A sonnet for W.R.Hamilton

      Irish mathematician William Rowan Hamilton (1805-1865) was also a poet (see, for example, this sonnet in a prior posting (13 October 2011).  Irish poet and physicist Iggy McGovern has written A Mystic Dream of 4:  A sonnet sequence based on the life of William Rowan Hamilton (Quaternia Press, 2013). 

The collection is prefaced by this quote from Hamilton:

"The quaternion [was] born, 

as a curious offspring of a quaternion of parents, 

say of geometry, algebra, metaphysics, and poetry."

Here is McGovern's opening sonnet.

GEOMETRY     by Iggy McGovern

Once, any pupil could define me best:
"points, lines, angles and figures", could amuse
The table with the Christmas cracker jest
About 'the squaw' on the hypotenuse! 

Visual-mathematical poetry

      The poems that I write and most of the poems that I include in this blog use mathematical patterns to structure their lines and stanzas or mathematical terminology in their content -- but blogger Kaz Maslanka is a mathematical poet who does something different:  his creations involve mathematical operations and symbols as well as words.  For example, the following visual poem -- involving symbols for "equals" and "divided by" -- comes from a recent posting (in his blog, "Mathematical Poetry") of what Maslanka calls an orthogonal space poem.

"Winning" -- a visual poem by Kaz Maslanka in a form related to the formula for the area of a rectangle,  A = lw or, alternatively, w = A/l.  (Double-click on the image to enlarge it.)

During July 29-August 1, 2015, Kaz Maslanka and I both plan to participate 
in the BRIDGES Math-and-the-Arts Conference at the University of Baltimore -- 
sharing our poetry and enjoying the work of others.  
Join us if you can; no registration fee is required for Friday "Family Day" events 
which include a poetry reading.

Imagine a Fractal

California poet Carol Dorf is also a math teacher and is poetry editor of the online journal TalkingWriting.  In the most recent issue of Talking-Writing is this fascinating poem by Brooklyn poet, Nicole Callihan, "How to Imagine a Fractal."  Enjoy Callihan's poetic play with recursion and infinite nesting -- be lulled by the back and forth of forever.

Carol Dorf's work has appeared in this blog:

  Her fan-letter to the author of a math book is here 

and a poem about fear of math is posted here.

How to Imagine a Fractal     by Nicole Callihan 

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?

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.

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.

Dimensions of a soul

In the poem below, Young Smith uses carefully precise terms of Euclidean geometry to create a vivid interior portrait.

     She Considers the Dimensions of Her Soul   by Young Smith

     The shape of her soul is a square.
     She knows this to be the case
     because she often feels its corners
     pressing sharp against the bone
     just under her shoulder blades
     and across the wings of her hips. 

Homage to Euclid

In my preceding post (20 March 2014) Katharine Merow's poem tells of the new geometries 

developed with variations of Euclid's Parallel Postulate.  

Martin Dickinson's poem, on the other hand, tells of richness within Euclid's geometry.

Poet and attorney Martin Dickinson is with the Environmental Law Institute and is a long term activist. The Nora School Poetry Series has scheduled both of us (along with Michele Wolf) to be part of a reading next month on April 24, 2014 .  It is my additional good fortune that conversations with Dickinson have included his sharing with me this mathy poem:

     Homage to Euclid       by Martin Dickinson

     What points are these,
     visible to us, yet revealing something invisible—
     invisible, yet real? 

A poet re-envisions space

University of Pennsylvania professor Robert Ghrist, in his September 19 lecture ("Putting Topology to Work") at the MAA's Carriage House, credited poet John Milton (1608-1674) with the first use of the word space as an abstract entity -- and, Ghrist asserted, by so doing, Milton opened a door to the study of abstract space (known in mathematics as topology).

The following material is a 24 September correction

from my 23 September posting.  For I discovered -- in a thoughtful email from Ghrist --

that the proper citation of "space" was not from line 50 of Book 1 but from line 89 of Book 7.  

(I invite you go to Project Gutenberg for Paradise Lost in its entirety.)

Here, below, I have replaced my original posting of  lines 44-74 of Book 1 

with lines 80 - 97 of Book 7 --  lines taken from my shelf copy of Milton's Paradise Lost,

 the 1968 Signet Classic Edition, edited by Christopher Ricks.

In the selection below and throughout his epic, Milton replaces past visions of hell down-in-the-earth and heaven up-in-the-sky with more complex and abstract configurations.

