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A question for the scientists # 1

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  • mountaingoatnewton
    Dear All Since I know a number of the major contributors to this forum are, like myself, scientists, I have a couple of questions / thoughts to share that
    Message 1 of 3 , Sep 15, 2013
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      Dear All

       

      Since I know a number of the major contributors to this forum are, like myself, scientists, I have a couple of questions / thoughts to share that might be of interest. Since I´m a chemist rather than a mathematician, the math gurus will have to forgive my imprecise terminology..

       

      So, the first question is this - in principle I climb prominent mountains, the more prominent the better. Since I don´t want to travel very widely all the time, I need to work on lists going down to P150m to provide enough target peaks near home. However, since I tend to work from lists with cutoff values like 150m, 600m and 1500m, and prioritise peaks on the higher lists I guess this leads to a certain bias as follows:

       

      If I take a given geographical area, like the European Alps, or the CONUS, and look at the number of peaks with P100-200m, P200-300m, P300-400m etc, am I right in thinking the number in each band will fall exponentially? Given a large enough dataset, and narrow enough bands, the curve should get reasonably smooth I suppose? Has anyone tried to model such distributions or even provided an equation to describe them? Does this look the same for different large datasets or does it somehow depend on topography or altitude? If I look at my own efforts, I have climbed a similar percentage of mountains in the Alps with P800-900m as I have with P600-700m but this percentage is far greater than for P500-600m, whilst that percentage is similar to the percentage with P200-300m. So, if I overlay a plot of my climbed peaks in bands with the peaks available, the shapes will be different. This tells me I am perhaps unfairly ignoring certain peaks just below the cut-offs I choose because we all (or at least most of us) work to these arbitary categories.

       

      Comments please? ;-)

       

      Lee

       

    • Adam Helman
      I have modeled the distribution of prominences, finding that a modified Power Law model fits the data well. The power law exponent is correlated with the
      Message 2 of 3 , Sep 16, 2013
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        I have modeled the distribution of prominences,
        finding that a modified Power Law model
        fits the data well.

        The power law exponent is correlated with the
        Underlying geology - weathering including 
        past glaciation. Volcanic hot spots (Hawaii)
        have the most unique results.

        I am traveling and lack the time for a fuller
        description until next month when home.

        Meanwhile, follow the link at upper right of
        main county highpointers FRL web page to
        read how climber accomplishments are 
        also power law distributed!

        I cannot copy and paste the link using this
        smartphone. To access, go to the cohp.org 
        home page and mouse-click the green site map
        at upper right above "Front Runner Lists".
        Then, as noted, follow the link at upper right
        labeled "Power Law".

                Adam Helman

        PS. I too am a chemist by education.

        Sent from my iPhone

        On Sep 15, 2013, at 4:52 AM, <mountaingoatnewton@...> wrote:

         

        Dear All

         

        Since I know a number of the major contributors to this forum are, like myself, scientists, I have a couple of questions / thoughts to share that might be of interest. Since I´m a chemist rather than a mathematician, the math gurus will have to forgive my imprecise terminology..

         

        So, the first question is this - in principle I climb prominent mountains, the more prominent the better. Since I don´t want to travel very widely all the time, I need to work on lists going down to P150m to provide enough target peaks near home. However, since I tend to work from lists with cutoff values like 150m, 600m and 1500m, and prioritise peaks on the higher lists I guess this leads to a certain bias as follows:

         

        If I take a given geographical area, like the European Alps, or the CONUS, and look at the number of peaks with P100-200m, P200-300m, P300-400m etc, am I right in thinking the number in each band will fall exponentially? Given a large enough dataset, and narrow enough bands, the curve should get reasonably smooth I suppose? Has anyone tried to model such distributions or even provided an equation to describe them? Does this look the same for different large datasets or does it somehow depend on topography or altitude? If I look at my own efforts, I have climbed a similar percentage of mountains in the Alps with P800-900m as I have with P600-700m but this percentage is far greater than for P500-600m, whilst that percentage is similar to the percentage with P200-300m. So, if I overlay a plot of my climbed peaks in bands with the peaks available, the shapes will be different. This tells me I am perhaps unfairly ignoring certain peaks just below the cut-offs I choose because we all (or at least most of us) work to these arbitary categories.

         

        Comments please? ;-)

         

        Lee

         

      • mountaingoatnewton
        Hi Adam, thanks for your reply I found the power law link on cohp.org, it is not exactly what I was asking but I guess the math follows the same principle.
        Message 3 of 3 , Sep 21, 2013
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          Hi Adam, thanks for your reply

           

          I found the power law link on cohp.org, it is not exactly what I was asking but I guess the math follows the same principle. Would be interested to hear your thoughts after you get back (I hope from a bagging trip..?)

           

          Lee

           

           



          --- In prominence@yahoogroups.com, <prominence@yahoogroups.com> wrote:

          I have modeled the distribution of prominences,
          finding that a modified Power Law model
          fits the data well.

          The power law exponent is correlated with the
          Underlying geology - weathering including 
          past glaciation. Volcanic hot spots (Hawaii)
          have the most unique results.

          I am traveling and lack the time for a fuller
          description until next month when home.

          Meanwhile, follow the link at upper right of
          main county highpointers FRL web page to
          read how climber accomplishments are 
          also power law distributed!

          I cannot copy and paste the link using this
          smartphone. To access, go to the cohp.org 
          home page and mouse-click the green site map
          at upper right above "Front Runner Lists".
          Then, as noted, follow the link at upper right
          labeled "Power Law".

                  Adam Helman

          PS. I too am a chemist by education.

          Sent from my iPhone

          On Sep 15, 2013, at 4:52 AM, <mountaingoatnewton@...> wrote:

           

          Dear All

           

          Since I know a number of the major contributors to this forum are, like myself, scientists, I have a couple of questions / thoughts to share that might be of interest. Since I´m a chemist rather than a mathematician, the math gurus will have to forgive my imprecise terminology..

           

          So, the first question is this - in principle I climb prominent mountains, the more prominent the better. Since I don´t want to travel very widely all the time, I need to work on lists going down to P150m to provide enough target peaks near home. However, since I tend to work from lists with cutoff values like 150m, 600m and 1500m, and prioritise peaks on the higher lists I guess this leads to a certain bias as follows:

           

          If I take a given geographical area, like the European Alps, or the CONUS, and look at the number of peaks with P100-200m, P200-300m, P300-400m etc, am I right in thinking the number in each band will fall exponentially? Given a large enough dataset, and narrow enough bands, the curve should get reasonably smooth I suppose? Has anyone tried to model such distributions or even provided an equation to describe them? Does this look the same for different large datasets or does it somehow depend on topography or altitude? If I look at my own efforts, I have climbed a similar percentage of mountains in the Alps with P800-900m as I have with P600-700m but this percentage is far greater than for P500-600m, whilst that percentage is similar to the percentage with P200-300m. So, if I overlay a plot of my climbed peaks in bands with the peaks available, the shapes will be different. This tells me I am perhaps unfairly ignoring certain peaks just below the cut-offs I choose because we all (or at least most of us) work to these arbitary categories.

           

          Comments please? ;-)

           

          Lee

           

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