Intersections -- Poetry with Mathematics

Counting Groundhogs

2012-02-01T23:03:00.002-05:00

     I grew up in a town about 25 miles from Punxsutawney, PA -- and Groundhog Day on February 2 was local-news only. This was the quiet time before television cameras mades stars of groundhogs and, back then, we knew them -- for their underground piracy as well as for their weather-forecasting.
     My father, a farmer, did not like groundhogs; he tried to keep them away from his fields by blocking their entrances to the networked burrows where they chewed the roots of crops planted overhead.  Fifty years after these farming days, I arrived at the following "what is this world coming to?" poem that features my mother and me watching groundhogs play in a field outside her sickroom. (The poem is, approximately, a sonnet -- in which the poet is not only counting groundhogs but also counting syllables . . ..)

Pennsylvania Farm View   by JoAnne Growney

   The green florescence of a young alfalfa field
   is streaked by dots and darts of playful brown—
   a hundred groundhogs celebrate a summer day
   as those oblivious to death are free to do.

   I see them from the window of my mother’s room
   where she’s confined in bed from stepping out
   onto a stair she thought was there. A fall,
   and now a taking stock — I count the rodents
   and forecast many nibbled roots. Such thieving
   didn’t happen when my father lived and farmed.
   I squeeze her hand; we winkle noses with attitude
   toward groundhogs and hyped-up Groundhog Day.
   She ends this rodent chapter with soft pride –-
   telling how she -- even at five -- could spell Punxsutawney.

January, 2012 -- dates, titles of posts

2012-02-01T21:30:00.003-05:00

2012 -- Previous Posts -- Dates, Titles
Jan 29 Juxtaposition
Jan 26 Counting the seconds -- and leap seconds
Jan 23 Counting fingers and blackbirds
Jan 20 Statistics feels like poetry
Jan 17 More statistics -- from Hiawatha
Jan 15 Average, more or less . . .
Jan 12 The Function Room
Jan 10 Is your favorite poet a mathematician?
Jan 8 Poetry heard at JMM
Jan 3 Euclid meets Broadway
Jan 3 From 2011 -- dates, titles of posts
And also, posted Jan 3, 2011, From 2010 -- titles and dates of posts

Juxtaposition

2012-01-29T19:08:00.004-05:00

One of my favorite phrases (loved for the sound of it) first came to my ears during my college studies of abstract algebra: "multiplication is denoted by juxtaposition" -- and, within the phrase, I best like to say "juxtaposition." I enjoy its movement in my mouth, its sibilance in my ears. And so, of course, I set out to find a poem using the word. Having failed over many years to find the word in someone else's poem, I have written my own:

   Multiplication     by JoAnne Growney

   Multiplication is the process
   of taking one number as many times
   as there are ones in another.

   Juxtaposition is the notation –-
   as in 3x or yz --
   to denote multiplication.

   Multiplication is a taking
   of one with ones.
   Multiplication takes times.

   When does one desire
   to do multiplication? Why
   might a product offend?

   How many times can one take
   without greed? How many
   juxtapositions to reach the end?

   This poem began while I was browsing Geo. W, Hull's Complete Arithmetic (Butler, Sheldon, & Co, 1895) – on my shelf and also available at Google Books.  I paused on page 33 at the definition of Multiplication – and the poem began.

Counting the seconds -- and leap seconds

2012-01-26T18:38:00.008-05:00

      Keeping time is a simple matter of counting -- counting seconds, summing them into minutes, hours, days. Or is it? Recent news has included mention of the changing length of our solar day and the need for insertion of leap seconds. (A leap second is a one-second adustment to the time kept by precise atomic clocks -- to keep this latter time close to mean solar time. No leap-seconds were added in 2011 but NPR and The Washington Post recently announced that a leap second will be added June 30, 2012. At 7:59:59 PM, Eastern time, the US Naval Observatory will skip a second to 8:00:00 PM. Wikipedia offers detailed background on this concept.)     Extra time is a fond wish for many of us -- and Leonard Orr has penned a love poem suggesting how one more second might be delightfully crowded with so much more than could happen in "regular" time.

   Leap Second     by Leonard Orr

   The news of the leap second excited me;
   I was only concerned with misspending it,
   a lost youth, a disspiated middle-age.
   You could have been standing naked on my back
   squeezing the melancholy from my chakras,
   your toes curling gently while I exfoliated.
   They said physicists measure a second by
   the excited waggling of Cesium 103,
   though its passionate vibrations could
   not be greater than mine. In the leap second
   my blood would have gushed gaily
   through several feet of arteries feverish for you,
   scarlet for you, I could have drawn in
   a deep breath of you or noticed how
   the soft ridges of our fingerprints fit together.
   We could have leaped as one in the leap second,
   hands interlocked, our four feet for that moment
   two feet above the crushed bedsprings,
   flying heavenward. I could have opened my eyes
   from deepest sleep in the leap second
   to see your face beside mine, to forget the world,
   to forget everything else except you.

Copyright Leonard Orr, first published in Isotope: A Journal of of Literary Nature and Science Writing 6.1 (Spring/Summer, 2008). Reprinted here from Leonard Orr's collection Why We Have Evening (Cincinnati: Cherry Grove, 2010).

Counting fingers and blackbirds

2012-01-23T20:12:00.005-05:00

Love of numbers is common in childhood -- and traditional nursery rhymes offer chances to know numbers as playmates and friends. "Four and twenty blackbirds baked in a pie . . . The king was in his counting house . . ." and so on. In "The Story of the Ten Blackbirds" poet Millicent Accardi combines a portrait of an amazing story-telling aunt with a collage of childhood memories, counted and remembered.

   The Story of the Ten Blackbirds     by Millicent Borges Accardi

   Blended at times into
   The three little pigs
   Or the Catholic Saints.

   Aunt Flossie ripped
   Pieces of newspaper
   Or envelopes into ten

   Roundish pieces
   Three of her fingers were lost
   Partially in an accident

   To the cotton mills of
   French Canada when she
   Was a child

   The index, cut at the nail
   The thumb in half,
   And her first lost at the joint.

   She licked each piece
   Of paper and attached
   Them dampened to

   The whole and the partial
   Digits. This little blackbird
   She said, went to market

   As she whirled her hands
   In the air then quickly behind
   Her back. Miraculously one

   Blackbird vanished
   This little bird was fat
   And forgot to pray to St Anthony

   Her hands shook and
   Another flew away
   On and on it went as I watched

   Rapt, kneeling at her feet
   Holding onto her legs, astonished
   At her magic tricks. Horrified

   By her fingers. With a whirl of her
   Tongue and a great fluttering
   All ten blackbirds returned

   Home to all ten fingers that
   Auntie Flossie held up for me
   To inspect, the sweaty bits of paper.

Accardi's poem appears in her collection Injuring Eternity (Mischevious Muse Press, 2010). Previous blog postings that also feature ideas from childhood rhymes include: 30 November 2011, 15 August 2011, 16 May 2011, 24 February 2011.

Statistics feels like poetry

2012-01-20T21:09:00.002-05:00

    Today's title comes from the following poem by statistician and poet Eveline Pye (introduced to this blog on 18 October, 2011).

   Numerical Landscape      by Eveline Pye

   Like a tracker, I smell the earth
   on my fingers, listen for the slightest
   echo as I stare out at a world
   where bell-shaped curves loom

   as mountains and negative exponentials
   foretell dangerous descents, imminent
   disaster. All around, cliff edges crash
   down to restless seas while a solitary

   outlier shines in the southern sky: a freak
   of random sampling or a guiding light?
   Are others buried deep, confounded
   by experimental design? On my path,

   a decision tree, so many branches spring
   from its trunk, so many choices. Statistics
   feels like poetry –- endless searching,
   never-ending uncertainty.

     Julian Champkin's lively article, "Eveline Pye: Poetry in Numbers" in Significance (The Royal Statistical Society, September 2011) is my source for this poem.
      For more poetry related to mathematics, enjoy a visit to talkingwriting.com where the editors have several articles and are posting a new math-related poem each Friday during January and February -- including, today, "Zero-Knowledge Proofs," a poem of mine.

More statistics -- from Hiawatha

2012-01-17T22:31:00.006-05:00

As the author of this poem owes a debt to Henry Wadsworth Longfellow, I too owe Greg Coxson -- who showed the poem to me.

Hiawatha Designs an Experiment by Maurice Kendall

Hiawatha, mighty hunter
He could shoot ten arrows upwards
Shoot them with such strength and swiftness
That the last had left the bowstring
Ere the first to earth descended.
This was commonly regarded
As a feat of skill and cunning.

One or two sarcastic spirits
Pointed out to him, however,
That it might be much more useful
If he sometimes hit the target.
Why not shoot a little straighter
And employ a smaller sample?

Hiawatha, who at college
Majored in applied statistics
Consequently felt entitled
To instruct his fellow men on
Any subject whatsoever
Waxed exceedingly indignant
Talked about the law of error,
Talked about truncated normals,
Talked about loss of information,
Talked about his lack of bias
Pointed out that in the long run
Independent observations
Even though they missed the target
Had an average point of impact
Very near the spot he aimed at
(With the possible exception
Of a set of measure zero.)

This, they said, was rather doubtful.
Anyway, it didn't matter
What resulted in the long run;
Either he must hit the target
Much more often than at present
Or himself would have to pay for
All the arrows that he wasted.

Hiawatha, in a temper
Quoted parts of R.A. Fisher
Quoted Yates and quoted Finney
Quoted yards of Oscar Kempthorne
Quoted reams of Cox and Cochran
Quoted Anderson and Bancroft
Practically in extenso
Trying to impress upon them
That what really mattered
Was to estimate the error.

One or two of them admitted
Such a thing might have its uses
Still, they said, he might do better
If he shot a little straighter.

