Playing Hopscotch . . . and Counting . . .

      Growing up on a Pennsylvania farm gave me lots of opportunities to use mathematics -- counting sheep, choosing patterns for planting, and many kitchen tasks.  I also enjoyed occasional times to join friends at in-town playgrounds and, on their paved areas, hopscotch was one of our arithmetical and geometrical activities.  Recently I came across a wonderful online collection of poems by Maya Angelou (1928 - 2014) -- and, within it, this slightly mathy poem that includes hopscotch and also speaks of racial injustice:  

     Harlem Hopscotch    by Maya Angelou

     One foot down, then hop! It's hot.
     Good things for the ones that's got.
     Another jump, now to the left.
     Everybody for hisself.  

Creating New Poems by Sampling Old Ones

      In its collection of Math Voices the American Mathematical Society (AMS) has a very interesting Feature Column -- a column written for students, teachers, and the general public -- that offers essays about math that it describes as "useful, fun, inspiring, or startling."  When browsing the column recently I found and enjoyed a column by Sara Stoudt of Bucknell University entitled "Sampled Poems Contain Multitudes" -- an article that gives readers an opportunity to experience Walt Whitman's poem, "Song of Myself" (a book-length poem with a total of 52 poem-sections, found here at the Poetry Foundation website) via a poem with a sample line for each section,  Here are the opening lines:

From Walt Whitman's "Song of Myself":

Bridges 2024 -- in Richmond, VA

      As she had done in numerous preceding years, mathematician-poet Sarah Glaz is once again an organizer for a poetry reading at the BRIDGES Math-Arts Conference -- this year to be held in Richmond, Virginia, August 1-5.

Bridges Poetry Reading Website

  Poetry Reading Sunday, August 4, 3:00 - 5:00 pm     

Science Museum of Virginia , Room: RF& P Forum

2500 West Broad Street    Richmond, Virginia

Speaking in Fibs . . .

     Syllable-count patterns often are used in poems--helping to give a rhythmic tempo to the words.  As I mention often, syllable counts -- and other word-patterns -- help me to discover new and special meanings to convey. When I start to write, my thoughts are scattered and need to be gathered and focused -- and a poetic form helps this to happen.  The sonnet and the villanelle have long been valued examples of poetry patterns.  More recent -- and more simple -- is the Fib.  Introduced by poet Gregory Pincus back in 2006, the Fib is a six-line poem whose syllables are counted by the first six Fibonacci numbers:  1, 1, 2, 3, 5, 8. (Each succeeding Fibonacci number is the sum of the two that precede it.)

     Since 2006, a journal aptly named The Fib Review has offered (available at this website) more than 40 issues of poems, all of whose lines have syllable-counts that are  Fibonacci numbers.  Here is a portion of one of the poems -- by Washington-based poet Sterling Warner --  (the complete poem is found here).

Here is a link to another blog posting that features poetry from The Fib Review.

And lots more FIBS may be found here.

EARTH DAY -- what are ways to preserve our planet?

Save
our
Mother
Earth -- conserve 
our resources, shift 
to non-polluting substances.

As many of you readers know, the poem above is an example of  a FIB -- a six-line poem with syllable-counts matching the first six Fibonacci numbers,  When I sit down to write about a particular topic, I often find the the FIB format is a good way to start -- developing an idea starting with single words and gradually developing longer phrases.   And, today, outside of this blog, I am trying to learn more about earth friendly substances.

If you have time to be interested in more mathy and earth-friendly poems, this link leads to the results of a blog search for climate change and this second link leads to previous Earth Day blog postings.

 This link leads to postings -- and poems -- in this blog related to CLIMATE.

And here is a link to several previous EARTH DAY postings..

Enjoying Math-Poetry Connections

           Poet Emily Lutken's first career was as a physician -- she specialized in family medicine and spent many years of practice in the Navaho Nation.  Following this she taught middle and high school math and science for several years , , , and now, retired, she has time for music, poetry, and other arts.

