Reservation Mathematics

Both a talented writer and an articulate conveyor of the culture of American Indians, Sherman Alexie is a Spokane / Coeur d’Alene Indian from Wellpinit, Washington.  Besides several collections of poetry, Alexie has published novels and short-stories; he wrote the screen-play for the 1998 film, Smoke Signals.  "Reservation Mathematics"  is from Alexie's poetry collection First Indian on the Moon, (Hanging Loose Press, 1993) and was previously posted in this blog in January 2011.

Reservation Mathematics     by Sherman Alexie

Balancing Opposites -- Tagore's Epigrams

Many important mathematical ideas occur as pairs of opposites:
         -2 and +2 (additive inverses), 5 and 1/5 (multiplicative inverses),  
         bounded and unbounded, rational and irrational, 
         convergent and divergent, finite and infinite
Some other familiar mathematical notions occur often in contrasting pairs but are not fully opposites:
         horizontal and vertical, positive and negative, 
         open and closed, perpendicular and parallel

Recently I have returned to reading work by Rabindranath Tagore (1861-1931; Bengal, India;  winner of the 1913 Nobel Prize in Literature) and I enjoy reflecting on contrasts posed by this reflective poet in a series of "Epigrams":

Epigrams      by Rabindranath Tagore

I will close my door to shut out all possible errors.
"But how am I to enter in?" cried Truth.  

Opposites, Balance

     Recently, and perhaps always, opposites have interested me.  For example, the complementary and sometimes  conflicting nuggets of advice contained in "Pinch a penny, waste a pound" and "It is best to prepare for the days of necessity."   And in  "Kindness effects more than severity" and "Spare the rod, spoil the child."   Maybe what I like best is the challenge of synthesizing opposite truths.
     Mathematics contains many pairs of entities that are, each in some different sense, opposites:

2 and -2      2 and 1/2

horizontal and vertical   differentiation and integration

And there are some arbitrary subdivisions that often are treated as if they are disconnected opposites:

pure vs. applied (creating mathematics vs. solving problems)

teaching and learning, creating vs. teaching, arts and sciences

In an ideal world, opposites exist with "Balance" -- which is the title of the following lovely and contemplative poem by Adam Zagajewski :

Love Physics

It turns out that one of the disadvantages of a long-term blog with lots of worthy material is that sometimes I lose track of fine work that I want to post.  And sometimes I find it again.  This morning I came across this poem by California conservationist Richard Retecki.

     Love Physics     by Richard Retecki

     equal forces
     oppositely directed
     canceled to zero

     then we tricked you
     exchanging pressure for light 

Three thousand, and two

Here is a small poem richly vivid with the contrasts of opposites:

                 beside a stone three
                 thousand years old: two
                 red poppies of today

by Christine M. Krishnasami, India, found in This Same Sky:  A Collection of Poems from around the World (selected by Naomi Shihab Nye, Aladdin Paperbacks, 1996).

Mother Courage -- and speaking of opposites

     Bertolt Brecht (1898-1956) was a poet, but I have not found mathematics in his poems.  Still, I want to note here a fantastic performance of his play, Mother Courage and her Children, starring Kathleen Turner and a talented ensemble at Washington,DC's Arena Stage.  Invited by my neighbors, Mitzi and Pati, I joined them yesterday for a riveting performance.   Here is a link to "How Fortunate the Man with None," a Brecht poem  heartily sung as "Solomon's Song" in the current musical production.
     And here, with a nod to the mathematical bent of this blog, is a quote from Brecht's Mother Courage that involves counting; also, it is one of many examples of a strategy that Brecht uses often and well -- encouraging an idea by speaking of its opposite. 

Geometry . . . a way of seeing

Today's poem is not only a fine work of art, it is also -- for me-- a doorway to memory.   I first heard it in the poet's voice when he visited Bloomsburg University in the late 1980s,  and I was alerted to the reading and to James Galvin's work by my most dear friend, BU Professor of English Ervene Gulley (1943-2008).   Ervene had been a mathematics major as an undergraduate but moved on from abstract algebra to Shakespeare.  Her compassion, her broad-seeing view, and her fierce logic served her well in the study and teaching of literature.  And in friendship.  I miss her daily.  She, like Galvin, questioned life and probed its geometry.

A whole and its parts

     Aristotle may have been the first to assert that a whole is more than the sum of its parts.  Mathematics textbooks are likely to say otherwise, postulating that a whole is equal to the sum of its parts. 

     Emily Dickinson also comments on the matter.

                (1341)         by Emily Dickinson
 
     Unto the Whole -- how add?
     Has "All" a further realm --
     Or Utmost an Ulterior?
     Oh, Subsidy of Balm!