Opposites -- in Life as in Mathematics

       Recently on NPR I heard an engaging interview with poet Kevin Young about his new collection Stones -- about memory and loss, and connection to the past -- and my interest led me to search online for more of his work.   At the Poetry Foundation website I found twenty of Young's poems, including this one which considers -- as mathematics also does -- pairs of opposites.

     Negative        by Kevin Young

       Wake to find everything black
       what was white, all the vice
       versa—white maids on TV, black

       sitcoms that star white dwarfs
       cute as pearl buttons. Black Presidents,
       Black Houses. White horse

       candidates. All bleach burns
       clothes black. Drive roads
       white as you are, white songs 

Geometry of a Neighborhood

     As we walk around, our views of our surroundings change;  lines that look parallel from one view appear to be converging from another . . . and so on.  The following poem by Massachusetts poet Martha Collins reflects on such view-changes:

House, Tree, Sky     by Martha Collins

If, when the pond is still
and nothing is moved
and the light is right.
you consider the angles
and make the proper approach,
you come to a bend
where a small white house
against a deep sky meets
the same white house against
the blue water:
stair rests on stair,
door opens on door,
tree grows out of tree.

It all starts with counting . . .

     Sometimes our focus on what is important -- in life, in love  . . . as in mathematics --  starts with counting.   This process is artfully expressed below in "Tally" by Romanian poet Lucian Blaga (1922-1985).

      Tally     by Lucien Blaga

       I tally in the ancient way.
       I count like the shepherd
       how many white. how many black
       --days, all year round.

       I count the steps, of the beautiful one,
       to the threshold of the door.
       I count how many startsthere are
       in the nest of the Mother Hen.

       However many, the lot--I count,
       smoke and illusions,
       the whole day--count, count
       roads and missed ways.

       I count the stones on which
       she crosses the ford, that beauty
       and all the sins for which
       hell will surely burn me.

Blaga's poem was translated from the Romanian by Brenda Walker and Stelian Apostolescu and is included in the anthology, Strange Attractors:  Poems of Love and Mathematics (AKPeters/CRC Press, 2008), edited by Sarah Glaz and JoAnne Growney.

More of Yeats and Geometry

      A blog-posting I made last week spoke of the use by poet William Butler Yeats (1865-1939) of geometry in his poetry.  Here is another vivid example:

The Second Coming    by William Butler Yeats

     Turning and turning in the widening gyre
     The falcon cannot hear the falconer;
     Things fall apart; the centre cannot hold;
     Mere anarchy is loosed upon the world,
     The blood-dimmed tide is loosed, and everywhere
     The ceremony of innocence is drowned;
     The best lack all conviction, while the worst
     Are full of passionate intensity.

     Surely some revelation is at hand;
     Surely the Second Coming is at hand.
     The Second Coming! Hardly are those words out
     When a vast image out of Spiritus Mundi
     Troubles my sight; somewhere in sands of the desert
     A shape with lion body and the head of a man,
     A gaze blank and pitiless as the sun,
     Is moving its slow thighs, while all about it
     Reel shadows of indignant desert birds.
     The darkness drops again; but now I know
     That twenty centuries of stony sleep
     Were vexed to nightmare by a rocking cradle,
     And what rough beast, its hour come round at last,
     Slouches towards Bethlehem to be born?     

 Read more about Yeats and his work here.

Intersecting lines of math, the arts, and justice

       A multimedia interdisciplinary project linking mathematics, the arts, and language -- and entitled  Rhythm of Structure -- was begun in 2003 by versatile mathematical artist and writer, John Sims.  I first learned of the project in 2010 when I was one of a group of writers invited to a weekend event at the Bowery Poetry Club at which Sims was then resident poet.  A catalog of the art and poetry gathered by Sims during that year is entitled Rhythm of Structure:  Mathematics, Art and Poetic Reflection, Bowery and Beyond and is available at this link.  

      Before moving on to a poem I am compelled to mention a recent instance of racial injustice; from May, 2021 this headline:

Political artist John Sims detained, handcuffed by S.C. police in his gallery apartment

found at this Yahoo site.  Sims, a black man and artist-in-residence at the Center for Contemporary art in Columbia, South Carolina, was arrested as an "intruder" as he entered his own apartment and gallery.  PLEASE, let us work together to end racially biased behavior! 

                                                               *   *   *

Yeats and Geometry

      Spelman College Professor Emeritus Colm Mulcahy is a mathematician and scholar whose talents and interests reach far and wide.  An email from him alerted me to a website exploring the work of his fellow Irishman, poet William Butler Yeats (1865-1939).  In particular Mulcahy alerted me to links between Yeats' poetry and Geometry.

     And these new connections to Yeats led me to think back to college days, to my reading of Yeats in a course in "Modern Poetry"  -- and to remember the way that my thoughts were swept into the air by "The Wild Swans at Coole."  I offer below its opening stanzas, followed by a link to the rest of the poem.

     The Wild Swans at Coole      by William Butler Yeats

      The trees are in their autumn beauty,
      The woodland paths are dry,
      Under the October twilight the water
      Mirrors a still sky;
      Upon the brimming water among the stones
      Are nine-and-fifty swans.

      The nineteenth autumn has come upon me
      Since I first made my count;
      I saw, before I had well finished,
      All suddenly mount
      And scatter wheeling in great broken rings
      Upon their clamorous wings.

       . . .                            Yeats' complete poem is available here at PoetryFoundation.org.

Seeing Mathematics Everywhere

     Ohio poet Cathryn Essinger has a twin brother who is a mathematician -- and links to mathematics sometimes appear in her poetry.   Here are the opening lines of a poem I especially enjoy -- the complete poem appeared in Poetry Magazine in 2002 and is available online here.

My Dog Practices Geometry     by Cathryn Essinger

     I do not understand the poets who tell me
     that I should not personify. Every morning
     the willow auditions for a new role

     outside my bedroom window—today she is
     Clytemnestra; yesterday a Southern Belle,
     lost in her own melodrama, sinking on her skirts.

     Nor do I like the mathematicians who tell me
     I cannot say, "The zinnias are counting on their
     fingers," or "The dog is practicing her geometry,"

     even though every day I watch her using
     the yard's big maple as the apex of a triangle
     from which she bisects the circumference   

          . . .                                                                                           To continue reading, follow this link.

The math of everyday life . . .

     Back in the 90's when I participated in several poetry workshops at Pennsylvania's Bucknell University, one of my fellow-students was Declan Synott and here -- found on Facebook -- is one of his poems, a mathy poem.

   Plowing     by Declan Synott

        In Brush Valley, near Rebersburg,
        a four-mule team pulls the furrow,
        and a 15 year old Amish boy stands atop the plow.
        He is part of the leather harness,
        leads to each animal.
        It’s a controlled chore. Methodical and mathematical.
        If you were to do the math, you’d know
        that it will take 38 passes,
        east to west, west to east to till this pasture.
        The job requires all of the morning
        and a good part of the afternoon.
        He swings at a horsefly’s bite, aligns his shoulders
        and keeps the animals moving.
        The soil breaks fresh, a dark rich brown,
        a dust plume in his wake.

There is more than one way to die . . .

      In the 1970's I had access to birth control and was fortunate to be able to be involved with adoption of children rather than abortion.  And I am saddened when a child is born into a world that has no plan of care for her or him.  Recent attempts to forbid abortion give me grave concerns -- concerns shared long ago in poems, using syllable-count patterns to control my ranting.  Here is one of these poems (also posted earlier in this blog).

Mathematics and Poetry -- Arts of the Heart

      On the opening pages of a Springer Reference, Handbook of the Mathematics of the Arts and Sciences, we find a list of 107 fascinating titles -- including two that link mathematics and poetry:

     "Mathematics and Poetry -- Arts of the Heart" by Gizem Karaali and Lawrence M. Lesser

     "Poems Structured by Mathematics"  by Daniel May

     Even for those of us who lack access to the Springer volume, the abstracts found at the links above offer lots of  valuable references -- and contact information for the authors.

     AND, if you are on Twitter, you can enjoy palindromes and other constrained verse by Anthony Etherin  ( @Anthony_Etherin ) -- an author whose latest book has the title SLATE PETALS.

Using "mathematics" in a poem

     One of my daily emails is poem-a-day from poets.org -- and yesterday's poem surprised me with the word "mathematics" appearing 4 times in its 28 lines.  Here are several lines:

from  Hunter heart a lonely is the     by Kyle Dacuyan

        child in a novel        that has neither       person nor a substance
        music         mathematics is a dream           makes me see myself

        more loving       when I listen       makes my heart go
        the hunter and a lonely       Remembering is a mathematics

        and the body in its illnesses     the stamina has symphonic
        calculus of living       in a sickness      I can listen now
      . . .

Dacuyan's complete poem -- for reading aloud and contemplation -- is available here.

Opposites Attract

     Poems by visual poet Karl Kempton are always fascinating and often mathy.  Here, from Kempton's collection, poems about something and nothing (Paper Press, 2015) is one of my favorites: 

zero
the mirror
oblivion holds
wearing the mask
of infinity

 

AND

Here is a link to Kempton's collection 3-CUBED:  MATHEMATICAL POEMS 1975-2003.

And here is a link to previous presentations of Kempton's work in this blog.

Shaping Poems with Numbers

      Numerical patterns can help guide our minds and fingers to create poems -- and one of the patterns I like is the Fibonacci numbers -- a number sequence for which the first non-zero numbers are both 1, and each succeeding number is the sum of the two preceding numbers.

          1, 1, 2, 3, 5, 8, 13, 21, 34, . . .

Formation of a six-line poem using the first 6 of these numbers as syllable-counts, gives a tiny poem that has been named a Fib.

