Are we speaking of "mathematics" or "poetry"?

     This week started with the excitement of an email message from Evelyn Lamb with a link to her Scientific American blog where she created a fun-to-take online poetry-math quiz based on an idea of mine (first published in 1992):

Can you tell the difference between mathematics and poetry?

Here’s a link to a SCIENTIFIC AMERICAN quiz to help you decide?

And a couple of centuries ago there was William Wordsworth -- who also contemplated both poetry and mathematics:

               On poetry and geometric truth
               and their high privilege of lasting life,
               From all internal injury exempt,
               I mused; upon these chiefly:  and at length,
               My senses yielding to the sultry air,
               Sleep seized me, and I passed into a dream.

William Wordsworth (1770-1850)

The Prelude, Book 5

Sustainability needs the arts AND mathematics . . .

The following poem is by Erica Jolly -- an Australian poet and retired teacher who is working hard to have the arts and the sciences integrated in Australian schools curricula.  “For too long, since the 1950s, we have witnessed serious losses across disciplines as science and mathematics have been deliberately separated from the arts and humanities,” Ms Jolly says.

"What has sustainability got to do with mathematics?"    by Erica Jolly

An exclamation attacking interdisciplinary themes in the national curriculum 

by Christopher Pyne on Q & A, 28 October 2013.

Does he not know or care
humankind must measure? 

Thanksgiving, 2015

Thinking toward Thanksgiving Day tomorrow, I am grateful for  --

 in addition to my children and grandchildren who will gather --

 all of the mathematic and poetic voices that help me see our world.
 Happy Thanksgiving wishes for all who read here!

Quoting Isaac Newton . . . . a "found" poem

     I do not know what
     I may appear to the world;
     but to myself I seem to have been
     only like a boy playing on the seashore,
     and diverting myself now and then
     finding a smoother pebble
     or a prettier shell than ordinary,
     whilst the great ocean of truth
     lay all undiscovered before me.

   -Isaac Newton, philosopher and mathematician (1642-1727)

Axiom: A Mathematics of Poetry

Today in a Facebook posting by Susanne Pumpluen

 I learned of Discov-her, an online journal 

featuring stories about women in Science. 

* * *

     The following poetry offering is by Richard Smyth who has written a parody of an introduction to the mathematics of logic (specifically Laws of Form by G Spencer Brown*, Julian Press, 1972).  Smyth founded Anabiosis Press which offers the poetry journal Albatross and which has now evolved into Anabiosis Online.  
     I invite you to enjoy this play of words and ideas:

AXIOM: A MATHEMATICS OF POETRY     by Richard Smyth

It shall be taken as given the idea of infinition. The idea of infinition stands in direct opposition to the idea of definition.

Definition
     Infinition is the act of making indefinite or unclear. That is to say, while some uses of language attempt to clarify, others attempt to obfuscate.

Construction
     Make a poem.  

Encouragement from fathers, a second view

     Despite the importance of fathers' encouragement (as noted in my post on 13 November), some women oppose their fathers' views.  Recently I have been enjoying Rachel Swaby's Headstrong: 52 Women Who Changed Science and the World  (Broadway Books, 2015) and yesterday my reading focused on her bios of Maria Agnesi (1718-1799) and Ada Lovelace (1815-1852) and the roles their fathers played in their lives.  Agnesi was a child prodigy who wished to be a nun but followed her father's wish that she research in mathematics until his death, when she was thirty-four; she devoted the rest of her life to serving the poor.  The education of Ada Lovelace was directed by her mother who did not see her father, the poet Lord Byron, as a solid foundation.  
     Poetic expression by a daughter somewhat resistant to her father's wishes comes from our youngest-ever US Poet Laureate Rita Dove in her poem, "Flash Cards": 

Encouragement from fathers

     It was my observation as a professor in a mostly-male mathematics department that the men who joined me in supporting opportunities for women were fathers of daughters.  They had come to see the world from a new perspective -- and saw that it needed changing.  Somewhat along these lines was a recent Washington POST article that told of recent research findings about socially responsible behavior from CEO's with daughters.
      With these thoughts in mind I started counting words . . . wanting to form a poem:

Limericks for Hedy Lamarr

     When seeking to draft a poem quickly, it is useful to have some sort of pattern to follow -- a pattern helping to dictate word choice.  This morning, upon discovering Google's online celebration of the 101st birthday of inventor and actress Hedy Lamarr, I have wanted to join the commemoration with a poem.  A verse pattern rather often used by hasty math writers is the limerick (see links below) -- and I have today constructed this pair of limericks to praise Lamarr.

     May a beautiful actress present
     Skills beyond stage and screen content?
          Yes!  Hedy Lamarr
          Excelled as a star,
     And had also talent to invent!  

It is clear that . . .

     "If I stand"     by Inger Christensen  (Denmark, 1935-2009)

               If I stand
               alone in the snow
               it is clear
               that I am a clock

               how else would eternity
               find its way around                

Translated from the Danish by Susannah Nied

Artificial Intelligence in the Library . . .

     Libraries are wonderful places and library book sales are temptations impossible to resist -- and so, during a recent trip to Boston and exploration of the historic public library buildings on Boylston Street, I purchased a copy of Living Proof  (Florida International University Press, 1985) by Edmund Skellings (1932-2012).  Born in Boston and a poet laureate of Florida, Skellings was a pioneer in the application of computers to the arts and humanities.  The word "proof" in his title was enough to make me pick up the book and I have relished the opportunity to turn up memories of a long ago graduate course in AI while reading this poem:

Artificial Intelligence     by Edmund Skellings

Euclid rolled over in his bones
When Newell & Simon instructed
Their machine to look for new proof
For bisecting the ordinary triangle.   

Mathematics and Poetry ARE Similar

        A recent email request sent me looking for a one-page article / quiz I had published in the American Mathematical Monthly in 1992 -- a list of 17 statements (quotations) each with a word missing.   The missing words are either "mathematics" or "poetry" (or a related word).  My claim is that, without using the author's name as a clue, it is difficult to decide which of these arts is intended.  I offer here the first four of the statements and suggest you reflect on missing words and then, if you wish, follow this link to a file with the entire list --   including also the author of each quote and (afterward) a list of the missing words.

_____  is the art of uniting pleasure with truth.   (Mathematics/Poetry)

To think the thinkable -- that is the ____'s aim.   (mathematician/poet)     

All _____ [is] putting the infinite within the finite.   (mathematics/poetry) 

The moving power of _____ invention is not reasoning 

                                                    but imagination.     (Mathematical/Poetic) 

The magic of mathematics (in art)

     Australian teacher and  poet Erica Jolly is convinced that breaking down the barriers that make silos of sciences and humanities subjects will promote better education systems and improve job prospects for students.  She brings mathematics into this engaging poem found in Holding Patterns, an online book of physics and engineering poems, part of the "Science Made Marvelous" project.

Sculpture at Questacon (Australia National Science and Technology Center)      

                                                                                by Erica Jolly

     It looks like magic --
     children are turning
     a great stone sphere
     this way and that
     smoothly, easily.  

JMM Seattle, 1-7-16 -- Poetry+Math+Art

 Read your mathy poems in Seattle!

An invitation to participate -- in January!  Read on!

 ANNOUNCING Poetry + Art + Math

 January 7, 2016, Thursday, 5:30 pm–7:00 pm.

Room 608, Washington State Convention Center, Seattle 

     At the Joint Mathematics Meetings (JMM) organized by Gizem Karaali, Pomona College; 

Lawrence M. Lesser, University of Texas at El Paso; and Douglas Norton, Villanova University. 

Celebrating waves of light . . .

     On October 8, Scotland's celebration of National Poetry Day had the theme "Light."  An online collection of themed poems suitable for children is available here.  From my Romanian friend, Doru Radu, who attended that celebration, I received poem-cards from the event. One of the cards contained a poem by filmmaker and poet Margaret Tait (1918-1999). I include that poem with its accompanying image below.  

