Remembering Lee Lorch

      Lee Lorch was a mathematician known for his social activism on behalf of black Americans as well as for his mathematics. He died in February of this year in Toronto, at age 98.  A life-long communist and a life-long crusader.  Last Thursday I attended a memorial service  (organized by Joe Auslander, a poetry-lover who one day had introduced me to the work of Frank Dux) for Lorch -- sponsored by the Mathematical Association for America and held at the MAA Carriage House in Washington, DC.  Friends and colleagues of Lorch spoke of his positive energy and the ways that he had enriched the lives of students and colleagues, of friends and strangers.  One of the speakers, Linda Braddy, a staff member of the Mathematical Association of America (MAA), did not talk about Lorch but about strategies for opening mathematical doors (as he had done) to new students. 

Hailstone numbers shape a poem

     One of my favorite mathy poets is Halifax mathematician Robert Dawson -- his work is complex and inventive, and fun to puzzle over.  Dawson's webpage at St Mary's University lists his mathematical activity; his poetry and fiction are available in several issues of the Journal of Humanistic Mathematics and in several postings for this blog (15 April 2012,  30 November 2013, 2 March 2014) and in various other locations findable by Google.
      Can a poem be written by following a formula?  Despite the tendency of most of us to say NO to this question we also may admit to the fact that a formula applied to words can lead to arrangements and thoughts not possible for us who write from our own learning and experiences.  How else to be REALLY NEW but to try a new method? Set a chimpanzee at a typewriter or apply a mathematical formula.
     Below we offer Dawson's "Hailstone" and follow it with his explanation of how mathematics shaped the poem from its origin as a "found passage" from the beginning of Dickens' Great Expectations.

Hypertext poetry

     We computer-screen readers all know hypertext; when we read along in Wikipedia or some other online document and come across an underlined term whose font color is light blue -- at such a point we may decide to keep on reading as if we had not noticed the light blue "hyperlink," or we may locate our cursor on that text, click our mouse, and link to a new screen of visual information.
     My first encounter with hypertext poetry was the work of Stephanie Strickland -- in her 1999 love poem, "The Ballad of Sand and Harry Soot," available at this link.  If you, however, are someone who is not yet comfortably familiar with hypertext poetry, I invite you to gain some experience with hyperlinked reading via a prose essay -- reading it first as a traditional essay and then exploring ways that hypertext can vary the experience of reading.

Mathy poems via e-mail

Publishing a blog about poetry and mathematics brings me new connections -- it is not unusual for a day to begin with an email from another poetry-math enthusiast who wants to share a link or a poem. One of these is retired USC biochemist Paul Geiger.  
     Using as raw material a poem by Shel Silverstein, Geiger created a 9x9 syllable-square:

S.C.S. STOUT     by Paul Geiger

       Apologizing and Acknowledging Shel Silverstein's 1974 poem
             "SARAH CYNTHIA SYLVIA STOUT WOULD NOT TAKE THE GARBAGE OUT"

Mathy Poetry from Bridges 2014

     This year's math-arts conference, Bridges 2014, was in Korea.  And a dozen of us who write poetry-with-mathematics -- unable to attend in person -- worked with coordinator Sarah Glaz to offer (on August 16, hosted by Mike Naylor) a virtual reading of work videotaped in advance by the poets and edited into a coherent whole by Steve Stamps. 

     The virtual reading is here on YouTube. 

Grandma Got STEM

     It was my good fortune last weekend to meet the sister-in-law of one of my neighbors, mathematician and Harvey Mudd professor, Rachel Levy.  Levy is also a blogger and her postings in Grandma Got STEM tell of achievements of women in science.
     I have looked for a poem to pair with my mention here of  Grandma Got STEM.  Although the following poem by Tami Haaland (found at the Poetry Foundation website) is not mathematical, it nicely brings to life a relationship between a grandmother and granddaughter -- and we wish for both of them "places to explore beyond the frame."

       Little Girl     by Tami Haaland

       She’s with Grandma in front
       of Grandma’s house, backed
       by a willow tree, gladiola and roses.