For me, using these Fibonacci numbers  -- starting small and growing -- as syllable counts offers a nice structure for developing my thoughts around a particular topic.  I like it for myself (a couple examples below) and I suggest to my students when I am asking them to share their math-related viewpoints. 

   When                                                   When
   your                                                      your
   father                                                   mother
   is mathy                                               is mathy
   what are the chances                          what are the chances
   that interest is passed to you?           that interest is passed to you?

 These days I celebrate the fact that I have granddaughters who like math!

BRIDGES -- connecting math and poetry

     The BRIDGES Math-Arts organization held its 2021 conference (early in August) online  -- and, although many of the meetings were available only to registrants, archives of papers are available at this link to all who are interested.  

BRIDGES papers and events that link poetry and mathematics have been thoughtfully publicized by University of Connecticut emeritus professor Sarah Glaz who has created a webpage "Mathematical Poetry at Bridges" for that purpose.  On that webpage are links to pages for individual Bridges conferences as far back as 2010 -- with poetry involvement in the conferences increasing in the later years.  Here is a link to "Mathematical Poetry at Bridges 2021" -- a page with links to sample poems from more than 30 poets and also video readings of numerous poems.     VISIT the site and savor the poems.

Below I offer one of the poems from the Bridges 2021 site.  Playing with various ideas of "infinity" poet and math teacher Amy Uyematsu has created "This Thing Called Infinity" -- and she given me permission to offer it here. 

     This Thing Called Infinity     by Amy Uyematsu

JHM -- a rich source of mathy poems

      Every six months the Journal of Humanistic Mathematics offers a new online issue and includes a generous offering of mathy poems.  Here is a link to the current issue (Vol, 11, No, 2, July 2021) and I offer --after a sample, which features a type of algebra problem -- the titles, authors, and links to JHM mathy poems.

    Train Algebra      by Mary Soon Lee

     Do not use a calculator. Show your work.
     Haruki leaves Chicago Union Station at 10:42 pm
     on a train traveling at 60 miles per hour.

     At 10:33 pm, Haruki boards the train.
     He’s abandoned his job,
     his collection of cactuses;
     has only his cell phone, his wallet,
     and a dog-eared paperback.
     He walks through two carriages
     before finding an open seat,
     apologizes as he sits down
     beside a woman his mother’s age.
     The woman glares at him. 

Once upon a time, 350 was our goal

     Back in 2007, 350 parts per million was the "safe upper limit" for CO₂ in our atmosphere -- a figure  presented by NASA scientist Jim Hansen in December 2007 and widely agreed upon.  From that number the website 350.org was born. On October 24, 2009, 350 Poems celebrated an international day of climate action with a posting, from poets all around the world, of 350 poems of 3.5 lines each --  each responding to concern for man-made climate change.   My own entry (#265 here in the listing) I offer below.
    It's sad news that recent data (more than 400 ppm of CO₂ in our atmosphere) verifies our greedy disregard of this important warning.  What can we do?

    The Spider     (265/350)        by JoAnne Growney

     Spinner of intricate, twenty-inch silk food snares.
     Twenty inches — not fifty or two hundred.
     She knows the limits to her senses.  Humans
     keep building bigger webs.

This 3.5 line poem was first posted almost ten years ago (here at this link). 

Poetry with Numbers -- from Lewis Carroll

     One of the timeless treasures on my bookshelves is a complete collection of work by Lewis Carroll (pen name for Charles Lutwidge Dodgson, 1832-1898) -- writer, puzzler, math guy . . . Here's a poem I found in "Answers to Knot 1" in A Tangled Tale.  (The problem, Knot 1, is stated below the poem.)

from   A Tangled Tale     a response (by authors named below) to a puzzle posed by Lewis Carroll

        The elder and the younger knight
           They sallied forth at three;
        How far they went on level ground
           It matters not to me;
        What time they reached the foot of hill,
           When they began to mount,
        Are problems which I hold to be
           Of very small account.

Favorite -- most visited -- Posts

Because this blog has more than a thousand posts, spread over more than eleven years of posting, finding best information can be challenging.  The SEARCH feature in the right-hand column) and this linked file of names of poets and math-people and blog-content topics can be useful.  And, when time permits, browsing offers lots of fun.  Here, for the curious are the TOP TEN postings -- that is the postings that have had the most visitors since the blog's beginning in March, 2010.    

ENJOY!

These are titles and links to the ten posts most visited in this blog since its beginning in 2010.

from September 2, 2010    Rhymes help to remember the digits of Pi   

from October 13, 2010   Varieties of Triangles -- by Guillevic

from March 29, 2010    "Mathematical" Limericks   

from February 11, 2011   Loving a mathematician (Valentine's Day and . . . )

from September 29, 2017   Poetry . . . Mathematics . . .  and Attitude  

from February 18, 2011   Srinivasa Ramanujan    

from January 8, 2016   The world is round . . . or flat!

from February 22, 2011    Poems of set paradox and spatial dimension

from  June 22, 2021    Interpreting Khayyam -- in Rhyme

from April 19, 2010      Poems with Fibonacci number patterns

 

Excitement from Finding a Proof . . . and then . . .

Recently I have been revisiting the poems that Sarah Glaz and I collected for the anthology, Strange Attractors:  Poems of Love and Mathematics (AK Peters / CRC Press, 2008) and renewing my enjoyment of them.  Here, from page 146, is  a sample.

The Proof by Theodore Deppe
 
I could live like this, waiting on the roof
for the great egret that flies overhead
at just this time, measuring the sun's height
with my fingers to see if the moment's come,
Annie studying the horizon as she describes
the last minutes of a show she watched
in which some mathematician -
she didn't catch the name - labours seven years
to solve a proof he's been enthralled by
since childhood, and though Annie tuned in
too late to know the nature of the problem,
she loves the pure joy with which he looks
into the camera and announces, I've found it -
there are tears in his eyes - I've found it.  

Love and Tensor Algebra

     Stanislaw Lem (1921-2006) was a Polish science fiction writer whose works have been widely translated.  Here is a poem of his (found here in a blog with final postings in 2007)  -- a poem that enthusiastically expresses love in the language of mathematics!

Love and Tensor Algebra      

                    by Stanislaw Lem (translated by Michael Kandel)

 Come, let us hasten to a higher plane
 Where dyads tread the fairy fields of Venn,
 Their indices bedecked from one to n
 Commingled in an endless Markov chain!

 Come, every frustum longs to be a cone
 And every vector dreams of matrices.
 Hark to the gentle gradient of the breeze:
 It whispers of a more ergodic zone.  

Distance Melts . . . between math and poetry . . .

      One of my early math-poetry connections was with applied mathematician John Lew (1934-2006) who contributed often to the Humanistic Mathematics Network Journal (predecessor of the Journal of Humanistic Mathematics -- in which this blog finds frequent math-poetry gems.)  With a doctorate in physics, Lew worked in applied mathematics for many years at the IBM Watson Research Center -- and maintained interests in literature and music, serving for a time as poetry editor of the Mensa Bulletin.  His sonnet below comes from his 1996 HMNJ article, "On Mathematics in Poetry."  Lew's complete article is available here.

      The Comet      by John Lew

      Near from infinity I came
               Drawn to your strong, unmoving light
      By some ascendance of its flame
              That charms the planets through their night.
      The distance melts, my spirit thaws,
              Sublimes, and in your radiance flies
      Soon, by the old, unchanging laws,
             An exhalation through the skies.
      Sweet perihelion!  May we touch,
            Our auras intermingle?  No,
      The impulse of my flight too much,
             I must again to darkness go;
      While you may stand, and watch my face
             Dwindle through trans-Plutonian space.

 An interesting controversy arose between Lew and me -- here is a link to a letter he wrote about a math-poetry "quiz" that I developed that had appeared in the American Mathematical Monthly (quiz available here).

Mathematics Humor -- in rhyming verse . . .

      At the website KOMPLEXIFY! a mathematician named Travis celebrates his love of mathematics in various ways, including humor and verse.  He supplies lots of limericks and parodies, including Tom Lehrer's parody of "That's Entertainment" entitled "That's Mathematics" which  I offer below.  (Here is a link to the rich list of Travis' poetic postings.)

That’s mathematics!       by Tom Lehrer

Counting sheep
When you’re trying to sleep,
Being fair
When there’s something to share,
Being neat
When you’re folding a sheet,
That’s mathematics!

When a ball
Bounces off of a wall,
When you cook
From a recipe book,
When you know
How much money you owe,
That’s mathematics! 

Limericks about Graphs -- Prize-Winners

     A couple of weeks ago I posted information about prize-winning poetry in the Writing portion of the 2021 MoMath Steven Strogatz Contest for high school students.  After finding that I began to look for the results of earlier contests.  Apparently 2020 was the first year of these contests and in that year, also, poems were winners -- limericks (with related drawings) by Sarah Thau.  “Limericks and poetry are not a typical way to convey information about math,” admits Thau, “but I think it makes it more palatable than learning functions by rote.  Who doesn’t love a limerick?”

      From her winning collection, entitled "Little Function Limericks," here is a sample of Thau's work:

The entire collection of Thau's limericks is found here.

 

 

Picture a Mathematician . . . describe HER . . .

     Mathematicians are not always white and nerdy and male . . . but, for the others who dare to specialize in science and mathematics, there are many stereotypes that need to be busted.  Written by Gioia De Cari, a former MIT student, the play "Truth Values" reveals a woman's experience as a student in a male-science environment.  And the documentary film, "Picture a Scientist" describes the unequal treatment -- and payment -- of female professors.

     While you are seeking ways to view Truth Values and Picture a Scientist perhaps you will want to write down some of your own views;  while you are gathering your thoughts, here are three of my syllable-square stanzas about women in math to reflect on.

