Folk music -- counting syllables

Learn about and support Women in Mathematics.  

One place to do that is here. 

Using 4x4 and 2x2 syllable-squares, I emphasize the counting that lies behind folk music in the following selection from "Some Walls" (lyrics by Mary Ann Kennedy, Pamela Rose, Randy Sharp -- but line breaks are mine), recorded by Peter, Paul, and Mary:

          Some walls

          Some walls are made
          of stone.  Sometimes
          we build our own.
          Some walls can stand 

Stars and men revolve in a cycle . . .

In a book-discussion group in which I participate, we are reading some of the short fiction of Jorge Luis Borges (1899-1986) and that reading has provoked me to dive again into my copy of his Selected Poems (Ed. Alexander Coleman, Penguin, 1999).  Here is one of Borges' poems that uses terminology from mathematics:

The Cyclical Night     by Jorge Luis Borges
                                             tr. Alistair Reid (1926-2014)
          to Sylvina Bullrich

 They knew it, the fervent pupils of Pythagoras:
 That stars and men revolve in a cycle,
 That fateful atoms will bring back the vital
 Gold Aphrodite, Thebans, and agoras. 

Include Arts in STEM -- and have STEAM !

Welcome to this blog where we support STEAM !

Visit YouTube for

 math-student, performance-poet Harry Baker's 

"A love poem for lonely prime numbers"

A bit more about Harry Baker can be found in this May 23, 2014 posting. 
In May 2015 visit Takoma Park Community Center Galleries for a STEAM exhibit organized by visual artist and poetry-lover Shanthi Chandrasekar.

Balancing Opposites -- Tagore's Epigrams

Many important mathematical ideas occur as pairs of opposites:
         -2 and +2 (additive inverses), 5 and 1/5 (multiplicative inverses),  
         bounded and unbounded, rational and irrational, 
         convergent and divergent, finite and infinite
Some other familiar mathematical notions occur often in contrasting pairs but are not fully opposites:
         horizontal and vertical, positive and negative, 
         open and closed, perpendicular and parallel

Recently I have returned to reading work by Rabindranath Tagore (1861-1931; Bengal, India;  winner of the 1913 Nobel Prize in Literature) and I enjoy reflecting on contrasts posed by this reflective poet in a series of "Epigrams":

Epigrams      by Rabindranath Tagore

I will close my door to shut out all possible errors.
"But how am I to enter in?" cried Truth.  

Lines of breathless length

Brief reflections on definitions of LINE . . .

          Breathless length     by JoAnne Growney

          A LINE, said Euclid, lies evenly
          with the points on itself --
          that is, it’s straight –-
          and Euclid did (as do my friends)
          named points as its two ends.

          The LINE of modern geometry
          escapes these limits
          and stretches to infinity.
          Just as unbounded lines
          of poetry.

A poem for your pocket

Years ago, when "Poem in Your Pocket Day" (April 30) was first celebrated, we did not have cellphones to carry poems with us easily.  Here is a tiny but memorable poem for you to carry with you tomorrow -- on your phone or in your pocket -- a poem to open and read, again and again.

     Addition     by Langston Hughes (1902-1967)

     7 x 7 + love =
     An amount
     Infinitely above:
     7 x 7 − love.

Hughes' poem "Addition" is found in Strange Attractors: Poems of Love and Mathematics (A K Peters, 2008) and was first posted in this blog, along with other poems linked to Black History Month on February 20, 2011.

Geometry of baseball

Many poems are written of baseball; a few of them involve mathematics --  see the posting for April 9, 2010 for math-related baseball poems by Marianne Moore (1877-1972) and Jerry Wemple; see the posting for September 18, 2011 for one by Jonathan Holden.
     Today I feature the opening stanza from a baseball poem by Pennsylvania poet, Le Hinton.

from   Our Ballpark    by Le Hinton

       This is the place where my father educated us:
       an open-air school of tutelage and transformation.
       This is where we first learned
       to count to three, then later to calculate the angle
       of a line drive bouncing off the left field wall.
       We studied the geometry and appreciated the ballet
       of third to second to first, a triple play.
              . . .

Earth Day -- April 22, 2015

Consider today the thoughtful words of this sonnet by Edna St. Vincent Millay (1892-1950):

     Read history: so learn your place in Time
     And go to sleep: all this was done before;
     We do it better, fouling every shore;
     We disinfect, we do not probe, the crime.
     Our engines plunge into the seas, they climb
     Above our atmosphere: we grow not more
     Profound as we approach the ocean's floor;
     Our flight is lofty, it is not sublime.
     Yet long ago this Earth by struggling men
     Was scuffed, was scraped by mouths that bubbled mud;
     And will be so again, and yet again;
     Until we trace our poison to its bud
     And root, and there uproot it: until then,
     Earth will be warmed each winter by man's blood.

