Division by zero

The November 2011 issue of the Scottish ezine, The Bottle Imp, is just out and it includes my review of poet Brian McCabe's Zero (Polygon, 2009). To stir your interest, I include a few lines from McCabe's title poem (which chronicles the irregular history of zero) -- and then offer a human interpretation of division by zero in a poem by Ann McNeal.

Something or Nothing -- Thinking about Zero

     The site of the 2019 Bridges Math-Arts conference has been announced  -- it will meet in Linz, Austria next July.  This link leads to the archives of the 2018 and earlier conferences.  Each recent year a poetry reading (coordinated by Sarah Glaz) has been part of the Bridges activities -- and this year a poetry anthology also was compiled.  Here is a poem by Canadian poet Alice Major that was featured both in this year's reading and in the anthology  -- a poem that also appears, along with other math and science poems, in Major's latest collection, Welcome to the Anthropocene. (University of Alberta Press, 2018).  Major's poem examines death and, as it does so, explores various meanings of zero.

Zero divided by zero     by Alice Major

There is no right answer.

The trains of logic crash, annihilate

certainty. Zero is just as good an answer

as one. Nothingness or loneliness.

There is no right answer.    

Number Personalities . . .

      Sometimes our experiences with objects or ideas leads us to assign them personalities -- a notion illustrated in the poem "Zero," by Sue Owen, a poem that lives on my shelf in the anthology Verse and Universe:  Poems about Science and Mathematics, edited by Kurt Brown (Milkweed Editions, 1998), and offered below.

Zero     by Sue Owen

       This is the story of zero,
       born to live a life
       of emptiness, only
       child of plus and minus.

       Its bones invisible
       so it could be seen through
       like an eye.
       With that vision, you could      

NOTHING is SOMETHING

Thinking today about ZERO -- zero tolerance, zero fear!

     In recent days, there's been widespread reporting of results of a study done by the National Academies of Sciences, Engineering and Medicine concerning the large number of instances of sexual harassment in scientific professions, the most common type being   "degrading jokes and comments that made women feel excluded."
     These findings take me back to the 1980's and "affirmative action" at Pennsylvania's Bloomsburg University (where I was a member of the Mathematics Department).  The University had an Affirmative Action Officer who worked to help faculty and staff develop behaviors and policies that endeavored to end discrimination against women and minorities.  One important test of the appropriateness of an activity was a "symmetry test" -- if a remark or act did not seem proper when the roles of two participants were reversed, then the original was probably something to avoid. In those days, my male colleagues needed to reconsider some of their behaviors and I needed to overcome my fear of speaking up.
      The concept of  zero as "something" that signifies "nothing" is an ever-thought-provoking one.  In support of ZERO TOLERANCE -- with a goal of NOTHING, I offer the following poem, "The Zero," by Israel Har.   

The Role of Zero

     In mathematics, as in poetry, multiple meanings are common and create power for the language.   For example, the number 0 is an idempotent element, an additive identity, a multiplicative annihilator -- and it also plays the role of something that may represent nothing.
     In Dorothea Tanning's poem below -- I found it at poets.org -- zero takes on still another of its roles, that of place-holder -- as in the numbers 101 and 5000, for example.

       Zero     by Dorothea Tanning (1910-2012)

       Now that legal tender has
                    lost its tenderness,
       and its very legality
               is so often in question.
       it may be time to consider
       the zero--
                    long rows of them.
            empty, black circles in clumps
                              of three, 

Dividing by Zero

Fairy godmothers have their magic wands and mathematician have division by zero as a way to make the impossible happen -- for example, we can show that 2 equals 3:

Latitude, longitude, and inauguration

Elizabeth Bodien now lives in a rural area in eastern Pennsylvania -- settling there after other lives in California, in Japan, in West Africa.  Here is a narrative poem using the geographic numbers of latitude and longitude drawn from the years that she was a childbirth instructor in West Africa.

Zero-Zero     by Elizabeth Bodien

Zero Man of India

     An interesting story that Google led me to is told in this article about "Zero Man of India" --  the article tells of  Shahbaz Khan, famously known as Shahbaz Hakbari, a multifaceted individual with talent in poetry, prose, mathematics, and education -- well-educated AND he he is a widely celebrated teacher.

"Mathematics and poetry may seem like two different worlds, but both require creativity, imagination, and thinking outside the box," Shahbaz Khan explained.

The article "Zero Man of India" contains many mentions of Khan/Hakbari's life as a poet -- but has no poems.  Nonetheless, the phrases quoted are poetic -- and, below, I have given two of them the shapes of  poems.

Zero Power

To neutralize the differing effects of any non-zero numbers -- to wipe out vast differences between numbers -- we may raise each of them to the power zero.*  When 0 is applied as the exponent for any nonzero number, the result is 1.  So 7⁰ = 1 and 5378 ⁰ = 1 and (.001)⁰ = 1.   And here are "zero power" and other mathematical concepts interpreted in a poem.

