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

- I have modeled the distribution of prominences,finding that a modified Power Law modelfits the data well.The power law exponent is correlated with theUnderlying geology - weathering includingpast glaciation. Volcanic hot spots (Hawaii)have the most unique results.I am traveling and lack the time for a fullerdescription until next month when home.Meanwhile, follow the link at upper right ofmain county highpointers FRL web page toread how climber accomplishments arealso power law distributed!I cannot copy and paste the link using thissmartphone. To access, go to the cohp.orghome page and mouse-click the green site mapat upper right above "Front Runner Lists".Then, as noted, follow the link at upper rightlabeled "Power Law".Adam HelmanPS. I too am a chemist by education.

Sent from my iPhoneOn 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

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 modelfits the data well.The power law exponent is correlated with theUnderlying geology - weathering includingpast glaciation. Volcanic hot spots (Hawaii)have the most unique results.I am traveling and lack the time for a fullerdescription until next month when home.Meanwhile, follow the link at upper right ofmain county highpointers FRL web page toread how climber accomplishments arealso power law distributed!I cannot copy and paste the link using thissmartphone. To access, go to the cohp.orghome page and mouse-click the green site mapat upper right above "Front Runner Lists".Then, as noted, follow the link at upper rightlabeled "Power Law".Adam HelmanPS. I too am a chemist by education.

Sent from my iPhoneOn 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