Fractal Geometry

Lee Felice Pinkas is one of the founding editors of cellpoems -- a poetry journal distributed via text message.  I found her poem,"The Fractal Geometry of Nature" in the Winter/Spring 2009 Issue (vol.14, no 1) of Crab Orchard Review.

The Fractal Geometry of Nature       by Lee Felice Pinkas

               Most emphatically, I do not consider
               the fractal point of view as a panacea. . .
                                             --Benoit Mandelbrot (1924-2010)

Father of fractals, we were foolish
to expect a light-show from you,

hoping your speech would fold upon itself
and mimic patterns too complex for Euclid. 

April Celebrates Poetry and Mathematics

On April 1 (the first day of National Poetry Month and Mathematics Awareness Month) Science writer Stephen Ornes offered a guest post at The Last Word on Nothing entitled "Can an Equation be a Poem?" and on April 2 the Ornes posting appeared again, this time in the blog Future Tense at Slate.com with the title "April Should Be Mathematical Poetry Month."
     In her comment on "Can an Equation be a Poem?" Scientific American blogger Evelyn Lamb (Roots of Unity)  mentioned her math-poetry post on March 21 entitled "What T S Eliot Told Me About the Chain Rule."  Lamb quotes lines from the final stanza "Little Gidding," the last of Eliot's Four Quartets.   Here is the entire stanza with its emphasis on the mysteries of time and perspective, the circular nature of things, the difficulty of discovering a beginning.    

Logic in limericks

In these lines, Sandra DeLozier Coleman (who participated in the math-poetry reading at the Joint Mathematics Meetings in Baltimore in January) speaks as a professor reasoning in rhyme, explaining truth-value technicalities of the logical implication, "If p then q" (or, in notation, p -- > q ).

     The Implications of Logic     by Sandra DeLozier Coleman

     That p --> q is true,
     Doesn’t say very much about q.
     For if p should be false,
     Then there’s really no loss
     In assuming that q could be, too.  

Can you SEE the monument?

Links to non-intersecting celebrations of April
as National Poetry Month      and      Mathematics Awareness Month

are available here and here.

Recently I revisited my copy of Elizabeth Bishop:  The Compete Poems, 1927-1979 (FSG, 1999) and turned to "The Monument" -- a poem mathematically interesting for its geometry.  Here are the opening lines; the complete text and many other Bishop poems are available online here:

from  The Monument     by Elizabeth Bishop  (1911-1979)

     Now can you see the monument? It is of wood
     built somewhat like a box. No. Built
     like several boxes in descending sizes
     one above the other.
     Each is turned half-way round so that
     its corners point toward the sides
     of the one below and the angles alternate.  

Split This Rock 2014 was great!

 Split This Rock calls poets to a greater role in public life 

and fosters a national network of socially engaged poets. 

Split this Rock's biennial 4-day poetry festival ended today and the air in Washington, DC is electric with the passion of engagement -- minds and bodies energized by fine poems that demand opportunity and justice for all.  I was glad to be there, participating in workshops and readings led by today's finest poetic voices. 

Women's History -- celebrate Caroline Herschel

     In the sixties when I spent a year at Bucknell University, I was a member of the "Department of Astronomy and Mathematics," a pairing of related disciplines. In past centuries, Mathematics was included in the liberal arts. In the twenty-first century often it is paired with Computer Science, and Astronomy is paired with Physics.  And so it goes.
      Poems by Laura Long tell of the pioneering work by astronomer Caroline Herschel -- a discoverer of eight comets, a cataloger of stars.  Long describes her recent collection,  The Eye of Caroline Herschel:  A Life in Poems (Finishing Line Press, 2013), in this way:      
                  This is a work of the imagination steeped in historical siftings 
                         and the breath between the lines.  
Here is the opening poem:  

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? 

One geometry is not enough

Writer Katharine Merow is in the Publications Department of the Washington DC headquarters of the MAA (Mathematical Association of America) and she is one of the poets who participated in the "Reading of Poetry with Mathematics" at JMM in Baltimore last January.  Here is the engaging poem Merow read at that event -- a poem that considers the 19th century development of new and "non-euclidean" geometries from variants of Euclid's fifth postulate, the so-called parallel postulate:

       Geometric Proliferation    by Katharine Merow

Making something of nothing

     Was zero invented or discovered?  When and how?  By whom?  In "The Origin of Zero" -- an article published in 2009 in in Scientific American --  John Matson introduces an interesting history of zero (something vs. nothing and so on...).  Recently through the Splendid Wake poetry project (with an open-to-all meeting on Friday March 21 -- go here for details) I have connected with Washington DC poet William Rivera who has shared with me this poem that also examines the puzzle of the somethingness of nothing.

