Verses that count

At about.com one finds a variety of information -- from the dates of the rapidly approaching 2012 Cherry Blossom Festival in Washington DC to divisibility rules for integers to a type of poetry called mathemetrics.  Mathemetrical poetry has one topic: the length of the poem itself. Enjoy:

An example:

   This poem
   contains 14 words
   (if we count numerals
   as words) and 62 symbols.

Chatting about REAL numbers

The term "real number" confuses many who are not immersed in mathematics.  For these, to whom 1, 2, 3 and the other counting numbers seem most real, the identification of the real numbers as all infinite decimals (i.e., all numbers representable by points on a number line) seems at first to go beyond intuition.  But, upon further reflection, the idea of a number as "real" iff it can represent a distance on a line to the right or left of a central origin, 0, indeed seems reasonable.

Professor Fred Richman of Florida Atlantic University takes on the questions of computability and enumerability of the real numbers in his poem, "Dialogue Between Machine and Man":

Mathematics in Romanian poetry

     When I first visited Romania, I met Doru Radu, then a teacher of English at Scoala Generala "Andre Muresanu" in Deva. And Doru introduced me to his favorite poet, George Bacovia (1881 - 1957). Over time, we together translated many of Bacovia's poems -- and the bilingual collection plumb de iarnă / lead of winter was published in 2002 (Ed., Gabriel Stanescu, Criterion Publishing). Recently I scrutinized that collection (no longer available in print, but here, online) to look for mathematical lines to post in this blog. Alas, Bacovia offers no more than a couple images from geometry: "alone in deserted squares" (in Pălind / Fading) and "the wide, oval mirror, framed with silver" (in Poemă în oglindă / Poem in the Mirror).
     Although Bacovia did not use mathematical imagery, a considerable number of Romanian poets do, and below I offer links to my earlier blog postings of work by Ion Barbu, Nina Cassian, Martin Sorescu, and Nichita Stanescu. Enjoy!  

Poetic Explorations of . . . Mathematicians

In the Journal of Humanistic Mathematics (Volume 1, Issue 2), we find "Numen^Rology: A Poetic Exploration of the Lives and Work of Famous Mathematicians" by Saskatchewan poet, Mari-Lou Rowley. In addition to the following poem, "On Diophantus Arithmetica," Rowley's JHM collection includes "Ode to Alan Turing" and "On Euclid’s Book VII – Elementary Number Theory: Proposition 8." Rowley's lines below wonderfully describe the emotional flow that comes with engaging in mathematics -- as mathematical terms are translated into the human terms of wanting and forthcoming, kneading, . . . and yielding.

Seeing Distance -- geometry in photography

One of my favorite poem-stanza styles is a syllable-square -- it distributes the weights of the words in a way that pleases me. The poem below has squares of several sizes and I post it as a prior-to-seeing-the-exhibit opposite to my response to photography currently displayed at the Smithsonian American Art Museum -- "Pilgrimage," by Annie Leibovitz. While many photographs, my own in particular, seem particularly flat, such was not the case with these. As if I were wearing special lenses, I was able to see and feel depth – not only in a view of Niagara Falls but also in the fabric and buttons of a dress that had belonged to Emily Dickinson.

Chaos and Order -- Stevens

An article by Jeff Gordinier, "For Wallace Stevens, Hartford as Muse," in the Travel Section of last Sunday's NY Times gives a gentle introduction to one of my favorite poets; the article also provoked me to escape for an hour into a rereading of selections from my copy of The Collected Poems (Vintage Books, 1990). Poems by Stevens (1879-1955) celebrate ideas and are, like pieces of mathematics, suggestive of a variety of situations. (Work by Stevens was featured in these earlier blog postings: 15 December 2010 (from "The Snow Man"), 4 May 2011 ("The Anecdote of the Jar"), and  13 May 2011 (from "Six Significant Landscapes"). Here, reconciling opposites, are two of the five sections of Stevens' "Connoisseur of Chaos" -- also from The Collected Poems.

