Sieve of Eratosthenes

The Sieve of Eratosthenes     by Robin Chapman

He was an ancient Greek
looking for primes,
those whole numbers divisible
only by 1 and themselves,
those new arrivals on the block,
fresh additions to the stock
of indivisibles spilling through
future time (for what is time

Amounting to Something

From the Fall/Winter 2013 issue of Poet Lore, a poem by David Wagoner about the arithmetic of expectations:

     Amounting to Something     by David Wagoner

     You were supposed to do that
     by saving yourself up
               like coins in a pig rescued
               just in time sometimes
     from in front of the candy counter  
     or the desk in the corridor

13 lads of Christmas

     In addition to waterfalls and geysers and the Aurora, Iceland has outstanding museums.  On the morning of December 10, I visited the National Museum of Iceland in Reykjavik -- and enjoyed a careful introduction to the history of this fascinating and friendly nation.  Something I missed, however, was seeing one of the 13 Yuletide Lads that are an Icelandic tradition and who visit the Museum one-by-one on the 13 days before Christmas, each wearing traditional costume and trying to pilfer the goodies he likes best.

Iceland -- poetry, stones

British translator and editor David McDuff blogs at "Nordic Voices in Print" -- a site that he uses as "a way of making some of my translations of Nordic poetry and prose available online."  Here is "stones" -- the third of a group of ten poems he has posted by Icelandic poet Sjón.  This one involves a few numbers and I present it here as a math-poetry token of the fascinating land I am planning to visit: a five-day Iceland vacation adventure, traveling with my Eastern Village neighbors Priscilla and Glenn. 

stones     by Sjón (translated by David McDuff)

Conversational mathematics

In recent weeks I have been experimenting with poems that use mathematical terminology, wondering whether -- since there are readers who are undaunted by unknown literary references (to Dante's Divine Comedy or Eliot's Prufrock, for example) -- some readers will relish a poem with unexplained mathematical connections.  In this vein I have offered "Love" (posted on on November 5) and now give the following poem, "Small Powers of Eleven are Palindromes":

Last year's prediction

This poem by Halifax mathematician and poet, Robert Dawson, appeared in LabLit  in December 2012 (just in time to offer gentle mocking of predicted disaster)!  Enjoy!

Survivor's Guide to the Baktun-13 Bug    by Robert Dawson

As you may know, at this years’ Winter Solstice
the 12-baktun Long Count will overflow.

Solving equations . . .

Although poets as long ago as Henry Lok (1553?-1608?), Elizabeth Tollett (1694-1854), and William Blake  (1757-1827) used mathematical imagery in their poems, the first collection of poetry-with-mathematics that I came to was Against Infinity:  An Anthology of Contemporary Mathematical Poetry (Primary Press, 1979), collected and edited by Ernest Robson and Jet Wimp.  This volume introduced me to poems I could use with my math students and one of my long-term favorites is "Algebra" by Linda Pastan who has, in turn, become one of my favorite poets. 

Algebra cadabra

It was my good fortune to meet Colette Inez back in the early 1990s when she was poet-in-residence at Bucknell University. Then, as now, I was collecting poems-with-mathematics, and I have long loved this poem that weaves figuring into forests.

Forest Children     by Colette Inez

We heard swifts feeding in air,
sparrows ruffling dusty feathers,
a tapping on stones, mud, snow, pulp
when rain came down, the hiss of fire.
Counting bird eggs in a dome of twigs,
we heard trees fall and learned
to name them on a page for school. 

A poet (math-daughter) speaks of math's beauty

I met Minnesota poet Roseann Lloyd when we served together on an AWP (Associated Writing Programs) conference panel on translation several years ago.  There I was considering, as I so often am, the translation of mathematics into representations that poets understand.  Roseann 's father was a mathematics professor and she learned early that "mathematics is its own beauty."  And she has permitted me to offer you this poem.

HOW MY DADDY CHANGED WHEN HE GAVE UP TEACHING COLLEGE FOR SELLING INSURANCE     by Roseann Lloyd

Once Daddy enthralled his students at SMS --
handsome in his navy blue suit and dusty hands,
chalk clicking out equations lickety-split.
A third-grader, I waited for him every day
in the cool marble hall.  Listened to the rhythm
of the chalk on the board.   Even then I knew
that pure math is an art equal to music, second
only to poetry in the realm of beauty.    

Counting responses

At the Poetry Foundation website, poet Audre Lorde (1934-1992) is described thus:

               A self-styled "black, lesbian, mother, warrior, poet," 

               writer Audre Lorde dedicated both her life 
               and her creative talent to confronting and addressing 
               the injustices of racism, sexism, and homophobia.