Geometry of distance

     Some of the poems herein arrive as gifts from friends.  Today's poem came via e-mail from Susan (a Californian whom I have gotten to know when she visits my neighbor, Priscilla).  Susan got it from Larry Robinson who connected me with the poet, Richard Retecki, for permission to post it here.
     As has been said in other contexts, It takes a village . . .    
     Thanks to you all!

     ascension           by Richard Retecki

               for Jonathan Glass

     the geometry
     of distance annoys
     is unfilled

A mathematician, a poet, a woman

When I contacted University of Kansas mathematician Judith Roitman for permission to include her poem "Sixth Cosmogony" in this poetry-math blog she was quick to point out that this is not really a mathy poem. For example, the math term "differentiated" in the first stanza of the poem is not being used in its mathematical sense. However, my motivations for including the poem remain. First, and quite important: this is a poem by a mathematician who is also a woman and a poet. Second, I am interested in mathematicians' reactions to seeing math terms in non-mathematical contexts; are mathematical meanings part of what you think of any time that you hear a math term such as "differentiate" or "factor" or "commute"?

Finding fault with a sphere . . .

     On November 9 I had the pleasure (hosted by Irina Mitrea and Maria Lorenz) of talking ("Thirteen Ways that Math and Poetry Connect") with the Math Club at Temple University and, on November 5, I visited Marion Cohen's "Mathematics in Literature" class at Arcadia University.  THANKS for these good times.

          This
          Fib
          poem
          says THANK-YOU
          to all those students
          from Arcadia and Temple 
          who participated in "math-poetry" with me --
          who held forth with sonnets, pantoums,
          squares, snowballs, and Fibs --
          poetry
          that rests
          on
          math.

      My Temple host, Irina Mitrea, and I share something else besides being women who love mathematics -- the Romanian poet, Nichita Stanescu (1933-83), is a favorite for both of us.  My October 23 posting ("On the Life of Ptolemy") offered one of Sean Cotter's recently published translations of poems by Stanescu and below I include more Stanescu-via-Cotter -- namely, two of the ten sections of "An Argument with Euclid."  These stanzas illustrate Stanescu at his best -- irreverently using mathematical terminology and expressing articulate anger at seen and unseen powers of oppression.

The best of the many

     Here I link to an article by David Alpaugh, "The New Math of Poetry," -- not brand-new, for it bears a date of February, 2010 , but I found it only recently and have been thinking about its description of the seemingly unrestrained quantity of poetry expected to be published on the Internet. What happens to poetry if each of us calls what she writes "poems" and publishes them online, making them as available as the lines penned by a Poet Laureate? 
     Most of what I feel about proliferation of poetry is excitement.  I love the democracy that lets all of us participate in poetry just as we all may run races, perhaps even taking a trophy in our neighborhood's turkey-day mile;  we do not pretend excellence but, simply, it is fun and good for us.  All of us who choose it can enjoy writing poems -- and experimentation with new forms -- and, from time to time, some surprising and splendid work will emerge. 

Universal and Particular -- Szymborska

Like Yves Bonnefoy (21 February 2012 posting), Wislawa Szymborska (who died on 1 February 2012) was born in 1923.  Like him she was concerned with the connections of the universal and the particular.  Here, in "A Large Number,"  she reflects, as she did in "A Contribution to Statistics," on the human meaning that lies behind numbers: 

Found in Flatland

Over the years I have shared with friends and students my copy of Edwin Abbott's Flatland (first published in England in 1884) and, alas, not all of these other readers have matched my level of excitement with the small volume.  Even though the book's Victorian attitudes are mostly at odds with my own views, still the tiny book opened me to possibilities of new ways of seeing. Since observing the Flatlanders stuck in two dimensions from my advantageous three-dimensional position, I have wondered how I can now make the leap from three to four or more dimensions.

Poems of set paradox and spatial dimension

Universal Paradox     by Sandra DeLozier Coleman

     One gigantic set made of all that there is
     Boggles the mind with paradoxes.
     For it is greater than all, but smaller than this —
     The set which consists of the subsets of it.

Art, poetry, and mathematics -- and Rafael Alberti

On September 23 I was privileged to hear Annalisa Crannell, mathematics professor at Lancaster's Franklin and Marshall College, speak on "Math and Art:  the Good, the Bad, and the Pretty."  This informative presentation, sponsored by the Mathematical Association of America (MAA) and pitched toward undergraduates, showed ways that artists use mathematics. 

What is the point? -- consider Euclid

A two-line poem by Chilean poet, Pablo Neruda (1904-73), found in my bilingual edition of Extravagaria, reminded me of the poetic nature of several of the opening expressions of Euclid's geometry.  Both of these follow: