Imagine new numbers

     As a child I wrote poems but abandoned the craft until many years later when I was a math professor; at that later time some of my poems related to ideas pertinent to my classroom.  For Number Theory classes "A Mathematician's Nightmare" gave a story to the unsolved Collatz conjecture; in Abstract Algebra "My Dance Is Mathematics" gave the mathematical history a human component.  
     My editor-colleague (Strange Attractors), Sarah Glaz, also has used poems for teaching --  for example, "The enigmatic number e."  And Marion Cohen brings many poems of her own and others into her college seminar course, "Truth & Beauty: Mathematics in Literature."  Add a west-coaster to these east-coast poet-teachers -- this time a California-based contributor: teacher, poet, and blogger (Math Mama Writes) Sue VanHattum.  VanHattum (or "Math Mama") is a community college math teacher interested in all levels of math learning.  Some of her own poems and selections from other mathy poets are available at the Wikispace, MathPoetry, that she started and maintains. Here is the poet's recent revision of a poem from that site, a poem about the invention (or discovery?) of imaginary numbers.

Imaginary Numbers Do the Trick      by Sue VanHattum    

Imaginary Numbers

     Today a fine poem that plays with the meanings of "real" and "imaginary" -- and one that I like a lot.  Its author, Scottish mathematician-statistician-poet Eveline Pye is, like me, these days enjoying being a grandmother.  

       Imaginary Numbers      by Eveline Pye

       A real life ends, but is imagined  
       by those left behind. An imagined  
       death becomes reality, eventually.   

       The square root of minus one  
       can't exist since a squared number 
       can’t be negative 

       but imaginary numbers yield  
       real answers in the real world.   
       The difference between reality 

       and imagination: a false oasis  
       that blurs, shimmers  
       and melts before my eyes.  

Pye's poem is included in the anthology Bridges Stockholm 2018 from Tesselations Publishing.  This article, "Eveline Pye:  Poetry in Numbers" is a great place to read more about the poet and her work.  

Looking back . . . titles, links to previous posts

      For your browsing pleasure,here are titles and links to previous blog postings.  Below are listed linked-titles of posts from 2018 and up-to now in 2019 and here is a link to a list of titles and links for posts prior to 2018.  

•       March 13   An Interview of/by a Mathy Poet
•       March 11   Celebrate Pi-Day on 3.14
•       March  6    Celebrate Math-Women with Poems!
•       March  4    Math in 17 Syllables

February 2019: 

• Solving for X, Searching for LIFE
• Stories of Black Mathematicians (event postponed)
• All Numbers are Interesting . . .
• George Washington, cherry tree, lifespan . . .
• Musical sounds of math words -- in a CENTO
• If 2017 was a poem title . . .
• Mathematics and Valentine's Day
• Speed flunking math . . . NO, NO!
• Quantum Lyrics -- Poems

Considering opposites . . . and finding union . . .

     The categorization of different points of view as opposites can disappear as a unified system embraces both of them.  In mathematics, the counting numbers and their opposites become the integers,the rational and irrational numbers join to give the reals, the real and imaginary numbers yield the complex numbers.  In our global world with its biases and dangers and uncertainties, we will, I hope, evaluate our differences and unite our strengths to form a larger, stronger unity.
     A syllable-square poem by Carmela Martino (offered below) illustrates one of the unifications that can benefit our society: inclusion of the arts to enrich the sciences, from STEM forming STEAM.

Carmela Martino's poem first appeared here at TeachingAuthors.

Numbers from the Piano

     Of all of the things we might try to say when we sit down to write a poem, which are the ones we should choose?  Sometimes we may say what first occurs to us -- begin to write and keep going until we are done.  This may suffice -- or it may seem to lack care.  To be more careful, we might seek a pattern to follow:  perhaps we might form lines whose syllable-counts follow the Fibonacci numbers.   Or construct a sonnet -- fourteen lines with five heart-beats per line and some rhyme.  Or devise a scheme of our own.

The magic of "i"

 An exciting math event occurred last week -- the opening of MoMath, 

a Manhattan museum that makes math fun.

