November is Native American Heritage Month

      Today, the day after Thanksgiving, is Native American Heritage Day -- a November event that was proclaimed in 2009 by President Obama and is part of Native American Indian Heritage Month (established in 1990 by President Bush.)  The disregard with which native Americans have been treated over many years has created huge wounds that will take long to heal.  Both mathematics and poetry can help to support justice and truth!  At present, the US Poet Laureate is Joy Harjo of the Muskogee Nation -- and Harjo is active in using the educational and healing powers of poetry.   Here is a link to some lines from Harjo's "Becoming Seventy" -- posted in this blog back in 2019.

     The website Poets.org helps us to celebrate Native American Heritage Month with a collection of poetic resources found at this link.  One of the poems offered -- which makes effective use of numbers in describing difficult situations -- is "Housing Conditions of One Hundred Fifty Chippewa Families" by Kimberly Blaeser.  I offer a few lines of that poem below -- followed by a link to the entire poem. 

Gather in Poems

 Gather in Poems -- a sort of Thanksgiving

     Last evening I attended a lovely virtual reading, "Gather in Poems," sponsored by the Academy of American Poets (advertised on Facebook) and moderated by  US Poet Laureate Joy Harjo.  One of the readers was a student poet -- high school junior Ethan Wang -- who shared a science-inspired poem by Rosebud Ben-Oni entitled "So They Say--They Finally Nailed--the Proton's Size--& Hope--Dies."  Here are a few lines from the poem -- and the entire poem may be found here.

. . .    I don’t believe hope dies
         just because old measurements got it
         wrong & there are no secret lives
         between protons & muons
         that cause the former to change
         in size,
         silencing all the music
         that drives us
         toward mystery
         rather than discovery.       . . .

One of the delightful--and free--services of the Academy of American Poets is free email delivery of "A Poem a Day."  Sign up here at https://poets.org.

Happy Fibonacci Day!

        Today, November 23 is Fibonacci Day . . . How are you celebrating?  Twitter poet Brian Bilston (@Brian_Bilston) has posted a Fibonacci poem -- with words-per-line counted by the Fibonacci numbers.  Here are its opening lines:

       I
       wrote
       a poem
       in a tweet
       but then each line grew
       to the word sum of the previous two
       until . . .

Use of the Fibonacci numbers in poetry has gotten frequent mention in this blog; here is a link to the results of a blog SEARCH using the term Fibonacci.  And find the rest of Brian's poem in this posting from August 31, 2020 -- or by browsing here on Twitter.

Shaping POETRY with GEOMETRY

Syllable-count constraints help me to think carefully about word choices as I construct a poem.  Here are square and triangular stanzas that came into my head recently while I was jogging.

In addition, when working with students,  I often find that they explore their ideas most easily when I suggest that they follow syllable-counting constraints.

Poetry and Mathematics -- opening doors . . .

Since 1998 The Bridges Organization has been offering conferences that publicize and celebrate links connecting mathematics and the arts.  Because of the Covid-19 pandemic, the 2020 conference was virtual -- but papers submitted to the conference are available online here.

One of the 2020 titles that has especially interested me is "Poetry in the Lesson of Mathematics" by Natalija Budinski and Zsolt Lavicza, available at this link.  The article describes a case study on how poetry can be used as a teaching tool in math classes -- helping students to understand complex mathematical concepts by writing about them using guidelines from poetry.

Links to additional Bridges articles by Budinski and by Lavicza are available via SEARCH here in the Bridges Archives.  And some of my earlier suggestions about using poetry in math classes are found in this posting.

In closing, a stanza from a long-ago poem of mine, "A Taste of Mathematics":

          She said, "A hot pepper
          is like mathematics--
          with strong flavor
          that takes over
          whatever
          it enters.