     On my shelf --- for my frequent rereading and enjoyment -- is a copy of Lutken's 2021 collection, Manifold:  poetry of mathematics. (3: A Taos Press, 2021).   Here is a favorite poem of mine from that collection:

   Prime Syllable Song    by Emily Lutken

          Prime 
          numbers
          do not care
          to make a rhyme.
          They blaze wild pathways.
          While others tow the line,
          they play crwths or smash guitars,
          unlike composite counts assigned
          to echo harmonic notes in time
          and avoid the oddball and ill-defined.
          Without primes, though, the music would be boring,
          the sing-song regularity, the constant whine
          would drive all of us absolutely batshit bonkers.

This link leads to more information about Manifold, in which the poem above is found.  This link leads to Lutken's website -- which includes more poetry and a bio of the poet.

This link leads to a poem by Lutken about a solar eclipse.  

Another of Lutken's poems, "Ars Parabola," appears in this blog at this link.

A blog posting written by ChatGPT 3.5

     For a long time I have been curious about what would result if I asked AI to write a blog post for me.  One day recently I signed in at https://chat.openai.com/ and was asked by ChatGPT 3.5,  "How can I help you today?"  Copied and pasted below is our conversation (copied from this link).  (I am disappointed that ChatGPT's respones did not, as my postings usually do, include a poem.)  Read -- and reflect!

I have a blog entitled "Intersections -- Poetry with Mathematics" and I would like Chat GPT to write a blog posting for me.  

From ChatGPT: 

Title: Exploring the Symmetry of Numbers: A Mathematical Poetic Journey

Welcome back to "  Intersections -- Poetry with Mathematics"! Today, let's delve into the captivating world where numbers and poetry intertwine, creating harmonies of symmetry and rhythm. Join me on this whimsical voyage where mathematical concepts dance with lyrical verses, inviting you to see the beauty in both.

Discovery Tool -- Following a Pattern

     When I pick up a pen to write on a particular subject, often it is useful me to try to follow a pattern for rhymes or syllable-counts -- for the effort to conform to a pattern challenges me to think about my topic in new ways.  In the history of poetry, rhyme-choices were frequent--yielding sonnets, villanelles and a variety of other forms.  

     In recent years, online and printed versions of poems have become very accessible and the principle, "Rhymes help us remember" has become less of a focus in poetry.  One of the popular connections between math and poetry has been the use of Fibonacci numbers to choose syllable counts;  especially  popular has been the FIB, a six-line stanza in which the syllable-counts are 1, 1, 2, 3, 5, and 8 -- the first six Fibonacci numbers.  (Inventor of the FIB was Greg Pincus, and lots of information is provided here in this 2010 blog posting, Poems with Fibonacci number patterns.)  

Explore a new idea by writing a poem . . .

      Often I try to unravel the intricacies of a new idea by writing -- using communication with my fingers as steps toward understanding.  And when I found the poem below (here at the website VIA NEGATIVA) I saw it also as a poem of discovery -- and I offer it to you:

Every Line Intersects the Line
                           at Infinity at Some Point                       by Luisa A. Igloria

"Out of nothing I have created a strange new universe."   - János Bolyai (1802-1860)

The optometrist asks you to look into 
the autorefractor: two dark lines form 

a road that stretches from where you sit
to a red barn at the horizon. If your brain 

tells you that you're looking at a point 
at infinity rather than just mere inches away, 

it helps the eyes focus. Things have to end 
somewhere, don't they? In projective geometry, 

Geometry in Poetry

     Poet Marian Christie's blog, Poetry and Mathematics -- found at https://marianchristiepoetry.net/ -- is a website I much enjoy visiting; there I learn many many new things.  (Here is a link that leads to a list of my previous postings that feature Christie and her work.)

    The idea that the shape of a poem may be part of its message is not new -- but Christie has brought more than line-length and syllable-count into the picture and today I focus on her Circular Poems.  

