A septina ("Safety in Numbers") -- and variations

Recall that a sestina is a 39 line poem of six 6-line stanzas followed by a 3-line stanza.  The 6-line stanzas have lines that end in the same six words, following this permutation pattern:

   123456   615243   364125
   532614   451362   246531

The final stanza uses two of the six end-words in each of its three lines.  An original pattern for these was 2-5, 4-3, 6-1 but this is no longer strictly followed.

Can sestina-like patterns be extended to other numbers?  Poet and mathematician Jacques Roubaud of the OULIPO investigated this question and he considered, in particular, the problem of how to deal with the number 7 of end-words -- for 7 does not lead to a sestina-like permutation.  Rombaud circumvented the difficulty (see Oulipo Compendium -- Atlas Press, 2005) by using seven 6-line stanzas, with end-words following these arrangements:

A permutation puzzle -- the sestina

In a sestina, line-ending words are repeated in six six-line stanzas in a designated permutation of the words; the thirty-nine-line poem ends with a three-line “envoi” that includes all six of the line-ending words.  (After the first, a stanza's end-words take those of the preceding stanza and use them in this order:  the 6th, then the 1st, then the 5th, 2nd, 4th and, finally, the 3rd. In the envoi, two of the six words are used in each line.)  Here is a sestina by Lloyd Schwartz that uses only six words -- but its punctuation and italics cleverly shape variations of meaning. 

A sestina from Rudyard Kipling

My father died many years ago, when I was still a young girl, and I have few possessions that were once his.  One is The First Jungle Book, signed "Fulton Simpson" with his hand; it is very precious.  By extension, all work by Rudyard Kipling (1865-1936) falls under my interest.  And a sestina by Kipling is worthy of note:

Sestina of the Tramp-Royal     by Rudyard Kipling

     1896

Speakin’ in general, I ’ave tried ’em all—
The ’appy roads that take you o’er the world. 
Speakin’ in general, I ’ave found them good 
For such as cannot use one bed too long, 
But must get ’ence, the same as I ’ave done, 
An’ go observin’ matters till they die.

Syllable-Sestina -- a square permutation poem

Some poetry is "free verse" but many poems are crafted by following some sort of form or constraint--they might be sonnets or ballads or pantoums or squares, or possibly even a newly invented form.  From poet Tiel Aisha Ansari I learned of a "syllable sestina challenge" from Wag's Revue. The desired poem contains six lines and only six syllables, which are repeated using the following permutation-pattern (the same pattern followed by the end-words in the stanzas of a sestina):

Half-twist and link -- in a Sestina

     Mobius strip       by Heidi Willamson

     A simple science trick to try at home.
     Half-twist a slip of paper. Link the ends
     to make an ‘O’. Take a pencil, trace a line that loops
     the shape formed by the surface. See
     how the in and out sides merge. The join
     tangles dimensions. There’s no front or back.

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.)

   

Permuting words and and enumerating poems

Caleb Emmons teaches mathematics at Pacific University.  Here is his very-clever description of the requirements for a poem to be a sestina -- spelled out in a poem that is itself 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.) 

"A Mother's Math is Never Done"

     In just a few days (on May 8) we will celebrate Mother's Day 2022 in the US.  And I am thinking back to the July 2018 issue the Journal of Humanistic Mathematics  -- a special issue with the theme Mathematics and Motherhood.   One of the poems presented in that issue is "A Mother's Math is Never Done,"  a sestina by JHM Editor, Gizem Karaali -- and I offer its initial stanza below, followed by a link to the complete poem.

A Mother's Math is Never Done    by Gizem Karaali

Beyond dark clouds is the blue sky.
The day will come to do your math,
Once you put away the clutter.
Someday again you know you'll fly.
Now's not the journey's end, just a detour on the path.
Only today, hold your breath, for you are a mother.     

 Go here for the rest of this sestina.  Enjoy especially the final stanza!!

The entire "Table of Contents" for Mathematics and Motherhood is available at this link.   

Using a Fano plane to create a poem

     South Dakota mathematician Daniel May enjoys finding connections between his discipline and other arts -- and herein we consider a constraint-structure for poetry that he has developed using a Fano plane.  In brief, a Fano plane (shown in the diagram below) consists of 7 points and 7 lines (the three sides of the triangle, the three altitudes of the triangle, and the circle) -- with each line containing 3 of the points. 

Fano Plane Diagram

May creates a poem by associating a word with each point of the Fano plane and then creates a three-line stanza for each line of the diagram.  Here is a template for the poem "adore" -- and the poem itself is offered below the diagram: 

From 2010 -- titles and dates of posts

List of postings  March 23 - December 31, 2010
A scroll through the 12 months of titles below may lead you to topics and poets/poems of interest. Also helpful may be the SEARCH box at the top of the right-hand column; there you may enter names or terms that you would like to find herein.
    Dec 31  The year ends -- and we go on . . .
    Dec 30  Mathematicians are NOT entitled to arrogance
    Dec 28  Teaching Numbers
    Dec 26  Where are the Women?
    Dec 21  A Square for the Season
    Dec 20  "M" is for Mathematics and . . .  

2012 posts -- titles and links

Scroll down to find titles and dates of posts in 2012 -- and, at the bottom, links to posts all the way back through 2011 to March 2010 when this blog was begun.   This link leads to a PDF file that lists searchable topics and names of poets and mathematicians presented herein.

Dec 30  A chance encounter
Dec 28  Explorers
Dec 25  Support STREET SENSE
Dec 24  Star, shine bright!
Dec 21  Skating (with math) on Christmas 

Prisoner's Dilemma -- and permutations

In game theory's original, single-play, Prisoner's Dilemma problem, two prisoners each are given the choice between silence and betrayal of the other. The optimal choice is betrayal -- and therein lies a paradox.  Volume 1.3 of the online journal Unsplendid includes the following poem by Isaac Cates that reveals the nature of this classic decision dilemma.

2013 (and prior) -- titles, dates of posts

Scroll down to find dates and titles (with links) of posts in 2013.  At the bottom are links to posts through 2012 and 2011 -- and all the way back to March 2010 when this blog was begun.   This link leads to a PDF file that lists searchable topics and names of poets and mathematicians presented herein.

Dec 30  Error Message Haiku
Dec 26  The angel of numbers . . .
Dec 23  Ah, you are a mathematician
Dec 20  Measuring Winter 

Splendid Wake project

On Wednesday, September 25, more than one hundred poets met at the George Washington University Gelman Library's Special Collection Conference Room to show support for the Splendid Wake project -- an effort to document poetry in the Washington, DC area from 1900 forward. Initiated more than a year ago by Myra Sklarew and Elisavietta Ritchie, the project will honor poets associated with our nation's capital.  Interested persons are invited to visit the project's main page and to consider a submission -- biographies and information about poetry projects of all sorts (journals, reading series, websites, and so on).  Management of the project is being coordinated by GW Special Collections Librarian Jennifer King (jenking @ gwu.edu).
     In celebration of this project, here is "Monuments," a sestina (a poetic form involving permutations of the line-end-words) by Myra Sklarew that honors some of DC's past poets.

From 2011 -- dates, titles of posts

List of postings January 1 - December 31, 2011
Scrolling through the 12 months of titles below may lead you to topics and poets/poems of interest. Also helpful may be the SEARCH box at the top of the right-hand column; there you may enter names or terms that you would like to find herein.
Dec 30  Good Numbers
Dec 26  A mathematical woman
Dec 22  Counting on Christmas
Dec 20  Thoughts Suggested by a College Examination
Dec 17  Ruth Stone counts
Dec 14  A puzzle with a partial solution
Dec 11  Poetry captures math student
Dec  8  Monsieur Probabilty
Dec  5  Poetic Pascal Triangle
Dec  2  Mathematics works with witchcraft 

From a math-friend and an Ohio poet

     One of the wonderful things about writing a blog about my paired passions of poetry and mathematics is that the blog connects me with fascinating and generous people whom I might not otherwise meet. One of these is Marylander Greg Coxson -- physicist, engineer, mathematician, Operations Researcher -- who took three years of Latin in high school and loves words.  With interests in art and poetry, Greg has organized exhibits of math-related art -- and is a regular recommender of mathy poems for this blog.
     A week or so ago Greg alerted me to an NPR interview with Ohio Poet Laureate Amit Majmudar (a radiologist as well as a poet) -- letting me know that Majmudar's poetry was rich with mathematical imagery.  Following Greg's lead, I found Majmudar's website and was able to contact both Majmudar and his publisher, Knopf, for permission to offer these mathematical poems.
     Here, from Amit Majmudar's new book Dothead, are two sections of the poem "Logomachia" -- sections alive with geometry and logic.  The first, "radiology," is visually vivid; the second, "the waltz of descartes and mohammed," is a sestina that plays with the logic of word-order.  

A square-root of dead weight . . .

     A poet  I love (Seamus Heaney, 1939-2013, 1995 Nobelist) has died. The NYTimes obituary for Heaney quotes one of my favorites of his poems, "Digging" -- also available at poetryfoundation.org.  Part of what I like about this Irishman's poetry is its design.  Not only do his poems offer musicality of language but they feel carefully constructed -- modeling real world phenomena as mathematical models do -- built with careful attention to structure and detail until varied factors have been erected into in integrated whole.  "Digging" ties together the physical activity of Heaney's father shoveling in the peat bogs of Ireland to his own probing with a pen for words. 

Celebrate Constraints -- Happy Birthday, OULIPO

Patrick Bahls and Richard Chess of the University of North Carolina at Ashville have organized a "Conference on Constrained Poetry" to be held on November 19-20 in celebration of the 50th Anniversary of OULIPO (short for French: OUvroir de LIttérature POtentielle), founded in 1960 by Raymond Queneau and François Le Lionnais. The group defines the term littérature potentielle as (rough translation): "the seeking of new structures and patterns that may be used by writers in any way they enjoy." Constraints are used to trigger new ideas and the Oulipo group is an ongoing source of novel techniques, often based on mathematical ideas -- such as counting letters and syllables, substitution algorithms,  permutations, palindromes, and even chess problems.

Journal of Humanistic Mathematics -- latest issue

     Every six months a wonderful treasure appears in my email-box -- an announcement, with links, to the latest issue of the Journal of Humanistic Mathematics.  Here is a link to the Table of Contents for this latest (July 2022) issue.

     Gathered and edited by Mark Huber (Claremont McKenna College) and Gizem Karaali (Pomona College) this open access journal contains a variety of articles and fiction and poetry.  With topics such as "Math in the Time of COVID" and "A Report about a Speaker Series Connecting Mathematics and Religion," the journal offers both depth and variety as its contents explore the humanistic aspects of mathematics.  Following more than twenty articles, we come to these poems: