Dangerous Surprises of Exponential Growth

      In 1968, while I was in graduate school at the University of Oklahoma, the journal Science published "The Tragedy of the Commons" by Garrett Hardin.  Hardin's article describes a situation in which shared resources are overused and exploited -- leading to depletion of resources for the future.  In recent years there has been much criticism of Hardin's essay (and criticism of Hardin) -- but for me it served as a wake-up call to concerns about the environment.  With environmental difficulties growing exponentially -- and with many of us not fully aware of the growing rapidity of exponential growth, I have posed to students this problem:

An 8x8 syllable-square

We may be close to the end before we realize it . . .

March for Climate -- again!

       The lines below are copied from a posting made on September 20, 2014 -- posted as I finalized plans to travel to New York City for a climate march.  From that March I saw some positive action BUT I am grieving over the changes in the last 100 days.

     To have a small carbon footprint I will march tomorrow with only a small sign -- one that wears a 3x3-square reminder that dates back to a 1968 essay, "Tragedy of the Commons,"  by ecologist Garrett Hardin (1915-2003). 

       There   is   no
       place to throw
       that ' s   away.

WHY is it taking us so long to act to preserve a habitable planet?  Do we not care about the world we are leaving for our grandchildren?

Visit JHM for Mathy Poems

     Today I'd like to direct you to the Journal of Humanistic Mathematics, an online open-access journal that features poetry in each issue.  The Table of Contents for the first issue of 2016 is now available here -- and I offer below a poem from Issue 1 of 2015.  (Before sharing the poem "Prisoner's Dilemma" by Raymond Greenwell I want also to mention that JHM is looking for investigative journalists and that today's "Poem of the Day" at Poets.org is "Evolution" by Linda Bierds and inspired by the work of Alan Turing.)
     I am particularly intrigued by Greenwell's poem because the Prisoner's Dilemma is a decision model close to my concerns about the environment. (More comments below.)

       Prisoner's Dilemma     by Raymond N. Greenwell

       Your best choice is my demise.
       My wise choice is your defeat.    

How many grains of sand?

     Sand beaches are places I love to walk.  Next to oceans and soft underfoot. 

Below I post a stanza from Richard Bready's "Times of Sand"  --

 a long poem that explores many of the numbers related to sand. 

     Contemplating grains of sand turns my thoughts to the pair of terms "finite" and "infinite."  One of my friends, university-educated, versed in literature and philosophy, offered "all of the grains of sand" as an example of an infinite set.   As we talked further, he proposed "the stars in the universe" as a second example. This guy, like many, equates "infinite" with "too large to count."  And then there is me; long ago in college I encountered a definition of "infinite" that went something like this:  A set is infinite if there is a one-to-one correspondence between the members of the given set  or one of its proper subsets with the set {1, 2, 3, . . ..} of counting numbers.

Marching for Climate

     Today I want to call attention to the growing global concern about climate change accentuated by the United Nations Climate Summit that opens September 23. Tomorrow (September 21) I will travel on a 6 AM bus  from Silver Spring to NYC to be part of the People's Climate March.  It is said that more than 500 buses of protesters are heading to New York. 29 marching bands will provide the soundtrack. 26 city blocks are being cordoned off for the march's line-up.   At the same time, more than 2,000 People's Climate events are taking place in over 160 countries around the world—from Hong Kong to Buenos Aires and from New York to San Francisco.

     To have a small carbon footprint I will march tomorrow with only a small sign -- one that wears a 3x3-square reminder that dates back to a 1968 essay, "Tragedy of the Commons,"  by ecologist Garrett Hardin (1915-2003). 

       There  is  no
       place to throw
       that's  away.

WHY is it taking us so long to act to preserve a habitable planet?  Do we not care about the world we are leaving for our grandchildren?

Tragedy of the Commons

Thinking in syllable-squares,
recalling ecologist Garrett Hardin (1915-2003)
and his 1968 wisdom, "Tragedy of the Commons."

Maximum               
may not be                   
optimum.