From an engineer who loves poetry . . .

João Augusto Sampaio is an Environmental and Civil Engineer who loves poetry; here is a sample:

by João Augusto Sampaio

 

Sampaio has let me know that he is on Instagram using @jota_sampa;  for another aspect of his work, this link leads to his lovely "visualizing math" posting of Ulam's Spiral, showing the distribution of primes. 

Voting and being counted . . .

      A story in the KIDSPOST section of today's Washington Post offers a reminder that 100 years ago today -- on August 18, 1920 --  the 19th Amendment to the US Constitution was officially ratified -- extending the right to vote to women.
      Here is a link to a poem by Evie Shockley,  women’s voting rights at one hundred (but who’s counting?) -- and, below, a few lines from that important poem:

           * * *
     one-mississippi
     two-mississippis

          * * *
     one vote was all fannie lou
     hamer wanted. in 1962, when
     her constitutional right was
     over forty years old, she tried
     to register. all she got for her
     trouble was literacy tested, poll
     taxed, fired, evicted, & shot
     at. a year of grassroots activism
     nearly planted her mississippi
     freedom democratic party
     in the national convention.

          * * *
For additional postings related to math and women and voting, here is a link to the results of a blog Search using the terms women and vote.

Heart Arithmetic

      During these days of protest and politics and pandemic, a diversion -- some playful thoughts about LOVE from poet Carl Sandburg (1878-1967).

        How Much?     by Carl Sandburg

       How much do you love me, a million bushels? 
       Oh, a lot more than that, Oh, a lot more. 
  
        And to-morrow maybe only half a bushel? 
        To-morrow maybe not even a half a bushel. 
  
        And is this your heart arithmetic?
        This is the way the wind measures the weather.

 

Poems can help us teach/learn mathematics . . .

     With increasing awareness of the value of integrating the arts in science and mathematics (expanding STEM to STEAM), numerous teachers are sharing their experiences of what works.  Here, from the archive for BRIDGES 2020, is "Poetry in the Lesson of Mathematics"-- an article by Natalija Budinski and Zsolt Lavicza that describes a series of mathematical poetry activities for math and science students.  Here's a sample of student lines (by F.T.):

           Because when you practice math a lot,
           it almost always pays off.

Another article "Enrich Mathematics Discussions with Poems" (written by me and available here) suggests class-inclusion of poems about the nature of mathematics and its history, the lives and contributions of mathematicians -- including the work of women and minorities -- and similarities between mathematics and poetry.  Discussion of student attitudes -- from excitement to math anxiety -- often can be facilitated by discussion of a poem; the article offers suggestions.  

To find a host of additional poetry samples, 

the blog Search offers a way to find poems on a topic of your choice.

Celebrate the Journal of Humanistic Mathematics

     Recently Vol.10, No.2 of the online Journal of Humanistic Mathematics has become available online.  This issue is a "Special Issue on Creativity in Mathematics" and the richly varied Table of Contents is available at this link.

Seven of the articles feature poetry with links to mathematics; these are:

     Poetry Folder:     Mental Logic: Two Poems     by Ashley Delvento
                           Natural by Design     by Craig Steele

     Poetry:         four seasons (haikus)     by Stephen Luecking
                    Dear Arithmetic     by Mary Soon Lee
                    Galileo's Verse     by Bruce F. McGuffin
                    Hexagons     by Barbara Quick
                    Changes and Deltas     by Jim Wolper

And here are a couple of samples: 

Point of Inflection -- and the coronavirus

     In the UK, the Radical Statistics Group describes itself as "using statistics to support progressive social change."  The June 2020 issue of their Journal -- Issue 126  -- is a "Coronavirus Special Issue" and it contains a poem by Texas professor-poet Lawrence Lesser.  Here are the opening stanzas.

     The Point of Inflection       by Lawrence M. Lesser

     The point of inflection
     is where towering terror of
     cumulative cases
     finally
     slows its rise.   

Census . . . correct counting is not easy. . .

