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?”    

Things to Count On

Tomorrow is my mother's birthday.  Born in 1912, she has been gone for several years now -- and tomorrow my sons and I will travel to Indiana, Pennsylvania to visit her grave and the farmhouse where I grew up.  In honor of my mother, I post this poem (also posted on October 1, 2010) that enumerates ways that numbers were vital in my early life.

Things to Count On            by JoAnne Growney  

Counting Years -- in p'Bitek's Song of Lawino

Okot p'Bitek (1931-1982) was a Ugandan poet; one of his central concerns was that African literature should be built on African rather than European foundations.  His epic poem Song of Lawino (East African Publishing House, 1966) is a narrative poem written in the voice of Lawino who appeals to her husband Ocol to stay true to his own customs, and to abandon his desire to be white.  Here is a section of that poem that addresses a system for counting years.

from   Song of Lawino      by Okot p'Bitek

            *
       Ocol tells me
       Things I cannot understand,      

A Voice Meant to be Spoken

     Last month the Library of Congress named a new poet laureate, Juan Felipe Herrera, a Californian and Mexican-American whose work often involves oral performance  - as in “187 Reasons Mexicanos Can’t Cross the Border,” (City Lights, 2007).  As I have learned about this poet I have found that I identify with his process,  "I write while I’m walking, on little scraps of paper,” he said.  (Wasn't walking also a writing strategy for William Wordsworth?)
     When I am introduced to the work of a new poet it has become my custom not only to enjoy her or his work but also to look for the ways that she or he uses mathematics.  The following poem is found, along with others by Herrera, at  Poets.org.   

Sex, Maths, and the Brain

I found this poetry in an abstract (with a link posted at "Women in Maths" on Facebook) for a lecture by Professor Gina Rippon entitled "Sex, Maths, and the Brain" at Aston University in Birmingham, England, on 30 June 2015.  Enjoy!

Is there such a thing as a maths 
brain? Are mathematicians born 
or made?  Is the lack of girls 
in maths subjects 
a 'brain' problem?

Celebrating angles and rainbows . . .

                      
       C  
       E
       L
       E
       B
 M A R R I A G E
       A     A
       T     Y  
       E

And let me add a bit of mathematics -- for my friends (both gay and straight) who love to play with language:
           A recent New Yorker article  ("Go Ask Alice" by Anthony Lane, 6-8-15,48-54) 
          on Lewis Carroll (1832-1898) offered this quote -- this "found" poem:

            Obtuse anger
            is that which is greater
            than right anger.

This year, 2015, marks the 150th anniversary of the publication of the first edition of Alice's Adventures in Wonderland.

The power of eleven

One of my recent poetry acquisition treasures is Measure for Measure:  An Anthology of Poetic Meters, edited by Annie Finch and Alexandra Oliver (Everyman's Lbrary, 2015).  From a DC poet and friend, Paul Hopper, a few weeks ago I received comments about one of the sections of this collection  -- a section containing stanzas in hendecasyllabics, that is, in 11-syllable lines  Hopper has sent a sample quatrain of hendecasyllabics that points to "Into Melody" by Lewis Turco.  A bit of mathematical terminology is found in the opening lines of Peter Kline's "Hendecasyllabics for Robert Frost" -- and I offer these samples below.

Hopper's quatrain:

Someone should build a large dodecahedron,
with a poem in hendecasyllabics
on each pentagonal face except the base.
I'd start with this poem by Lewis Turco. 

Found poetry -- Mary Cartwright

Recently I have been reading about mathematician Mary Cartwright (1900-1998) and working to develop a poem about her -- relying on a fine article/interview by my friend Jim Tattersall published in the The College Mathematics Journal (September 2001).  Her work on the foundations of chaos theory was prominently presented in a 2013 BBC News article.   A couple of days ago my acquisition of Rachel Swaby's book -- Headstrong Women:  52 Women Who Changed Science and the World  (Broadway Books, 2015) -- added to my information about Cartwright.  Here, from quotations offered by Tattersall and Swaby, are some of Cartwright's poetic words (reflecting on the ages and genders of mathematicians). First, speaking of her employment at Cambridge:

I regret to say that my impression 
when I began research was that, in general,
less qualified men were employed quite a lot, 
which eliminated some quite good women.