Nothing Changes Everything     by William Rivera

Tomorrow is Pi Day

     Tomorrow is Pi Day and I offer no new poems but supply links to several previous posts.  Poetry of π may be found on 23 August 2010 (an "irrational sonnet" by Jacques Bens),  6 September 2010 (featuring work by Kate Bush,  Robert Morgan and Wislawa Szymborska),  10 September 2010 (mnemonics for π, especially from Mike Keith) , 15 March, 2011,(a poem by Lana Hechtman Ayers)  27 November 2011 (a poem by Brian McCabe) and 10 March 2013 (the opening lines of a poem "3.141592 . . ." by Peter Meinke).

Tragedy of the Commons

Thinking in syllable-squares,
recalling ecologist Garrett Hardin (1915-2003)
and his 1968 wisdom, "Tragedy of the Commons."

Maximum               
may not be                   
optimum.

SHE measures the heavens . . .

Today is International Women's Day, celebrated with a charming video at google.com and here with lines from Enheduanna (2285-2250 BCE), the earliest woman known to me who was both poet and mathematician.

     The true woman who possesses exceeding wisdom,
     She consults a tablet of lapis lazuli,
     She gives advice to all lands,
     She measures off the heavens, she places the
               measuring cords on the earth.

These lines (found in the preface, translated from Sumerian sources by Ake W Sjoberg and E Bergmann S J) and much more poetry-with-math are found in Strange Attractors:  Poems of Love and Mathematics (AK Peters, 2008) -- a collection edited by Sarah Glaz and me.

A poetry album by Lucille Clifton

March is Women's History Month and here, today, I celebrate by acknowledging a special woman, Lucille Clifton (1936-2010).  From 1979–1985 Clifton served as Poet Laureate of Maryland.  Her poetry celebrates both her African-American heritage and her womanhood.  Here is "album," a poem in Clifton's spare and un-capitalized style -- and containing a few numbers to help us keep track of the times that are changing.

album     by Lucille Clifton

Sociology of Numbers

Robert Dawson is a mathematics professor at St Mary's University in Halifax, Nova Scotia -- an active mathematician who complements his research activity with mathematics education and with poetry. The following Dawson poem appeared here in 2013 -- in the Journal of Humanistic Mathematics, a journal whose every issue contains some poetry-with-mathematics.

Some Contributions to the Sociology of Numbers     by Robert Dawson

The ones you notice first are the natural  numbers.
Everybody knows their names; they are the anchors,
the stars, the alphas, the reference points. And of course
the rational numbers, who hang out with them,
sit next to them in arithmetic class.

Long division is difficult . . .

Last Monday included a visit with old friends of whom I see too little, Silver Spring artist Mark Behme -- with whom I did some art-poetry collaboration a few years  back -- and Chevy Chase artist-writer-economist-activist, Kyi May Kaung.  After lunch at nearby Mandalay we three walked to Mark's studio and hung out for a while, admiring and talking about his new work.  When I arrived home, I dug out several poems developed from Mark's sculpture -- finding some pieces I'd not thought about for a while.  Here is one of these, a mathy poem that partners with Mark's "Split Tales."

          Which Girl Am I?      by JoAnne Growney

          The girl who’s not forced to divide

          into the good girl and the real one

          is a lucky one.  I was eleven

          when I felt a crack begin.

Angles in Alaska

Last Thursday evening I was honored to read in Takoma Park's Third Thursday poetry series -- along with poets Judy Neri and Kathleen O'Toole -- and my reading focused on poems of my times in Alaska.  The brilliant geometry of  our 49th state affected me strongly and "Angles of Light" became the title poem for a chapbook I published with Finishing Line Press in 2009.  Here is section 3 (of 7) from that poem.

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.

Wartime recurrence

In mathematics, it is not unusual to define an entity using a recurrence relation. 
For example, in defining powers of a positive integer:
       The 2nd power of  7  may be defined as  7  x  7¹ ;
               the 3rd power of  7  may be defined as  7  times  7², 
              and the 4th power is  7  times  7³,
              and, in general, for any positive integer n,  7ⁿ⁺¹  =  7  x  7ⁿ. 