 

Still thinking about complex and imaginary numbers (see Sue VanHattum's poem in the December 16 posting), I want to offer a couple of stanzas by Paul Hartal -- selected from "Voyage around the Square Root of Minus 1"  -- stanzas that are part of a lengthy consideration of connections between the arts and the sciences.  I do not always agree with Hartal's viewpoints -- but they are interesting to consider.

from  Voyage around the Square Root of Minus One     by Paul Hartal 

. . .  Mathematical equations are embedded
       with mysterious forces
       and their uncanny power transcends
       the cognitive faculties of the human mind.

Stimulate Math Class Discussion with Poems

     Sometimes teachers want to understand more about their students' attitudes and concerns about learning a particular subject.  Often, rather than asking direct questions like, "What is your difficulty?" or "Why don't you like geometry?" it can be useful to stimulate discussion with a poem.   The website of the Academy of American Poets, offers at this link a wide selection of poems about school subjects.  Scrolling down through this long list, eventually one comes to Poems for Math Class -- with poems for Algebra, Calculus, and Geometry.  

     One of the Academy's suggested poems is "Calculations" by Brenda Cardenas  -- I offer the first stanza below -- the complete poem is included here in this posting from November, 2017.  

          from    Calculations      by Brenda Cárdenas    

Mathematical 'grooks' from Piet Hein

Piet Hein (Denmark, 1905-1996) was many-faceted--by times a philosopher, mathematician, designer, scientist, inventor of games and poet. He also created a new poetic form that he called 'grook' ("gruk" in Danish). Hein wrote over 10,000 grooks, most in Danish or English, published in more than 60 books. Some say that the name is short for 'GRin & sUK' ("laugh & sigh", in Danish).  Here are samples, with links to more:

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 

Is mathematics discovered -- or invented?

The issue of whether mathematics is invented or discovered is posed often.  Less frequently, queries as to where poetry falls in these categories. Perhaps individual answers to these questions depend on how each of us, from the inside, views the workings of the mind.   Here we have, from poet (and math teacher) Amy Uyematsu,"The Invention of Mathematics."  

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.

A Life Made to Count

     The title of this blog-post is part of a headline from The Washington Post -- a headline for a review by GW Professor Lisa Page  of a posthumously published and recently released memoir by Katherine Johnson (1918 - 2020) :  My Remarkable Journey:  A Memoir, written with assistance from Joylette Hylick, Katherine Moore and Lisa Frazier Page (Amistad, 2021).

     As you might expect, numbers are at the center of Johnson's memoir -- numbers never intimidated Johnson — in fact, they thrilled her. The symmetry, the structural interplay of equations and formulas, were always in her head.  (Read a bit of the book here.)

     As Johnson looked back over her life of more than one hundred years, I too was prompted to looks back -- to an article of mine entitled "MATHEMATICS AND POETRY:  ISOLATED OR INTEGRATED?" and published in the Humanistic Mathematics Network Newsletter (forerunner of the Journal of Humanistic Mathematics) in May, 1991 -- and available here.  And I can't resist quoting a bit from the article, sharing some phrases from the poem "Poetry" by Marianne Moore (1887-1972).

       . . . things are important not because a
       high-sounding interpretation can be put upon them
       but because they are useful . . . the same thing
       may be said for all of us—that we do not admire
       what we cannot understand. 

       [Not until we] can present for inspection,
       imaginary gardens with real toads in them
       shall we have it . . .

Moore's complete poem is available here.

2014 (and prior) -- titles, dates of posts

Scroll down to find titles and dates of posts in 2014.  At the bottom are links to lists of posts through 2013 and 2012 and 2011 -- and all the way back to March 2010 when this blog was begun.   This link leads to a PDF file that lists searchable topics and names of poets and mathematicians presented herein. 

Dec 30  Be someone TO COUNT ON in 2015
Dec 28  A Fractal Poem
Dec 25  A thousand Christmas trees
Dec 24  The gift of a poem
Dec 20  The Girl Who Loved Triangles 

The wealth of ambiguity

When we read these lines by Robert Burns (1759-1796),

     Oh my luv is like a red, red rose,
     That's newly sprung in June . . .
    
we don't know whether he compares a woman he loves to a flower or whether it is his own emotion he describes.  And the multiplicity of meanings is a good and pleasing thing.  Similarly, when we read the problem,

     Solve the equation, x² + 4 = 0 

Mathematics . . . an encrypted love song . . .

      Australian poet Geoffrey Lehmann is also a writer of children's books and a tax lawyer.  This mathy poem comes from his collection, Spring Forest (Faber & Faber, 1994); I found it in the anthology A Quark for Mister Mark:  101 Poems about Science (editors--Maurice Riordan, Jon Turney; Faber & Faber, 2000) -- a collection introduced to me by Australian poet, Erica Jolly.

       Not Yet Found     by Geoffrey Lehmann

       I chose the name Spring Forest
       and I've yet to find the spring.

       Some unfinished equations
       are the closest I've come
       to the puzzle of why I'm here.   

Mathy Poets plan for 2021 BRIDGES Conference

      The Annual BRIDGES Math-Art Conference will be virtual again this year (August 2-6, 2021) and mathematician-poet Sarah Glaz has developed an online array of poets and poetry to be part of this program.  Bios and sample poems are already available here.

      Participating poets include:  Marian Christie, Carol Dorf, Susan Gerofsky. David Greenslade, Emily Grosholz, JoAnne Growney, Lisa Lajeunesse, Marco Lucchesi, Mike Naylor, Osmo Pekonen, Tom Petsinis, Eveline Pye, Any Uyematsu, Ursula Whitcher -- and, also, these open-mike participants: Susana Sulic, S. Brackert Robertson, Stephen Wren, Marion Deutsche Cohen, Connie Tetteborn, Jacob Richardson, Robin Chapman. Stephanie Strickland.  (Bios and sample poems here.)

     Here is a sample from the BRIDGES poetry program:

Descartes   by Eeva-Liisa Manner
                        translated from the Finnish by Osmo Pekonen

I thought, but I wasn't.
I said animals were machines.
I had lost everything but my reason.  

Poetically exploring the the invention of "i"

     Today's posting features work by Punya Mishra, professor and administrator at Arizona State University -- a writer who offers explanations of mathematical concepts in his poems, explanations that can appeal to students!   Mishra's website features several mathy poems and in our email correspondence he said that "The Mathematical i" is his favorite.  Here are are several stanzas:

from  The Mathematical i     by Punya Mishra

       The negative numbers were full of dismay
       We have no roots, they were heard to  say
       What, they went on, would be the fruit
       of trying to find our square root?

       Matters seem to be getting out of hand
       Since the negatives have taken a stand,
       On the fact that positives have two roots, while they have none.
       They plead, would it have killed anybody to give us just one?
       The square roots of 4 are + and – 2! As for -4 ?  How unfair,
       He has none! None at all. Do the math gods even care?

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, 

One-sentence Poems

     Recently I came across the website onesentencepoems.com and, enjoying the items' brevity, I did some browsing -- and term-searching -- looking for mathy poems.  Here are two samples by teacher and poet Jeffrey Park -- originally from Baltimore, now a teacher in Germany.

By Degrees   

She always sleeps with protractor and compass
on the bedside table, never knowing when
a sudden fit of geometry will strike in the night.

Numeric

Numbers pelt down from an infinite sky, neither irrational nor imaginary,
the angular ones, 4s and 7s, doing maximum damage.

These one-sentence poems -- and another --  by Jeffrey Park are found online here.

The epitome -- Euler's Identity

Mathematics is a visual language.  As with poetry, placement on the page is a key ingredient of meaning.  Here is one of my favorite visual poems, "The Transcendence of Euler's Formula," by Neil Hennessy, a Canadian poet and computer scientist.  For additional math-poetry from Neil, follow the link.

          epitome
          epitome
          epitome
          epi+ome
          epItome
          _____________
          epit0me