Universal and Particular -- Szymborska

Like Yves Bonnefoy (21 February 2012 posting), Wislawa Szymborska (who died on 1 February 2012) was born in 1923.  Like him she was concerned with the connections of the universal and the particular.  Here, in "A Large Number,"  she reflects, as she did in "A Contribution to Statistics," on the human meaning that lies behind numbers: 

Universal and Particular

Poet Yves Bonnefoy (b 1923) is one of France's greatest living poets. And Bonnefoy's university studies included mathematics. I read recently of Bonnefoy in the Wall Street Journal Bookshelf posting for 11 February 2012 by Micah Mattix entitled "The Pursuit of Presence." This reminder sent me to my bookshelf to review the poet's work with mathematics in mind. I found a bit of attitude toward the subject in a prose poem entitled "Devotion" when he used the phrase "stern mathematics." And Section 1 of "Trial by Ordeal" (offered below) ends with the word "proof."
     Mattix opened his Bonnefoy article with a quote: If I had to sum up in a sentence the impression Shakespeare makes upon me," the poet Yves Bonnefoy wrote in an early essay, "I should say that, in his work, I see no opposition between the universal and the particular." This universal-particular pairing (evident in Bonnefoy, as in Shakespeare) led my thoughts to the mathematical pairing, global-local, which I explore briefly following Bonnefoy's poem.* 

Langston Hughes could do anything!

In the 1970s when I was a new professor (at Pennsylvania's Bloomsburg University), a particular colleague and I would chat occasionally about our teaching methods and compare them with the ways we'd been taught. We agreed that many of our teachers seemed to dump mathematics on us in any manner whatever -- supposing that, if we were smart enough, we would pick it up. We thought we were better teachers than our predecessors and yet I am haunted by knowing that the privileged -- whether by wealth or education or birthplace or whatever -- seldom see their advantage over those who are different. Still, some of us survive unlikely odds, being lucky enough to have an "I can do anything" attitude like that expressed by poet Langston Hughes (1902 - 1967) in "I, Too":

2012 Split This Rock Poetry Festival -- March 22-25

Earlybird registration ends February 22 for the 2012 Split this Rock Poetry Festival in Washington, DC, March 22-25.  Honoring poet June Jordan, the four-day festival will feature more than a dozen noted poets whose work speaks out against indifference and injustice.  One of these is is Minnie Bruce Pratt -- and here is her "Someone is Up," one of the poems featured in the Spring 2012 issue of the Beloit Poetry Journal, published in support of the Split this Rock Festival and presenting work of festival poets.  As in many poems of provocation and witness, numbers provide the specifics that pin down the message.  (See also poetry by Festival Director Sarah Browning in the February 5 posting.)

Counting (with sadness) in Syria

Burmese poet ko ko thett is an activist-scholar and, at present, a resident of Vienna, Austria. I became acquainted with his work through Kyi May Kaung, a writer, artist, Burma-activist-scholar, and friend who currently lives in the Washington, DC area. Here is a poem by ko ko thett  -- for Syria.

the 5000th    by ko ko thett

                        for syria

Be My Valentine

Unlike many newspapers, the British Guardian publishes poems -- and, on February 10, 2012, they offered a selection to celebrate the upcoming Valentine's day. Included, among work by more than a dozen notables, are poems by Wislawa Szymborska, John Donne, Derek Walcott (whose poem "Love After Love" is one of my favorites), Sir Walter Raleigh, Lord Byron, and Carol Ann Duffy -- and a poem by John Fuller that is seasoned with some mathematical terminology. You will need to visit the Guardian article online for the whole of Fuller 's poem, "Valentine," but here are several snippets to whet your interest. (Enjoy the fun of rhyming mathematics with attics!) 

Recursion

A mathematician may face a dilemma over the meaning of an ordinary term -- for words like "group" and "identity" and "random" (to name a few) have precise mathematical definitions that differ from their common meanings. Canadian poet Peter Norman's title, "Recursion," however, uses the term as it is used mathematically.  While a definition of "recursion" is widely available in mathematics texts, it was missing in my several English dictionaries -- and I found it only in the OED (though, even there,  noted as now rare or Obs.) : "a backward movement, return."   The term "return" indicates previous forward motion. In mathematical recursion (illustrated below by the Fibonacci sequence) as in Norman's poem, going backward is possible only because forward motion is known. (Interested readers will find an introduction to mathematical recursion following the poem.)

     Recursion    by Peter Norman

     I fall awake alone. Outside,
     nocturnal rain ascends.  

Is Math for Women?

