Symbols shape our thoughts

     In mathematics -- as in spoken languages -- we have learned to use symbols to shape our thoughts.  Pioneering artist Marcel Duchamp (1887-1968) carefully expresses this important idea in terms of chess. 
  
     “The chess pieces are the block alphabet
     which shapes thoughts; and these thoughts, although
     making a visual design on the chess-board,
     express their beauty abstractly, like a poem...

     I have come to the personal conclusion
     that while all artists are not chess players,
     all chess players are artists.”

―Marcel Duchamp

This and other stimulating statements from Duchamp are available here.

During these days of celebration of the life of Muhammad Ali (1942-2016) I have refreshed my memory of his notable quotes (many of which are found here).  Here is one with some numbers:

     A man who views the world 

the same at 50 

     as he did at 20 

has wasted 30 years of his life.

A poem, a contradiction . . .

     One strategy for proving a mathematical theorem is a "proof by contradiction."  In such a proof one begins by supposing the opposite of what is to be proved -- and then reasons logically to obtain a statement that contradicts a known truth. This contradiction verifies that our opposite-assumption was wrong and that our original statement-to-be-proved is indeed correct.   (An easily-read introduction to "proof-by-contradiction" is given here.)
       Peggy Shumaker is an Alaskan poet whom I had the pleasure of meeting at a reading at Bloomsburg University where I was a math professor a few years ago.  Her poem, "What to Count On," below, has a beautiful surprise after a sequence of negations -- and reminds me of the structure of a proof-by-contradiction.

What to Count On     by Peggy Shumaker

Not one star, not even the half moon       
       on the night you were born
Not the flash of salmon
       nor ridges on blue snow 
Not the flicker of raven’s
       never-still eye 

Aesop's fables in verse ... the price of greed ...

     The farmhouse* in which I grew up had a room we called "The Library" because of its small bookshelf with my father's books -- including selections from Kipling and Twain and Aesop's Fables.  I liked to read.  And a lot of the morals are now stored in my head.  Recently I have found and enjoyed poetry versions of some of these in Jean de La Fontaine's Selected Fables (Dover, 2000) -- see also Project Gutenberg.  Here is one about the mathematics of greed ... .

The Hen with the Golden Eggs    by Jean de La Fontaine (1621-1695)

                                   translated by Walter Thornbury

My little story will explain
An olden maxim, which expresses
How Avarice, in search of gain,
May lose the hoard that it possesses.

Mathy poems OUT LOUD

     Here is a link to "Applied Mathematics" written and recited by London poet Dan Simpson.   This link leads to several math-arts samples (including two poems -- the first is by Gizem Karaali and you may scroll down to hear my poem, "A Taste of Mathematics") recorded by Samuel Hansen. (The complete text of "A Taste of Mathematics" is available here.)  This link connects to information about a 2014 YouTube video featuring a varied list of mathy poets.

The Man Who Knew Infinity

     A few days ago I followed a broken link on the Poetry Foundation website and the site offered me this cryptic quatrain by American poet J. V. Cunningham (1911-1985) -- it is the final stanza of a poem I have posted here.

       Error is boundless.
       Nor hope nor doubt,
       Though both be groundless,
       Will average out.
               – J.V. Cunningham, from “Meditation on Statistical Method”

     Often on my mind these recent days has been the film I saw last week -- "The Man Who Knew Infinity" -- and I invite you to follow these links to poetry concerning its central characters, mathematicians Srinivasa Ramanujan (1887-1920) and G. H. Hardy (1877-1947).

In Wyalusing, counting pelicans

     The number in the title of Robin Chapman's poem first attracted me to it and the mention of Wyalusing in the first line drew me further in -- for Wyalusing is the name of a small town in northeastern Pennsylvania (a region in which I lived and taught -- at Bloomsburg University -- for many years).  But, of course, Google was able to tell me of another Wyalusing, a park in Wisconsin, home state of the poet, and a place advertised as having plentiful bird-watching.  Enjoy:

       One Hundred White Pelicans     by Robin Chapman

       Over Wyalusing, riding thermals, they shine
       and disappear, vanish like thought,
       re-emerge stacked, stretched, 
       a drifting fireworks' burst.   

A math problem or a word problem?

     One of my recent poetry-finds has been the anthology Regreen:  New Canadian Ecological Poetry, edited by Madhur Anand and Adam Dickinson (Scrivener Press, 2009) and in it some small mentions of mathematics.  The following poem by artist and poet Erin Robinsong considers things big and small -- and observes some paradoxes. Is math the puzzle or the explanation or . . .?

SEED : CEDE   by Erin Robinsong  

Looking into the peach-pit, we find a vast spaciousness, as if actually looking into a pit –

A math problem:
A peach pit is weighed against
the year’s yield plus the tree: 
30 g, 900 kg.
Which weighs more? 

Squaring the Circle -- from the POETRY App

     One of my smart-phone delights is the App (available from PoetryFoundation.org) that gives me a selection of poems on the go. (My posting for 15 October 2015 gives a description of how the App works.)  A few days ago, spinning its dials -- matching the categories "Humor," "& Arts and Sciences"-- I found the exceptional poem "Squaring the Circle" in which poet Philip Fried has some fun with the impossible problem.   ("Squaring the Circle" first appeared in the July /August 2014 issue of Poetry and Fried has given me permission to include it here.)

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 6 x 6 syllable-square -- and links to more . . .

          Last Sunday's paper had
          an essay by a clown
          who said as long as I
          play dumb people let me
          do what I want.  And I
          cannot stop wondering.

 6, a perfect number    

Find lots of mathy poems here at TalkingWriting.com; this week featuring Sarah Glaz.

At this link find poems, etc. by Spelman College math students working with Colm Mulcahy.

Poems that count: Eight Buffalo

     In mid-April at the Split This Rock Poetry Festival, one of the sessions I attended and valued had the title " "Eco-Feminist Poetry, Intersectionality, & the End of the Earth."  In the midst of my concern about ecology and women is my addiction to mathematics -- and a poem by Cecilia Llompart started me counting.  See if you, too, count the word "buffalo" eight times during this poem; and shudder when you read the final word.

       Eight Buffalo      by Cecilia Llompart

       An obstinacy of buffalo 
       is not to say that the buffalo 
       are stubborn. No, not like 
       a grass stain. More that 
       the very bulk of one— 

Can you multiply with Roman numerals?

     Canadian writer Siobhan Roberts (whom I know from BIRS workshops) has a recent New Yorker article that celebrates the 100th birthday and achievements of Claude Shannon (1916 -2001) -- often referred to as "the father of the information age." Most of the important information in that article I leave for you to read for yourself, but I call to your attention to one of Shannon's accomplishments featured therein -- Claude Shannon built a machine for doing arithmetic with Roman numerals.  This connects to poetry via a poem by Ron Padgett, below.

The Roman numeral system has largely been abandoned 

because arithmetic is less cumbersome with a place-value system.

 Here is a link to a site that exhibits procedures for Roman numeral arithmetic.

 The Roman Numerals     by Ron Padgett

       It must have been hard
       for the Romans to multiply
       —I don’t mean reproduce,
       but to do that computation.

Talking-Writing offers Math Poems

     In recent weeks, the online journal Talking-Writing has been featuring math poems and last Monday they posted my "Skagway Study" -- which follows a style explored in one of my favorite poems by Wislawa Szymborska.
      Carol Dorf, poetry editor of Talking-Writing, is a math teacher as well as a poet and her work as well as those of others with math interest are explored in "Wild Equations," the Spring 2016 Issue of Talking-Writing.   Here are some links:

By Giavanna Munafo    "Twenty-Four Hours"

By JoAnne Growney    "Skagway Study" 

By Alice Major     "Euclid's Iron Hand" and "Bird Singularities"

By Amy Uyematsu   "Three Quick Studies of Math-Art"

By Carol Dorf   "Action Potential" and "e"

By Eveline Pye   "Celestial Navigation," "Three," and "The Law of Statistics"

By Larry Lesser    "Margins" 

By Katie Manning   "28, 065 Nights" and "Week by Week" (Fibonacci poem)

By Stephanie Strickland   "Doomed calculations which God acknowledged

                                                Islands (Invaginated by Saltwater
                                           Bays with a Stream and Another Both Flowing
                                              All Through Them along Enfolded Paths)" 

Earlier this week in an American Mathematical Society blog posting entitled "Math and Verbal Gymnastics," Duquesne University mathematician Anna Haensch also celebrated the join of mathematics and poetry.

"The Mathematician"

     Here is a selection from "The Mathematician," a long poem -- found in its entirety in The Rumpus -- by Oregon poet Carl Adamshick and recommended to me by poet R Joyce Heon  --  for a sample of her ekphrastic poems, follow this link and go to pages 37-42.  And this link leads to more poems (in this blog) starring mathematicians --- and a few of them are women!!

from   The Mathematician     by Carl Adamshick

What I do is calculate.
I’ve always seen the world as numbers,
buildings and trees factors,
math as a language better suited for explaining
how things work
than the formula of grammar.

Women in Mathematics Count!

     The theme for 2016 Mathematics Awareness Month is "The Future of Prediction."  And today I am wondering what date can be predicted for when the achievements of women in mathematics will be recognized with the same awareness as those of men.

How many female mathematicians can you name? 

Here are links to two articles to to help you lengthen your list of math-women:  "12 Brilliant Female Mathematicians You Should Know" -- an article by Olivia Harrison whose list starts with Hypatia (who lived around 400 AD) and continues to the 21st century, featuring Maryam Mirzakhani, an Iranian mathematician at Stanford who in 2014 won the prestigious Fields Medal for her work related to the symmetry of curved surfaces. Judy Green adds important names in her article "How Many Women Mathematicians Can You Name?"
     For still more, visit my 2015 post "The culture for women in math and the sciences";  additionally, a search of this blog using "math women" will lead to a host of  names and links.  Enjoy!
     Here are the closing lines of a poem of mine about the brilliant mathematician, Emmy Noether (1883-1935):   

           In spite of Emmy's talents,
           always there were reasons
           not to give her rank
           or permanent employment.
           She's a pacifist, a woman.
           She's a woman and a Jew.
           Her abstract thinking
           is female and abstruse.

           Today, history books proclaim that Noether
           is the greatest mathematician
           her sex has produced. They say she was good
           for a woman.

The full poem is available here.