       Who did she ever want
       to please? But Grandma
       seems half-pleased and annoyed.

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. 

Poetry in Math Journals

         The Mathematical Intelligencer (publisher of the poem by Gizem Karaali given below) and the Journal of Humanistic Mathematics (an online, open-access journal edited by Mark Huber and Gizem Karaali) are periodicals that include math-related poetry in each issue.  For example, in the most recent issue of JHM, we have these titles:

Articles:
     Joining the mathematician's delirium to the poet's logic'': Mathematical Literature and Literary Mathematics     by Rita Capezzi and Christine Kinsey
     How Do I Love Thee? Let Me Count the Ways for Syllabic Variation in Certain Poetic Forms     by Mike Pinter

Poems:

     Computational Compulsions     by Martin Cohen

     Jeffery's Equation     by Sandra J. Stein

     The Math of Achilles     by Geoffrey A. Landis

And here, from Gizem Karaali, is a poetic view of the process of mathematical discovery:  the blank white page, the muddy flow of thoughts, the clarity that eventually (sometimes) blooms:

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'Neil.
     As we have been floating from topic to topic, it may be apt to end with the final stanza of my relevantly titled poem: 

Narrated by a mathematician

Recently translated by Adam Morris, the novel With My Dog-Eyes (Melville House, 2014) by Brazilian writer Hilda Hilst (1930-2004) is narrated by a mathematician-poet. That fact of narration is what first drew me to the book. (See also this July 3 posting.)  And then there is (related in Morris's introduction to the translation) Hilst's sad life, perhaps mirrored in her characters.  These are the opening lines from the novel's narrator:

       The cross on my brow
       The facts of what I was
       Of what I will be:
       I was born a mathematician, a magician
       I was born a poet. 

Squaring the Circle

Reminding us of the ancient unsolvable problem that so many attempted, the July/August 2014 issue of Poetry Magazine contains "Squaring the Circle," a poem by Philip Fried.  Here are the opening lines; please follow the Poetry Magazine link above to enjoy the full poem.

from  Squaring the Circle     by Philip Fried

       It's a little-known fact that God's headgear --
       A magician's collapsible silk top hat,
       When viewed from Earth, from the bottom up
       Is, sub specie aeternitatis,

       A pluperfect halo, both circle and square,
         . . .

    

Two previous posts that also consider the circle-squaring problem include 10 May 2010 and 21 April 2010.

Divided selves, some of them savvy

     For social connections, it is desirable not to be pegged as a member of an outcast group.  And thus a mathematician is likely to have at least two selves -- one who lives in the world of mathematics and another separate social self that negotiates that rest-of-the-world where many fear and shun mathematics. I found a situation somewhat similar when I studied at Hunter College in Manhattan:  I needed a separate self who negotiated the city. The problem-solving farm girl who knew small towns well and big cities slightly seemed better equipped to adapt to city conversations than her fellow students could chat about anything west of the Hudson.  How many hundred miles must you drive to get to Pennsylvania? they wondered.  (The Delaware River boundary of PA is about 75 miles west of the George Washington Bridge.)
     In this vein, I present a poem that focuses on the country vs city divide -- and it involves a square look and a number.

     Green Market, New York   by Julia Spicher Kasdorf

A math prof's lament

The mathematical connection for this poem is the fact that it was inspired by regrets for a missed opportunity in a mathematics class -- an opportunity missed by me and thus by one of my students.  There are so many ways to be wrong!

Lament of a Professor
        at the End of the Spring Semester     by JoAnne Growney

I took an extra step to bridge the gap
between us, blind to your matching backward step.
We've moved in tandem until I'm angry
at you, and at me — I thought you needed
lenience, but reprimands instead
would have changed the direction of our cadence
and given you a chance to lead the dance.

A poem about another of my students, "The Prince of Algebra" is available here.  And this link will take you to the poems in my collection, My Dance is Mathematics (Paper Kite Press, 2006).