At a River Poets reading at the public library in Bloomsburg, Pennsylvania on December 1, 2011, Carol Ann Heckman surprised me with her poem, "The Calculus Road Not Taken," presented below.  Not only is she a fine poet, but Carol Ann is curious about mathematics.  As a college student she was turned away by negative feedback from a math professor. But now she is reassessing her situation and ready to tackle calculus. Here she has fun with her calculus-deprived situation in lively verse:

The Calculus Road Not Taken   by Carol Ann Heckman  

               for JoAnne Growney

If I had only conquered
calculus
this wouldn't have
happened--the flood,
the earthquake, the
two hurricanes
in succession

Strength from Numbers

During March 22-25, 2012, the third Split This Rock Poetry Festival:  Poems of Provocation and Witness will be held in Washington, DC. This year's festival honors activist poet June Jordan (1936  - 2002) but the festival would not be happening without the vision and untiring efforts of DC poet Sarah Browning, Director of Split This Rock and DC Poets Against the War, and author of Whiskey in the Garden of Eden.  Like any good protester, she makes effective use of the specificity of numbers in her poems.

Szymborska (1923-2012) on Statistics

Polish poet Wislawa Szymborska (1923-2012)  won the 1996 Nobel Prize for literature; I am saddened by her death -- yesterday, February 1, at her home in Krakow. But one cannot help but rejoice for her poems.  Szymborska did not shy from use of mathematical ideas.  As in this sample:

   A Contribution to Statistics   by Wislawa Szymborska

    Out of every hundred people

    those who always know better:
   -- fifty-two,    

Counting Groundhogs

     I grew up in a town about 25 miles from Punxsutawney, PA -- and Groundhog Day on February 2 was local-news only. This was the quiet time before television cameras mades stars of groundhogs and, back then, we knew them for their underground piracy as well as for their weather-forecasting.
     My father, a farmer, did not like groundhogs; he tried to keep them away from his fields by blocking their entrances to the networked burrows where they chewed the roots of crops planted overhead.  Fifty years after these farming days, I arrived at the following "what is this world coming to?" poem that features my mother and me watching groundhogs play in a field outside her sickroom. (The poem is, approximately, a sonnet -- in which the poet is not only counting groundhogs but also counting syllables . . ..)

Juxtaposition

One of my favorite phrases (loved for the sound of it) first came to my ears during my college studies of  abstract algebra: "multiplication is denoted by juxtaposition"  -- and,  within the phrase, I best like to say "juxtaposition." I enjoy its movement in my mouth, its sibilance in my ears. And so, of course, I set out to find a poem using the word. Having failed over many years to find the word in someone else's poem, I have written my own:

   Multiplication     by JoAnne Growney

   Multiplication is the process
   of taking one number as many times
   as there are ones in another.

Counting the seconds -- and leap seconds

      Keeping time is a simple matter of counting -- counting seconds, summing them into minutes, hours, days. Or is it? Recent news has included mention of the changing length of our solar day and the need for insertion of leap seconds.   (A leap second is a one-second adustment to the time kept by precise atomic clocks -- to keep this latter time close to mean solar time. No leap-seconds were added in 2011 but NPR and The Washington Post recently announced that a leap second will be added June 30, 2012. At 7:59:59 PM, Eastern time, the US Naval Observatory will skip a second to 8:00:00 PM.  Wikipedia offers detailed background on this concept.)     Extra time is a fond wish for many of us -- and Leonard Orr has penned a love poem suggesting how one more second might be delightfully crowded with so much more than could happen in "regular" time. 

Counting fingers and blackbirds

Love of numbers is common in childhood -- and traditional nursery rhymes offer chances to know numbers as playmates and friends.  "Four and twenty blackbirds baked in a pie . . . The king was in his counting house . . ." and so on.  In "The Story of the Ten Blackbirds" poet Millicent Accardi combines a portrait of an amazing story-telling aunt with a collage of childhood memories, counted and remembered.

   The Story of the Ten Blackbirds     by Millicent Borges Accardi

   Blended at times into
   The three little pigs
   Or the Catholic Saints.

Statistics feels like poetry

    Today's title comes from the following poem by statistician and poet Eveline Pye (introduced to this blog on 18 October, 2011).

   Numerical Landscape      by Eveline Pye

   Like a tracker, I smell the earth
   on my fingers, listen for the slightest
   echo as I stare out at a world
   where bell-shaped curves loom

More statistics -- from Hiawatha

As the author of this poem owes a debt to Henry Wadsworth Longfellow, I too owe Greg Coxson -- who showed the poem to me.