These lines are found on my shelf in Collected Sonnets (Revised and Expanded Edition) by Edna St. Vincent Millay (Harper & Row, 1988).  AND, recall the arithmetic of a sonnet:  14 lines (or breaths) and 5 iambs (or heartbeats) per line. 

April celebrates Math and Poetry

     April is National Poetry Month and Mathematics Awareness Month. Yesterday I was able to attend several of the popular and crowded events at the National Math Festival (Here's a link to "A Field Guide to Math on the National Mall" where you can see photos of items pointed out to yesterday's visitors.) and tomorrow evening (April 20) I will be part of a reading that features poetry of math and science at the DC Science Cafe (at Busboys & Poets, 5th &K Streets, 6:30 PM).  
     For tomorrow evening's reading I intend to wear my red-peppers earrings; one of the poems I will offer will be "A Taste of Mathematics" (from my collection Red Has No Reason and posted in its entirety at this link). Here is the poem's final stanza:

            She said, "Hot peppers
            are like mathematics —
            with strong flavor
            that takes over
            what they enter." 
 

Remembering Abraham Lincoln

Today -- April 14, 2015 -- marks the 150th birthday of the assassination of President Abraham Lincoln (1809 - 1865) and April 15 is the date on which he died. Lincoln loved poetry and trained his reasoning with Euclid's geometry.  Here is a brief sample of his own poetry (found -- along with other samples -- at PoetryFoundation.org).

       Abraham Lincoln     by Abraham Lincoln

       Abraham Lincoln
       his hand and pen
       he will be good but
       god knows When

From my copy of Walt Whitman's Leaves of Grass (Signet Classics, 1955), from the section "Memories of Lincoln," I have copied these well-known and thoughtful (and non-mathematical) lines:

Time is no straight line . . .

Swedish poet and Nobel Laureate Tomas Transtromer (1931-2015) died last month. At his website I found this poem that reflects on the arithmetic and geometry of life:

Reply to a Letter    by Tomas Transtromer

In the bottom drawer I find a letter which arrived for the first time twenty- six years ago. A letter written in panic, which continues to breathe when it arrives for the second time.

A house has five windows; through four of them daylight shines clear and still. The fifth window faces a dark sky, thunder and storm. I stand by the fifth window. The letter.

Man Ray's "Human Equations"

     Art lovers in Washington, DC have the opportunity (until 5/10/15) to see, on exhibit at The Phillips Collection, "Man Ray -- Human Equations: A Journey from Mathematics to Shakespeare." I visited the exhibit on February 19 on the occasion of a poetry reading by Rae Armantrout -- she presented work of hers that she felt captured the spirit of Man Ray's work.  (Bucknell poet Karl Patten, whom I had as a poetry teacher years ago, insisted that "Every Thing Connects" and, indeed, this is the title of one of the poems in Patten's collection The Impossible Reaches.  Both of these phrases that became titles for Patten seem also to describe Man Ray's and Armantrout's work:  they have taken seemingly disparate objects and reached across seemingly impossible gaps to relate them.  As often happens in mathematics.)   

Mathematics and poetry -- are the same ! ! !

Last week the Art Works Blog posted an interview with mathematician, poet, and translator, Enriqueta Carrington.  You will want to follow the link and read the whole thing.  Here is a paragraph:

quoting Enriqueta Carrington:

Mathematics and poetry are the same thing,
 or one is a translation of the other.

Well, perhaps that is an overstatement; 
but both math and poetry are about beautiful patterns, 
about creating, gazing at, and sharing them, 

and about appreciating those created by others.

It is not necessary to be a great mathematician or a great poet 
to enjoy this beauty, as I can tell you from my own experience.

Several years ago, at a time near the beginning of this poetry-math blog, in the posting for April 8, 2010, is a pantoum by Carrington.  And here is another of hers, this time a Fibonacci poem -- whose lines increase in word-count that matches the first eight Fibonacci numbers:  1, 1, 2, 3, 5, 8, 13, 21.

April is . . . a time for math and poetry . . .

     Once upon a time
     I counted to the tenth prime
     and found a word to rhyme.

Tomorrow is not only April Fool's Day -- it also begins "National Poetry Month" and "National Mathematics Awareness Month."  I hope you will scroll down through this blog for math-poetry intersections -- and that you will like what you find and return for more.

