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.

The Math Lady Sings

     One of my daily emails results from a Google Alert -- which I have set up to let me know of new web-postings (or old information newly accessed) that contain the terms "mathematics" and "poetry." (Another online delight comes when I Google "mathematics poetry" (or "math poetry") and browse the images that occur at the top of the list that Google offers.  What fun!)
     It is through a Google Alert notification that I learned of the poetry book It Ain't Over Till the Math Lady Sings by Michelle Whitehurst Goosby (Trafford, 2014).  This Math Lady was the subject of an article by Jennifer Calhoun in the Dotham Eagle (Dotham, AL)  -- and Calhoun put me in in touch with the poet who graciously offered permission for me to present one of her poems here.  Goosby is a teacher and the poem poses a number puzzle for readers to solve.

Five Naturals

Consecutively Odd  

by Michelle Whitehurst Goosby

In Praise of Fractals

     Philosopher Emily Grosholz is also a poet -- a poet who often writes of mathematics. Tessellations Publishing has recently (2014) published her collection Proportions of the Heart:  Poems that Play with Mathematics (with illustrations by Robert Fathauer) and she has given me permission to present one of the fine poems from that collection.

In Praise of Fractals     by Emily Grosholz

               Variations on the Introduction to
               The Fractal Geometry of Nature by Benoit Mandelbrot
               (New York: W. H. Freeman and Company, 1983)

Euclid’s geometry cannot describe,
nor Apollonius’, the shape of mountains,
puddles, clouds, peninsulas or trees.
Clouds are never spheres, 

Imaginary Number

Last week (on November 6) I was invited to read some of my poems at the River Poets reading in Bloomsburg, PA (where I lived and taught for a bunch of years).  Among the friends that I had a chance to greet were Susan and Richard Brook -- and, from them, received this mathy poem by Pullitzer-Prize-winning-poet Vijay Seshadri.

Imaginary Number     by Vijay Seshadri

The mountain that remains when the universe is destroyed
is not big and is not small.
Big and small are

comparative categories, and to what
could the mountain that remains when the universe is destroyed
be compared?    

In college she studied mathematics

     In the third paragraph of the Wikipedia bio for Marguerite Duras (1914-1996), we read "At 17, Marguerite went to France, her parents' native country, where she began studying for a degree in mathematics."  I had the opportunity, several weeks ago at AFI Silver, to enjoy a screening of an exquisite restoration of "Hiroshima Mon Amour," a 1959 film for which Duras wrote the screenplay (nominated for an academy award).
    At the website goodreads.com I found this mathy (and poetic) quote that I recognized as from the film:

Composite or Prime?

 Her age 

is 9.
 

Is that 9

composite

or prime?

     I have a wonderful collection of grandchildren and am continually on the lookout for both math and poetry activities to include in the things that they enjoy.  Recently I mail-ordered retired fourth-grade teacher Franny Vergo's collection Mathapalooza:  A Collection of Math Poetry for Primary and Intermediate Students (AuthorHouse, 2013).  Here is a sample from that collection: 

A big voice, Galway Kinnell (1927-2014)

     Last week master poet Galway Kinnell died (NYTimes obituary).  One finds a detailed bio and a baker’s dozen of his best poems at the Poetry Foundation website -- do a search using the poet's name.  Many of Kinnell's poems are about nature -- somewhat in the way that mathematics may be about science  --  that is, he uses the images of nature to speak multiply of complex issues.  Here is a poem about identity that includes several math terms.

     The Gray Heron    by Galway Kinnell (1927-2014)

     It held its head still
     while its body and green
     legs wobbled in wide arcs 

Poetry from the words of Lord Kelvin

Do not imagine that mathematics 

is hard and crabbed, and repulsive 

to common sense. 

It is merely the etherealization

of common sense.

Tomorrow is Halloween

Typing Halloween in this blog's SEARCH Box will lead you to a 2010 posting of "Ghost Stories Written"  -- an algebra-related poem by Charles Simic;  this Poetry Foundation link will lead to a host of other seasonal poems.

Counting into the Future . . .

