Wednesday, January 26, 2022

Keep Exploring . . .

     In addition to its published magazine, Scientific American has a large variety of blogs.  One of my favorites was Roots of Unity by mathematician Evelyn Lamb.  The blog -- with several hundred postings -- adds to the also-frequent articles that Lamb has contributed to that magazine,  In her posting, "What T. S. Eliot Told Me about the Chain Rule," she quotes these lines from "Little Gidding" by T. S. Eliot (published in Eliot's 1966 collection, Four Quartets) and discusses the outcomes of difficulty and confusion coupled with curiosity, energy, and persistence -- frequent ingredients of the process of learning new mathematics.

     from Little Gidding     by T. S. Eliot (1888-1965)

       We shall not cease from exploration
       And the end of all our exploring
       Will be to arrive where we started
       And know the place for the first time.

Read more at Lamb's blog posting, "What T. S. Eliot Told Me about the Chain Rule."

Thursday, January 20, 2022

Celebrating mathematics with song . . .

     Some of the most memorable links between mathematics and the arts are found in song-lyrics.  For example, "That's Mathematics" by retired American musician, singer-songwriter, satirist, and mathematician   Tom Lehrer (now aged 93):  Here is the opening stanza (the complete lyrics are found at this link):

    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!             More mathy lyrics (by Lehrer and others) are found here.

     A current math educator offers us lots more lyrics to learn from and enjoy; from Larry Lesser -- a professor at the University of Texas in Austin -- is a long-time creator of math-music works.  Here's a link to a list.

 This blog also has previously published lots of Lesser's fine work; here's a link.

Monday, January 17, 2022

Eyes on the Prize

     Today, the 3rd Monday in January, we celebrate the birthday of civil rights leader, Rev Martin Luther King, Jr,, (1929-1968) -- and I have been refreshing my memory of his courageous activity by watching episodes of the award-winning television series about civil rights struggles in the US, "Eyes on the Prize."

Here, in King's words (from his 1957 book, Stride Toward Freedom):

       If
       you
       can't fly
       then run, if
       you can't run then walk,
       if you can't walk then crawl, but what-
       ever you do you have to keep moving forward . . .

Download of a pdf of Stride Toward Freedom is available here.
    Previous postings in this blog featuring Martin Luther King may be found here.

Thursday, January 13, 2022

+ plus magazine . . . living mathematics

     One of the very fine sources of interesting and new ideas from mathematics is +plus magazine -- available since 1997 from the University of Cambridge --  at this link.  Way back in 2010 they featured a Fib from this blog (at this link) and they have been generous in their mentions of Strange Attractors:  Poems of Love and Mathematics (A K Peters/CRC Press, 2008), edited by Sarah Glaz and me.  They also have introduced (at this link) a wonderful collection of scientific Haiku (SCIKU  Icon Books, 2014) -- edited by Simon Flynn, written by students at the Camden School for Girls.  Here are two samples from that collection:

          Gravity

               An attractive force
               Between all objects with mass
               Just like you and me.

          Dissolving confusion


               To some, solutions
               Are answers; to chemists they
               Are still all mixed up.


Enjoy exploring this innovative online mathy magazine.

Tuesday, January 11, 2022

Write to learn ... follow constraints ... find poems

     Some people (myself included) take lots of notes during a lecture or other program -- for it seems that the physical activity of placing the words on the page is part of the process of installing the ideas in memory.  For me, also, the creation of a paragraph or a poem depends on the teamwork of hands and brain.

     One of the ways that poets engage themselves in creating new thoughts is by accepting the guidance of formal constraints -- creating the fourteen lines of a sonnet or the nineteen lines of a villanelle with strict patterns of rhythm and rhyme and repetition.  Below I consider the question of what I want for my birthday  --  and use that in my struggle to write a sonnet:

You asked me
      for a birthday gift suggestion . . . 
by JoAnne Growney    

Thursday, January 6, 2022

Mathematics gives our world its shape . . . fractals

     Poet Robin Chapman and Julien Clinton Sprott both were professors at the University of Wisconsin-Madison when their art-poetry collection  Images of a Complex World -- The Art and Poetry of Chaos first appeared (World Scientific Publishing, 2005) -- and now both are emeritus professors: Chapman in the Department of Communication Studies and Disorders and Sprott in the Department of Physics.  Here is one of the poems from that collection: 

          Bifurcations     by Robin Chapman

           This is the path that pitchforks
           in the yellow wood -- the one
           where you wanted to travel both,
           science and poetry,
           physics and art,
           and so bounced unpredictably back and forth,
           taking each as far as you could.