Venn Diagrams

      During these days of classifying people and points of view, my thoughts turn again and again to Venn Diagrams and I am then reminded of a thoughtful poem about math in grade-school days (by Pennsylvania poet and professor Marjorie Maddox) that I first read long ago -- and I offer it here:  

Learn about Venn Diagrams here

Venn Diagrams     

          by Marjorie Maddox   

There, stuck in that class,
chalking circles on a board 
       so high your toes ached,
an inch of sock exposed,
all for the sake of subsets,
        intersection.
That teacher with the tie too bright for day,
wide as your fingers spread  

Special Days for Mathematics

Today is the birthday of black mathematician, astronomer, almanac-writer and puzzle-maker Benjamin Banneker (1731-1806) -- and some of his puzzles were poems:  this link leads to this blog's previous postings of his work.

This week (November 9-14) is  2020 Maths Week in England.  Learn more, via an introductory video, here.

During these Covid-19 days of isolation I am particularly aware of distances that separate me from those I love . ..  and the numbers that keep track of it all.  Here are opening lines from the poem "Distances" by Peter Meinke that reflect on the changeable meanings of numbers. 

Varieties of SQUARE poems

     When writing a poem on a topic about which I feel strongly, I often like to use constraints -- such as patterns of syllable-counts or rhymes -- to help me to process my ideas carefully.   A recent post by mathematician-poet Marian Christie does a delightful job of showing how the square can be used to shape very fine poems.  Here is a link to Christie's post, "Mathematical forms in poetry:  Square poems" -- a posting which includes examples of acrostic poems and grid poems, palindromes, Latin squares and visual poetry.

     Below I offer one of Christie's own poems, "Earth Geometry" -- a poem that involves the square and the cube in its structure and thereby relates to ancient theories of matter and to a more current belief that the cube is a basic structure of the earth. (View Christie's full explanation here.)

Voting is on the calendar!

Poetry often surprises us by using familiar words in new ways -- and such is also the case with this cryptarithmetic puzzle -- offered by Evelyn Lamb in her AMS page-a-day calendar for tomorrow, Election Day.

               VOTES
           + VOTES
            CHANGE

In this puzzle (which Lamb credits to Manan Shah at mathmisery.com) each letter represents a base ten digit, no letter represents more than one digit at a time and no digit can be paired with more than one letter.  There are no leading zeroes; there are two solutions.  While you are waiting for results from the November 3 US election, this puzzle can help you pass the time in a way that's FUN!

Seeking wisdom in mathematical Haiku

 During these difficult pre-election coronavirus days I have been turning to poetry, and especially favoring -- for their brevity -- Haiku.  The January 2018 issue of the Journal of Humanistic Mathematics offers a folder "Math in Seventeen Syllables:  A Folder of Mathematical Haiku" -- with more than thirty poets sharing poetic insights using this ancient form.  Here is one, by Laura Kline, that spoke to me today:

          Peaceful living and
          Nicely balanced equations
          How we long for both

For more mathy Haiku, follow this link to the results of a blog-search using "Haiku".

Math Songs by Tom Lehrer -- Political, etc.

      All of the songs of musician and math-teacher and nonagenarian Tom Lehrer are now in the public domain (at this link).  His mathy item, "The Derivative Song," was included here in an early post in this blog.  Today I have particularly enjoyed his "Political Action Song" which begins with these words:

     Now when it comes to anything political,
     We're int'rested, we're militant, we're critical.
     Though it's not quite evident
     Who we represent,
     We take stands and issue statements by the score.
     Ev'ry candidate, we know,
     Though he won't admit it's so,
     Would give anything to be the one we're for, we're for,
     Would give anything to be the one we're for.     .  .  .    

Spirit of Delight . . .

        The true spirit of delight, the exaltation,

        the sense of being more than man,

        which is the touchstone of the highest excellence,

        is to be found in mathematics as surely as in poetry.