     Remember that you have only until November 1 to submit a winning "poem of provocation and witness" to the Split This Rock Poetry Contest.  If you don't already,  you will want also to subscribe to Split This Rock's Poem of the Week.  This week's poem ("Past Tense" by Sam Taylor) opens with these numbers:

       In the Great Depression of 2047,
       a time of sorrow rivaled only
       by the Global Unification Wars
       of Spring 2029 to 2033,
       in the Merlona Plague of 2104, 
       in the year of the forest die-off,
       after the atmospheric hue reduction . . . .

From Nude Descending an Empire (University of Pittsburgh Press, 2014).  Apatelodes merlona is a species of moth.

Dimensions of Discovery

Along the one-dimensional straight line
there are points and segments
but no curves or squares.

In the flat plane of two dimensions 

there are points and segments 

and circles and squares.

In the vast space of three dimensions 
there are points and segments 
and squares and spheres.

In a space of four dimensions 

there is more than 

we can imagine.

ABC of statistics

     Songwriter Larry Lesser is a co-organizer (with Gizem Karaali) of a poetry-with-mathematics reading at the Joint Mathematics Meetings in San Antonio next January.  And sometimes Lesser writes poetry.  He has told me that his poem below was in response to an abecedarian poem in a 2006 paper of mine, "Mathematics of Poetry" published in the online journal JOMA -- and available here.

Statistic Acrostic   by Lawrence Mark Lesser and Dennis K. Pearl

     A
     Better
     Confidence:
     Data.
     Expectations
     Fit
     Good.

Martin Gardner collected poems

     Last week the Mathematical Association of America (MAA) had a special program honoring Martin Gardner (1914-2010); tomorrow (October 21) is the 100th anniversary of his birth.   The shelving in the MAA meeting room displayed copies of many of Gardner's approximately one hundred books.  However, none of the books displayed were books of poetry and, indeed, Gardner referred to himself as "an occasional versifier" but not a poet.  Nonetheless he helped to popularize OULIPO techniques in his monthly (1956-81) Scientific American column, "Mathematical Games," and he also was a collector and editor of anthologies, parodies, and annotated versions of familiar poetic works.  Here is a link to his Favorite Poetic Parodies.  And one may find Famous Poems from Bygone Days and The Annotated Casey at the Bat and half a dozen other titles by searching at amazon.com using "martin gardner poetry." 

Poetry Reading 1-11-15 at JMM in San Antonio

You are invited to a poetry reading 
sponsored by the Journal of Humanistic Mathematics

at the 2015 Joint Mathematics Meetings (JMM)

Gonzalez Convention Center   Room 205  San Antonio, Texas
Sunday, January 11, 2015, 5:30 - 7:00 p.m. 

     All poets who write of mathematics and all who are interested in mathematical poetry are invited. Join the gathering to share poems and to enjoy the company of like-minded poetic-math people!  The reading is sponsored by the Journal of Humanistic Mathematics  and will be hosted by Gizem Karaali and Larry Lesser.    
     Although last-minute decisions to participate are possible -- you may simply show up and sign up to read -- we invite and encourage poets to submit poetry (≤ 3 poems, ≤ 5 minutes) and a bio in advance, and, as a result, be listed on our printed program. Inquiries and submissions (by December 1, 2014) may be made to Gizem Karaali (gizem.karaali@pomona.edu).

Taken out of context . . .

Sometimes good lines fit so well into their poems that their individual merits go unrecognized.  And then, taken out of context, they can lead lives of their own.  Here is a start for a collection of such lines.

From Poets.org here are two lines from "Ceriserie" by Joshua Clover:   

       Mathematics: Everyone rolling dice and flinging Fibonacci, going to the opera, counting everything.

       Fire: The number between four and five.

Love Physics

It turns out that one of the disadvantages of a long-term blog with lots of worthy material is that sometimes I lose track of fine work that I want to post.  And sometimes I find it again.  This morning I came across this poem by California conservationist Richard Retecki.

     Love Physics     by Richard Retecki

     equal forces
     oppositely directed
     canceled to zero

     then we tricked you
     exchanging pressure for light 

Can poetry change the climate for frogs?

      Poems affect our spirits as well as our minds. And Split This Rock is looking for poems that protest and witness, world-changing poems.  Go here for information about their Eighth Annual Poetry Contest (with submission deadline November 1, 2014).
     Here in this blog, as I present connections between poetry and mathematics, I provide some poems of protest and advocacy.  I advocate attention to problems of climate change -- to keep our world habitable; I advocate full recognition of women in the sciences -- for a not dissimilar reason.  We must not waste our resources.

Journal of Math in the Arts features Poetry

A special issue of the Journal of Mathematics and the Arts entitled "Poetry and Mathematics" is now available online at this link.  An introduction by guest editor Sarah Glaz is available (for free download) here.   In this opening piece, one of the items that Glaz includes is her own translation of a math-puzzle poem from Bhaskara's (1114-1185) Lilavati that is charming.  I offer it here:
 
       Ten times the square root of a flock
       of geese, seeing the clouds collect,
       flew towards lake Manasa, one-eighth
       took off for the Sthalapadmini forest.
       But unconcerned, three couples frolicked
       in the water amongst a multitude of
       lotus flowers. Please tell, sweet girl,
       how many geese were in the flock.

Clearing the Air with a Poem

     Every poem has a climate -- a collection of emotional tones that overlay and underlay its words. Today -- as the U.N. meets in NY to discuss the future climate of our planet -- I have been looking for mathy poems with a climate of advocacy, verses that let the world know that we must, soon and vigorously, take action to keep our earth habitable.
      One of the things I found is a poem (involving a couple of numbers and mathy words) by Simon Armitage that is printed on material that cleanses the air around it by absorbing pollutants.  A small photo from the website of Sheffield University is shown below -- and I urge you to follow the Sheffield link for the story of the poem and this link to see the full poem more clearly and the story behind it.  Here is Armitage's opening stanza. 

Marching for Climate

     Today I want to call attention to the growing global concern about climate change accentuated by the United Nations Climate Summit that opens September 23. Tomorrow (September 21) I will travel on a 6 AM bus  from Silver Spring to NYC to be part of the People's Climate March.  It is said that more than 500 buses of protesters are heading to New York. 29 marching bands will provide the soundtrack. 26 city blocks are being cordoned off for the march's line-up.   At the same time, more than 2,000 People's Climate events are taking place in over 160 countries around the world—from Hong Kong to Buenos Aires and from New York to San Francisco.

     To have a small carbon footprint I will march tomorrow with only a small sign -- one that wears a 3x3-square reminder that dates back to a 1968 essay, "Tragedy of the Commons,"  by ecologist Garrett Hardin (1915-2003). 

       There  is  no
       place to throw
       that's  away.

WHY is it taking us so long to act to preserve a habitable planet?  Do we not care about the world we are leaving for our grandchildren?

Remembering Lee Lorch

      Lee Lorch was a mathematician known for his social activism on behalf of black Americans as well as for his mathematics. He died in February of this year in Toronto, at age 98.  A life-long communist and a life-long crusader.  Last Thursday I attended a memorial service  (organized by Joe Auslander, a poetry-lover who one day had introduced me to the work of Frank Dux) for Lorch -- sponsored by the Mathematical Association for America and held at the MAA Carriage House in Washington, DC.  Friends and colleagues of Lorch spoke of his positive energy and the ways that he had enriched the lives of students and colleagues, of friends and strangers.  One of the speakers, Linda Braddy, a staff member of the Mathematical Association of America (MAA), did not talk about Lorch but about strategies for opening mathematical doors (as he had done) to new students. 

Hailstone numbers shape a poem

     One of my favorite mathy poets is Halifax mathematician Robert Dawson -- his work is complex and inventive, and fun to puzzle over.  Dawson's webpage at St Mary's University lists his mathematical activity; his poetry and fiction are available in several issues of the Journal of Humanistic Mathematics and in several postings for this blog (15 April 2012,  30 November 2013, 2 March 2014) and in various other locations findable by Google.
      Can a poem be written by following a formula?  Despite the tendency of most of us to say NO to this question we also may admit to the fact that a formula applied to words can lead to arrangements and thoughts not possible for us who write from our own learning and experiences.  How else to be REALLY NEW but to try a new method? Set a chimpanzee at a typewriter or apply a mathematical formula.
     Below we offer Dawson's "Hailstone" and follow it with his explanation of how mathematics shaped the poem from its origin as a "found passage" from the beginning of Dickens' Great Expectations.

