Loving the difference quotient ... and more ...

     From Philadelphia poet-mathematician, Marion Cohen, a new collection  -- Closer to Dying (Word Tech, 2016).  When I received the book a few days ago and began to read I did, of course, seek out mathy poems.  Two of these are included below. In this first poem Cohen has some fun with the terms and symbols of introductory calculus.  In the second, she tells of an encounter of the sort that happens to many mathematicians  -- meeting someone who supposes that mathematicians do what calculators do. (This link leads to a collection of mathy poems (including ones by Cohen) at talkingwriting,com.)

Primes and a paradox

       Canadian poet Alice Major has loved and admired science and mathematics since girlhood and this background brings to her mathy poems both charm and amazement -- qualities that those of us who seriously studied mathematics easily lack.  At the recent BRIDGES conference I had a chance to hang out with Alice for a while and to purchase her latest collection, Standard Candles  (University of Alberta Press, 2015). Such fun to experience her views of infinities and paradoxes, of triangles and symmetries and formulas and ... .  
     Alice has given me permission to post two of her poems here; read on and enjoy "The god of prime numbers" and "Zeno's paradox."  

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.

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.

Found: Elementary Calculus

Here is a poem by Saskatchewan poet Karen Solie.

       Found     by Karen Solie

       Elementary Calculus

                From    Elementary Calculus  A. Keith and W. J. Donaldson.
                          Glasgow:  Gibson, 1960.

       Speed (like distance)
       is a magnitude and has no
       direction; velocity (like displacement)

       has magnitude and direction.  

Graffiti Calculus

     In my dreams I am an artist -- a cartoonist, perhaps, or a graffiti artist -- so skilled with lines and curves and so clever that my art gives pleasure AND delivers a punch.
     And so I am gratefully into the math-art connections provoked by a new book by Mary-Sherman Willis -- aptly titled Graffiti Calculus (CW Books, 2013).  I first met Willis in December, at Cafe Muse (where I will read next Monday, Feb 3 with Stephanie Strickland) and it was my pleasure also to hear her read again from that collection at the Joint Mathematics Meetings.  These poems by Willis give us, in sixty poetic chapters, the story of a mother seeking her son by following his graffiti tags through the city.  Here is a sample, sections 5 and 6: 

Love mathematics!

In the stanzas below, I have some fun with math terminology.  Hope you'll enjoy it too.

       Love!        by JoAnne Growney

       Love algebra!  Through variable numbers
       of factored afternoons and prime evenings,
       party in and out of your circle of associates,
       identify your identity,  meet your inverse.  

Calculus (and calyculus)

For lots of years I have subscribed to A.Word.A.Day, founded by Anu Garg, and on 3 June 2013  -- offered in the category of "words that appear to be misspellings" -- the word that appeared in my email was calyculus (kuh-LIK-yuh-luhs), a noun designating a cup-shaped structure.  From this, of course, my thoughts turned to calculus and to poems on that subject.  Below I offer "UR-CALCULUS" by Jonathan Holden.  This Kansan poet has said that that his physicist father would write equations while sitting at the dining room table -- and "UR-CALCULUS" considers mathematics from a boy-riding-in-the-back-seat-of-a-car point of view.  

     UR-CALCULUS     by Jonathan Holden

               The child is the father of the man. 
                        -- W. W. Wordsworth

     Back then, "Calculus"
     was a scary college word,
     and yet we studied it
     from the back seat, we studied  
     the rates at which
     the roadside trees went striding 

Related rates -- in fiction and poetry

     During the Memorial Day weekend I had the opportunity to read Black Rice (WSI, 2013), a novella by Burmese-American poet, artist, activist -- and friend -- Kyi May Kaung; I strongly recommend this book to you.  (My 5-star review of Kaung's book is available here at amazon.com -- follow the link and scroll down.)
     Here, in this blog, we mention topics if and only if they relate to both mathematics and poetry.  Read on and you will see!
     Midway through Black Rice, the narrator (speaking of an overflowing stream) reveals a negative attitude toward mathematics -- a strategy often used to provoke readers to experience empathy:  "Ahhh, just like me."  Here are the Burmese soldier's words:

Limericks and a Cardioid -- for Valentine's Day

     Oh, math-lover most divine,

     for you this mathy Valentine --

          found when I looked
          in a calculus book --  
     a cardioid is the heart-sign. 

Summing thin slices

This poem by recent (2008-2010) poet laureate Kay Ryan at first made me think of calculus, of integration, summing all the thin slices to find the area under a curve.  And then the poem moved me on. 