Uncertainty . . .

     Sometimes we find things of great value when we are looking for something else -- in fact, Argentinian writer Jorge Luis Borges has said, The best way to find a good thing is to go looking for something else . . .
     One of my recent stumbles (while looking for work by Borges) was onto the website of Robert Ronnow -- and I have found it a fun place to browse.  Here is a sample, a poem from his recent collection, The Scientific Way to Do Mathematics:

Uncertainty       by Robert Ronnow

                                                       --with a line by Pico Iyer

There cannot be two identical things in the world. Two
hydrogen atoms
offer infinite locations within their shells for electrons.
Thus, nothing can be definitely eventually known. 

Seeing the NEWS in square stanzas

Reading today's Washington Post, a surprising statistic:

               Sharks don't kill
               as   many
               as cows do.
 

In the years 2001 to 2013 in the US an average of 20 deaths annually were caused by cows, 

compared with 1 during each of those years from sharks.

Also, Pope Francis has spoken out, expressing his concerns for our environment:

               Pope Francis,
               like me, sees
               climate change--

               a real
               problem.

Judith Grabiner and Howard Nemerov

     Last evening at the Distinguished Lecture Series sponsored by the MAA it was my privilege to hear an outstanding presentation by Judith Grabiner entitled "Space: Where Sufficient Reason Isn't Enough."  (I invite you to go to the MAA website to learn more about Grabiner and her talk.)
     Grabiner is a math-woman I have long admired and, after the lecture, while I was shaking her hand and thanking her for the excellent presentation, I took a moment to ask her if she had any favorite mathy poems.  Although surprised by my question she was able to cite Elizabeth Barrett Browning's Sonnet XLIII  that counts the ways of love -- a few lines of which are found here -- and the name Howard Nemerov, whom readers of this blog know is one of my favorite poets.
     You may scroll down to find Nemerov's "Magnitudes" (found also at PoetryFoundation.com and PoemHunter.com along with other work by this fine poet).  Poet Laureate of the United States during 1988-1990, Howard Nemerov  (1920-1991) served as a combat pilot during World War II and maintained a continuing interest in the stars and navigation.  Here are links to my earlier postings of poems by this favorite poet.

"Two Pair"      "Grace to Be Said at the Super Market"
"Lion and Honeycomb"     "Creation Myth on a Mobius Band"
"To David, About His Education"     "Found Poem"    "Figures of Thought"

And here, expressing concerns about our planet, is Nemerov's "Magnitudes":

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 

Square stanzas for Women in Maths

Women

in Maths --

it all

adds up.

     Go here for "It All Adds Up" -- a story in plus Magazine by Rachel Thomas about the recent Women in Maths conference sponsored by the London Mathematical Society.

     And if you know of POEMS that celebrate women in mathematics, please contact me (email address at bottom of blog) or post a link in the comments to this post.

A portrait of TB in numbers

Poet Sarah Browning recently directed me to "Tuberculosis in Numbers," a fine poem by M. Brett Gaffney that appears in the latest issue of Rogue Agent.  The poem opens this way:

Tuberculosis in Numbers     by M. Brett Gaffney

        “In the past, we have been unable to get a true picture of the TB situation
        in Louisville due to the method of keeping statistics.” – Dr. Oscar O. Miller

Two weeks coughing when the mother’s only son
finds three bloody tissues—thinks of maple leaves.

Ten days at the sanatorium, four ribs taken. One father teaches
his boy how to wait by filling in crossword puzzles—
twelve across, seven letters: to eat or devour.  

The boy’s mother dies four months after his thirteenth birthday.
Tuesday morning at nine, it rains. His father smokes one cigarette, two.
Men come and take her body away. Under the sheet, ten toes.

One priest. Four lines of scripture. . . .

Gaffney's complete poem is available here.