(If you are near Washington, DC, consider a visit to MathFest on Saturday, April 18.)

Science Verse

Recently coincidence has brought to me two collections of poems about  science -- first, the 2014 issue of The Nassau Review, a gift from editor and poet Christina M. Rau. The second collection is a "used" children's book, Science Verse (by John Scieszka and Lane Smith) found at the wonderful Kensington Row Bookshop (scroll down their webpage to find out about their monthly poetry readings).  I include below two rhyming stanzas from Science Verse, followed two selections from The Nassau Review 2014 -- a poem by Diane Giardi which is a parody (or isomorphic image) of a nursery rhyme and a poem  by Katherine Hauswirth which may or may not consider infinity.

Hey Diddle Diddle

Hey diddle diddle, what kind of riddle

Is this nature of light?

Sometimes it's a wave,

Other times a particle . . .

But which answer will be marked right?

The problem of time

Californian Brenda Hillman is a poet whose work I like and admire.  In "Time Problem" she weaves prime numbers into a deft description of the dilemma of not enough time.

       Time Problem     by Brenda Hillman

       The problem
       of time.      Of there not being 
       enough of it.

       My girl came to the study
       and said Help me;
       I told her I had a time problem 
       which meant:
       I would die for you but I don’t have ten minutes. 
       Numbers hung in the math book 
       like motel coathangers. The Lean 
       Cuisine was burning

March 23 -- Emmy Noether's birthday

Today, March 23, 2015, Google celebrates the 133rd birthday of mathematician Emmy Noether.  In support of the celebration here is a link to "My Dance is Mathematics," a poem I wrote to honor this pioneering mathematician.  I hope that celebrations of Noether and other math-women will help to create a world in which these lines from my poem about her are no longer true:

          If a woman's dance is mathematics,
          she dances alone.

March 21 -- World Poetry Day

Yesterday poetry was celebrated around the world -- the Guardian reported the event with mention of Cafés around the world that offered a cup of coffee in exchange for a poem.  The occasion caused me to turn to one of my favorite international collections, The Horse Has Six Legs (Graywolf, 2010) -- an anthology of Serbian poetry translated and edited by poet Charles Simic.  On 29 April 2011 I posted "Forgetful Number" by Yugoslav poet Vasko Popa (1922-1991) -- and here is another of Popa's poems.  This one is part of a cycle of poems about "the little box" and it involves recursion.

       Last News about the Little Box     by Vasko Popa

       The little box that contains the world
       Fell in love with herself
       And conceived
       Still another little box.   

Multiplied by Rain

     There are many mathematical terms that are used in daily life -- not only multiplied and divided and negative but also closure and identity and field and commute -- and it is fun for me, a math person, to see poets use such terms in new and thoughtful ways.
     Poet Jane Hirschfield weaves words into fine tapestries that give us new dimensions of meaning.  The Table of Contents of her new book, The Beauty (Knopf, 2015), is scattered with mathematical terms -- we find zero, plus, subtraction,  and the final title, "Like Two Negative Numbers Multiplied by Rain."  This poem first appeared in Poetry (2012) and is available at the Poetry Foundation website along with more than thirty additional Hirshfield poems.

Like Two Negative Numbers Multiplied by Rain   by Jane Hirshfield

     Lie down, you are horizontal.
     Stand up, you are not. 

A Russian toast (with mathematics)

Several weeks ago I had the pleasure of visiting the Washington Museum of Poetry and Music -- a collection in Rockville, MD gathered and maintained in the home of Uli Zislin who has lived in the US since 1996. (Among other treasures, the musuem has recordings of poets Anna Akhmatova, Boris Pasternak, Osip Mandelstam, and Anastasia Tsvetaeva.)    At the time of my visit, Zislin presented me with one of his own poems that includes a bit of mathematics.  The original Russian version of Zislin's poem is at the bottom of this post.  Prior to that I offer a translation into English by Arlington poet, teacher, and award-winning Russian translator, Katherine Young.  Thank you, Katherine.

        A Pedagogical Toast     by Uli Zislin

                 translated by Katherine E. Young

       Friends and colleagues, pedagogues!
       We’re not philosophers, not gods.
       We’re simply people, soldiers of God,
       destined to suffer and to love.  

Three Greguerías

From Portugal, from Francisco -- who emailed me the gift of these lines:

Three Greguerías   by Rámon Gómez de la Serna (1888-1963)
                                             translated by Francisco J Craveiro de Carvalho and JoAnne

Holding her hoop the little girl goes to school and to the playground,
to play with the circle and its tangent.

Zeros are the eggs from which all the other numbers are hatched.

Numbers are the best acrobats in the world: they stand on top of each other without falling down.

Ramón Gómez de la Serna is considered the father of the greguería -- a one-liner in which he combined gentle humor with a metaphor. 

Similar, self-similar -- fractals, a poem

      In geometry two objects are said to be similar if they have the same shape --- which happens if their angles are the same size and occur in the same sequence. For example, any pair of triangles with angles 30, 60, and 90 degrees are similar; also, the lengths of pairs of corresponding sides of these triangles have the same ratio.
      A term used in the terminology of fractals is self-similarity: a self-similar object has exactly (or approximately) the same shape as a part of itself.  A variety of objects in the real world, such as ferns and coastlines, are approximately self-similar: parts of them show the same statistical properties at many scales. At the end of this post are a couple of diagrams that illustrate how a fractal may be developed.  But first, experience the generative beauty of self-similarity via a poem by Maryland poet Greg McBride.  Mathematician Benoit Mandelbrot (1924-2010), quoted in McBride's epigraph, often is nicknamed "the father of fractals."

The mathematician, she . . . .

     Tomorrow, March 8, is the International Day of the Woman -- and I celebrate the day with mixed feelings.  YES, there are many women I want to celebrate. BUT WHY are they not celebrated daily, equally with men? And a more specific concern, WHY, when the word "mathematician" is used, is the person assumed to be a man. (There is, on the other hand, a nice non-gendered neutrality in numbers -- as in this first stanza of "Numbers," by Mary Cornish, found below.)
      In this posting I celebrate Grace Brewster Murray Hopper (1906-1992) -- a mathematician with a doctorate from Yale, a navy admiral, a computer scientist who led in the development of COBOL, an early (c.1959) programming language.  A person I had the good fortune to meet when she visited Bloomsburg University in 1984 to receive an honorary Doctor of Science Degree.  Hopper was imaginative and articulate; here is some poetry found in her words.

                               If it's a 
                               good idea,
                               do it.  

Celebrate Pi -- write in Pilish

On 3/14/15 many of us will celebrate  π - day; for those who like to gaze on the digits of  π,  one hundred thousand of them are available here.  In honor of this upcoming special day I have composed a small stanza in Pilish (the language whose word-lengths follow the digits of  π ). 

3.  1  4  

Get a list,

 1  5  

I shout,

   9  2  6  5  3  5

Women in Maths -- on Facebook

     Recently I prepared an item for Rachel Levy's Grandma Got STEM blog that told a bit about my granddaughters who like math.  My preparation for that posting led me to focus on my wish to have math be a fun place for girls to hang out -- a place for lots of girls:  feminine girls, sporty girls, popular girls, silly girls (as well as geek girls).  Mathematics has mostly been a lonely place for females -- my first  girl-friend who was also a math person was a colleague whom I met in my 40s (see my poem for Toni, "Girl-Talk").   I want mathematics to be a welcoming place for my granddaughters. A place with friends.
     Related to this concern, wonderful news came in my email box recently from Susanne Pumpluen (video) at the University of Nottingham.  She has started a Women in Maths page on Facebook .  There one can find bios, videos, news links and FRIENDS.  Visit.  LIKE. Offer your comments and support. 

Reflections on Logic

Miroslav Holub (1923-1998), Czech poet and immunologist who excelled in both endeavors, is one of my favorite poets.  He combines scientific exactitude with empathy and absurdity.  Here is a sample:

       Brief Reflections on Logic     by Miroslav Holub

                                     translated by Stuart Friebert and Dana Habova

       The big problem is everything has
           its own logic.  Everything you can
           think of, whatever falls on your head.
           Somebody will always add the logic.
           In your head or on it.  

Found poetry - words of Dirac

The epigraph for Richard Bready's "Times of Sand" (a stanza of which I posted a few days ago on 21 February) is a quote from British physicist Paul Dirac (1902-1984, founder of quantum theory).  This quote reminded me how often we find poetry within well-written prose -- and I have gone to WikiQuotes and found more poetic words from Dirac:

       If you are 
       receptive 
       and humble, 

       mathematics 
       will lead you 
       by the hand. 

How many grains of sand?

     Sand beaches are places I love to walk.  Next to oceans and soft underfoot. 

Below I post a stanza from Richard Bready's "Times of Sand"  --

 a long poem that explores many of the numbers related to sand. 

     Contemplating grains of sand turns my thoughts to the pair of terms "finite" and "infinite."  One of my friends, university-educated, versed in literature and philosophy, offered "all of the grains of sand" as an example of an infinite set.   As we talked further, he proposed "the stars in the universe" as a second example. This guy, like many, equates "infinite" with "too large to count."  And then there is me; long ago in college I encountered a definition of "infinite" that went something like this:  A set is infinite if there is a one-to-one correspondence between the members of the given set  or one of its proper subsets with the set {1, 2, 3, . . ..} of counting numbers.

The numbers say it all . . .

The title of my posting today, "The numbers say it all" comes from the final line of "After Leviticus," by Detroit poet Philip Levine.  Levine (1928-2015) died this past Saturday.  Often termed "a working class poet," this fine writer won many awards for his work. 

     After Leviticus     by Philip Levine

     The seventeen metal huts across the way
     from the great factory house seventeen
     separate families. Because the slag heaps
     burn all day and all night it’s never dark,
     so as you pick your way home at 2 A.M.
     on a Saturday morning near the end

America, land of equals (perhaps)

Preparing to celebrate (after Valentine's Day) Presidents' Day, remembering particularly George Washington (b February 22, 1732) and Abraham Lincoln (b February 12,1809), I offer a few lines by Walt Whitman (1819-1892).

       America     by Walt Whitman

       Centre of equal daughters, equal sons,
       All, all alike endear'd, grown, ungrown, young or old,
       Strong, ample, fair, enduring, capable, rich,
       Perennial with the Earth, with Freedom, Law and Love,
       A grand, sane, towering, seated Mother,
       Chair'd in the adamant of Time.        [1888]

This poem is found here in the Walt Whitman Archive.

Surreal parabola, Mobius strip

     When a math term appears in a poem, will its usage make sense to a mathematician? Some mathematical folks are critical of poetic use of math words because precision may be lost to "poetic license." Others feel a pleasing tension between the mathness of a term and the stretched or layered meanings suggested by the poem. With these thoughts in mind, consider these two mathematically-titled poems "Mobius Strip" and "Parabola" by Robert Desnos (France, 1900-1945), translated by Amy Levin and selected from "A sampling of French surrealist poetry."

     Mobius Strip     by Robert Desnos (trans. Amy Levin)

     The track I'm running on
     Won't be the same when I turn back
     It's useless to follow it straight
     I'll return to another place

Celebrate Black History, Valentine's Day

February is Black History Month and on the 14th we celebrate love with Valentine's Day.  To find in this blog a variety of mathy poems on these topics (and many others) use the SEARCH box found at the top of the right-hand column of this blog.

Moebius Strip

Following a lead from Francisco, I found (here) this tiny poem by Michael Hessel-Mial:

       moebius strip

       a belt of clouds
       twist it, latch it
       twisted

       which way will it rain?

To find more poems that feature the Mobius strip  locate the SEARCH box at the top of the this blog's right-hand column -- and enter the term mobius.  Alternatively, the search box also works for a myriad of other topics.

Is winter half over?

     Today (February 2) those of us with roots in Pennsylvania join enthusiasts from everywhere as we  look to mythical groundhog Punxsutawney Phil for a forecast concerning prolonged winter or early spring.  This morning Phil's forecast was bleak but not unexpected: we will have six more weeks of winter.
     This news that our winter is only half over has led me to a poem (found in the illustrated anthology Talking to the Sun, edited by Kenneth Koch and Kate Farrell, published in 1985 by the Metropolitan Museum of Art):

      Another Sarah     by Anne Porter (1911-2011)
                 for Christopher Smart
       When winter was half over
       God sent three angels to the apple-tree
       Who said to her
       "Be glad, you little rack
       Of empty sticks,
       Because you have been chosen.

       In May you will become
       A wave of living sweetness
       A nation of white petals
       A dynasty of apples."

Another winter poem by Porter with a bit of mathematics is included in this post for 25 November 2012.

Twined Arcs, Defying Euclid

     The English language has adopted into current usage many terms from other languages.  French terms like coup de grace and haut monde have for many years been found in English dictionaries.  Recently, computer terms such as bite and captcha and google have achieved widespread use.  In addition, those of us who are fluent in the language of mathematics find that its terms sometimes offer a concise best way to describe a non-mathematical phenomenon.
     Mathematician-poet Sarah Glaz weaves mathematical terms into her poem, "Departures in May" -- a poem that uses the language of geometry to vivify the presence of loss, death and other dark forces.

       Departures in May     by Sarah Glaz

       Big things crush, inside the brain,
       like plaster of Paris on stone;
       a taste of splintered metal;
       terra-cotta hardness of heart's desire.
       Statues motionless
       at railroad depots,
       proclaim imitation as life.

