Monday, October 22, 2018

Describing a scene with numbers

     Lana Hechtman Ayers is a versatile and accomplished poet who also has a degree in mathematics --  in her poem below, she paints a picture with numbers.

       Algebra     by Lana Hechtman Ayers

       4 women
       of 3 generations
       are walking along
       2nd Street together
       in the rain
       without any number
       of umbrellas.

Thursday, October 18, 2018

Read your Math-Poetry in Baltimore, 1/18/19

You are invited be part of a reading of math-linked poetry 
sponsored by the Journal of Humanistic Mathematics  and  SIGMAA-ARTS
Baltimore Convention Center  Room 301  
Friday, January 18, 2019  7 - 8:30 PM

 Celebrate MATH PEOPLE with poems! 

All interested in mathematical poetry/art are welcome.  Come to share your poems about famous or not-famous math personalities (the researcher, the teacher, the geek, the reluctant student, or whomever) – or join us simply to enjoy hearing the work of others!   Though we do not discourage last-minute decisions to participate, we encourage poets to 
          submit poetry (up to 3 poems, reading time up to 5 minutes) 
                    and a 40-word bio         in advance  (by early November)
so you can be listed in our printed program. Early submissions are encouraged, by November 1 would be GREAT -- but submissions will be considered into mid or late November.    Send submissions (and inquiries) to Gizem Karaali (gizem.karaali AT pomona.edu). Organizers of the event include JoAnne Growney, Gizem Karaali, Lawrence M. Lesser, and Douglas Norton.

Wednesday, October 17, 2018

Math-themed -- and seasonal -- Haiku

      Artist and computer scientist Stephen Luecking, now retired from teaching at DePaul University, has sent me some of his Haiku with mathematical imagery; enjoy!
fractals vein the leaves  
swirling in random descent  
autumn winds howling    

crystal hexagons  
drifting from darkening clouds  
earth sleeps in white gown  

Monday, October 15, 2018

Can numbers be a bridge to understanding. . . ?


Fifty-Fifty     by Carl Sandburg (1878-1967)

       What is there for us two
       to split fifty-fifty,
       to go halvers on?
            A Bible, a deck of cards?
            a farm, a frying pan?
            a porch, front steps to sit on?
       How can we be pals
            when you speak English
            and I speak English
            and you never understand me
            and I never understand you?

This poem is on my shelf in Sandburg's collection, Honey and Salt (Harcourt, Brace; 1963).

Friday, October 12, 2018

The music of twelve tones -- in poems

     Inspired by the musical composition strategy twelve-tone technique -- devised by Austrian composer Arnold Schoenberg (1974-1951), in which all 12 notes of the chromatic scale are sound as often as one another in a piece of music -- American poet Elizabeth Bartlett (1911-1994) has developed the twelve-tone poem.  In Bartlett's words:
       The poem consists of 12 lines, divided into couplets. 
       Each couplet contains 12 syllables, using the natural cadence of speech. 
       The accented sounds of the words are considered tones. 
       Only 12 tones are used throughout the poem, repeated various times. 
       As a result, the poem achieves a rare harmony that is purely lyrical, 
                    enriching its imagery and meaning

The following poem is on my shelf in Memory Is No Stranger (Ohio Univ. Press, 1981), a collection of Bartlett's twelve-tone poems; it also is found in the math-poetry anthology Against Infinity (Primary Press, 1979).

       The Infinite Present   by Elizabeth Bartlett

       Because I longed
       to comprehend the infinite  

Wednesday, October 10, 2018

Math-Poetry Contest for Maryland Students

Submission deadline:  November 9, 2018
Winners Announced:  December 12, 2018
Winning Poems Presented:  January 19, 2019
     The American Mathematical Society is conducting a math poetry contest for Maryland students–middle school, high school, and undergraduate students -- as part of the 2019 Joint Mathematics Meetings in Baltimore (Jan. 16-19, Baltimore Convention Center).   The contest is free to enter; information is at this link.  Winning poems will be printed on posters and poets will read them at the meeting as part of Mathemati-Con, a math festival for students.