Hiawatha, to convince them,
Organized a shooting contest
Laid out in a proper manner
Of designs experimental
Recommended in the textbooks
(Mainly used for tasting tea, but
Sometimes used in other cases)
Randomized his shooting order
In factoral arrangements
Used in the theory of Galois
Fields of ideal polynomials
Got a nicely balanced layout
And successfully confounded
Second-order interaction.

All the other tribal marksmen
Ignorant, benighted creatures,,
Of experimental set-ups
Spent their time in preparation
Putting in a lot of practice
Merely shooting at a target.

Thus it happened in the contest
That the scores were most impressive
With one solitary exception.
This (I hate to have to say it)
Was the score of Hiawatha,
Who, as usual, shot his arrows
Shot them with great strength and swiftness
Managing to be unbiased
Not, however, with his salvo
Managing to hit the target.

There, they said to Hiawatha,
That is what we all expected.

Hiawatha, nothing daunted,
Called for pen and called for paper
Did analyses of variance
Finally produced the figures
Showing beyond preadventure
Everybody else was biased
And the variance components
Did not differ from each other
Or from Hiawatha's
(This last point, one should acknowledge
Might have been much more convincing
If he hadn't been compelled to
Estimate his own component
From experimental plots in
Which the values all were missing.

Still, they didn't understand it
So they couldn't raise objections.
This is what often happens
With analyses of variance.)

All the same, his fellow tribesmen
Ignorant, benighted heathens,
Took away his bow and arrows,
Said that though my Hiawatha
Was a brilliant statistician
He was useless as a bowman,
As for variance components
Several of the more outspoken
Made primeval observations
Hurtful to the finer feelings
Even of a statistician.

In a corner of the forest

Dwells alone my Hiawatha
Permanently cogitating
On the normal law of error
Wondering in idle moments
Whether an increased precision
Might perhaps be rather better
Even at the risk of bias
If thereby one, now and then, could
Register upon the target.

Kendall's poem first appeared in The American Statistician in 1959.

Average, more or less . . .

2012-01-15T20:43:00.000-05:00

The wit of American poet J. V. Cunningham (1911–1985) is here applied to statistics.

   Meditation on Statistical Method     by J. V. Cunningham

   Plato, despair!
   We prove by norms
   How numbers bear
   Empiric forms,

   How random wrong
   Will average right
   If time be long
   And error slight,

   But in our hearts
   Hyperbole
   Curves and departs
   To infinity.

   Error is boundless.
   Nor hope nor doubt,
   Though both be groundless,
   Will average out.

“Meditation on Statistical Method” is found in The Exclusions of a Rhyme: Poems and Epigrams (Ohio University/Swallow Press, 1997) and online (along with additional Cunningham poems) at PoetryFoundation.org.

The Function Room

2012-01-12T22:25:00.002-05:00

For each of us who's studied mathematics, the word "function" triggers important mathematical meanings. And so, when I read Patrice Phillips un-mathematical poem "The Function Room," I automatically add a mathematical layer to the meaning. Do you?

   The Function Room     by Patrice Phillips

   We worked in the kitchen
   of the function room,
   me and black Jackson
   and the cook, he's Vince.
   We waxed the linoleum
   and set out the frills
   for the chromium people
   who came to those
   Friday night functions.

   Six hundred kumquats
   rolled in pastrami,
   Green frou-frou toothpicks or red?
   [Isn't that some of
   black Jackson's shrimp salad
   stuck there on that cummerbund?]
Each function night you could
   smell the hair tonic
   from out in the parking lot.

   After the party we
   gathered up lipsticks
   left in the ladies' room.
   We swept up the chicory,
   we played with the olives.
   I took some shrimp salad
   home for my cat,
   but he wouldn't eat it,
   so I quit.

I found Phillips' poem in Messages: A Thematic Anthology of Poetry edited by X J Kennedy (Little, Brown, 1973). For those readers who would like to review the definition of function, here's a snip from WolframAlpha:

From WolframAlpha, definitions of function:
(click on image to enlarge)

Is your favorite poet a mathematician?

2012-01-10T10:25:00.002-05:00

     The Joint Mathematics Meetings in Boston last week gave a fine opportunity for me to connect with both mathematicians and poets, old friends and new ones. And to enjoy a celebration of the connections between poetry and mathematics. In the January 6 poetry reading sponsored by the Journal of Humanistic Mathematics, there was much fine poetry. Several of the poems were by Carol Dorf -- whose work was read by Elizabeth Langosy, executive editor of the online literary magazine, TalkingWriting. Good reads in the Jan/Feb 2012 issue of TalkingWriting include both Dorf's introduction to some featured math-connected poems -- entitled "Why Poets Sometimes Think in Numbers" -- and Langosy's impressions of the math-poetry reading.
     The Boston poetry event (co-organized by Gizem Karaali) reminds me of another reading twenty years ago -- in January 1992, Alvin White and I hosted a poetry reading at JMM in Baltimore. One of my favorite poems from that time was by American University professor Dan Kalman, "Ode to a Triangular Matrix." I offer it here:

Ode to a Triangular Matrix      by Dan Kalman

Oh, thou three corner array, noblest of matrices:
   Thy divine figure reveals itself
   reflected in multiple zeros
   exclaiming your secrets in proud display.

Where the common matrix guards its determinant
   as a potent talisman
   never to be revealed,
save after careful incantation,
   arcane mutterings,
   unending and errorless calculation,
You, oh forthright soul of linearity
   requiring merely a show of sincerity,
   a token computation,
willingly exhibit your psyche's key elements
   worn in a bold slash,
   yea, a sash,
and whose product, your determinant
   is offered for our edification.

The chaotic matrix
   whose aspect is disordered
has at its core,
   its very kernel,
   a confused maze of conflicting directions.
Lest we come to know its true
   meaning, worth, rank,
   it hides this kernel from our sight,
misleading and confusing us,
   annihilating enemies in secret alleyways
   and under cover of night.

But you, three sided paragon,
   disdain such rank duplicity;
   declaim your true intentions;
show every multiplicity
   the measure of your heart, your soul,
   your innermost dimensions.

And there is no mistake about the values that you hold.
With characteristic candor that is striking to behold,
and without undue modesty, your honesty is tangible:
your values worn for all to see with pride on your diagonal.

And you and all your fellows faithful ever do remain
you multiply together and your offspring are the same,
and in all your combinations, too, your virtues are unchanged.

Indeed, you are a model for the race of matrix kind,
   In simple fact,
   In artful grace,
   In guileless art,
   In graceful form,
You show this humble student all that he could hope to find.

Kalman's poem was first published in Issue #7 of the Humanistic Mathematics Network Journal. It also is available on his webpage.

Poetry heard at JMM

2012-01-08T11:05:00.006-05:00

In Boston on Friday evening, January 6, at the 2012 Joint Mathematics Meetings, these folks gathered and read -- for a delighted audience in Room 312 of Hynes Convention Center -- some poems of mathematics.
     Poets who submitted work in advance and were on the "Poetry with Mathematics" program included:
          Jacqueline Lapidus, Judith Johnson, Rosanna Iembo (accompanied by the violin of her daughter Irene Iaccarino), Charlotte Henderson, Carol Dorf (read by Elizabeth Langosy), Sandra Coleman, Marion Cohen, Tatiana Bonch (read by John Hiigli), Harry Baker (via video presented by reading organizer Gizem Karaali -- an editor of the online Journal of Humanistic Mathematics, which sponsored the the reading), and JoAnne Growney (also an organizer of the reading).
     Participants during an "open reading" included:
          Mary Buchinger, Chris Caragianis, Rip Coleman, Seth Goldberg, Joshua Holden, Ann Perbohner, Pedro Poitevin, and Jason Samuels.

     I look forward to ongoing connections with these fine poets and to the possibility of obtaining permissions to offer their work here in my blog. Several have contributed to previous postings: Sandra Coleman, Marion Cohen, and Jacqueline Lapidus.
     In closing, an abecedarian poem (different than the one I offered at the January 6 reading) that celebrates mathematics:

     ABC     by JoAnne Growney

   Axes beget coordinates,
   dutifully expressing
   functions, graphs,
   helpful in justifications,

   keeping legendary mathematics
   new or peculiarly quite rational

   so that understanding's visual
   with x, y, z.

Euclid meets Broadway

2012-01-03T07:50:00.002-05:00

Several years ago while visiting my older son in Colorado Springs I also went to nearby Boulder where, driving along Broadway, I came to a street sign that made me gasp with delight. I was at the intersection of Broadway and Euclid.  That fact, that suggestion of a merge of two worlds, needed to be part of a poem. Some time later I wrote:

   Butterfly Proposal     by JoAnne Growney

   The future looks sad and scares you.
   Don’t let forebodings hush the echoes
   of old voices—we need the past to build
   high spirits. I’ll write you
   into a poem.

   A butterfly on your hand proposes life—
   a promise drawn at the intersection
   of Broadway and Euclid, a fortunate convergence
   that counters disillusion. Butterflies
   are transient, illogical

   while you wear every sort of rule
   impalpable and tight. You shrink from praise
   and flounder in the caramel of fear’s sweet heat.
   Your moth-mind skitters everywhere;
   your deeds all are polite.

   Twist your finger with rubber bands:
   the throb will keep you sane. You don’t
   have to fix each broken thing. Adjust your ears;
   hear slowly. Into the pauses
   understanding.