A Circular poem by Marian Christie

Poetry of Science

     One of the interesting regular online postings is a new science poem EVERY FRIDAY -- offered by Sam Illingworth via an email subscription or in his  Poetry of Science blog.  Recently I have found and valued Illingworth's interview late in 2020 with poet Donald Beagle, author of the poetry collection, Driving into the Dreamtime (Library Partners Press, 2020).

     One of Beagle's publications involved editing a poetry collection by James Radcliffe Squires (1917-1993) -- a collection in which many of the poems are informed by science.  Here is a sample from Squires' collection Where the Compass Spins -- now presented in Radcliffe Squires: Selected Poems; edited by Donald Beagle).

          “…We are one motion and we see
          Another. Then we overtake two flying birds
          And at the crisis of the wan parabola
          Assume their speed. Thus motion dies…”

The lines above are from Squires' poem “The Subway Bridge, Charles Station to Kendall.”  This same poem concludes by touching upon the Einsteinian concept of the gravitational bending of light: “Faring with the straightness that curves. The line / Of brightness bending as it nears the sun.”    When you have an available hour, visit and enjoy the whole of Illingworth's 2020 posting about Donald Beagle's poetry.

Shaping a Poem with Fibonacci numbers

      One of my favorite websites to visit is this varied and thoughtful "Poetry and Mathematics"  collection of postings by Marian Christie.

     Throughout history, people who write poems have often been aided by constraints.  When we sit down to write, writing the words that first occur to us -- then shaping the word into extended meanings but following a pattern of rhythm or rhyme or word-count . . . or . . .  .  For many poets the sonnet, for example, has been a poetic structure that shapes thoughts into special arrangements of words.

     In long-ago days, when print and screen versions of poems were not easily available, rhyme schemes were an important aid -- helping one's memory to keep a poem in one's head.  Now, aided by widely available print and online visibility, poetry has moved into new forms -- including a variety of visual arrangements.  

Math Class -- Express POINT OF VIEW with a POEM

       Often students in a math class feel hesitant about expressing their point of view about the subject -- and these attitudes may emerge more easily via a writing assignment.  A writing format that many students respond to easily is an acrostic poem.  Such a poem is obtained by first selecting a relevant math term -- perhaps INTEGER or ADDITION or EXPONENT or  . . . and using each of its letters as the first letter of a line of poetry.  Here is a brief sample using MATH --  one of many examples I found as the result of an internet search using the terms "acrostic poem on mathematics".

Available at this link

Go here for lots more:   Acrostic Poem On Mathematics - Bing images

TRITINA -- a tiny SESTINA

     In several previous postings (collected at this link) this blog has considered the poetry form called a sestina:    a sestina has 39 lines and its form depends on 6 words -- arrangements of which are the end-words of 6 6-line stanzas; these same words also appear, 2 per line, in the final 3-line stanza.

     The American poet Marie Ponsot (1921-2019) invented the tritina, which she described as the square root of the sestina.   the tritina is a ten-line poem and, instead of six repeated words, you choose three, which appear at the end of each line in the following sequence: 123, 312, 231; there is a final line, which acts as the envoi -- and includes all three words in the order they appeared in the first stanza.  Poinsot has said -- and I agree -- poetic forms like the tritina are "instruments of discovery . . . they pull things out of you."  Read more here in an article by poet Timar Yoseloff.)

   

BRIDGES Math-Poetry in Halifax -- July 27-31, 2023

     BRIDGES, an annual conference that celebrates connections between mathematics and the arts, will be held this year in Halifax Nova Scotia, July 27-31.  (Conference information available at this link.)  A poetry reading is one of the special event at BRIDGES and Sarah Glaz, retired math professor and poet, is one of the chief organizers of the event.  Here at her University of Connecticut website, Glaz has posted information about the July 30 reading along with bios and sample poems from each of the poets.   For poets not part of this early registration, an Open Mic will be available (if interested, contact Glaz -- contact information is available here at her website.)