Poetry-math images; Expectation

     Search engines are very useful in my search for mathy poets and poems.  Recently I have noticed that a link to images  has been offered prior to the verbal links when I have queried Google using "mathematics poetry."  Some of the visuals are quotations, some are book-covers, some are poems.  When you have time, explore and enjoy! 

     Finding more via Google that I expected connected me with an old poem.  Here, unearthed recently, is "Expectation"  -- some lines from the 1980s, when I was beginning to write poems.
 

Expectation            

Don't let mathematics                Don't let mathematics
teach you to expect two              teach you to expect one
to be more than one.                 to be the sum of its parts.

Girls who like math

Often I think about the interactions of girls with mathematics and recently I have been feeling delighted that all of my school-age granddaughters like math. In fact, Harvey Mudd mathematician Rachel Levy has included views from these girls (and from me) here in her blog, "Grandma Got STEM."

T h i s
g i r l
d o e s
m a t h

S u m
f o r
f u n
 

s o
 i f 

1

To read selections from several of my favorite poems about girls-in-math (including Sharon Olds' poem "The One Girl at the Boys' Party" and Kyoko Mori's poem, "Barbie Says Math is Hard") follow this link to a posting made on 10 June 2010.  Another math-girls post was back on  26 December 2010.  Or use the SEARCH box (upper right) to find poems related to your own choice of topics.

Probability and Coincidence

     On page 26 of my copy of the latest New Yorker is a poem by Lia Purpura entitled "Probability."  In her brief poem Purpura renders with poetic power the astonishment each of us feels when meeting a long-ago classmate at an out-of-town super market or some other unexpected event.  Take time to follow the link and read this poem.
     Recently several friends have shared with me their amazement at unexpected coincidences and I have been tempted to illustrate -- perhaps with the birthday paradox --  how likely to happen unexpected events may be.

  With more than 23 persons in a room the chances are more than 50-50

 that two of them will share a birthday (same day, maybe different years).

Many websites offer explanation of this "birthday paradox" -- here is one.

To add two and two

     Today I call attention again (as in my post for 6 January, 2015) to the extensive  Science-Poetry collection edited by Norman Hugh Redington and Karen Rae Keck. Mathy (rather than bawdy) limericks are featured in the collection; for example, this one by an unknown author:

       There was an old man who said, "Do
       Tell me how I'm to add two and two?
            I'm not very sure
            That it doesn't make four --
       But I fear that is almost too few."  

Opposites, Balance

     Recently, and perhaps always, opposites have interested me.  For example, the complementary and sometimes  conflicting nuggets of advice contained in "Pinch a penny, waste a pound" and "It is best to prepare for the days of necessity."   And in  "Kindness effects more than severity" and "Spare the rod, spoil the child."   Maybe what I like best is the challenge of synthesizing opposite truths.
     Mathematics contains many pairs of entities that are, each in some different sense, opposites:

2 and -2      2 and 1/2

horizontal and vertical   differentiation and integration

And there are some arbitrary subdivisions that often are treated as if they are disconnected opposites:

pure vs. applied (creating mathematics vs. solving problems)

teaching and learning, creating vs. teaching, arts and sciences

In an ideal world, opposites exist with "Balance" -- which is the title of the following lovely and contemplative poem by Adam Zagajewski :

The Geometry of Winter, with Eagles

A poetry-listening opportunity in the Washington, DC area:

Poet Martin Dickinson will read from his new collection, My Concept of Time, 
on Sunday, January 11 at Arlington's Iota Cafe. 

AND -- if you 're San Antonio on January 11, 2015 you'll want to attend  

the 5:30 PM poetry-with-math reading (details here) 

at the Gonzales Convention Center, sponsored by JHM.

 

From My Concept of Time, here's a poem of the geometry of our winter world.

          Fourteen Eagles, Winter     by Martin Dickinson
                                  for Phyllis

          We spot them, first almost imaginary
          thin pencil lines or scratches on our glasses.

