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Re: [hr100] Re: Hardrock is only 90 miles!

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  • Matt Mahoney
    ... Another factor that distorts the space-time metric is sleep deprivation. I found that after about 44 hours that all of the trails were twice as long and
    Message 1 of 4 , May 12 8:45 AM
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      --- Roger Wiegand <rwiegand@...> wrote:
      Another factor that distorts the space-time metric is
      sleep deprivation. I found that after about 44 hours
      that all of the trails were twice as long and twice as
      steep.

      Furthermore, there was no longer a linear mapping of
      the terrain to my map, resulting in my map becoming
      useless for navigational purposes, resulting in my
      getting completely lost, resulting in a 51 hour DNF
      two years ago.

      > 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.

      Will this be on the course? I found some sections
      around Grant-Swamp pass that are not quite on the
      course but are far more difficult than anything we
      would normally have to do. It would be interesting to
      explore these regions in a normal space-time continuum
      to see if they really are as vertical as they seemed
      at the time. Just to make sure we don't miss the
      start, I would recommend we get up about 15 hours
      early and bring ropes.


      =====
      -- Matt Mahoney, matmahoney@...

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    • Curiel, Tyler
      Roger, I read with great care your cogent arguments. However, have you also considered the gravitational effects of the mass of runners, not to mention their
      Message 2 of 4 , May 12 8:50 AM
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        Roger, I read with great care your cogent arguments. However, have you also
        considered the gravitational effects of the mass of runners, not to mention
        their equipment? I suggest you make that a 12 miler just to be safe. /TC

        -----Original Message-----
        From: Roger Wiegand [mailto:rwiegand@...]
        Sent: Friday, May 12, 2000 9:18 AM
        To: hr100@egroups.com
        Subject: Re: [hr100] Re: Hardrock is only 90 miles!


        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




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