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?”    

Poems and Primes

     Recently Press 53 offered a "Prime 53 Poem" poetry challenge -- to write a poem meeting these conditions:
     ·      Total syllable count of 53
     ·      Eleven total lines 
     ·      First three stanzas are three lines each with a 7 / 5 / 3 syllable count 
     ·      Final stanza must be two lines with a 5 / 3 syllable count, for a total syllable count of 53
     ·      Rhyme scheme (slant/soft rhymes are fine) aba cdc efe gg
A Prime 53 poem’s total line count is a prime number (11), the syllable count in each line is a prime number (7 / 5 / 3) with each line of the last two-line stanza a prime number (5 / 3), and the poem’s total syllable count is a prime number (53).

Composite or Prime?

 Her age 

is 9.
 

Is that 9

composite

or prime?

     I have a wonderful collection of grandchildren and am continually on the lookout for both math and poetry activities to include in the things that they enjoy.  Recently I mail-ordered retired fourth-grade teacher Franny Vergo's collection Mathapalooza:  A Collection of Math Poetry for Primary and Intermediate Students (AuthorHouse, 2013).  Here is a sample from that collection: 

Poems starring mathematicians - 3

Today's poems illustrate the satirical humor and rhyme that frequently inhabit poems by mathematicians. (Previous postings of poems about mathematicians include March 23, April 14, and April 15.)

I Even Know of a Mathematician      by John L Drost

        “I even know of a mathematician who slept with his wife only
                   on prime-numbered days…” Graham said.
                            ―Paul Hoffman, The Man Who Loved Only Numbers

Analysis of a sacred site

Poet Allison Hedge Coke descends from moundbuilders and mixed ancestry from several Native American communities with several Europoean ones.  Her verse play, Blood Run, is dedicated to the original citizens of the former city now named Blood Run along the Big Sioux River and to all who work to preserve sacred sites. Moreover, the entire text is mathematically encoded.   Chadwick Allen, an English professor whose interests include American Indian and New Zealand Maori literatures and cultures, has written an article for American Literature that explores the sacred numbers and thematic geometry that connects Hedge Coke's verse with the sacred site; we will offer a sample of Allen's analysis following "Snake Mound"from Blood Run: 

2017 is prime!

     For her December 31 posting in Roots of Unity (Scientific American blog) mathematician Evelyn Lamb wrote about favorite primes -- and starring in her list is our new year-number, 2017.
     My own relationship with primes also is admiring-- here is an excerpt from my poem, "Fool's Gold," (found in full here) that suggests a prime as a suitable birthday gift:

          Select and give a number.  I like large primes—
          they check my tendency to subdivide
          myself among the dreams that tease
          like iron pyrites in declining light.

     "Fool's Gold" appears in my chapbook, My Dance is Mathematics (Paper Kite Press, 2006); the collection is now out-of-print but is available online here. 
     Several poems about primes have been included in earlier postings in this blog.  For example, here is a link to a 2013 posting of "The Sieve of Erastosthenes" by Robin Chapman.  And, for further exploration, here is a link to the results of searching the six years of postings using the term "prime." 

Writing a Proof in Verse -- with ChatGPT3

     Academician Punya Mishra (from Arizona State) is active in integrating various topics and learning patterns.  Back in 2020, at this link I featured his poem, "The Mathematical i"  -- and Mishra has recently shared with me some of his explorations with poetry created by artificial intelligence.

     Back in 2010, Mishra wrote a fascinating poem (The Infinity of Primes")  -- a poem that is also a proof -- which begins with these stanzas:

     Over numbers and their combinations if you sit and mull
     You will find that not one of them is uninteresting and dull.
     But it is a certain class of figures that most attention stirs
     Yes, I am speaking of those special ones, the prime numbers.

     Prime numbers are interesting, the mathematician posits,
     ‘Cos they make up all the others, the so-called composites.
     Here’s an imperfect analogy, a simple little working rule,
     Consider the prime to be an atom, then a composite’s a molecule. 

                        . . .               Mishra's complete 17-stanza poem is available here.

Mishra recently explored the the ability of ChatGPT3 to create a proof of the infinity of the set of primes;  The stanzas below offer a start of a proof-attempt; its completion and two other attempts are available at this link.

Poetry-application of The Fundamental Theorem of Arithmetic

Destructive effects of human greed and neglect on the earth's natural environment are echoed hauntingly in the repetitions within "We Are the Final Ones" -- a dirge-like poem I've constructed using the Fundamental Theorem of Arithmetic.  (For those unfamiliar with the theorem, brief explanation is included in paragraphs that follow the poem):

Prime -- with rhythm and rhyme

     Earlier this year, an email from James D. Herren let me know about his recent e-book, Wit and Wonder, Poetry with Rhythm and Rhyme --  a collection developed to be enjoyed by readers from 5th grade onward.  Herren is an advocate of energetic rhyming verse, AND his collection has some mathy stuff -- including these two little poems.  Thanks, Dave! 

          Prime   by James D Herren

          Our love is prime –  
          Divisible by none
          But you and I,
          For you and I Are One.      

Once upon a Prime . . .

      British Mathematician Sarah B. Hart is receiving wide-spread publicity and praise in recent days for the publication of her book Once Upon a Prime:  The Wondrous Connections Between Mathematics and Literature (Flatiron Books:  New York, 2023).  (Here is a link to an enthusiastic review in The New York Times by Jordan Ellenberg.)   

     My copy of Hart's book arrived last week and I have been enjoying not only the information but the point of view.  Hart's opening chapter is "One, Two, Buckle My Shoe:  The Patterns of Poetry" and, for those of you who don't have the book yet, an excerpt from opening pages of the chapter is included here in an article in Literary Hub.