After having read this offering, you may wonder if I think it is mathematical. I'm not sure about that -- but for me it is an inner portrait. The poem looks into the mind of a mathematician, a female one. It tells what it finds there. Other portraits of mathematicians may be found at these links: In 2011: December 8 Monsieur Probability, November 13 Portraits of a Mathematician, July 5 Mathematicians at work, July 2 Mathematicians divide, Jan 30 Sonnet for a geometry teacher, Jan 28 Poems starring mathematicians - 8. In 2010, Dec 8 Poems starring mathematicians -- 7, July 20 In the same family -- a poet and a mathematician, May 14 Poems starring Mathematicians -- 6 (Mandelbrot), May 4 Poems starring Mathematicians -- 5, April 28 Poems starring mathematicians -- 4, April 26 Poems starring mathematicians -- 3, April 15 Poems starring mathematicians - 2, April 14 Poems starring mathematicians - 1, March 23 Poetry of Logical Ideas .

From 2011 -- dates, titles of posts

2012-01-03T07:42:00.002-05:00

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 bottom of the blog 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

Nov 30 Echoes of childhood rhymes
Nov 27 How much for a digit of PI?
Nov 24 Open and Closed -- Tomas Transtromer
Nov 21 Reading the Rubaiyat
Nov 18 Equivalence
Nov 15 Portrait of Max Dehn
Nov 13 Portraits of a mathematician
Nov 10 Mathematics of desire
Nov 7 Mathematician-Poet Glaz
Nov 5 Four colors will do
Nov 2 Division by zero

Oct 30 What can 7 objects say? Or 100?
Oct 28 Music on the hypotenuse
Oct 27 Submit math-science poetry
Oct 25 Chaos Over the Hors d'Oeuvres
Oct 23 Permutations and Centos
Oct 20 A whole and its parts
Oct 18 Things the fingers know
Oct 16 A small Fib
Oct 13 Hamilton -- mathematician, poet, Irishman
Oct 12 Like poetry, mathematics is beautiful
Oct 11 Numbers from the Piano
Oct 9 Counting the women
Oct 8 How I won the raffle
Oct 4 Action at a distance

Sept 30 The square root of Everest
Sept 28 Math meets Dr Seuss
Sept 26 Learning to count
Sept 24 Mathematical theorems tornadoing
Sept 22 The wealth of ambiguity
Sept 21 Poetry at JMM -- in Boston 6-Jan-2012
Sept 18 Baseball, math, and poetry
Sept 16 Best words in the best order
Sept 14 Analysis of a sacred site
Sept 11 A Piece of Coffee -- Stein with some math terms
Sept 6 Symmetric 4 x 4 square
Sept 4 Applying statistics . . .
Sept 2 Two ways to compute 1/3

Aug 30 This plane of earthly love
Aug 27 Earthquake and Hurricane
Aug 26 350: Science --> Poetry --> Music
Aug 24 A thousand and fifty-one waves
Aug 19 Half-twist and link -- in a Sestina
Aug 17 Lieber's INFINITY -- poetic prose
Aug 15 Some cat!
Aug 10 The hypotenuse of an isosceles triangle
Aug 8 Can a mathematician see red?
Aug 5 Banach's Match Box Problem
Aug 4 Cantor Ternary Set
Aug 2 Puzzle play

July 29 Mathematical Induction -- principle, perhaps poem
July 26 Bridges in Coimbra
July 24 Little Infinite Poem
July 21 The wind, counting
July 18 Finding a square root
July 15 I have dreamed geometry
July 11 Seeking a universal language
July 8 Ancestry -- what counts
July 5 Mathematicians at work
July 2 Mathematicians divide

June 29 5 x 5 and 6 x 6
June 26 The Joys of Mathematics
June 23 Creation Myth on a Mobius Band
June 20 Something for nothing
June 17 Circling -- with Rilke
June 15 Found in Flatland
June 13 Stanescu -- poetic mathematics
June 12 Lagrange points
June 9 Counting on things -- a prose poem
June 7 Right triangle
June 5 Math lyrics -- Lehrer et al
June 2 A square poem of Romania

May 31 Fear of math
May 30 Once a student of Euclid
May 27 The Bridges of Konigsberg
May 25 Hikmet -- painting with numbers
May 22 Spacetime
May 19 Personal geometry
May 17 Poems with permutations
May 16 Which is the BEST order?
May 13 Would rationalists wear sombreros?
May 11 If p, then q.
May 9 Poetry generators
May 6 Permuting words and and enumerating poems
May 4 A jar in Tennessee

Apr 29 Forgetful Number
Apr 26 Perpendicularity -- a symmetric relation
Apr 23 Attitudes of Numbers
Apr 21 Earth Day, 2011
Apr 20 Two and four and eight and birds
Apr 18 Teaching math with a poem
Apr 17 A picture should extend beyond its frame
Apr 14 Finding poems with "numbers"
Apr 13 Conditional statements
Apr 10 What can mathematics do?
Apr 7 A poetic perspective on algebra
Apr 5 What color is 3?
Apr 3 April -- month of poetry and mathematics

Mar 30 Coleridge: A Mathematical Problem
Mar 27 The Nightmare of an Unsolved Problem
Mar 24 Numbers are more than numbers
Mar 22 Celebrating Newman's "World of Mathematics"
Mar 20 Counting: 1, 2, 3, 4, 5, . . .
Mar 18 Who are our prophets?
Mar 16 9 9-square stanzas
Mar 15 Remembering Pi-day, a day late
Mar 13 Teaching Math
Mar 7 Numerology
Mar 4 Journal of Humanistic Mathematics -- V1, Issue 1
Mar 2 Perfect as soap bubbles

Feb 28 Immense polygons of evening
Feb 24 Counting rhymes -- Catalan, Bell numbers
Feb 22 Poems of set paradox and spatial dimension
Feb 20 Black History Month -- celebrate Haynes and Hughes...
Feb 18 Srinivasa Ramanujan
Feb 16 Thinking about Thinking
Feb 14 Puzzles, puzzlers, and parody
Feb 12 Loving a mathematician (Valentine's Day and . . ...
Feb 10 Dividing by Zero
Feb 8 How much math does a math-poem need?
Feb 6 Electronic poetry -- Stephanie Strickland
Feb 4 AWP avoids mathematics
Feb 2 Painting tragedy with numbers

Jan 31 Romanian poets -- Cassian and Barbu
Jan 30 Sonnet for a geometry teacher
Jan 28 Poems starring mathematicians - 8
Jan 26 Self-portrait with numbers
Jan 24 Poem and parody -- isomorphic?
Jan 22 Integrals -- a poem
Jan 20 Hyperbolic effects
Jan 18 Poetry inspired by Chaos
Jan 17 Dr King's dream and Black math students
Jan 14 Rather like an elephant
Jan 12 Geometry and autism
Jan 10 Tribute to four teachers
Jan 7 Which are "real" numbers?
Jan 5 Mathematics and race
Jan 3 New poems from old -- by permutation
Jan 3 From 2010 -- titles and dates of posts
Jan 3 In 2010 -- poets, mathematicians, key words

Good numbers . . .

2011-12-30T13:07:00.003-05:00

     My wish for the New Year 2012 is that you will have good numbers -- that your happiness will have high peaks, that your sadness and grief will weigh no more than you can bear.
     In the spirit of assessment and introspection that captures many of us at year-end, I offer a small poem, "Good Fortune" -- one that I wrote in late December ten years ago when I was, as I am now, taking stock. "Good Fortune" appeared in my 2006 chapbook, My Dance Is Mathematics (Paper Kite Press -- available online here). Another tiny poem, a more recent one, "14 Syllables" -- from Red Has No Reason (Plain View Press, 2010) -- continues the focus on assessment using numbers.

     Good Fortune     by JoAnne Growney

     is good numbers—
     the length of a furrow,
     the count of years,
     the depth of a broken heart,
     the cost of camouflage,
     the volume of tears.

     14 Syllables   (from Red Has No Reason by JoAnne Growney)

     A hen lays eggs
     one by one;
     the way you
     count life
     is life.

Happy New Year, 2012!

I hope to see many friends at the 2012 Joint Mathematics Meetings --
PLEASE COME to the POETRY READING
on Friday, January 6 at 5 PM in Room 312 at Boston's Hynes Auditorium --
sponsored by the Journal of Humanistic Mathematics.

A mathematical woman

2011-12-26T15:16:00.001-05:00

As in an earlier posting (20 December 2011), today's feature includes verse by Lord Byron (1788-1824). This time the source is Byron's satiric poem Don Juan. In Canto I, the poet describes Don Juan's mother, Donna Inez, as learned and "mathematical." Here are several stanzas about her -- sagely seasoned with words like "theorem," "proof," and "calculation."

from Don Juan, Canto I by Lord Byron

His mother was a learned lady, famed
For every branch of every science known
In every Christian language ever named,
With virtues equall'd by her wit alone,
She made the cleverest people quite ashamed,
And even the good with inward envy groan,
Finding themselves so very much exceeded
In their own way by all the things that she did.

Her memory was a mine: she knew by heart
All Calderon and greater part of Lope,
So that if any actor miss'd his part
She could have served him for the prompter's copy;
For her Feinagle's were an useless art,
And he himself obliged to shut up shop—he
Could never make a memory so fine as
That which adorn'd the brain of Donna Inez.

Her favourite science was the mathematical,
Her noblest virtue was her magnanimity,
Her wit (she sometimes tried at wit) was Attic all,
Her serious sayings darken'd to sublimity;
In short, in all things she was fairly what I call
A prodigy—her morning dress was dimity,
Her evening silk, or, in the summer, muslin,
And other stuffs, with which I won't stay puzzling.

She knew the Latin—that is, 'the Lord's prayer,'
And Greek—the alphabet—I 'm nearly sure;
She read some French romances here and there,
Although her mode of speaking was not pure;
For native Spanish she had no great care,
At least her conversation was obscure;
Her thoughts were theorems, her words a problem,
As if she deem'd that mystery would ennoble 'em.

She liked the English and the Hebrew tongue,
And said there was analogy between 'em;
She proved it somehow out of sacred song,
But I must leave the proofs to those who 've seen 'em;
But this I heard her say, and can't be wrong
And all may think which way their judgments lean 'em,
'''T is strange—the Hebrew noun which means "I am,"
The English always use to govern d--n.'

Some women use their tongues—she look'd a lecture,
Each eye a sermon, and her brow a homily,
An all-in-all sufficient self-director,
Like the lamented late Sir Samuel Romilly,
The Law's expounder, and the State's corrector,
Whose suicide was almost an anomaly—
One sad example more, that 'All is vanity'
(The jury brought their verdict in 'Insanity').

In short, she was a walking calculation,
Miss Edgeworth's novels stepping from their covers,
Or Mrs. Trimmer's books on education,
Or 'Coelebs' Wife' set out in quest of lovers,
Morality's prim personification,
In which not Envy's self a flaw discovers;
To others' share let 'female errors fall,'
For she had not even one—the worst of all.

O! she was perfect past all parallel—
Of any modern female saint's comparison;
So far above the cunning powers of hell,
Her guardian angel had given up his garrison;
Even her minutest motions went as well
As those of the best time-piece made by Harrison:
In virtues nothing earthly could surpass her,
Save thine 'incomparable oil,' Macassar!

The entire text of Don Juan is available online here -- from Project Gutenberg.

Counting on Christmas

2011-12-22T06:32:00.004-05:00

one1

2 two 21

3 three 3 31

4 4 four 4 41

5 five 5 5 5 five 51

6 six 6 6 six 6 6 six 61

7 7 7 seven 7 seven 7 7 71

8 eight 8 8 8 eight 8 8 8 eight 81

9 nine 9 9 nine 9 9 9 nine 9 9 nine 91

10 ten 10 10 10 10 ten 10 10 10 10 ten 101

11 eleven 11 11 11 11 11 11 11 11 11 eleven 111

12 twelve 12 12 12 12 12 12 12 12 12 12 twelve 121

HAPPY1

HOLI -1

DAYS !!1

Thoughts Suggested by a College Examination

2011-12-20T08:08:00.003-05:00

Just when I was convinced that mathematical subject matter appears proportionately more in modern than in classical poetry, I turned again to work by Lord George Gordon Byron (1788-1824) and began to contradict myself. Here (from Byron's Complete Poetical Works) is "Thoughts Suggested by a College Examination." As is common today in literature and verse, the mathematicians (and scientists) are found wanting (though we are not the only deficient ones).

Thoughts Suggested by a College Examination     by Lord Byron

High in the midst, surrounded by his peers,
Magnus his ample front sublime uprears:
Plac'd on his chair of state, he seems a God,
While Sophs and Freshmen tremble at his nod.
As all around sit wrapt in speechless gloom,
His voice, in thunder, shakes the sounding dome;
Denouncing dire reproach to luckless fools,
Unskill'd to plod in mathematic rules.

Happy the youth in Euclid's axioms tried,
Though little vers'd in any art beside;
Who, scarcely skill'd an English line to pen,
Scans Attic metres with a critic's ken.
What, though he knows not how his fathers bled,
When civil discord pil'd the fields with dead,
When Edward bade his conquering bands advance,
Or Henry trampled on the crest of France:
Though marvelling at the name of Magna Charta,
Yet well he recollects the laws of Sparta;
Can tell what edicts sage Lycurgus made,
While Blackstone's on the shelf, neglected laid;
Of Grecian dramas vaunts the deathless fame,
Of Avon's bard, rememb'ring scarce the name.

Such is the youth whose scientific pate
Class-honours, medals, fellowships, await;
Or even, perhaps, the declamation prize,
If to such glorious height, he lifts his eyes.
But lo! no common orator can hope
The envied silver cup within his scope:
Not that our heads much eloquence require,
Th' Athenian's glowing style, or Tully's fire.
A manner clear or warm is useless, since
We do not try by speaking to convince;
Be other orators of pleasing proud:
We speak to please ourselves, not move the crowd:
Our gravity prefers the muttering tone,
A proper mixture of the squeak and groan:
No borrow'd grace of action must be seen,
The slightest motion would displease the Dean;
Whilst every staring Graduate would prate,
Against what he could never imitate.

The man, who hopes t' obtain the promis'd cup,
Must in one posture stand, and ne'er look up;
Nor stop, but rattle over every word--
No matter what, so it can not be heard:
Thus let him hurry on, nor think to rest:
Who speaks the fastest's sure to speak the best;
Who utters most within the shortest space,
May, safely, hope to win the wordy race.

The sons of science these, who, thus repaid,
Linger in ease in Granta's sluggish shade;
Where on Cam's sedgy banks, supine, they lie,
Unknown, unhonour'd live, unwept for die:
Dull as the pictures, which adorn their halls,
They think all learning fix'd within their walls:
In manners rude, in foolish forms precise,
All modern arts affecting to despise;
Yet prizing Bentley's, Brunck's, or Porson's note,
More than the verse on which the critic wrote:
Vain as their honours, heavy as their ale,
Sad as their wit, and tedious as their tale;
To friendship dead, though not untaught to feel,
When Self and Church demand a bigot zeal.
With eager haste they court the lord of power,
Whether 'tis Pitt or Petty rules the hour;
To him, with suppliant smiles, they bend the head,
While distant mitres to their eyes are spread.
But should a storm o'erwhelm him with disgrace,
They'd fly to seek the next, who fill'd his place.
Such are the men who learning's treasures guard!
Such is their practice, such is their reward !
This much, at least, we may presume to say--
The premium can't exceed the price they pay.    (1806)

A footnoted version of Byron's poem is available here.   Previous postings offer pre-20th-century poems of mathematics by Margaret Cavendish (10 May 2010), Samuel Taylor Coleridge (30 March 2011),  William Rowan Hamilton (13 October 2011), and William Blake (8 November 2010).

Ruth Stone counts

2011-12-17T19:15:00.003-05:00

It seemed as if she might write -- and write well -- forever. But she did not. Moreover, poems by award-winning poet Ruth Stone (1915-2011) are not celebrated for their use of mathematical imagery. Still, she noticed numbers. She counted. As in "All in Time."

   All in Time     by Ruth Stone

   Behind the glass door of the waiting room,
   one hundred and fifty passive-agressive
   passengers girded up for Galveston.
   The bearded conductor let them out
   one by one to the named coaches.
   A mother who says to her baby,
   "Now you lie there until I tell you to move."
   And four small girls, hair in tight cornrows,
   quietly smiling at something you can't see.
   An old sixties-type hippie father
   is on the bench with you. He's going
   off to Boise to say good-bye to his daughter
   who is on her way to a Peace Corps
   medical team. He has ten minutes to catch
   his train in Chicago. He shows you her picture.
   "One tribe," he says, "so they don't have
   any wars. Flat and grassy," he says,
   "just the beginnings of mountains.
   Twenty-six months," he says. "That's
   a long time, you know." And then the friend
   you haven't seen for seven years until
   this visit, the friend who seems to have emerged
   like a cicada, shrill and predestined,
   gets there with the coffee and carries
   your heavy cases onto the train.
   You both cry. She has begun to think you are
   her mother and you have retreated
   into your wounded child. When you say good-bye
   you pull apart like Velcro.

"All in Time" is in Stone's collection Ordinary Words (Paris Press, 1999).

A puzzle with a partial solution

2011-12-14T13:27:00.007-05:00

     When we have experiences near to each other, we may try to connect them. We form superstitions. "Bad things come in threes" -- and something similar for good things. And we make poetry -- offering new associations that delight and surprise.
     Gertrude Stein is one of my favorite poets. She was, like me, born in Pennsylvania (though she, unlike me, left and became Parisian). She creates almost-meaning from unlikely juxtapositions. I find in her work the delight of a puzzle to which I can find a partial solution. And come back for more. Here are two stanzas from Stein's "Stanzas in Meditation" that play with some mathematical meanings.

from Stanzas in Meditation    by Gertrude Stein

   Part I
   Stanza XIII

   She may count three little daisies very well
   By multiplying to either six nine or fourteen
   Or she can be well mentioned as twelve
   Which they may like which they can like soon
   Or more than ever which they wish as a button
   Just as much as they arrange which they wish
   Or they can attire where they need as which say
   Can they call a hat or a hat a day
   Made merry because it is so.

   Part III

Stanza V

It is not a range of a mountain

   Of average of a range of a average mountain
   Nor can they of which of which of arrange
   To have been not which they which
   Can add a mountain to this.
   Upper an add it then maintain
   That if they were busy so to speak
   Add it to and
   It not only why they could not add ask
   Or when just when more each other
   There is no each other as they like
   They add why then emerge an add in
   It is of absolutely no importance how often they add it.

From Stanzas in Meditation by Gertrude Stein (Sun & Moon Classics, 2000); this collection will also be available 17 January 2012 in a "corrected edition."

Poetry captures math student

2011-12-11T07:36:00.003-05:00

This sonnet retells a familiar story -- a teacher influences a student's choice of studies. Prior to reading, many in mathematics may wonder: how can a student leave mathematics for poetry when mathematics is poetry? Whatever your view, I think you will enjoy this poem.

Prof of Profs by Geoffrey Brock

For Allison Hogge, in memory of Brian Wilkie

I was a math major—fond of all things rational.
It was the first day of my first poetry class.
The prof, with the air of a priest at Latin mass,
told us that we could “make great poetry personal,”

could own it, since poetry we memorize sings
inside us always. By way of illustration
he began reciting Shelley with real passion,
but stopped at “Ozymandias, King of Kings;

Look on my Works, ye Mighty, and despair!”—
because, with that last plosive, his top denture
popped from his mouth and bounced off an empty chair.

He blinked, then offered, as postscript to his lecture,
a promise so splendid it made me give up math:
“More thingth like that will happen in thith clath.”

Brock's poem was first published in Poetry (July/August 2008); I found it at the Poetry Foundation website.

Monsieur Probabilty

2011-12-08T13:40:00.006-05:00

In recent months, I have encountered a variety of poems about mathematicians (Links to several of these are provided at the end of this post.) and one of the sources is Scottish poet Brian McCabe's collection Zero (Polygon, 2009). It is said that life imitates art -- and this is vividly demonstrated by the art of mathematics as lived by Abraham de Moivre (1667-1754). Here is McCabe's poem.

Monsieur Probability by Brian McCabe

Abraham de Moivre 1667-1754

You must remember old Abe de Moivre.
Handsome Frenchman. The nose not quite aquiline
but a nose of note nonetheless. The lip curled
in the manner of the French, as if prepared
to dismiss any poorly expressed idea.
The facial bones gaunt, but refined.
Always in Slaughter’s. He used to slaughter me
at chess -- for a groat, or a cup of coffee.
I didn’t grudge him it. He’d fallen on hard times.
Had to teach the brats of the nobility.
Always carried a few pages he’d cut
from the Principia wherever he went.
If you needed to know the odds on anything,
de Moivre was your man. Monsieur Probability
we called him. His Doctrine of Chances
became known as the Gambler’s Bible,
though he didn’t like to hear it called that,
him being a devoted Protestant.
Not that he’d had much luck:
thrown in jail by Louis the Fourteenth
when he scrapped the edict of Nantes.
After that he came to St Martin’s Lane.
Newton himself would consult him,
take him home for a bit of discourse.
It was him got de Moivre that commission
to decide who came up with the Calculus –
Leibniz or Newton, that great debate.
The Society was taking no chances.
That was the last he saw of Lady Luck.
Reduced to advising the likes of me
on my chances of winning a wager.
Always poring over his figures he was,
almost went blind towards the end.
Used to sleep over twenty hours a day.
They say it was the somnolence killed him.
He could always tell the outcome of anything,
even foretold the day of his own death:
said he slept a quarter hour more every day
so he worked out that when he slept for twenty-four
that would be the day -- and he was right.
And what, sir, are the chances of that?

"Moseiur Probability" was a featured selection (in October 2009) of the Scottish Arts Council.

Links to earlier postings of poems about mathematicians. In 2011: November 13 Portraits of a Mathematician, July 5 Mathematicians at work, July 2 Mathematicians divide, Jan 30 Sonnet for a geometry teacher, Jan 28 Poems starring mathematicians - 8. In 2010, Dec 8 Poems starring mathematicians -- 7, July 20 In the same family -- a poet and a mathematician, May 14 Poems starring Mathematicians -- 6 (Mandelbrot), May 4 Poems starring Mathematicians -- 5, April 28 Poems starring mathematicians -- 4, April 26 Poems starring mathematicians -- 3, April 15 Poems starring mathematicians - 2, April 14 Poems starring mathematicians - 1, March 23 Poetry of Logical Ideas .

Poetic Pascal Triangle

2011-12-05T22:21:00.009-05:00

First published in 2007 in Mathematics Magazine, Caleb Emmons' poem "Dearest Blaise" has the form of (Blaise) Pascal's Triangle. That original publication offered also a challenge: what is the next line of Emmons' poem?   What is your guess?

DEAREST BLAISE     by Caleb Emmons

                       1
             1             1
        1            he         1
     1       saw      the     1
    1      pure        simple        idea     1
1   truly       distilling       arithmetic        later   1
1 poetic mathematization uncharacteristically sentimentalized Pascal 1

Emmons is a member of the mathematics department at Oregon's Pacific University; prior postings of his work in this blog include: 4 March 2011 and 6 May 2011.

Mathematics works with witchcraft

2011-12-03T14:49:00.006-05:00

T. A. Noonan sometimes uses the languages of mathematics and computer science as tools in her experimental poetry, gathered in her collection The Bone Folders (Sundress Publications, 2011). These poems examine -- at times with mathematical vocabularies and notations -- the complexities of love and loss in the regime change in a coven of Louisiana witches. Here, for example, is Noonan's opening poem, "Difference Engine."

(Click on poem to enlarge.)

Also from The Bone Folders, here is "A Chaos Theory" -- in which goddesses and their spells dance with mathematical notation.

Echoes of childhood rhymes

2011-11-30T00:23:00.001-05:00

For those of us who live and breathe mathematics, there is much of it that affects us deeply. Even those of us whose mathematics is mostly arithmetic have a literature of number that we hold close . And does anything affect us more than the counting rhymes of our childhood? Washington, DC poet Rosemary Winslow uses emotionally-charged repetition of nursery-rhyme numbers to help us know incest in "Four Five Six."

   from Four Five Six . . .

   she slid into the cold kingdom
   behind the blue curtain
   clump clump clump clump
   his boots coming

   she began --
   one two
   unbuckle the shoe
   three four
   open the door

   and she did
   and he did

   his heaviness against her

   five six pick
   up the stick
   seven eight
   lay it straight

   and she did
   and he did

   smoke in the room
   kerosene that smell

   seven eight
   open the gate

   and she did
   she flew without wings
   under the stairs
   an alcove
   honeycombs he kept there
   his thumping thighs erased
        . . .

The lines above are the first of four sections of "Four Five Six" -- found in Rosemary Winslow's collection, Green Bodies (Word Works Books, 2009).

How much for a digit of PI?

2011-11-27T19:29:00.004-05:00

Scottish poet Brian McCabe writes playfully of numbers. In the following poem he imagines an auction of the digits of π.

   Three Point One Four One Five Nine Two
   Six Five Three Five Eight Nine Seven Nine
   Three Two Three Eight Four Six Two Six
       Four Three Three Eight Three Two
         Seven Nine Five Zero Two Eight             by Brian McCabe

             Ludolf van Ceulen 1540 - 1610

   The final item is the gravestone
   of Ludolf van Ceulen of Leyden,
   seventeenth-century mathematician.
   He spent most of his life
   calculating the value of pi
   by the Archimedes method
   to the first . . . ah, thirty-five digits.
   They are engraved on the stone
   beside the date of his death: 1610.

   A decade later his painstaking work
   was obsolete. This is his stone.

   May we start the bidding at three?
   We have it from the gentleman
   in the hat from the University of Texas.
   Three thousand one hundred dollars
   from the bidder on line from Leyden.
   From the man in the hat from Texas
   we have three thousand one hundred
   and forty dollars. From Leyden
   we have one hundred and forty-one.
   Three thousand one hundred and
   forty-one dollars and fifty cents
   from the man in the hat from Texas.
   From Leyden we have fifty-nine cents.
   Any more bids? Sold to the bidder
   who is on line from Leyden! So:
   the tombstone of Ludolf van Ceulen
   is returned to the place of his death
   for three thousand one hundred and
   forty-one dollars and fifty-nine cents.
   Or the value of pi to the sixth digit.
   Cheap at the price, considering.

McCabe's poem is found in his collection Zero (Polygon, 2009). Computation of π continues in 2011 as a worldwide contest; a recent record was set with more than 5 trillion digits.
Previous blog postings on π may be found at these links: in 2011, Mar 15 Remembering Pi-day, a day late; in 2010  Aug 23 The Irrational Sonnet -- an Oulipian form, Sept 2 Rhymes help to remember the digits of Pi, Sept 6 More of Pi in Poetry.

Open and Closed -- Tomas Transtromer

2011-11-24T11:22:00.013-05:00

A background in mathematics gives my enchantment with words a special twist. Each time I see familiar math terms in a poem I layer their mathematical meanings amid their mainstream ones. Two such terms are "open" and "closed." (I'll supply brief mathematical explanation at the end of this post but, first, here is "Open and Closed Spaces" -- a poem by the winner of the 2011 Nobel prize for Literature, Swedish poet Tomas Transtromer. )

Open and Closed Spaces   by Tomas Transtromer

A man feels the world with his work like a glove.
He rests for a while at midday having laid aside the gloves on the shelf.
There they suddenly grow, spread
and black-out the whole house from inside.

The blacked-out house is away out among the winds of spring.
'Amnesty,' runs the whisper in the grass: 'amnesty.'
A boy sprints with an invisible line slanting up in the sky
where his wild dream of the future flies lika a kite bigger than the suburb.

Further north you can see from a summit the blue endless carpet of pine forest
where the cloud shadows
are standing still.
No, are flying.

     This poem is in Transtromer's collection, New Collected Poems, translated by Robin Fulton (Bloodaxe Books, 1997/2011). The Swedish original of "Open and Closed Spaces" and several other Transtromer poems (selected by Lars Rydquist, head librarian, Nobel Library of the Swedish Academy) are available at the Nobel prize web site.
     In mathematics an intuitive characterization of an "open" set of points is that each of its points is surrounded by points also in the set. For example, the points interior to a circle form an open set. The circle itself is a set of boundary points for the interior points. If we add these boundary points to the interior points we have a "closed" set.

Reading the Rubaiyat

2011-11-21T01:03:00.003-05:00

Omar Khayyam (1048-1131) was a mathematician who wrote poetry. Here are two quatrains from his Rubaiyat.

        XLVI

   For in and out, above, about, below,
   'Tis nothing but a Magic Shadow-show
        Play'd in a Box whose Candle is the Sun
   Round which we Phantom Figures come and go.

        XLVII

   And if the Wine you drink, the Lip you press,
   end in the Nothing all Things end in -- Yes --
        Then fancy while Thou art, Thou art but what
   Thou shalt be -- Nothing -- Thou shalt not be less.

Found in Rubaiyat of Omar Khayyam, rendered into English Verse by Edward Fitzgerald (Grammercy Books, 1992).

Equivalence

2011-11-18T07:09:00.001-05:00

In telling the time, we commonly refer to hours that differ by a multiple of 12 using the same number. Sixty hours after 3 o'clock it is again 3 o'clock. The clock relationship -- with its times that are named by the same number but are not, after all, exactly the same -- illustrates the mathematical notion of an "equivalence relation." In "Equivalencies," the insights of poet Judith McCombs stretch this mathematical concept.

