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5SVUI BOE #FBVUZ " $PVSTF JO .BUI BOE -JUFSBUVSF By Marion Deutsche Cohen
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e can use math to explore and explain mysteries of the universe. Literature can also serve this purpose. After thinking about this intersection for some time, I developed the course “Truth and Beauty: Mathematics in Literature,� which explores math-inspired writings, as well as the math that inspired them. The course offers students an opportunity to get in touch with the emotional aspects of math and to develop an appreciation of math and literature and how they can connect. . . . offers students Our texts are a fiction anthology, Fantasia an opportunity to Mathematica, and a poetry anthology, Strange get in touch with Attractors: Poetry of Love and Mathematics. (See [math’s] emotional the box for other mathinspired writings.) Our course readings consist aspects . . . of approximately 10 stories and 10 poems. Each reading generates two assignments, “math� and “non-math.� “Math� assignments consist of problems and questions about the math that inspired or is otherwise related to the reading. I strive to find mathematics that is not too difficult for non-math majors yet not boring for math majors. “Non-math� assignments are open-ended questions related to the reading and in turn sometimes to students’ lives. (A piece of literature often means more if the reader has been in a similar situation or can, however subtly, identify with one of the characters.) Both sets of questions are for written homework and class discussion. Admittedly, the math assignments are sometimes shorter than the non-math, and going over them takes up less class time. Balancing time spent on math and non-math work is achieved via the readings themselves and via our conversations. The semester ends with a math final and three writing assignments: a critique of a math poem of the students’ choosing, an ungraded math poem they compose, and an eight-page term paper on any class-related topic. For the last assignment, I hand out a list of suggestions, including, “How has your view of math or literature shifted as a result of this course?� To give a feel for the class, here is the treatment of one reading, “An Old Arithmetician,� a charming story from the 19th century (Mary E. Wilkins, http://home.comcast.net/~wilkinsfreeman/ Short/OldArithmetician.htm). Its heroine is an old, uneducated village woman who happens to love and excel at “sums,� as she puts it. The villagers admire her for this and hand her whatever sums they can’t do themselves. The story shows, in subtle, often humorous, ways, just how hooked on math a person can be and
why, as well as the possible life conflicts caused by being so mesmerized. In addition to portraying this math-oriented character, the plot involves mathematics; the woman’s preteen granddaughter, whom she is raising, gets lost, partly because of the woman’s involvement in her latest sum. One passage depicts her inner struggling: Is it okay to work on the sum while her granddaughter is missing? I read the story aloud to the class, to make this first exposure to math literature relaxing and enjoyable. Since the word “sum,� appearing often in the story, is used synonymously with “math,� I teach the class that there’s more to sums than adding. Summation formulas, infinite series . . . “You think sums are easy? Well, look at this!� The math homework consists of problems, both straightforward and challenging, that use these summation formulas. The writing (non-math) assignment for this story includes the following questions: (1) Have you known or know of a mathematician (in any sense of the word) who made an impression on you?
Math-Inspired Literature Some literature containing mathematics is well known, such as Edwin A. Abbott’s Flatland and Lewis Carroll’s Alice’s Adventures in Wonderland. Others, less so, such as Alex Kasman’s Reality Conditions (MAA, 2005), a collection of “math fiction�; my own poetry collection Crossing the Equal Sign (Plain View Press, 2007); the anthology Fantasia Mathematica edited by Clifton Fadiman (Springer, 1997); and the poetry anthology Strange Attractors: Poetry of Love and Mathematics edited by JoAnne Growney and Sarah Glaz (AK Peters, 2009). The posthumously celebrated Leonard Michaels wrote seven so-called Nachman Stories about a mathematician. Kasman operates a vast site, Mathematical Fiction (http:// www.kasmana.people.cofc.edu/MATHFICT), that collects information about all significant references to mathematics in fiction. Growney has a blog, Intersections (poetrywithmathematics.blogspot.com), where she features “math poetry� and musings (see page 19). In recent years, several fictionalized accounts have appeared of the lives of famous mathematicians, such as The Indian Clerk about Ramanjuan, and novels about mathematicians, such as The Housekeeper and the Professor and The Curious Incident of the Dog in Nighttime. —Marion Deutsche Cohen
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(2) The story raises questions about polarities between art (or science) vs. life (or love), and between passion vs. responsibilities. Can you think of such polarities in your own life? (3) Do you wonder “what the heck does she see in sums?” or do you get her? We’ve had lively and penetrating conversations. Students have told of mathematical uncles, math-buff parents, favorite teachers; one student told us about her father who “didn’t know any real math but was always asking us riddles that seemed mathematical.” Students have shared polarities they’ve known—friends vs. work, family vs. friends, introvert vs. extrovert, religious upbringing vs. a growing interest in science. And yes, the students get the old woman in the story.
$POWFSTJOH BCPVU 1PFUSZ In the course, poetry is handled the same way as fiction. We often spend as much time on one poem as on one story. A poem, after all, can say as much as a story. As a brief example, one untitled poem includes the phrase “the mystery of the known.” A non-math question for this poem is, “Are there things that are explained and understood but still seem mysterious to you?” All of us chipped in with answers, such as the moon, certain machines, and math things such as the Cantor middle-third set (not to mention Cantor’s transfinites, which were mysterious to Cantor himself). The high point of the course (the first time it ran) came for me
when a student focused the term paper on how it felt to write a poem titled “The Value of My Mind.” The poem reads, in part: I have a value inside my head that cannot be written, nor seen nor said. It is something that I hold most dear yet has kept me restless for years. ... This value is love, this value is sorrow. This value will haunt me even tomorrow. In the term paper, the student wrote, “I took this opportunity to say and express certain things I feel in my mathematical life that I hadn’t felt comfortable sharing with the class. I was afraid of looking like a whack job. This class has allowed me to understand my love for math through writing. The poem allowed me to explain the dream because unlike an explanation, a poem doesn’t have to be straightforward . . . it can dance around the meaning and still get the truth across to its reader.” I was excited to witness the birth of a new “math poet.” I wrote on the paper, alongside the A+, “You’re in for a math-loving and wonderful life.” That sentence sums up how I feel about those who connect literature and mathematics. Marion Deutsche Cohen teaches at Arcadia University; email: cohenm@arcadia.edu; http://www.marioncohen.net.
The award-winning documentary exploring the
art and science of origami
Available for purchase at the Joint Mathematics Meetings MAA Booth 901-911
“. . . reveals origami itself as richer and more intricate than you could imagine . . . and by the end, you find yourself convinced that the mystery of folding could be one of the universe’s deep secrets.” — Chris Anderson, Curator, TED
Photo/Vanessa Gould
Between the Folds
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Poetry: We Have an App for That By JoAnne Growney
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am often asked why I chose “poetry with mathematics” as a subject for a blog. It strikes many people as a coupling of opposites. I have loved math from a young age. While I prepared to be a mathematics teacher, I thought poetry was something I could continue on the side. Not so. Still, my love of poetry remained. Around 1980 I discovered the anthology Against Infinity (Primary Press, 1979), edited by Drexel mathematicians Ernest Robson and Jet Wimp (a.k.a. Jet Foncannon). This small book contains a rich variety of poems with mathematical connections, and, with it in hand, I saw ways to bring poetry into my university classrooms as an “application” of mathematics. Since that discovery, I’ve enthusiastically collected poems whose texts contain mathematical imagery or whose structures are influenced by mathematics. Aided by other collectors and friends, my knowledge of the ways mathematics affects poetry keeps growing. I’ve published several articles on these topics, but the sprawling range of collected poems (and related information) gathered over the years has at last drawn me to the prolonged serial publication now available online via a blog. In March 2010, I began postings for Intersections—Poetry with Mathematics, and dozens of entries to date show a mere tip of my iceberg of files. My initial examples of “mathematical” poetry included primarily lines of verse that incorporate mathematical terminology. For example, I liked “The One Girl at the Boys Party” by Sharon Olds (The Dead and the Living, Knopf, 1984) for the way it used mathematical terminology to praise girls—who were, at that time, my best but most reluctant students. They will strip to their suits, her body hard and indivisible as a prime number, they’ll plunge in the deep end, she’ll subtract her height from ten feet, divide it into hundreds of gallons of water, the numbers bouncing in her mind like molecules of chlorine …
In recent years, my poetic interests have expanded to include visual and experimental poetry, sometimes involving algorithms and constraints (such as those popularized by the OULIPO). Readers are invited to visit http://poetrywithmathematics. blogspot.com and explore its postings—and also to contribute comments and offer links to even more math-poetry examples and ideas. Formerly a professor of mathematics at Bloomsburg University in Pennsylvania, JoAnne Growney is now a poet in Maryland; email: japoet@msn.com; website: http://joannegrowney.com.
A Taste of Mathematics
A mathematician left the convention focused on 9, the digit that sits in the billionth decimal place of pi, ratio of circumference to width of the yellow circle that parted the clouds as she strolled down Commerce Street to the Rio Rio Café for lunch and a beer.
On fire with jalapeños she went shopping for a souvenir. She bought earrings— red-red plastic peppers with green stems.
She said, “Hot peppers are like mathematics— with strong flavor that takes over what they enter.” —JoAnne Growney
Author’s Note: Announcement of the billionth decimal digit of π was made at the annual Joint Mathematics Meetings in San Antonio in January 1993. Recent reports claim calculation of at least 5 trillion digits. “A Taste of Mathematics” can be found in JoAnne Growney’s new collection, Red Has No Reason (Plain View Press, 2010).