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: 

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.

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. 

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.

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 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:

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.) 

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):

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.