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.

Angles in Alaska

Last Thursday evening I was honored to read in Takoma Park's Third Thursday poetry series -- along with poets Judy Neri and Kathleen O'Toole -- and my reading focused on poems of my times in Alaska.  The brilliant geometry of  our 49th state affected me strongly and "Angles of Light" became the title poem for a chapbook I published with Finishing Line Press in 2009.  Here is section 3 (of 7) from that poem.

Excitement of Proving a Theorem

Wow!  From first sighting, I have loved this description:

       I prove a theorem and the house expands:
       the windows jerk free to hover near the ceiling,
       the ceiling floats away with a sigh.

These lines from "Geometry" by Rita Dove express -- as well as any string of twenty-four words I can think of -- the excitement experienced from proving a theorem.

Wartime recurrence

In mathematics, it is not unusual to define an entity using a recurrence relation. 
For example, in defining powers of a positive integer:
       The 2nd power of  7  may be defined as  7  x  7¹ ;
               the 3rd power of  7  may be defined as  7  times  7², 
              and the 4th power is  7  times  7³,
              and, in general, for any positive integer n,  7ⁿ⁺¹  =  7  x  7ⁿ. 

Several weeks ago I attended a reading of fine poetry here in Silver Spring at the Nora School  -- a reading that featured DC-area poets Judith Bowles, Luther Jett, and David McAleavey.  I was delighted to hear in "Recessional" -- one of the poems presented that evening by Jett -- the mathematical pattern of recurrence, building stepwise  with a potentially infinite number of steps (as with the powers of 7, above) into a powerful poem.  I include it below:  

Mother Courage -- and speaking of opposites

     Bertolt Brecht (1898-1956) was a poet, but I have not found mathematics in his poems.  Still, I want to note here a fantastic performance of his play, Mother Courage and her Children, starring Kathleen Turner and a talented ensemble at Washington,DC's Arena Stage.  Invited by my neighbors, Mitzi and Pati, I joined them yesterday for a riveting performance.   Here is a link to "How Fortunate the Man with None," a Brecht poem  heartily sung as "Solomon's Song" in the current musical production.
     And here, with a nod to the mathematical bent of this blog, is a quote from Brecht's Mother Courage that involves counting; also, it is one of many examples of a strategy that Brecht uses often and well -- encouraging an idea by speaking of its opposite. 

To love, in perfect syllables

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

        Lesson in Latin     by Lewis Carroll    (May 1888)   

Love and Mathematics -- Please be my Valentine!

Poet extraordinaire Maxine Kumin (1925-2014) died yesterday.  

Here is a link to a wonderful eleven of her poems from Persimmon Tree. 

Late in 2007, AKPeters released Strange Attractors:  Poems of Love and Mathematics, edited by Sarah Glaz and me.  Recently at a Howard County Math Festival I met a young man who browsed my copy of this anthology and found it the perfect Valentine.  And so might you.  Below I include a sample from the collection -- a love sonnet by Jean de Sponde (1557-1595), translated from the French by David Slavitt.

 Several previous postings have offered love poems of mathematics and mathematicians; 

these include 9 February 2013, 12 February 2012, 12 February 2011, 10 November 2011,  

30 August 2011, 12 February 2011, and 20 July 2010.

Six Million

       Sometimes numbers become labels for particular events.  When I was growing up, all of us knew 1492 as a label for the discovery of America.  And 1941 recognized Pearl Harbor.  The following selection from a poem by Israeli poet Yehuda Amichai (1924-2000) reminds us of the awful importance of 6 million. 
       While mentioning this poem of witness and remembering, I want also to remind you of the very special Split This Rock Poetry Festival: Poems of Provocation & Witness, to held in Washington, DC, March 27-30, 2014. (Early-bird registration ends on Valentine's Day, February 14th at midnight.)  Hope to see you there. 

Forecasting snow and poetry

Snowbound

is that other world
in which no schedules sit
and no ambitions flare
to interrupt the bluest sky
and whitest field
and coldest air

On shoulders of giants . . .

     Washington, DC is a city rich with both poetry and mathematics.  Last Tuesday evening I attended a Mathematical Association of America (MAA) lecture by author and math historian William Dunham (whom I knew when he taught for a bunch of years at Pennsylvania's Muhlenberg College, in Eastern Pennsylvania, not so far from my employer, Bloomsburg University).  Dunham spoke of insights gained by many hours reading the correspondence of British mathematician and scientist, Sir Isaac Newton (1642-1727).  The discoverer of "gravity,"  and, moreover, both a genius and a disagreeable man.  Still, Newton was a man who gave a nod to his predecessors, "If I have seen further it is by standing on ye sholders of Giants."

