Lines of breathless length

Brief reflections on definitions of LINE . . .

          Breathless length     by JoAnne Growney

          A LINE, said Euclid, lies evenly
          with the points on itself --
          that is, it’s straight –-
          and Euclid did (as do my friends)
          named points as its two ends.

          The LINE of modern geometry
          escapes these limits
          and stretches to infinity.
          Just as unbounded lines
          of poetry.

Remembering Abraham Lincoln

Today -- April 14, 2015 -- marks the 150th birthday of the assassination of President Abraham Lincoln (1809 - 1865) and April 15 is the date on which he died. Lincoln loved poetry and trained his reasoning with Euclid's geometry.  Here is a brief sample of his own poetry (found -- along with other samples -- at PoetryFoundation.org).

       Abraham Lincoln     by Abraham Lincoln

       Abraham Lincoln
       his hand and pen
       he will be good but
       god knows When

From my copy of Walt Whitman's Leaves of Grass (Signet Classics, 1955), from the section "Memories of Lincoln," I have copied these well-known and thoughtful (and non-mathematical) lines:

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.

In Praise of Fractals

     Philosopher Emily Grosholz is also a poet -- a poet who often writes of mathematics. Tessellations Publishing has recently (2014) published her collection Proportions of the Heart:  Poems that Play with Mathematics (with illustrations by Robert Fathauer) and she has given me permission to present one of the fine poems from that collection.

In Praise of Fractals     by Emily Grosholz

               Variations on the Introduction to
               The Fractal Geometry of Nature by Benoit Mandelbrot
               (New York: W. H. Freeman and Company, 1983)

Euclid’s geometry cannot describe,
nor Apollonius’, the shape of mountains,
puddles, clouds, peninsulas or trees.
Clouds are never spheres, 

Fractal Geometry

Lee Felice Pinkas is one of the founding editors of cellpoems -- a poetry journal distributed via text message.  I found her poem,"The Fractal Geometry of Nature" in the Winter/Spring 2009 Issue (vol.14, no 1) of Crab Orchard Review.

The Fractal Geometry of Nature       by Lee Felice Pinkas

               Most emphatically, I do not consider
               the fractal point of view as a panacea. . .
                                             --Benoit Mandelbrot (1924-2010)

Father of fractals, we were foolish
to expect a light-show from you,

hoping your speech would fold upon itself
and mimic patterns too complex for Euclid. 

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? 

One geometry is not enough

Writer Katharine Merow is in the Publications Department of the Washington DC headquarters of the MAA (Mathematical Association of America) and she is one of the poets who participated in the "Reading of Poetry with Mathematics" at JMM in Baltimore last January.  Here is the engaging poem Merow read at that event -- a poem that considers the 19th century development of new and "non-euclidean" geometries from variants of Euclid's fifth postulate, the so-called parallel postulate:

       Geometric Proliferation    by Katharine Merow

Poems and primes

Friday morning, 1-17-2014, looking north from the Baltimore Convention Center

       This past week I enjoyed Thursday and Friday at the Joint Mathematics Meetings at the Convention Center in Baltimore, a time for connecting with some old friends and making some new ones.  I gave a presentation in one of the sessions on the Intersection of Mathematics and the Arts, sharing poems -- such as Sherman Stein's "Mathematician" -- that can help non-maths to understand more clearly the nature of mathematics.  The handout for my talk contained a list of more than thirty poems that can help to communicate the nature of mathematics and it is available for download here. 

From order to chaos -- a sonnet

Fractals    by Diana Der-Hovanessian

                             Euclid alone has looked on beauty bare
                                                    --Edna St. Vincent Millay

Euclid alone began to formulate
the relation of circle, plane and sphere
in equations making it quite clear
that symmetry is what we celebrate. 

Lincoln and Euclid -- common notions

     This afternoon I enjoyed the recently-released film, Lincoln -- appreciating Sally Fields as Mary Todd, Tommy Lee Jones as Thaddeus Stevens and (especially) Daniel Day-Lewis as Abraham Lincoln. An absorbing drama -- inspiring and also informative.  With a slight mention of mathematics:  in a film conversation with two-young telegraph operators, Lincoln reflected on his study of Euclid and shared with the young men the first of Euclid's common notions:

     Things that are equal to the same thing are equal to each other. 