17 syllables -- and other art

What is he talking about?  What does he mean?
The thought-provoking riddle posed by these 17 syllables (presented here as 3 square stanzas) from Ludwig Wittgenstein (1889-1951)  is something I found on the the wall of the National Gallery of Modern Art in Rome, not far from a replica of "Fountain" by Marcel Duchamp (1887-1968).  Photos of both are shown below.

What you are

regarding

as a gift 

is a 

problem 

for you 

to solve.

Add and subtract to get . . . a minimalist poem

Thinking today of poet Bob Grumman (1941-2015) with special gratitude for the way he expanded my poetic horizons.  For example, he introduced me to this addition-subtraction minimalist poem by LeRoy Gorman -- called "the day":

                          un + s = up;
                          up - s = un.

More information about Gorman and several more poetry samples are available here.

Galileo in Florence

Poetry found in the words of Galileo Galilei (1564-1642):

"Philosophy is written in this grand book,
the universe, which stands continually
open to our gaze. 

But the book cannot be understood unless one first 
learns to comprehend the language and read the letters
in which it is composed.

It is written in the language of mathematics,

In the Tuscan sun

View
the
statue
in Pisa
of Fibonacci,
mathematician in the sun.  

Sonnets from The Voyage of the Beagle

 The sonnet is a song of the body as well as of the mind:

14 breaths    
5 heartbeats each breath

A few weeks ago I had the opportunity to be part of a poetry reading that also featured Rick Mullin -- who serves science as an editor of the Chemical and Engineering News -- and whose latest poetry book is a collection of sonnets that offer a magical and musical retelling of  Darwin's voyage -- in Sonnets from The Voyage of the Beagle (Dos Madres Press, 2014). Here are two selections from that collection -- the opening sonnet (first of a triptych) and a later one that features geometry of birds.

     After Uranus     by Rick Mullin
      On reading Richard Holmes 

       I

     There was an age when poetry and science
     shared the province of discovery,
     when Coleridge wished he's studied chemistry
     and Humphry Davy, in exact defiance
     of the Royal Society, blew things up.

Folk music -- counting syllables

Learn about and support Women in Mathematics.  

One place to do that is here. 

Using 4x4 and 2x2 syllable-squares, I emphasize the counting that lies behind folk music in the following selection from "Some Walls" (lyrics by Mary Ann Kennedy, Pamela Rose, Randy Sharp -- but line breaks are mine), recorded by Peter, Paul, and Mary:

          Some walls

          Some walls are made
          of stone.  Sometimes
          we build our own.
          Some walls can stand 

Stars and men revolve in a cycle . . .

In a book-discussion group in which I participate, we are reading some of the short fiction of Jorge Luis Borges (1899-1986) and that reading has provoked me to dive again into my copy of his Selected Poems (Ed. Alexander Coleman, Penguin, 1999).  Here is one of Borges' poems that uses terminology from mathematics:

The Cyclical Night     by Jorge Luis Borges
                                             tr. Alistair Reid (1926-2014)
          to Sylvina Bullrich

 They knew it, the fervent pupils of Pythagoras:
 That stars and men revolve in a cycle,
 That fateful atoms will bring back the vital
 Gold Aphrodite, Thebans, and agoras. 

Include Arts in STEM -- and have STEAM !

Welcome to this blog where we support STEAM !

Visit YouTube for

 math-student, performance-poet Harry Baker's 

"A love poem for lonely prime numbers"

A bit more about Harry Baker can be found in this May 23, 2014 posting. 
In May 2015 visit Takoma Park Community Center Galleries for a STEAM exhibit organized by visual artist and poetry-lover Shanthi Chandrasekar.

