Speaking, understanding . . . where is truth?

     A review in the Washington Post of a new book about Oscar Wilde opens with this quote:

"Man is least himself when he talks in his own person."

and Wilde's words have gotten me thinking again about subtleties of language.
     Also in recent news, the death of Nobelist V. S. Naipaul (1932-2018) -- and here is one of  this writer's thought-provoking statements:

            Non-fiction can distort;
            facts can be realigned.
            But fiction never lies.            V.S. Naipaul, A Bend in the River

My own thoughts about language most often focus on the condensed languages of mathematics and poetry -- and the need for frequent re-readings before understanding arrives.  Here, below, I include a poem by Stephanie Strickland that speaks eloquently of the struggles in which our minds engage concerning objects and the symbols that represent them -- struggles that are involved in creating and reading both mathematics and poetry . . .

     Striving All My Life     by Stephanie Strickland

     Maxwell said: There is no more powerful way
     to introduce knowledge to the mind than … as many different
     ways as we can, wrenching the mind   

Qualitative thinking in a quantitative era . . .

Chemistry Nobelist  Roald Hoffman also is a poet, 

and an advocate of holistic education.

Many thanks to Australian poet and STEAM advocate, Erica Jolly, 

for reminding me of the importance of Hoffmann's work.

HEIGHT     by Roald Hoffmann

The man
who said
when you're on top
of a mountain
you can't see it
was a miner. 

The tiny poem above is found here on Hoffmann's website.

Mathematician, Poet -- Blind to the worth of Women

     As we study mathematics and learn of outstanding mathematicians, many of us do not also learn which of those mathematicians also were poets.  A posting that I found recently in Marian Christie's blog, Poetry and Mathematics, features poetry by  Scottish physicist James Clerk Maxwell (1831-39).

     Maxwell's verse also is featured in the math-poetry anthology, Strange Attractors:  Poems of Love and Mathematics (A.K Peters, Ltd., 2008);  preview available here at amazon.com.

     Below I offer a stanza from a Maxwell poem (posted in this blog back in December, 2015) -- a stanza that shows the long-mistaken attitude that has existed about inferior abilities of math-women: 

The minute in infinity

From  Treatise on Infinite Series     by Jacob Bernoulli

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

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

Those trains in word problems -- who rides them?

    A Problem in a Math Book     by Yehuda Amichai (1924-2000)

     I remember a problem in a math book
     about a train that leaves from place A and another train
     that leaves from place B. When will they meet?
     And no one ever asked what happens when they meet:
     will they stop or pass each other by, or maybe collide?
     And none of the problems was about a man who leaves from place A
     and a woman who leaves from place B. When will they meet, 

It is clear that . . .

     "If I stand"     by Inger Christensen  (Denmark, 1935-2009)

               If I stand
               alone in the snow
               it is clear
               that I am a clock

               how else would eternity
               find its way around                

Translated from the Danish by Susannah Nied

The Cube of the Rainbow

     Later this week a scheduled screening (in nearby Takoma Park, MD) of a film about Emily Dickinson (1830-1886) has prompted me to return to some rereading of Dickinson's verse -- which is occasionally mathematical.   For example:

       We shall find the Cube of the Rainbow     by Emily Dickinson

       We shall find the Cube of the Rainbow.
       Of that there is no doubt.
       But the Arc of a Lover's conjecture
       Eludes the finding out.

The stanza above is found in many places; my source is Strange Attractors:  Poems of Love and Mathematics, ed. by S Glaz and JA Growney (AK Peters/CRC Press, 2008).  This link leads to previous postings of Dickinson's work in this blog.

Integrals -- a poem

Integrals    by Jonathan Holden

     Erect, arched in disdain,
the integrals drift from left
across white windless pages
to the right,
serene as swans. 

After loss we have nothing--which is something ...

     A poet whose work I much admire is A. E. Stallings -- born in the US, in Georgia, but now living in Greece.  This poem -- a sonnet -- deals with the paradox that nothing is something -- as with the integer zero and with the absence of a loved one.  The poem was written for her father who taught statistics at Georgia State University.

