Halloween Poems

            Double, double toil and trouble;
            Fire burn and caldron bubble.
            Cool it with a baboon's blood,
            Then the charm is firm and good.          from Shakespeare's Macbeth

Shakespeare's lines above are part of a collection of Halloween Poems offered at this link by the Poetry Foundation -- not a mathy group of poems but fun to read at this time of year.  Enjoy!

Visual Mathematical Poetry

          A wonderful place to visit -- and to stay for a while -- is the blog maintained by Kazmier Maslanka, Mathematical Poetry, found here at this link.  Maslanka's poetry is visual -- and here is a lovely sample that features the golden ratio:

"Golden Fear" by Kaz Maslanka

This link leads to Maslanka's blog and this link leads to information about "Rule 42, Stretched Language" -- an upcoming show at California's Bonita Museum that features his work.

Maslanka has been noted numerous times in this blog --
here is a blog link to another image from his mathematical-poetry-art.
This link leads to a thoughtful interview with Maslanka.

Inspired by Ten

      Here is an intriguing poem by Massachusetts poet Ellen Wehle that focuses on ten;  it is one of the works collected in Strange Attractors: Poems of Love and Mathematics (AK Peters/CRC Press, 2008).

    The Song of 10     by Ellen Wehle

     From the Romans' decem our decibels and decimal system, O tenfold
     the sorrows of Israel, Decameron tales mean to be told over ten nights

     in December, solstice month frozen in moondrifts of snow.  Our fingers
     and toes.  Kingly ten-pointed stags reigning over Europe's greenwoods,

     for miners a measure in tons of coal or type of tallow candle weighted
     ten per pound, the legion poor mending by by its light.  What else is there

     to say?  Higher than nine.  A number whose power is mighty to multiply,
     comprising one and nil, wand and egg, gold spindle and heavenly wheel

     of goddess Fate who turns time and tides; what our parents say summer
     evenings, hearing our voices dart and flicker in neighboring yards before

     we dance from them into darkness and love's rule ends--I'll count to ten.

Maths and Poetry: Beauty is the Link

     One of the American Mathematical Society's pre-Covid Programs for students was a MATH POETRY Contest -- and details and resources are listed at this link.  An article offered there has the title "Maths and Poetry:  Beauty is the Link" -- an article by Peter Lynch, (emeritus professor at University College of Dublin's School of Mathematics & Statistics) published in 2019 in The Irish Times and available at this link.   Lynch also has a blog, That'sMaths.  The Irish Times article is available in his blog and he has a second posting about poetry entitled "Patterns in Poetry, Music, and Morse Code" -- it's available here.

     And today I also am thinking back to "Number Theory" by mathematician-poet Olga Taussky-Todd (1906-1995); I first posted it at this link in November of 2014; here are several of its lines.

       Number theory is like poetry
       they are both of the same kind
       they start a fire in your mind.
       Number theory is not just clever and smart
       it has a beauty that fills your heart.

A(nother) blog that celebrates Math-and-Poetry

      Recently I have come to know another strong advocate of math-poetry connections.  Marian Christie (read about her here) has had longtime interest in both mathematics and poetry and her blog -- available at  https://marianchristiepoetry.net/ -- explores topics that include "Poetry and Fractals," "Poetry and Number Sequences,"  "Poetry and Permutations," . . . reflection symmetry and square poems and Fibonacci poems . . .. and lots more.  Allow yourself time to explore when you visit https://marianchristiepoetry.net/. 

     When I am working with a group of students are nervous about their ability to write a poem, I often start by asking them to write a Fib, because it starts with single syllables,  In her posting about Fibonacci poems, Christie offers this simple     example of how the Fib structure can lead you to a poem. 
               I
               like
               playing
               with patterns
               in crochet, music,
               poetry and mathematics.

If you are new to Fibs, try this CHALLENGE: using the same first two lines as Christie used above, create a Fibonacci poem.  And then another ... and another.

Global Math Week -- in 2021, October 10-16

      The week of October 10-16, 2021 has been proclaimed as GLOBAL MATH WEEK 2021.  At this link is offered a list of math-celebration activities -- and these include creation of a poster which begins:

            MATH IS  . . .  

In response to this I recall a quote from physicist Albert Einstein (1879-1955):  

          "Pure mathematics is, in its way, the poetry of logical ideas."

More of my views about the similarities
between math and poetry are available here.

STEM Writing Contest for ages 11-19 (NYTimes)

A recent item from The Learning Network in the New York Times announces their 3rd annual STEM Writing Contest -- with submission dates, Feb. 2 - March 9, 2022.   The Times states:

We invite students to choose an issue or question in science, technology, engineering, math or health, then write an engaging 500-word explanation.

Students aged 11 to 19 anywhere in the world attending middle or high school can participate.  Here is a link to contest submission information.

And, perhaps some engaging explanations will include a few words of poetry!

Presenting Gauss in Verse

     German mathematician Karl Friedrich Gauss (1777-1855) is one of history's most prolific and influential mathematicians -- and he is interestingly described in the following acrostic poem. 

 K arl Friedrich Gauss       by Stuart J, Silverman

A puzzle, that his brash genius often shrank,
R eluctant to publish? Hardly. The fact is he
L ingered, perfecting this or that theory
F orged in the heat of his private think tank.
R eworked his proofs until some thought they stank.
I nside and out, of misplaced purity.
E ntered the ages, one of a company
D ecidedly small -- not its only crank.
R ancor and jealousy, admittedly touched him,
I mpelled the pettish note to Bolyai,
C ruelly sent, perhaps on a whim,
H ead and heart each going its separate way.
G ranted the meanness, vanity, display,
A ll such human failings, what he worked would change
U nder his hand to the gold of a new day.
S ettled into its fame, his thought would range
S ecurely through the numinous and strange.

This poem by Silverman is on my shelf in the collection Against Infinity:  An Anthology of Contemporary Mathematical Poetry, edited by Ernest Robson and Jet Wimp (Primary Press, 1979).  This collection is out of print but copies may be located here at bookfinder.com.  

What are the COSTS of GENIUS?

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.