A mathematician is probably too close to her subject matter to speak playfully about it -- and thus she, even more than others, appreciates a phrase like "each equation is a playful catch, like bees into a jar," offered by Lisa Rosenberg in the poem below. In "Introduction to Methods of Mathematical Physics," Rosenberg uses a child's anxiety about insects as a way to describe fear of mathematics and offers a smidgen of respect for "those few" who are fearless.
Introduction to Methods of Mathematical Physics by Lisa Rosenberg
You must develop a feeling for these symbols
that crawl across a page, for the text overrun
with scorpions. Like those books about insects
you read as a child, scared to touch the magnified photos,
After observing that
1 = 1
and 1 + 3 = 4
and 1 + 3 + 5 = 9
and 1 + 3 + 5 + 7 = 16
and 1 + 3 + 5 + 7 + 9 = 25
it seems easy to conclude that, for any positive integer n, the sum of the first n odd integers is n2.
The term butterfly effect has entered everyday vocabulary from the mathematics of chaos theory and refers to the possibility of a major event (such as a tornado) starting from something so slight as the flutter of a butterfly wing. This sensitivity to small changes is a characteristic of chaotic systems. Recent news in Science magazine (9 May 2014) has drawn my attention to sea butterflies -- and the effect that ocean acidification is having on the lives of these tiny, fragile creatures -- and the environmental warning that this portends. From the details offered in Science, I have constructed this poem of 4x4 square-stanzas:
Warned by Sea Butterflies by JoAnne Growney
Sea butterflies --
no larger than
a grain of sand,
named for the way
Here is a small poem richly vivid with the contrasts of opposites:
beside a stone three
thousand years old: two
red poppies of today
by Christine M. Krishnasami, India, found in This Same Sky: A Collection of Poems from around the World (selected by Naomi Shihab Nye, Aladdin Paperbacks, 1996).
Here is a poem by Saskatchewan poet Karen Solie.
Found by Karen Solie
Elementary Calculus
From Elementary Calculus A. Keith and W. J. Donaldson.
Glasgow: Gibson, 1960.
Speed (like distance)
is a magnitude and has no
direction; velocity (like displacement)
has magnitude and direction.
My maternal grandfather, James Edgar Black (1871-1931) was a western Pennsylvanian, a carpenter, and a man I never knew. But Ed, one of my cousins, found among our grandfather's long-stored things a scrapbook of collected poems and other miscellany that he recently passed on to me.
From John Dawson -- a professor emeritus of mathematics at the Penn State York campus and well-known for his publications in mathematical logic, often focusing on the life and work of Kurt Godel -- a poem on a topic that this blog visits from time to time, portraits of mathematicians.
Public Image by John W. Dawson, Jr.
Please,
I'm not an accountant.
No,
Mine doesn't always balance either.
What do I do then?
Well,
On good days
I prove theorems;
Here is a bit of light verse from the pen of John Updike (1932-2009).
ZULUS LIVE IN LAND
WITHOUT A SQUARE by John Updike
A Zulu lives in a round world. If he does not leave his reserve.
he can live his whole life through and never see a straight line.
--headline and text from The New York Times
In Zululand the huts are round,
The windows oval, and the rooves
Thatched parabolically. The ground
Is tilled in curvilinear grooves.
Somewhere in a high school English class was a small topic that intrigues me still -- "questions that expect the answer 'yes'." A door opened. Letting me see that what we say has expectations as well as information. In graduate school math classes we considered the warning word "obviously" -- in a proof, it was likely to mean "I'm sure it's true but am not able to explain."
As I muse today about language I am wondering how unsaid words affect the population of women in mathematics, affect the numbers (too small) of women publishing mathematics. Thinking about this in the light of a wonderful time on Saturday greeting visitors to an AWM (Association for Woman in Mathematics) booth at the biennial USA Science and Engineering Festival. Temple University professor and AWM member Irina Mitrea did an amazing job planning and coordinating the AWM booth where hundreds of young people got some hands-on experience with secret codes and ciphers.