     Sine Qua Non     by A. E. Stallings

       Your absence, father, is nothing. It is naught—
       The factor by which nothing will multiply,
       The gap of a dropped stitch, the needle's eye
       Weeping its black thread. It is the spot
       Blindly spreading behind the looking glass.
       It is the startled silences that come
       When the refrigerator stops its hum,
       And crickets pause to let the winter pass.

       Your absence, father, is nothing—for it is
       Omega's long last O, memory's elision,
       The fraction of impossible division,
       The element I move through, emptiness,
       The void stars hang in, the interstice of lace,
       The zero that still holds the sum in place.

"Sine Qua Non" is found in Stallings' collection Hapax (Northwestern University Press, 2006) and also in the anthology Strange Attractors:  Poems of Love and Mathematics (AK Peters/CRC Press, 2008).

 A wonderful collection of Stallings' poems is available at the PoetryFoundation website -- and more about this poet and her work is may be found here at her at Stallings' website.

Fibs in NZ -- and climate change

     A few days ago, on August 21, it was Poet's Day in New Zealand and the blog sciencelens.com featured a math-poetry theme; that posting mentions the anthology, Strange Attractors:  Poems of Love and Mathematics (for which Sarah Glaz and I are co-editors) and offers several Fibs, poems whose syllable-counts follow the first six non-zero Fibonacci numbers (1, 1, 2, 3, 5, 8, . . .., with each succeeding number the sum of the two preceding). 

Venn Diagrams

      During these days of classifying people and points of view, my thoughts turn again and again to Venn Diagrams and I am then reminded of a thoughtful poem about math in grade-school days (by Pennsylvania poet and professor Marjorie Maddox) that I first read long ago -- and I offer it here:  

Learn about Venn Diagrams here

Venn Diagrams     

          by Marjorie Maddox   

There, stuck in that class,
chalking circles on a board 
       so high your toes ached,
an inch of sock exposed,
all for the sake of subsets,
        intersection.
That teacher with the tie too bright for day,
wide as your fingers spread  

Love and Tensor Algebra

     Stanislaw Lem (1921-2006) was a Polish science fiction writer whose works have been widely translated.  Here is a poem of his (found here in a blog with final postings in 2007)  -- a poem that enthusiastically expresses love in the language of mathematics!

Love and Tensor Algebra      

                    by Stanislaw Lem (translated by Michael Kandel)

 Come, let us hasten to a higher plane
 Where dyads tread the fairy fields of Venn,
 Their indices bedecked from one to n
 Commingled in an endless Markov chain!

 Come, every frustum longs to be a cone
 And every vector dreams of matrices.
 Hark to the gentle gradient of the breeze:
 It whispers of a more ergodic zone.  

Teaching math with a poem

Sarah Glaz is an algebraist (University of Connecticut) who uses poetry to teach mathematics. At her web page, scroll down to "Recent Articles" to see titles and links to three such papers.   One of the articles is "The Enigmatic Number e: A History in Verse and its Uses in the Mathematics Classroom" -- and it contains an annotated version of the poem whose opening stanzas are found below; it's found in the Digital Library of the Mathematical Association of America (MAA), Loci:  Convergence (April 2010). 

A Prayer of Numbers

     Whether our language is music or mathematics, computer code or cookery --  as we learn to love the language and treat it with good care, we find poetry.  Because mathematics is a concise language, with emphasis on placing the best words in the best order, it often is described by mathematicians and scientists as poetry.  Alternatively, and more accessible to most readers than poetic mathematics, we find verses by poets who include the objects and terminology of mathematics in their lines.

     One of my favorite poems of numbers is the portrait "Number Man," by Carl Sandburg (1878-1967),  found in The Complete Poems of Carl Sandburg (Harcourt, 2003).  This poem also appears in Strange Attractors:  Poems of Love and Mathematics (A K Peters, 2008) -- a varied collection of math-related poems edited by Sarah Glaz and me.