     One of the challenges of applying mathematics is doing it correctly.  Each of us has a limited view, often affected by biases such as racism and sexism. And Covid-19 concerns have further-limited our access to accurate information in situations such as counting election-ballots or counting all Americans for the 2020 census.  The following thoughtful poem, "Census," is not new; it was first published in 1981.  What does it show us about counting?

     Census     by Carol Muske-Dukes

     Here's how we were counted: 
     firstborn, nay-sayers, 
     veterans, slow-payers, 
     seditionists, convicts, 
     half-breeds, has-beens, 
     the nearly defined dead, 
     all the disenfranchised live.

Prove it . . .

This post's title "Prove it" occurs several times within the poem,

DREAMers Mark Themselves     by Maricielo Ampudia Gutiérrez,

a poem (found here, followed by an author bio) that arrived in a recent e-mail from the socially-engaged poetry group, Split This Rock -- and I have been reflecting on its use of the term "prove it" as compared with mathematical usage.  The poem by Gutiérrez is included in a rich poetry database maintained by Split this Rock.

     One of the editors of the online journal Better Than Starbucks, Joseph E. Petta, has let me know of his liking for poems with links to mathematics and encourages submissions.  Petta's "Experimental & Form Poetry" section of the July August 2020 issue contains a thoughtful a thoughtful matrix poem, a word-prison:

Freedom        by Stuthi Iyer

Both of these poems offer ideas for thoughtful contemplation -- for math people and for others!

A favorite recursion . . .

      memories bring back

            memories bring back

                   memories bring back  

                          memories bring back

                                 memories . . .
          

Finishing halfway . . .

     Recently I have enjoyed thinking about the poem "Bunny Slope" by Polish poet Tadeusz Dabrowski (found here in The Paris Review, Issue 219, Winter 2016) and offered below.

     When I write a poem, the first draft often is the longest -- I spill words onto the page and then attempt to edit out what does not need to be said.  When I read poetry, I like it when the poem does not "tell all" but offers a framework for my discovery.

Bunny Slope      by Tadeusz Dabrowski

                                   (translated from Polish by Antonia Lloyd-Jones)

     When I’m writing a poem,
     there’s less and less of it.

     As I approach the mountains,
     they vanish behind a gentle hill,
     behind the bunny slope. 

Math-Arts Connections -- links to rich reading . . .

     The Table of Contents for the  latest issue of the Journal of Mathematics and the Arts offers titles for a rich array of "Artists Viewpoints" -- brief articles (assembled under the leadership of Guest Editor, Susan Happersett) in which artists who link mathematics with various genres talk about their views and processes.  (Access to these articles currently is FREE -- through 2020.)

     One of the 53 artists' viewpoints contained therein is mine, and here is a permanent link to that brief article ("Everything Connects") that links my mathematics and poetry.  Another math-poet whose work is featured is South Dakota mathematician Dan May, whose article "In the beginning all is null" features multiple-choice poetry.

Poetry contest winners --- π-ku

     The website Aperiodical.com is described as "a meeting-place for people who already know they like maths and would like to know more"  -- and one of its organizing forces is Katie Steckles.  Several weeks ago, Katie initiated a  π-ku poetry contest -- looking for 3-line submissions that follow the digits of the π-approximation 3.14.

          For example,      Green grass and
                                blue
                                sky and sun's heat.
                                                                      In π-ku
                                                                      I
                                                                      shrink what I think.

The numbers 3, 1, and 4 also may -- instead of counting syllables -- count words.

                  Today in July
                  sunshine
                  pushes the temperature skyward.

To enjoy the winning results in the Aperiodical π-ku contest, go here.  

 

A thoughtful Fibonacci poem

     An email message from Washington, DC poet and blogger Karren Alenier alerted me to this mathy Fibonacci poem found online in the Summer 2020 Issue (#36) of The Fib Review.  The poet., Roberto Christiano, has given me permission to offer it to you here.

the irrational   by Roberto Christiano

irrational
numbers
c'est moi?
a number that
cannot be expressed by the
ratio of two integers / and what's an integer?  

