Homage to Godel

From Erica Jolly, an Australian poet and online friend, I have learned of a fine anthology of science poems --  A Quark for Mister Mark:  101 Poems about Science, edited by Maurice Riordan and Jon Turney (Faber and Faber, 2000).  A poem in that collection that was new to me -- and one I like a lot -- is "Homage to Gödel" by German poet Hans Magnus Enzensberger; I offer it below.  This link leads to a thoughtful review (by Richard Dove) of Enzensberger's poetry -- one of Dove's observations is that thought processes fascinate Enzenberger; "Homage to Gödel" illustrates that fascination. 

     Homage to Gödel     by Hans Magnus Enzensberger  

(translated from German by the poet)

     'Pull yourself out of the mire
     by your own hair': Münchhausen's theorem
     is charming, but do not forget:
     the Baron was a great liar. 

Celebrating Ada Lovelace

Recently I have purchased the anthology, Raising Lilly Ledbetter:  Women Poets Occupying the Workplace (edited by Caroline Wright, M.L. Lyons & Eugenia Toledo, Lost Horse Press, 2015), and have found in it dozens of wonderful poems, including several that celebrate women of science.  Below I offer a poem by New York poet Jo Pitkin that honors Ada Lovelace (1815-1852).  

Bird, Moon, Engine     by Jo Pitkin

Like a fence or a wall to keep me from harm,
tutors circled me with logic, facts, theorems.
But I hid the weeds growing wild in my mind.

By age five, I could plot the arc of a rainbow.
I could explain perpendicular and parallel.
In my mind, I heard the wind in wild weeds. 

Math fun with song lyrics

Song-writer Bill Calhoun is a faculty member in the Department of Mathematics, Computer Science and Statistics at Pennsylvania's Bloomsburg University (where I also hung out for many years). He belongs, along with colleagues Erik Wynters and Kevin Ferland, to a band called "The Derivatives."  And Bill has granted permission for me to include several of his math lyrics (parodies) here. (In this previous post, we consider the connection between song parodies and mathematical isomorphism.)  My first Calhoun selection deals with difficult mathematical questions concerning classification of infinite sets and decidability.  Following that, later lyrics consider proving theorems and finding derivatives.

Questions You Can’t Ever Decide*      by Bill Calhoun

(These lyrics match the tune of  "Lucy in the Sky with Diamonds" by Lennon and McCartney.)

Picture yourself in  a world filled with numbers,
But the numbers are really just words in disguise.
Gödel says “How can you prove you’re consistent,
If you can’t tell that this is a lie?”    

Excitement of Proving a Theorem

Wow!  From first sighting, I have loved this description:

       I prove a theorem and the house expands:
       the windows jerk free to hover near the ceiling,
       the ceiling floats away with a sigh.

These lines from "Geometry" by Rita Dove express -- as well as any string of twenty-four words I can think of -- the excitement experienced from proving a theorem.

Two cultures

The opening poem of Uneasy Relations by mathematician-poet Michael Bartholomew-Biggs is concerned with similarities and differences between mathematical and poetic cultures -- a topic of immense interest also to me and one that I too try to address in my verse.  I wonder --  HOW can I show non-mathematicians that good mathematics is poetry??!!  And, moreover, how can I (mostly a mathematician) write (as advocated by Wallace Stevens and agreed with by other poets) of things rather than (as mathematics wants) of ideas.  OR, may one make poetry of ideas?

   Two Cultures     by Michael Bartholomew-Biggs

   Graves claimed there isn't
   much money in poetry:
   and none vice-versa.

   The first part stays true
   if we replace poetry
   by mathematics. 

Split This Rock 2014

     Plan now to attend the 4th national biennial Split This Rock Poetry Festival: Poems of Provocation & Witness in Washington, DC, March 27-30, 2014.  The sixteen poets to be featured at the 2014 festival are:  Sheila Black, Franny Choi, Eduardo C. Corral, Gayle Danley, Natalie Diaz, Joy Harjo, Maria Melendez Kelson, Yusef Komunyakaa, Dunya Mikhail, Shailja Patel, Wang Ping, Claudia Rankine, Tim Seibles, Myra Sklarew, Danez Smith, and Anne Waldman.   The website SplitThisRock.org offers photographs and more information about the festival.  It will be awesome!  

Kaplansky sings Kaplansky (and Pi)

     I first knew of mathematician Irving Kaplansky (1917-2006) through his monograph, Infinite Abelian Groups -- it was one of my texts for a graduate seminar (with Gene Levy) at the University of Oklahoma in the 1960s.  Later I knew Kaplansky as a songwriter, author of new lyrics for "That's Entertainment."  Kaplansky's adaptation, "That's Mathematics," dedicated to his former student, math-musician-songwriter Tom Lehrer, and to his daughter, singer Lucy Kaplansky, is given below.
      In 1999, in Science News, writer Ivars Peterson (now Director of Publications for the MAA -- Mathematical Association of America) wrote an article about Kaplansky's songwriting in which he mentions  his daughter, Lucy Kaplansky, a singer who frequently performs her father's songs.  A YouTube recording of Lucy singing "The Song of Pi" (in which there is a correspondence between musical notes and the first fourteen digits of pi) is available here.  (Lyrics for "The Song of  Pi" and information about the correspondence are available in Peterson's article.)