Balancing Opposites -- Tagore's Epigrams

Many important mathematical ideas occur as pairs of opposites:
         -2 and +2 (additive inverses), 5 and 1/5 (multiplicative inverses),  
         bounded and unbounded, rational and irrational, 
         convergent and divergent, finite and infinite
Some other familiar mathematical notions occur often in contrasting pairs but are not fully opposites:
         horizontal and vertical, positive and negative, 
         open and closed, perpendicular and parallel

Recently I have returned to reading work by Rabindranath Tagore (1861-1931; Bengal, India;  winner of the 1913 Nobel Prize in Literature) and I enjoy reflecting on contrasts posed by this reflective poet in a series of "Epigrams":

Epigrams      by Rabindranath Tagore

I will close my door to shut out all possible errors.
"But how am I to enter in?" cried Truth.  

Lines of breathless length

Brief reflections on definitions of LINE . . .

          Breathless length     by JoAnne Growney

          A LINE, said Euclid, lies evenly
          with the points on itself --
          that is, it’s straight –-
          and Euclid did (as do my friends)
          named points as its two ends.

          The LINE of modern geometry
          escapes these limits
          and stretches to infinity.
          Just as unbounded lines
          of poetry.

A poem for your pocket

Years ago, when "Poem in Your Pocket Day" (April 30) was first celebrated, we did not have cellphones to carry poems with us easily.  Here is a tiny but memorable poem for you to carry with you tomorrow -- on your phone or in your pocket -- a poem to open and read, again and again.

     Addition     by Langston Hughes (1902-1967)

     7 x 7 + love =
     An amount
     Infinitely above:
     7 x 7 − love.

Hughes' poem "Addition" is found in Strange Attractors: Poems of Love and Mathematics (A K Peters, 2008) and was first posted in this blog, along with other poems linked to Black History Month on February 20, 2011.

Geometry of baseball

Many poems are written of baseball; a few of them involve mathematics --  see the posting for April 9, 2010 for math-related baseball poems by Marianne Moore (1877-1972) and Jerry Wemple; see the posting for September 18, 2011 for one by Jonathan Holden.
     Today I feature the opening stanza from a baseball poem by Pennsylvania poet, Le Hinton.

from   Our Ballpark    by Le Hinton

       This is the place where my father educated us:
       an open-air school of tutelage and transformation.
       This is where we first learned
       to count to three, then later to calculate the angle
       of a line drive bouncing off the left field wall.
       We studied the geometry and appreciated the ballet
       of third to second to first, a triple play.
              . . .

Earth Day -- April 22, 2015

Consider today the thoughtful words of this sonnet by Edna St. Vincent Millay (1892-1950):

     Read history: so learn your place in Time
     And go to sleep: all this was done before;
     We do it better, fouling every shore;
     We disinfect, we do not probe, the crime.
     Our engines plunge into the seas, they climb
     Above our atmosphere: we grow not more
     Profound as we approach the ocean's floor;
     Our flight is lofty, it is not sublime.
     Yet long ago this Earth by struggling men
     Was scuffed, was scraped by mouths that bubbled mud;
     And will be so again, and yet again;
     Until we trace our poison to its bud
     And root, and there uproot it: until then,
     Earth will be warmed each winter by man's blood.

These lines are found on my shelf in Collected Sonnets (Revised and Expanded Edition) by Edna St. Vincent Millay (Harper & Row, 1988).  AND, recall the arithmetic of a sonnet:  14 lines (or breaths) and 5 iambs (or heartbeats) per line. 

April celebrates Math and Poetry

     April is National Poetry Month and Mathematics Awareness Month. Yesterday I was able to attend several of the popular and crowded events at the National Math Festival (Here's a link to "A Field Guide to Math on the National Mall" where you can see photos of items pointed out to yesterday's visitors.) and tomorrow evening (April 20) I will be part of a reading that features poetry of math and science at the DC Science Cafe (at Busboys & Poets, 5th &K Streets, 6:30 PM).  
     For tomorrow evening's reading I intend to wear my red-peppers earrings; one of the poems I will offer will be "A Taste of Mathematics" (from my collection Red Has No Reason and posted in its entirety at this link). Here is the poem's final stanza:

            She said, "Hot peppers
            are like mathematics —
            with strong flavor
            that takes over
            what they enter." 
 

