Earthquake and Hurricane

It would not be easy to argue that a poem whose numbers merely identify its stanzas is "mathematical" but "Curriculum Vitae," found at poets.org and written by Pullitzer Prize winning poet Lisel Mueller, also contains the words "earthquake" and "hurricane" and thereby is significant on this Saturday in Silver Spring -- five days after a 5.8-magnitude earthquake damaged both the Washington Monument and the National Cathedral and on the very day that millions of us are watching the progress of Hurricane Irene as it storms north along the eastern coast of the US. In acknowledgment of these days, I invite you to read this fine poem:

350: Science --> Poetry --> Music

350 parts per million is the "safe upper limit" for CO₂ in our atmosphere presented by NASA scientist Jim Hansen in December 2007 and widely agreed upon.  From that number 350.org .was born. On October 24, 2009, 350 Poems celebrated an international day of climate action with a posting, from poets all around the world, of 350 poems of 3.5 lines each --  each responding to concern for man-made climate change. 

A thousand and fifty-one waves

Twenty-five years ago I had an enormous appetite for poems by Stevie Smith (1902-1971).  I loved the way that they seemed so unstudied -- playful and yet spot on and profound.    Smith did not use much mathematics in her poetry, but she wrote this poem, "Numbers." 

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.

Lieber's INFINITY -- poetic prose

It has surprised me to discover that some of my best-remembered learning took place at the hands of teachers I did not particularly like.  One of these was a professor who introduced me, via outside reading assignments, to books by Lillian R. Lieber (1886-1986).  Her free-verse-style lines in Infinity:  Beyond the Beyond the Beyond gave me insights into the calculus I had recently completed as well as the set theory of my current course. (Lieber wrote not just as a mathematician but also as a human being, as a wonderfully informed and openly opinionated person.  For this, too, I treasure her work.)

Some cat!

My title is a borrowing from E. B. White's Charlotte's Web -- which I saw recently with grandchildren at Glen Echo Park's Adventure Theater. It (the title above) refers to my wonderful Himlayan, Noah, who lived to 15 years and 3 months;  this posting is done in his memory.  Herein we connect cats with mathematics.

The hypotenuse of an isosceles triangle

Detroit poet, Philip Levine, has been selected as the new Poet Laureate of the United States. Selected by the librarian of Congress (James Billington), Levine follows poet W. S. Merwin in the honored position.  A Poet Laureate is responsible merely for giving readings in October and May but some laureates also use the position to proselytize for poetry.   Here, from Levine's early collection, What Work Is (Knopf, 1992), is a poem that looks back on a math-art moment in a middle-school classroom.

Can a mathematician see red?

Held late in July, this year's 2011 Bridges (Math-Arts) Conference in Coimbra, Portugal included a poetry reading for which I'd been invited to read but was, at the last minute, unable to attend. (See also 26 July 2011). Poets Sarah Glaz and Emily Grosholz each, however, read favorite selections from my work.  Glaz read one of my square poems, "The Bear Cave" (see 19 June 2011) and Grosholz read the poem shown below, "Can a Mathematician See Red?"

Banach's Match Box Problem

A poetry collection by Susan Case (see also 5 July 2011 posting)  -- The Scottish Cafe (Slapering Hole Press, 2002) -- celebrates the lives and minds of a group of mathematicians in Poland during World War II. Its observations and insights add a new dimension to the important story of the Scottish Book to which it refers -- a book in which the mathematicians reorded their problems and solutions. First published in a mimeographed edition in 1957 by Stanislaw Ulam, The Scottish book: mathematics from the Scottish Café (Birkhäuser, 1981) may now be seen and searched at GoogleBooks.  Case's collection includes statements of two of the Scottish Book's problems:  here, below, is "problem 193" -- which I offer as a "found poem."  A photo of its Scottish Book solution follows.

Cantor Ternary Set

The second issue of the Journal of Humanistic Mathematics has recently been posted -- with more new poems.  The first issue contained a poem by Philip Holmes about one of the most amazing collections of numbers in all of mathematics, the  Cantor Ternary Set.  This set, discovered by Henry John Stephen Smith (1826-1883) but popularized by Georg Cantor (1845-1918) consists of all the real numbers whose base 3 or ternary representations involve only the digits 0 and 2. Like a fishing net, the Cantor Ternary Set is mostly holes. "Gaps" by Philip Holmes spreads it out before us -- and reflects on what else it may represent:

Puzzle play

In volume 4 of The World of Mathematics (James R Newman, Editor; Dover 2003), in a section entitled "Amusements, Puzzles, and Fancies," is an essay by Edward Kasner and James R. Newman entitled "Pastimes of Past and Present Times." This piece is prefaced by a quote from Mark Twain: "Work consists of whatever a body is obliged to do, and play consists of whatever a body is not obliged to do." One of the characteristics that mathematicians and poets have in common  is that both enjoy mind-play -- mental adventures with ideas or numbers or words, dancing and shaping into some new thing.

Mathematical Induction -- principle, perhaps poem

One of my teachers -- I think it was Mr Smith in "College Algebra" during my freshman year at Westminster -- gave me these words to remember:

     When confronted
     with a statement
     that seems true
     for all positive integers
     the wise student
     uses mathematical induction
     as her proof technique. 

Bridges in Coimbra

     Newton's binomial is as beautiful as Venus de Milo.
     What happens is that few people notice it.

                -- Fernando Pessoa (as Álvaro de Campos) (1888-1935)
                    translated from the Portuguese by Francisco Craveiro

Little Infinite Poem

   Little Infinite Poem       by Federico Garcia Lorca

               For Luis Cardoza y Aragón

      To take the wrong road
   is to arrive at the snow,
   and to arrive at the snow
   is to get down on all fours for twenty centuries and eat
         the grasses of the cemeteries.

The wind, counting

     Who can ever forget
     listening to the wind go by
     counting its money
     and throwing it away?

Finding a square root

Here is an old poem (1849) by George Van Waters that offers instruction on finding a square root. This process was part of my junior high learning at the Keith School in Indiana, PA lots of years ago but I suppose the algorithm is seldom taught in 21st century classrooms.  (In case the poem's directions are unclear, additional instruction is offered here.)

I have dreamed geometry

   Descartes     by Jorge Luis Borges

   I am the only man on earth, but perhaps there is neither earth nor man.
   Perhaps a god is deceiving me.
   Perhaps a god has sentenced me to time, that lasting illusion.
   I dream the moon and I dream my eyes perceiving the moon.
   I have dreamed the morning and evening of the first day.

Seeking a universal language

Is mathematics a universal language?  Not only is this universality often postulated but also it was said  -- some decades back -- that devices were broadcasting into space the intial decimal digits of pi, expecting that other intelligent beings would surely recognize the sequence of digits.  Robert Gethner examines this arrogance in a poem.

Ancestry -- what counts

Etheridge Knight began writing poetry while an inmate at the Indiana State Prison and published his first collection, Poems from Prison, in 1968.  His poem "The Idea of Ancestry" shows us what a man in prison finds time to count:

   The Idea of Ancestry   by Etheridge Knight

          1
  
   Taped to the wall of my cell are 47 pictures: 47 black
   faces: my father, mother, grandmothers (1 dead), grand-
   fathers (both dead), brothers, sisters, uncles, aunts,
   cousins (1st and 2nd), nieces, and nephews. They stare
   across the space at me sprawling on my bunk. I know
   their dark eyes, they know mine. I know their style,
   they know mine. I am all of them, they are all of me;
   they are farmers, I am a thief, I am me, they are thee.

Mathematicians at work

     About her collecton, The Scottish Café (Slapering Hol Press, 2002), Susan Case offers this note:
     This series of poems is loosely based upon the experiences of the mathematicians of the Scottish Café, who lived and worked in Lvov, Poland (now L'viv, Ukraine), a center of Eastern European intellectual life before World War II, close to the area from which my own ancestors emigrated to the United States.  A book, known as the Scottish Book, was kept in the Café and used to write down some of their problems and solutions.  Whoever offered a proof might be awarded a prize.
     Here is "Fixed Points," the opening poem from Case's collection:

Mathematicians divide

One of my fine graduate courses at Hunter College was a "World Poetry" course taught by William Pitt Root.  One of our texts was Against Forgetting:  Twentieth-Century Poetry of Witness (W W Norton, 1993), edited by Carolyn Forché.  In this collection is found "To Myself," a poem that confronts fear, by Abba Kovner (1818-1987), a hero of anti-Nazi resistance. Kovner dares to open the poem with the word "Mathematicians."

5 x 5 and 6 x 6

Many poets have found the sonnet to be an ideal poetic form -- its iambic pentameter lines are like five heartbeats assembled in a single breath;  its fourteen lines are a good number for considering a matter carefully. My own frequent form is different -- not a sonnet but a square of some or another dimension.   Here are two of my recent syllable-squares.

     I squint with tension,
     puzzle over this:         
     dissatisfaction's
     itchy appetites
     are my happiness.

The Joys of Mathematics

   The Joys of Mathematics     by Peter Boyle

   At fifty I will begin my count towards the infinite numbers.

   At negative ninety nine I will start my walk towards the
      infinitesimally small.

Creation Myth on a Mobius Band

On the  website of Bert-Jaap Koops, I found this small poem by a poet I admire greatly, Howard Nemerov (1920-1991).

     Creation Myth on a Moebius Band   by Howard Nemerov

     This world’s just mad enough to have been made
     by the Being His beings into Being prayed.

Something for nothing

     Among my favorite mathematical ideas are the seeming-paradoxes -- notions that require a twist and a turn and a leap before one can say "aha."  Using a symbol for "nothing" is one of those leap-requiring ideas.  I don't remember when I first understood zero, but I have enjoyed watching my children -- and now grandchildren -- grapple with ideas of things that are absent rather than present. 
     Here, from Hailey Leithauser, is a poem  that celebrates the cipher. 

Circling -- with Rilke

Ranier Maria Rilke (1875-1926) was born in Prague but emigrated to Germany and is one of the great modern lyric poets.   The following Rilke poems draw on images of circles.

Found in Flatland

Over the years I have shared with friends and students my copy of Edwin Abbott's Flatland (first published in England in 1884) and, alas, not all of these other readers have matched my level of excitement with the small volume.  Even though the book's Victorian attitudes are mostly at odds with my own views, still the tiny book opened me to possibilities of new ways of seeing. Since observing the Flatlanders stuck in two dimensions from my advantageous three-dimensional position, I have wondered how I can now make the leap from three to four or more dimensions.

Stanescu - poetic mathematics

Today I found a link to a recent article, "Matematica şi poezia," that considers commonalities among the arts and mathematics and, therein, mentions a poem by Nichita Stanescu (1933-1984) which Gabriel Prajitura and I have translated.  The poem, "Poetic Mathematics," is dedicated to Romanian mathematician Solomon Marcus.  Here is Gabi's and my translation: 

Lagrange points

The Italian-French mathematician Josef Lagrange discovered the existence of five special "Lagrange points" (aka Lagrangian points) in the vicinity of two orbiting bodies where a third, smaller body can orbit at a fixed distance from the larger ones. More precisely, Lagrange Points mark positions where the gravitational pull of the two large bodies precisely cancels the centripetal acceleration required to rotate with them. Poet Catherine Daly considers these points in a poem:  

Counting on things -- a prose poem

Russell Edson is one of the contemporary masters of the prose poem (a poem whose words are organized into paragraphs rather than stanzas). A selection from May Swenson's prose poem (and short novel) "Giraffe" is available in the October 19 blog posting. Here is Edson's poem "One Two Three, One Two Three" -- which considers the secrets hidden inside one's head.  Another mind, even that of one of our children, is a mystery incompletely known to any of us.

Right Triangle

The shape of a poem influences our reading of it -- short lines cause reading with lots of pauses whereas we read long lines quickly to get the entire line completed in a single breath. Moreover, some poetry is intended to be primarily visual -- to be taken in as a seen-image rather than read.  UBU Web offers several example of early visual poetry and one may also explore the  UBU Web site for modern examples.  Visual poetry may also be termed "concrete" poetry; consider, for example, "Concrete Block" by Michael J. Garofalo:

Math lyrics -- Lehrer et al

Mathematicians with poetic tendency often use their word-talents to write song-lyrics rather than poems; a master of the song-writing art was/is Tom Lehrer.  As an undergraduate at Harvard in the 1940s,  Lehrer majored in mathematics; he is best known for songs he recorded in the 1950s and 1960s.  Here are Lehrer's lyrics for "The Derivative Song" -- written to be sung to the tune of "There'll Be Some Changes Made" (by Benton Overstreet, with original lyrics by Billy Higgins).

A square poem of Romania

When I'm working on a poem that resists my efforts to express what I must say, sometimes I turn to the square for a rescue -- that is, I attempt to find the best words by re-forming the poem as a square (same number of lines as syllables per line).  That is how I came to the following poem, "The Bear Cave,"  (a 9 x 9 square). 

Fear of math

California poet Carol Dorf is a high school math teacher (and has taught in a science museum) -- and images from math and science permeate her work.  An article on math anxiety (and its connections to the brain) in today's Washington Post brought to my mind this poem of hers: 

Once a student of Euclid

The Chair     by Charles Simic

The chair was once a student of Euclid.

The Bridges of Konigsberg

From the August 1997 issue of The Mathematical Intelligencer, we have this poem by Judith Saunders about a long-standing puzzle solved solved by the mathematical giant, Leonhard Euler (1707-1783).

Hikmet -- painting with numbers

Living is no laughing matter . . . 

These are words of Turkish poet, playwright, novelist and memoirist Nazim Hikmet (1902-63), who spent much of his life in prison or exile for his political beliefs.  In the following poem by Hikmet we see a portrait that builds from the numbers that characterize the landscape of Ibrahim Balaban's painting.  As you read Hikmet's poem, consider the value of numbers in portraiture.  Though they do not have the textures of color nor the movement of lines, numbers have shapes and edges that may much enrich our seeing. 

Spacetime

   Spacetime     by Miroslav Holub (1932-1998)

   When I grow up and you get small,
   then --

Personal geometry

We have recently passed the first anniversary of the death (6 May 2010) of Elena Shvarts, one of Russia's finest contemporary poets. Here is her "Poetica -- More Geometrico" (translated into English by Thomas Epstein).

Poems with permutations

     Below, in the May 16 posting, this blog considered all of the permutations of a few words -- in search of "the best" arrangement. Today we illustrate word-permutations in poems.
     First, a few lines from poet Gertrude Stein (1874-1946) -- who was masterful in her distortions of ordinary syntax and in her use of language in new ways. Stein played with both repetition and rearrangement; here is a brief example:

     Money is what words are.
     Words are what money is.
     Is money what words are.
     Are words what money is.

Which is the BEST order?

At Bartleby.com, we find  a quote from Samuel Taylor Coleridge (1772-1834) which says, in part " ... poetry—the best words in their best order." 

Consider the two orderings of the words "were" and "we." (To choose which is best is not possible until we know more of what the writer wishes to say.)

          We were!
          Were we?

Would rationalists wear sombreros?

This final section of "Six Significant Landscapes," by attorney and insurance executive (and poet) Wallace Stevens (1879-1955), playfully explores the limitations of rigid thinking. 

If p, then q.

     Today's posting (as also on April 13)  presents variations of the conditional statment -- a sentence of the form "If ___, then ___" in which mathematical theorems often are expressed. (For example, "If m is an odd integer, then m² is an odd integer.")   More generally, a conditional is a statement of the form "If p, then q" -- where p and q denote statements. Poet E. C. Jarvis plays with the language of logical statements and with the idiomatic phrase "Mind your p's and q's" in his poem, "A Simple Proposition." 

Poetry generators

Blogger edde addad had an undergraduate major in creative writing -- and later earned a PhD in computer science.  He has written about and created poetry-generating programs. addad is one of the contributors to the blog Gnoetry Daily -- which offers ongoing discussion and examples of collaborative human-computer poetry generation.  Here is  "Mystery" -- a poem generated by eGnoetry (assisted by addad!):

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 jar in Tennessee

     Several of my early insights concerning the connections between poetry and mathematics grew from ideas presented by poet Jonathan Holden -- of whom interviewer Chris Ellis (in 2000) asked this question:
     Ellis:  You have drawn similarities between poetry and mathematics. Can you explain the association or similarity between poetry and math in a way the mathematically challenged can grasp?
     Holden: The "poetry and mathematics" analogy was simply to demonstrate, for those with some mathematical sophistication, that both languages "measure" things.

Forgetful Number

A lovely poem about more than a number . . .

    Forgetful Number  by Vasko Popa

    Once upon a time there was a number
    Pure and round like the sun
    But lonely very lonely

    It started to calculate by itself 

Perpendicularity -- a symmetric relation

     In 2010 both my October 13 and November 20 posts feature small poems by the French poet Guillevic (1909-97). Strongly drawn to his work, I have purchased the collection Geometries (Englished by Richard Sieburth, Ugly Duckling Presse, 2010); Guillevic has found in each geometric figure a personality and a voice. Buy the book and enjoy! Here is one of my favorites from the collection:    

Attitudes of Numbers

     I like Bruce Snider 's "The Certainty of Numbers" (which you may already have found online at The Poetry Foundation website, featured in the April 14  posting) even though I disagree with the initial attitude toward mathematics expressed by its narrator.  Writing a poem can be a voyage of discovery with the narrator's view flexing as the poem progresses.  
     Snider's poem brings to mind a view of mathematics that repeatedly bothers me:  I wonder why some people -- who would not complain about the fixendess of spellings of "cat" or "dog" or "sum" -- dislike mathematics for the so-called rigidity of  arithmetic facts such as "2 + 4 = 6."  ? ? ?

Earth Day, 2011

      My father, a farmer, was respectful of our earth's resources.  Replenish what you take, he taught.   But some of us consume without replacement as if the earth is infinite in its capacities. 
     When growth is exponential, we may not see its consequences before it is too late.  (Have we already destroyed the balances of nature?)  The following 8 x 8 syllable-square poem restates a oft-used math-textbook question -- and reminds us that little time may be left to solve environmental problems.