Bertrand Russell (1872-1970)

2020 Nobel Laureates -- Mathematics and Poetry

     Both mathematics and poetry are languages for conveying complex ideas . . . for example, Oxford mathematical physicist Roger Penrose uses mathematics to study black holes and as a foundation for his notion that the universe as we know it is not unique but one in a series of universes.  Recently the Royal Swedish Academy of Sciences has awarded award one-half of  the 2020 Nobel Prize in Physics 2020 to Roger Penrose for the discovery that "black hole formation is a robust prediction of the general theory of relativity."

     The 2020 Nobel Prize in Literature has been awarded to US Poet Louise Glück.  In 2003 Glück was selected US Poet Laureate of the US and she has twelve published poetry collections in addition to lots of online offerings.  An interesting complement to her poetry is her 1994 collection of essays, Proofs and Theories;  Essays on Poetry   In her opening essay, "Education of the Poet" (available online here) she makes this statement that relates well to mathematics:

  "I loved those poems that seemed so small on the page
but that swelled in the mind; . . ."

Celebrating Ada Lovelace

     Today, 13 October 2020, is  Ada Lovelace Day -- celebrated each year on the second Tuesday of October and an international celebration of the achievements of women in science, technology, engineering and math (STEM).  Born to a famous father, poet Lord Byron -- and first known as Augusta Ada Byron (1815-1852), Countess of Lovelace — this talented woman became far better known as "Ada Lovelace" (1815-1852).  Lovelace worked on an early mechanical computer, "the Analytical Engine" -- and, because of her recognition of the varied applications of this machine, she is often regarded to be one of the first computer programmers.

Here is a link to a poem, "Bird, Moon, Engine" by Jo Pitkin that celebrates Ada Lovelace (with opening stanzas offered below) and this link leads to some of Lovelace's own poetic words.  At this link are the results of a blog search using "Ada Lovelace" that leads to the aforementioned works and lots of other poems about math women.

Brilliant Math-Women -- Share the News!

     Recently (10/10/2020), NPR had an interview with former teachers of Louisville shooting victim Breonna Taylor  -- an interview that celebrated her love of and talent for mathematics.  Read about it here.  I write to applaud this celebration AND to encourage increased recognition of math-women while they are alive.

A wonderful way to celebrate math-women is the annual essay contest sponsored by the Association for Women in Mathematics -- open to students from middle school to college; contest information is available here.  Interviews may be conducted now; essay submission begins December 1.

A repeat from this posting back in 2010

Here is a link to a list of previous posts involving "women" and "mathematics".

Mathy Rhymes

     Yesterday's note on "A Mathematical Morsel Every Day" -- an American Mathematical Society page-a-day calendar for 2020 assembled by mathematician and writer Evelyn Lamb -- is a fact that involves the first six digits in the decimal expansion of  π :    314159 is a prime number.

And, because this is a math-poetry blog, I have turned this information into a syllable-square rhyme:

           3     1     4

           1     5     9

           is a prime!

Perhaps you'd like to explore more:    Here's a link to previous blog postings with ideas by Evelyn Lamb.    Rhymes often help us to remember; here is a link to postings of rhymes used to remember the digits of π.    AND here is a link to some postings that feature square stanzas.

The Domain of the Function . . .

     Recently I found, in The Literary Nest, the mathy poem, "Functional" by retired math teacher and active poet Carol Dorf.  Dorf's poem is a pantoum -- and the interplay of math terminology with repeated lines, gives us some new thoughts to think.  Enjoy!

     Functional     by Carol Dorf

     Fanatic is the word of the day.
     The domain of the function is the set of inputs.
     How did the programmer know in advance?
     The range is the set of outputs.  

Poetry Enriches Science -- a growing point of view!

     Recently I found and enjoyed the article "Scientists Take On Poetry," an article by Katherine Wright in Physics  --  a free, online magazine from the American Physical Society.  After the following lead-in:

Stuck with how to present your latest scientific project? Try a poem.

