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.
     For me, understandings of infinite sets and infinite processes is one of the valued rewards of calculus and other college math courses.  And I am disappointed to see Americans (and others) who consume our earth's resources as if they were infinite.  As if they did not understand that any finite number can be exhausted.  A long time ago in graduate school I began to worry -- initially influenced by a now-famous 1968 Science essay, "Tragedy of the Commons,"  by ecologist Garrett Hardin (1915-2003). (See also my posting for  11 March 2014; to find postings on climate change or other specific topics, this search box can be useful.)

     And here, on the subject (sand) that started these musings -- is the closing stanza of Bready's poem:

              from Times of Sand      by Richard Bready  

                                    . . .  The age
          Of any grain on any hand may be
          More than two thousand million years, by stage
          In magma, granite, river, delta, sea,
          Stone, uplift, ice, beach, dune, and desert. Gauge
          Of deep time, it implies activity:
          To crystallize what little bit one knows,
          In chance and change, an angle of repose.

The complete text (with footnotes) of "Times of Sand" is available here -- posted in Through the Sandglass, a blog by London geologist Michael Welland.