Hiawatha Designs an Experiment   by Maurice Kendall

Hiawatha, mighty hunter
He could shoot ten arrows upwards
Shoot them with such strength and swiftness
That the last had left the bowstring
Ere the first to earth descended.
This was commonly regarded
As a feat of skill and cunning.

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,

The Function Room

For each of us who's studied mathematics, the word "function" triggers important mathematical meanings. And so, when I read Patrice Phillips un-mathematical poem "The Function Room," I automatically add a mathematical layer to the meaning.  Do you?

Is your favorite poet a mathematician?

     The Joint Mathematics Meetings in Boston last week gave a fine opportunity for me to connect with both mathematicians and poets, old friends and new ones. And to enjoy a celebration of the connections between poetry and mathematics. In the January 6 poetry reading sponsored by the Journal of Humanistic Mathematics, there was much fine poetry. Several of the poems were by Carol Dorf -- whose work was read by Elizabeth Langosy, executive editor of the online literary magazine, TalkingWriting.  Good reads in the Jan/Feb 2012 issue of TalkingWriting include both Dorf's introduction to some featured math-connected poems -- entitled "Why Poets Sometimes Think in Numbers" -- and Langosy's  impressions of the math-poetry reading.    

Poetry heard at JMM

In Boston on Friday evening, January 6, at the 2012 Joint Mathematics Meetings, these folks gathered and read -- for a delighted audience in Room 312 of Hynes Convention Center -- some poems of mathematics.
     Poets who submitted work in advance and were on the "Poetry with Mathematics" program included:
          Jacqueline Lapidus, Judith Johnson, Rosanna Iembo (accompanied by the violin of her daughter Irene Iaccarino), Charlotte Henderson, Carol Dorf (read by Elizabeth Langosy), Sandra Coleman, Marion Cohen, Tatiana Bonch (read by John Hiigli), Harry Baker (via video presented by reading organizer Gizem Karaali -- an editor of the online Journal of Humanistic Mathematics, which sponsored the the reading), and JoAnne Growney (also an organizer of the reading).
     Participants during an "open reading" included: 
          Mary Buchinger, Chris Caragianis, Rip Coleman, Seth Goldberg, Joshua Holden, Ann Perbohner, Pedro Poitevin, and Jason Samuels.

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

From 2011 -- dates, titles of posts

List of postings January 1 - December 31, 2011
Scrolling through the 12 months of titles below may lead you to topics and poets/poems of interest. Also helpful may be the SEARCH box at the top of the right-hand column; there you may enter names or terms that you would like to find herein.
Dec 30  Good Numbers
Dec 26  A mathematical woman
Dec 22  Counting on Christmas
Dec 20  Thoughts Suggested by a College Examination
Dec 17  Ruth Stone counts
Dec 14  A puzzle with a partial solution
Dec 11  Poetry captures math student
Dec  8  Monsieur Probabilty
Dec  5  Poetic Pascal Triangle
Dec  2  Mathematics works with witchcraft 

Good numbers . . .

     My wish for the New Year 2012 is that you will have good numbers -- that your happiness will have high peaks, that your sadness and grief will weigh no more than you can bear.
     In the spirit of assessment and introspection that captures many of us at year-end, I offer a small poem, "Good Fortune" -- one that I wrote in late December ten years ago when I was, as I am now, taking stock. "Good Fortune" appeared in my 2006 chapbook, My Dance Is Mathematics (Paper Kite Press -- available online here). Another tiny poem, a more recent one, "14 Syllables" -- from Red Has No Reason (Plain View Press, 2010) -- continues the focus on assessment using numbers. 

A mathematical woman

As in an earlier posting (20 December 2011), today's feature includes verse by Lord Byron (1788-1824). This time the source is Byron's satiric poem Don Juan. In Canto I, the poet describes Don Juan's mother, Donna Inez, as learned and "mathematical." Here are several stanzas about her -- sagely seasoned with words like "theorem," "proof," and "calculation."