Hypertext poetry

     We computer-screen readers all know hypertext; when we read along in Wikipedia or some other online document and come across an underlined term whose font color is light blue -- at such a point we may decide to keep on reading as if we had not noticed the light blue "hyperlink," or we may locate our cursor on that text, click our mouse, and link to a new screen of visual information.
     My first encounter with hypertext poetry was the work of Stephanie Strickland -- in her 1999 love poem, "The Ballad of Sand and Harry Soot," available at this link.  If you, however, are someone who is not yet comfortably familiar with hypertext poetry, I invite you to gain some experience with hyperlinked reading via a prose essay -- reading it first as a traditional essay and then exploring ways that hypertext can vary the experience of reading.

Mathy poems via e-mail

Publishing a blog about poetry and mathematics brings me new connections -- it is not unusual for a day to begin with an email from another poetry-math enthusiast who wants to share a link or a poem. One of these is retired USC biochemist Paul Geiger.  
     Using as raw material a poem by Shel Silverstein, Geiger created a 9x9 syllable-square:

S.C.S. STOUT     by Paul Geiger

       Apologizing and Acknowledging Shel Silverstein's 1974 poem
             "SARAH CYNTHIA SYLVIA STOUT WOULD NOT TAKE THE GARBAGE OUT"

Mathy Poetry from Bridges 2014

     This year's math-arts conference, Bridges 2014, was in Korea.  And a dozen of us who write poetry-with-mathematics -- unable to attend in person -- worked with coordinator Sarah Glaz to offer (on August 16, hosted by Mike Naylor) a virtual reading of work videotaped in advance by the poets and edited into a coherent whole by Steve Stamps. 

     The virtual reading is here on YouTube. 

Grandma Got STEM

     It was my good fortune last weekend to meet the sister-in-law of one of my neighbors, mathematician and Harvey Mudd professor, Rachel Levy.  Levy is also a blogger and her postings in Grandma Got STEM tell of achievements of women in science.
     I have looked for a poem to pair with my mention here of  Grandma Got STEM.  Although the following poem by Tami Haaland (found at the Poetry Foundation website) is not mathematical, it nicely brings to life a relationship between a grandmother and granddaughter -- and we wish for both of them "places to explore beyond the frame."

       Little Girl     by Tami Haaland

       She’s with Grandma in front
       of Grandma’s house, backed
       by a willow tree, gladiola and roses.

       Who did she ever want
       to please? But Grandma
       seems half-pleased and annoyed.

Changing colors, counting syllables

Changing Colors

by JoAnne Growney

Blue

yoyo --

awkwardly

stopping-starting,

rising-plummeting,

seeking self-control. Please,

mother-friend-lover-child, don't

pull string.  Let me collect myself.

I  lift  myself  to  the  treetops,

soar with the golden eagle,

find rest on fleecy clouds.

My orb embraces

everybody --

powerful,

yellow 

sun. 

Poetry in Math Journals

         The Mathematical Intelligencer (publisher of the poem by Gizem Karaali given below) and the Journal of Humanistic Mathematics (an online, open-access journal edited by Mark Huber and Gizem Karaali) are periodicals that include math-related poetry in each issue.  For example, in the most recent issue of JHM, we have these titles:

Articles:
     Joining the mathematician's delirium to the poet's logic'': Mathematical Literature and Literary Mathematics     by Rita Capezzi and Christine Kinsey
     How Do I Love Thee? Let Me Count the Ways for Syllabic Variation in Certain Poetic Forms     by Mike Pinter

Poems:

     Computational Compulsions     by Martin Cohen

     Jeffery's Equation     by Sandra J. Stein

     The Math of Achilles     by Geoffrey A. Landis

And here, from Gizem Karaali, is a poetic view of the process of mathematical discovery:  the blank white page, the muddy flow of thoughts, the clarity that eventually (sometimes) blooms:

My best dream is floating . . .

     Today I want to urge you to visit several sites in addition to my blog.  For example, there is the recent announcement of 2014 Fields Medal (equivalent to a Nobel prize) winners -- the four winners include the first female mathematician (Maryam Mirzakhani) ever to be selected as a Fields Medalist (equivalent to a Nobel Prize) and a mathematician who loves poetry (Manjul Bhargava).    
     With the help of a "Google Alert" I found a YouTube video of Alexandria Marie reading "The Mathematics of Heartbreak" at a Dallas Poetry Slam.  A link in an email from Texas computer scientist,  Dylan Shell, alerted me to these mathematical lyrics (new words for old tunes) in a mathbabe posting by Cathy O'Neil.
     As we have been floating from topic to topic, it may be apt to end with the final stanza of my relevantly titled poem: 

Narrated by a mathematician

Recently translated by Adam Morris, the novel With My Dog-Eyes (Melville House, 2014) by Brazilian writer Hilda Hilst (1930-2004) is narrated by a mathematician-poet. That fact of narration is what first drew me to the book. (See also this July 3 posting.)  And then there is (related in Morris's introduction to the translation) Hilst's sad life, perhaps mirrored in her characters.  These are the opening lines from the novel's narrator:

       The cross on my brow
       The facts of what I was
       Of what I will be:
       I was born a mathematician, a magician
       I was born a poet. 

Squaring the Circle

Reminding us of the ancient unsolvable problem that so many attempted, the July/August 2014 issue of Poetry Magazine contains "Squaring the Circle," a poem by Philip Fried.  Here are the opening lines; please follow the Poetry Magazine link above to enjoy the full poem.

from  Squaring the Circle     by Philip Fried

       It's a little-known fact that God's headgear --
       A magician's collapsible silk top hat,
       When viewed from Earth, from the bottom up
       Is, sub specie aeternitatis,

       A pluperfect halo, both circle and square,
         . . .

    

Two previous posts that also consider the circle-squaring problem include 10 May 2010 and 21 April 2010.

Divided selves, some of them savvy

     For social connections, it is desirable not to be pegged as a member of an outcast group.  And thus a mathematician is likely to have at least two selves -- one who lives in the world of mathematics and another separate social self that negotiates that rest-of-the-world where many fear and shun mathematics. I found a situation somewhat similar when I studied at Hunter College in Manhattan:  I needed a separate self who negotiated the city. The problem-solving farm girl who knew small towns well and big cities slightly seemed better equipped to adapt to city conversations than her fellow students could chat about anything west of the Hudson.  How many hundred miles must you drive to get to Pennsylvania? they wondered.  (The Delaware River boundary of PA is about 75 miles west of the George Washington Bridge.)
     In this vein, I present a poem that focuses on the country vs city divide -- and it involves a square look and a number.

     Green Market, New York   by Julia Spicher Kasdorf

A math prof's lament

The mathematical connection for this poem is the fact that it was inspired by regrets for a missed opportunity in a mathematics class -- an opportunity missed by me and thus by one of my students.  There are so many ways to be wrong!

Lament of a Professor
        at the End of the Spring Semester     by JoAnne Growney

I took an extra step to bridge the gap
between us, blind to your matching backward step.
We've moved in tandem until I'm angry
at you, and at me — I thought you needed
lenience, but reprimands instead
would have changed the direction of our cadence
and given you a chance to lead the dance.

A poem about another of my students, "The Prince of Algebra" is available here.  And this link will take you to the poems in my collection, My Dance is Mathematics (Paper Kite Press, 2006).

Fixing something wrong

          If there's something
          wrong with the third
          act,   it's   really
          in  the  first  act.

This quote from Billy Wilder, Austrian-born writer and film-director (1906-2002), reminds me of a similar observation I have made about my mathematical work -- when a reviewer notes a problem near the end, usually the fix is near the beginning.          And so it goes . . .

Each equation is a playful catch . . .

A mathematician is probably too close to her subject matter to speak playfully about it -- and thus she, even more than others, appreciates a phrase like "each equation is a playful catch, like bees into a jar," offered by Lisa Rosenberg in the poem below.  In "Introduction to Methods of Mathematical Physics," Rosenberg uses a child's anxiety about insects as a way to describe fear of mathematics and offers a smidgen of respect for "those few" who are fearless. 

Introduction to Methods of Mathematical Physics    by Lisa Rosenberg

You must develop a feeling for these symbols
that crawl across a page, for the text overrun

with scorpions.  Like those books about insects
you read as a child, scared to touch the magnified photos,

Poems with "equation" in the title

     One of the ways to explore this blog is to go to the right hand column and find the instruction, SEARCH.
     A few moments ago I did this and entered the word "equation" and found a long list of links, many of the latter ones redundant since they are picking up archive listings of earlier postings.  But the early ones can be fun to explore.  Here are five of  the first six items that the SEARCH BOX produced.  And the first two of these links yield poems with "equation" in the title.  Enjoy!