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.

2015 (and prior) -- titles, dates, links for posts

If you wish to easily BROWSE past postings . . .

Scroll down to find titles and dates and links to postings in 2015.  

OR follow these year-number links to go to lists of posts through 2014, 2013, 2012 and 2011 -- and all the way back to March 2010 when this blog was begun. At the top of the column to the right is a SEARCH box for the blog and this link leads to a PDF file of searchable topics and names of poets and mathematicians presented herein.  Scrolling down the right-hand column leads to a partial list of LABELS that are linked to a list of blogs that contain them.
   Dec 31  Precision leads to poetry . . .
   Dec 28  Can a woman learn science (or mathematics)?
   Dec 24  And now welcome Christmas . . .
   Dec 22  Let us not forget . . .
   Dec 20  Who put the pie in Pythagoras?
   Dec 18  A student writes poetry for a math class . . .
   Dec 15  Generalized Pythagorean Theorem--a visual poem? 

Generalized Pythagorean Theorem--a visual poem?

While thinking about my December 13 posting featuring work by Richard Kostelanetz -- visual poetry with numbers -- I was browsing a fascinating book by Ivan Moscovich, The Puzzle Universe:  A History of Mathematics in 315 Puzzles (Firefly Books, 2015) and came to the following diagram.  I offer it as a visual poem. 

In addition to the squares, what other areas constructed on the sides of a right triangle may be correctly summed to give a third area of the same shape?

Visual poems with numbers

     I have a good friend who does not care for the sorts of poetry that are written today.  When I asked what he likes he cited "When I Was One-and-Twenty" by A E Housman (1859-1936) and the sonnet "Ozymandias" by Percy Bysshe Shelley (1792-1822).   My own preferences in poems, on the other hand, are less certain.  I like to explore, to discover what new things may be said within new forms and constraints.  The following selection, "Notes on Numbers" by Richard Kostelanetz, introduces some of the ideas that this artist/writer/critic explores in his visual poetry -- with numbers -- examples of which are available through links offered at the end of this posting.

Notes on Numbers      by Richard Kostelanetz  

Daughter and Father - a warm geometry . . .

     Kate Stange is a mathematician -- from the Canadian province of Ontario and now at the University of Colorado -- whose father, Ken Stange, is a visual artist and poet. I met them on the internet via our combined interests in the intersections of poetry and mathematics. Lots of years ago, Kate gathered an online anthology of mathy poems. One of her recent online ventures is the development of WIN -- Women in Number Theory.  Below I offer one of Ken Stange's poems, taken from his collection Advice to Travellers (Penumbra, 1994).

Don't Mistake Your Mirror for a Window on the World     by Ken Stange

A reflection is both a thought about the world and the image we see in the mirror. -- Hippokrites

Consider your daughter's first smile.   
.    

Math and Poetry and Climate

Canadian poet Madhur Anand is also an Environmental Scientist; her love of nature and concerns for preserving a habitable climate pervade her work -- and she also scatters throughout it some mathematics.  You can imagine my delight when I found in her new collection (A New Index for Predicting Catastrophes) a poem (included below) that features the identity matrix.  Read on!

No Two Things Can Be More Equal    by Madhur Anand

In undergrad I learned about the identity 
matrix. Ones on the main diagonal and zeros 
elsewhere. Anything multiplied by it is itself. 

Visual-mathematical poetry

      The poems that I write and most of the poems that I include in this blog use mathematical patterns to structure their lines and stanzas or mathematical terminology in their content -- but blogger Kaz Maslanka is a mathematical poet who does something different:  his creations involve mathematical operations and symbols as well as words.  For example, the following visual poem -- involving symbols for "equals" and "divided by" -- comes from a recent posting (in his blog, "Mathematical Poetry") of what Maslanka calls an orthogonal space poem.