Counting on Christmas

 11

 one1

 2 two 21

 3 three 3 31

 4 4  four  4 41

 5 five 5 5 5 five 51

 6 six 6 6 six 6 6 six 61

 7 7 7 seven 7 seven 7 7 71

 8 eight 8 8 8 eight 8 8 8 eight 81

 9 nine 9 9 nine 9 9 9 nine 9 9 nine 91

 10 ten 10 10 10 10 ten 10 10 10 10 ten 101

 11 eleven 11 11 11 11 11 11 11 11 11 eleven 111

 12 twelve 12 12 12 12 12 12 12 12 12 12 twelve 121

 HAPPY1

  HOLI  -1

 DAYS !!1

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).

Ruth Stone counts

It seemed as if she might write -- and write well -- forever.  But she did not.  Moreover, poems by award-winning poet Ruth Stone (1915-2011) are not celebrated for their use of mathematical imagery.  Still, she noticed numbers.  She counted.  As in "All in Time."  

A puzzle with a partial solution

     When we have experiences near to each other, we may try to connect them. We form superstitions. "Bad things come in threes" -- and something similar for good things. And we make poetry -- offering new associations that delight and surprise.
     Gertrude Stein is one of my favorite poets. She was, like me, born in Pennsylvania (though she, unlike me, left and became Parisian).   She creates almost-meaning from unlikely juxtapositions.  I find in her work the delight of a puzzle to which I can find a partial solution. And come back for more. Here are two stanzas from Stein's "Stanzas in Meditation" that play with some mathematical meanings.

Poetry captures math student

This sonnet retells a familiar story -- a teacher influences a student's choice of studies. Prior to reading, many in mathematics may wonder:  how can a student leave mathematics for poetry when mathematics is poetry?  Whatever your view, I think you will enjoy this poem.

Prof of Profs       by Geoffrey Brock

     For Allison Hogge, in memory of Brian Wilkie

I was a math major—fond of all things rational.
It was the first day of my first poetry class.
The prof, with the air of a priest at Latin mass,
told us that we could “make great poetry personal,”

Monsieur Probabilty

In recent months, I have encountered a variety of poems about mathematicians (Links to several of these are provided at the end of this post.) and one of the sources is Scottish poet Brian McCabe's  collection Zero (Polygon, 2009).    It is said that life imitates art -- and this is vividly demonstrated by the art of mathematics as lived by Abraham de Moivre (1667-1754).  Here is McCabe's poem. 

Poetic Pascal Triangle

First published in 2007 in Mathematics Magazine, Caleb Emmons' poem "Dearest Blaise" has the form of (Blaise) Pascal's Triangle.  That original publication offered also a challenge:  what is the next line of Emmons' poem?   What is your guess?  

Mathematics works with witchcraft

T. A. Noonan sometimes uses the languages of mathematics and computer science as tools in her experimental poetry, gathered in her collection The Bone Folders (Sundress Publications, 2011).  These poems examine -- at times with mathematical vocabularies and notations -- the complexities of love and loss in the regime change in a coven of Louisiana witches.  Here, for example, is Noonan's opening poem, "Difference Engine." 

Echoes of childhood rhymes

For those of us who live and breathe mathematics, there is much of it that affects us deeply.  Even those of us whose mathematics is mostly arithmetic have a literature of number that we hold close .  And does anything affect us more than the counting rhymes of our childhood?  Washington, DC poet Rosemary Winslow uses emotionally-charged repetition of nursery-rhyme numbers to help us know incest in "Four Five Six." 

How much for a digit of PI?

Scottish poet Brian McCabe writes playfully of numbers.  In the following poem he imagines an auction of the digits of π.

   Three Point One Four One Five Nine Two
   Six Five Three Five Eight Nine Seven Nine
   Three  Two Three Eight Four Six Two Six
       Four Three Three Eight Three Two
         Seven Nine Five Zero Two Eight             by Brian McCabe 

Open and Closed -- Tomas Transtromer

A background in mathematics gives my enchantment with words a special twist. Each time I see familiar math terms in a poem I layer their mathematical meanings amid their mainstream ones. Two such terms are "open" and "closed." (I'll supply brief mathematical explanation at the end of this post but, first, here is "Open and Closed Spaces" -- a poem by the winner of the 2011 Nobel prize  for Literature, Swedish poet Tomas Transtromer. )

Reading the Rubaiyat

Omar Khayyam (1048-1131) was a mathematician who wrote poetry.  Here are two quatrains from his Rubaiyat.

        XLVI

   For in and out, above, about, below,
   'Tis nothing but a Magic Shadow-show
        Play'd in a Box whose Candle is the Sun
   Round which we Phantom Figures come and go.  

