A student writes poetry for a math class . . .

A recent fun experience for me has been correspondence with Melanie Simms, a poet and math student at Pennsylvania's Bloomsburg University, where I taught for a bunch of years.  Melanie recently completed the course "Mathematical Thinking" -- a course that I helped to develop during my years at BU and one for which I wrote a textbook (Mathematics in Daily Life:  Making Decisions and Solving Problems, McGraw-Hill, 1986).   The course was developed to offer general quantitative skills for students majoring in fields (such as English or Art)  that do not have a specific mathematics requirement.  Melanie's instructor for the course, Paul Loomis, is a singer and songwriter and, with him as first reader, Melanie composed a mathematical poem involving course material.  She has shared the poem with me and has given me permission to post it here.

     The Mathematics of Chance      by Melanie Simms

     The gods of chance
     Have left me skewed
     My distribution, variable!
     With ranges far, and ranges wide
     My navigation's terrible! 

Generalized Pythagorean Theorem--a visual poem?

While thinking about my December 13 posting featuring work by Richard Kostelanetz -- visual poetry with numbers -- I was browsing a fascinating book by Ivan Moscovich, The Puzzle Universe:  A History of Mathematics in 315 Puzzles (Firefly Books, 2015) and came to the following diagram.  I offer it as a visual poem. 

In addition to the squares, what other areas constructed on the sides of a right triangle may be correctly summed to give a third area of the same shape?

Visual poems with numbers

     I have a good friend who does not care for the sorts of poetry that are written today.  When I asked what he likes he cited "When I Was One-and-Twenty" by A E Housman (1859-1936) and the sonnet "Ozymandias" by Percy Bysshe Shelley (1792-1822).   My own preferences in poems, on the other hand, are less certain.  I like to explore, to discover what new things may be said within new forms and constraints.  The following selection, "Notes on Numbers" by Richard Kostelanetz, introduces some of the ideas that this artist/writer/critic explores in his visual poetry -- with numbers -- examples of which are available through links offered at the end of this posting.

Notes on Numbers      by Richard Kostelanetz  

Alphamath - poetry built on 4, 8

Since the late 1960s Toronto poet Victor Coleman has been energetically committed to innovated poetic practices.  A fine introduction to this poet is offered by Alex Porco in this linked review of Coleman's recent book, ivH: An Alphamath Serial (Book Thug, 2010).
          

          ivH: An Alphamath Serial is a book-length poem composed in the tradition 

of such precursors as Pythagoras, who taught that Number was the essence of all things; 

Plato, who argued that geometry was the foundation of all knowledge; 

Colorful mathematics for your smartphone

     "Bhaskara II (1114-1185) was an Indian mathematician and astronomer. He composed the Siddhanta Siromani, a treatise in four parts -- Lilavati (basics), Bijaganita (algebra), Grahaganita (planetary motion) and Goladhyaya (spheres)."
     This quotation comes from an early page of a new (2015) graphic e-book entitled The Illustrated Lilavati -- the text is based on a 1816 John Taylor translation, edited and illustrated for lilboox by Somdip Datta and available for download on smartphones and other devices.  Lilavati (named for the daughter of Bhaskara) was written in 1150 and was a standard textbook for arithmetic in India for many years.
     This e-book contains 25 illustrated problems (and solutions); here is the first:

This blog (then and now) and Pascal

     When I began this blog in 2010, I imagined up to 100 postings -- I saw it as a way to share math-related poetry that I had written and gathered during my years of teaching.  Now, as I prepare my 748th post, I am thinking about how I can organize my posts to make them findable and useful to the reader who visits and browses herein.

One thing that I have recently done is to update the blog's searchability -- 
in the right column you will find a search box.  

If you enter a term like "math" into the box, the search finds most of the posts in the entire blog and is thus not very helpful -- but you might try the term "triangle" and you would find about 20 relevant posts; one of them (from October 13, 2010) has the title "Varieties of triangles -- by Guillevic" and is the most-visited entry herein.  If you are, like me, someone who looks for math publicity and opportunities for girls, you may choose to enter "girl" in the search box.  This search, too, will lead to about 20 postings. 