Math-Poetry for a virtual BRIDGES Conference

     Due to the COVID-19 pandemic this year's 2020 Bridges Math-Arts Conference will not be held.  One of the regular events at this international conference has been a poetry reading organized by mathematician and poet Sarah Glaz.  This year, Glaz has prodded math-poets to develop on-line videos of their poems and offers a wonderful program of poetry here at this link.  (Brief poet-bios and links to more info about each are also found at the preceding link.)

Participating poets, with links to their poetry videos are: 

Sarah Glaz,  Tatiana Bonch-Osmolovskaya,   Robin Chapman,  Marian Christie,  Carol Dorf,  Susan Gerofsky,  Emily Grosholz,  Gizem Karaali,  Lisa Lajeunesse,  Marco Lucchesi,   Alice Major,   Mike Naylor,   Eveline Pye,  Stephanie Strickland,  Ursula Whitcher,

Marion Cohen,   Maria Mannone reads Federico Favali's poem,   JoAnne Growney    Hedy Hempe,   Philip Holmes,    Lawrence (Larry) Lesser,  Kaz Maslanka,  Daniel May,   Iggy McGovern,   Tom Petsinis,   Susan Sulic.

Thank you, Sarah Glaz, for organizing and presenting all of this poetry!

We look forward to the forthcoming BRIDGES 2020 Poetry Anthology

Wonderful math-poetry . . . in lots of online places

      Carol Dorf, poetry editor of the online journal, TalkingWriting, has been sharing (during the pandemic) daily poems via e-mail -- and occasionally they are a bit mathematical.  For example, "Morning Song" by Sawako Nakayasu (found here at Poets.org) has this opening line . . . .

     Every time, these days, it seems, an equation gets forced.  . . .

At Poets.org, as at many poetry websites, there is an opportunity to search -- using, for example, "geometry" or "equation" -- and to find lots of poems with mathematical connections.

     Carol Dorf is a retired math teacher and a wonderful poet;  this link leads to poems from her published in this blog and this link leads to "Wild Equations,"   a collection of some the mathy poems found in TalkingWriting.

     An ongoing source of original and delightful math-poetry is the Journal of Humanistic Mathematics.  Visit often and explore! 

AND, one more item . . .  Recently I revisited Issue 17 (Released November 1, 1917)  of The Cordite Poetry Review which has the theme "Mathematics."  That issue is online here.  Many of the poems seem at first quite distant from the theme -- but browsing the collection of 60 poems (selected by Fiona Hile) has proved thought-provoking.  Here is a sample, "Venn Diagram" by Caroline Williamson.

Life Lessons in Math and Rhyme

     One of my former colleagues at Pennsylvania's Bloomsburg University is statistician Reza Noubary.  This Iran-born mathematician has a love of poetry as well as mathematics and here are a few lines from his recent collection, Feelings and Dealings (Archway Publishing, 2020).

                    In a math book there is wisdom.

                    In a theorem there is a kingdom.

                    No solution can be made up or faked.

                    The reasoning buys you freedom.

There is a secret in every equation that provokes curiosity and passion.

To uncover it we need to see its beauty and realize

its worth to complete the mission.

The outcome is refreshing; it always results in long-term compassion.

It is satisfying as participants understand its

logic and its beautiful expression.

Thank you, Reza, for these words.

 

Independence . . .

     Tomorrow, July 4, the US celebrates "Independence" Day and I am reflecting on the following quote by Albert Einstein (1879-1955):

     How can it be that mathematics, 
     being after all a product of human thought 
          . . . independent of experience, 
     is so admirably appropriate
     to the objects of reality?

(found here, along with lots of Einstein quotes) 

I am trying to decide to what degree I agree with Einstein's words.

Opening our minds to New Views . . .

     One of the values of study of mathematics is that to make progress we must continually revise our ways of looking at things. (Yes, there can be numbers less than zero . . . Yes, there can be different sizes for infinite sets . . . )  And a challenge for our society today is to carefully reconsider our racism.   Recently the American Mathematical Society's Blog On Math Blogs has offered this thoughtful posting, "What does anti-racism in mathematics look like?"  
     From visual poet Karl Kempton (who celebrates a birthday today) I offer a visual-poetry reminder of multiple ways of viewing a situation -- illustrated by two views of dividing the number 8.

For more ways of looking at 8 and other mathematical poems by Kempton, go here.

Considering opposites . . . and finding union . . .

     The categorization of different points of view as opposites can disappear as a unified system embraces both of them.  In mathematics, the counting numbers and their opposites become the integers,the rational and irrational numbers join to give the reals, the real and imaginary numbers yield the complex numbers.  In our global world with its biases and dangers and uncertainties, we will, I hope, evaluate our differences and unite our strengths to form a larger, stronger unity.
     A syllable-square poem by Carmela Martino (offered below) illustrates one of the unifications that can benefit our society: inclusion of the arts to enrich the sciences, from STEM forming STEAM.

Carmela Martino's poem first appeared here at TeachingAuthors.

Math-poetry in The Mathematical Intelligencer

     In a recent e-mail, this message:  "The Mathematical Intelligencer. Vol. 42 No. 2 is now available online."  Most Intelligencer articles require a subscription or a fee-payment but one that is freely available to all of us is the poem, "Pandemic Math:  X and Y Axes" by Wisconsin painter and poet Robin Chapman.  Here are its opening lines:

          I'm thinking of those graphs we anxiously scan each day
          carry news of infection's spread, asking if we
          will find death stalking our neighborhoods . . .

Chapman's complete poem is available here.  

Counting on ... and on ... BLACK LIVES MATTER!

     In these days of learning to recognize the racism and racial injustice that has gone on in the United States for SO LONG I am reminded of a poem, "Learning to Count" by Romanian poet Nichita Stanescu (1933-1983) (posted at this link back in 2011), a poem that captures the horror of barbarianism.

     Learning to count     by Nichita Stanescu                   
                        
     Hairy and sweaty sit                            
     the barbarian Hittites.       
     Learning to count they pull from corpses
     fingers, legs, arms, eyes.                                    
     Oh, divided ones,    
     how bloody              
     is the idea of having ideas!  

Principles of Accounting -- in verse!

      Quarantining has turned poetry readings into Zoom events -- and that brought Pennsylvania poet Barbara Crooker to my computer a couple of weeks ago via a reading sponsored by The Word Works..  A delight for me to reconnect with someone whom I knew from my years in Bloomsburg.  Barbara -- who is a very fine poet one whose work has often appeared on The Writer's Almanac  -- has given me permission to share the following mathy poem (found in her collection, Some Glad Morning, Pitt Poetry Series, 2019).

      Principles of Accounting      by Barbara Crooker

     Nearly summer, and the trees are banking on green,
     calculating their bonuses in numerators of leaves.
     Outside my window, the crows are ganging up
     on someone, thugs in their hoodies of night.
     I'm feeling the number of days begin to feel finite,
     no longer uncountable as blades of grass. 

Everybody counts -- Axioms for diversity

Found here in the 2016 Notices of the American Mathematical Society --

these words that are mathematical, poetic AND important!

 

Unconscious(?) bias

       Wherever she goes
       there is mathematics --
       but THEY don't call
       her a mathematician . . .  
                                       SHE
       is a girl
       or a woman,
       a teacher,
       a student 
                    or perhaps
       a scholar,
                    maybe 
       an aspiring poet . . .
  

Learning from Copernicus

     These days are challenging ones -- HOW can we live safely?  How can we live morally? How can we learn that none of us is the center of the universe?
     Today, read the poetic words of Paul Tran and consider these questions.

