Monday, August 16, 2010

Poetry and applied mathematics

Back in the 1980's when I began taking examples of poetry into my mathematics classrooms at Bloomsburg University, I think that I justified doing so by considering poetry as an application of mathematics.  For example, Linda Pastan applies algebra to give meaning to her poem of the same title.  Here are the opening lines.


     I used to solve equations easily.
     If train A left Sioux Falls
     at nine o'clock, traveling
     at a fixed rate,
     I knew when it would meet train B.
     Now I wonder if the trains will crash;
     or else . . .

Linda Pastan's "Algebra" appeared in Aspects of Eve -- and again in Carnival Evening:  New and Selected Poems  (W W Norton, 1998).  My July 1 posting includes the opening lines of another of Pastan's poem, "Infinity."

A poem which almost-perfectly captures the spirit of applied mathematics is "Figures of Thought" by Howard Nemerov; in his three stanzas of decreasing size, the structure mimics the tightening spiral.  To read this poem is to enter the poet's sense of wonder at the way a mathematical curve (representable by an equation) fits as a model of several of the phenomena of life and living.

     Figures of Thought

     To lay the logarithmic spiral on
     Sea-shell and leaf alike, and see it fit,
     To watch the same idea work itself out
     In the fighter pilot's steepening, tightening turn
     Onto his target, setting up the kill,
     And in the flight of certain wall-eyed bugs
     Who cannot see to fly straight into death
     But have to cast their sidelong glance at it
     And come but cranking to the candle's flame --

     How secret that is, and how privileged
     One feels to find the same necessity
     Ciphered in forms diverse and otherwise
     Without kinship -- that is the beautiful
     In Nature as in art, not obvious,
     Not inaccessible, but just between.

     It may diminish some our dry delight
     To wonder if everything we are and do
     Lies subject to some little law like that,
     Hidden in nature, but not deeply so.

Poet Laureate of the United States during 1988-1990, Howard Nemerov  (1920-91) served as a combat pilot during World War II. From 1969 a teacher at Washington University, Nemerov won the Pulitzer Prize in 1978 for his Collected Poems.

Developing more fully the intersection of poetry and applied mathematics is a fine article in the Autumn 2009 issue of The American Scholar,  written by Joel E. Cohen of The Rockefeller University and Columbia University, entitled "A Mindful Beauty: What Poetry and Applied Mathematics Have in Common." Cohen's thought-provoking article compares structural patterns in a poem by A E Housman "With rue my heart is laden" with formulas from his recent research.

With the intent of drawing you to read the whole of Cohen's article, I present here two of his thought-provoking paragraphs--one copied from the first half of the article, the other from near the end:

"Like poetry, applied mathematics combines multiple meanings, economy, pattern, and mystery. In its scientific or practical applications, applied mathematics points to something external. It also alludes to prior mathematics. Its few symbols convey a lot. Its use of symbols often involves internal repetition, symmetry, and chiasmus. It is replete with unexpected truths, unexpected applications, and diverse proofs that illuminate different aspects of a single truth." 
"As apples do differ from oranges, poetry does differ from applied mathematics, despite their commonalities. For example, in poetry, but not mathematics, sound and “mouthfeel” (Galway Kinnell) matter. In applied mathematics, unlike poetry, calculation and shared scientific concepts and data, rather than intimate experience, lend conviction. Examples of differences could be multiplied. They do not undermine the significance of the similarities."

Finally, I want to mention recent activity by one of the long-term bloggers (since 2005) featuring poetry-with-mathematics, namely  Kaz Maslanka.  His mathematical-poetry blogspot has recently collected viewpoints on "What is 'mathematical poetry'?" and readers here may find this, and other items Kaz has posted, to be of interest.  

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