Equivalencies by Judith McCombs

The fear of not writing, of having no words,

Is the muscles not working, the pack top-heavy,
the hard slime on ledges where the ankle gives way

is the sledge hammer current at the bottom of waves
coming too fast and the swimmer unable

is the baby hung up in the birth canal,
the contractions building but its heartbeat stalls

is the hemorrhage of vision with nothing made yours,
is the flicker of brain waves in the same stuck dream.

The writing is easy, the having is easy,

is the meadows opening, is the blessed deep breath
in the mouth of the runner, is the long easy strides

riding and passing the crests of the earth,
is the surge of delivery, the new being riding

the pulsing red channel, is the mountains riding
the slower upheavals of strata and drift,

is the white surge riding the hull of the seed
as it breaks into life, the shapes spilling over

and the words coming through, the deep dream opening
and the words coming true, the words
coming through.

"Equivalencies" appears in McCombs' collection The Habit of Fire: Poems Selected and New (Word Works, 2005).

Portrait of Max Dehn

2011-11-15T22:32:00.003-05:00

Today I offer a poem by Portuguese mathematician F. J. Craveiro de Carvalho -- its initial English publication was in Topology Atlas, 2005 -- about an outstanding mathematician, Max Dehn. Dehn inhabited Craveiro's office via a Springer-Verlag Poster. Here is a portion of Craveiro's introduction to the poem.
     Throughout the years Springer-Verlag has been producing a number of posters featuring distinguished mathematicians . . . Some twenty years ago or so I was lucky enough to get hold of one which . . . portrays a group of Gottingen mathematicians. The year is 1899 . . . and the group is remarkable. Among others it includes Max Dehn . . . Max Dehn's life has always interested me. He solved one of Hilbert's famous problems, the third, and things like Dehn twists, Dehn surgery, Dehn's lemma, for instance, crop up frequently in Topology and Group Theory related areas. Unfortunately he was one of the few mathematicians unable to obtain a job in accordance with his mathematical talent after being force to flee from Germany in 1939.      The poem below was written after years of contemplating the poster I mention above, which hangs on the wall facing my desk, in my office.

   Portrait of Max Dehn     by Francisco José Craveiro de Carvalho

   This is the summer season
   of the quiet year of 1899
   in Gottingen.
   In the background there is a river
   or a stage-setting that creates a river.

   Only we still know
   that the young Max Dehn
   will have to rush
   out of the photograph
   and get rid of his coat
   high collars shirt and life
   to try and get to and find himself
   on a strange shore.

     The English translation of Craveiro's poem is by Professor Manuel Portela, Faculdade de Letras, Universidade de Coimbra, Portugal. The original Portuguese version of this poem was first published in Gazeta de Matematica, # 149, July 2005.
     Background information for the poem may be found at Topology Atlas.  For more of Max Dehn's story, see the October 2002 issue of the Notices of the American Math Society for an article entitled "Max Dehn, Kurt Gödel, and the Trans-Siberian Escape Route" by John W Dawson, Jr. Additional portraits of mathematicians are highlighted in the posting for  13 November 2011.
     Craveiro is active in translating poetry into Portuguese.   At this site are several of his poems and his translations (including Portuguese versions of two of mine).  Here is a math-poem-with-translation by poet / blogger Diane Lockward.

Portraits of a mathematician

2011-11-13T01:42:00.007-05:00

Ideas for this posting began with my post on 30 October 2011 in which I selected 7 favorite lines of poetry as a sort of self-portrait. That posting led to an exchange with blogger Peter Cameron -- which prompted me to write these abecedarian portraits of a mathematician.

   I know a mathematician . . .     by JoAnne Growney

   always busy
   counting, doubting
   every figured guess,
   haply idling,
   juggling, knowing
   logic, measure, n-dimensions,
   originating
   playful quests,
   resolutely seeking theorems,
   unknowns vanish :
   wrong xs, ys -- zapped.

After this next poem are links to still more verse portraits of mathematicians.

          Mathematician       by JoAnne Growney

          naming

          optimizing
          permuting
          quartering

          reflects

          solving
          topologizing

          unifies
          verifies
          wonders

          x-trapolating
          yielding
          zeroing
          angling
          branching

          commutes
          differentiates
          equates
          factors
          groups

          halving
          intersecting
          juxtaposing
          knotting

          longing . . . .

Links to earlier postings of poems about mathematicians. In 2011: July 5 Mathematicians at work,   July 2 Mathematicians divide,  Jan 30 Sonnet for a geometry teacher, Jan 28 Poems starring mathematicians - 8. In 2010, Dec 8 Poems starring mathematicians -- 7, July 20 In the same family -- a poet and a mathematician, May 14 Poems starring Mathematicians -- 6 (Mandelbrot), May 4 Poems starring Mathematicians -- 5, April 28 Poems starring mathematicians -- 4, April 26 Poems starring mathematicians -- 3, April 15 Poems starring mathematicians - 2, April 14 Poems starring mathematicians - 1, March 23 Poetry of Logical Ideas .

Mathematics of desire

2011-11-10T23:53:00.004-05:00

Last Monday evening, I listened with pleasure to Pennsylvania (Fogelsville) poet Barbara Crooker read at Cafe Muse (with Meredith Davies Hadaway and Erin Murphy). Barbara writes fine poems -- and reads them well. Although she offered no mathematical poems that evening, hearing her reminded me to hunt for her love poem "The Irrational Numbers of Longing . . " and to offer it to you here:

The Irrational Numbers of Longing,
The Infinite Mathematics of Desire by Barbara Crooker

This day could be reduced to three elements:
green grass, blue hills, yellow fields of mustard,
solid in its planes as any late Cézanne. It makes me think
of the curves your hips and back make when you are sleeping,
the way my fingers travel the back road of your spine,
the landscape of our bodies under the quilt.

I want to relearn the language of plane geometry,
the relationship of curves in space, the friction
between positive and negative numbers, improper
fractions, your lovely smooth surface, the angle
of intersection, where we come together in the dark.

This poem comes from Crooker's collection Radiance (Word Press, 2005). Another Crooker poem -- connecting geometry and autism -- was featured on 12 January 2011.

Mathematician-Poet Glaz

2011-11-07T22:30:00.007-05:00

     Sarah Glaz, a professor-mathematician at the University of Connecticut -- and a poet -- is at the forefront of appreciation and advocacy of mathematics as an art and closely connected to other arts, particularly poetry. Her webpage offers more than a hundred links to "Undergraduate Resources; Math Links for Information and Fun" and to scholarly articles that offer teachers and students math-poetry ideas to ponder carefully. This link, for example goes to an article entitled "The Poetry of Prime Numbers" that Glaz presented at the Bridges 2011 Conference in Portugal.
     One of my favorites of Glaz' poems is this one whose structure relies on the Fundamental Theorem of Arithmetic (see note following the poem).  Here is "January 2009" :

13            January 2009      by Sarah Glaz

12=2²x3       Anuk is dying for Anuk is dying in the white of winter
11               The coldest month
10=2x5        Anuk is dying in the falling snow
9=3²            The white of winter for Anuk is dying
8=2³            Anuk is dying for the white of winter
7                The drift of time
6=2x3          Anuk is dying in the white of winter
5                The falling snow
4=2²            Anuk is dying for Anuk is dying
3                The white of winter
2                 Anuk is dying
1               ·

    "January 2009" first appeared in Recursive Angel, (May/June, 2011) along with the following note:
The poem's structure follows The Fundamental Theorem of Arithmetic, which states that every positive integer greater than one may be expressed in a unique way as a product of powers of distinct prime numbers. This technique first appeared in Carl Andre's poem, "On the Sadness" (Numerals 1924-1977, Yale University Art Gallery Catalog Exhibit, 1978).
     Andre's poem also appears in the anthology Strange Attractors: Poems of Love and Mathematics (A K Peters, 2008) -- edited by Sarah Glaz and me.    Poetry by Glaz appears also in these postings: 18 April 2011, 23 April 2010 and 31 March 2011 (a translation from Romanian, poetry by Ion Barbu).

Four colors will do

2011-11-05T07:23:00.002-04:00

     As I work with Gizem Karaali, an editor of the Journal of Humanistic Mathematics, to plan a reading of mathematical poetry at the JMM (Joint Mathematics Meetings) in Boston on 6 January 2012, my thoughts return to a poetry reading that I helped to organize at JMM in Baltimore in 1992. One of the participants was a friend and former colleague, Frank Bernhart, whose work used the pattern of a number of "mathematical" poems -- following the rythmn of a well-known song.
     Bernhart is an expert on the Four-Color Theorem and his poem celebrates its history -- including consideration of its proof (in 1976) by Kenneth Appel and Wolfgang Haken. (The theorem asserts that any map drawn on a flat surface or on a sphere requires only 4 colors to ensure that no regions sharing a boundary segment have the same color.)

Cartographic Claustropobia       by Frank Bernhart
(A Four Color History Tour)

          DIRECTIONS: read like "Higgledy-piggledy, My Black Hen," or
          "The Wonderful One-Hoss Shay," contrasting smooth and staccato phrases.

One color, TWO color, THREE-and-FOUR,
In coloring maps, do WE-need-more?
The map of England, Guthrie tried,
With EXACTLY four he's SATIS-fied.
So he told DeMorgan, who THEN told Cayley,
And plenty of others -- the news spread daily.
Til Kempe, a lawyer, made demonstration,
Earned himself a nice ovation.

PLANE maps or SPHERE maps -- it don't matter,
Makes no difference, 'cept in patter.
But torus and Klein sack, please refuse,
All higher surfaces you MUST NOT use.
Abstain from topology, draw simple lines,
Let the map be described by finite signs.
And using the Kuratowski planarity rule,
You may trade the map for its planar dual.

Two color, THREE color, FOUR-and-Five,
said Percy John Heawood, not now alive,
are always enough, and I'll attemp'
to repair the gap I found in Kempe.
For years he labored, with great agility
To make four suffice, with high probability,
Accompanied by false proofs, dare we mention?
The authors could hold a crackpot convention.

Now, finally, thankfully, the answer's FOUR,
in colorful cartography -- no NEED for more.
And what team broke the century-long spell?
None other than Haken and his FRIEND Appel.
The easiest direction, discharging, entails
pages and pages of tiny details.
The other direction, reduction, is cuter:
here billions of steps were left to computer.

DISCHARGE-ing, REDUCE-ing, what's that get?
An awkward and large unavoidable set.
Kempe's methds were extended, as though on a leash
considerably lengthened by Birkhoff and Heesch.
Plus a tribe of coworkers who nobly increased
the list of reductions without help in the least
from computers. Some people say "It's a cheat.
Your proof is in part an unprintable feat."

One year, TWO years, THREE-and-FOUR,
Better throw in a dozen more.
The years roll by, the proof is firm,
Jut a few little errors to make them squirm!
But all soon are fixed, JUST LIKE NEW,
the critics now have better THINGS to do.
A nice short proof is NOT in sight,
Better to avoid all colors and PAINT things white.

FOUR                              Any   flat map
  FOUR                              we draw we may
FOUR                              color with four
FOUR                              c o l o r s   only.


For a variety of math-song lyrics, including work by Tom Apostol and Tom Lehrer, visit this page maintained by Math Professor Joel W Robbin of the University of Wisconsin.

Division by zero

2011-11-02T23:05:00.007-04:00

The November 2011 issue of the Scottish ezine, The Bottle Imp, is just out and it includes my review of poet Brian McCabe's Zero (Polygon, 2009). To stir your interest, I include a few lines from McCabe's title poem (which chronicles the irregular history of zero) -- and then offer a human interpretation of division by zero in a poem by Ann McNeal.

from "Zero" by Brian McCabe

     Even when it came into its own
     in The Opening of the Universe
     and Bramagupta wrote
     a debt minus zero is a debt,
     a fortune minus zero is a fortune
     it confounded him still:
     zero divided by zero is zero.
     Perhaps it will outlive us at last:
     implacable, inscrutable to the end.

     While division of any nonzero number by itself yields 1, in modern mathematics we differ from Bramagupta's view; zero divided by zero is said to be indeterminate -- that is (applying the definition of division, expresed in terms of multiplication) the quotient of zero divided by zero might be any number at all.
     Blogger Ann McNeal is an emerita professor of physiology. I found her poem about zero, "Higher Mathematics," in the collection, Love Over 60: an anthology of women's poems (Mayapple Press, 2010); it appeared first in Paper Street.

   Higher Mathematics     by Ann McNeal

   You can't do that, Miss Sharp said
   from her place by the blackboard.
   Six divided by zero has no answer.
   Write the word Impossible.

   When a number is divided by itself,
   the answer is one. When a woman
   is divided by her fantasies,
   by ambition, unswept floors,

   family, highways,
   meetings, bedsheets,
   the answer is unknowable.

   If any number is divided by one,
   the answer is herself, feet
   on the ground, knowingness,
   porcupines, potatoes.

   Dividing by zero is not the problem.
   When someone is divided by zero,
   the answer is gloriously infinity,
   one number after another up past
   a trillion, always more.

   So the woman, who is not divided
   now by children, obligations,
   anyone else's dirty dishes --
   a woman divided by nothng
   but herself is whole.

Another poem on dividing by zero may be found in my posting for 10 February 2011 -- and a variety of other postings also have poems of zero. These may be found using the SEARCH THIS SITE link located in the bottom border of this blog.

What can 7 objects say? Or 100?

2011-10-30T21:32:00.002-04:00

     A friend, a high school art teacher, had one of her students paint a portrait of her -- not of her bodily self but a still life of the seven possessions that she felt best defined her. Since that time, more than seven years ago, I have been trying to decide what my seven objects would be. How might I portray me?
     An article in today's NY Times, "Stuff that Defines Us," reminded me that I have neglected that project. The article tells of the British Museum's ambitious and fascinating project to choose 100 objects from their collection to summarize the history of the world.

     Such challenges appeal to both the mathematician in me and the poet in me. To say the most, accurately, in seven objects -- or 100. An invigorating challenge.
     Unable thus far to make my list of seven objects, today I compromised, limited my choice horizons. I would choose my seven favorite lines of poetry. I did this -- in a few quick minutes -- and I present them below. Brought to mind quickly, they leave much forgotten -- but they are a start. They do not include Denise Levertov or June Jordan or Derek Walcott. Others, too, deserve a place. But perhaps fast is best; and perhaps I will catch a new glimpse of self, mirrored in these lines.

   I lift mine eyes unto the hills
   How does your garden grow?
   I make my magic / of forgotten things
   I learn by going where I have to go
   Will go on prancing, proud and unafraid
   As truth can live with right and wrong
   Rage, rage against the dying of the light

(Lines are from the Book of Psalms, Mother Goose, Muriel Rukeyser, Theodore Roethke, Adrienne Rich, E E Cummings, and Dylan Thomas.)

                    M Y S
                          E
                     V
                       E
                     N

Music on the hypotenuse

2011-10-28T18:40:00.007-04:00

Dr. Cai Tianxin is a professor of mathematics (specializing in number theory) at Zhejiang University, China. He also is an accomplished and well-known poet.

   The Number and the Rose     by Cai Tianxin

   Pythagoras played music on the hypotenuse
   while devising the system of rational numbers
   a labyrinth as transparent as quartz
   his home was on Samos on the Aegean Sea
   as a child he never wanted to be a sailor
   nor was he ever enticed by the beautiful girls of Salonika
   numbers were the treasured roses of his heart
   those crimson, orange, yellow, or pure white flowers
   were the perfect expressions of his unequalled mind
   urging him to write his famous assertion “all things are numbers”
   Leonardo once, in Florence, devoted himself to this principle
   neglecting the charms of the young beauty Genevra
   finally giving up for reasons we don’t know

The original Chinese version of "The Number and the Rose" is available here; the poem is found in Cai Tianxin's book Song of the Quiet Life , translated by Robert Berold and the poet (Deep South, South Africa, 2006).   The poet's article "Mathematicians and Poets" (appearing, in translation, in the April 2011 issue of the Notices of the American Mathematical Society) was noted in this blog's posting on 18 March 2011.

* * * * *
The Halloween season is, of course, upon us.

For "Ghost Stories Written" by Charles Simic, visit the post for 29 October 2010.

Submit math-science poetry

2011-10-27T22:09:00.005-04:00

During the month of November, the online journal Talking Writing is seeking submission of poetry with connections to mathematics and the science. Submit 4-6 poems to editor@talkingwriting.com.

O T T

ON E
ONE N N

These visual poems "One" and "Ten," above, are mine.

Chaos Over the Hors d'Oeuvres

2011-10-25T22:10:00.007-04:00

Some systems of equations can produce vast changes in output with only small changes in input. Or not. This sensitivitiy to initial conditions is a key characteristic of chaos. As happens not infrequently in mathematics, the term chaos also carries larger-world meanings additional to the correct ones -- indeed, the phenomena studied in chaos theory are not haphazardly disordered but are complex. Very very complex. Judy Neri's poem addresses this topic.

Chaos Over the Hors d'Oeuvres   by Judy Neri

  Chaos is in
  they said at the dinner party;
everybody's talking about it.

Chaos:
the mathematical notion
that the slightest change
can turn order into disorder,
the circle into a tangled skein.

Dinosaurs could come back to life
and pigs could fly.

Just nudge that stone
one millimeter to the left and
an explosion will rip the planet
  from its domesticated course
to wander dark space forever.

Any mother knows this,
how the smallest pebble on the track
can cut the thread of her child's design,
end the comforing shuttle of the years.

Now they worry
  chaos won't stop --
everybody's talking about it,
how it wanders our streets,
                                     wilding --
          O mathematicians, can't you mend?

     Non-mathematicians who live with mathematicians often write of mathematics with special insight. Such is the case with Judy, whose spouse is Umberto Neri, retired from the mathematics department at the University of Maryland. "Chaos Over the Hors d'Oeuvres" is found in Neri's collection Always the Trains (New Academia Publishing, 2008).
     An earlier post on this blog of poetry-with-math by family members of mathematicians appeared on 20 July 2010. Poems of Chaos Theory and the Butterfly Effect have been posted on 18 January 2011 and 22 November 2010.

Permutations and Centos

2011-10-23T08:04:00.002-04:00

A Cento is a collage poem made of lines taken from other poems -- such as a sonnet composed of lines from fourteen of Millay's sonnets, or Shakespeare's -- or from newspaper articles or television advertisements or whatever. Here's a three-line sample from a Cento, "Patchwork," composed by Joanna Migdal to celebrate women poets.

   I dwell in Possibility.                                              (Emily Dickinson, #657)
   Yes, for that most of all.                                        (Denise Levertov, “The Secret”)
   It’s four in the afternoon. Time still for a poem.
                                                                                 (Phyllis McGinley, “Public Journal”)

One recent day sitting at my computer, waiting on telephone-hold, I began to explore the idea of a Cento using my blog-titles. I printed a list of titles, selected some I liked, and began to arrange them. Eventually my chosens shrunk to five (from July, August, and September). Though it seemed easy to do the arranging in my head, I also went to a text permutation generator and asked it to list all of the 5! = 120 possible permutations of the five titles. Whle it was a tedious procedure, reviewing the complete list was also helpful -- suggesting possibilities I'd overlooked. This one is my favorite:

     The wind, counting
     A thousand and fifty-one waves.
     Mathematical theorems tornadoing --
     The square root of Everest,
     This plane of earthly love.