Notes:  The pitchforking path in the opening lines draws my thoughts to Robert Frost's poem, "The Road Not Taken." A bifurcation is, in general, a division of a structure into two parts. But when it happens over and over, things might change from patterned to chaotic . . .  Here is a link to earlier postings in this blog on fractals and chaos; here is a link to previous postings of poems by Robin Chapman.  This link leads to discussion of "bifurcation" at WolframMathWorld.  On page 82 of the art-poetry collection by Chapman and Sprott is this comment about the term:  There are dozens of different types of bifurcations, and they represent an active area of current research.  Below (and appearing on page 83 of the collection) is the following illustration:

In the preface to Images of a Complex World -- The Art and Poetry of Chaos, Sprott describes his process of choosing mathematical patterns and colors that would appeal to the human eye and Chapman offers insight into the inspirations for her poems.

Monday, January 3, 2022

India's National Math Day -- Poetic Quotes

     A recent math holiday that I remembered after it had passed is National Mathematics Day in India -- held on December 22 and celebrating the birth anniversary of Indian mathematician Srinivasa Ramanujan (1870-1920).   (An interesting math-item from India is the claim that the first recorded use of zero occurred there.)

     Ramanujan is celebrated in a poem by Jonathan Holden.  Its opening lines: 

Holden's complete poem is found here in this posting from 2/19/2011.

Friday, December 31, 2021

Year-end Counting -- with Gratitude

     Year
     ends.
     I count --
     and count on --
     mathy poems shared
     here by countless poets. THANK YOU!

Monday, December 27, 2021

Amid uncertainties -- compose a Fib

How many Corona-virus cases will the new year bring?

Stop,
Think!       
Wonder
What to say . . .
I gather my thoughts
and hope I can make a poem.

Monday, December 20, 2021

Christmas is coming . . .

     This morning I did a blog search to see which of my previous posts included the word "Christmas" -- and this link leads to the results.  And, for me as for many, a very familiar favorite (also posted back in December 2015) -- linking Christmas and numbers -- is this:

This Wikipedia link offers some history of this song.

Wednesday, December 15, 2021

One-sentence Poems

     Recently I came across the website onesentencepoems.com and, enjoying the items' brevity, I did some browsing -- and term-searching -- looking for mathy poems.  Here are two samples by teacher and poet Jeffrey Park -- originally from Baltimore, now a teacher in Germany.

By Degrees   

She always sleeps with protractor and compass
on the bedside table, never knowing when
a sudden fit of geometry will strike in the night.

Numeric

Numbers pelt down from an infinite sky, neither irrational nor imaginary,
the angular ones, 4s and 7s, doing maximum damage.

These one-sentence poems -- and another --  by Jeffrey Park are found online here.

Monday, December 13, 2021

Mathematician with the Soul of a Poet

      One of my long-time math-poetry connections has been with math-teacher-artist-writer Sandra DeLozier Coleman (This link leads to her prior appearances in this blog.)  Coleman has had a long-term interest in the Russian mathematician-and-poet Sofia Kovalevskaya (1850-1891) and has recently published Mathematician with the Soul of a Poet -- Poems and Plays of Sofia Kovalevskaya  (Bohannon Hall Press, 2021, available here from amazon.com); this volume that contains Coleman's translations from Russian along with background and thoughtful commentary.  The opening section of the book begins with these words from Kovalevskaya:

     I understand that you are surprised I can work at the same time
     in both literature and mathematics.  Many who have not had the 
     chance to learn more about mathematics confuse it with arithmetic
     and consider it to be a dry and arid science.  In truth, however,
     this science requires the greatest imagination, and one of the most
     respected mathematicians of our century has very rightly said
     that it is not possible to be a great mathematician without having
     the soul of a poet.                                                     S V. Kovalevskaya

Thank you, Sandy Coleman, for sharing Kovalevskaya's words with us!

Wednesday, December 8, 2021

STEM Writing Contests -- reminders . . .