Here is a CENTO I have composed using a line of poetry from each of the sample poems (found online at this link) by the 2023 BRIDGES poets:

Measuring Infinity

      One of my recent excitements has been to learn about a current exhibit at New York's Guggenheim Museum, " Gego:  Measuring Infinity".  At the Guggenheim website for the exhibit, we learn:

Gego, or Gertrud Goldschmidt (b. 1912, Hamburg; d. 1994, Caracas), first trained as an architect and engineer at the Technische Hochschule Stuttgart (now Universität Stuttgart). Fleeing Nazi persecution in 1939, she immigrated to Venezuela, where she settled permanently, fully embarking on an artistic career in the 1950s that would span more than four decades. In two- and three-dimensional works across a variety of mediums, Gego explored the relationship between line, space, and volume. 

After visits to the Guggenheim website, I wanted more -- and I purchased a featured book, also entitled Gego: Measuring Infinity, and available at this link.  On page 19 of this lovely book, a bit of poetry.  Written in homage to Gego in 1979 by Venezuelan poet Alfredo Silva Estrado (1933-2009), the poem speaks of Gego's experimentation with structure, space, light, shadow, line, and grid.  Quoting from the Guggenheim book, we have Estrado's words:

Exploring the truth with a FIB

     Recently I have been reconnected with British-Israeli mathematician-educator, Yossi Elran  (whom I met at a conference in Banff several years ago).  Elran is well known for his puzzle-book, Lewis Carroll's Cats And Rats... And Other Puzzles With Interesting Tails (World Scientific, 2021).  He is in the process of writing a sequel to this book and it will include some math-poetry; probably some Fibs (poems  -- often with just 6 lines -- with syllable-counts per line that follow the Fibonacci numbers).   Elran's recent email query about Fibs helped me to remember that I had one waiting to be posted, a Fib about missed opportunities and status for women.  Here is is:

Exploring the truth with a FIB        by JoAnne Growney

April -- Mathematics & Statistics Awareness Month

      Found at the website of the American Statistical Association this fine page of resources for Mathematics and Statistics Awareness Month for students and teachers.  

This photos shows resource topics available at the link given above.

     One of my own recent activities has been to revisit an old book, Poetry and Mathematics by Scott Buchanan (J. B. Lippincott, 1962), originally published in 1929.   Buchanan (1895-1968) was a philosopher who had majored in mathematics as an undergraduate; his career involved both teaching and consulting -- and work at a political think tank.  Here are some of his words:

Is a proof the opposite of a poem?

      One of the valuable online sources from the MAA (Mathematical Association of America) is the Math Values blog -- found at this link -- a blog that explores COMMUNICATION, COMMUNITY, INCLUSIVITY, and TEACHING and LEARNING.  Using the SEARCH feature, I entered "poetry" and found this variety of resources -- including mention of the Steven Strogatz Prize for Math Communication -- SHARE YOUR LOVE OF MATH WITH THE WORLD -- a contest for high school students with deadline April 28, 2023.  Entry categories include Art, Audio, Performance, Social Media, Video, and Writing.  Guidelines are available here.

     Back in June, 2021 at this link I shared a portion of the poem by Julia Schanen that won in the Writing category that year.  It's second line is the title of this blog posting -- and the complete poem is available here.  A 2022 Strogatz winner was Wyeth Renwick -- and this blog posting features his poem.

     I close with two of my favorite lines of poetry:

        The Secret Sits     by Robert Frost (1874-1963)

               We dance around in a ring and suppose,
               But the Secret sits in the middle and knows.

Patterns of the Wind

     Sometimes a poem contains just a sample of mathematics -- but a very memorable one.   Such is the case with "I Like the Wind" by Robert Wrigley in the 6 September 2010 issue of The New Yorker.  I offer below its opening lines.

       We are at or near that approximate line
       where a stiff breeze becomes
       or lapses from a considerable wind,
       and I like it here, the chimney smokes
       right-angled from west to east but still
       for brief intact stretches
       the plush animal tails of their fires. 

  (The poem continues here for 34 more lines.)