In my childhood home, numbers were used with care and precision. There would be teasing when I would use the adverb "too" --- as if when I said "I had to walk too far" I had tried to describe an unbounded distance, greater than any possible span. Now as an adult I continue to be cautious (and intrigued) with use of that word. And I am drawn to the uses of "too many" and "count" in the following poem from David Orr, poetry columnist for the New York Times Book Review.
The Chameleon by David Orr
Alone among the superheroes,
He failed to keep his life in balance.
Power Man, The Human Shark--they knew
To hold their days and nights in counterpoise,
Their twin selves divided together,
As a coin bears with ease its two faces.
As a Columbia undergraduate, media artist Millie Niss (1973-2009) majored in mathematics and was enrolled in a math PhD program at Brown University when she decided to make writing her full-time career. Before her untimely death in 2009 Niss was well-established in Electronic Literature. Here is a link to "Morningside Vector Space," one of the poems at Niss's website Sporkworld (at Sporkworld, click on the the E-poetry link).
Niss's electronic poem retells a story (inspired by the Oulipian Raymond Queneau's Exercises de Style) in many different styles and following many different constraints. The computer is central to the retelling as the text varies almost smoothly along two dimensions, controlled by the position of the mouse pointer in a colored square (to the right in the screen-shot below). Behind this poetry is the mathematical concept of a two-dimensional vector space, in which each point (or text) has a coordinate with respect to each basis vector (version of the text, or dimension along which the text can change).
Sometimes numbers become labels for particular events. When I was growing up, all of us knew 1492 as a label for the discovery of America. And 1941 recognized Pearl Harbor. The following selection from a poem by Israeli poet Yehuda Amichai (1924-2000) reminds us of the awful importance of 6 million.
While mentioning this poem of witness and remembering, I want also to remind you of the very special Split This Rock Poetry Festival: Poems of Provocation & Witness, to held in Washington, DC, March
27-30, 2014. (Early-bird registration ends on Valentine's Day, February
14th at midnight.) Hope to see you there.
Washington, DC is a city rich with both poetry and mathematics. Last Tuesday evening I attended a Mathematical Association of America (MAA) lecture by author and math historian William Dunham (whom I knew when he taught for a bunch of years at Pennsylvania's Muhlenberg College, in Eastern Pennsylvania, not so far from my employer, Bloomsburg University). Dunham spoke of insights gained by many hours reading the correspondence of British mathematician and scientist, Sir Isaac Newton (1642-1727). The discoverer of "gravity," and, moreover, both a genius and a disagreeable man. Still, Newton was a man who gave a nod to his predecessors, "If I have seen further it is by standing on ye sholders of Giants."
It is hard to know what to say.
Pete Seeger died yesterday at age 94.
94 = 2 x 47. 47 is prime.
Here is a link to Pete singing "Little Boxes."
Song lyrics are poems.
This past weekend a review by Teller (magician of the Penn & Teller team) of an autobiography of Martin Gardner appeared in the NYTimes Book Review. According to Teller, Gardner (1914-2010) wrote the memoir, Undiluted Hocus-Pocus: The Autobiography of Martin Gardner, at the age of 95 on an old electric typewriter in his single-room assisted-living apartment in Norman, Oklahoma.
In addition to waterfalls and geysers and the Aurora, Iceland has outstanding museums. On the morning of December 10, I visited the National Museum of Iceland in Reykjavik -- and enjoyed a careful introduction to the history of this fascinating and friendly nation. Something I missed, however, was seeing one of the 13 Yuletide Lads that are an Icelandic tradition and who visit the Museum one-by-one on the 13 days before Christmas, each wearing
traditional costume and trying to pilfer the goodies he
likes best.
British translator and editor David McDuff blogs at "Nordic Voices in Print" -- a site that he uses as "a way of making some of my translations of Nordic poetry and prose available online." Here is "stones" -- the third of a group of ten poems he has posted by Icelandic poet Sjón. This one involves a few numbers and I present it here as a math-poetry token of the fascinating land I am planning to visit: a five-day Iceland vacation adventure, traveling with my Eastern Village neighbors Priscilla and Glenn.
stones by Sjón (translated by David McDuff)
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