     N to the Zero Power     by Laurie Clemens

     He holds one photograph
     featuring one man and one woman.

     Three birds perch on two wires
     forming an isosceles triangle over the last
     red brick street in town.

Seeing the World through a dual prism . . .

     Based in Melbourne, Australia, Tom Petsinis is a mathematics adviser at Deakin University and is author of nine poetry collections as well as theatrical works and books of fiction.  He also is involved in the worldwide BRIDGES organization --which meets annually to investigate and celebrate connections between mathematics and the arts.  This year's BRIDGES conference will be held July 27-31 in Halifax, Nova Scotia and next year's conference is planned for August 1-5, 2024 at Virginia Commonwealth University in Richmond, Virginia.

     Below is "Zero" -- a mathy poem by Petsinis which is also offered as a sample at this BRIDGES link (a link that advertises and celebrates those poets participating in the 2022 conference).

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?”    

Inventing Zero

     A Pennsylvania friend who is now in Oklahoma, Sharon Solloway -- whom I got to know when we were both faculty members at Bloomsburg University (now part of Commonwealth University)  --  shared with me on Facebook the following mathy poem,  "Inventing Zero" by Canadian astronomer Rebecca Elson (1960-1999).  Found in Elson's collection,  A  Responsibility to Awe (Carcanet Classics, 2018)  "Inventing Zero" is available along with other samples of Elson's work here at this link.

       Inventing Zero      by Rebecca Elson

               First it was lines in the sand,
               The tangents, intersections,
               Things that never met,
               And you with your big stick,
               Calling it geometry,   

I'm tired of being a zero vector . ..

there are more       to figures       than ever meets       the eye

     Inexhaustible GOOGLE has led me to a website "The Best Philippine Short Stories" which contains not only stories but also artwork and poems.  Eileen Tupaz, now a central character in Quezon City's White Space Wellness Studio, has given me permission to include samples of her math poems first published by BPSS -- poems written in 2000 when she was a student at Ateneo de Manila University.

Poems by Eileen Tupaz

     soulmates
  
     we are all of us
     nonsingular creatures
     whose identities
     must be affirmed
     before our inverses
     can be found   

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.

Blogging about Math and Poetry

      One of my recent online pleasures has been visiting the Poetry Blogging Network -- I was led there because it mentions my blog but I also found a rich array of other treasures to explore.  One of these is the book of kells -- a blog written by poet, editor, and teacher Kelli Russell Agodon.

     One of the very special poems I found (posted on February 3, 2024 ) is "Zero Sums" by Luisa A. Igloria  -- I offer below its opening lines:

     Zero Sums     by Luisa A. Igloria

          Driving back from the gym, I listen to
          a radio program where two mathematicians

          are talking about zero. I'm parked in front
          of my house, but their conversation keeps me

          glued to the seat. One of them says in math,
          whatever operation you do, you need to also be 

          able to undo—just like with multiplication and
          division. Unless you divide by zero, in which case

          you get the impossible. Or you get . . . .                   

Igloria's complete poem is found here.. 

.More about Virginia poet Luisa Igloria is available here.

This link leads to an earlier blog posting that features work by Igloria.

The gift of a poem

     In this holiday season of giving, sometimes the gifts are poems -- and sometimes mathy poems.  A few days ago, "Zero" by Robert Creeley (1926-2005) arrived in an email from Francisco José Craveiro de Carvalho, a Portuguese mathematician who loves poetry and has translated many math-related poems into his native language -- a seeker and finder of such poems who shares them with me.  (See also 23 October 2010 and 17 September 2013.)  At this time of giving and receiving, enjoy playing with these thoughts of zero as nothing or something.

          Zero     by Robert Creeley

                              for Mark Peters

          Not just nothing,
          Not there's no answer,
          Not it's nowhere or
          Nothing to show for it -- 

The infinitude of ecstacy -- a la Israel Lewis

Israel Lewis is the pen name of a polymath who earned his living as a scientist and is a writer in his retirement.  His webpage offers a variety of his creations--many of them permeated with mathematics.

Number personalities

In his collection, Zero, Scottish poet Brian McCabe raises questions about numerical classifications.  He begins "The Fifth Season" with "Everyone talks of the four / -- none speak of the fifth." Another poem, "The Seventh Sense, " moves from a similar beginning " . . . none speak of the seventh" into a dreamy apprehension of the magical possibilities of items not yet classified. The following selection from Zero, "Triskaidekaphobia," offers remedies for the fear of bad luck brought by 13. 

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

Zero-sum game -- in a poem by Okigbo

Game theory (with origins in the 1930s) was initially developed to analyze competitive decisions in which one individual does better at another's expense--"zero sum" games--and this term has become a part of everyday vocabulary; here we find it in a poem by Christopher Okigbo (1932-1967), a Nigerian poet.