Several weeks ago I attended a reading of fine poetry here in Silver Spring at the Nora School  -- a reading that featured DC-area poets Judith Bowles, Luther Jett, and David McAleavey.  I was delighted to hear in "Recessional" -- one of the poems presented that evening by Jett -- the mathematical pattern of recurrence, building stepwise  with a potentially infinite number of steps (as with the powers of 7, above) into a powerful poem.  I include it below:  

Mother Courage -- and speaking of opposites

     Bertolt Brecht (1898-1956) was a poet, but I have not found mathematics in his poems.  Still, I want to note here a fantastic performance of his play, Mother Courage and her Children, starring Kathleen Turner and a talented ensemble at Washington,DC's Arena Stage.  Invited by my neighbors, Mitzi and Pati, I joined them yesterday for a riveting performance.   Here is a link to "How Fortunate the Man with None," a Brecht poem  heartily sung as "Solomon's Song" in the current musical production.
     And here, with a nod to the mathematical bent of this blog, is a quote from Brecht's Mother Courage that involves counting; also, it is one of many examples of a strategy that Brecht uses often and well -- encouraging an idea by speaking of its opposite. 

To love, in perfect syllables

     While looking for Valentine verse with a math connection, I opened my copy of The Complete Illustrated Works of Lewis Carroll (Chancellor Press, 1982).  And found this one in which Carroll (a pen name for English mathematician Charles Lutwidge Dodson (1832-1898)) uses the word one twice and the word half twice and has counted sounds so that in each line the number of syllables is either a cube of an integer or is perfect.

        Lesson in Latin     by Lewis Carroll    (May 1888)   

Love and Mathematics -- Please be my Valentine!

Poet extraordinaire Maxine Kumin (1925-2014) died yesterday.  

Here is a link to a wonderful eleven of her poems from Persimmon Tree. 

Late in 2007, AKPeters released Strange Attractors:  Poems of Love and Mathematics, edited by Sarah Glaz and me.  Recently at a Howard County Math Festival I met a young man who browsed my copy of this anthology and found it the perfect Valentine.  And so might you.  Below I include a sample from the collection -- a love sonnet by Jean de Sponde (1557-1595), translated from the French by David Slavitt.

 Several previous postings have offered love poems of mathematics and mathematicians; 

these include 9 February 2013, 12 February 2012, 12 February 2011, 10 November 2011,  

30 August 2011, 12 February 2011, and 20 July 2010.

Six Million

       Sometimes numbers become labels for particular events.  When I was growing up, all of us knew 1492 as a label for the discovery of America.  And 1941 recognized Pearl Harbor.  The following selection from a poem by Israeli poet Yehuda Amichai (1924-2000) reminds us of the awful importance of 6 million. 
       While mentioning this poem of witness and remembering, I want also to remind you of the very special Split This Rock Poetry Festival: Poems of Provocation & Witness, to held in Washington, DC, March 27-30, 2014. (Early-bird registration ends on Valentine's Day, February 14th at midnight.)  Hope to see you there. 

Forecasting snow and poetry

Snowbound

is that other world
in which no schedules sit
and no ambitions flare
to interrupt the bluest sky
and whitest field
and coldest air

On shoulders of giants . . .

     Washington, DC is a city rich with both poetry and mathematics.  Last Tuesday evening I attended a Mathematical Association of America (MAA) lecture by author and math historian William Dunham (whom I knew when he taught for a bunch of years at Pennsylvania's Muhlenberg College, in Eastern Pennsylvania, not so far from my employer, Bloomsburg University).  Dunham spoke of insights gained by many hours reading the correspondence of British mathematician and scientist, Sir Isaac Newton (1642-1727).  The discoverer of "gravity,"  and, moreover, both a genius and a disagreeable man.  Still, Newton was a man who gave a nod to his predecessors, "If I have seen further it is by standing on ye sholders of Giants."

Little Boxes

It is hard to know what to say.
Pete Seeger died yesterday at age 94.  
94 = 2 x 47.  47 is prime.
Here is a link to Pete singing "Little Boxes."
Song lyrics are poems.

Graffiti Calculus

     In my dreams I am an artist -- a cartoonist, perhaps, or a graffiti artist -- so skilled with lines and curves and so clever that my art gives pleasure AND delivers a punch.
     And so I am gratefully into the math-art connections provoked by a new book by Mary-Sherman Willis -- aptly titled Graffiti Calculus (CW Books, 2013).  I first met Willis in December, at Cafe Muse (where I will read next Monday, Feb 3 with Stephanie Strickland) and it was my pleasure also to hear her read again from that collection at the Joint Mathematics Meetings.  These poems by Willis give us, in sixty poetic chapters, the story of a mother seeking her son by following his graffiti tags through the city.  Here is a sample, sections 5 and 6: 

Mathematics is like . . .

For angling may be said to be so like the mathematics,
that it can never be fully learnt; at least not so fully, 
but that there will still be more new experiments left 
for the trial of other men that succeed us.  

 Izaak Walton (1594-1683), The Compleat Angler (1653-1676)