Equivalence

In telling the time, we commonly refer to hours that differ by a multiple of 12 using the same number. Sixty hours after 3 o'clock it is again 3 o'clock. The clock relationship -- with its times that are named by the same number but are not, after all, exactly the same -- illustrates the mathematical notion of an "equivalence relation." In "Equivalencies," the insights of poet Judith McCombs stretch this mathematical concept.

Equivalencies     by Judith McCombs

The fear of not writing, of having no words,

Is the muscles not working, the pack top-heavy,
the hard slime on ledges where the ankle gives way

Portrait of Max Dehn

Today I offer a poem by Portuguese mathematician F. J. Craveiro de Carvalho -- its initial English publication was in Topology Atlas, 2005 -- about an outstanding mathematician, Max Dehn. Dehn inhabited Craveiro's office via a Springer-Verlag Poster.  Here is a portion of  Craveiro's introduction to the poem.

Portraits of a mathematician

Ideas for this posting began with my post on 30 October 2011 in which I selected 7 favorite lines of poetry as a sort of self-portrait.  That posting led to an exchange with blogger Peter Cameron -- which prompted me to write these abecedarian portraits of a mathematician.

   I know a mathematician . . .     by JoAnne Growney  

   always busy
   counting, doubting
   every figured guess,
   haply idling,
   juggling, knowing
   logic, measure, n-dimensions,
   originating
   playful quests,
   resolutely seeking theorems,
   unknowns vanish :
   wrong xs, ys -- zapped. 

Mathematics of desire

Last Monday evening, I listened with pleasure to Pennsylvania (Fogelsville) poet Barbara Crooker read at Cafe Muse (with Meredith Davies Hadaway and Erin Murphy). Barbara writes fine poems -- and reads them well. Although she offered no mathematical poems that evening, hearing her reminded me to hunt for her love poem "The Irrational Numbers of Longing . . " and to offer it to you here:

Mathematician-Poet Glaz

     Sarah Glaz, a professor-mathematician at the University of Connecticut -- and a poet -- is at the forefront of appreciation and advocacy of mathematics as an art and closely connected to other arts, particularly poetry.  Her webpage offers more than a hundred links to "Undergraduate Resources; Math Links for Information and Fun" and to scholarly articles that offer teachers and students math-poetry ideas to ponder carefully.  This link, for example goes to an article entitled "The Poetry of Prime Numbers" that Glaz presented at the Bridges 2011 Conference in Portugal.
     One of my favorites of Glaz' poems is this one whose structure relies on the Fundamental Theorem of Arithmetic (see note following the poem).  Here is "January 2009"  :

Four colors will do

     As I work with Gizem Karaali, an editor of the Journal of Humanistic Mathematics, to plan a reading of mathematical poetry at the JMM (Joint Mathematics Meetings) in Boston on 6 January 2012, my thoughts return to a poetry reading that I helped to organize at JMM in Baltimore in 1992. One of the participants was a friend and former colleague, Frank Bernhart, whose work is guided by the rhythm pattern of a well-known song.
     Bernhart is an expert on the Four-Color Theorem and his poem celebrates its history -- including consideration of its proof (in 1976) by Kenneth Appel and Wolfgang Haken. (The theorem asserts that any map drawn on a flat surface or on a sphere requires only 4 colors to ensure that no regions sharing a boundary segment have the same color.)

Division by zero

The November 2011 issue of the Scottish ezine, The Bottle Imp, is just out and it includes my review of poet Brian McCabe's Zero (Polygon, 2009). To stir your interest, I include a few lines from McCabe's title poem (which chronicles the irregular history of zero) -- and then offer a human interpretation of division by zero in a poem by Ann McNeal.

What can 7 objects say? Or 100?

     A friend, a high school art teacher, had one of her students paint a portrait of her -- not of her bodily self but a still life of the seven possessions that she felt best defined her.  Since that time, more than seven years ago, I have been trying to decide what my seven objects would be.  How might I portray me?    
     An article in today's NY Times, "Stuff that Defines Us," reminded me that I have neglected that project.  The article tells of the British Museum's ambitious and fascinating project to choose 100 objects from their collection to summarize the history of the world.

Music on the hypotenuse

Dr. Cai Tianxin is a professor of mathematics (specializing in number theory) at Zhejiang University, China. He also is an accomplished and  well-known poet.