     Copernicus   by Paul Tran (from The New Yorker, link below)

     Who doesn’t know how
     doubt lifts the hem of its nightgown

     to reveal another inch of thigh
     before the face of faith?

     I once didn’t. I once thought I was
     my own geometry,
     my own geocentric planet

Does nothing exist?

     From Montreal mathematician, poet, and artist Alex Ionut, this highly imaginative poem, "The Empty Set Exists."  -- a poem stimulated by his study of the Euler spiral (clothoid) and a 3-D version that he calls "the spherical clothoid."  

       The empty set exists   by Alexandru Ionut

       To see her would be like touching death
       It's axiomatic, the foundation of any metric
       You love her because she's her

       Double entendre across the stanza
       But her hair, only spirals

       My love for her, pure vector
       Imaginary, hypercomplex
       Unmixed evil, I bow to Lord Kelvin
       Maxwell's demon, my Hamiltonian angel  

Women in Theory -- Math to Give

     The June, 2020 Conference of Women in Theory (of Computer Science) has been postponed to next year.  But these energetic mathy women got together virtually and performed a song.  I offer below the opening stanzas;  for the performance and complete lyrics, follow this link to YouTube.

      I Will Survive   (lyrics by Avi Wigderson (Princeton, IAS)

      At first I was afraid, I was petrified
      I worried I could never fit this proof on just one slide
      But then I spent so many nights 
                     thinking why it is so long
      And I grew strong
      And learned exactly what went wrong

      A problem wor-thy, of attack
      Just proves its worth by vigorously fighting back
      I should have used error correction, 
                     should have sampled yet again
      I should have stayed the course 
                     and found there is so much that I can gain
          . . .

For the YouTube version (with lyrics) of the complete song (8 stanzas), go here.

Which permutation of lines yields the best poem?

     A fascinating article about poet Jericho Brown (by Allison Glock in Garden and Gun magazine) reminded me of the vital role of line-arrangement in creating a poem.  (Emory University professor Brown has won the Pulitzer Prize in poetry for his collection The Tradition  (Copper Canyon Press, 2019)).
      Glock's article, "Jericho Rising," tells of various factors that have influenced Brown's poetry and describes his process of arranging lines, typed on separate strips of paper, into poems.  Three of the lines shown in the article are:

       What is the history of the wound? 

  We'll never see their faces or know their names.      

       And a grief so thick you could touch it.

THE STORY OF MATHEMATICS -- in a poem

     A mathy poem that I have learned about from Carol Dorf (poet and retired math teacher and poetry editor at talkingwriting.com) is "The Story of Mathematics" by poet and teacher Sarah Dickenson Snyder.  Offered below, "The Story of Mathematics" first appeared in the Spring 2020 issue of 300 Days of Sun -- it is a poem for which I have needed (and enjoyed) the challenge of several re-readings, both silent and aloud, to take it in.

     The Story of Mathematics    by Sarah Dickenson Snyder

     ​It starts with a shell –
     its curve and shine,

     the way a line peaks.
     It starts with a star

     and the arc
     between bone and light.

Counting . . . and more counting . . .

     Poet and retired math teacher and poetry editor (talkingwriting.com) Carol Dorf has been staying connected during the covid-19 pandemic by sharing poems.  Many of her emailed shares are works I know, but the item below came as new -- a mathy poem by David Ignatow (1914-1997) from his collection Against the Evidence: Selected Poems 1934-1994. (Wesleyan University Press, 1993).  Consider, with Ignatow, what is finite?  what is countable?

Information     by David Ignatow  

Links to mathy poems . . .

     The Annual Bridges Math-Arts Conference will not be meeting this year but mathematician Sarah Glaz has arranged for lots of math-poetic activity online -- go here and scroll down for links to poetry-presentations that she has arranged.  
     Glaz has gathered a Bridges 2020 Poetry Anthology (not yet published) that contains five of my mathy poems.  I read aloud two of them -- 

"Love Mathematics" and "A Baker's Dozen" -- here on YouTube.  