     Number Man     by Carl Sandburg

          (for the ghost of Johann Sebastian Bach)

     He was born to wonder about numbers.

It all starts with counting . . .

     Sometimes our focus on what is important -- in life, in love  . . . as in mathematics --  starts with counting.   This process is artfully expressed below in "Tally" by Romanian poet Lucian Blaga (1922-1985).

      Tally     by Lucien Blaga

       I tally in the ancient way.
       I count like the shepherd
       how many white. how many black
       --days, all year round.

       I count the steps, of the beautiful one,
       to the threshold of the door.
       I count how many startsthere are
       in the nest of the Mother Hen.

       However many, the lot--I count,
       smoke and illusions,
       the whole day--count, count
       roads and missed ways.

       I count the stones on which
       she crosses the ford, that beauty
       and all the sins for which
       hell will surely burn me.

Blaga's poem was translated from the Romanian by Brenda Walker and Stelian Apostolescu and is included in the anthology, Strange Attractors:  Poems of Love and Mathematics (AKPeters/CRC Press, 2008), edited by Sarah Glaz and JoAnne Growney.

Fondness for numbers . . .

     Today I am looking back to a posting on 23 April 2011 that includes the first stanza of one of my favorite mathy poems; here is a copy-and-paste of a part of that day's entry.
      A poem that offers affection for mathematics is "Numbers," by Mary Cornish, found as Poem 8 at Poetry 180 (a one-a-day collection of poems for secondary students) as well as at The Poetry Foundation. Cornish's poem begins with this stanza:

     I like the generosity of numbers.
     The way, for example,
     they are willing to count
     anything or anyone:
     two pickles, one door to the room,
     eight dancers dressed as swans.   

Black History Month -- celebrate Haynes and Hughes

Living on the border of Washington DC I am exposed to items of local history for our nation's capital.  One such item involves the "discovery" of Langston Hughes (1902-1967) by poet Vachel Lindsay (1879 - 1931) at the Marriott Wardman Park Hotel, a leading conference hotel in the city.   A second story is a mathematical one.  Martha Euphnemia Lofton Haynes (1890-1980), a fourth-generation Washingtonian, was the first black woman to earn a PhD in mathematics -- conferred in 1943 by Catholic University. 

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."  ? ? ?

Giving thanks for poems

     As Thanksgiving approaches I am thankful not only for many blessings but also for the numbers I use to count them -- eight grandchildren, four children, two parents, one sister, one brother, an uncountable number of friends.  And I am thankful for poetry.  Here is one of my favorite math-related poems.

How to Find the Longest Distance Between Two Points   
  
                                                     by James Kirkup (England, 1919 - 2009)

From eye to object no straight line is drawn,
Though love's quick pole directly kisses pole.
The luckless aeronaut feels earth and moon
Curve endlessly below, above the soul
His thought imagines, engineers in space.

Imagine new numbers

     As a child I wrote poems but abandoned the craft until many years later when I was a math professor; at that later time some of my poems related to ideas pertinent to my classroom.  For Number Theory classes "A Mathematician's Nightmare" gave a story to the unsolved Collatz conjecture; in Abstract Algebra "My Dance Is Mathematics" gave the mathematical history a human component.  
     My editor-colleague (Strange Attractors), Sarah Glaz, also has used poems for teaching --  for example, "The enigmatic number e."  And Marion Cohen brings many poems of her own and others into her college seminar course, "Truth & Beauty: Mathematics in Literature."  Add a west-coaster to these east-coast poet-teachers -- this time a California-based contributor: teacher, poet, and blogger (Math Mama Writes) Sue VanHattum.  VanHattum (or "Math Mama") is a community college math teacher interested in all levels of math learning.  Some of her own poems and selections from other mathy poets are available at the Wikispace, MathPoetry, that she started and maintains. Here is the poet's recent revision of a poem from that site, a poem about the invention (or discovery?) of imaginary numbers.

Imaginary Numbers Do the Trick      by Sue VanHattum