   The Number and the Rose     by Cai Tianxin 

Submit math-science poetry

During the month of November, the online journal Talking Writing is seeking submission of poetry with connections to mathematics and the science.  Submit 4-6 poems to editor@talkingwriting.com.
  

          O                                T     T                 

          ON                                 E               
          ONE                           N     N                

These visual poems "One" and "Ten," above, are mine.

Chaos Over the Hors d'Oeuvres

Some systems of equations can produce vast changes in output with only small changes in input.  Or not.  This sensitivitiy to initial conditions is a key characteristic of chaos.  As happens not infrequently in mathematics, the term chaos also carries larger-world meanings additional to the correct ones -- indeed, the phenomena studied in chaos theory are not haphazardly disordered but are complex.  Very very complex.  Judy Neri's poem addresses this topic. 

Permutations and Centos

A Cento is a collage poem made of lines taken from other poems -- such as a sonnet composed of lines from fourteen of Millay's sonnets, or Shakespeare's -- or from newspaper articles or television advertisements or whatever. Here's a three-line sample from a Cento, "Patchwork," composed by Joanna Migdal to celebrate women poets.

   I dwell in Possibility.                                              (Emily Dickinson, #657)
   Yes, for that most of all.                                        (Denise Levertov, “The Secret”)
   It’s four in the afternoon. Time still for a poem.   
                                                                        (Phyllis McGinley, “Public Journal”) 

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! 

Things the fingers know

Blogger Peter Cameron sent me a link to an lively article, "Eveline Pye: Poetry in Numbers"  in the September 2011 issue of the statistics magazine, Significance.  Written by Julian Champkin, the article tells of Eveline Pye -- lively and interesting Glasgow statistician, teacher, and poet -- and includes a selection of her work. One of the poems offered therein is "Solving Problems."

A small Fib

My dilemma

   I've
   lost
   the art
   of careful
   thought, asea in floods
   of  trivial  information.               by JoAnne Growney

Hamilton -- mathematician, poet, Irishman

     October 15-22 is Maths Week in Ireland -- as I learned from this article in the Irish Times celebrating maths and the Irish mathematician Willam Rowan Hamilton (1805 - 1865).  Turns out that Hamilton's quaternions are useful in design of video games and 3D effects in the cinema.
     Hamilton -- a mathematician, astronomer, and physicist -- was also a poet; a contemporary and friend of Samuel Taylor Coleridge and William Wordsworth. His poems do not speak of mathematics -- but here is a sonnet he wrote to honor Jean Baptiste Joseph Fourier (1768 – 1830), a prominent French mathematician and physicist.

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: 

Numbers from the Piano

     Of all of the things we might try to say when we sit down to write a poem, which are the ones we should choose?  Sometimes we may say what first occurs to us -- begin to write and keep going until we are done.  This may suffice -- or it may seem to lack care.  To be more careful, we might seek a pattern to follow:  perhaps we might form lines whose syllable-counts follow the Fibonacci numbers.   Or construct a sonnet -- fourteen lines with five heart-beats per line and some rhyme.  Or devise a scheme of our own.

Counting the women

     The stimulus for this posting appeared a few weeks ago in the Washington Post -- in an article that considers the loneliness of women in STEM fields (science, technology, engineering, math). 
     For me, it was never a conscious thing -- the counting.  It simply happened.  The numbers are small and you know, if you are a woman and a mathematician in a room full of mathematicians, how many women are in the room.  Any room.  It is a small counting number.  Sometimes it is 1. 

How I won the raffle

Dannie Abse is a deservedly celebrated Welsh poet -- and before his retirement he was also  a physician.  I first saw "How I Won the Raffle" in Poetry  in 1992 -- now it also is included in his collection Be Seated Thou (Sheep Meadow Press, 2000).

   How I Won the Raffle     by Dannie Abse

   After I won the raffle with the number
   1079,
   the Master of Ceremonies asked me why,
   ‘Why did you select that particular number?’

Action at a distance

One of the great things about writing this blog is the people who have -- out of the blue and across the miles -- sent along a great poem or tidbit.  One of the valuable contributors is Tim Love, a British computer guy and poet -- and also a blogger (at LitRefs). The mysterious concept of "Action at a Distance" drives this Love poem:

The square root of Everest

Of the poets who frequently use mathematical ideas in their work, Howard Nemerov (1920-1991) is one of my favorites.  Recently, while browsing at The Writer's Almanac, I found this poem.