Fixing something wrong

          If there's something
          wrong with the third
          act,   it's   really
          in  the  first  act.

This quote from Billy Wilder, Austrian-born writer and film-director (1906-2002), reminds me of a similar observation I have made about my mathematical work -- when a reviewer notes a problem near the end, usually the fix is near the beginning.          And so it goes . . .

Each equation is a playful catch . . .

A mathematician is probably too close to her subject matter to speak playfully about it -- and thus she, even more than others, appreciates a phrase like "each equation is a playful catch, like bees into a jar," offered by Lisa Rosenberg in the poem below.  In "Introduction to Methods of Mathematical Physics," Rosenberg uses a child's anxiety about insects as a way to describe fear of mathematics and offers a smidgen of respect for "those few" who are fearless. 

Introduction to Methods of Mathematical Physics    by Lisa Rosenberg

You must develop a feeling for these symbols
that crawl across a page, for the text overrun

with scorpions.  Like those books about insects
you read as a child, scared to touch the magnified photos,

Poems with "equation" in the title

     One of the ways to explore this blog is to go to the right hand column and find the instruction, SEARCH.
     A few moments ago I did this and entered the word "equation" and found a long list of links, many of the latter ones redundant since they are picking up archive listings of earlier postings.  But the early ones can be fun to explore.  Here are five of  the first six items that the SEARCH BOX produced.  And the first two of these links yield poems with "equation" in the title.  Enjoy! 

Mathematicians are not free to say . . .

The poetry of a mathematician is constrained by the definitions she knows from mathematics.  Even though all but one of the prime integers is odd, she cannot use the words "prime" and "odd" as if they are interchangeable.  She cannot use the words "rectangle" and "box" as synonyms.  But the ways that non-math poets dare to engage with math words can be delightful to mathematical ears and eyes.  For example:

       The Wasp on the Golden Section     by Katy Didden

Palindromes

     Palindromic numbers are not uncommon  -- recently (in the July 12 posting) power-of-eleven palindromes are mentioned.  Palindromic poems are more difficult to find but see, for example, the postings for October 6, 2010 and October 11, 2010.

     At a  recent Kensington Row Bookshop poetry reading, Hailey Leithauser revealed that all but one of the poems in her recent collection Swoop (Graywolf Press, 2014) contain a palindrome.  

And here are a couple of my favorite palindromic phrases:

(the impossible integer)

Never 
odd or 
even. 

(the mathematician's answer when she is offered cake)
  "I prefer pi."

Prove It

After observing that

               1  =  1
and         1 + 3  =  4
and         1 + 3 + 5  =  9
and         1 + 3 + 5 + 7  =  16
and         1 + 3 + 5 + 7 + 9  =  25

it seems easy to conclude that, for any positive integer n, the sum of the first n odd integers is n².

Looking back . . .

I have been visiting my hometown of Indiana, Pennsylvania and not finding time to complete a new post -- and so I have looked back.  On July 9, 2010 I offered a sonnet by Australian poet Jordie Albiston that begins with these lines:
 
     math (after)

     first you get the number-rush as anyone
     might do      you watch your world turn to
     nought      put your foot upon the path re
     what cannot be said      I’ve heard before
 . . .

I invite you to go to the original post and read the rest.

Poetry as Pure Mathematics

A recent email from Portuguese mathematician-poet F J "Francisco" Craveiro de Carvalho brought a 40-year-old stanza to my attention. First published in the May, 1974 issue of POETRY Magazine, we have these enigmatic lines by William Virgil Davis.  Enjoy!

       The Science of Numbers:  Or Poetry as Pure Mathematics

       Whatever you add you add at your peril.
       It is far better to subtract.  In poetry,
       Multiplication borders on madness.
       Division is the mistress we agree to sleep with. 

Mathematician and Poet

     Should I do it?  Should I do a blog post on a novel by Brazilian poet Hilda Hilst (1930-2004) that I have begun to read but don't yet know how to understand?
     Hilst's novel, With My Dog-Eyes, newly translated by Adam Morris (Melville House, 2014), attracted my attention because its narrator is a mathematician and a poet.  Here are the lines with which the novel begins:

      from   With My Dog-Eyes     by Hilda Hilst

       The cross on my brow
       The facts of what I was
       Of what I will be:
       I was born a mathematician, a magician
       I was born a poet.