Wright's article tells of numerous scientists who have been poets and offers visual poetry by Stephany Mazon and Manjula Silva.  The article quotes Sam Illingworth, a poet and geoscientist at the University of Australia, "Poetry is a great tool for interrogating and questioning the world."  Illingworth heads the Editorial Team of an online journal, Consilience -- a newish journal that describes itself as "the online poetry journal exploring the spaces where the sciences and the arts meet."  The current issue has the theme "uncertainty" and offers 19 poems; one of these is "Heisenberg's uncertainty principle" by Alicia Sometimes -- and it begins with these words:

       The reality we can put into words is never reality itself

       we cannot measure
       the position (x) and the momentum (p)
       of a particle with absolute precision
         . . .

This link leads to the rest of Sometimes' poem and to others offered in Consilience.

TalkingWriting with Mathematics

     TalkingWriting is an online journal that's celebrating its 10th birthday -- TEN YEARS of including mathematics in its mix of poetry.  This mathy connection has grown strong through the poetry editorship of Carol Dorf, poet and retired math teacher.  In this anniversary issue, poems are paired with works of visual art and the effect is stunning; from it,  I offer below samples of poems by Amy Uyematsu and by me.      
      Amy Uyematsu's poem "Lunes During This Pandemic"  thoughtfully applies the counting structure of the "lune" (aka "American Haiku") with three-line stanzas of 3/5/3 words per line.

Poetry-math resources -- for classrooms and for fun

 This link leads to my article 

"Enrich Discussions about Mathematics with Poems" -- 

an article that offers links to poems that introduce mathematicians and air math-attitudes -- 

items that can benefit from a bit of attention in many math classes. 

    

Lots of ideas/suggestions are available at this link!

If a Garden of Numbers . . .

      In a summer email from math-poet-editor Carol Dorf,  I first enjoyed "If a Garden of Numbers" -- a mingling of numbers with the natural world -- by California poet Cole Swensen.  I offer its opening lines below followed by a link to the complete poem.

If a Garden of Numbers      by Cole Swenson 

If a garden is the world counted
                                                      and found analogue in nature
One does not become two by ever ending
                                                                    so the stairs must be uneven in number

Misunderstanding mathematicians . . .

      One of the comments that non-maths often make when they meet a math-person is "Oh, I never was good at math."  An awkward start to possible friendship.  Another awkward beginning rests on the assumption that mathematics is primarily calculation, that the main task of mathematicians is to organize numbers.  This error is the focus of the following poem -- written in the early 90s before our banking was done electronically.

"Misunderstanding" is found in my poetry collection, My Dance is Mathematics -- its poems are online here.  For non-maths (and the rest of us, too) one of the wonderful up-to-date online sources for "living mathematics" is +plus magazine -- and of course +plus includes poetry

What is x?

     This thoughtful poem by versatile poet Mary Peelen appeared in the Winter, 2016 issue of The Massachusetts Review.   

       Variable     by Mary Peelen 

       The x could have been
       anything at all,

       the sound of wind chimes,
       a gong, a choir, a cantor,

       a mermaid, a schoolmarm,
       cathedral bells.

       Instead—what a lark—
       it’s laughter. 

Venn Diagram Poem

     One of my granddaughters has been working with Venn diagrams in her middle school math class.  And my thoughts turned to this poem -- back in 2018, Twitter poet Brian Bilston (@brian_bilston) celebrated the August 4 birthday of the diagram's inventor, logician John Venn (1834-1923), with this clever poem in a Venn diagram.

Lots more of Brian's poetry adventures can be found here at his website.

TEACHERS are important ... enlarge Hardy's view!

     One of the classics written about mathematics is G. H. Hardy's 1940 book-essay, A Mathematician's Apology -- a treatise that gives valued insights into the nature of mathematics, its beauty, and the roles of mathematicians.   But today I want to urge us all to enlarge Hardy's view (shown in the box below) which offers scorn for those who talk ABOUT mathematics instead of creating it.  Our teachers and the others who spread mathematics out into the world ALSO are vital.