Syllable-square thoughts about Math Women

Numbers keep track of memories . . .

     Sometimes the specific nature of counting can help us, for a bit of time, to steer our thoughts for away from sadness.  Here is a poem in which numbers give a grieving partner a framework through which to speak.  (This selection is from The Widows' Handbook (Kent State University Press, 2014), an anthology gathered and edited by Jacqueline Lapidus and Lise Menn.)

      Camp Numbers     by Barbara Bald   

      I’ve been in these woods seven days,
      fed our fish twelve shrimp pellets,
      filled two hummingbird feeders with red juice,
      given our cat ten doses of pink medicine.

      I’ve live-trapped twenty-eight field mice
      with the Tin Cat trap you bought,
      rescued our Brittany’s toy four times from the river,
      seen one person, the gas man fixing the fridge, in two days.

      I’ve written thirteen poems,
      five about your untimely death,
      cleaned six cabinets to rid rodent remnants,
      replaced one roll of toilet paper in the outhouse.

      I am still waiting for one of you.

Learn more about poet and educator and nature-lover Barbara Bald here at her website.

Looking back . . . to previous posts . . .

  BROWSE and ENJOY!

Back in January 2020 I gathered a list of titles of previous posts and posted it here at this link.  And below I offer titles of postings -- with links -- since that time.

And, if you are looking for a post on a particular topic,
you are invited to explore the SEARCH feature in the right-hand column
OR to browse the list of  Labels (also to the right) -- and click on ones that interest you.

 

TITLES OF POSTS (with links) 

June, 2021    

      Math Communication with Poetry -- Strogatz Prize

      One More Love Poem

      Interpreting Khayyam -- in Rhyme   

      Putting CALCULUS into a poem . . .  

      Images of a Complex World   

      Encryption and Love   

      Every Seventeen Years . . .   

      A Life Made to Count   

      A Few Lines of Parody   

      Euclid and Barbie -- and attitudes toward math . . .

 

May, 2021      

      A Mathy Rhyme from Twitter   

      A Rhymer and an Analyst -- a Friendship   

      What does CANCEL mean? -- some poetic wordplay!   

      MoMath Celebrates Limericks!  

      Reflecting on Pi . . .   

      Keeping Track of Chairs   

      Mathematical Forms in Poetry . . .  

      Mathy Jokes    

      Climate Concerns   

      Celebrate Math-Women -- Celebrate AWM  

Math Communication with Poetry -- Strogatz Prize

Recently I have learned -- through Mo-Math (National Museum of Mathematics) -- of the of the Steven H. Strogatz Prize -- recognizing high school students for outstanding math communication projects.  Winners for the 2021 Contest were announced yesterday -- and information about upcoming contests is available here.

     This year's Strogatz winner in the Writing category was a poem by Julia Schanen, entitled "Math Person."  Below I offer Schanen's opening lines -- and the sample is followed by a link to the full text of her poem -- of mathematics and of the painful isolation that a 10th grade math girl often feels. 

One More Love Poem

     Expressing love with mathematical terminology is beautifully done in "One More Love Poem" by  Dunya Mikhail  -- this poem was offered by poets.org in their poem-a-day feature on April 2, 2021 and it deserves to be widely shared.

One More Love Poem     by Dunya Mikhail

       If I had one more day
       I would write a love poem
       composed of one word
       repeated like binary code.

       I’ll multiply it by the number
       of days that passed
       without saying it to you
       and I’ll add the days   

Interpreting Khayyam -- in Rhyme

     Eleventh century Persian scholar Omar Khayyam (1048-1131) is described by Wikipedia as a polymath -- he was a mathematician, astronomer, philosopher and poet (and the foregoing Wikipedia link summarizes his accomplishments).  My former colleague, Reza Noubary, a math-stat professor at the Bloomsburg (PA) University, shares Khayyam's Persian heritage and also has a wide variety of achievements; one of his recent adventures has been with poetry.  In 2020 his poetry collection, Feelings and Dealings, appeared -- and this year has brought forth his collection Khayyam in Rhyme (Fulton Books, 2021).

     Khayyam in Noubary's volume is revealed as a mathematician through his thought-patterns more than through his words.  Here is an intriguing sample from Chapter 1 (available for online browsing here); this sample shows first, the original Farsi, followed by two "translations"of the four that are offered): 

Putting CALCULUS into a poem . . .

 Can our world be described using calculus?

     The poem-a-day offering this morning (6/21/21) from poets.org gives me new ideas about describing a problem-situation using some terms from mathematics.  I offer part of the poem below, followed by a link to the complete work.

from  Disintegrating Calculus Problem     by McKenzie Toma

A dramatic clue lodged in a rockface. Set in a shimmering sound belt slung around the grasses. Collections of numbers signify a large sum, a fatness that cannot be touched. Numbers are heart weight in script. Calculus means a small pebble pushed around maniacally. Binding affection, instead of fear, to largeness.  

