Poetry with Numbers -- from Lewis Carroll

     One of the timeless treasures on my bookshelves is a complete collection of work by Lewis Carroll (pen name for Charles Lutwidge Dodgson, 1832-1898) -- writer, puzzler, math guy . . . Here's a poem I found in "Answers to Knot 1" in A Tangled Tale.  (The problem, Knot 1, is stated below the poem.)

from   A Tangled Tale     a response (by authors named below) to a puzzle posed by Lewis Carroll

        The elder and the younger knight
           They sallied forth at three;
        How far they went on level ground
           It matters not to me;
        What time they reached the foot of hill,
           When they began to mount,
        Are problems which I hold to be
           Of very small account.

Logic and Poetry -- from Lewis Carroll

     Australian poet Erica Jolly has alerted me to Lapham's Quarterly -- a magazine, both print and digital, that offers the view that history is the root of all education.  In particular, Jolly directed me to Lapham's presentation of "Sense and Nonsense:  Babies cannot manage crocodiles" by Lewis Carroll.  One of the Lewis Carroll logic puzzles presented therein relates to poetry -- and so I offer it here:

   1. No interesting poems are unpopular among people of real taste;
   2. No modern poetry is free from affectation;
   3. All your poems are on the subject of soap bubbles;
   4. No affected poetry is popular among people of real taste;
   5. No ancient poem is on the subject of soap bubbles.
Answer:  All your poems are uninteresting.

     That the Answer/Conclusion follows using the rules of logic requires some calculations which the interested reader is invited to pursue.  A solution (and additional puzzles) may be found here.

Choosing what words mean . . .

     Nineteenth century writer and mathematician Lewis Carroll (1832-1898) gave his character, Humpty Dumpty, these words:  "When I use a word, it means just what I choose it to mean -- neither more nor less."  And so it is in mathematics -- where, for example, the term "rational" (used in the poem"The Disposition of Art," shown below) has a precise meaning that differs from its typical conversational usage.
     The photo below shows computer-generated art by Silver Spring artist Allen Hirsh -- and, beside it, a framed version of the poem mentioned above.  Our work was exhibited together at last summer's BRIDGES and MAA conferences.  A clearer presentation of Hirsh's art -- "An Outgrabed Mome Rath" -- is available here.  My poem is presented below, beneath the photo.  

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.

Impossible Things Before Breakfast

Literary works by Charles Lutwidge Dodgson (1832-1898, aka Lewis Carroll) are crammed with mentions of mathematics.   One of my favorites (found here with numerous others, including "Ambition, Distraction, Uglification, Derision") is this exchange from Carroll's Alice in Wonderland.

          "Alice laughed: "There's no use trying," she said; "one can't believe impossible things."
          "I daresay you haven't had much practice," said the Queen.  "When I was younger, I always did it for half an hour a day.  Why, sometimes I've believed as many as six impossible things before breakfast."
                                                                                       Alice in Wonderland 

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)   

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.

Poem and parody -- isomorphic?

In mathematics, algebraic systems that have different objects but the same structure are described as isomorphic.  The parody in poetry illustrates the same idea -- a new poem is created that matches the form of a chosen poem, but uses different words.  For example, here are the opening stanzas of a poem published in 1799 by Robert Southey (1777-1843) that was later parodied by Lewis Carroll (1832-1898) in Alice's Adventures in Wonderland.

Special square stanzas

My recent posting (November 14)  of a symmetric stanza by Lewis Carroll illustrates one variety of  "square" poem -- in which the number of words per line is the same as the number of lines.  My own square poems (for examples, see October 7 or June 9) are syllable-squares; that is, each stanza has the same number of syllables per line as there are lines. Lisa McCool's poem below is, like Carroll's, a word-square; in McCool's poem --  in addition to the 6x6 shape -- the first words of each line, when read down, match the first line of the poem, and the last words of each line, when read down, match the last line of the poem.

Symmetric stanza

Although the following stanza by mathematician-author Lewis Carroll first appears to be a merely melodramatic example of Victorian verse, a bit of scrutiny reveals its special symmetry.

     I often wondered when I cursed,
     Often feared where I would be—
     Wondered where she’d yield her love
     When I yield, so will she,
     I would her will be pitied!
     Cursed be love! She pitied me…

This 6 line stanza by Carroll (well-known for for his nonsense verse) reads the same both horizontally and vertically. 

David Blackwell (1919 - 2010) -- and Game Theory

     David Blackwell, the first black scholar to be admitted to the National Academy of Sciences, a probabilist and statistician, died early this month. His NY Times and Washington Post obituaries tell of his many contributions. Blackwell's career connects to poetry through his interest in the Theory of Games.  He was co-author with Meyer Girshick of Theory of Games and Statistical Decisions, 1954, one of the early treatises on game theory.  

Sense and Nonsense

     Nonsense verse has a prominent place in the poetry that mathematicians enjoy. Perhaps this is so because mathematical discovery itself has a playful aspect--playing, as it were, with non-sense in an effort to tease the sense out of it.      Lewis Carroll, author of  both mathematics and literature, often has his characters offer speeches that are a clever mix of sense and nonsense. For example, we have these two stanzas from "Fit the Fifth" of The Hunting of the Snark, the words of the Butcher, explaining to the Beaver why 2 + 1 = 3.