Here is a counting poem by this fine, bold poet:

Inequality of Compromise

This past week I attended a wonderfully stimulating BIRS (Banff International Research Station) Conference  -- a gathering of creative writers in mathematics and the sciences -- and, as I told colleagues at Banff of early days in my long-term interest in the poetry of mathematics, I recalled the fine collection Against Infinity:  An Anthology of Contemporary Mathematical Poetry (Primary Press, 1979), collected and edited by Ernest Robson and Jet Wimp.  Today I pulled it from my shelves and again turned its pages.  "Compromise" by Missouri mathematician Charles S. Allen caught my eye.  Here it is: 

The minute in infinity

From  Treatise on Infinite Series     by Jacob Bernoulli

Even as the finite encloses an infinite series
      And in the unlimited limits appear,
So the soul of immensity dwells in minutia
      And in narrowest limits no limits inhere.
What joy to discern the minute in infinity!
      The vast to perceive in the small, what divinity! 
 
                    Translated from the Latin by Helen M. Walker

Found in the anthology, Strange Attractors: Poems of Love and Mathematics (A K Peters, 2008), edited by Sarah Glaz and me.  A complete table of Contents for this collection may be found here.

Like advanced math?

One thing leads to another . .. . poet Amy Eisner connected me to mathematician Jordan Ellenberg who knew of Easy Math (Sarabande Books, 2013) by Lauren Shapiro -- and Lauren gave me permission to post her "Bent Syllogism."

 Bent Syllogism     by Lauren Shapiro

There was a pattern to the way the mythical beasts
flew over the dreary town, but we were too dreary
to understand it.  The psychologist, too, was in touch
with extraterrestrials, but she had to stand on the spire
of a church and wear 3-D glasses to see them. 

Love mathematics!

In the stanzas below, I have some fun with math terminology.  Hope you'll enjoy it too.

       Love!        by JoAnne Growney

       Love algebra!  Through variable numbers
       of factored afternoons and prime evenings,
       party in and out of your circle of associates,
       identify your identity,  meet your inverse.  

Neruda speaks of numeration

The collection, Late and Posthumous Poems, 1968-1974 (Grove Press, 1988) by Chilean Nobelist Pablo Neruda (1904-1973) offers to readers a collection of Neruda's later work, ably translated by Ben Belitt.  Here is a poem that explores the vast world opened by the invention of numeration.

     28325674549     by Pablo Neruda

     A hand made the number.
     It joined one little stone
     to another, one thunderclap
     to another,
     one fallen eagle
     to another, one
     arrowhead to another,
     and then with the patience of granite
     the hand 
     made a double incision, two wounds,
     and two grooves:  and a
     number was born.

On poetry and geometric truth . . .

          On poetry and geometric truth
          And their high privilege of lasting life,
          From all internal injury exempt,
          I mused; upon these chiefly:  and at length,
          My senses yielding to the sultry air,
          Sleep seized me, and I passed into a dream.

                                                  William Wordsworth (1770-1850)
                                                  from The Prelude, Book 5

From order to chaos -- a sonnet

Fractals    by Diana Der-Hovanessian

                             Euclid alone has looked on beauty bare
                                                    --Edna St. Vincent Millay

Euclid alone began to formulate
the relation of circle, plane and sphere
in equations making it quite clear
that symmetry is what we celebrate. 

Two cultures

The opening poem of Uneasy Relations by mathematician-poet Michael Bartholomew-Biggs is concerned with similarities and differences between mathematical and poetic cultures -- a topic of immense interest also to me and one that I too try to address in my verse.  I wonder --  HOW can I show non-mathematicians that good mathematics is poetry??!!  And, moreover, how can I (mostly a mathematician) write (as advocated by Wallace Stevens and agreed with by other poets) of things rather than (as mathematics wants) of ideas.  OR, may one make poetry of ideas?

   Two Cultures     by Michael Bartholomew-Biggs

   Graves claimed there isn't
   much money in poetry:
   and none vice-versa.

   The first part stays true
   if we replace poetry
   by mathematics. 

Two-line poems -- Landays -- from Afghanistan

Celebrate Activist Poetry -- At Nov. 1 Event

BE THERE on November 1, 2013 at the Goethe-Intitut in Washington DC when poet and journalist Eliza Griswold is  honored with the Split this Rock Freedom Plow Award (register here for this important event) for Poetry and Activism for her work collecting and introducing the folk poems of Afghan women to America.  The June issue of Poetry Magazine is entirely dedicated to landays -- two-line poems by Afghan women that capture dark, funny, and revealing moments that few outsiders ever witness.  (Edited and introduced by Griswold, the poems are magnificently supplemented by photographs by Seamus Murphy.)

Here are three landays from Griswold's Poetry collection, each selected for inclusion here because it includes at least one number: 

Topology for poets

     The title of this posting ("Topology for Poets") comes from Maryland Poet Amy Eisner's poem "Lure" (offered below) -- a poem that plays with math concepts.  (In mathematics, "topology" is a variant of geometry in two shapes are "equivalent" if one could be obtained from the other by stretching or bending.)   
     It was my pleasure to meet Amy when she read in the Takoma Park Third Thursday Poetry Series earlier this year.   I like her work.  Enjoy!

Lure    by Amy Eisner

1.

My friend is crocheting a fishing line. This is not a gift and keeps no one warm.
This is withdrawing. Persisting in a flaw. Forfending.