WRITING deepens UNDERSTANDING!

For the reason above -- and for the possibility of winning recognition and prizes --  please consider the following contests.

The NYTimes has announced its 3rd annual STEM Writing Contest -- information is found here and 500-word submissions are invited during the period Feb 2-March 9, 2022.

To increase awareness of women’s ongoing contributions to mathematics, the Association for Women in Mathematics and Math for America are cosponsoring an essay contest for biographies based on interviews of math-women working in or retired from mathematical careers. The contest is open to students in Grades 6–8, Grades 9–12, and Undergraduate.  For more information, please visit the contest webpage or  contact the organizer, Dr. Johanna Franklin, at johanna.n.franklin (at) hofstra.edu.   The submission deadline is February 1, 2022.

Monday, December 6, 2021

Stories of Quadrilaterals

     Sometimes I have time to browse my shelves and rediscover old favorites.  Several of this blog's much-read poems have come from Scottish author Brian McCabe (Find blog search results at this link) -- and below I offer the first part of McCabe's two-part poem ("Two Quadrilaterals") entitled "The Restless Square."

Two Quadrilaterals    by Brian McCabe

     Part 1.  The Restless Square  

          There was a square who yearned
          to become something else.

          It stretched its legs to mimic
          an elegant rectangle but
          lost its balance, leaned over
          in a perilous parallelogram.    

Thursday, December 2, 2021

Divided -- for facial recognition

Recently-retired Virginia dentist Eric Forsbergh sent me a mathy poem about the fascinating -- and controversial  -- process of facial recognition.   Enjoy!

      Divided                                                 
                  Data-driven approach divided the face into 63 segments.
                                                                Nature Genetics, Jan. 2021

       This, you can’t refute:
       How data banks embed us.

       Graphics now drag anyone
       into granularity. As if
       the features of a wave drew back
       to reveal a pebble beach.

Tuesday, November 30, 2021

Art / Poem / Numbers (posted 7/14/13, then lost)

     Recently I discovered a typo in my posting on July 14, 2013 of "Poem 25" by Kurt Schwitters.  My attempt to fix my typo led to accidental deletion of that post and so, I offer again this diagram-poem.  The poem -- IS THIS REALLY A POEM? --  appears in Numerals: 1924 - 1977 -- gathered by Yale Professor of Art History Rainer Crone (1942-2016), published 1978 by the Yale University Art Gallery. 

Poem 25 (elementary)     by Kurt Schwitters, 1923


A final comment -- when I read this "poem" aloud, I like the sounds of the words!

Monday, November 29, 2021

Sometimes ONE is also TWO

     A long-time supporter of this blog and of math-poetry connections is Gregory Coxson, Research Engineer at the US Naval Academy-- and he has recently shared with me the following poem, a translation of work by German writer and scientist Johann Wolfgang von Goethe (1749-1832); publication and translation details may be found online here.  Coxson was drawn back to his memories of this math-linked poem with the arrival of November and at his campus the bright-yellow leaves of the ginkgo trees.

     Ginkgo Biloba      translation of work by Johann Wolfgang von Goethe

       In my garden’s care and favour
       From the East this tree’s leaf shows
       Secret sense for us to savour
       And uplifts the one who knows.

       Is it but one being single
       Which as same itself divides?
       Are there two which choose to mingle
       So that each as one now hides?

       As the answer to such question
       I have found a sense that’s true:
       Is it not my song’s suggestion
       That I’m one and also two?

More about Goethe's poem can be found here at WisdomPortal.com.

Monday, November 22, 2021

Equation Poetry

     The term "Equation Poetry" is the title of an article by Radoslav Rochallyi  -- and posted on 11/9/ 2021 here in the MATH VALUES blog.  Rochallyi is a poet, essayist, and interdisciplinary artist living in Prague, Czech Republic and author of eight books of poetry.   For Rochallyi, "mathematical" poetry is not poetry about mathematics but poetry whose form is determined by a mathematical rule. 

     For example, he uses the formula for the area of a circle --  a = π r²  --  to form this example of Equation poetry:

     And, from the binomial formula,    

if we let x = time, a = being, n = now, and k = know -- our binomial formula becomes this poem:
 
Visit Rochallyi's article at this link to learn lots more. 
 

Thursday, November 18, 2021

MANIFOLD: Poetry Inspired by Mathematics

     One of my recent pleasant pastimes has been spending time with MANIFOLD:  Poetry of Mathematics  by E R Lutken.   This poet's experiences prepare her well for merging different points of view -- a Southerner from a family that loved learning, Lutken became a family physician who spent years on the Navajo Nation AND then became a teacher of science and mathematics.  Read more about Lutken and MANIFOLD here.  

The "luc bat" is a Vietnamese poetic form that means "six-eight" -- 
Lutken's poem consists of alternating lines of six and eight syllables.

         Ars Parabola     by E R Lutken

Luc Bat for Horace and MacLeish  
       
          Can’t say what a poem is or not
          but graph it and the plot
          might trace that perfect spot for one
          whose vertex taps the sun:
          abscissa makes a run from rhyme
          to none and metric time
          devolves from frozen symmetry.
          Equal distance of free
          line and focal point defines sure
          sense, logic’s stare obscured
          as symbols play in pure sound’s bright
          flare. White-hot words ignite
          a sharp savor, the bite, the risk,
          an ordinate of bliss.

"Ars Parabola" is from MANIFOLD, by E R Lutken, 3: A Taos Press, 2021,  presented here with permission of 3: A Taos Press and the poet.  The poem first appeared in Welter Literary Journal.

Tuesday, November 16, 2021

Aelindromes -- and Pi

     On Twitter, I have seen frequent posts by UK-based writer Anthony Etherin -- and, encouraged by mathy poet Marian Christie, I have found it interesting to explore his work.  Etherin focuses on constrained, formal, visual, and experimental poetry -- he tweets @Anthony_Etherin; he manages Penteract Press.  AND  Etherin has invented a new type of writing-constraint called the aelindrome -- a bit like the palindrome ( such as  top spot  or  never odd or even ) except that the reversals involve more than one letter.   Here is a simple example of an aelindrome: 

melody, a bloody elm  which can be divided into   m el ody ablo ody el m

Found in a Twitter posting by @Anthony_Etherin on 10/21/21 is this aelindrome whose segment-lengths follow the first 14 digits of pi;  31415926535897

       Moonless Moonlight        by Anthony Etherin

       Low, fatal nights! Late, moonless.... Tense, we glitch.
       We swim bled sky, along the ashy glow.
       Shy glow along the ambled sky, we switch.
       We glisten -- see slate moonlight's natal flow.

Go here to learn more of Anthony Etherin and his work.

Wednesday, November 10, 2021

After loss we have nothing--which is something ...

     A poet whose work I much admire is A. E. Stallings -- born in the US, in Georgia, but now living in Greece.  This poem -- a sonnet -- deals with the paradox that nothing is something -- as with the integer zero and with the absence of a loved one.  The poem was written for her father who taught statistics at Georgia State University.

     Sine Qua Non     by A. E. Stallings

       Your absence, father, is nothing. It is naught—
       The factor by which nothing will multiply,
       The gap of a dropped stitch, the needle's eye
       Weeping its black thread. It is the spot
       Blindly spreading behind the looking glass.
       It is the startled silences that come
       When the refrigerator stops its hum,
       And crickets pause to let the winter pass.

       Your absence, father, is nothing—for it is
       Omega's long last O, memory's elision,
       The fraction of impossible division,
       The element I move through, emptiness,
       The void stars hang in, the interstice of lace,
       The zero that still holds the sum in place.

"Sine Qua Non" is found in Stallings' collection Hapax (Northwestern University Press, 2006) and also in the anthology Strange Attractors:  Poems of Love and Mathematics (AK Peters/CRC Press, 2008).

 A wonderful collection of Stallings' poems is available at the PoetryFoundation website -- and more about this poet and her work is may be found here at her at Stallings' website.

Monday, November 8, 2021

A Hundred Thousand Billion Poems

 Celebrate Raymond Queneau (1903-1976).

     In a recent posting, mathy blogger Ben Orlin noted (here in Math with Bad Drawings)  that 2021 is the 60th anniversary of an amazing poetry collection, One Hundred Thousand Billion Poems, by Raymond Queneau.  The collection consist of 14 sonnets, with each line of each sonnet on a separate strip of paper -- allowing formation of a poem using any of the 14 first lines, any of the 14 second lines, and so on.  Here is an link to a earlier blog posting that introduces Queneau's collection and includes and interactive way to create a sonnet from the collection.