"Winning" -- a visual poem by Kaz Maslanka in a form related to the formula for the area of a rectangle,  A = lw or, alternatively, w = A/l.  (Double-click on the image to enlarge it.)

During July 29-August 1, 2015, Kaz Maslanka and I both plan to participate 
in the BRIDGES Math-and-the-Arts Conference at the University of Baltimore -- 
sharing our poetry and enjoying the work of others.  
Join us if you can; no registration fee is required for Friday "Family Day" events 
which include a poetry reading.

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.

Hypertext poetry

     We computer-screen readers all know hypertext; when we read along in Wikipedia or some other online document and come across an underlined term whose font color is light blue -- at such a point we may decide to keep on reading as if we had not noticed the light blue "hyperlink," or we may locate our cursor on that text, click our mouse, and link to a new screen of visual information.
     My first encounter with hypertext poetry was the work of Stephanie Strickland -- in her 1999 love poem, "The Ballad of Sand and Harry Soot," available at this link.  If you, however, are someone who is not yet comfortably familiar with hypertext poetry, I invite you to gain some experience with hyperlinked reading via a prose essay -- reading it first as a traditional essay and then exploring ways that hypertext can vary the experience of reading.

Celebrating a math-woman

I am continually searching for poems that feature past and current math-women.
When you find one (or create one) I will be glad to have you send it along.

The lunar crater L Herschel is named for astronomer Caroline Lucretia Herschel (1750-1848) -- and I have celebrated this math-woman earlier with two fine poems:  "Letter from Caroline Herschel" by Siv Cedering , and "Planetarium" by Adrienne Rich.  Now Herschel is the focus of a forthcoming book by poet Laura Long, The Eye of Caroline Herschel: A Life in Poems, (Finishing Line Press, 2013).  Here, from that collection, is "The Taste of Mathematics:  Caroline Herschel at 31" -- this poem also appears, along with a note about the full collection, in the July 2013 issue of The Journal of Humanistic Mathematics.  

BRIDGES 2013 -- Math-Art in the Netherlands

Since 1998, Summer BRIDGES Conferences have been held -- enthusiastic gatherings where theater and visual art and music and poetry and mathematics engage participants in lively exchange.  This year's conference is July 27-31 in Enschede, the Netherlands, and mathematician-poet Sarah Glaz has organized an outstanding group of talented readers to share their poetry on Sunday, July 28.  Following the featured readers will be an open reading -- and interested readers are invited to email Glaz using the address found here. 
      One of  the scheduled readers on July 28 in Enschede is Scottish poet and statistician Eveline Pye; shown below is one of the poems she will read --  "Love of Algebra" : 

Places to go, ideas to see

     Today I want to suggest interesting internet locations to visit.
     This first link leads to an hour-long documentary on YouTube on the life of Srinivasa Ramanujan (1887-1920). Prepared in 1987 for the commemoration of Ramanujan's 100th birthday, this documentary honors a mathematical genius from whom we continue, still in the 21st century, to learn.  Ramanujan was celebrated earlier in this blog, on 18 February 2011, with a poem by Jonathan Holden.
     I want also to direct you to a Scientific American Guest Blog posting on 9 February 2013 by Bob Grumman.  Since his first SA Guest Blog posting on 28 July 2012, Grumman has been offering, about once a month, his unique views on the intersections of mathematics and poetry.  Primarily interested in visual poetry, Grumman features his own work along with that of numerous other poets -- including e e cummings, Betsy Franco, Scott Helmes, Gerald Kaufman. and Kaz Maslanka.  The 9 February 2013 posting features work by California activist Karl Kempton -- and I offer a sample below to encourage you to visit the SA blog for more of Karl's interesting work. 

Rhyme, beauty, and usefulness

     For many years poetry was transmitted orally and rhymes were vital because they are easily remembered.  In recent years, however, free verse and concrete/visual poems have become vital parts of what we think of as poetry.  Rhyme lost importance when printed poetry became readily available and memory was no longer needed to keep a poem available.  Now, in the 21st century, electronic devices make visual poetry also readily accessible (see, for example, UbuWeb) and poems may also be animated and interactive.

