Puzzle poems from Benjamin Banneker

Benjamin Banneker (1731 - 1806) was a free African American mathematician and almanac author -- also an astronomer, surveyor, and farmer. (I learned of his work through my friend Greg Coxson, an engineer, teacher, and fan of mathematical poetry -- and Coxson learned of Banneker through a school project of his son.)  Beyond building a wooden clock and helping to lay out the borders of Washington, DC, Banneker predicted the 1789 solar eclipse and included rhyming math puzzles in his almanac.  Coxson introduced me to a fine website, established by by John F. Mahoney of Washington, DC's Benjamin Banneker Academic High School, entitled The Mathematical Puzzles of Benjamin Banneker.
     Banneker's Almanack had an eclectic mix of astronomy/astrology, medical advice, weather prediction, and other things.  Here's a math-problem-poem from that Almanack -- found, along with others, at Mahoney's site: 

How should a professor groom for math class?

     One of the rewards of many new endeavors is making new friends -- and one of the special connections I have made through math-poetry endeavors is Gregory Coxson, an engineering professor at the US Naval Academy.  Greg has frequently alerted me to new mathy poems and, this fall, he sent me an interesting poem that he had written, a thoughtful comment on looking beyond appearances to what is more important. 

My PDE Professor    by Gregory Coxson

He sometimes wore those marine corps sweaters
  The ones in army green, that look the best
On more triangular figures than his.
  And then those ridiculous epaulets
How did his wife let him out of the house?    

Dinner at a Math Conference . . .

     A strong advocates of humanistic mathematics -- supporting links between mathematics and the arts -- is Greg Coxson, both a poetry fan and a Research Engineer in the Department  Electrical and Computer Engineering at the US Naval Academy.  Greg has been, over the years of this blog, a valuable contributor of information about mathy poems and poets.  Recently Greg has turned his hand to some poetry of his own -- and he has sent me this:

Crawfish Dinner at a Computational Theory Conference 

by Greg Coxson

In this drama, the crawfish come off the best
   Offered by our host as a gift of local color,
They look up innocently from their pile,
   Radiant in their trim carmine carapaces.

Next, there are the computational theorists
   Many of them from a more formal continent
Some are my heroes I am seeing up-close now,
   Not from photos at the end of reference sections.   

A Poetry Cube

      Gregory Coxson, professor and researcher in the Department of Electrical and Computer Engineering at the US Naval Academy, is a supporter of integration of the arts with the sciences and enjoys writing poems.  (Here is a link to his previous appearances in this blog.)   Recently Greg has sent me what he calls a CUBE poem (6 stanzas, 6 lines per stanza, 6 syllables per line).   It's FUN to read -- I offer it below:

If I Wrote Poetry     by Gregory Coxson

If I wrote poetry
  It would be efficient,
Stripped-down, like Chinese art,
  Only the sparest lines
Placed by easy habit
  Learned from ten thousand tries    

Poetry on the Side . . .

     My friend Gregory Coxson (engineering professor at the US Naval Academy) is an explorer of new ideas and I enjoy his frequent emails that share his discovered math-poetry connections.  Recently Coxson introduced me to the website of retired Virginia Tech professor Ezra Brown and, following the link Inspirational and Fun Stuff, I found this interesting collection of number-related Haiku --  beginning with a recollection of September 11. 

Day of Horror

There is no doubt that
on September Eleventh
God sat down and cried.

“I worked hard…”

Bach was prolific:
One thousand compositions
and twenty children.  

Sometimes ONE is also TWO

     A long-time supporter of this blog and of math-poetry connections is Gregory Coxson, Research Engineer at the US Naval Academy-- and he has recently shared with me the following poem, a translation of work by German writer and scientist Johann Wolfgang von Goethe (1749-1832); publication and translation details may be found online here.  Coxson was drawn back to his memories of this math-linked poem with the arrival of November and at his campus the bright-yellow leaves of the ginkgo trees.

     Ginkgo Biloba      translation of work by Johann Wolfgang von Goethe

       In my garden’s care and favour
       From the East this tree’s leaf shows
       Secret sense for us to savour
       And uplifts the one who knows.

       Is it but one being single
       Which as same itself divides?
       Are there two which choose to mingle
       So that each as one now hides?

       As the answer to such question
       I have found a sense that’s true:
       Is it not my song’s suggestion
       That I’m one and also two?

More about Goethe's poem can be found here at WisdomPortal.com.

Clear the head for best thinking by walking

     An engineer -- and friend -- who is a long-time supporter of the STEM to STEAM program is US Naval Academy Professor Greg Coxson.  Although a member of the Electrical and Computer Engineering Department, Coxson has a strong interest in the arts.  He reads widely and has suggested a number of poems  for this blog.  Recently his recommendation was "Solvitur Ambulando" by Billy Collins, a poem found on pages 92-93 of the collection The Rain in Portugal (Random House, 2016).   Below I offer the opening stanza and the final, mathematical, portion of Collins' fine poem.  (Go to the book and read more!)

from   Solvitur Ambulando    "It is solved by walking."     by Billy Collins

       I sometimes wonder about the thoughtful Roman
       who came up with the notion
       that any problem can be solved by walking.
. . .  