          The earth's disk flattens out
          where this pale land becomes the bay, 

from MIT Science-Poetry -- The Cal-Dif-Fluk Saga

     Recently I have enjoyed browsing a voluminous online 19th century Science-Poetry collection (Watchers of the Moon) hosted by MIT, gathered and edited by Norman Hugh Redington and Karen Rae Keck. Google led me to the site in a search for " poetry of calculus" and I found there found a fascinating item by J. M. Child:  The Cal-Dif-Fluk Saga (from The Monist: A Quarterly Magazine Devoted to the Philosophy of Science -- Open Court Publishing, 1917) and described as "a  pseudo-epic about the invention of calculus."  
     Child was a translator (from Latin into English) of the works of Isaac Barrow and Gottfried Leibniz and his poem presents the names of well-known mathematicians in clever scrambles:  Isa-Tonu is Newton, Zin-Bli is Leibniz, Isa-Roba is Barrow, Gen-Tan-Agg stands for Barrow's Gen-eral method of Tan-gents and of Agg-regates while Shun-Fluk and Cal-Dof refer to the methods of Newton and Leibniz.  One may, with a fair amount of work, enjoy this dramatization of warriors and weapons -- battles that were part of the development of calculus.  Here from the middle of the Saga (from Section 6 (of 17)), is a sample of Child's lines illustrating the struggles that calculus required.

The Role of Zero

     In mathematics, as in poetry, multiple meanings are common and create power for the language.   For example, the number 0 is an idempotent element, an additive identity, a multiplicative annihilator -- and it also plays the role of something that may represent nothing.
     In Dorothea Tanning's poem below -- I found it at poets.org -- zero takes on still another of its roles, that of place-holder -- as in the numbers 101 and 5000, for example.

       Zero     by Dorothea Tanning (1910-2012)

       Now that legal tender has
                    lost its tenderness,
       and its very legality
               is so often in question.
       it may be time to consider
       the zero--
                    long rows of them.
            empty, black circles in clumps
                              of three, 

2014 (and prior) -- titles, dates of posts

Scroll down to find titles and dates of posts in 2014.  At the bottom are links to lists of posts through 2013 and 2012 and 2011 -- and all the way back to March 2010 when this blog was begun.   This link leads to a PDF file that lists searchable topics and names of poets and mathematicians presented herein. 

Dec 30  Be someone TO COUNT ON in 2015
Dec 28  A Fractal Poem
Dec 25  A thousand Christmas trees
Dec 24  The gift of a poem
Dec 20  The Girl Who Loved Triangles 

Be someone TO COUNT ON in 2015

By any means of counting, 

the number of incarcerated persons in the United States 

is TOO LARGE

and the proportion of prisoners with BLACK SKIN

is TOO GREAT
  and there is TOO MUCH VIOLENCE and DEATH in our prisons.

RESOLVE to stop the violence (RSVP)  in America's prisons!  Work for fair sentencing and Equal Justice!  Let your resolutions for the New Year 2015 be inspired by a poem;  the one below is from Poetry, 2009, found at poetryfoundation.org  -- and you may find more at Split This Rock.

To the voice of the retired warden of Huntsville Prison
(Texas death chamber)                 by Averill Curdy

Until wolf-light I will count my sheep,
       Adumbrated, uncomedic, as they are.
       One is perdu, two, qualm, three
                           Is sprawl, four, too late,

A Fractal Poem

    A fractal is an object that displays self-similarity -- roughly, this means that the parts have the same shape as the whole -- as in the following diagram which shows successive stages in the development of the "box fractal" (from Wolfram MathWorld). 

   
Michigan poet Jack Ridl and I share an alma mater (Pennsylvania's Westminster College) and we recently connected when I found mathematical ideas in the poems in his collection Broken Symmetry  (Wayne State University Press, 2006); from that collection, here is "Fractals" -- offering us a poetic version of self-similar structure:

       Fractals    by Jack Ridl

       On this autumn afternoon, the light  
       falls across the last sentence in a letter,
       just before the last movement of Brahms’ 
       Fourth Symphony, a recording made more 
       than 20 years ago, the time when we were  
       looking for a house to rehabilitate, maybe  

A thousand Christmas trees

My email poem-a-day today from www.poets.org is "Christmas Trees" by Robert Frost (1874-1963); this 1916 poem includes some calculations and reflections based on the line:

       “A thousand trees would come to thirty dollars.”

Frost's poem has provoked me to thoughts of inflation and conservation; for the full poem, follow the link given with the title above.  And, if your time permits, go back to previous "Christmas" postings in this blog at these links:  23 December 2013,  24 December 2012,  21 December 2012,  22 December 2011, and 2 September 2010.

The gift of a poem

     In this holiday season of giving, sometimes the gifts are poems -- and sometimes mathy poems.  A few days ago, "Zero" by Robert Creeley (1926-2005) arrived in an email from Francisco José Craveiro de Carvalho, a Portuguese mathematician who loves poetry and has translated many math-related poems into his native language -- a seeker and finder of such poems who shares them with me.  (See also 23 October 2010 and 17 September 2013.)  At this time of giving and receiving, enjoy playing with these thoughts of zero as nothing or something.

          Zero     by Robert Creeley

                              for Mark Peters

          Not just nothing,
          Not there's no answer,
          Not it's nowhere or
          Nothing to show for it -- 

The Girl Who Loved Triangles

     I found this poem by Michigan poet Jackie Bartley when I was browsing old issues of albatross (edited by Richard Smyth) and she has give me permission to post it here.  Like Guillevic (see, for example, this earlier post), Bartley has found personalities in geometric figures.

To the Girl Who Loved Triangles     by Jackie Bartley

          Triangulation:  Technique for establishing the distance between two points
                                      using a triangle with at least one side of known length.

One girl in a friend's preschool class
loves the triangle.  Tanya's favorite shape,
the children call it.  Simple, three sided, at least

one slope inherent, slip-slide down
in the playground of mind.  Tension and its
release.  Sure balance, solid as the pyramids.  The 

Fractals -- poems and photos

     Marc Frantz and Annalisa Crannell have written about mathematics and art (Viewpoints:  Mathematical Perspectives and Fractal Geometry in Art: Princeton University Press, 2011) and now Frantz (who is both a mathematician and an artist, a painter) has collaborated with a poet -- Robin Walthery Allen --  to develop a collection entitled Dance of Eye and Mind (not yet published).  I am honored to present a poem-photo pair from this exquisite collection.

     What is in us that must reach the top,
     that longs to look down upon the world as if a god?
     Don’t we know that in this infinite space
     the same rocks at the seashore know the secret of each peak?

Our curve is a parabola

Found in the essay, "Intellect" (1841) --  these words by 19th century American philosopher and poet Ralph Waldo Emerson (1803-1882):

     When we are young, we spend much time and pains
     in filling our note-books with all definitions
     of Religion, Love, Poetry, Politics, Art, 
     in the hope that, in the course of a few years,
     we shall have condensed into our encyclopaedia
     the net value of all the theories
     at which the world has yet arrived.
   
     But year after year our tables get no
     completeness, and at last we discover
     that our curve is a parabola,
     whose arcs will never meet.    

A mathy Haiku

Found at the froth magazine website, this Haiku by Christopher Daniel Wallbank.

Mathematics

I, mathematics,
One plus root five over 2.
My soul is golden. 

 Note:  In mathematics, two quantities p and q (p>q) are in the golden ratio 

if the ratio p/q is equal to the ratio (p+q)/q.  The value of the golden ratio -- 

often represented by the Greek letter phi (φ) -- is 1.618...  or (1+√5)/2.

Here is a link to another mathy froth poem, this one "Division" by Ryley-Sue.

A scientist writes of scientists

     Wilkes-Barre poet Richard Aston is many-faceted -- a teacher, an engineer, a textbook author, a technical writer.  And Aston writes of those whose passion he admires-- in his latest collection, Valley Voices (Foothills Publishing, 2012) we meet laborers, many of them miners from the Wyoming Valley where he makes his home.  Aston also writes of scientists and mathematicians -- and he has given permission for me to offer below his poems that feature Marie Curie, Isaac Newton, and Galileo Galilei.  With the mind of a scientist and the rhythms of poetry, Aston brings to us clear visions of these past lives.

Scientist     by Richard Aston

It took more than a figure, face, skin, and hair
for me to become Marie Curie,
wife of simple, smiling, selective, Pierre
who could recognize — because he was one — my genius.

Poet as mathematician

     Lillian Morrison (1917-2014) was a NYC poet and librarian whose work I first met in the poetry-with-math anthology, Against Infinity.  Here is one of her poems from that collection.

       Poet as Mathematician    by Lillian Morrison

       Having perceived the connexions, he seeks
       the proof, the clean revelation in its

       simplest form, never doubting that somewhere
       waiting in the chaos, is the unique

       elegance, the precise, airy structure,
       defined, swift-lined, and indestructible.

Morrison's insightful poem disappoints me in one important way:  her mathematician-poet is "he."  Another Morrison poem, "The Locus of a Point," may be found in my posting for 15 September 2014.

Geometry of Love

     A couple of weeks ago my "Google Alert" linked me to a posting of a science poem concerning "the geometry of love."  The posting -- at The Finch and Pea -- is a poem that is both elegant and precise (and one that has been included in the anthology, Strange Attractors:  Poems of Love and Mathematics, that Sarah Glaz and I collected and edited several years ago).  Here it is:

The Definition of Love     by Andrew Marvell (England, 1621-1678)

My love is of a birth as rare
As ‘tis for object strange and high;
It was begotten by Despair
Upon Impossibility.  

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.