A poem, a contradiction . . .

     One strategy for proving a mathematical theorem is a "proof by contradiction."  In such a proof one begins by supposing the opposite of what is to be proved -- and then reasons logically to obtain a statement that contradicts a known truth. This contradiction verifies that our opposite-assumption was wrong and that our original statement-to-be-proved is indeed correct.   (An easily-read introduction to "proof-by-contradiction" is given here.)
       Peggy Shumaker is an Alaskan poet whom I had the pleasure of meeting at a reading at Bloomsburg University where I was a math professor a few years ago.  Her poem, "What to Count On," below, has a beautiful surprise after a sequence of negations -- and reminds me of the structure of a proof-by-contradiction.

What to Count On     by Peggy Shumaker

Not one star, not even the half moon       
       on the night you were born
Not the flash of salmon
       nor ridges on blue snow 
Not the flicker of raven’s
       never-still eye 

Poems that count: Eight Buffalo

     In mid-April at the Split This Rock Poetry Festival, one of the sessions I attended and valued had the title " "Eco-Feminist Poetry, Intersectionality, & the End of the Earth."  In the midst of my concern about ecology and women is my addiction to mathematics -- and a poem by Cecilia Llompart started me counting.  See if you, too, count the word "buffalo" eight times during this poem; and shudder when you read the final word.

       Eight Buffalo      by Cecilia Llompart

       An obstinacy of buffalo 
       is not to say that the buffalo 
       are stubborn. No, not like 
       a grass stain. More that 
       the very bulk of one— 

Counting those who grieve . . .

Each day's email brings me a Poem-a-Day from Poets.org and today's selection by Matthew Olzmann considers the tragedies from gun-violence in our news too often these days. Numbers are "objective" -- and count those who watch and grieve as well as the guns and shooters -- or are they?  Here is an excerpt from Olzmann's poem, "Letter Beginning with Two Lines by Czesław Miłosz":

          . . .   Did I say
          I had “one” student who

          opened a door and died?
          That’s wrong.

          There were many.
          The classroom of grief  

Let us not forget . . .

At this time of year in the Northern Hemisphere, many are without shelter -- and are cold.  Let us think of them  -- as Cecil Day-Lewis (1904-1972) does in "A Carol" below (a poem whose lines for the most part maintain an alternating 6-5 syllable count and which contains the small number two).  Let us remember to share our warmth.

       A Carol     by Cecil Day-Lewis 

       Oh hush thee, my baby,
       Thy cradle's in pawn:

Counting Years -- in p'Bitek's Song of Lawino

Okot p'Bitek (1931-1982) was a Ugandan poet; one of his central concerns was that African literature should be built on African rather than European foundations.  His epic poem Song of Lawino (East African Publishing House, 1966) is a narrative poem written in the voice of Lawino who appeals to her husband Ocol to stay true to his own customs, and to abandon his desire to be white.  Here is a section of that poem that addresses a system for counting years.

from   Song of Lawino      by Okot p'Bitek

            *
       Ocol tells me
       Things I cannot understand,      

Folk music -- counting syllables

Learn about and support Women in Mathematics.  

One place to do that is here. 

Using 4x4 and 2x2 syllable-squares, I emphasize the counting that lies behind folk music in the following selection from "Some Walls" (lyrics by Mary Ann Kennedy, Pamela Rose, Randy Sharp -- but line breaks are mine), recorded by Peter, Paul, and Mary:

          Some walls

          Some walls are made
          of stone.  Sometimes
          we build our own.
          Some walls can stand 

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 :

Be someone TO COUNT ON in 2015

By any means of counting, 

the number of incarcerated persons in the United States 

is TOO LARGE

and the proportion of prisoners with BLACK SKIN

is TOO GREAT
  and there is TOO MUCH VIOLENCE and DEATH in our prisons.

RESOLVE to stop the violence (RSVP)  in America's prisons!  Work for fair sentencing and Equal Justice!  Let your resolutions for the New Year 2015 be inspired by a poem;  the one below is from Poetry, 2009, found at poetryfoundation.org  -- and you may find more at Split This Rock.

To the voice of the retired warden of Huntsville Prison
(Texas death chamber)                 by Averill Curdy

Until wolf-light I will count my sheep,
       Adumbrated, uncomedic, as they are.
       One is perdu, two, qualm, three
                           Is sprawl, four, too late,

Counting into the Future . . .

     Remember that you have only until November 1 to submit a winning "poem of provocation and witness" to the Split This Rock Poetry Contest.  If you don't already,  you will want also to subscribe to Split This Rock's Poem of the Week.  This week's poem ("Past Tense" by Sam Taylor) opens with these numbers:

       In the Great Depression of 2047,
       a time of sorrow rivaled only
       by the Global Unification Wars
       of Spring 2029 to 2033,
       in the Merlona Plague of 2104, 
       in the year of the forest die-off,
       after the atmospheric hue reduction . . . .

From Nude Descending an Empire (University of Pittsburgh Press, 2014).  Apatelodes merlona is a species of moth.

Changing colors, counting syllables

Changing Colors

by JoAnne Growney

Blue

yoyo --

awkwardly

stopping-starting,

rising-plummeting,

seeking self-control. Please,

mother-friend-lover-child, don't

pull string.  Let me collect myself.

I  lift  myself  to  the  treetops,

soar with the golden eagle,

find rest on fleecy clouds.

My orb embraces

everybody --

powerful,

yellow 

sun. 

Behind the cards -- mathematics

A couple of weeks ago at an MAA math lecture by Alissa Crans on the Catalan numbers, I sat near card-trick mathematician Colm Mulcahy.  And I asked him if he knew any poems about card tricks and their mathematics.
   Though he at first said "no," Mulcahy turned out to have a couple of connections up his sleeve.  From Matthew Wright he learned of "The Card Players" -- a colorful sonnet from Philip Larkin's 1974 collection High Windows and available here with selections of Adriaen Brouwer's art.  
     And Bruce Reznick reminded him of the lyrics for "The Gambler" by Kenny Rogers.  The complete lyrics may be found here; I include below a stanza that offers some instruction about counting.

Squirrel Arithmetic

     My maternal grandfather, James Edgar Black (1871-1931) was a western Pennsylvanian, a carpenter, and a man I never knew.  But Ed, one of my cousins, found among our grandfather's long-stored things a scrapbook of collected poems and other miscellany that he recently passed on to me.  

How many grains of sand?

Recently one of my friends used "all the grains of sand" as an example of an infinite set "because it is impossible to count them all" and -- even as I rejected his answer -- I wondered how many of my other friends might agree with it.  In the following poem, mathematician Pedro Poitevin considers a similar question as he reflects on the countability of the birds in the night sky.

       Divertimentum Ornithologicum      by Pedro Poitevin

                              After Jorge Luis Borges's Argumentum Ornithologicum.

       A synchrony of wings across the sky
       is quavering its feathered beats of flight.
       Their number is too high to count -- I try 

Too many selves

In my childhood home, numbers were used with care and precision.  There would be teasing when I would use the adverb "too" --- as if when I said "I had to walk too far" I had tried to describe an unbounded distance, greater than any possible span.  Now as an adult I continue to be cautious (and intrigued) with use of that word.  And I am drawn to the uses of "too many" and "count" in the following poem from David Orr, poetry columnist for the New York Times Book Review.

The Chameleon    by David Orr

Alone among the superheroes,
He failed to keep his life in balance.
Power Man, The Human Shark--they knew
To hold their days and nights in counterpoise,
Their twin selves divided together,
As a coin bears with ease its two faces.

A Cento from Arcadia

Last week I had the enjoyable privilege of visiting with mathematician-poet Marion Cohen's math-lit class, "Truth and Beauty" at Arcadia University -- and the class members helped me to compose a Cento (given below), a poem to which each of us contributed a line or two of poetry-with-mathematics.  Participants, in addition to Dr. Cohen and me, included these students: 
          Theresa, Deanna, Ian, Collin, Mary, Grace, Zahra, Jen, Jenna, 
          Nataliya, Adeline, Quincy, Van, Alyssa, Samantha, Alexis, Austin.
Big thanks to all!

To love, in perfect syllables

     While looking for Valentine verse with a math connection, I opened my copy of The Complete Illustrated Works of Lewis Carroll (Chancellor Press, 1982).  And found this one in which Carroll (a pen name for English mathematician Charles Lutwidge Dodson (1832-1898)) uses the word one twice and the word half twice and has counted sounds so that in each line the number of syllables is either a cube of an integer or is perfect.

        Lesson in Latin     by Lewis Carroll    (May 1888)   

Last year's prediction

This poem by Halifax mathematician and poet, Robert Dawson, appeared in LabLit  in December 2012 (just in time to offer gentle mocking of predicted disaster)!  Enjoy!

Survivor's Guide to the Baktun-13 Bug    by Robert Dawson

As you may know, at this years’ Winter Solstice
the 12-baktun Long Count will overflow.

Emily Dickinson

     Although I do not consider any of Emily Dickinson's poems "mathematical," I find that she does not shy from using the terminology of mathematics. For example, her repetition of the word "circumference" noted in an earlier posting.  (To search this blog for mentions of Dickinson (1830 - 1886) or any other poet or topic, follow the instructions offered in green in the column to the right.)
     Dickinson is on my mind these recent days following my opportunity last Saturday evening to attend a session of a conference held by the Emily Dickinson International Society.  A gracious invitation by Martha Nell Smith enabled me to attend a program that featured two long-time friends, actor Laurie McCants of the Bloomsburg Theatre Ensemble, performing a scene from her one-woman show, Industrious Angels, and Stephanie Strickland, a New York poet who, along with collaborator Nick Montfort, offered background and performance for Sea and Spar Between, a poetry generator that works with language patterns for these two writers.

Count your things

     In the development of human culture, mathematics began with counting.  And so it also begins with each child as she/he grows.
     Someone said that a person is wealthy when she has more things than she can count.  Another view is that true wealth is having no need to count.  Whether or not either is is correct, we can appreciate "My/My/My" by poet Charles Bernstein (begun below and completed at poets.org).

My/My/My        by Charles Bernstein   

          Count these number of things you call mine. This is the distance between
          you and enlightenment.                                 —Swami Satchidananda

                        (for Jenny)

my pillow

my shirt

A poem for your pocket

April is National Poetry Month.

April is National Mathematics Awareness Month.

Today, April 19, is Poem-in-Your-Pocket Day.

Here is a mathy poem that will fit in your pocket.

       14 Syllables     by JoAnne Growney

       A hen lays eggs
       one by one;
       the way you
       count life
       is life.

The poem "14 Syllables" is collected in Red Has No Reason (Plain View Press, 2010).