          Write
          a
          thoughtful
          poem that
          shows ways math is most
          amazing -- a subject we love!

The stanza above is a Fib -- whose lines have syllables counted by the first six Fibonacci numbers.

Monday, October 8, 2018

A special Fibonacci poem

     A recent email from Marian Christie -- a nominally retired mathematics teacher from Aberdeenshire  -- alerted me to her very special sort of Fibonacci poem, one in which the number of letters-per-line follows the Fibonacci numbers AND the length of each word is a Fibonacci number AND the poem speaks about the objects counted by these Fibonacci numbers.

Pathways      by Marian Christie

O
I
am
not
going
anywhere
unaccompanied
by life’s patterns: a whorl
in a pinecone, branches on oak or elm trees, 
the petal count of a daisy, the helix at the heart of a chrysanthemum,
the shell of a nautilus swimming in the ocean. A sequence hides in the shape of
                                                                                   probabilities, and in my own DNA. 

Poet's Note: In this poem the number of letters per line is determined by the Fibonacci sequence: the first line has zero letters while the last line, representing the twelfth number in the sequence, contains 89 letters. In addition, the letters of each word add up to a Fibonacci number.  
Christie's poem was first published on the UK-based website IndependentVariable.

Friday, October 5, 2018

Line and design -- poetry by Adrienne Rich

     A poem I first read during my high school years -- and have loved ever since -- is "Aunt Jennifer's Tigers" by Adrienne Rich (1929-2012).  Found along with that poem in Collected Early Poems 1950-1970  (W W Norton, 1994) is another poem by Rich that I also like a lot -- and offer below -- this one containing a bit of mathematics and a lot to reflect on . . .

          Boundary     by Adrienne Rich

          What has happened here will do
          To bite the living world in two,
          Half for me and half for you.
          Here at last I fix a line
          Severing the world’s design
          Too small to hold both yours and mine.
          There’s enormity in a hair
          Enough to lead men not to share
          Narrow confines of a sphere
          But put an ocean or a fence
          Between two opposite intents.
          A hair would span the difference.

Wednesday, October 3, 2018

The equal sign--and poetry--from Robert Recorde

  A poetic introduction of the equal sign (by Robert Recorde): 

This image is an excerpt from Recorde's The Whetstone of Witte (1557)

    Robert Recorde was born in Wales around 1510-12; he taught mathematics at both Oxford and Cambridge and got his MD from Cambridge in 1545 -- and became a physician to royalty.  He published a number of mathematical works -- one of the best known being The Whetstone of Witte (1557) -- a photographic copy of several of its pages is available here. He is lauded for the invention of the equal sign, first appearing, as shown above, in The Whetstone of Witte.  -- This article from 2015 in WalesOnline cites Recorde's greatest achievement to be making mathematics accessible to a general reader.   

Sunday, September 30, 2018

Counting syllables . . . measuring memory

Political events of this past week (involving a candidate nominated by President 45 to serve on the Supreme Court) have triggered my thinking about the transience of memory.  Here is a Syllable-Snowball poem that includes some of these musings:

What happened back then?

My
sister
disagrees --
her version of
our  growing-up  lives
   so          often         discrepant
     from mine. Each new year -- 
  new           distances,
new    angles,
shape our
 views.

Wednesday, September 26, 2018

Name five!

     A recent mailing from the National Museum of Women in the Arts offered me this challenge:  name five female artists!  Including friends who are artists made this easy -- but I needed a bit of internet help to list five famous names.  This effort has suggests another challenge: 
 NAME (at least) FIVE FEMALE MATHEMATICIANS ! 
One way to meet math-women is through a variety of poems that celebrate them -- lots of poems about math-women are found in this blog.  The Search and Labels features (in right-hand column of blog) can be useful.  Here are several links to get started:
       A poem by Brian McCabe about Sophie Germain;
              a poem by Eavan Boland about Grace Murray Hopper;    
                     a poem by Carol Dorf about Ada Lovelace;
                            a poem of mine about Sofia Kovalevsky;
                                   a poem of mine about Emmy Noether
And this link leads to a great variety of math-women resources.