For Hazlett -- an Exquisite Corpse poem

At the recent BRIDGES Math-Art Conference at Towson University, I led a Sunday afternoon Poetry-with-Mathematics Workshop.  One of our writing topics was women mathematicians and, using material from a richly varied website of biographies of math-women, supported by Agnes Scott College, we workshop participants read a bio of Olive Clio Hazlett (1890-1974) and each wrote sentences of the form "This woman . . . " which I have assembled and and slightly edited into the following poem.

Remembering Sophia Kovalevsky

With Reason: A Portrait     by JoAnne Growney   (June 2012)

        Sophia Kovalevsky *    (1850-1891)

Because she was Russian  . . .
Because she had abundant curly hair . . .
Because she loved mathematics . . .
Because she was born in the 19th century . . .
Because lecture notes for calculus papered  her nursery walls . . .
Because her parents forbade her to leave home . . .
Because a woman could not travel abroad from Russia 
                    without her father or a husband . . .
Because she found a kind man to marry . . .
Because ideas came to her in torrents . . .
Because she married a man she did not love . . .

Sophie Germain dressed as a man to study math

One of the fine sources for biographies and other topics in the history of mathematics is MacTutor History of Mathematics archive, hosted by the University of St Andrews in Scotland.  Poet Brian McCabe cites this archive for historical information he used as background for his poems starring mathematicians -- found in his collection, Zero (Polygon, 2009).  Here is McCabe's poem for the outstanding French mathematician, Sophie Germain (1776-1831). 

Sum of moments

Here is a 3x3 square poem -- inspired by a recently-found margin-note I made in Differential and Integral Calculus (by Ross R Middlemiss) when it was my text for an introductory calculus course at Westminster College all those years ago:

          The sum of

          the moments

          is zero.

While the pages of text near the note go on with discussions and diagrams of slices and sums and limits -- they introduce the centroid, the moment of inertia, and the radius of gyration, and are importantly informative -- it is the margin-note that has today delighted me.  I wonder if the girl who wrote it saw it as I do today. I like the mystery.

Is Math for Women?

At a River Poets reading at the public library in Bloomsburg, Pennsylvania on December 1, 2011, Carol Ann Heckman surprised me with her poem, "The Calculus Road Not Taken," presented below.  Not only is she a fine poet, but Carol Ann is curious about mathematics.  As a college student she was turned away by negative feedback from a math professor. But now she is reassessing her situation and ready to tackle calculus. Here she has fun with her calculus-deprived situation in lively verse:

The Calculus Road Not Taken   by Carol Ann Heckman  

               for JoAnne Growney

If I had only conquered
calculus
this wouldn't have
happened--the flood,
the earthquake, the
two hurricanes
in succession

Lieber's INFINITY -- poetic prose

It has surprised me to discover that some of my best-remembered learning took place at the hands of teachers I did not particularly like.  One of these was a professor who introduced me, via outside reading assignments, to books by Lillian R. Lieber (1886-1986).  Her free-verse-style lines in Infinity:  Beyond the Beyond the Beyond gave me insights into the calculus I had recently completed as well as the set theory of my current course. (Lieber wrote not just as a mathematician but also as a human being, as a wonderfully informed and openly opinionated person.  For this, too, I treasure her work.)

Teaching Numbers

Californian Gary Soto  writes for both children and adults and much of his work suits both groups.  Here from A Fire in My Hands (Houghton Mifflin, 2006) is "Teaching Numbers":

Ghosts of Departed Quantities

     Years ago in calculus class I excitedly learned that an infinite number of terms may have a finite sum.  Manipulation of infinities seems somewhat routine to me now but my early ideas of calculus enlarged me a thousand-fold.  Algebra was a language, geometry was a world-view, and calculus was a big idea.  Like any big idea, even though it had been hundreds of years in formation, it met with resistance.  In 1764 Bishop George Berkeley attacked the logical foundations of the calculus that Isaac Newton had unified.  Here, from the online mathematics magazine plus,  is a description of the attack.

Excitement in mathematics classrooms

Poems from three women illustrate a range of emotional content in the mathematics classroom: Rita Dove's "Geometry" captures the excitement of a new mathematical discovery.  Sue VanHattum's "Desire in a Math Class" tells of undercurrents of emotion beneath the surface in a formal classroom setting.  Marion Deutsche Cohen's untitled poem [I stand up there and dance] offers a glimpse of what may go on in a teacher's mind as she performs for her class.