She knows there’s something perverse in it. Like growing a mold garden.
Fishing does involve a hook, a line, and a net. But not like this.

Mathematics of love . . .

"Mathematics of Love" is the title poem of a collection by John Edwin Cohen (1941-2012), published in 2011 by Anaphora Literary Press and presented here with press permission.  Cohen has used mathematics playfully and does what a mathematician never dares to do, use a mathematical term with other than its precise meaning. Still, perhaps, even math folks may enjoy this application of geometric shape and poetic license!

Mathematics of Love     by John Edwin Cohen

1.   

       Engine of joy
       arithmetic and sincere
       holding the hemisphere
              and geometry of
              youth

Circle Power

Everything the Power of the World does is done in a circle

         by Black Elk (1863-1950)  (translated from Sioux)

Everything the Power of the World does
is done in a circle.  The sky is round,
and I have heard that the earth is round
like a ball, and so are all the stars.
The wind, in its greatest power, whirls. 

"My Proteins"

The mysteries of science are sometimes explored in poems and, in this vein, I was delighted to find "My Proteins" by Jane Hirshfield (a poet whose work I like and admire) on page 56 of the September 16, 2013 issue of The New Yorker.   As she explores the riddles of who she is and where she came from, she has these lines-with-numbers (stanzas 3 and 4):

from My Proteins      by Jane Hirshfield

     Ninety percent of my cells, they have discovered,
     are not my own person,
     they are other beings inside me.

     As ninety-six percent of my life is not my life.
          . . .

Look for the entire poem; and enjoy! 
Another exploration of what the self is and isn't may be found in Hirshfield's "My Skeleton"  -- today's Poem-A-Day selection from Poets.org.  Jane Hirshfield's poem "Mathematics" is available here in my post for 23 June 2010.

Mathews retells Dowland (with permutations)

 In my post for 6 September 2013 I presented Oulipian Harry Mathews' poem "Multiple Choice" -- a poem whose alternative story lines might be represented by a tree diagram.  That poem was but one of 29 variations (or "Exercises in Style") by Harry Mathews as he retold again and again a tale first offered by lute-player and composer John Dowland (1563-1626), a musician whose work still finds audience today.   Here is Dowland's tale, from which Matthews created 29 alternative versions.  (See "Trial Impressions" in Armenian Papers, Poems 1954-1984 (Princeton University Press, 1987, out of print) and in A Mid-Season Sky:  Poems 1953-1991 (Carcanet, 1992).) 

Split This Rock 2014

     Plan now to attend the 4th national biennial Split This Rock Poetry Festival: Poems of Provocation & Witness in Washington, DC, March 27-30, 2014.  The sixteen poets to be featured at the 2014 festival are:  Sheila Black, Franny Choi, Eduardo C. Corral, Gayle Danley, Natalie Diaz, Joy Harjo, Maria Melendez Kelson, Yusef Komunyakaa, Dunya Mikhail, Shailja Patel, Wang Ping, Claudia Rankine, Tim Seibles, Myra Sklarew, Danez Smith, and Anne Waldman.   The website SplitThisRock.org offers photographs and more information about the festival.  It will be awesome!  

Measuring the World . . .

     Yesterday afternoon, at the Goethe Institut in Washington DC, I saw a wonderful film, "Measuring the World." Based on a popular 2005 novel by Daniel Kehlmann, the story of a friendship between preeminent German mathematician Carl Friedrich Gauss (1777-1855) and Prussian naturalist Alexander von Humboldt (1769-1859).  The film offers a delightful interplay of personalities and ideas as it darts between the explorations of these two men -- one digging inside his head for mathematics and the other traveling over mountains, through jungles, across oceans. 

Sonnet -- To Science

Edgar Allan Poe's "Sonnet -- To Science" was the "Poem-A-Day" selection of poets.org last week on September 29.  The poem is in the public domain and I offer it to you below. As Poe speaks of science I wonder whether -- if he had not announced his subject -- we might as easily imagine he is speaking of poetry. 

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.

Averaging . . . geometry of the center

Perhaps partly due to his experience as an Air Force pilot during World War II,  Harold Nemerov (1920 - 1991) uses geometry with deft precision as he describes phenomena around him.  Here is a poem inspired by a 1986 news item.

Found Poem     by Howard Nemerov 

           after information received in The St. Louis Post-Dispatch, 4 v 86

The population center of the USA
Has shifted to Potosi, in Missouri.

The calculation employed by authorities
In arriving at this dislocation assumes

That the country is a geometric plane,
Perfectly flat, and that every citizen,

A poet re-envisions space

University of Pennsylvania professor Robert Ghrist, in his September 19 lecture ("Putting Topology to Work") at the MAA's Carriage House, credited poet John Milton (1608-1674) with the first use of the word space as an abstract entity -- and, Ghrist asserted, by so doing, Milton opened a door to the study of abstract space (known in mathematics as topology).

The following material is a 24 September correction

from my 23 September posting.  For I discovered -- in a thoughtful email from Ghrist --

that the proper citation of "space" was not from line 50 of Book 1 but from line 89 of Book 7.  

(I invite you go to Project Gutenberg for Paradise Lost in its entirety.)

Here, below, I have replaced my original posting of  lines 44-74 of Book 1 

with lines 80 - 97 of Book 7 --  lines taken from my shelf copy of Milton's Paradise Lost,

 the 1968 Signet Classic Edition, edited by Christopher Ricks.

In the selection below and throughout his epic, Milton replaces past visions of hell down-in-the-earth and heaven up-in-the-sky with more complex and abstract configurations.

BRIDGES poems, from 17 poets

Due to the hard work of mathematician-poet Sarah Glaz, poetry has been an important part of recent BRIDGES-Math-Art Conferences. And, under her editing, a Bridges 2013 Poetry Anthology has been released, featuring poetry from these poets who participated in one or more of the three most recent BRIDGES conferences (Enschede, Netherlands, 2013; Towson, Maryland, 2012; Coimbra, Portugal, 2011). 

Perfect circle, Haiku

          Perfect circle round
               the moon
          In the center of the sky

by Jack Kerouac (1922-1969), from Book of Haikus  (Penguin, 2003).  Thanks, Francisco.

PS.  If Kerouac were a mathematician he'd have noticed that "perfect" is implied by the definition of "circle" and is unnecessary.  But Kerouac was a poet and he saw a different necessity.

Consider Pascal

     Mathematician Blaise Pascal (France, 1623-1662) is known for his explorations with computing machines, for his ideas concerning probabilities, for trying to make rational a decision to believe in God and eternal life, for his explorations of the cycloid and the limacon (curves generated by rolling circles) and a host of other topics.
     I was introduced to Melbourne poet, novelist, and mathematician (he teaches at Victoria University of Technology), Tom Petsinis by South-African editor of Poetry-International, Liesl Jobson.  Here from Petsinis' collection, Naming the Number (Penguin, 1998) is "Pascal's Tooth," (a poem also available at the Poetry-International site).  In the grip of severe pain, Petsinis ponders the ideas of Pascal.  

Kaplansky sings Kaplansky (and Pi)

     I first knew of mathematician Irving Kaplansky (1917-2006) through his monograph, Infinite Abelian Groups -- it was one of my texts for a graduate seminar (with Gene Levy) at the University of Oklahoma in the 1960s.  Later I knew Kaplansky as a songwriter, author of new lyrics for "That's Entertainment."  Kaplansky's adaptation, "That's Mathematics," dedicated to his former student, math-musician-songwriter Tom Lehrer, and to his daughter, singer Lucy Kaplansky, is given below.
      In 1999, in Science News, writer Ivars Peterson (now Director of Publications for the MAA -- Mathematical Association of America) wrote an article about Kaplansky's songwriting in which he mentions  his daughter, Lucy Kaplansky, a singer who frequently performs her father's songs.  A YouTube recording of Lucy singing "The Song of Pi" (in which there is a correspondence between musical notes and the first fourteen digits of pi) is available here.  (Lyrics for "The Song of  Pi" and information about the correspondence are available in Peterson's article.)

Nature poems -- at Stillwater

     As noted in my 5 August posting, the Stillwater poetry festival (organized by Kevin Clark) was scheduled for last Saturday, September 7 -- and I was (though delayed by the death of a car battery) able to attend.  A time to catch up with old friends -- River Poets Dave Barsky, Carol Ann Heckman, and Janet Locke, and Wilkes-Barre poet Richard Aston.  Poets and musicians featured at the festival included Lester Hirsh, Pamela Kavanaugh, James Pingry, Doug McMinn, Jack Troy, Julia Spicher Kasdorf, and Sheryl St. Germain. 
     The theme at Stillwater was Nature/Agriculture and my 5 August post included poems from conference organizer Clark and featured reader Kasdorf -- poems that involved both nature and mathematics.  Although found in Kasdorf's opening poem, "Double the Digits," mathematics was scarce.  Sheryl St. Germain, the final reader (currently a Pittsburgher, transplanted from New Orleans) briefly mentions computation and measurement in her "Hurricane Season ."   The full poem is available through St Germain's website; here is one of its stanzas. 

Mathematical structure and Multiple choice

     A sonnet repeats the iambic rhythm of the heart beat (da-DUM, da-DUM, . . .) with a line length corresponding to a typical breath (5 heartbeats); it thus seems easy to internalize the numerical structure that guides such a poem. 
     A decision tree offers a very different choice of mathematical structure for a poem -- displaying for a reader different choices among stanzas.  Originally proposed to the OULIPO by founder Francois Le Lionnais, and referred to as a multiple-choice narrative, such a structure allows readers of a poem to choose among subsequent events. Instead of reading the poem vertically, we may jump about, choosing the sequence we want to read.

Poetry-with-math in Baltimore -- 17 Jan 2014

At the Joint Mathematics Meetings in Baltimore (January 15-18, 2014), the Journal of Humanistic Mathematics (under the leadership of editors Mark Huber and Gizem Karaali) will sponsor a poetry reading.  Mark your calendar now! (And be sure to scroll down past the reading announcement to poems from last year's JHM reading in San Diego by poets Katie Manning and Karen Morgan Ivy.)

 Friday,  January 17, 2014. 4:30 - 6:30 PM

 Room 308  Baltimore Convention Center  

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. 

Poetry in a math text

     In the 1980s, all students at Bloomsburg University were required to take at least one mathematics course and I worked with colleagues to develop a suitable offering -- one that did not require expertise in algebra but which emphasized problem-solving.  Our course became "Mathematical Thinking" -- and I began to develop suitable materials -- eventually writing and publishing Mathematics in Daily Life:  Making Decisions and Solving Problems (McGraw-Hill, 1986).  Each of the twenty-two chapters of this textbook is introduced with a relevant quote.  Chapter 11, "Visualizing the Structure of Information with a Tree Diagram," opens with two lines by one of my favorite poets, Theodore Roethke:

               Once upon a tree              
               I came across a time.

Celebrating a math-woman

I am continually searching for poems that feature past and current math-women.
When you find one (or create one) I will be glad to have you send it along.

The lunar crater L Herschel is named for astronomer Caroline Lucretia Herschel (1750-1848) -- and I have celebrated this math-woman earlier with two fine poems:  "Letter from Caroline Herschel" by Siv Cedering , and "Planetarium" by Adrienne Rich.  Now Herschel is the focus of a forthcoming book by poet Laura Long, The Eye of Caroline Herschel: A Life in Poems, (Finishing Line Press, 2013).  Here, from that collection, is "The Taste of Mathematics:  Caroline Herschel at 31" -- this poem also appears, along with a note about the full collection, in the July 2013 issue of The Journal of Humanistic Mathematics.  

Out of 100 -- in the Klondike Gold Rush

Adding to my recent post on 19 August I note that OEDILF is seeking submissions.   
Join the project:  submit limerick definitions of  (math)  terms for OEDILF consideration.

One of my favorite poets is the 1996 Nobelist Wislawa Szymborska (1923 - 2012, Poland); one of my favorites of her poems is "A Contribution to Statistics."  Szymborska's poem served as a model for a poem of mine shown below, about Gold Rush Days in Skagway, Alaska.  Written while I was poet-in-residence at Klondike Gold Rush National Historical Park, (in Skagway), this poem draws on historical data from the park's library to paint a bleak picture of wealth and survival in those gold-mad days.  

Counting in the Klondike     by JoAnne Growney
   
                        after Wisława Szymborska

Of 100 who left Seattle for Skagway in 1898
40 made it to the gold fields
8 found gold.    

OEDILF - the Limerick Dictionary

     At this site  Editor-in-Chief Chris Strolin is coordinating development of OEDILF: The Omnificent English Dictionary In Limerick Form.  So far, definitions are available (and being submitted) for terms beginning with letter-pairs Aa - Fd -- and completion of the dictionary is predicted at the OEDILF website for 2043.
     I have mentioned OEDILF before -- on 5 December 2012 and 29 March 2010. And today I offer a draft limerick about "factors" -- I am at this point, however, dissatisfied with my use of the plural rather than simply "factor."  More work needed.

Pushkin inspires Seth -- novels in verse

      My enjoyment of novels in verse began to thrive when a friend and I determined to get into Vikram's Seth's The Golden Gate (Random House, 1986) by taking turns reading its sonnets aloud to each other. After several dozen aloud, I could hear the voice even when I read silently and I went on to finish alone. And I loved it. I have gone on to enjoy several more works by Seth -- none of them poems but all wonderful stories, well told.
      Seth has said that he was moved to write by the novel Alexander Pushkin's verse novel Eugene Onegin noted here on 10 August 2013 -- a novel of interest to mathematicians because of its link to Markov Chains. Seth's novel (reviewed here) also was made into an opera. These first two stanzas -- each containing the numbers 26 and 1980 -- introduce the novel's computer-guy, John:

Emily Dickinson

     Although I do not consider any of Emily Dickinson's poems "mathematical," I find that she does not shy from using the terminology of mathematics. For example, her repetition of the word "circumference" noted in an earlier posting.  (To search this blog for mentions of Dickinson (1830 - 1886) or any other poet or topic, follow the instructions offered in green in the column to the right.)
     Dickinson is on my mind these recent days following my opportunity last Saturday evening to attend a session of a conference held by the Emily Dickinson International Society.  A gracious invitation by Martha Nell Smith enabled me to attend a program that featured two long-time friends, actor Laurie McCants of the Bloomsburg Theatre Ensemble, performing a scene from her one-woman show, Industrious Angels, and Stephanie Strickland, a New York poet who, along with collaborator Nick Montfort, offered background and performance for Sea and Spar Between, a poetry generator that works with language patterns for these two writers.

Pushkin poetry, Markov chains

A Markov chain is a mathematical process that can be used to answer questions such as these:
          If the current letter I am reading is a vowel, what is the probability 
          that the next letter will be a vowel?  A consonant? 
Answers from these may be combined to create more lengthy predictions -- about the 3rd letter after a given one, or the 10th -- and so on. 
     A recent article by Brian Hayes in American Scientist (brought to my attention by Greg Coxson) alerted me to the fact that it is 100 years since the Russian mathematician A. A. Markov (1856 - 1922) announced his findings about these transition probabilities -- and, moreover, his work was based on analysis of poetry; the poetry was Eugene Onegin, a verse-novel in iambic tetrameter by Alexander Pushkin (1799-1837). Markov's analyis dealt with Pushkin's novel as a long string of alphabetic characters and he tabulated the categories of vowels and consonants for about 20,000 letters. (For a host of details, visit Hayes' careful and interesting article.)

Feynman Point poems

The Feynman Point is a sequence of six 9s that occurs in the decimal expansion of π -- these 9s are found in positions 762 - 767 following the decimal point.  When writing in Pilish (using word-lengths that correspond to digits of π), the Feynman Point offers a particular challenge since 9-letter words are infrequent.  I learned about the Feynman Point here.  AND I found a splendid database that makes the difficult task of choosing 6 9-letter words easily doable.   Here is my first Feynman Point poem:
 
      Scratchers sleepwalk --
      seriously screening sentences,
      slantwise.

Mike Keith's Pilish short story, Cadeic Cadenza, has this Feynman Point: 

Poetry on Back Roads -- Stillwater Festival

     On Saturday, September 7, a poetry festival will happen in Stillwater, PA (a small town not far from Bloomsburg where I lived and professored for many years).  From noon to 9 at the Stillwater Memorial Park (63 McHenry Street (Rt 487) Stillwater, PA), organized by Kevin Clark, held in a revival-style tent, the the reading will have nature and agriculture as its theme -- and featured poets will include Julia Spicher Kasdorf, Sheryl St Germain, and Jack Troy.  (And there will be two open mic sessions.)
     Offered below are two poems by festival participants -- these are poems of numbers and travels (and more):  "Double the Digits" by Penn State poet, Julia Spicher Kasdorf, and "Tag Clouds," by Stillwater festival organizer, Kevin Clark (contact using StillwaterPoetry-at-yahoo-dot-com). 

Nursery Rhyme Mathematics

During the last week of July I was in California, vacationing with family (including six of my grandchildren).  Most of these kids have grown past a fascination with nursery rhymes, but I still like them -- and think it's likely that memorization of rhymes helps with learning to read and count. 

Here is one of my favorites, "A Diller, a Dollar."

Number personalities

In his collection, Zero, Scottish poet Brian McCabe raises questions about numerical classifications.  He begins "The Fifth Season" with "Everyone talks of the four / -- none speak of the fifth." Another poem, "The Seventh Sense, " moves from a similar beginning " . . . none speak of the seventh" into a dreamy apprehension of the magical possibilities of items not yet classified. The following selection from Zero, "Triskaidekaphobia," offers remedies for the fear of bad luck brought by 13. 

Another 17-word Haiku

If a poet uses only one-syllable words, the resulting Haiku is a bit longer than usual -- as in this Haiku in which the word lengths also follow an increase/decrease pattern, 1-2-3-4-5-6-7-8-9-8-7-6-5-4-3-2-1: 

I am the girl voice.
Drafts scribed -- thoughts stretched, smoothed, squared, sighed --
catch here now my I.

I have offered other 17-word Haiku in these postings -- 27 June 2013 and 16 July 2013 -- and the latter of these is my entry into the Haiku-to Mars contest.  To vote for that Haiku to be one of three sent to Mars by NASA on the Maven spacecraft next November, click here.  (Voting ends July 29.)

A poem with two numbers

My friend Carol Ann Heckman has studied with Denise Levertov and feeds voraciously on her work.  For many years I have loved Levertov's "The Secret" and today, rereading an email from Carol Ann, I went looking for a mathy poem by this beloved poet.  I found the following -- with two numbers (and a hint of recursion):

     The Mockingbird of Mockingbirds     by Denise Levertov

     A greyish bird
     the size perhaps of two plump sparrows,
     fallen in some field,
     soon flattened, a dry
     mess of feathers--
     and no one knows
     this was a prince among his kind,
     virtuoso of virtuosos,
     lord of a thousand songs,
     debonair, elaborate in invention, fantasist,
     rival of nightingales.

This poem rests on my bookshelf in Levertov's collection, Breathing the Water (New Directions, 1987).

Poets at BRIDGES

These seven poets will be reading math-related poems at the upcoming (July 27-31) BRIDGES Conference in Enschede, the Netherlands; biographical information about the coordinator, Sarah Glaz, and each of the poets is available here. With each poet's name I have offer a date that is linked to one of my postings of his/her work:         
          Michael Bartholomew-Biggs    19 October 2012
          Tatiana Bonch-Osmolovskaya   10 March 2013
          Carol Dorf   31 May 2011
          Sarah Glaz   7 November 2011
          Emily Grosholz  24 September 2010
          Alice Major   30 December 2012
          Eveline Pye 12 April 2012
Here (and also to be offered at BRIDGES) is an elegant and thoughtful poem by Alice Major  -- "For Mary, Turning Sixty" -- that compares mathematical meanings of terms with personal ones. 

BRIDGES 2013 -- Math-Art in the Netherlands

Since 1998, Summer BRIDGES Conferences have been held -- enthusiastic gatherings where theater and visual art and music and poetry and mathematics engage participants in lively exchange.  This year's conference is July 27-31 in Enschede, the Netherlands, and mathematician-poet Sarah Glaz has organized an outstanding group of talented readers to share their poetry on Sunday, July 28.  Following the featured readers will be an open reading -- and interested readers are invited to email Glaz using the address found here. 
      One of  the scheduled readers on July 28 in Enschede is Scottish poet and statistician Eveline Pye; shown below is one of the poems she will read --  "Love of Algebra" : 

Haiku to Mars -- select and vote

     Each of us may now (July 15 - 29) vote for one of the thousands of Haiku submitted to NASA's "Haiku for Mars" contest. Three top vote-getters will be selected for transmission to our red planet. I invite you to vote (at this link) for my entry. My contest Haiku also is shown below; it follows a particular number scheme -- formed from one-syllable words with word-lengths following this pattern: 1-2-3-4-5-6-7-8-9-8-7-6-5-4-3-2-1.

I go for Mars, start

dreams -- flights straight, stretched, streamed, whirled bright.

Round bold red am I.

THANKS for your vote. 

Counting on numbers

Alan Michael Parker's anthologized and highly regarded poem "Family Math" begins in the style of a typical word-problem from Algebra -- and continues with a weaving of the ways that numbers describe our lives.

Family Math     by Alan Michael Parker

I am more than half the age of my father,
who has lived more than twice as long
as his father, who died at thirty-six.

Pool -- a game of geometry?

     Years ago I taught  a "liberal arts mathematics" course -- and for a time we used the text  Mathematics, a Human Endeavor: A Textbook for Those Who Think They Don't Like the Subject by Harold R. Jacobs (W H Freeman, 1971);  the text's topics included one new to me, the geometry of the paths of billiard balls.  The ease I found with this mathematics ill-prepared me for the skill I needed to avoid embarrassment at a neighbor's new pool table -- and the memories of it all drew me immediately into Dan Brown's poem, "Why I Never Applied Myself to Pool," found in the March 2013 issue of Poetry.

       Why I Never Applied Myself to Pool      by Dan Brown

Grandma got STEM

     There are so many fine websites to visit and blogs to read that it is hard to get to them all. One of my recent pleasures has been Grandma Got STEM (STEM  = Science, Technology, Engineering, Mathematics), orchestrated by Rachel Levy, Harvey Mudd College, Mathematics.  Recent entries there that I've enjoyed are Martha Siegel (Towson University, Mathematics) and Carol Jo Crannell (mother of Annalisa Crannell, Franklin and Marshall College, Mathematics and Art).
     For a while I wondered how I might link these STEM pioneers to poetry and this morning was delighted to discover in a bio of poet Mei-Mei Berssenbrugge that her Chinese mother was a mathematician.  And these initial stanzas of Berssenbrugge's poem "Tan Tien" illustrate her familiarity with mathematical vocabulary.

Calculus (and calyculus)

For lots of years I have subscribed to A.Word.A.Day, founded by Anu Garg, and on 3 June 2013  -- offered in the category of "words that appear to be misspellings" -- the word that appeared in my email was calyculus (kuh-LIK-yuh-luhs), a noun designating a cup-shaped structure.  From this, of course, my thoughts turned to calculus and to poems on that subject.  Below I offer "UR-CALCULUS" by Jonathan Holden.  This Kansan poet has said that that his physicist father would write equations while sitting at the dining room table -- and "UR-CALCULUS" considers mathematics from a boy-riding-in-the-back-seat-of-a-car point of view.  

     UR-CALCULUS     by Jonathan Holden

               The child is the father of the man. 
                        -- W. W. Wordsworth

     Back then, "Calculus"
     was a scary college word,
     and yet we studied it
     from the back seat, we studied  
     the rates at which
     the roadside trees went striding 

Miroslav Holub -- "what use is it?"

     In earlier postings I have expressed my admiration for the Czech poet Miroslav Holub (1923-1998)  -- a research scientist who also wrote fine poetry.  In a biographical sketch of Holub at poetryfoundation.org, the poet is quoted as saying, " . . . I'm afraid that, if I had all the time in the world to write my poems, I would write nothing at all."   There is no agreed standard for the amount of time  to spend on a creative work.  Many poets devote their full time to their craft;  others fear over-writing and strictly limit their writing and editing.  In each aspect of our lives it is possible to do too much or too little thinking about things.  And so it goes.
      My post on 5 April 2013 linked to several math-related Holub poems.  And here is another; in "Magnetism," Holub focuses on the sometimes-silly, sometimes-practical, sometimes-too-limiting question often put to mathematics or science, "what use is it?"

Magnetism     by Miroslav Holub

17-word Haiku

     On 25 May 2013 this blog contained an announcement of NASA's Haiku-to-Mars contest.  The contest rules are here -- and July 1 is the deadline for submission.  Voting to select three favorite submissions will begin on July 15.  For my own submission I decided to use numerical constraints -- I limited my Haiku to one-syllable words and used an increasing-decreasing pattern of the lengths of words.  Here is an example (not the one I submitted, which begins "I go for Mars . . .").

A is the sign first
spread through thoughts –- stretched, breathed, squared, sighed.
Trace thru all to Z.

Symmetric squares

Sometimes we find meaning among disparate objects when they are juxtaposed. Here are nine words I have chosen because of the ways they are spelled. Using them to form two squares. Are my squares poems?

     S A F E
     A R E A
     F E A R
     E A R N

Why is SHE less known? . . .

Sometimes matching words to a syllable-count helps to bring focus to my musings.  Here are two stanzas for which I used the Fibonacci numbers as lengths for the lines I built as I considered the continuing invisibility of most math-women. (I have some hope that the second of these is primarily remembering -- and is not true of family child-care today.)

8-5-3-2-1-1    A FIB

HE is famous but SHE is not.
Yet we once judged her
potential
greater
than
his.

Balancing an Equation

     I grew up on a farm and spent my middle life in a small town and now live in a city.  A sort of immigrant.  A farm girl who became a professor.  A balancing act.
     Some years back, one of my math department colleagues posted on his office door a quote from George Bernard Shaw (1856-1950) :   

     The reasonable man adapts himself to the world: the unreasonable one persists 
     in trying to adapt the world to himself. Therefore all progress depends 
     on the unreasonable man.

At one time I much agreed with the Shaw quote.  Now (perhaps because I am older or because I now live near to Washington, DC and contentious party politics) I am more admiring of balance than unreasonableness.  Here is a lovely poem by Caroline Caddy about balance and numbers. 

What is not possible?

     It is impossible for a number to be greater than 2 if it is not greater than 1.  It is impossible to find a rational number whose square is 2.   Up to now it has not been possible to show that π is a normal number.  Mathematicians like the challenge of the impossible.  To challenge, to prove, to refute.
     In the poem below Chelsea Martin devises an entertaining web of circular reasoning to explore the impossibility of eating at MacDonald's.

McDonalds Is Impossible       by Chelsea Martin

Eating food from McDonald's is mathematically impossible.
Because before you can eat it, you have to order it.
And before you can order it, you have to decide what you want.
And before you can decide what you want, you have to read the menu.
And before you can read the menu, you have to be in front of the menu.
And before you can be in front of the menu, you have to wait in line.
And before you can wait in line, you have to drive to the restaurant.
And before you can drive to the restaurant, you have to get in your car.
And before you can get in your car, you have to put clothes on. 

Count your things

     In the development of human culture, mathematics began with counting.  And so it also begins with each child as she/he grows.
     Someone said that a person is wealthy when she has more things than she can count.  Another view is that true wealth is having no need to count.  Whether or not either is is correct, we can appreciate "My/My/My" by poet Charles Bernstein (begun below and completed at poets.org).

My/My/My        by Charles Bernstein   

          Count these number of things you call mine. This is the distance between
          you and enlightenment.                                 —Swami Satchidananda

                        (for Jenny)

my pillow

my shirt

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 Man-Made Universe and "found" poems

 Some poems are found rather than crafted.
It's such fun -- can happen to anyone -- 
to be reading along and find a poem. 

     This post continues (from the June 4 posting) consideration of lines that were not initially written as poetry but have been later discovered to have the desirable characteristics of a poem.
     In an early-April posting I offered a poem-in-a-photo, a poem created of book spines -- and the bottom book in my pile of six is Mathematics, the Man-Made Universe:  an Introduction to the Spirit of Mathematics by Sherman K Stein (Third Edition, Freeman, 1976).  Reprinted in 2010 in paperback format, Stein's textbook -- for a "general reader," a curious person who is not a mathematician -- has been on my shelf for many years and, though I never taught from it, I have enjoyed it and shared it with friends (and I love its title). Recently, in the opening paragraph of Stein's Chapter 19 (page 471), I found a poem:

A poem from an airline call center

     Poet Laura LeHew offers us "The New Math"-- a "found" poem that features conversations and calculations from call center negotiations to reschedule an airline flight -- posted in April, 2011 by the nonprofit literary arts collective [PANK].
     LeHew's poem starts out like this:

The New Math     by Laura LeHew
     a found poem 

Credit for the call center in India
to change your flight to the wrong day,
again

                                                                                      ($350.00) USD

Geometry of distance

     Some of the poems herein arrive as gifts from friends.  Today's poem came via e-mail from Susan (a Californian whom I have gotten to know when she visits my neighbor, Priscilla).  Susan got it from Larry Robinson who connected me with the poet, Richard Retecki, for permission to post it here.
     As has been said in other contexts, It takes a village . . .    
     Thanks to you all!

     ascension           by Richard Retecki

               for Jonathan Glass

     the geometry
     of distance annoys
     is unfilled