A recent butterfly effect

The term butterfly effect has entered everyday vocabulary from the mathematics of chaos theory and refers to the possibility of a major event (such as a tornado) starting from something so slight as the flutter of a butterfly wing. This sensitivity to small changes is a characteristic of chaotic systems.  Recent news in Science magazine (9 May 2014) has drawn my attention to sea butterflies -- and the effect that ocean acidification is having on the lives of these tiny, fragile creatures -- and the environmental warning that this portends.  From the details offered in Science, I have constructed this poem of 4x4 square-stanzas:

       Warned by Sea Butterflies     by JoAnne Growney

       Sea butterflies --
       no larger than
       a grain of sand,
       named for the way  

Of all geometries, feathery is best . . .

The title for this post comes from Twinzilla (The Word Works, 2014), by Charleston poet Barbara Hagerty.  The title character of this collection is one of several poetic personalities that inhabit Hagerty's verse, and she offers a playful view of life's dualities -- sometimes versed in mathematical terminology.  Here's a sample.  

     Twinzilla Cautions *     by Barbara G. S. Hagerty

     Do not accept packages from unknown persons.
     Beware non-native strangers who may be concealing
     hazardous contraband "down there."
     Question algebra.  Dismantle thoughts traveling
     the brain's baggage carousel in parabolas.

Is mathematics discovered or invented?

My neighbor, Glenn, is fond of asking math-folks that he meets the question "Is mathematics discovered or invented?" -- and when he asked the question of MAA lecturer William Dunham the response was one word, delivered with a smile, "Yes." The question of invention versus discovery -- which may apply to poetry or to mathematics  --  is thoughtfully considered in "Notes toward a Supreme Fiction" by Wallace Stevens (1879-1955); here are a few lines from that poem.

       from It Must Give Pleasure,  VII     by Wallace Stevens

     He imposes orders as he thinks of them,
     As the fox and the snake do. It is a brave affair.
     Next he builds capitols and in their corridors,    

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).

Found: Elementary Calculus

Here is a poem by Saskatchewan poet Karen Solie.

       Found     by Karen Solie

       Elementary Calculus

                From    Elementary Calculus  A. Keith and W. J. Donaldson.
                          Glasgow:  Gibson, 1960.

       Speed (like distance)
       is a magnitude and has no
       direction; velocity (like displacement)

       has magnitude and direction.  

Number theory is like poetry

     Austrian-born Olga Taussky-Todd (1906-1995) was a noted and prolific mathematician who left her homeland for London in 1935 and moved on to California in 1945. Her best-known work was in the field of matrix theory (in England during World War II she started to use matrices to analyze vibrations of airplanes) and she also made important contributions to number theory. In the math-poetry anthology, Against Infinity, I found a poem by this outstanding mathematician.  

And Now I See . . .

     One of the ways we overcome our nervous shyness about our disabilities is by talking about them, and writing about them.  And by encountering the poetry of Kathi Wolfe.  I enjoy her work out-loud -- she is a frequent performer of her poems at local DC-area venues  -- and on the page.
     Kathi's "Blind Ambition" (in which she speaks of the monsters in arithmetic) is offered below; I first discovered this poem when it was posted by Split this Rock as poem of the week.  

Impossible Things Before Breakfast

Literary works by Charles Lutwidge Dodgson (1832-1898, aka Lewis Carroll) are crammed with mentions of mathematics.   One of my favorites (found here with numerous others, including "Ambition, Distraction, Uglification, Derision") is this exchange from Carroll's Alice in Wonderland.

          "Alice laughed: "There's no use trying," she said; "one can't believe impossible things."
          "I daresay you haven't had much practice," said the Queen.  "When I was younger, I always did it for half an hour a day.  Why, sometimes I've believed as many as six impossible things before breakfast."
                                                                                       Alice in Wonderland 

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.  

