- 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 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

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@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 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:

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

I think Mulder and Scully are entered, undercover, to investigate

>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.

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

________________________________________________________________