Remembering Abraham Lincoln

Today -- April 14, 2015 -- marks the 150th birthday of the assassination of President Abraham Lincoln (1809 - 1865) and April 15 is the date on which he died. Lincoln loved poetry and trained his reasoning with Euclid's geometry.  Here is a brief sample of his own poetry (found -- along with other samples -- at PoetryFoundation.org).

       Abraham Lincoln     by Abraham Lincoln

       Abraham Lincoln
       his hand and pen
       he will be good but
       god knows When

From my copy of Walt Whitman's Leaves of Grass (Signet Classics, 1955), from the section "Memories of Lincoln," I have copied these well-known and thoughtful (and non-mathematical) lines:

Time is no straight line . . .

Swedish poet and Nobel Laureate Tomas Transtromer (1931-2015) died last month. At his website I found this poem that reflects on the arithmetic and geometry of life:

Reply to a Letter    by Tomas Transtromer

In the bottom drawer I find a letter which arrived for the first time twenty- six years ago. A letter written in panic, which continues to breathe when it arrives for the second time.

A house has five windows; through four of them daylight shines clear and still. The fifth window faces a dark sky, thunder and storm. I stand by the fifth window. The letter.

Man Ray's "Human Equations"

     Art lovers in Washington, DC have the opportunity (until 5/10/15) to see, on exhibit at The Phillips Collection, "Man Ray -- Human Equations: A Journey from Mathematics to Shakespeare." I visited the exhibit on February 19 on the occasion of a poetry reading by Rae Armantrout -- she presented work of hers that she felt captured the spirit of Man Ray's work.  (Bucknell poet Karl Patten, whom I had as a poetry teacher years ago, insisted that "Every Thing Connects" and, indeed, this is the title of one of the poems in Patten's collection The Impossible Reaches.  Both of these phrases that became titles for Patten seem also to describe Man Ray's and Armantrout's work:  they have taken seemingly disparate objects and reached across seemingly impossible gaps to relate them.  As often happens in mathematics.)   

Mathematics and poetry -- are the same ! ! !

Last week the Art Works Blog posted an interview with mathematician, poet, and translator, Enriqueta Carrington.  You will want to follow the link and read the whole thing.  Here is a paragraph:

quoting Enriqueta Carrington:

Mathematics and poetry are the same thing,
 or one is a translation of the other.

Well, perhaps that is an overstatement; 
but both math and poetry are about beautiful patterns, 
about creating, gazing at, and sharing them, 

and about appreciating those created by others.

It is not necessary to be a great mathematician or a great poet 
to enjoy this beauty, as I can tell you from my own experience.

Several years ago, at a time near the beginning of this poetry-math blog, in the posting for April 8, 2010, is a pantoum by Carrington.  And here is another of hers, this time a Fibonacci poem -- whose lines increase in word-count that matches the first eight Fibonacci numbers:  1, 1, 2, 3, 5, 8, 13, 21.

April is . . . a time for math and poetry . . .

     Once upon a time
     I counted to the tenth prime
     and found a word to rhyme.

Tomorrow is not only April Fool's Day -- it also begins "National Poetry Month" and "National Mathematics Awareness Month."  I hope you will scroll down through this blog for math-poetry intersections -- and that you will like what you find and return for more.

(If you are near Washington, DC, consider a visit to MathFest on Saturday, April 18.)

Science Verse

Recently coincidence has brought to me two collections of poems about  science -- first, the 2014 issue of The Nassau Review, a gift from editor and poet Christina M. Rau. The second collection is a "used" children's book, Science Verse (by John Scieszka and Lane Smith) found at the wonderful Kensington Row Bookshop (scroll down their webpage to find out about their monthly poetry readings).  I include below two rhyming stanzas from Science Verse, followed two selections from The Nassau Review 2014 -- a poem by Diane Giardi which is a parody (or isomorphic image) of a nursery rhyme and a poem  by Katherine Hauswirth which may or may not consider infinity.

Hey Diddle Diddle

Hey diddle diddle, what kind of riddle

Is this nature of light?

Sometimes it's a wave,

Other times a particle . . .

But which answer will be marked right?

The problem of time

Californian Brenda Hillman is a poet whose work I like and admire.  In "Time Problem" she weaves prime numbers into a deft description of the dilemma of not enough time.

       Time Problem     by Brenda Hillman

       The problem
       of time.      Of there not being 
       enough of it.

       My girl came to the study
       and said Help me;
       I told her I had a time problem 
       which meant:
       I would die for you but I don’t have ten minutes. 
       Numbers hung in the math book 
       like motel coathangers. The Lean 
       Cuisine was burning

March 23 -- Emmy Noether's birthday

Today, March 23, 2015, Google celebrates the 133rd birthday of mathematician Emmy Noether.  In support of the celebration here is a link to "My Dance is Mathematics," a poem I wrote to honor this pioneering mathematician.  I hope that celebrations of Noether and other math-women will help to create a world in which these lines from my poem about her are no longer true:

          If a woman's dance is mathematics,
          she dances alone.

March 21 -- World Poetry Day

Yesterday poetry was celebrated around the world -- the Guardian reported the event with mention of Cafés around the world that offered a cup of coffee in exchange for a poem.  The occasion caused me to turn to one of my favorite international collections, The Horse Has Six Legs (Graywolf, 2010) -- an anthology of Serbian poetry translated and edited by poet Charles Simic.  On 29 April 2011 I posted "Forgetful Number" by Yugoslav poet Vasko Popa (1922-1991) -- and here is another of Popa's poems.  This one is part of a cycle of poems about "the little box" and it involves recursion.

       Last News about the Little Box     by Vasko Popa

       The little box that contains the world
       Fell in love with herself
       And conceived
       Still another little box.   

Multiplied by Rain

     There are many mathematical terms that are used in daily life -- not only multiplied and divided and negative but also closure and identity and field and commute -- and it is fun for me, a math person, to see poets use such terms in new and thoughtful ways.
     Poet Jane Hirschfield weaves words into fine tapestries that give us new dimensions of meaning.  The Table of Contents of her new book, The Beauty (Knopf, 2015), is scattered with mathematical terms -- we find zero, plus, subtraction,  and the final title, "Like Two Negative Numbers Multiplied by Rain."  This poem first appeared in Poetry (2012) and is available at the Poetry Foundation website along with more than thirty additional Hirshfield poems.

Like Two Negative Numbers Multiplied by Rain   by Jane Hirshfield

     Lie down, you are horizontal.
     Stand up, you are not. 

A Russian toast (with mathematics)

Several weeks ago I had the pleasure of visiting the Washington Museum of Poetry and Music -- a collection in Rockville, MD gathered and maintained in the home of Uli Zislin who has lived in the US since 1996. (Among other treasures, the musuem has recordings of poets Anna Akhmatova, Boris Pasternak, Osip Mandelstam, and Anastasia Tsvetaeva.)    At the time of my visit, Zislin presented me with one of his own poems that includes a bit of mathematics.  The original Russian version of Zislin's poem is at the bottom of this post.  Prior to that I offer a translation into English by Arlington poet, teacher, and award-winning Russian translator, Katherine Young.  Thank you, Katherine.

        A Pedagogical Toast     by Uli Zislin

                 translated by Katherine E. Young

       Friends and colleagues, pedagogues!
       We’re not philosophers, not gods.
       We’re simply people, soldiers of God,
       destined to suffer and to love.  

Three Greguerías

From Portugal, from Francisco -- who emailed me the gift of these lines:

Three Greguerías   by Rámon Gómez de la Serna (1888-1963)
                                             translated by Francisco J Craveiro de Carvalho and JoAnne

Holding her hoop the little girl goes to school and to the playground,
to play with the circle and its tangent.

Zeros are the eggs from which all the other numbers are hatched.

Numbers are the best acrobats in the world: they stand on top of each other without falling down.

Ramón Gómez de la Serna is considered the father of the greguería -- a one-liner in which he combined gentle humor with a metaphor. 