Which hat? (from Slovenia)

     For a long time I have highly valued the work of Eastern European poets -- including Wislawa Szymborska, Miroslav Holub, Nichita Stanescu, Nina Cassian -- and have been pleased to find mathematical imagery in their work.  Early in November I had the privilege of attending a reading at the Goethe-Institut Washington that featured Slovenian poet Aleš Šteger -- born in 1973, winner of many awards, and described as the most translated Slovenian author of his generation.  A fun event -- from which I give you one of his slightly-mathematical offerings.

     Hat     by   Aleš Šteger (trans. Brian Henry)

     Who lives under the hat?
     Under the hat, which are three?
     Three hats. 

Are we speaking of "mathematics" or "poetry"?

     This week started with the excitement of an email message from Evelyn Lamb with a link to her Scientific American blog where she created a fun-to-take online poetry-math quiz based on an idea of mine (first published in 1992):

Can you tell the difference between mathematics and poetry?

Here’s a link to a SCIENTIFIC AMERICAN quiz to help you decide?

And a couple of centuries ago there was William Wordsworth -- who also contemplated both poetry and mathematics:

               On poetry and geometric truth
               and their high privilege of lasting life,
               From all internal injury exempt,
               I mused; upon these chiefly:  and at length,
               My senses yielding to the sultry air,
               Sleep seized me, and I passed into a dream.

William Wordsworth (1770-1850)

The Prelude, Book 5

Sustainability needs the arts AND mathematics . . .

The following poem is by Erica Jolly -- an Australian poet and retired teacher who is working hard to have the arts and the sciences integrated in Australian schools curricula.  “For too long, since the 1950s, we have witnessed serious losses across disciplines as science and mathematics have been deliberately separated from the arts and humanities,” Ms Jolly says.

"What has sustainability got to do with mathematics?"    by Erica Jolly

An exclamation attacking interdisciplinary themes in the national curriculum 

by Christopher Pyne on Q & A, 28 October 2013.

Does he not know or care
humankind must measure? 

Thanksgiving, 2015

Thinking toward Thanksgiving Day tomorrow, I am grateful for  --

 in addition to my children and grandchildren who will gather --

 all of the mathematic and poetic voices that help me see our world.
 Happy Thanksgiving wishes for all who read here!

Quoting Isaac Newton . . . . a "found" poem

     I do not know what
     I may appear to the world;
     but to myself I seem to have been
     only like a boy playing on the seashore,
     and diverting myself now and then
     finding a smoother pebble
     or a prettier shell than ordinary,
     whilst the great ocean of truth
     lay all undiscovered before me.

   -Isaac Newton, philosopher and mathematician (1642-1727)

Axiom: A Mathematics of Poetry

Today in a Facebook posting by Susanne Pumpluen

 I learned of Discov-her, an online journal 

featuring stories about women in Science. 

* * *

     The following poetry offering is by Richard Smyth who has written a parody of an introduction to the mathematics of logic (specifically Laws of Form by G Spencer Brown*, Julian Press, 1972).  Smyth founded Anabiosis Press which offers the poetry journal Albatross and which has now evolved into Anabiosis Online.  
     I invite you to enjoy this play of words and ideas:

AXIOM: A MATHEMATICS OF POETRY     by Richard Smyth

It shall be taken as given the idea of infinition. The idea of infinition stands in direct opposition to the idea of definition.

Definition
     Infinition is the act of making indefinite or unclear. That is to say, while some uses of language attempt to clarify, others attempt to obfuscate.

Construction
     Make a poem.  

Encouragement from fathers, a second view

     Despite the importance of fathers' encouragement (as noted in my post on 13 November), some women oppose their fathers' views.  Recently I have been enjoying Rachel Swaby's Headstrong: 52 Women Who Changed Science and the World  (Broadway Books, 2015) and yesterday my reading focused on her bios of Maria Agnesi (1718-1799) and Ada Lovelace (1815-1852) and the roles their fathers played in their lives.  Agnesi was a child prodigy who wished to be a nun but followed her father's wish that she research in mathematics until his death, when she was thirty-four; she devoted the rest of her life to serving the poor.  The education of Ada Lovelace was directed by her mother who did not see her father, the poet Lord Byron, as a solid foundation.  
     Poetic expression by a daughter somewhat resistant to her father's wishes comes from our youngest-ever US Poet Laureate Rita Dove in her poem, "Flash Cards": 