Use a phone App to find mathy poems

A day late, Happy Birthday, E. E. Cummings 

(b 14 October 1894, d 3 September 1962).

     One of my favorite poetry sites is PoetryFoundation.org -- publisher of POETRY Magazine and supplier of a wonderful phone app (also entitled POETRY).  The app offers access to an enormous data-base of poems, sorted into categories that may be accessed using a SPIN feature, activated by touch.  Spinning the upper layer of categories can lead to "Humor" or "Joy" or "Insecurity" or  . . ..  Spinning the lower layer of categories can lead to "& Life" or  "& Nature" or . . . . When my spin picked the match of "Humor" and "& Arts and Sciences" I found a list of 263 poems.  One was Lewis Carroll's "Jabberwocky."  I also found the tiny poem "Nothing"  by Ken Mikolowski that plays with meaning as mathematicians also love to do. 

Daughter and Father - a warm geometry . . .

     Kate Stange is a mathematician -- from the Canadian province of Ontario and now at the University of Colorado -- whose father, Ken Stange, is a visual artist and poet. I met them on the internet via our combined interests in the intersections of poetry and mathematics. Lots of years ago, Kate gathered an online anthology of mathy poems. One of her recent online ventures is the development of WIN -- Women in Number Theory.  Below I offer one of Ken Stange's poems, taken from his collection Advice to Travellers (Penumbra, 1994).

Don't Mistake Your Mirror for a Window on the World     by Ken Stange

A reflection is both a thought about the world and the image we see in the mirror. -- Hippokrites

Consider your daughter's first smile.   
.    

Toward Infinity . . .

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

     Newton's Orange:  Infinity     by  Ewa Lipska   

A mathematician's favorite poet

     A summertime gift book that I have much enjoyed reading is Love & Math: The Heart of Hidden Reality by Edward Frenkel (Basic Books, 2013).  I admire the way Frenkel's memoir braids mathematics together with the other threads of his life.  Including poetry.  Like me, he chooses E E Cummings as one of his favorite poets.  And he used lines from Cummings' 1931 poem "the surely" as an epigram for a 2007 book that summarized his work.
     Below I include the entire text of Cummings' poem, with Frenkel's epigraph highlighted in bold face.

the surely     

Cued
motif smites truly to Beautifully
retire through its english

the Forwardflung backwardSpinning hoop returns fasterishly

A subtraction problem

Let's solve this subtraction problem:

                    Women do the job
            minus   the recognition.    
                           ____________________________

      The "found poem" above is from a headline for an article by Petula Dvorak in the Washington Post on 21 August 2015.  Dvorak's full headline was a bit longer, "Women do the job minus the training and recognition."  (Indeed Dvorak's article portrays the military as an even more difficult environment for women than the STEM fields.)
       Also found in the Post (this past weekend) an enthusiastic review by Marcia Bartusiak of Eileen Pollack's The Only Woman In the Room:  Why Science Is Still a Boys' Club.  Another problem to solve!!!

C K Williams -- Three Mile Island

A poet whose work I have long enjoyed, C K Williams  (1936-1915), died a few days ago.  (You may find a generous sample of his poems online -- for example at PoetryFoundation.org and Poets.org.)  Williams is a poet whose writing does not tend toward mathematics but his very fine poem "Tar" (about the Three Mile Island nuclear plant crisis of 1979, a year when I lived in Pennsylvania not far away) has a few numbers.  I present below the first stanza of  "Tar" and, beneath it, a link to the rest of the poem.

from   Tar        by C. K. Williams

The first morning of Three Mile Island: those first disquieting, 
       uncertain, mystifying hours.    

Choosing what words mean . . .

     Nineteenth century writer and mathematician Lewis Carroll (1832-1898) gave his character, Humpty Dumpty, these words:  "When I use a word, it means just what I choose it to mean -- neither more nor less."  And so it is in mathematics -- where, for example, the term "rational" (used in the poem"The Disposition of Art," shown below) has a precise meaning that differs from its typical conversational usage.
     The photo below shows computer-generated art by Silver Spring artist Allen Hirsh -- and, beside it, a framed version of the poem mentioned above.  Our work was exhibited together at last summer's BRIDGES and MAA conferences.  A clearer presentation of Hirsh's art -- "An Outgrabed Mome Rath" -- is available here.  My poem is presented below, beneath the photo.  

Words of Ada Lovelace

These poetic words of Ada Lovelace (1815-1852) -- concerning translation of mathematical principles into practical forms -- I found here:

Those who view mathematical science,
not merely as a vast body
of abstract and immutable truths,
whose intrinsic beauty, symmetry and logical completeness,
when regarded in their connexion together as a whole,
entitle them to a prominent place 
in the interest of all profound and logical minds,  

Shaping sentences with Fibonacci numbers . . .

Counting words . . ..  

     1                One
     1               person
     2               with courage
     3               makes a majority.               Andrew Jackson (updated)

Counting syllables . . .

     1               Life
     1               is
     2               painting
     3               a picture
     5               not doing a sum.                    Oliver Wendell Holmes, Jr.

Songs of mathematics . . .

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

Circle Song     by Lawrence Mark Lesser

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

It starts with counting . . .

Mathematical imagery is one of the many features I enjoy in the work of Canadian environmental scientist and poet Madhur Anand.  Here is a sample from her new collection (A New Index for Predicting Catastrophes).
 

Background:  In an experiment designed to test the truth of a given statement 

(often called the null hypothesis), a Type I error occurs if the experiment results in a true hypothesis 
being rejected (a "false positive") and a Type II error occurs if a false hypothesis is accepted. 

Type One Error     by Madhur Anand

I avoid news, talk to strangers, walk around the block
a thousand times and toss nickels for random samples.
I still get a few false positives.  I'm fine.  It's good. 

Mathematical Modeling

My friend and colleague, University of Connecticut mathematician Sarah Glaz, is an accomplished poet and is active in coordinating math-poetry activities -- via her website, the annual BRIDGES Conference, the anthology Strange Attractors: Poems of Love and Mathematics . . . .  Here is one of her mathy poems -- this one a pantoum, first published in London Grip.

Mathematical Modelling     by Sarah Glaz

Mathematical modelling may be viewed
As an organizing principle
That enables us to handle
A vast array of information      

The answer is NO

This past weekend I have much enjoyed reading Mathematics:  a novel  by Jacques Roubaud  (Dalkey Archive Press, reprint 2010, translated from the French by Ian Monk); Roubaud is a mathematician, poet, and member of the OULIPO.  And here is a found poem from Chapter 1:
.
          A
          question
          posed to a
          lively colleague:

          do you tell your
          dancing partners
          that you practice
          mathematics?

For me, like so many of us -- females especially -- revelation of a connection to mathematics leads to an awkward moment, an impediment to a possible relationship.  And so we say things like "I am at the university" or "I am doing some writing" or . . .

Hate Math -- 21 Reasons (NOT) . . .

Two four-letter words that I want NEVER to be used TOGETHER are hate and math.  A lively contradiction to my wish is provided by the following piece by slam poet Shappy Seasholtz.

(For details on the World Poetry Slam to be held in Washington DC on Oct. 7-10, 

scroll down to the bottom of this posting.)

21 Reasons Why I Hate Math     by Shappy Seasholtz

1 - It's my worst subject.
2 - I failed Algebra in high school.
3 - When I retook Algebra in high school during the final exam the principal announced that the space shuttle had just blown up.
4 - The space shuttle probably blew up because of a mathematical error. 

Three (or fewer) choices

Here is a link to an anthology of English translations of work by Chilean poet and mathematician, Nicanor Parra.   Some rank Nicanor Segundo Parra Sandoval (born 5 September 1914) among the most important poets of Spanish language literature.   Parra describes himself as an "anti-poet," having a distaste for poetic pomp and function; after recitations he exclaims "Me retracto de todo lo dicho" ("I take back everything I said").  I posted Parra's small poem "Thoughts" here in October, 2010-- and below I offer another example of Parra's play with ideas and words and numbers:   

       The Last Toast   by Nicanor Parra

       Whether we like it or not,
       We have only three choices:
       Yesterday, today and tomorrow.  

Caught in an infinite loop . . ..

Philadelphian Marion Cohen has been a mathematician since girlhood and a poet almost that long.  Besides her mathematics and writing, she teaches an interdisciplinary math-and-literature course at Arcadia University.  Here is a sample of Cohen's math poetry -- which imaginatively links mathematics to everyday life, sort of -- from her recent collection, Parables for a Rainy Day (Green Fuse Press, 2013).

Weirdness at 22nd and Walnut     by Marion D. Cohen    

Primes and a paradox

       Canadian poet Alice Major has loved and admired science and mathematics since girlhood and this background brings to her mathy poems both charm and amazement -- qualities that those of us who seriously studied mathematics easily lack.  At the recent BRIDGES conference I had a chance to hang out with Alice for a while and to purchase her latest collection, Standard Candles  (University of Alberta Press, 2015). Such fun to experience her views of infinities and paradoxes, of triangles and symmetries and formulas and ... .  
     Alice has given me permission to post two of her poems here; read on and enjoy "The god of prime numbers" and "Zeno's paradox."  

Reservation Mathematics

Both a talented writer and an articulate conveyor of the culture of American Indians, Sherman Alexie is a Spokane / Coeur d’Alene Indian from Wellpinit, Washington.  Besides several collections of poetry, Alexie has published novels and short-stories; he wrote the screen-play for the 1998 film, Smoke Signals.  "Reservation Mathematics"  is from Alexie's poetry collection First Indian on the Moon, (Hanging Loose Press, 1993) and was previously posted in this blog in January 2011.

Reservation Mathematics     by Sherman Alexie

Found on Facebook

A numerical poem, recently found on Facebook -- at this link:
 

Buffalo 66

     Nearly twenty years ago, in the formative years of River Poets (in Bloomsburg, PA), Jim Murray from Shamokin, then a student at Bloomsburg University) and I both were part of the group that gathered at Phillips Emporium for monthly poetry readings.  We became friends who kept in touch as he traveled to South Dakota and South Korea -- and I almost got to hear him read in Bloomsburg last month. 
     In recent weeks I have been enjoying journeying with Jim across the years and miles, seeing his reflections and insights (and sense of humor) as revealed through his poetry collections, Almost Normal (hardcoalstudios.com, 2012) and Normal:  The Last Ride of a Poet (hardcoalstudios.com, 2015).  Moreover, a visit to Murray's Hard Coal Studios website reveals other facets of his creative activity -- his comics, his ghost stories, his novella, and more.    Here is a sample (a short poem from Almost Normal) set in the old Capitol Theatre (now a restaurant) located along Main Street in Bloomsburg back in the 90s when single theaters were losing viewers to multiplexes.

MatHEmatics / MatSHEmatics

     Last week at the 2015 BRIDGES Math-Arts Conference in Baltimore I gave a short talk on using poetry to celebrate and inspire math girls and women, to recognize achievements and to encourage speaking out -- and also to encourage staying and building community in what often is now a lonely field.  Through a poem we can open doors that help us to talk about difficult issues -- such as isolation or loneliness or misgivings or discrimination. 
     A time-clock at BRIDGES kept me from saying all that I would have wished --  I would like to have quoted the following lines, spoken by a girl and found in "Hanging Fire" by Caribbean-American poet Audre Lorde (1934-1992).

from   Hanging Fire      by Audre Lorde 

          Nobody even stops to think
          about my side of it
          I should have been on the Math Team
          my marks were better than his . . .  