Thanks to my neighbor, Mark Willey, for help with the YouTube recording!

Doubling and redoubling . ..

     The mathematics of repeated doubling and concerns about COVID-19 have led Virginia dentist and poet Eric Forsbergh to write "A Fable" (offered below): 

     Fable     by Eric Forsbergh

     A child seeks the raja out.

     A grain of rice is held out on the child’s fingertip.
     The child seeks to live, someday to reproduce.

     “I ask this. One grain doubled,
     doubled again, on a chessboard every square.”
     The raja’s not alarmed.
     He sends a soldier out to get a loaded scoop.
     “Maybe a small pail.” he calls out as an afterthought.

A rhyme about a prime

     Tomorrow, May 16, is the birthday of Pafnuty Chebyshev (1821-1894), who was one of the founders of Russian mathematics and the first to prove (in 1850) a conjecture (about positive integers) made in 1845 by French mathematician Joseph Bertrand (1822-1900) and sometimes referred to as Bertrand's postulate.  This rhyming couplet celebrates that conjecture:

               Chebyshev said, and I'll say it again:
               There's always a prime between n and 2n.

Thanks to Evelyn Lamb's AMS Page-A-Day Calendar for its May 10 alert to the info above.

What would I do without NUMBERS?

     Sometimes familiar things that are very important are taken for granted.  Many of us do that with numbers . . . California poet and artist Mary Fabilli (1914-2011) considered their importance in the following thoughtful poem:

     Numbers     by Mary Fabilli

     What would I do
     without numbers?
     A 7 there and a 3 here,
     days in a month
     months in a year
     AD and BC
     and all such symbols

     the track of time

Geometry of a Shadow

     This morning while exercising I listened to an old CD that had been stored with materials I used when involved with the The Children's Museum (in Bloomsburg, PA).  The recording included selections from A Child's Garden of Verses by Robert Louis Stevenson (1850-1894) and as I listened to "My Shadow" I connected it with my blog -- a poem of geometry and mappings.  Here it is; enjoy!

     My Shadow    by Robert Louis Stevenson (1850–1894)
 
     I HAVE a little shadow that goes in and out with me,   
     And what can be the use of him is more than I can see.   
     He is very, very like me from the heels up to the head;   
     And I see him jump before me, when I jump into my bed. 

Squaring the circle . . . or not . . .

     Start with a CIRCLE -- is it possible, using only a straightedge and compass, to construct a SQUARE with the same area as the starting circle?  This problem, posed by ancient geometers, was long believed to be impossible, but not proven so until 1882 when Ferdinand von Lindemann proved that π is transcendental.
     Freelance editor and math-geek Sam Hartburn offers at her website a fun-to-read poem on this topic.  The first stanza is offered below, followed by a link to the full poem text -- and a recording. 

 (not) Squaring the Circle     by Sam Hartburn

          So I had this circle, but I wanted a square
          Don’t ask why, that’s my affair
          The crucial aspect of this little game
          Is that the area should stay the same
          Ruler and compass are the tools to use
          It’s been proven impossible, but that’s no excuse
          Many have tried it, but hey, I’m me
          I’m bound to find something that they couldn’t see

          So, here we go
                . . .

Hartburn's complete poem (and recording) may be found here.

Remembering Eavan Boland, Grace Hopper

     Irish poet Eavan Boland (1944-2020) died last week and news of her death has caused me to look back and remember.  In this year in which the US celebrates 100 years of women's suffrage, I am reminded of this poem in the Irish Times in which Boland celebrated 100 years of Irish women's suffrage, a poem entitled "Our future will become the past of other women."  Here is a brief excerpt from that poem:
                         A hundred years ago a woman’s vote
                         Becoming law became the right
                         Of Irish women. We remember them
                         As we celebrate this freedom.

One of my favorite of Boland's poems is her tribute to another master of language, Grace Murray Hopper (1906-1988) -- Hopper was a computer pioneer and a navy rear admiral.  Here is the opening stanza of Boland's poem: