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