An immeasurable continuum

This poem by Emily Warn (a founder of PoetryFoundation.org) uses mathematical terminology to introduce us to the immeasurable horror of death by slow torture.  May our nation never again engage in such atrocities!

The Vanishing Point     by Emily Warn

You slow down to watch cumulus clouds stream across the
sky. You choose a more circuitous route home and pass a
tree with white bags tied around random apples. The apples
remind you of clouds, how each hangs in the sky, singular
yet part of a flock. Each item in the flock is a coordinate of
earth and sky, enumerating space. The flocks of apples and
clouds are actual infinities, an endless collection of discrete
items that one can conceivably count to the end. This is

Toward Infinity . . .

     During summer teaching opportunities a dozen or more years ago in Deva, Romania I met Doru Radu who taught English there -- and our mutual love of poetry led us to collaborate on English translations of work by Romanian poets George Bacovia and Ileana Malancioiu.  Now Doru is in Poland and he is translating Polish poetry into Romanian.  One of his favorite poets is Ewa Lipska -- a poet I have met via Poetry International.  Below is her poem "Newton's Orange:  Infinity" -- found at Poetry International together with the original Polish poem.
     As I have noted before, "infinity" is a term whose varied uses fascinate me.  Sometimes I wonder how much of my "mathematical" understanding of the concept I might some day incorporate into a poem.

     Newton's Orange:  Infinity     by  Ewa Lipska   

Songs of mathematics . . .

     Larry Lesser is a songwriter who uses lyrics for teaching as well as entertainment.  A varied sample of his creations for doing this are presented in his article "Mathematical lyrics;  noteworthy endeavours in education" found in the "Poetry and Mathematics / Special Issue" of the Journal of Mathematics and the Arts, March-June 2014).
     One of the article's enchanting items is a song for children -- "Circle Song" -- which Lesser has written to the familiar tune of "Twinkle, Twinkle, Little Star"; this lyric offers a way to remember critical formulas for a circle.

Circle Song     by Lawrence Mark Lesser

Take your finger 'round the jar:
Circumf'rence equals 2πr!  

Twined Arcs, Defying Euclid

     The English language has adopted into current usage many terms from other languages.  French terms like coup de grace and haut monde have for many years been found in English dictionaries.  Recently, computer terms such as bite and captcha and google have achieved widespread use.  In addition, those of us who are fluent in the language of mathematics find that its terms sometimes offer a concise best way to describe a non-mathematical phenomenon.
     Mathematician-poet Sarah Glaz weaves mathematical terms into her poem, "Departures in May" -- a poem that uses the language of geometry to vivify the presence of loss, death and other dark forces.

       Departures in May     by Sarah Glaz

       Big things crush, inside the brain,
       like plaster of Paris on stone;
       a taste of splintered metal;
       terra-cotta hardness of heart's desire.
       Statues motionless
       at railroad depots,
       proclaim imitation as life.

My best dream is floating . . .

     Today I want to urge you to visit several sites in addition to my blog.  For example, there is the recent announcement of 2014 Fields Medal (equivalent to a Nobel prize) winners -- the four winners include the first female mathematician (Maryam Mirzakhani) ever to be selected as a Fields Medalist (equivalent to a Nobel Prize) and a mathematician who loves poetry (Manjul Bhargava).    
     With the help of a "Google Alert" I found a YouTube video of Alexandria Marie reading "The Mathematics of Heartbreak" at a Dallas Poetry Slam.  A link in an email from Texas computer scientist,  Dylan Shell, alerted me to these mathematical lyrics (new words for old tunes) in a mathbabe posting by Cathy O'Neill.
     As we have been floating from topic to topic, it may be apt to end with the final stanza of my relevantly titled poem: 

Homage to Euclid

In my preceding post (20 March 2014) Katharine Merow's poem tells of the new geometries 

developed with variations of Euclid's Parallel Postulate.  

Martin Dickinson's poem, on the other hand, tells of richness within Euclid's geometry.

Poet and attorney Martin Dickinson is with the Environmental Law Institute and is a long term activist. The Nora School Poetry Series has scheduled both of us (along with Michele Wolf) to be part of a reading next month on April 24, 2014 .  It is my additional good fortune that conversations with Dickinson have included his sharing with me this mathy poem:

     Homage to Euclid       by Martin Dickinson

     What points are these,
     visible to us, yet revealing something invisible—
     invisible, yet real? 

Writing mathy poems - a student activity

On the web-page of mathematician-poet Sarah Glaz I found a link to this file of math-related poems that she prompted students to write when she visited an Arcadia University class session of "Truth and Beauty:  A Course in Mathematics and Literature" taught by mathematician-poet Marion Cohen.  The writing was prompted by an activity-list developed by mathematician-poet Carol Dorf.  Poems by Whitney Boeckel and Olivia Lantz particularly caught my eye and, with their permission, I present them here:

The angel of numbers . . .

This poem by Hanns Cibulka (1920 - 2004) -- translated from the German by Ewald Osers -- is collected in the anthology, Strange Attractors:  Poems of Love and Mathematics, edited by Sarah Glaz and me (A K Peters, 2008).