When objects are near one another, even if they are very different, their proximity prods us to look for -- and often find -- a relationship among them. Such is the secret of a Cento.

If if sounds like fun to you, please do your own expermentation with my blog titles and create a Cento. Submit it as a comment to the blog.  (Titles for January - September, 2011 are found here; titles for 2010 are found here).   And, thanks in advance for your participation.

A whole and its parts

2011-10-20T20:13:00.002-04:00

     Aristotle may have been the first to assert that a whole is more than the sum of its parts. Mathematics textbooks are likely to say otherwise, postulating that a whole is equal to the sum of its parts.

    Emily Dickinson also comments on the matter.

                (1341)         by Emily Dickinson

     Unto the Whole -- how add?
     Has "All" a further realm --
     Or Utmost an Ulterior?
     Oh, Subsidy of Balm!

        From Poems by Emily Dickinson, Volume 3 (Hayes Barton Press, 1955).

     I am unsure whether it has been my study of mathematics or a childhood full of fables and their morals -- A stitch in time saves nine, Haste makes waste, Little by little gets to the goal . . . -- that's given me the habit of testing every truth with an opposite. Perhaps haste makes wealth or the whole is less than the sum of its parts. As poet I have had this latter experience: a quartet of finely crafted lines fail to hold together into a stanza, or fourteen lines in perfect rhythm and rhyme have not summed to the the song of a sonnet.

     And so it goes.

Things the fingers know

2011-10-18T23:08:00.007-04:00

Blogger Peter Cameron sent me a link to an lively article, "Eveline Pye: Poetry in Numbers" in the September 2011 issue of the statistics magazine, Significance. Written by Julian Champkin, the article tells of Eveline Pye -- lively and interesting Glasgow statistician, teacher, and poet -- and includes a selection of her work. One of the poems offered therein is "Solving Problems."

   Solving Problems      by Eveline Pye

   How do you know the right thing to try? he says,
   jabbing paper with his finger. Good question,
   I say, playing for time as I have no answer he wants
   to hear. Solving these equations is part intuition,
   but first, you learn to manipulate x's and y's until
   decisions are made in your fingers, not your head --
   like typing an access code at the ATM, changing gear
   in the car or signing a cheque -- until it all becomes
   muscle memory -- the same way Reubens painted
   hands, again and again or Keats scribbled rhyme
   after rhyme -- and then you go with the flow
   and, if you are lucky, there is a sweet, sweet moment
   as the plum falls into your eager hands, and if not,
   you try, and try -- on and on until your head bursts.

At Glasgow Caledonian University, Pye teaches statistics -- where she helps to educate Renaissance men and women who will be at home in both quantitative and literary cultures.  Bravo, Eveline Pye!

A small Fib

2011-10-16T10:09:00.001-04:00

My dilemma

   I've
   lost
   the art
   of careful
   thought, asea in floods
   of trivial information.               by JoAnne Growney

Poems with lines whose syllable count follow the Fibonaci numbers are called Fibs. Primarily, these are six lines -- with syllable-lengths 1, 1, 2, 3, 5, and 8 -- but variations also occur.

Facts about the Fibonacci numbers and several poems are found in these prrevious postings:
     April 19, 2010 Poems with Fibonacci Number Patterns
     April 29, 2010 A Numerical Poem (Fibonacci)
     October 31, 2010 The Fib -- a form that gathers strength
     January 5, 2011 Mathematics and Race
     February 4, 2011 AWP avoids mathematics

Hamilton -- mathematician, poet, Irishman

2011-10-13T23:41:00.004-04:00

October 15-22 is Maths Week in Ireland -- as I learned from this article in the Irish Times celebrating maths and the Irish mathematician Willam Rowan Hamilton (1805 - 1865). Turns out that Hamilton's quaternions are useful in design of video games and 3D effects in the cinema.
Hamilton -- a mathematician, astronomer, and physicist -- was also a poet; a contemporary and friend of Samuel Taylor Coleridge and William Wordsworth. His poems do not speak of mathematics -- but here is a sonnet he wrote to honor Jean Baptiste Joseph Fourier (1768 – 1830), a prominent French mathematician and physicist.

(Click on poem to enlarge.)

This poem and others by Hamilton may be found in Life of Sir Willam Rowan Hamilton by Robert Perceval Graves. Now a google-ebook, originally published by Hodges, Figgis, &co and part of a series from Dublin University Press.

Like poetry, mathematics is beautiful

2011-10-12T07:49:00.000-04:00

     Congratulations to Justin Southey who is completing his doctoral studies in mathematics at the University of Johannesburg under the direction of Michael Henning. Recently Justin contacted me to ask permission to include one of my poems in the introduction to his dissertation, "Domination Results: Vertex Partitions and Edge Weight Functions." Here is a portion of Justin's request:

I first came across your poetry (in particular, the poem ["Like Poetry, Mathematics is Beautiful"]) in a small publication produced for maths enthusiasts and olympiad entrants while at school in South Africa in the late 1990's. For my undergraduate degree I was lucky enough to be enrolled in a university where I was able to major in both mathematics and drama and I selected your poem as the poetry choice for my final performance examination. I believe I owe the distinction received in that course to the strong affinity I held with the subject matter. To this day it remains one of the few poems I can still recite by heart and I'm only sorry for not contacting you about it at the time. Now, I am in the process of finalizing the thesis for my PhD in graph theory and I would very much like to include your poem in the introduction.

     Thank you, Justin, for the honor of inspiring your work. (Interested readers make look back to postings on 10 January 2011 and 14 June 2010 for tributes to several who inspired me.)
      The poem, "Like Poetry, Mathematics is Beautiful" (first published in the May 1994 issue of the American Mathematical Monthly), was written early in my poetry career -- and I look back on it with nostalgia. It is not a good poem but it says something that needs to be said -- mathematics, like poetry, is full of beauty (a matter indisputable among those who know the language) and is too-often misunderstood as mere calculation.

   Like Poetry, Mathematics is Beautiful

   Timidly I ask
   each one I meet if they
   find mathematics beautiful
   or useful, and each one dares to say,
   "Useful, of course. I use it every day."
   And if I seem to want a proof,
   they all go on to tell
   that daily they subtract and add
   to keep a checkbook; sometimes also
   they multiply to find how many squares
   they need to tile the kitchen floor.

   Mathematics is not only plus
   and minus, not just counting one,
   two, three. There are rules to bend
   defiantly, so parallels
   will meet before infinity. Look
   at the magic of unending terms
   that converge to a finite sum:
   start with one-half plus half of one-half
   plus half of the last again and again.
   Though we go on forever, we never
   pass one. Do you find me di fficult? Oh, dear!

   Suppose, instead, I ask
   if poetry is beautiful
   or useful. Will each person say,
   "Useful, of course. I use it every day."
   And if I seem to want a proof,
   will they go on to say that they
   use rhymes to call to mind the days
   of a month -- like "Thirty hath
   September" -- and to remember
   how to spell words with 'i' and 'e'.

   I have a faint, enduring hope
   that someday folks will see
   mathematics to be
   as lovely
   as poetry.
                                                 by JoAnne Growney

Numbers from the Piano

2011-10-11T07:09:00.004-04:00

     Of all of the things we might try to say when we sit down to write a poem, which are the ones we should choose? Sometimes we may say what first occurs to us -- begin to write and keep going until we are done. This may suffice -- or it may seem to lack care. To be more careful, we might seek a pattern to follow: perhaps we might form lines whose syllable-counts follow the Fibonacci numbers.   Or construct a sonnet -- fourteen lines with five heart-beats per line and some rhyme. Or devise a scheme of our own.

     Nova Scotia poet John Devlin has written a long poem, "Enigma of the Piano" in which piano-numbers structure the poem. Specifically, the poem has stanza-lengths of 9 and 13  -- where 9/13 is the ratio of black keys to white on an 88-key piano keyboard. Devlin's long poem has 22 = 9 + 13 pages -- nine of these have a nine-line stanza (each line starting with a vowel) followed by a thirteen-line stanza (each line starting with a consonant) and thirteen of them have the stanza lengths reversed. Page 12 of the poem is offered below; the complete poem is available here.

   The imaginary Lady flits down the corridors of the palace of the King of
   Time. The King is robed in robes of green and gold. He is melancholie againe
   because the spring blossoms are faded and fallen. So blind Queen Eva plays
   for him a curious sarabande upon the cembalo. The fires in the grates burn with
   flames purple and green this cold summer morning. Candles in the dome ignite
   fire in the centre of the palace where this ménage à cinq gathers for a late
   cold supper. The Lady in gray flits back and forth through the enfilade of
   doorways in the south front while the clavichord soothes the King who reclines
   with his face to the wall. She passes five mirrors on her vain journey, and
   sees in each the fading shadow of her wan smiles. Five times she passes and at
   last she looks in the last of the series of looking-glasses. Intersection of this
   ménage results in implosion of the central dome with no loss of life or
   damage to the precious frescoes. The King of Time is a new invention

   in this pentagonal palace, draughty on a rainy Monday morning when candles
   in the dome must be lit for a game of bridge-plus-one. The King’s Fool
   invented this peculiar game for five adults: one woman and four men.
   A gyroscope governs the length of each game. The pope’s birthday
   is celebrated with venison pie and stale mead. The altar Easter lilies
   in the castle chapel are limp and brown and soon to be tossed out for compost
   in the kitchen gardens. The Fatima is adored once again
   and the holy candles lit smell like toast. The imaginary Lady in gray
   at last ceases her questing and rolls to a complete stop beneath the burnt dome.

Using the numbers 7 and 18 (the numbers of vowels and consonants in his complete name) Devlin has written an autobiographical poem, The Ghost on the Mezzanine, available (as a pdf file) here.