Star, shine bright!

*
on
top
give
light
freely
forever
abundant
brilliant
everywhere

Be our

light!

For more visual poetry of Christmas, enjoy a visit to Bob Grumman's Guest Blog posting for Scientific American.  Thanks, Bob, and Happy Holiday wishes to all.

Surprise me!

Bob Grumman, a mathy poet whose work has appeared in this blog (21 June 2010) and a blogger, has recently been invited to write a Guest Blog for Scientific American.  Here is a wonderful sentence about poetry that I have taken from his posting on 22 September 2012 (the third of his guest postings).

           And I claim that nothing is more important for a poet 
               than finding new ways to surprise people with the familiar.

Visit Grumman's Guest Blog to find his illustrations of poetic surprise; after a pair of visual poems, ten x ten and Ellipsonnet, he discusses a poem by Louis Zukovsky in which the poet describes his poetics using the integral sign from calculus:

∫ 

Zukovsky's definite integral (which Grumman tells us is carefully copyright-protected) has the lower limit "speech" and upper limit "music." 

Poetry heard at JMM

In Boston on Friday evening, January 6, at the 2012 Joint Mathematics Meetings, these folks gathered and read -- for a delighted audience in Room 312 of Hynes Convention Center -- some poems of mathematics.
     Poets who submitted work in advance and were on the "Poetry with Mathematics" program included:
          Jacqueline Lapidus, Judith Johnson, Rosanna Iembo (accompanied by the violin of her daughter Irene Iaccarino), Charlotte Henderson, Carol Dorf (read by Elizabeth Langosy), Sandra Coleman, Marion Cohen, Tatiana Bonch (read by John Hiigli), Harry Baker (via video presented by reading organizer Gizem Karaali -- an editor of the online Journal of Humanistic Mathematics, which sponsored the the reading), and JoAnne Growney (also an organizer of the reading).
     Participants during an "open reading" included: 
          Mary Buchinger, Chris Caragianis, Rip Coleman, Seth Goldberg, Joshua Holden, Ann Perbohner, Pedro Poitevin, and Jason Samuels.

Submit math-science poetry

During the month of November, the online journal Talking Writing is seeking submission of poetry with connections to mathematics and the science.  Submit 4-6 poems to editor@talkingwriting.com.
  

          O                                T     T                 

          ON                                 E               
          ONE                           N     N                

These visual poems "One" and "Ten," above, are mine.

Found in Flatland

Over the years I have shared with friends and students my copy of Edwin Abbott's Flatland (first published in England in 1884) and, alas, not all of these other readers have matched my level of excitement with the small volume.  Even though the book's Victorian attitudes are mostly at odds with my own views, still the tiny book opened me to possibilities of new ways of seeing. Since observing the Flatlanders stuck in two dimensions from my advantageous three-dimensional position, I have wondered how I can now make the leap from three to four or more dimensions.

Right Triangle

The shape of a poem influences our reading of it -- short lines cause reading with lots of pauses whereas we read long lines quickly to get the entire line completed in a single breath. Moreover, some poetry is intended to be primarily visual -- to be taken in as a seen-image rather than read.  UBU Web offers several example of early visual poetry and one may also explore the  UBU Web site for modern examples.  Visual poetry may also be termed "concrete" poetry; consider, for example, "Concrete Block" by Michael J. Garofalo:

How much math does a math-poem need?

Poems offered in this blog vary in the levels of mathematics they contain.  One mathematical reader commented privately that in some of the poems the use of mathematical terms is "purely decorative."  Indeed, some people have particular expectations for poetry that relates to mathematics -- they want the content to use mathematical notation or to present a mathematical truth. Such as, perhaps, this abbreviated statement of the four-color theorem (formulated as a 4x4 square):