roger

Roger A. Wiegand

http://www.math.unl.edu/~rwiegand