Phenomenal Woman

Yesterday morning Maya Angelou (1928-2014) left us. But she has not left us alone.  Her voice is with us, cheering us to be more than we were, to be all that we can become.  Places to read her words and words about her include PoetryFoundation.org (scroll down past the bio for links to poems), Poets.org, The Washington Post, and Angelou's website.

Angelou's poetry is filled with the geometry and motion of womanhood.  For example: 

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 

Math rap

     Harry Baker is a Slam Champion who studies Maths at Bristol University, UK -- and his poetry sometimes features math, often having fun with the topic.  His web page has a link to a rap about maths and at the JMM reading in Boston in 2012, Baker submitted this rap, 59 (a love story, now on YouTube), for presentation that evening.

Public Image of a Mathematician

From John Dawson -- a professor emeritus of mathematics at the Penn State York campus and well-known for his publications in mathematical logic, often focusing on the life and work of Kurt Godel -- a poem on a topic that this blog visits from time to time, portraits of mathematicians.

       Public Image     by John W. Dawson, Jr.

       Please,
       I'm not an accountant.
       No,
       Mine doesn't always balance either.
       What do I do then?
       Well,
       On good days
       I prove theorems; 

Pound on poetry and mathematics

HERE at PoetryFoundation.org we find an article by Carl Sandburg (1878-1967), published in POETRY Magazine in 1916, in which Sandburg offers highest praise to poet Ezra Pound (1885-1972). Sandburg includes this quote from a 1910 essay by Pound that connects poetry and mathematics.

"Poetry is a sort of inspired mathematics, which gives us equations, 

not for abstract figures, triangles, spheres and the like, but equations 

for the human emotions.  If one have a mind which inclines to magic

rather than science,  one will prefer to speak of these equations 

as spells or incantations; it sounds more arcane, mysterious, recondite."

The complete article is available here.

And, in a footnote* to the poem "In a Station of the Metro" -- found in my Norton Anthology of Modern Poetry we find a bit more of Pound's mathematical thinking. 

Land without a square

Here is a bit of light verse from the pen of John Updike (1932-2009).

ZULUS LIVE IN LAND 
WITHOUT A SQUARE     by John Updike

               A Zulu lives in a round world.  If he does not leave his reserve. 
     he can live his whole life through and never see a straight line.
                                             --headline and text from The New York Times

In Zululand the huts are round,
The windows oval, and the rooves
Thatched parabolically.  The ground
Is tilled in curvilinear grooves.

Barbie (b 1959) said (c 1990) "math is hard"

On April 24 I had the pleasure of reading at the Nora School with Martin Dickinson and Michele Wolf.  Back in March I had posted Dickinson's "Homage to Euclid" but mathematics is not a a focus of Wolf's work.  However, her poem below about Barbie has numbers, and any mention of Barbie reminds me of the controversy over "math is hard" -- one of the speeches uttered by an early 90's version of this doll.  (Please visit this posting from June 14, 2010 --  on "Girls and Mathematics" for additional Barbie-comments and more Barbie poetry.)   Here, now, please enjoy Wolf's poem:

Barbie Slits Open Her Direct-Mail Offer to Join AARP  
                                                                             by Michele Wolf

My worth is most inflated when, on tiptoes, I pose
In my original box, never handled, especially if I date
Back to '59 or '60.  But that is rare.  I am more used
To breaking out, to being the damp flamingo
Pecking to leave the shell.  I prefer moving forward.
I was an astronaut in '65, a surgeon in '73.  Last year

May 6, 1954

I learned about it via a news broadcast on Pittsburgh radio station KDKA and, for some reason, the event stuck firmly in my memory.  I was 13 years old and on May 6, 1954 Roger Bannister ran a mile in less than 4 minutes. The integer 4 is a perfect square as was Bannister's age then -- 25.  Alternatively, 13 is prime.  As is 60 + 13 = 73.  Yesterday marked 60 years since Bannister broke the record. I have come to love running.  And playing with numbers.