Ideas are peeled into fours and pinned on the warm corners of earth to flap in a wind. Wind, the product of a swinging axe that splits the sums. This math flowers on the tender back of the knee.     . . . .

     McKenzie Toma's complete poem appears here (with other poem-a-day offerings at poets.org) and and here (along with several others of her poems).

Images of a Complex World

     One of the treasures on my bookshelf is Images of a Complex World: The Art and Poetry of Chaos by University of Wisconsin poet Robin Chapman and physicist Julien Clinton Sprott (World Scientific, 2005).  The following image by Sprott accompanies a poem entitled "The Traveling Salesman's Problem is NP-Difficult." Beneath the art, I offer the poem's opening lines -- and the complete poem and other art-poetry samples from the collection are available at this link.   

an image of chaos by Julien Clinton Sprott

 

from:  The Traveling Salesman's Problem is NP-Difficult   by Robin Chapman 

 

     We were all for optimization of student opportunities

Encryption and Love

One of my recent book-acquisitions is The Woman who Smashed Codes by Jason Fagone  -- a story of Elizebeth Smith Friedman who transitioned from teaching and scholarship to codebreaking and became a hero of the National Security Agency during the much of the first half of the twentieth century.   In this book I have found (on page 91, discussion of some of the ideas of information-theory pioneer Claude Shannon; the story of Elizebeth includes telling of her meeting and falling in love with another codebreaker, William Friedman, and Fagone brings Shannon into the story with this remark:

     . . . according to Shannon, making yourself understood by another person
        is essentially a problem in cryptology ... When you fall in love, you develop
        a compact encoding to share mental states more efficiently, cut noise,
        and bring your beloved closer.   All lovers, in this light, are codebreakers . . .

Also connecting love and mathematics is a poetry anthology from more than a dozen years ago -- a collection that I helped Sarah Glaz to gather and edit (and now available as an e-book):  Strange Attractors:  Poems of Love and Mathematics (A K Peters/CRC Press, 2008).  On page 135, these cryptic lines from Rafael Alberti, used as an epigraph for the poem "Mathematics" by Hanns Cibulka.

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

Cibulka's "Mathematics" may be found here.  And this link leads to other postings in this blog that relate to Strange Attractors. 

Every Seventeen Years . . .

Millions of Brood X 17-year cicadas have recently emerged in the Washington, DC area and they are the subjects of laughter, fear, recipes, and so on.  (Wikipedia information about these cicadas is available here.)  Washington Post writer John Kelly has asked readers to celebrate the cicadas with verse -- and below I offer one of the Haiku that Kelly gathered recently.

Found here in The Washington Post

A Life Made to Count

     The title of this blog-post is part of a headline from The Washington Post -- a headline for a review by GW Professor Lisa Page  of a posthumously published and recently released memoir by Katherine Johnson (1918 - 2020) :  My Remarkable Journey:  A Memoir, written with assistance from Joylette Hylick, Katherine Moore and Lisa Frazier Page (Amistad, 2021).

     As you might expect, numbers are at the center of Johnson's memoir -- numbers never intimidated Johnson — in fact, they thrilled her. The symmetry, the structural interplay of equations and formulas, were always in her head.  (Read a bit of the book here.)

     As Johnson looked back over her life of more than one hundred years, I too was prompted to looks back -- to an article of mine entitled "MATHEMATICS AND POETRY:  ISOLATED OR INTEGRATED?" and published in the Humanistic Mathematics Network Newsletter (forerunner of the Journal of Humanistic Mathematics) in May, 1991 -- and available here.  And I can't resist quoting a bit from the article, sharing some phrases from the poem "Poetry" by Marianne Moore (1887-1972).

       . . . things are important not because a
       high-sounding interpretation can be put upon them
       but because they are useful . . . the same thing
       may be said for all of us—that we do not admire
       what we cannot understand. 

       [Not until we] can present for inspection,
       imaginary gardens with real toads in them
       shall we have it . . .

Moore's complete poem is available here.

A Few Lines of Parody

      Recently I re-found -- in my copy of The Mathematical Magpie by Clifton Fadiman (1904-1999)  (Simon and Schuster, 1962) -- these lines by Lewis Untermeyer (1885-1977):

    EINSTEIN:  A PARODY IN THE MANNER OF EDW-N MARKH-M

    We drew our circle that shut him out,
    This man of Science who dared our doubt.
    But ah, with a fourth-dimensional grin
    He squared a circle that took us in.

Untermeyer's lines first appeared in his Collected Parodies.    Here is a link to a second edition (1997) of The Mathematical Magpie (for which the title page description includes:  stories, subsets of essays, rhymes, anecdotes, epigrams . . . rational or irrational . . .)

Euclid and Barbie -- and attitudes toward math . . .