Similar, self-similar -- fractals, a poem

      In geometry two objects are said to be similar if they have the same shape --- which happens if their angles are the same size and occur in the same sequence. For example, any pair of triangles with angles 30, 60, and 90 degrees are similar; also, the lengths of pairs of corresponding sides of these triangles have the same ratio.
      A term used in the terminology of fractals is self-similarity: a self-similar object has exactly (or approximately) the same shape as a part of itself.  A variety of objects in the real world, such as ferns and coastlines, are approximately self-similar: parts of them show the same statistical properties at many scales. At the end of this post are a couple of diagrams that illustrate how a fractal may be developed.  But first, experience the generative beauty of self-similarity via a poem by Maryland poet Greg McBride.  Mathematician Benoit Mandelbrot (1924-2010), quoted in McBride's epigraph, often is nicknamed "the father of fractals."

The mathematician, she . . . .

     Tomorrow, March 8, is the International Day of the Woman -- and I celebrate the day with mixed feelings.  YES, there are many women I want to celebrate. BUT WHY are they not celebrated daily, equally with men? And a more specific concern, WHY, when the word "mathematician" is used, is the person assumed to be a man. (There is, on the other hand, a nice non-gendered neutrality in numbers -- as in this first stanza of "Numbers," by Mary Cornish, found below.)
      In this posting I celebrate Grace Brewster Murray Hopper (1906-1992) -- a mathematician with a doctorate from Yale, a navy admiral, a computer scientist who led in the development of COBOL, an early (c.1959) programming language.  A person I had the good fortune to meet when she visited Bloomsburg University in 1984 to receive an honorary Doctor of Science Degree.  Hopper was imaginative and articulate; here is some poetry found in her words.

                               If it's a 
                               good idea,
                               do it.  

Celebrate Pi -- write in Pilish

On 3/14/15 many of us will celebrate  π - day; for those who like to gaze on the digits of  π,  one hundred thousand of them are available here.  In honor of this upcoming special day I have composed a small stanza in Pilish (the language whose word-lengths follow the digits of  π ). 

3.  1  4  

Get a list,

 1  5  

I shout,

   9  2  6  5  3  5

Women in Maths -- on Facebook

     Recently I prepared an item for Rachel Levy's Grandma Got STEM blog that told a bit about my granddaughters who like math.  My preparation for that posting led me to focus on my wish to have math be a fun place for girls to hang out -- a place for lots of girls:  feminine girls, sporty girls, popular girls, silly girls (as well as geek girls).  Mathematics has mostly been a lonely place for females -- my first  girl-friend who was also a math person was a colleague whom I met in my 40s (see my poem for Toni, "Girl-Talk").   I want mathematics to be a welcoming place for my granddaughters. A place with friends.
     Related to this concern, wonderful news came in my email box recently from Susanne Pumpluen (video) at the University of Nottingham.  She has started a Women in Maths page on Facebook .  There one can find bios, videos, news links and FRIENDS.  Visit.  LIKE. Offer your comments and support. 

Reflections on Logic

Miroslav Holub (1923-1998), Czech poet and immunologist who excelled in both endeavors, is one of my favorite poets.  He combines scientific exactitude with empathy and absurdity.  Here is a sample:

       Brief Reflections on Logic     by Miroslav Holub

                                     translated by Stuart Friebert and Dana Habova

       The big problem is everything has
           its own logic.  Everything you can
           think of, whatever falls on your head.
           Somebody will always add the logic.
           In your head or on it.  

Found poetry - words of Dirac

The epigraph for Richard Bready's "Times of Sand" (a stanza of which I posted a few days ago on 21 February) is a quote from British physicist Paul Dirac (1902-1984, founder of quantum theory).  This quote reminded me how often we find poetry within well-written prose -- and I have gone to WikiQuotes and found more poetic words from Dirac:

       If you are 
       receptive 
       and humble, 

       mathematics 
       will lead you 
       by the hand. 

How many grains of sand?

     Sand beaches are places I love to walk.  Next to oceans and soft underfoot. 

Below I post a stanza from Richard Bready's "Times of Sand"  --

 a long poem that explores many of the numbers related to sand. 