What is not possible?

     It is impossible for a number to be greater than 2 if it is not greater than 1.  It is impossible to find a rational number whose square is 2.   Up to now it has not been possible to show that π is a normal number.  Mathematicians like the challenge of the impossible.  To challenge, to prove, to refute.
     In the poem below Chelsea Martin devises an entertaining web of circular reasoning to explore the impossibility of eating at MacDonald's.

McDonalds Is Impossible       by Chelsea Martin

Eating food from McDonald's is mathematically impossible.
Because before you can eat it, you have to order it.
And before you can order it, you have to decide what you want.
And before you can decide what you want, you have to read the menu.
And before you can read the menu, you have to be in front of the menu.
And before you can be in front of the menu, you have to wait in line.
And before you can wait in line, you have to drive to the restaurant.
And before you can drive to the restaurant, you have to get in your car.
And before you can get in your car, you have to put clothes on. 

Power of a theorem

My poetry-math colleague Sarah Glaz has sent me the following pantoum -- which she says was inspired by Ken Yee's pantoum posted in this blog on 6 March 2013.  Thanks, Sarah, for this poem that not only involves permutations of lines but which also aptly connects the adventure of exploring mathematics with the adventure of self-exploration.  Bravo!

A pantoum for the power of theorems      by Sarah Glaz

          The power of the Invertible Matrix Theorem lies
          in the connections it provides among so many important
          concepts… It should be emphasized, however, that the
          Invertible Matrix Theorem applies only to square matrices.
                                           ―David C. Lay, “Linear Algebra”
 
The power of a theorem lies
In the connections it provides
Among many important concepts
Under a certain set of assumptions  

A mathematical woman

As in an earlier posting (20 December 2011), today's feature includes verse by Lord Byron (1788-1824). This time the source is Byron's satiric poem Don Juan. In Canto I, the poet describes Don Juan's mother, Donna Inez, as learned and "mathematical." Here are several stanzas about her -- sagely seasoned with words like "theorem," "proof," and "calculation."

Portraits of a mathematician

Ideas for this posting began with my post on 30 October 2011 in which I selected 7 favorite lines of poetry as a sort of self-portrait.  That posting led to an exchange with blogger Peter Cameron -- which prompted me to write these abecedarian portraits of a mathematician.

   I know a mathematician . . .     by JoAnne Growney  

   always busy
   counting, doubting
   every figured guess,
   haply idling,
   juggling, knowing
   logic, measure, n-dimensions,
   originating
   playful quests,
   resolutely seeking theorems,
   unknowns vanish :
   wrong xs, ys -- zapped. 

Mathematical theorems tornadoing

This poem is fun!

   Horse’s Adventure    by Jason Bredle 

   The horse discovered a gateway to another
   dimension, and with nothing else to do, moseyed
   into it just for grins, and man, you
   don’t even want to know what happened
   next—it was just, like, Horse at the French
   Revolution. Horse in Franco’s living room.

Mathematicians at work

     About her collecton, The Scottish Café (Slapering Hol Press, 2002), Susan Case offers this note:
     This series of poems is loosely based upon the experiences of the mathematicians of the Scottish Café, who lived and worked in Lvov, Poland (now L'viv, Ukraine), a center of Eastern European intellectual life before World War II, close to the area from which my own ancestors emigrated to the United States.  A book, known as the Scottish Book, was kept in the Café and used to write down some of their problems and solutions.  Whoever offered a proof might be awarded a prize.
     Here is "Fixed Points," the opening poem from Case's collection:

Mathematicians are NOT entitled to arrogance

Godfrey Harold “G. H.” Hardy (1877 – 1947) was an English mathematician known for his achievements in number theory and mathematical analysis. One of Hardy's lasting contributions is his 1940 essay, ;A Mathematician's Apology, which offers his self-portrait of the mind of a working mathematician. Here, written in lines and stanzas -- as a found poem -- is the opening paragraph of Hardy's essay:

Theorem-proof / Cut-up / poems

     For mathematicians, reading a well-crafted proof that turns toward its conclusion with elegance and perhaps surprise -- this mirrors an encounter with poetry.  But can one have that poetry-math experience without being fluent in the language of mathematics?  Below I offer a proof (a version of Euclid's proof of the infinitude of primes) and a "cut-up" produced from that proof-- and I invite readers (both mathematical and non-mathematical) to consider them as poems.

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.