     Teacher-poet-musician Glen Brown has shared with me his mathy poem that has for its epigraph a controversial line once spoken (back in 1992) by Mattel's Teen Talk Barbie.   Brown makes playful use of a variety of math terms but with an somewhat sexist point of view.

     Euclid and Barbie      by Glen Brown
                                Math class is tough.
                                                            --Barbie
     Sure it doesn’t add up:
     countless camping and skiing trips with Ken,
     swimming and skating parties without danger,
     dancing and shopping engagements
     with Midge and Skipper
     like an infinite summer vacation.
     Nothing here hints at a dull math class
     for integral Barbie and her complex playmates!

A Mathy Rhyme from Twitter

When I have a bit of extra time, it is fun for me to visit Twitter (my postings may be found as JoAnne Growney @MathyPoems) and to find introductions to lots of interesting topics in math and poetry -- and to lots of brief poems.   Recently I came upon the following post by Algebra Etc. @AlgebraFact.

A Rhymer and an Analyst -- a Friendship

     Several recent emails have turned my attention again to Irish mathematician (?and poet?) William Rowan Hamilton (1805-1865).  Available online here is Life of Sir William Rowan Hamilton by Robert Perceval Graves (Dublin University Press, 1882) -- and here is a link to a posting of a poem by Hamilton published in this blog back in 2011. Graves tells of the friendship between Hamilton and poet William Wordsworth and this link leads to some commentary about their connection.  Here are some of Wordsworth's words:

You send me showers of verses, which I receive with much pleasure, as do we all; yet have we fears that this employment may seduce you from the path of Science, which you seem so destined to tread with so much honour to yourself and profit to others. Again and again I must repeat, that the composition of verse is infinitely more of an art than men are prepared to believe, and absolute success in it depends upon innumerable minutia, which it grieves me you should stoop to acquire a knowledge of.

     Current investigation into the life of Hamilton has suggested that  parts of Graves' work has been misinterpreted and that -- over time --  Hamilton's reputation has undeservedly declined; here is a link to a 2017 article by Anne van Weerden and Steven Wepster, "A most gossiped about genius: Sir William Rowan Hamilton" -- an article that adds new insights into the Hamilton story.  

What does CANCEL mean? -- some poetic wordplay!

      Lawrence "Larry" Lesser is a professor in the Mathematical Sciences Department at the University of Texas in El Paso and a widely published creator of mathy poems.  Here are the opening stanzas of  a poem that appeared in the Winter 2021 issue of Teaching for Excellence and Equity in Mathematics (TEEM), a journal of the NCTM affiliate organization TODOS: Mathematics for ALL. 

 from     ₵AN
           ₵EL           by Lawrence Mark Lesser

      Cancel is from Latin for ‘make like a lattice’,
      like crisscrossed wood fencing
      in our backyard where we safely
      dine with friends,

      or like COVID-caused crossouts
      on calendars--  
      a cancelled appointment (dis-appointment)
      or music event (dis-concerting).

      Teachers don’t like saying ‘cancel’
      lest students get carried away,
      cancelling sixes of 26/65,  
      which does equal two-fifths 

MoMath Celebrates Limericks!

     New York's Museum of Mathematics celebrated National Limerick Day on May 12 with an online program of contributors reading their mathy limerick stanzas.  I did not learn of the reading in time to apply for participation but here is a sample I might have submitted.

       In baseball the diamonds are square--
            And the ball has the shape of a sphere.
            Nine guys make a team--
       So, two teams make eighteen--
       And fans cheer when plays come in pairs.

     The limericks read at the May 12 MoMath program may be found here  -- and here is a link to the results of a SEARCH in this blog for "limerick."  The sample offered above was posted long ago, back in April 2010.

Reflecting on Pi . . .

     A few months ago I got an email from Adaobi Chiemelu, a Nigerian poet and spoken word artist who studied studied mathematics at the University of Nigeria.  Recently Adaobi has sent me one of their poems -- about division and infinity and pi and . . . 

Dividing Together     by Adaobi Chiemelu

The cake was holy communion
You picked one piece not fatter than your two fingers
You smiled
You watched as the next person went on to do same 
          and put the same in their mouth
You thought of pi     

Keeping Track of Chairs

 The first steps in mathematics . . . COUNTING!

      I grew up on a farm and keeping track by counting happened often -- counting chickens, counting sheep, counting the number of weeks until the early transparent apples will be ripe . . . and when I read Tom Wayman's poem in Poet Lore I found a similar habit of relentless counting.    I have not been able to obtain more than short-term permission for posting -- and so I offer here just a sample and, beneath, a a link to the full poem.

from Fifty Years of Stacking Chairs     by Tom Wayman

     Two of these chairs at a time
     are easily manageable, so back at the empty rows
     I fold three and haul them with both hands
     across the space. Next trip I try
     four: fingers on each hand curved
     under the metal backrests of
     two chairs. Fifty years 

Mathematical Forms in Poetry . . .