Perfect as soap bubbles

An alert to today's poem came from Greg Coxson, a University of Wisconsin-educated, Silver Spring-based, radar engineer who loves mathematics and poetry.  The poem is by Howard Nemerov  (1920-1991) and it builds to a presentation of its perfect mathematical image near its end.  

Poetry of Mathematics--David Eugene Smith, 1926

      Recently poetry-fan and occasional versifier Greg Coxson, a Research Engineer in the Department  Electrical and Computer Engineering at the US Naval Academy, sent me a link to an essay by mathematician and teacher David Eugene Smith (1869-1944) -- published in The Mathematics Teacher in 1926 and entitled THE POETRY OF MATHEMATICS.  Greg has been, over the years of this blog, a valuable contributor of information about mathy poems and poets -- and some poetry of his own.

     Early in the essay, Smith quotes Thoreau:

We have heard much about the poetry of mathematics, but very little of it has yet been sung.  The ancients had a juster notion of their poetic value than we.  The most distinct and beautiful statements of any truth must take at last the mathematical form. 

     Lots of quotes and viewpoints are offered in Smith's essay and, at the end he speaks of the role of teachers " . . .  mathematics may become and does become poetry in the enthusiasm of an inspired and an inspiring teacher."

The Secret Sits     by Robert Frost (1874-1963)

               We dance round in a ring and suppose,
               But the Secret sits in the middle and knows.

Lots more of Frost's words are available here.

A Man-Made Universe and "found" poems

 Some poems are found rather than crafted.
It's such fun -- can happen to anyone -- 
to be reading along and find a poem. 

     This post continues (from the June 4 posting) consideration of lines that were not initially written as poetry but have been later discovered to have the desirable characteristics of a poem.
     In an early-April posting I offered a poem-in-a-photo, a poem created of book spines -- and the bottom book in my pile of six is Mathematics, the Man-Made Universe:  an Introduction to the Spirit of Mathematics by Sherman K Stein (Third Edition, Freeman, 1976).  Reprinted in 2010 in paperback format, Stein's textbook -- for a "general reader," a curious person who is not a mathematician -- has been on my shelf for many years and, though I never taught from it, I have enjoyed it and shared it with friends (and I love its title). Recently, in the opening paragraph of Stein's Chapter 19 (page 471), I found a poem:

Number Patterns in Nature

     Naval Academy engineering professor and math-poetry fan Gregory Coxson has recently introduced me to poetry by Mattie Quesenberry Smith at VMI (for a bio of Smith, go to this page, scroll down, click on BIO) -- she and I have connected and she has shared with me several of her mathy poems; here is one about the Fibonacci numbers -- a number pattern found in nature:  

     Fibonacci Found It       by Mattie Quesenberry Smith

        It is spring on House Mountain,
          And I am wondering how
          Fibonacci found it
          And believed that it matters,
          That sequence of numbers
          Hinging on what precedes them,   
          Running this springtime show.
          Soon spring will be sanguine,
          Shouting from steep shadows,
          And the eight-petaled bloodroot,
          A robust and pure lion
          Rooted in his bloody rhizome,
          Is a rare know-it-all.
          A leaf encircles his stem.
          Its strange, veined palm
          Shields him from blood’s loss.

 ”Fibonacci Found It” was first published in Thirty Days: The Best of the Tupelo Press 30/30 Project’s First Year,” edited by Marie Gauthier, Tupelo Press, 2015. Reprint rights are retained by author.

More statistics -- from Hiawatha

As the author of this poem owes a debt to Henry Wadsworth Longfellow, I too owe Greg Coxson -- who showed the poem to me.

Hiawatha Designs an Experiment   by Maurice Kendall

Hiawatha, mighty hunter
He could shoot ten arrows upwards
Shoot them with such strength and swiftness
That the last had left the bowstring
Ere the first to earth descended.
This was commonly regarded
As a feat of skill and cunning.

A sestina from Rudyard Kipling

My father died many years ago, when I was still a young girl, and I have few possessions that were once his.  One is The First Jungle Book, signed "Fulton Simpson" with his hand; it is very precious.  By extension, all work by Rudyard Kipling (1865-1936) falls under my interest.  And a sestina by Kipling is worthy of note:

Sestina of the Tramp-Royal     by Rudyard Kipling

     1896

Speakin’ in general, I ’ave tried ’em all—
The ’appy roads that take you o’er the world. 
Speakin’ in general, I ’ave found them good 
For such as cannot use one bed too long, 
But must get ’ence, the same as I ’ave done, 
An’ go observin’ matters till they die.

Math in Shakespeare . . .

