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• I just got my Hardrock entry booklet today. Very nicely done, But on page 2 of the course description, item 6, it says: All mileage used were obtained by map
Message 1 of 4 , May 6, 2000
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I just got my Hardrock entry booklet today. Very nicely done, But on page 2
of the course description, item 6, it says:

"All mileage used were obtained by map measurement with on the ground wheel
measurement verifications for over half the course. To correct for vertical
changes on the map measurements, the vertical distances are added directly
to horizontal distances to obtain the totals"

If we subtract the vertical distance (66,000 ft. = 12.5 miles) from the
total distance (101.7 miles), we obtain a horizontal component of 89.2
miles. Then applying Pythagoras' theorem, which is the correct method of
combining horizontal and vertical distances (assuming a constant grade), we
have

sqrt(89.2^2 + 12.5^2) = 90.1 miles.

So this course is really not has hard as everyone says it is :-)

Also, a couple of minor errata:

1. Carl Yates is listed as -27 years old (a lingering Y2K bug maybe, or did
we make an exception to the minimum age requirements?)

2. At the absolute bottom of the all time finishers results (sorted by
time), Fred Vance and I (with * by our names) are listed as finishing
unofficially in 51:08 in '98. Our actual time was 51:38:34 (a blistering
34:23/mile pace, and I had the blisters to prove it).

-- Matt Mahoney, matmahoney@...
• Matt: Your point on the methodology used to obtain the distances for the Hardrock is well taken. It is done very deliberately for the following reason. Over
Message 1 of 4 , May 10, 2000
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Matt:

Your point on the methodology used to obtain the distances for the
Hardrock is well taken. It is done very deliberately for the
following
reason.

Over the years, Charlie and I have measured between 150 and 200 miles
of trail in Colorado and New Mexico by pushing a bike wheel fitted
with a Jones counter. In 1992 and 93 Rick Trujillo measured about
half of the Hardrock course using this wheel.

All the courses were then laid out and measured on the map using the
Pythagorean theorem as you suggest. Correlation with the in field
measurements was poor and systematically biased low. We have assumed
the in field measurements are the more accurate numbers. The best fit
of the map to field turned out to be the the vertical distances are
added directly to horizontal distances to obtain the totals.

John Cappis

--- In hr100@egroups.com, "Matt Mahoney" <matmahoney@y...> wrote:
> I just got my Hardrock entry booklet today. Very nicely done, But
on page 2
> of the course description, item 6, it says:
>
> "All mileage used were obtained by map measurement with on the
ground wheel
> measurement verifications for over half the course. To correct for
vertical
> changes on the map measurements, the vertical distances are added
directly
> to horizontal distances to obtain the totals"
>
> If we subtract the vertical distance (66,000 ft. = 12.5 miles) from
the
> total distance (101.7 miles), we obtain a horizontal component of
89.2
> miles. Then applying Pythagoras' theorem, which is the correct
method of
> combining horizontal and vertical distances (assuming a constant
> have
>
> sqrt(89.2^2 + 12.5^2) = 90.1 miles.
>
> So this course is really not has hard as everyone says it is :-)
>
> Also, a couple of minor errata:
>
> 1. Carl Yates is listed as -27 years old (a lingering Y2K bug
maybe,
or did
> we make an exception to the minimum age requirements?)
>
> 2. At the absolute bottom of the all time finishers results (sorted
by
> time), Fred Vance and I (with * by our names) are listed as
finishing
> unofficially in 51:08 in '98. Our actual time was 51:38:34 (a
blistering
> 34:23/mile pace, and I had the blisters to prove it).
>
> -- Matt Mahoney, matmahoney@y...
• 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
Message 1 of 4 , May 12, 2000
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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
• Roger wrote: ... I think Mulder and Scully are entered, undercover, to investigate just this phenomenon. Scully will be the one running in heels, so
Message 1 of 4 , May 12, 2000
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Roger wrote:
<snip>
>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.

I think Mulder and Scully are entered, undercover, to investigate
just this phenomenon. Scully will be the one running in heels, so
she'll be EZ to pick out.

The truth is out there.

Mike

________________________________________________________________
Dr. Mike Farris mfarris@...
Associate Professor of Biology http://www.hamline.edu/~mfarris
Hamline University, St. Paul, MN 55014
________________________________________________________________
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