Encouragement from fathers

     It was my observation as a professor in a mostly-male mathematics department that the men who joined me in supporting opportunities for women were fathers of daughters.  They had come to see the world from a new perspective -- and saw that it needed changing.  Somewhat along these lines was a recent Washington POST article that told of recent research findings about socially responsible behavior from CEO's with daughters.
      With these thoughts in mind I started counting words . . . wanting to form a poem:

Limericks for Hedy Lamarr

     When seeking to draft a poem quickly, it is useful to have some sort of pattern to follow -- a pattern helping to dictate word choice.  This morning, upon discovering Google's online celebration of the 101st birthday of inventor and actress Hedy Lamarr, I have wanted to join the commemoration with a poem.  A verse pattern rather often used by hasty math writers is the limerick (see links below) -- and I have today constructed this pair of limericks to praise Lamarr.

     May a beautiful actress present
     Skills beyond stage and screen content?
          Yes!  Hedy Lamarr
          Excelled as a star,
     And had also talent to invent!  

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

Artificial Intelligence in the Library . . .

     Libraries are wonderful places and library book sales are temptations impossible to resist -- and so, during a recent trip to Boston and exploration of the historic public library buildings on Boylston Street, I purchased a copy of Living Proof  (Florida International University Press, 1985) by Edmund Skellings (1932-2012).  Born in Boston and a poet laureate of Florida, Skellings was a pioneer in the application of computers to the arts and humanities.  The word "proof" in his title was enough to make me pick up the book and I have relished the opportunity to turn up memories of a long ago graduate course in AI while reading this poem:

Artificial Intelligence     by Edmund Skellings

Euclid rolled over in his bones
When Newell & Simon instructed
Their machine to look for new proof
For bisecting the ordinary triangle.   

Mathematics and Poetry ARE Similar

        A recent email request sent me looking for a one-page article / quiz I had published in the American Mathematical Monthly in 1992 -- a list of 17 statements (quotations) each with a word missing.   The missing words are either "mathematics" or "poetry" (or a related word).  My claim is that, without using the author's name as a clue, it is difficult to decide which of these arts is intended.  I offer here the first four of the statements and suggest you reflect on missing words and then, if you wish, follow this link to a file with the entire list --   including also the author of each quote and (afterward) a list of the missing words.

_____  is the art of uniting pleasure with truth.   (Mathematics/Poetry)

To think the thinkable -- that is the ____'s aim.   (mathematician/poet)     

All _____ [is] putting the infinite within the finite.   (mathematics/poetry) 

The moving power of _____ invention is not reasoning 

                                                    but imagination.     (Mathematical/Poetic) 

The magic of mathematics (in art)

     Australian teacher and  poet Erica Jolly is convinced that breaking down the barriers that make silos of sciences and humanities subjects will promote better education systems and improve job prospects for students.  She brings mathematics into this engaging poem found in Holding Patterns, an online book of physics and engineering poems, part of the "Science Made Marvelous" project.

Sculpture at Questacon (Australia National Science and Technology Center)      

                                                                                by Erica Jolly

     It looks like magic --
     children are turning
     a great stone sphere
     this way and that
     smoothly, easily.  

JMM Seattle, 1-7-16 -- Poetry+Math+Art

 Read your mathy poems in Seattle!

An invitation to participate -- in January!  Read on!

 ANNOUNCING Poetry + Art + Math

 January 7, 2016, Thursday, 5:30 pm–7:00 pm.

Room 608, Washington State Convention Center, Seattle 

     At the Joint Mathematics Meetings (JMM) organized by Gizem Karaali, Pomona College; 

Lawrence M. Lesser, University of Texas at El Paso; and Douglas Norton, Villanova University. 

Celebrating waves of light . . .

     On October 8, Scotland's celebration of National Poetry Day had the theme "Light."  An online collection of themed poems suitable for children is available here.  From my Romanian friend, Doru Radu, who attended that celebration, I received poem-cards from the event. One of the cards contained a poem by filmmaker and poet Margaret Tait (1918-1999). I include that poem with its accompanying image below.  

Use a phone App to find mathy poems

A day late, Happy Birthday, E. E. Cummings 

(b 14 October 1894, d 3 September 1962).