Finding fault with a sphere . . .

     On November 9 I had the pleasure (hosted by Irina Mitrea and Maria Lorenz) of talking ("Thirteen Ways that Math and Poetry Connect") with the Math Club at Temple University and, on November 5, I visited Marion Cohen's "Mathematics in Literature" class at Arcadia University.  THANKS for these good times.

          This
          Fib
          poem
          says THANK-YOU
          to all those students
          from Arcadia and Temple 
          who participated in "math-poetry" with me --
          who held forth with sonnets, pantoums,
          squares, snowballs, and Fibs --
          poetry
          that rests
          on
          math.

      My Temple host, Irina Mitrea, and I share something else besides being women who love mathematics -- the Romanian poet, Nichita Stanescu (1933-83), is a favorite for both of us.  My October 23 posting ("On the Life of Ptolemy") offered one of Sean Cotter's recently published translations of poems by Stanescu and below I include more Stanescu-via-Cotter -- namely, two of the ten sections of "An Argument with Euclid."  These stanzas illustrate Stanescu at his best -- irreverently using mathematical terminology and expressing articulate anger at seen and unseen powers of oppression.

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.

An algorithm shapes a poem

Mathematics sometimes appears in poetry via patterns that follow the Fibonacci numbers. The pattern of Pascal's triangle also has been used.  In her intriguing collection, Do the Math  (Tupelo Press, 2008),  poet Emily Galvin (now also a California attorney) uses these and more.  Just as Euclid's Algorithm involves an interaction between two numbers, the following poem by Galvin applies the algorithm in a conversation between two voices.

Euclid's Algorithm    by Emily Galvin

These ten scenes happen on the blank stage.

A and B could be any two people, so long as

they've been together for longer than either

can remember.

Euclid meets Broadway

Several years ago while visiting my older son in Colorado Springs I also went to nearby Boulder where, driving along Broadway, I came to a street sign that made me gasp with delight.  I was at the intersection of Broadway and Euclid. That fact, that suggestion of a merge of two worlds, needed to be part of a poem. Some time later I wrote:

   Butterfly Proposal     by JoAnne Growney

Thoughts Suggested by a College Examination

Just when I was convinced that mathematical subject matter appears proportionately more in modern than in classical poetry, I turned again to work by Lord George Gordon Byron (1788-1824) and began to contradict myself. Here (from Byron's Complete Poetical Works) is "Thoughts Suggested by a College Examination."  As is common today in literature and verse, the mathematicians (and scientists) are found wanting (though we are not the only deficient ones).

Once a student of Euclid

The Chair     by Charles Simic

The chair was once a student of Euclid.

Coleridge: A Mathematical Problem

 "A Mathematical Problem" by Samuel Taylor Coleridge (1772-1834) -- found online at Elite Skills Classics -- uses verse to describe construction of an equilateral triangle; Coleridge introduces the poem with a letter to his brother telling of his admiration of mathematics, a view rather rare among poets.   

Who are our prophets?

Here is the opening sentence of an article, "Mathematicians and Poets," by Cai Tianxin, a mathematics professor at Zhejiang University -- it appears in the April 2011 issue of Notices of the AMS:

     "Mathematicans and poets exist in our world as uncanny prophets."  

Black History Month -- celebrate Haynes and Hughes

Living on the border of Washington DC I am exposed to items of local history for our nation's capital.  One such item involves the "discovery" of Langston Hughes (1902-1967) by poet Vachel Lindsay (1879 - 1931) at the Marriott Wardman Park Hotel, a leading conference hotel in the city.   A second story is a mathematical one.  Martha Euphnemia Lofton Haynes (1890-1980), a fourth-generation Washingtonian, was the first black woman to earn a PhD in mathematics -- conferred in 1943 by Catholic University. 

Puzzles, puzzlers, and parody

     For lots of fun, go to plus online magazine at this link to find a poem that requires a knight's tour of a chess board for you to unscramble its words and read its eight lines.