     Mathematics      by Hanns Cibulka     (trans. Ewald Osers)

                  And the angel of numbers
                  is flying
                  from 1 to 2...
                       —Rafael Alberti

The minute in infinity

From  Treatise on Infinite Series     by Jacob Bernoulli

Even as the finite encloses an infinite series
      And in the unlimited limits appear,
So the soul of immensity dwells in minutia
      And in narrowest limits no limits inhere.
What joy to discern the minute in infinity!
      The vast to perceive in the small, what divinity! 
 
                    Translated from the Latin by Helen M. Walker

Found in the anthology, Strange Attractors: Poems of Love and Mathematics (A K Peters, 2008), edited by Sarah Glaz and me.  A complete table of Contents for this collection may be found here.

Like advanced math?

One thing leads to another . .. . poet Amy Eisner connected me to mathematician Jordan Ellenberg who knew of Easy Math (Sarabande Books, 2013) by Lauren Shapiro -- and Lauren gave me permission to post her "Bent Syllogism."

 Bent Syllogism     by Lauren Shapiro

There was a pattern to the way the mythical beasts
flew over the dreary town, but we were too dreary
to understand it.  The psychologist, too, was in touch
with extraterrestrials, but she had to stand on the spire
of a church and wear 3-D glasses to see them. 

BRIDGES poems, from 17 poets

Due to the hard work of mathematician-poet Sarah Glaz, poetry has been an important part of recent BRIDGES-Math-Art Conferences. And, under her editing, a Bridges 2013 Poetry Anthology has been released, featuring poetry from these poets who participated in one or more of the three most recent BRIDGES conferences (Enschede, Netherlands, 2013; Towson, Maryland, 2012; Coimbra, Portugal, 2011). 

Your Favorite Number

In the Washington, DC area's Beltway Poetry Quarterly, edited by Kim Roberts, I recently found this lively number-poem by Pennsylvania poet Barbara DeCesare in the Summer 2012 issue that features poets in the federal government.  Enjoy.

     Your Favorite Number   by Barbara DeCesare

     I hope you have a damn good reason
     because when you let a number like that in,
     it’ll turn on you so fast.
     36: spine on spine, a grudge,
     a house divided, half-sisters,
     or the twins,

Average, more or less . . .

The wit of American poet J. V. Cunningham (1911–1985) is here applied to statistics.

   Meditation on Statistical Method      by J. V. Cunningham 

   Plato, despair!
   We prove by norms
   How numbers bear
   Empiric forms,

Like poetry, mathematics is beautiful

     Congratulations to Justin Southey who is completing his doctoral studies in mathematics at the University of Johannesburg under the direction of Michael Henning. Recently Justin contacted me to ask permission to include one of my poems in the introduction to his dissertation, "Domination Results:  Vertex Partitions and Edge Weight Functions."  Here is a portion of Justin's request: 

Lieber's INFINITY -- poetic prose

It has surprised me to discover that some of my best-remembered learning took place at the hands of teachers I did not particularly like.  One of these was a professor who introduced me, via outside reading assignments, to books by Lillian R. Lieber (1886-1986).  Her free-verse-style lines in Infinity:  Beyond the Beyond the Beyond gave me insights into the calculus I had recently completed as well as the set theory of my current course. (Lieber wrote not just as a mathematician but also as a human being, as a wonderfully informed and openly opinionated person.  For this, too, I treasure her work.)

Little Infinite Poem

   Little Infinite Poem       by Federico Garcia Lorca

               For Luis Cardoza y Aragón

      To take the wrong road
   is to arrive at the snow,
   and to arrive at the snow
   is to get down on all fours for twenty centuries and eat
         the grasses of the cemeteries.

Numerology

On her website Deanna Rubin describes herself this way, "I have a degree in Technical Writing and Computer Science from Carnegie Mellon University, and my head is full of random numbers."  Illustrating this latter claim is her poem, "Numerology":    

Sonnet for a geometry teacher

Wisconsin poet Ronald Wallace has fun with math-words in the following sonnet that celebrates a teacher of plane geometry. 

One type of "mathematical" poetry

When I began (in the 1980s) collecting examples of "mathematical poetry," I sought lines of verse that included some mathematical terminology.  More recently, my view has expanded to include structual, visual, and algorithmic influcences from mathematics; however, the two samples from the work of William Blake (1757-1827), presented below, fit into that initial category -- selected as "mathematical" because of their vocabulary -- one speaks of "infinity," the other of "symmetry."  (Blake was an artist as well as poet and his volumes of poetry were illustrated with his prints.)  The following stanza is the opening quatrain for Blake's poem "Auguries of Innocence." 

A Lemma by Constance Reid

Constance Reid (1918-2010), died on October 14.  Sister of a mathematician (Julia Robinson), Reid wrote first about life in World War II factories that supported the war effort and then, later, several biographies (including one of her sister) and other books about mathematics.  Kenneth Rexroth's poem "A Lemma by Constance Reid" (offered below) is based on material appearing in Reid's popular book From Zero to Infinity:  What Makes Numbers Interesting (Thomas Y Crowell, 1955).  Reid is known for the enthusiasm and clarity with which she presented mathematical ideas--seeking to attract and to satisfy non-mathematical readers.