To David, About His Education       by Howard Nemerov

Math meets Dr Seuss

Blogger Sue VanHattum (MathMamaWrites) sent me a link to a posting on another blog, kGuac, on which she found a Dr Seussical expression of the quadratic formula -- written by blogger Katie Benedetto for extra credit in her college abstract algebra class.  Here are several stanzas of Katie's poem:  

Learning to count

The childhood of Romanian poet Nichita Stanescu (1933-1983) took place during World War II and his teen years during his country's adjustment to a new Communist system; his dark images are drawn from a culture largely unknown to the outside world.  Often, however, he utilized mathematical imagery or terminology; here is his "Learning to count." 

Mathematical theorems tornadoing

This poem is fun!

   Horse’s Adventure    by Jason Bredle 

   The horse discovered a gateway to another
   dimension, and with nothing else to do, moseyed
   into it just for grins, and man, you
   don’t even want to know what happened
   next—it was just, like, Horse at the French
   Revolution. Horse in Franco’s living room.

The wealth of ambiguity

When we read these lines by Robert Burns (1759-1796),

     Oh my luv is like a red, red rose,
     That's newly sprung in June . . .
    
we don't know whether he compares a woman he loves to a flower or whether it is his own emotion he describes.  And the multiplicity of meanings is a good and pleasing thing.  Similarly, when we read the problem,

     Solve the equation, x² + 4 = 0 

Poetry at JMM -- in Boston 6-Jan-2012

Call for Submissions:
     The Journal of Humanistic Mathematics will host a reading of poetry-with-mathematics on Friday, January 6, 5-7 PM in Boston’s Hynes Convention Center at the annual Joint Mathematics Meetings. Reading organizers include JHM editors, Gizem Karaali and Mark Huber, and poetry-math blogger, JoAnne Growney.  Although the reading is open to all, without pre-selected readers, we will prepare a written program of poets who submit their work by our December 1 deadline. Both mathematician-poets and others who use mathematics in their poems are invited to submit.

Baseball, math, and poetry

The end of summer approaches and, with it, the end of the baseball season.  This blog celebrated the triplet (baseball, mathematics, poetry) on 9 April 2010, featuring samples from and links to poems by Marianne Moore and Jerry Wemple. Today we herald the same trio, this time with "Night Game" by Jonathan Holden.

Best words in the best order

     Writers of mathematics strive for clear and careful wording, especially in the formulation of definitions. Well-specified definitions can enable theorems to be proved succinctly. For example, the relation "less than" (denoted <) for the positive integers {1,2,3,...} may be defined as follows:

     If  a  and  b  are integers, then 
               a < b  if  b - a  is a positive integer. 

     Although the simple definition of "less than" as "to the left of" in the list {1,2,3,...} is intuitively clear, the formal definition above is better suited for mathematical arguments. It defines "less than" in terms of the known term, "positive." This sort of sequencing of definitions is common in mathematics -- one may go on to define "greater than" in terms of "less than," and so on.
     Saying things in the best way is also a goal of poetry. Well known to many are these words of poet Samuel Taylor Coleridge (1772–1834): 

Analysis of a sacred site

Poet Allison Hedge Coke descends from moundbuilders and mixed ancestry from several Native American communities with several Europoean ones.  Her verse play, Blood Run, is dedicated to the original citizens of the former city now named Blood Run along the Big Sioux River and to all who work to preserve sacred sites. Moreover, the entire text is mathematically encoded.   Chadwick Allen, an English professor whose interests include American Indian and New Zealand Maori literatures and cultures, has written an article for American Literature that explores the sacred numbers and thematic geometry that connects Hedge Coke's verse with the sacred site; we will offer a sample of Allen's analysis following "Snake Mound"from Blood Run: 

A Piece of Coffee -- Stein with some math terms

I love the poetry of Gertrude Stein.  Perhaps this is so because I have never taken a class in which her work was taught and I have never read it with pressure to "understand."  I enjoy reading Stein's poems aloud.  Because they keep me alert -- both eye and tongue.  Because they puzzle me. And because I sometimes see something amazing, true and almost within reach.  Here, from Tender Buttons / Objects: is "A Piece of Coffee."