     Yesterday, April 23, is the day on which William Shakespeare's birthday is celebrated; he was born long ago in 1564 and the actual date is uncertain.   The BBC Radio Newshour today featured this event in its broadcast  and told of ways that Shakespeare used mathematical ideas in his writing.  A broadcast recording is available at this link; the Shakespeare-math info begins at approximately 25 minutes into the show.   Ideas come from a book that is coming out next September,  Much Ado About Numbers: Shakespeare's Mathematical Life and Times by Rob Eastaway. 

One of the interesting items I found as I browsed was the phrase

    eight score eight       in Othello -- a three-syllable way for saying 168.

     Here is a link to an article that focuses on Shakespeare's use of zero.

Puzzles, puzzlers, and parody

     For lots of fun, go to plus online magazine at this link to find a poem that requires a knight's tour of a chess board for you to unscramble its words and read its eight lines.

Poetry by Victorian Scientists

     Thanks to Greg Coxson who has recently alerted me to this 2011 article by Paul Collins in New Scientist, "Rhyme and reason: The Victorian poet scientists."  In the article, Collins is reviewing an anthology edited by Daniel Brown entitled The Poetry of Victorian Scientists: Style, Science and Nonsense (Cambridge University Press, Reprint-2015).
     The article has links to poetry by James Clerk Maxwell (1831-1879), William J. Macquorn Rankine (1820-1872), and James Joseph Sylvester (1814-1897).  Below I offer two of the eight entertaining stanzas from Rankine's poem, "The Mathematician in Love." (This poem and Maxwell's "A Lecture on Thomson's Galvanometer" also appear in the wonderful anthology that Sarah Glaz and I edited -- Strange Attractors:  Poems of Love and Mathematics (A K Peters/CRC Press, 2008, now available as an e-book.)

from  The Mathematician in Love     by William J Macquorn Rankine  

Celebrate Francis Su

     In this morning's email I got a link (Thanks, Greg Coxson!) to this story that celebrates the talented mathematician and compassionate human being, Francis Su.  Dr Su (of Harvey Mudd College) has recently completed a term as president of the Mathematical Association of America.  Here is a link to Dr Su's retiring presidential address -- for which he received a standing ovation.  Read.  Learn.  Admire.  Celebrate.  Imitate!
     Scrolling down in this blog to my posting for January 11, 2017 will lead you to links to several poems that celebrate mathematicians. And a blog-SEARCH using "mathematician" will find even more such poems.  Enjoy!

       A thorough advocate in a just cause, 
             a penetrating mathematician facing the starry heavens, 
                   both alike bear the semblance of divinity.
                                                                     -- Goethe (1749-1832)

From a math-friend and an Ohio poet

     One of the wonderful things about writing a blog about my paired passions of poetry and mathematics is that the blog connects me with fascinating and generous people whom I might not otherwise meet. One of these is Marylander Greg Coxson -- physicist, engineer, mathematician, Operations Researcher -- who took three years of Latin in high school and loves words.  With interests in art and poetry, Greg has organized exhibits of math-related art -- and is a regular recommender of mathy poems for this blog.
     A week or so ago Greg alerted me to an NPR interview with Ohio Poet Laureate Amit Majmudar (a radiologist as well as a poet) -- letting me know that Majmudar's poetry was rich with mathematical imagery.  Following Greg's lead, I found Majmudar's website and was able to contact both Majmudar and his publisher, Knopf, for permission to offer these mathematical poems.
     Here, from Amit Majmudar's new book Dothead, are two sections of the poem "Logomachia" -- sections alive with geometry and logic.  The first, "radiology," is visually vivid; the second, "the waltz of descartes and mohammed," is a sestina that plays with the logic of word-order.  

Pushkin poetry, Markov chains

A Markov chain is a mathematical process that can be used to answer questions such as these:
          If the current letter I am reading is a vowel, what is the probability 
          that the next letter will be a vowel?  A consonant? 
Answers from these may be combined to create more lengthy predictions -- about the 3rd letter after a given one, or the 10th -- and so on. 
     A recent article by Brian Hayes in American Scientist (brought to my attention by Greg Coxson) alerted me to the fact that it is 100 years since the Russian mathematician A. A. Markov (1856 - 1922) announced his findings about these transition probabilities -- and, moreover, his work was based on analysis of poetry; the poetry was Eugene Onegin, a verse-novel in iambic tetrameter by Alexander Pushkin (1799-1837). Markov's analyis dealt with Pushkin's novel as a long string of alphabetic characters and he tabulated the categories of vowels and consonants for about 20,000 letters. (For a host of details, visit Hayes' careful and interesting article.)

Circle Power

Everything the Power of the World does is done in a circle

         by Black Elk (1863-1950)  (translated from Sioux)

Everything the Power of the World does
is done in a circle.  The sky is round,
and I have heard that the earth is round
like a ball, and so are all the stars.
The wind, in its greatest power, whirls.