          I . . . never  
          will run out
          of numbers.

A pure mathematician (not!)

Poet Arthur Guiterman (1871-1943) was known for his humorous verse. Here is "A Pure Mathematician" -- a poem that stereotypes mathematicians in familiar, unflattering ways (from The Laughing Muse (Harper Brothers, 1915)).  In contrast to Guiterman's verse that pokes fun at mathematicians, I invite you to visit this posting from 28 January 2011 to read Sherman Stein's "Mathematician" -- a poem that not only is more fair to the profession but also features a female mathematician.

     A Pure Mathematician     by Arthur Guiterman

     Let Poets chant of Clouds and Things 
          In lonely attics! 
     A Nobler Lot is his, who clings 
          To Mathematics. 
     Sublime he sits, no Worldly Strife 
          His Bosom vexes, 
     Reducing all the Doubts of Life 
          To Y's and X's. 

Math, Magic, Mystery -- and so few women

Today, April 30, is the final day of Mathematics Awareness Month 2014; this year's theme has been "Mathematics, Magic and Mystery" and it celebrates the 100th anniversary of the birth of one of the most interesting men of mathematics; educated as a philosopher, Martin Gardner wrote often about mathematics and sometimes about poetry.  Gardner described his relationship to poetry as that of "occasional versifier" -- he is the author, for example, of:

     π goes on and on
     And e is just as cursed
     I wonder, how does π begin
     When its digits are reversed?   

Words that warn

     Somewhere in a high school English class was a small topic that intrigues me still -- "questions that expect the answer 'yes'."  A door opened.  Letting me see that what we say has expectations as well as information. In graduate school math classes we considered the warning word "obviously" -- in a proof, it was likely to mean "I'm sure it's true but am not able to explain."
     As I muse today about language I am wondering how unsaid words affect the population of women in mathematics, affect the numbers (too small) of women publishing mathematics.  Thinking about this in the light of a wonderful time on Saturday greeting visitors to an AWM (Association for Woman in Mathematics) booth at the biennial USA Science and Engineering Festival.  Temple University professor and AWM member Irina Mitrea did an amazing job planning and coordinating  the AWM booth where hundreds of young people got some hands-on experience with secret codes and ciphers.

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!

Remembering Nina Cassian

Exiled Romanian poet Nina Cassian (1924-2014) died last week in Manhattan.  Cassian was an outspoken poet whom I admired for her political views; she also was connected to mathematics -- in her subject matter and her friends.  (See, for example, this posting from January 31, 2011.)

       Equality     by Nina Cassian

       If I dress up like a peacock,
       you dress like a kangaroo.
       If I make myself into a triangle,
       you acquire the shape of an egg.
       If I were to climb on water,
       you'd climb on mirrors.

       All our gestures
       Belong to the solar system.

"Equality" is in Cheerleaders for a Funeral (Forrest Books, 1992), translated by the author and Brenda Walker.

Poetry of Romania - Nora School, Apr 24

     During several summers teaching conversational English to middle-school students in Deva, Romania, I became acquainted with the work of Romanian poets.  These included:  Mikhail Eminescu (1850-1889, a Romantic poet, much loved and esteemed, honored with a portrait on Romanian currency), George Bakovia (1881-1957, a Symbolist poet, and a favorite poet of Doru Radu, an English teacher in Deva with whom I worked on some translations of Bacovia into English), Nichita Stanescu  (1933-1983, an important post-war poet, a Nobel Prize nominee -- and a poet who often used mathematical concepts and images in his verse).
     On April 24, 2014 at the Nora School here in Silver Spring I will be reading (sharing the stage with Martin Dickinson and Michele Wolf) some poems of Romania -- reading both my own writing of my Romania experiences and some translations of work by Romanian poets.     Here is a sample (translated by Gabriel Praitura and me) of  a poem by Nichita Stanescu:

Dimensions of a soul

In the poem below, Young Smith uses carefully precise terms of Euclidean geometry to create a vivid interior portrait.

     She Considers the Dimensions of Her Soul   by Young Smith

     The shape of her soul is a square.
     She knows this to be the case
     because she often feels its corners
     pressing sharp against the bone
     just under her shoulder blades
     and across the wings of her hips. 

A Vector Space Poem

     As a Columbia undergraduate, media artist Millie Niss (1973-2009) majored in mathematics and was enrolled in a math PhD program at Brown University when she decided to make writing her full-time career.  Before her untimely death in 2009 Niss was well-established in Electronic Literature.   Here is a link to "Morningside Vector Space," one of the poems at Niss's website Sporkworld (at Sporkworld, click on the the E-poetry link).
     Niss's electronic poem retells a story (inspired by the Oulipian Raymond Queneau's Exercises de Style) in many different styles and following many different constraints. The computer is central to the retelling as the text varies almost smoothly along two dimensions, controlled by the position of the mouse pointer in a colored square (to the right in the screen-shot below).  Behind this poetry is the mathematical concept of a two-dimensional vector space, in which each point (or text) has a coordinate with respect to  each basis vector (version of the text, or dimension along which the text can change).

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. 

April Celebrates Poetry and Mathematics

On April 1 (the first day of National Poetry Month and Mathematics Awareness Month) Science writer Stephen Ornes offered a guest post at The Last Word on Nothing entitled "Can an Equation be a Poem?" and on April 2 the Ornes posting appeared again, this time in the blog Future Tense at Slate.com with the title "April Should Be Mathematical Poetry Month."
     In her comment on "Can an Equation be a Poem?" Scientific American blogger Evelyn Lamb (Roots of Unity)  mentioned her math-poetry post on March 21 entitled "What T S Eliot Told Me About the Chain Rule."  Lamb quotes lines from the final stanza "Little Gidding," the last of Eliot's Four Quartets.   Here is the entire stanza with its emphasis on the mysteries of time and perspective, the circular nature of things, the difficulty of discovering a beginning.    

Logic in limericks

In these lines, Sandra DeLozier Coleman (who participated in the math-poetry reading at the Joint Mathematics Meetings in Baltimore in January) speaks as a professor reasoning in rhyme, explaining truth-value technicalities of the logical implication, "If p then q" (or, in notation, p -- > q ).

     The Implications of Logic     by Sandra DeLozier Coleman

     That p --> q is true,
     Doesn’t say very much about q.
     For if p should be false,
     Then there’s really no loss
     In assuming that q could be, too.  

Can you SEE the monument?

Links to non-intersecting celebrations of April
as National Poetry Month      and      Mathematics Awareness Month

are available here and here.

Recently I revisited my copy of Elizabeth Bishop:  The Compete Poems, 1927-1979 (FSG, 1999) and turned to "The Monument" -- a poem mathematically interesting for its geometry.  Here are the opening lines; the complete text and many other Bishop poems are available online here:

from  The Monument     by Elizabeth Bishop  (1911-1979)

     Now can you see the monument? It is of wood
     built somewhat like a box. No. Built
     like several boxes in descending sizes
     one above the other.
     Each is turned half-way round so that
     its corners point toward the sides
     of the one below and the angles alternate.  

Split This Rock 2014 was great!

 Split This Rock calls poets to a greater role in public life 

and fosters a national network of socially engaged poets. 

Split this Rock's biennial 4-day poetry festival ended today and the air in Washington, DC is electric with the passion of engagement -- minds and bodies energized by fine poems that demand opportunity and justice for all.  I was glad to be there, participating in workshops and readings led by today's finest poetic voices. 

Women's History -- celebrate Caroline Herschel

     In the sixties when I spent a year at Bucknell University, I was a member of the "Department of Astronomy and Mathematics," a pairing of related disciplines. In past centuries, Mathematics was included in the liberal arts. In the twenty-first century often it is paired with Computer Science, and Astronomy is paired with Physics.  And so it goes.
      Poems by Laura Long tell of the pioneering work by astronomer Caroline Herschel -- a discoverer of eight comets, a cataloger of stars.  Long describes her recent collection,  The Eye of Caroline Herschel:  A Life in Poems (Finishing Line Press, 2013), in this way:      
                  This is a work of the imagination steeped in historical siftings 
                         and the breath between the lines.  
Here is the opening 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? 

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

Making something of nothing

     Was zero invented or discovered?  When and how?  By whom?  In "The Origin of Zero" -- an article published in 2009 in in Scientific American --  John Matson introduces an interesting history of zero (something vs. nothing and so on...).  Recently through the Splendid Wake poetry project (with an open-to-all meeting on Friday March 21 -- go here for details) I have connected with Washington DC poet William Rivera who has shared with me this poem that also examines the puzzle of the somethingness of nothing.

Nothing Changes Everything     by William Rivera

Tomorrow is Pi Day

     Tomorrow is Pi Day and I offer no new poems but supply links to several previous posts.  Poetry of π may be found on 23 August 2010 (an "irrational sonnet" by Jacques Bens),  6 September 2010 (featuring work by Kate Bush,  Robert Morgan and Wislawa Szymborska),  10 September 2010 (mnemonics for π, especially from Mike Keith) , 15 March, 2011,(a poem by Lana Hechtman Ayers)  27 November 2011 (a poem by Brian McCabe) and 10 March 2013 (the opening lines of a poem "3.141592 . . ." by Peter Meinke).

Tragedy of the Commons

Thinking in syllable-squares,
recalling ecologist Garrett Hardin (1915-2003)
and his 1968 wisdom, "Tragedy of the Commons."

Maximum               
may not be                   
optimum.

SHE measures the heavens . . .

Today is International Women's Day, celebrated with a charming video at google.com and here with lines from Enheduanna (2285-2250 BCE), the earliest woman known to me who was both poet and mathematician.

     The true woman who possesses exceeding wisdom,
     She consults a tablet of lapis lazuli,
     She gives advice to all lands,
     She measures off the heavens, she places the
               measuring cords on the earth.

These lines (found in the preface, translated from Sumerian sources by Ake W Sjoberg and E Bergmann S J) and much more poetry-with-math are found in Strange Attractors:  Poems of Love and Mathematics (AK Peters, 2008) -- a collection edited by Sarah Glaz and me.

A poetry album by Lucille Clifton

March is Women's History Month and here, today, I celebrate by acknowledging a special woman, Lucille Clifton (1936-2010).  From 1979–1985 Clifton served as Poet Laureate of Maryland.  Her poetry celebrates both her African-American heritage and her womanhood.  Here is "album," a poem in Clifton's spare and un-capitalized style -- and containing a few numbers to help us keep track of the times that are changing.

album     by Lucille Clifton

Sociology of Numbers

Robert Dawson is a mathematics professor at St Mary's University in Halifax, Nova Scotia -- an active mathematician who complements his research activity with mathematics education and with poetry. The following Dawson poem appeared here in 2013 -- in the Journal of Humanistic Mathematics, a journal whose every issue contains some poetry-with-mathematics.

Some Contributions to the Sociology of Numbers     by Robert Dawson

The ones you notice first are the natural  numbers.
Everybody knows their names; they are the anchors,
the stars, the alphas, the reference points. And of course
the rational numbers, who hang out with them,
sit next to them in arithmetic class.

Long division is difficult . . .

Last Monday included a visit with old friends of whom I see too little, Silver Spring artist Mark Behme -- with whom I did some art-poetry collaboration a few years  back -- and Chevy Chase artist-writer-economist-activist, Kyi May Kaung.  After lunch at nearby Mandalay we three walked to Mark's studio and hung out for a while, admiring and talking about his new work.  When I arrived home, I dug out several poems developed from Mark's sculpture -- finding some pieces I'd not thought about for a while.  Here is one of these, a mathy poem that partners with Mark's "Split Tales."

          Which Girl Am I?      by JoAnne Growney

          The girl who’s not forced to divide

          into the good girl and the real one

          is a lucky one.  I was eleven

          when I felt a crack begin.