     One of my favorite poetry sites is PoetryFoundation.org -- publisher of POETRY Magazine and supplier of a wonderful phone app (also entitled POETRY).  The app offers access to an enormous data-base of poems, sorted into categories that may be accessed using a SPIN feature, activated by touch.  Spinning the upper layer of categories can lead to "Humor" or "Joy" or "Insecurity" or  . . ..  Spinning the lower layer of categories can lead to "& Life" or  "& Nature" or . . . . When my spin picked the match of "Humor" and "& Arts and Sciences" I found a list of 263 poems.  One was Lewis Carroll's "Jabberwocky."  I also found the tiny poem "Nothing"  by Ken Mikolowski that plays with meaning as mathematicians also love to do. 

Daughter and Father - a warm geometry . . .

     Kate Stange is a mathematician -- from the Canadian province of Ontario and now at the University of Colorado -- whose father, Ken Stange, is a visual artist and poet. I met them on the internet via our combined interests in the intersections of poetry and mathematics. Lots of years ago, Kate gathered an online anthology of mathy poems. One of her recent online ventures is the development of WIN -- Women in Number Theory.  Below I offer one of Ken Stange's poems, taken from his collection Advice to Travellers (Penumbra, 1994).

Don't Mistake Your Mirror for a Window on the World     by Ken Stange

A reflection is both a thought about the world and the image we see in the mirror. -- Hippokrites

Consider your daughter's first smile.   
.    

Toward Infinity . . .

     During summer teaching opportunities a dozen or more years ago in Deva, Romania I met Doru Radu who taught English there -- and our mutual love of poetry led us to collaborate on English translations of work by Romanian poets George Bacovia and Ileana Malancioiu.  Now Doru is in Poland and he is translating Polish poetry into Romanian.  One of his favorite poets is Ewa Lipska -- a poet I have met via Poetry International.  Below is her poem "Newton's Orange:  Infinity" -- found at Poetry International together with the original Polish poem.
     As I have noted before, "infinity" is a term whose varied uses fascinate me.  Sometimes I wonder how much of my "mathematical" understanding of the concept I might some day incorporate into a poem.

     Newton's Orange:  Infinity     by  Ewa Lipska   

A mathematician's favorite poet

     A summertime gift book that I have much enjoyed reading is Love & Math: The Heart of Hidden Reality by Edward Frenkel (Basic Books, 2013).  I admire the way Frenkel's memoir braids mathematics together with the other threads of his life.  Including poetry.  Like me, he chooses E E Cummings as one of his favorite poets.  And he used lines from Cummings' 1931 poem "the surely" as an epigram for a 2007 book that summarized his work.
     Below I include the entire text of Cummings' poem, with Frenkel's epigraph highlighted in bold face.

the surely     

Cued
motif smites truly to Beautifully
retire through its english

the Forwardflung backwardSpinning hoop returns fasterishly

A subtraction problem

Let's solve this subtraction problem:

                    Women do the job
            minus   the recognition.    
                           ____________________________

      The "found poem" above is from a headline for an article by Petula Dvorak in the Washington Post on 21 August 2015.  Dvorak's full headline was a bit longer, "Women do the job minus the training and recognition."  (Indeed Dvorak's article portrays the military as an even more difficult environment for women than the STEM fields.)
       Also found in the Post (this past weekend) an enthusiastic review by Marcia Bartusiak of Eileen Pollack's The Only Woman In the Room:  Why Science Is Still a Boys' Club.  Another problem to solve!!!

C K Williams -- Three Mile Island

A poet whose work I have long enjoyed, C K Williams  (1936-1915), died a few days ago.  (You may find a generous sample of his poems online -- for example at PoetryFoundation.org and Poets.org.)  Williams is a poet whose writing does not tend toward mathematics but his very fine poem "Tar" (about the Three Mile Island nuclear plant crisis of 1979, a year when I lived in Pennsylvania not far away) has a few numbers.  I present below the first stanza of  "Tar" and, beneath it, a link to the rest of the poem.

from   Tar        by C. K. Williams

The first morning of Three Mile Island: those first disquieting, 
       uncertain, mystifying hours.    

Choosing what words mean . . .