Little Boxes

It is hard to know what to say.
Pete Seeger died yesterday at age 94.  
94 = 2 x 47.  47 is prime.
Here is a link to Pete singing "Little Boxes."
Song lyrics are poems.

Graffiti Calculus

     In my dreams I am an artist -- a cartoonist, perhaps, or a graffiti artist -- so skilled with lines and curves and so clever that my art gives pleasure AND delivers a punch.
     And so I am gratefully into the math-art connections provoked by a new book by Mary-Sherman Willis -- aptly titled Graffiti Calculus (CW Books, 2013).  I first met Willis in December, at Cafe Muse (where I will read next Monday, Feb 3 with Stephanie Strickland) and it was my pleasure also to hear her read again from that collection at the Joint Mathematics Meetings.  These poems by Willis give us, in sixty poetic chapters, the story of a mother seeking her son by following his graffiti tags through the city.  Here is a sample, sections 5 and 6: 

Mathematics is like . . .

For angling may be said to be so like the mathematics,
that it can never be fully learnt; at least not so fully, 
but that there will still be more new experiments left 
for the trial of other men that succeed us.  

 Izaak Walton (1594-1683), The Compleat Angler (1653-1676)

Extraneous -- and so on

     Since my junior high math days, when I first heard the word "extraneous," I have loved the sound of it, the feel of my mouth when I say it, the mystery of how solving an equation can lead to extra solutions.   And then learning to check found-solutions to see if they were true solutions -- a process that has been multiply useful to me far afield from mathematics.
     My love for this math-word drew me quickly to the title of a poem by Alex Walsh, a high school student from Oberlin, Ohio, who presented her work at the poetry-with-math reading at JMM in Baltimore last Friday.   Here are her poems "Convergence" and "The Extraneous Solution" :

Word problems

       Scarcity:  Why Having Too Little Means So Much (a Times book by S. Mullainathan and E. Shafir, released last September) considers not only the facts but the feelings of scarcity and finds similarities between those those with too little time and those with too little money.  The authors report, further, that persons experiencing scarcity do not have the luxury of doing well in their studies -- of mathematics or poetry -- because the scarcity demands their first attention.
       And  . . . this connection between external environment and a student's learning brings me to a poem by Dian Sousa, a poem that gives us some things to think about.  

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. 

Poetry-with-math, Jan 17, Baltimore

Please join us!

 A Reading of Poetry with Mathematics

  Friday,  January 17, 2014   4:30 - 6:30 PM
 Room 308  Baltimore Convention Center 

At the national Joint Mathematics Meetings in Baltimore, the Journal of Humanistic Mathematics is sponsoring a poetry reading.  Following participation by these poets,who have submitted work in advance, there will be an open reading in which interested audience members will be invited to share their math-related poems.  Participating poets include: Gizem Karaali, Katharine Merow, Karen Morgan Ivy, Mary-Sherman Willis, Alex Walsh, Ted Theodosopoulos, Stephanie Strickland, Myra Sklarew, JoAnne Growney, E. Laura Golberg, Sandra DeLozier Coleman, Rosanna Iembo, and Irene Iaccarino (musician).

Sunrise gives

each  of  us

a shadow.

Writing mathy poems - a student activity

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

The discipline of mathematics

This poem remembers one of my students.

       The Prince of Algebra      by JoAnne Growney

       Madam Professor,
       let me introduce myself.
       I'm Albert James,
       whom you may know
       by my test score
       that's lower than my age.

Martin Gardner, again

     This past weekend a review by Teller (magician of the Penn & Teller team) of an autobiography of Martin Gardner appeared in the NYTimes Book Review.  According to Teller, Gardner (1914-2010) wrote the memoir, Undiluted Hocus-Pocus:  The Autobiography of Martin Gardner, at the age of 95 on an old electric typewriter in his single-room assisted-living apartment in Norman, Oklahoma.    

Count what counts

When I visited Iceland last month, I looked in the bookstores of Reykjavik for bilingual (Icelandic-English) poetry collections; I found none. I did, however, acquire a copy of  The Sayings of the Vikings (Gudrun Publishing, 1992), a translation by Bjorn Jonasson of Hávamál -- "sayings of the high one" -- from the Poetic Edda, a collection of Old Norse poems from the Viking era and attributed to Odin.  Here are several samples that involve number or measurement:

     The Nature of  Hospitality

     I would be invited
     everywhere
     if I needn't eat at all. 

2013 (and prior) -- titles, dates of posts

Scroll down to find dates and titles (with links) of posts in 2013.  At the bottom are links to posts through 2012 and 2011 -- and all the way back to March 2010 when this blog was begun.   This link leads to a PDF file that lists searchable topics and names of poets and mathematicians presented herein.

Dec 30  Error Message Haiku
Dec 26  The angel of numbers . . .
Dec 23  Ah, you are a mathematician
Dec 20  Measuring Winter 

Error Message Haiku

Found at Komplexify.com, a variety of (often-amusing) mathematical verses -- including a collection of Error Message Haiku.  Approaching a New Year, I have been reflecting on my device-dependencies and considering resolutions about them -- and musing over some of these wistful substitutions for machine messages I dread:

       A crash reduces
       Your expensive computer
       To a simple stone.

       Chaos reigns within.
       Reflect, repent, and reboot.
       Order shall return.  

The angel of numbers . . .

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

     Mathematics      by Hanns Cibulka     (trans. Ewald Osers)

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

Ah, you are a mathematician

Thanks to Arturo Sangalli of the Writer's Union of Canada -- and fellow-participant in a recent Banff creativity conference --  who reminded me of this poem.  And thanks to Bill Dunham who has spread it widely by including it in The Mathematical Universe  (Wiley, 1997).  These brief stanzas were written in the early 1990s  when many of us kept our financial facts in checkbooks rather than online; still current, however, is the mistaken image of mathematicians as those whose task it is to keep numbers clean and orderly.

          Misunderstanding     by JoAnne Growney

          Ah, you are a mathematician,
              they say with admiration
              or scorn.    

Measuring Winter

Thomas Campion (1567-1620) was an English composer, physician, and poet.   I found this poem at poetryfoundation.org.

Now Winter Nights Enlarge     by Thomas Campion

Now winter nights enlarge
    The number of their hours;
And clouds their storms discharge
    Upon the airy towers.

Sieve of Eratosthenes

The Sieve of Eratosthenes     by Robin Chapman

He was an ancient Greek
looking for primes,
those whole numbers divisible
only by 1 and themselves,
those new arrivals on the block,
fresh additions to the stock
of indivisibles spilling through
future time (for what is time

Amounting to Something

From the Fall/Winter 2013 issue of Poet Lore, a poem by David Wagoner about the arithmetic of expectations:

     Amounting to Something     by David Wagoner

     You were supposed to do that
     by saving yourself up
               like coins in a pig rescued
               just in time sometimes
     from in front of the candy counter  
     or the desk in the corridor

13 lads of Christmas

     In addition to waterfalls and geysers and the Aurora, Iceland has outstanding museums.  On the morning of December 10, I visited the National Museum of Iceland in Reykjavik -- and enjoyed a careful introduction to the history of this fascinating and friendly nation.  Something I missed, however, was seeing one of the 13 Yuletide Lads that are an Icelandic tradition and who visit the Museum one-by-one on the 13 days before Christmas, each wearing traditional costume and trying to pilfer the goodies he likes best.

Iceland -- poetry, stones

British translator and editor David McDuff blogs at "Nordic Voices in Print" -- a site that he uses as "a way of making some of my translations of Nordic poetry and prose available online."  Here is "stones" -- the third of a group of ten poems he has posted by Icelandic poet Sjón.  This one involves a few numbers and I present it here as a math-poetry token of the fascinating land I am planning to visit: a five-day Iceland vacation adventure, traveling with my Eastern Village neighbors Priscilla and Glenn. 

stones     by Sjón (translated by David McDuff)

Conversational mathematics

In recent weeks I have been experimenting with poems that use mathematical terminology, wondering whether -- since there are readers who are undaunted by unknown literary references (to Dante's Divine Comedy or Eliot's Prufrock, for example) -- some readers will relish a poem with unexplained mathematical connections.  In this vein I have offered "Love" (posted on on November 5) and now give the following poem, "Small Powers of Eleven are Palindromes":