    Let us use geometry as Edwin Markham does -- and include

in the important world of mathematics those persons who communicate about that world.

          Outwitted     by Edwin Markham (1852-1940)

          He drew a circle that shut me out--
               Heretic, rebel, a thing to flout.
          But Love and I had the wit to win:
               We drew a circle that took him in!

Poetry in SCIENTIFIC AMERICAN

     The September 2020 issue of Scientific American contains a poem by British Poet Laureate Simon Armitage -- "Bring Back the Leaf"  -- AND an announcement that from now on each monthly issue will contain poetry. Like!
     Although this poem is not mathematical, I offer news of it here because the Scientific American's inclusion of the arts with the sciences and mathematics (STEM enlarged to STEAM) is a very important step.

From:  "Bring Back the Leaf"      by Simon Armitage

Bring back, bring back the leaf.
Bring back the tusk and the horn
unshorn.
Bring back the fern, the fish, the frond and the fowl,
the golden toad and the pygmy owl,
revisit the scene
where swallowtails fly
through acres of unexhausted sky.

The complete poem, "Bring Back the Leaf" is available here.

 At this link is info about a Simon Armitage poem that helps to clean the air . . .

 

Another Fibonacci poem . . .

     Through many years of the history of poetry, the sonnet has been a treasured form -- as poets strive carefully to match the iambic pentameter rhythm and some pattern of rhyme, this concentrated thinking leads to careful word choices and memorable poems.  (Here is a link to a mathy sonnet by a math teacher's son, John Updike.)
     Modern poetry has many "free verse" poems that follow no particular form AND ALSO a variety of new forms.  One particularly popular format (appearing often in this blog) is to count syllables-per-line using the Fibonacci numbers   Here an interesting example by poet Marian Christie which describes increasing complexities of crocheting using Fibonacci syllable-counts.

"Crochet" -- a FIB by Marian Christie

 Christie's poem was first published in here in Issue 36 of The Fib Review.

Poetry on Twitter

      Dubbed the "unofficial poet laureate of Twitter" Brian Bilston (a pen-name) sometimes uses mathematics to shape his poems; for example, this poem whose word-counts follow the Fibonacci numbers:

from "Brian Bilston's  POETRY LABOETRY"

Look for Brian on Twitter (@brian_bilston) 

and also on Facebook (www.facebook.com/BrianBilston/).

Links and comments for many of my blog-posts also on twitter on Twitter  @mathypoems

and a search using the hash-tag #NPRpoetry leads to lots of interesting stuff!

Ten thousand parts of cat . . .

As a cat-lover, I am drawn to David Manning's mathy poem that I offer below:  

       Live Round     by David T. Manning

       All ten thousand
       parts of cat run
       like seventeen jewels
       in velvet.  Target locked,
       she tucks white forepaws.
       folds couchant     and waits.
       One thousand gyros idling
       quietly, ordnance round
       of bottled death with nose
       that never sleeps
       tuned to the frequency
              of mouse.

After a long career as organic chemist, David Manning turned to poetry.  "Live Round" is on my shelves in his collection Negotiating Physics and Other Poems from a Peaceable Kingdom  (Old Mountain Press, 1999).

What can we count on?

As the August days grow shorter in a hot summer of social distancing, here is a sample of my thoughts:
 
        I learned to count
        on my fingers.
        Now, years later,
        in twenty-twenty
        what can I count on? 

And I'd like also to make a quick mention of a project I've been part of -- with results that you are likely to enjoy. Gathered by Rosemary Winslow and Catherine Lee, a collection of thoughtful essays,  DEEP BEAUTY --  Experiencing Wonder When the World Is on Fire (Woodhall Press, 2020).  My essay, "When I'm Quiet Enough to See" tells of beauty's connection to my childhood on a farm, to poetry, to mathematics, and is available here.

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.