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

Mathy Rhymes

     Yesterday's note on "A Mathematical Morsel Every Day" -- an American Mathematical Society page-a-day calendar for 2020 assembled by mathematician and writer Evelyn Lamb -- is a fact that involves the first six digits in the decimal expansion of  π :    314159 is a prime number.

And, because this is a math-poetry blog, I have turned this information into a syllable-square rhyme:

           3     1     4

           1     5     9

           is a prime!

Perhaps you'd like to explore more:    Here's a link to previous blog postings with ideas by Evelyn Lamb.    Rhymes often help us to remember; here is a link to postings of rhymes used to remember the digits of π.    AND here is a link to some postings that feature square stanzas.

Number theory is like poetry

     Austrian-born Olga Taussky-Todd (1906-1995) was a noted and prolific mathematician who left her homeland for London in 1935 and moved on to California in 1945. Her best-known work was in the field of matrix theory (in England during World War II she started to use matrices to analyze vibrations of airplanes) and she also made important contributions to number theory. In the math-poetry anthology, Against Infinity, I found a poem by this outstanding mathematician.  

Primes and a paradox

       Canadian poet Alice Major has loved and admired science and mathematics since girlhood and this background brings to her mathy poems both charm and amazement -- qualities that those of us who seriously studied mathematics easily lack.  At the recent BRIDGES conference I had a chance to hang out with Alice for a while and to purchase her latest collection, Standard Candles  (University of Alberta Press, 2015). Such fun to experience her views of infinities and paradoxes, of triangles and symmetries and formulas and ... .  
     Alice has given me permission to post two of her poems here; read on and enjoy "The god of prime numbers" and "Zeno's paradox."  

Mathematicians are not free to say . . .

The poetry of a mathematician is constrained by the definitions she knows from mathematics.  Even though all but one of the prime integers is odd, she cannot use the words "prime" and "odd" as if they are interchangeable.  She cannot use the words "rectangle" and "box" as synonyms.  But the ways that non-math poets dare to engage with math words can be delightful to mathematical ears and eyes.  For example:

       The Wasp on the Golden Section     by Katy Didden

The Math Lady Sings

     One of my daily emails results from a Google Alert -- which I have set up to let me know of new web-postings (or old information newly accessed) that contain the terms "mathematics" and "poetry." (Another online delight comes when I Google "mathematics poetry" (or "math poetry") and browse the images that occur at the top of the list that Google offers.  What fun!)
     It is through a Google Alert notification that I learned of the poetry book It Ain't Over Till the Math Lady Sings by Michelle Whitehurst Goosby (Trafford, 2014).  This Math Lady was the subject of an article by Jennifer Calhoun in the Dotham Eagle (Dotham, AL)  -- and Calhoun put me in in touch with the poet who graciously offered permission for me to present one of her poems here.  Goosby is a teacher and the poem poses a number puzzle for readers to solve.

Five Naturals

Consecutively Odd  

by Michelle Whitehurst Goosby

Math can lead us to Poetry . . .

      As I age and find myself slowing down in my math-poetry ventures it is a delight to see other mathy writers surging with energy and thoughtful publications.

     One frequent source of math-arts connections is Sarah Hart, Professor Emerita of Mathematics, School of Computing and Mathematical Sciences, Birbeck University, London.  Here is a link to an article by Hart containing material excerpted from her collection Once Upon a Prime:  The Wondrous Connections Between Mathematics and Literature (Flatiron Books:  New York, 2023).  

     Once Upon a Prime is a prose explanation completed with frequent literary examples.  Here is a poem that her daughter, Emma, wrote "for Mummy's book." 

Conversational mathematics

In recent weeks I have been experimenting with poems that use mathematical terminology, wondering whether -- since there are readers who are undaunted by unknown literary references (to Dante's Divine Comedy or Eliot's Prufrock, for example) -- some readers will relish a poem with unexplained mathematical connections.  In this vein I have offered "Love" (posted on on November 5) and now give the following poem, "Small Powers of Eleven are Palindromes":

A rhyme about a prime

     Tomorrow, May 16, is the birthday of Pafnuty Chebyshev (1821-1894), who was one of the founders of Russian mathematics and the first to prove (in 1850) a conjecture (about positive integers) made in 1845 by French mathematician Joseph Bertrand (1822-1900) and sometimes referred to as Bertrand's postulate.  This rhyming couplet celebrates that conjecture:

               Chebyshev said, and I'll say it again:
               There's always a prime between n and 2n.

Thanks to Evelyn Lamb's AMS Page-A-Day Calendar for its May 10 alert to the info above.

War and Resistance -- in Eleven Three-line Stanzas

      Recently I searched work by Ukranian authors at the Poetry International website -- hoping to find poems with mentions of mathematics -- but I did not.  Eventually, though, praise of a poem by UK Poet Laureate Simon Armitage led me to "Resistance" (published here in The Guardian) with uses a prime number (11) of stanzas, each with a prime number (3) of lines, to speak of the Russian invasion of Ukraine and its effects.  Here are the opening stanzas:

       Resistance       by Simon Armitage

          It’s war again: a family
             carries its family out of a pranged house
                under a burning thatch.

          The next scene smacks
             of archive newsreel: platforms and trains
                (never again, never again),

          toddlers passed
             over heads and shoulders, lifetimes stowed
                in luggage racks.

          It’s war again: unmistakable smoke
             on the near horizon mistaken
                for thick fog. Fingers crossed.          . . .     

     for the rest of Resistance, follow this link.

     Ukrainian-born Ilya Kaminsky is a very fine poet now living in the US.  Here is a link to one of his poems that describes too many of us, "We Lived Happily During the War."