     Contemplating grains of sand turns my thoughts to the pair of terms "finite" and "infinite."  One of my friends, university-educated, versed in literature and philosophy, offered "all of the grains of sand" as an example of an infinite set.   As we talked further, he proposed "the stars in the universe" as a second example. This guy, like many, equates "infinite" with "too large to count."  And then there is me; long ago in college I encountered a definition of "infinite" that went something like this:  A set is infinite if there is a one-to-one correspondence between the members of the given set  or one of its proper subsets with the set {1, 2, 3, . . ..} of counting numbers.

The numbers say it all . . .

The title of my posting today, "The numbers say it all" comes from the final line of "After Leviticus," by Detroit poet Philip Levine.  Levine (1928-2015) died this past Saturday.  Often termed "a working class poet," this fine writer won many awards for his work. 

     After Leviticus     by Philip Levine

     The seventeen metal huts across the way
     from the great factory house seventeen
     separate families. Because the slag heaps
     burn all day and all night it’s never dark,
     so as you pick your way home at 2 A.M.
     on a Saturday morning near the end

America, land of equals (perhaps)

Preparing to celebrate (after Valentine's Day) Presidents' Day, remembering particularly George Washington (b February 22, 1732) and Abraham Lincoln (b February 12,1809), I offer a few lines by Walt Whitman (1819-1892).

       America     by Walt Whitman

       Centre of equal daughters, equal sons,
       All, all alike endear'd, grown, ungrown, young or old,
       Strong, ample, fair, enduring, capable, rich,
       Perennial with the Earth, with Freedom, Law and Love,
       A grand, sane, towering, seated Mother,
       Chair'd in the adamant of Time.        [1888]

This poem is found here in the Walt Whitman Archive.

Surreal parabola, Mobius strip

     When a math term appears in a poem, will its usage make sense to a mathematician? Some mathematical folks are critical of poetic use of math words because precision may be lost to "poetic license." Others feel a pleasing tension between the mathness of a term and the stretched or layered meanings suggested by the poem. With these thoughts in mind, consider these two mathematically-titled poems "Mobius Strip" and "Parabola" by Robert Desnos (France, 1900-1945), translated by Amy Levin and selected from "A sampling of French surrealist poetry."

     Mobius Strip     by Robert Desnos (trans. Amy Levin)

     The track I'm running on
     Won't be the same when I turn back
     It's useless to follow it straight
     I'll return to another place

Celebrate Black History, Valentine's Day

February is Black History Month and on the 14th we celebrate love with Valentine's Day.  To find in this blog a variety of mathy poems on these topics (and many others) use the SEARCH box found at the top of the right-hand column of this blog.

Moebius Strip

Following a lead from Francisco, I found (here) this tiny poem by Michael Hessel-Mial:

       moebius strip

       a belt of clouds
       twist it, latch it
       twisted

       which way will it rain?

To find more poems that feature the Mobius strip  locate the SEARCH box at the top of the this blog's right-hand column -- and enter the term mobius.  Alternatively, the search box also works for a myriad of other topics.

Is winter half over?

     Today (February 2) those of us with roots in Pennsylvania join enthusiasts from everywhere as we  look to mythical groundhog Punxsutawney Phil for a forecast concerning prolonged winter or early spring.  This morning Phil's forecast was bleak but not unexpected: we will have six more weeks of winter.
     This news that our winter is only half over has led me to a poem (found in the illustrated anthology Talking to the Sun, edited by Kenneth Koch and Kate Farrell, published in 1985 by the Metropolitan Museum of Art):

      Another Sarah     by Anne Porter (1911-2011)
                 for Christopher Smart
       When winter was half over
       God sent three angels to the apple-tree
       Who said to her
       "Be glad, you little rack
       Of empty sticks,
       Because you have been chosen.

       In May you will become
       A wave of living sweetness
       A nation of white petals
       A dynasty of apples."

Another winter poem by Porter with a bit of mathematics is included in this post for 25 November 2012.

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.