Algebra (sort of) in a short story

 Tomorrow I head to Baltimore for the BRIDGES Math-Arts Conference.

Explore the conference program at this link.  Would love to see you there!

It is my occasional delight to learn of a new mathy poem in an email message from Francisco José Craveiro de Carvalho, a Portuguese mathematician who loves poetry and has translated many math-related poems to and from his native language -- a seeker and finder of such poems who shares them with me.  (See also 23 October 2010, 17 September 2013, and 24 December 2014.)  A recent message from this friend alerted me to "Problem," an algebra-like short story (?prose poem?) by prize-winning author Lydia Davis. Enjoy!

Math and Poetry and Climate

Canadian poet Madhur Anand is also an Environmental Scientist; her love of nature and concerns for preserving a habitable climate pervade her work -- and she also scatters throughout it some mathematics.  You can imagine my delight when I found in her new collection (A New Index for Predicting Catastrophes) a poem (included below) that features the identity matrix.  Read on!

No Two Things Can Be More Equal    by Madhur Anand

In undergrad I learned about the identity 
matrix. Ones on the main diagonal and zeros 
elsewhere. Anything multiplied by it is itself. 

The culture for women in math and the sciences

Perhaps the phrase "ordinary" women scientists is an oxymoron -- but it should not be.  Women should be free to populate the full range of aspiration and dedication to science or any other profession.   In this spirit, I offer below the opening lines of a thought-provoking poem, "Ordinary Women Scientists," by science writer and poet Mary Alexandra Agner, from the excellent and important anthology Raising Lilly Ledbetter:  Women Poets Occupy the Workspace.

     Here are links to several recent items about math-women:

This link leads to a young mathematician's view of being "a female role model."

Here is a report of a panel at Harvard discussing roles of women in mathematics. 

Here is a link to the Women in Maths Facebook page where visitors 

may post information and offer support for math women.

This link leads to my poem celebrating Emmy Noether.  Here we celebrate Caroline Herschel.

Here at mathblogging.org is a place to find all sorts of math-links.

     from    Ordinary Women Scientists          by Mary Alexandra Agner       
                                                                                      for R.C.
      leave the lab late, flasks washed and waiting,
      computer on an overnight crunch job,
      warm dinner in the microwave
      while wondering at excited water molecules,
      wave their kids goodnight, grateful    

Terror/Mathematics

Several friends have sent me links to the poem "Terror/Mathematics" by Zeina Hashem Beck -- written after the beheading of 21 Christian Egyptians in Libya in February 2015 and published online here in One Throne Magazine.  To illustrate the style (with some mathematical symbols) and the power of the poem I offer the first couple of stanzas below -- and invite you to go to the One Throne website for all seven stanzas.

from   Terror/Mathematics     by Zeina Hashem Beck

                   After the beheading of 21 Christian Egyptians in Libya, February 2015

Try calculated, think math.
Capture and + the numbers,
- the Muslims.  21 is what you are

left with, which is 3 x 7.  Any multiple of 3
is blasphemous, is  √all evil,
and we will / its neck open. 

Islam is an X
in an equation we never    . . .                  (You may go here for the rest . . . )
 

Celebrating Ada Lovelace

Recently I have purchased the anthology, Raising Lilly Ledbetter:  Women Poets Occupying the Workplace (edited by Caroline Wright, M.L. Lyons & Eugenia Toledo, Lost Horse Press, 2015), and have found in it dozens of wonderful poems, including several that celebrate women of science.  Below I offer a poem by New York poet Jo Pitkin that honors Ada Lovelace (1815-1852).  

Bird, Moon, Engine     by Jo Pitkin

Like a fence or a wall to keep me from harm,
tutors circled me with logic, facts, theorems.
But I hid the weeds growing wild in my mind.

By age five, I could plot the arc of a rainbow.
I could explain perpendicular and parallel.
In my mind, I heard the wind in wild weeds.