      During recent days, one of my special enjoyments has been finding time to read Marian Christie's blog -- a delightful collection of poetry and poetic musings with frequent connections to mathematics.  Christie's biographical sketch (available here) indicates that she, like me, grew up enjoying both poetry and math.  She became a math teacher and, after her years of teaching ended, she turned her attention to poetry.  Below I present a sample of her mathy poetry, followed by links to several of her postings.

Today, in a season that is approaching summer, I coolly offer Christie's "Midwinter" poem (found here in her blog)  -- a stanza in which the poet uses Pascal's triangle to pattern her words:

a Pascal-triangle poem -- find it and lots of other mathy poems here.

Here, next, are links to several of Christie's math-poetry blog postings.  ENJOY!

Mathy Jokes

     In a recent search for funny mathy poems I have discovered the collection by G. Patrick Vennebush pictured below as well as a sequel to that edition and a related blog.

Book info available at this link.

Although most of the jokes are not poetic, some are.  Here is a brief sample from the blog:

                 With my head in an oven
                 And my feet on some ice,
                 I’d say that, on average,
                 I feel rather nice!

Read more and enjoy . . .

Climate Concerns

      Ideas become internalized when we WRITE about them -- and I encourage students AND all of us to write about climate change and efforts to save our planet.  And then to act on our words!   Here are three small syllable-squares, first appearing in a post more than ten years ago and expressing my ongoing concerns for precarious imbalances we have created within our natural environment.

This link leads to several previous posts found using the search terms climate change.

Celebrate Math-Women -- Celebrate AWM

1   This
2   year's the
3   fiftieth
4   birthday of the
5   Association
6   for Women in Mathe-
7   matics.  Join celebrations --
8   hear lectures, game with playing cards,
9   interview, write essays that feature
10  math women you admire.  Speak up -- cheer girls
11  who do well in math class; look back, remember,
12  laud stars of the past  --  support A W M.

 The Association for Women in Mathematics (AWM) is a national organization devoted to encouraging women and girls to study and to have active careers in the mathematical sciences, and to promote equal opportunity and the equal treatment of women and girls in the mathematical sciences.  Founding in 1971 and celebrating math-women with outreach, networks and partnerships, playing cards, essay contest (for students in middle school through college) . . . and so much more.

Explore AWM's Website and their lively WOMEN DO MATH site.

Polyform Puzzles -- presented in verse

     Many math-loving folks gather periodically at meetings called  G4G (Gatherings for Gardner) to celebrate the life and contributions of Martin Gardner (1914-2010) -- a versatile author whom I know best from his "Mathematical Games" column in Scientific American -- a column that often connected math and poetry. 

     Here is a link to the YouTube channel for G4G Celebrations -- a place to view presentations of ideas that honor the spirit of Martin Gardner.   For one of the recent meetings of G4G (online due to Covid), graphic artist and designer of recreational mathematics puzzles, Kate Jones, offered a visual and poetic presentation entitled A Periodic Table of polyform puzzles.

This is the 3rd slide of Jones' presentation, "A Periodic Table of polyform puzzles"

      This link leads to a pdf of the 29 slides of Jones' presentation and this link leads to a 24-minute PowerPoint recording of the production; eventually this event will be available on the YouTube Channel noted above.   Jones describes this creation in this way:  It’s like a very condensed book on the subject; using rhymed couplets allowed for even more compact delivery of the information.  She adds:  at the gamepuzzles website, the various individual items in the puzzles can be seen more simply.

     Here is a link to an earlier posting in this  blog that includes a Fibonacci poem by Jones -- created for the 2016 meeting of G4G.

A Visit to Mathland -- where Reason rules!

Published in 1979 by PRIMARY PRESS, out of print -- try your library!

Before purchasing this anthology (found at a math conference) I had never seen a collection of mathy poems -- but then, many years later, I helped to edit one (Strange Attractors:  Poems of Love and Mathematics).   Today I offer an old favorite from Against Infinity  -- the poem "A Visit to Mathland" by Naomi Replansky (born May 23, 1918):

A Visit to Mathland  by Naomi Replansky  (for M., Z., and L., citizens thereof)

 I was a timid tourist
 to the land of mathematics:
 how do you behave in a country
 where Reason rules?   

Mean, Median, Mode -- and Poetry and Bananas!

 A wonderful resource for mathy poems for students is  “S.T.E.A.M. Powered Poetry Videos for Pk-8”  -- and I have recently connected there with poet and teacher, Heidi Bee Roemer; I offer a sample of her work below:

This poem --  and much more -- found at https://steampoweredpoetry.com/.

Across the curriculum, “S.T.E.A.M. Powered Poetry Videos for Pk-8” promotes poetry in the classroom using multiple methods and strategies. In addition to kid-friendly poetry videos, this vlog features crafts, classroom activities, and reference lists for related children’s books that offer additional information on each poem’s subject.  Learn more at this link about Heidi Bee Roemer and her collaborators.