     Nineteenth century writer and mathematician Lewis Carroll (1832-1898) gave his character, Humpty Dumpty, these words:  "When I use a word, it means just what I choose it to mean -- neither more nor less."  And so it is in mathematics -- where, for example, the term "rational" (used in the poem"The Disposition of Art," shown below) has a precise meaning that differs from its typical conversational usage.
     The photo below shows computer-generated art by Silver Spring artist Allen Hirsh -- and, beside it, a framed version of the poem mentioned above.  Our work was exhibited together at last summer's BRIDGES and MAA conferences.  A clearer presentation of Hirsh's art -- "An Outgrabed Mome Rath" -- is available here.  My poem is presented below, beneath the photo.  

Words of Ada Lovelace

These poetic words of Ada Lovelace (1815-1852) -- concerning translation of mathematical principles into practical forms -- I found here:

Those who view mathematical science,
not merely as a vast body
of abstract and immutable truths,
whose intrinsic beauty, symmetry and logical completeness,
when regarded in their connexion together as a whole,
entitle them to a prominent place 
in the interest of all profound and logical minds,  

Shaping sentences with Fibonacci numbers . . .

Counting words . . ..  

     1                One
     1               person
     2               with courage
     3               makes a majority.               Andrew Jackson (updated)

Counting syllables . . .

     1               Life
     1               is
     2               painting
     3               a picture
     5               not doing a sum.                    Oliver Wendell Holmes, Jr.

Songs of mathematics . . .

     Larry Lesser is a songwriter who uses lyrics for teaching as well as entertainment.  A varied sample of his creations for doing this are presented in his article "Mathematical lyrics;  noteworthy endeavours in education" found in the "Poetry and Mathematics / Special Issue" of the Journal of Mathematics and the Arts, March-June 2014).
     One of the article's enchanting items is a song for children -- "Circle Song" -- which Lesser has written to the familiar tune of "Twinkle, Twinkle, Little Star"; this lyric offers a way to remember critical formulas for a circle.

Circle Song     by Lawrence Mark Lesser

Take your finger 'round the jar:
Circumf'rence equals 2πr!  

It starts with counting . . .

Mathematical imagery is one of the many features I enjoy in the work of Canadian environmental scientist and poet Madhur Anand.  Here is a sample from her new collection (A New Index for Predicting Catastrophes).
 

Background:  In an experiment designed to test the truth of a given statement 

(often called the null hypothesis), a Type I error occurs if the experiment results in a true hypothesis 
being rejected (a "false positive") and a Type II error occurs if a false hypothesis is accepted. 

Type One Error     by Madhur Anand

I avoid news, talk to strangers, walk around the block
a thousand times and toss nickels for random samples.
I still get a few false positives.  I'm fine.  It's good. 

Mathematical Modeling

My friend and colleague, University of Connecticut mathematician Sarah Glaz, is an accomplished poet and is active in coordinating math-poetry activities -- via her website, the annual BRIDGES Conference, the anthology Strange Attractors: Poems of Love and Mathematics . . . .  Here is one of her mathy poems -- this one a pantoum, first published in London Grip.

Mathematical Modelling     by Sarah Glaz

Mathematical modelling may be viewed
As an organizing principle
That enables us to handle
A vast array of information      

The answer is NO

This past weekend I have much enjoyed reading Mathematics:  a novel  by Jacques Roubaud  (Dalkey Archive Press, reprint 2010, translated from the French by Ian Monk); Roubaud is a mathematician, poet, and member of the OULIPO.  And here is a found poem from Chapter 1:
.
          A
          question
          posed to a
          lively colleague:

          do you tell your
          dancing partners
          that you practice
          mathematics?

For me, like so many of us -- females especially -- revelation of a connection to mathematics leads to an awkward moment, an impediment to a possible relationship.  And so we say things like "I am at the university" or "I am doing some writing" or . . .

Hate Math -- 21 Reasons (NOT) . . .

Two four-letter words that I want NEVER to be used TOGETHER are hate and math.  A lively contradiction to my wish is provided by the following piece by slam poet Shappy Seasholtz.

(For details on the World Poetry Slam to be held in Washington DC on Oct. 7-10, 

scroll down to the bottom of this posting.)

21 Reasons Why I Hate Math     by Shappy Seasholtz

1 - It's my worst subject.
2 - I failed Algebra in high school.
3 - When I retook Algebra in high school during the final exam the principal announced that the space shuttle had just blown up.
4 - The space shuttle probably blew up because of a mathematical error.