A few words in closing:

          14 Syllables

          A hen lays eggs
          one by one;
          the way you
          count life
          is life.

from JoAnne Growney's collection Red Has No Reason (Plain View Press, 2010).

Monday, September 24, 2018

Celebrate math students -- a Fibonacci poem!

     South Dakota mathematician Dan May teaches mathematics at Black Hills State University where he also leads workshops for middle school teachers, explores musicology and the connections between poetry and discrete mathematics. He has been involved in math-poetry activities at Bridges Math-Arts conferences but, more importantly, he has been involved with BEAM (Bridge to Enter Advanced Mathematics), a program offering varied academic assistance to underserved students, including a summer residential program. The following Fibonacci poem celebrates that adventure.

BEAM: A Fibonacci Poem     by Dan May

Now
you 
are home — 
Brooklyn, Queens, 
the Bronx, your boroughs. 
Only yesterday still at camp, 
learning knots and graphs, writing proofs on infinity. 
I taught you the one hundred and sixty-eight automorphisms of the Fano plane. 
You wear hijabs, or Jordans, or both. Diverse faces 
display the doubts of twelve-year-olds. 
But each of you, when 
you get it — 
your face 
lights 
Up.

Author’s Note: The poem’s syllable line count follows the 
Fibonacci sequence numbers 1, 1, 2, 3, 5, 8, 13, 21 forward and backward.  
This poem and several others of Dan May's math-linked poems may be found here.

Thursday, September 20, 2018

A mathy poem for sale . . . in Kenya

     A vernacular poem by Kenyan writer Alexander Nderitu ("Kenya's Shakespeare") -- entitled "Mathabu ma Carey Francis" (in English, "The Mathematics of Carey Francis) -- is being auctioned by the poet for bids starting at a million Kenya shillings (a bit less than $1000 US).  Notable about this auction piece is that the background design on which the poem will appear is the poet's DNA sequence.

The opening stanza of Nderitu's poem 

From
Wikipedia, this statement about Edward Carey FrancisEdward Carey Francis (13 September 1897 – 27 July 1966) was a British mathematician and Anglican missionary to Kenya, where he became "arguably the most influential educationist in Kenya's modern history."  

Monday, September 17, 2018

Time and Precision . . . .

   California poet Carol Dorf is a semi-retired secondary school mathematics teacher who is an important force in poetry.  Not only a fine poet, Carol also is Poetry Editor of TalkingWriting, an online journal that sometimes features mathy poems.  It has been my pleasure to meet Carol and to read with her on several occasions, most recently at the 2017 Bridges Conference in Waterloo, Ontario.  The following poem is one that Carol read at Bridges 2018 and it is included in the Bridges Stockholm 2018 Poetry Anthology; it is a thoughtful reflection on the way that time -- and precision in its measurement -- varies in our lives.

Announce the Hour You Have Clocks For    by Carol Dorf
     
Time progresses through the bells 
announcing each moment of occupation: 
toilet, wash, dress, eat, work a, break, work b . . . 
eat, undress, wash, toilet. 

Schematic, yes. Our clocks' precision  
increases until the second, 

Thursday, September 13, 2018

Meeting Math People via Poems

     Mathematics classes are crowded with vital material and it is hard to find time to also consider the PEOPLE of mathematics -- one way to do this is by offering poems.  In the September issue of Math Horizons, my brief article, "Mathematics and Poetry" offers a variety of samples -- introducing poems by mathematicians (including William Rowan Hamilton) and poems about mathematicians (Brian McCabe writing about Sophie Germaine, Cathryn Essinger writing about her super-logical brother).  
     Here are a pair of lines from Voltaire about mathematician and scientist Émilie Du Châtelet:

               She has, I assure you, a genius rare.
               With Horace and Newton, she can compare. 

     A wonderful poem to add to those quoted in the article is in the voice of a math student who protests discrimination; it is by Caribbean-American poet Audre Lorde (1934-1992) and entitled "Hanging Fire" -- the complete poem is posted here.

               I should have been on the Math Team
               my marks were better than his

Here is a link to a pdf of the Math Horizons article.  The article does not contain web-links, BUT each of the poems may be found by searching this blog using the poet's name.

Wednesday, September 12, 2018

Math Limerick Stories

     Mathematics teacher Josephine Johansen is a talented teacher who works to help her students LOVE mathematics.  Below are two stanzas from her illustrated tale, "The Algebra of Tree Wisdom" --written in limerick stanzas: 

Pat says "Say you put on your ring 
Then your necklace to you I bring 
Whichever you choose
To do first, you'll not lose
You'll still be dressed for your fling."

Pete adds "On the other hand
Putting shoes and socks on as planned
        Is not commutative
       Won’t switching order give
An outcome that would be unplanned."  

Monday, September 10, 2018

OEDLIF -- with definitions in limerick form

     Since 2004, ODELIF, the Oxford English Dictionary in Limerick Form has been assembling limerick definitions of English words.  I learned about this amazing project in the Washington Post -- in a weekly column by Pat Myers entitled "The Style Invitational".  Each year, Myers invites readers to submit limericks that define terms in a particular alphabetic range.  This year's contest requested limericks that define words beginning with gl- to go-Follow this link (and scroll) down to see some of the winners (announced this past weekend).
     Alas, none of the winning limericks involved math terms, and so I offer here one of my non-winning submissions.
When you have time, visit ODELIF -- browse its limerick offerings and consider contributing some of your own. And, if you like, add limericks here via your comments below.

Thursday, September 6, 2018

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.    

Tuesday, September 4, 2018

As a new school-year starts, a Latin Square poem

 With MATH in the middle, 
 here is a LATIN-SQUARE poem that starts and ends with GIRLS 

girls
do
great
math
do
math
girls
great
great
girls
math
do
math
great
do
girls


Wednesday, August 29, 2018

Math Is Beautiful and So Are You

 Read on for a poem of love and mathematics! 

    This poem celebrates an upcoming wedding . . .  one of my two wonderful sons will be getting married next Saturday to a lovely and special woman -- and this delightful occasion also will bring a host of scattered family members together.  I am thrilled by all of this and offer, for readers also to celebrate, a lovely poem:

Math Is Beautiful and So Are You     by Becky Dennison Sakellariou

     If n is an even number
     then I'll kiss you goodnight right here, 
     but if the modulus k is the unique solution,
     I'll take you in my arms for the long night.  

Monday, August 27, 2018

Upcoming in Washington -- National Book Festival

     The BOOK WORLD section of this past weekend's Washington POST offers the program for The Library of Congress National Book Festival that will occur next Saturday, September 1, 2018 at the Walter E. Washington Convention Center.  The festival has a Poetry Stage and two of the poets who will appear have been featured in past postings in this blog.  The posting on August 2, 2018 featured "American Arithmetic" by Natalie Diaz and back on June 14, 2017 was posted a section of "Life on Mars" by Tracy K. Smith.  (Smith is Poet Laureate of the Library of Congress, currently in her second term in that position.)
     Numbers can be powerful in describing hardships of poverty -- as in this stanza from "Theft" -- a poem that appears (pages 57-62) in Tracy Smith's collection duende (Graywolf Press, 2007).

from Theft     by Tracy K. Smith

Wednesday, August 22, 2018

The Arithmetic of Identity

     There is never enough time to read all that I wish  -- so much poetry and mathematics awaits my attention.  The Portuguese poet Fernando Pessoa is one whose work is in my queue.  Recently I have been exploring Pessoa's poetic prose in The Book of Disquiet   (Ed. Jeronimo Pizarro, Trans. Margaret Jull Costa, New Directions, 2017).  Below I offer the first two paragraphs of Section 152, The River of Possession -- I have delighted in their play with numbers and meaning: 

          It is axiomatic of our humanity that we are all different.  We only look alike from a distance and, therefore, when we are least ourselves.  Life, then, favors the undefined; only those who lack definition, and who are all equally nobodies, can coexist.
          Each one of us is two, and whenever two people meet, get close or join forces, it's rare for those four to agree,  If the dreamer in each man of action frequently falls out with his own personal man of action, he's sure to fall out with the other person's dreamer and man of action.

In a later paragraph, Pessoa adds:    Love requires us to be both identical and different, which isn't possible in logic, still less in life.

     Thank you to Portuguese mathematician-poet Francisco Jose Craiveiro de Carvalho -- who led me to Pessoa.  Allen Ginsburg's poem "Salutations to Fernando Pessoa" is available here.

Monday, August 20, 2018

Celebrating Visual Poetry

     One of my delights in both poetry and mathematics is the multiplicity of meanings that come from careful attention to a particular text.  Today I have been revisiting the work of visual-poets Robert "Bob" Grumman (1941-2015) and  Karl Kempton and loving the surprises as I rediscover them.  Visual-mathematical poet Kazmier Maslanka in his blog, "Mathematical Poetry,"  generously features the work of many other poets beside his own -- and here (from this link) is one of Kempton's poems:
by Karl Kempton

Wednesday, August 15, 2018

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.  

Monday, August 13, 2018

Speaking, understanding . . . where is truth?

     A review in the Washington Post of a new book about Oscar Wilde opens with this quote:
"Man is least himself when he talks in his own person."
and Wilde's words have gotten me thinking again about subtleties of language.
     Also in recent news, the death of Nobelist V. S. Naipaul (1932-2018) -- and here is one of  this writer's thought-provoking statements:

            Non-fiction can distort;
            facts can be realigned.
            But fiction never lies.            V.S. Naipaul, A Bend in the River

My own thoughts about language most often focus on the condensed languages of mathematics and poetry -- and the need for frequent re-readings before understanding arrives.  Here, below, I include a poem by Stephanie Strickland that speaks eloquently of the struggles in which our minds engage concerning objects and the symbols that represent them -- struggles that are involved in creating and reading both mathematics and poetry . . .

     Striving All My Life     by Stephanie Strickland

     
Maxwell said: There is no more powerful way
     to introduce knowledge to the mind than … as many different
     ways as we can, wrenching the mind   

Friday, August 10, 2018

Code switching -- and a Fib . . .


     1       When 
     1        I
     2        speak to
     3        you, I wish
     5        to be understood.
     8        If I change my language for you
    13       am I being thoughtful -- or phony and insincere?

     My recent viewing of the film Sorry to Bother You --  in which a black telemarketer is helped to succeed by using a "white" voice -- has led me to think more about times that I, often unconsciously, switch my language for different listeners.  
     I grew up on a farm and learned early that farmer lingo was not welcomed in my chatter with town friends, and later, as a mathematics professor, I saved my academic and my mathematical vocabularies for "suitable" occasions and did not use them with my farm family or small-town friends.  Indeed, much of my life I have completely avoided math vocabulary in almost all social situations.  Mostly, I have thought of this "code-switching" as politeness, though I can see that it also conceals parts of myself.
      This thinking about "different languages" has led me to look back to a posting from 2013 that involves a fine poem by June Jordan, "Problems of Translation: Problems of Language" that considers measurements on maps.            What does three inches mean?
This link leads to more information 
about poems structured by the Fibonacci numbers.

Wednesday, August 8, 2018

American Arithmetic

     Last Monday -- with visiting friends (Janet and Terry) from Pennsylvania -- I again visited the National Museum of the American Indian and this visit, rather than focusing on the contributions of a particular native culture, seemed to draw me to exhibits focused on numbers -- most notably on the figures related to Cherokee relocation via the Trail of Tears.  This visit to the museum also allowed me to discover that a variety of books are for sale in the museum's second-floor gift shop and I found this collection of poetry which I have begun to read and love:
Edited by Heid E Erdrich (Graywolf Press, 2018)
   
Within the collection, the poem "American Arithmetic" by Mojave poet Natalie Diaz quickly caught my eye -- and she has given me permission to offer it here:

       American Arithmetic     by Natalie Diaz
     
       Native Americans make up less than
       one percent of the population of America.
       0.8 percent of 100 percent.

       O, mine efficient country.     

Friday, August 3, 2018

Highlighting Poetry-Math Favorites

     Looking back over the eight years of  postings in this blog, I find several items that have stood out in their popularity.  In case you have missed any of these, I list their titles (with links) below.
          The favorite posting, by a large margin, is: 
     "Varieties of triangles -- by Guillevic" posted on October 13, 2010.
Three other postings fall into second place:
          "Mathematical Limericks" posted on March 29, 2010,   
          "Loving a mathematician (Valentine's Day and . . .)" on February 12, 2011,
          "Rhymes help to remember the digits of Pi" on September 2, 2010.
Two more-recent and popular postings are:
          "The World is Round or Flat" on January 8, 2016,
          "Celebrate Math-Women" on March 2, 2017.

The list of labels in the lower right-hand column of  the blog gives the names of numerous mathematicians and topics that are featured in the blog -- and one may click on any label to retrieve the posts.  Additionally, the blog's SEARCH feature may be used to locate postings on a particular topic of interest.

Thursday, August 2, 2018

Looking back -- dates, titles, links for past postings

Scroll down to find titles and links to posts going back to this blog's start in March, 2010.  
If you are searching for a particular topic or poet, 
      Jun 18  Choose the right LINE     

Tuesday, July 31, 2018

Mathematics and Motherhood

     The latest issue of the Journal of Humanistic Mathematics focuses on the theme "Mathematics and Motherhood" -- go here to explore the Table of Contents.  In that issue is my poem "Wondering" - found here.

for your editorship of this fine publication.

Monday, July 30, 2018

Sixty years is a long time . . ..

      Yesterday in my Honda, in heavy traffic -- driving to my present home in Silver Spring, MD from a high school reunion weekend in Indiana, PA -- my thoughts began to shape a poem.  Here, with thanks to Kathy Rend Armstrong and a host of other classmates who helped get a bunch of us together for a 60th reunion of the Indiana Joint High School Class of 1958.  Here is my brief poem.


     For readers unfamiliar with the Fibonacci numbers, here is a link to an explanation, and this link leads to other postings of Fibonacci poems in this blog.

Thursday, July 26, 2018

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.   

Monday, July 23, 2018

Poetry at BRIDGES 2018

The 2018 Brides Math-Arts Conference in Stockholm will take place this week -- July 25-29, 2018.  Mathematician Sarah Glaz has been a leader in stimulating the poetry portion of this conference -- including organization of a reading to be held on Saturday, July 28 and a Poetry Anthology, of which a portion of the cover is shown below.

Poetry Anthology
edited by Sarah Glaz, Tessellations Publishing

Here, from the anthology, is a sample of its finery -- a poem by mathematician, poet, and editor, Sarah Glaz:  

Friday, July 20, 2018

Counting insects, counting on them . . .

     Recently I had the opportunity to vacation in southern Portugal with my older daughter and her family and there -- with clear, bright-blue skies and cooled-down night-time temperatures -- not only did we vacationers thrive but so do many insects.  Their busy behavior reminded me of their presence on the childhood farm in Pennsylvania on which I grew up and their important role as partners in the agricultural process -- pollinating and irrigating and . . . 
    And so -- jet lagged yet continuing in my appreciation of the population-mathematics of insects -- I offer below a poem of bees by Emily Dickinson (1830-1886), also found here.  Another bee-poem by Dickinson posted back in August 2013 is available at this link.

The most important population   (1746)   by Emily Dickinson

       The most important population
       Unnoticed dwell,
       They have a heaven each instant
       Not any hell.

       Their names, unless you know them,
       'Twere useless tell.
       Of bumble-bees and other nations
       The grass is full.

An interesting Smithsonian article, "Bees May Understand Zero . . ." may be found here and the Washington POST has featured bees at this  recent link and this earlier one.