Here is a link to other postings from this blog that include Queneau.

Wednesday, November 3, 2021

Enjoy the Possibilities in a Multiple-Choice Poem

     Just as a test-taker mulls over which answer is correct, a poet mulls over word choices and what should come next.  South Dakota mathematician-poet Daniel May (professor at Black Hills State University) has broadly captured these decision choices in a poetry-form called a Digraph Poem or a Multiple Choice Poem.  I first learned of this idea several years ago at a Bridges Math-Art Conference at Waterloo, Canada when May and a colleague, Courtney Huse Wika, presented a paper entitled "The Poetics of a Cyclic Directed Graph" (available online here in the Bridges Archives).   In this paper is a poetry-creation by Huse Wika that involves various choices and orders of stanzas.

    This mixing of stanzas came to my attention again via a paper by May entitled "In the beginning all is null" which appeared in Journal of Mathematics and the Arts, Volume 14, Issue 1-2 (2020) as one of a group of "artist's statements."  In this latter paper, May thoughtfully describes his process of composing his poem --  he composed eight eight-line stanzas -- and the reader was to read a stanza, choose and read another stanza, and so on with a third.  In all, eight poems -- each sharing stanzas with others. 

     Recently a new online multidisciplinary journal, Poetrishy, has been born -- and it's first issue features another Multiple-Choice/Digraph poem by Dan May entitled "What the Body Does Next" --and available here.   Although you will need to follow the link I've offered to actually read the poem, I offer below a small screen-shot  -- so that you can get a sense of its structure.

Issue 1 of Poetrishy also contains work by these mathy poets -- Larry Lesser, Marian Christie, and  Marion Deutsche Cohen.  And several more authors whose work is fun to explore.

Monday, November 1, 2021

Interview a Math Woman -- then Write and Win . . .

     Amalie "Emmy" Noether (1885-1932) is one of the outstanding mathematicians of all-time -- and yet, during her lifetime she got very little of the recognition that she deserved.

Consider these lines:
          Today history books proclaim that Noether
          is the greatest mathematician
          her sex has produced.  They say she was good --
          for a woman.    
 
              a stanza from my poem "My Dance is Mathematics"

In the past, people both inside and outside of mathematics have discriminated against women and minorities -- but the Association for Women in Mathematics -- AWM -- works to change that.   One of their activities to increase awareness of math-woman and their achievements is an annual essay contest.

Here is this year's announcement:

To increase awareness of women’s ongoing contributions to mathematics, the Association for Women in Mathematics and Math for America are cosponsoring an essay contest for biographies based on interviews of women working in or retired from mathematical careers. The contest is open to students in Grades 6–8, Grades 9–12, and Undergraduate.    For more information, contact the organizer, Dr. Johanna Franklin, at johanna.n.franklin@hofstra.edu or see the contest webpage at
https://awm-math.org/awards/student-essay-contest/.   The deadline is February 1, 2022.


Wednesday, October 27, 2021

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!

Monday, October 25, 2021

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.

Wednesday, October 20, 2021

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.

Monday, October 18, 2021

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.

Wednesday, October 13, 2021

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.


Monday, October 11, 2021

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.

Tuesday, October 5, 2021

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!

Monday, October 4, 2021

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?

Wednesday, September 29, 2021

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 

Monday, September 27, 2021

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.

Wednesday, September 22, 2021

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.

Monday, September 20, 2021

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.

Wednesday, September 15, 2021

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 is 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! 

                                                               *   *   *

Monday, September 13, 2021

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.

Wednesday, September 8, 2021

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.

Monday, September 6, 2021

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.

Tuesday, August 31, 2021

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).



Monday, August 30, 2021

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.

Wednesday, August 25, 2021

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.

Monday, August 23, 2021

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.

Wednesday, August 18, 2021

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!

Monday, August 16, 2021

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

Friday, August 13, 2021

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. 

Monday, August 9, 2021

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). 


Tuesday, August 3, 2021

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.

Saturday, July 31, 2021

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

 

Friday, July 23, 2021

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.