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Great Circles: The Transits of Mathematics and Poetry (eBook)

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Great Circles: The Transits of Mathematics and Poetry (eBook)

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Words That Count: Discovering the Mathematics of Poetry (Article)

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Words That Count: Discovering the Mathematics of Poetry (Article)

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In a 2011 article for the American Mathematical Society, mathematician Cai Tianxin made a striking claim. He wrote, "It could be said that mathematics and poetry are the freest intellectual activities of human beings." ¹

His suggestion is doubly daring: first, because it brings together two arts that are typically placed side by side only to show the contrast between left-brained, technical, objective studies and those that are right-brained, creative, and subjective; and second, because it attributes freedom to what are arguably the most formal, structured, and precise uses of numbers and words respectively. That being said, by the end of this essay, I hope to persuade you that both premises of Tianxin's claim are justifiable. ²

Like Tianxin, I believe firmly that mathematics and poetry exist in cooperation rather than competition. Poetry is a language built on schemes, tropes, and condensed syntax. Giving order to poetry are the same rhythm, harmony, and order that characterize a balanced equation in math or chemistry. Not all poetry is written with a regular meter, but learning to recognize the formal rhythms of poetry will grant you access to the work of great poets across the centuries and also give you a foundation for understanding poetry that deviates from those forms. As American poet Wallace Stevens said, "In poetry, you must love the words, the ideas and the images and rhythms with all your capacity to love anything at all." ³

I find it helpful to think of a poem's meter as its internal rhythm. Poets measure rhythm based on the number of accented, or stressed, syllables in each line. To determine the meter of a poem, you will need to know two things: 1) the number of stressed syllables in each line, and 2) the pattern of stressed and unstressed syllables.

In normal speech, we do not emphasize all syllables of a word equally. For example, we say "beGINNing" rather than "BEginning" or "beginnING." Of course, some pronunciations vary. At Thanksgiving, some family members may say "PEcan" while others may use "peCAN" to talk about the same food item. When you are teaching students to identify meter, you can turn it into a game that uses the whole body. Have your child stand up when he says a stressed syllable and sit down when he says an unstressed syllable. Alternately, ask him to read standing up, rising onto his toes when he says an unstressed syllable and thumping his heels on the floor as he says each stressed syllable.

Emily Dickinson is an excellent poet to read for meter. Read the following two lines of poetry aloud, and see if you can identify the stressed syllables.

Because I could not stop for Death -

He kindly stopped for me -

Some variation is perfectly normal, but your reading probably sounded something like this:

"beCAUSE I COULD not STOP for DEATH -

he KINDly STOPPED for ME."

Get ready, because I am going to ask you to apply some mathematical thinking. If you are given the fraction 8/4, you might notice that you can divide both the numerator and the denominator by 4, leaving the simpler number form, 2. Similarly, if you are given the equation 4x + 4y = 8, you might notice that all of the elements are divisible by 4. So, a simpler form would be x + y = 2.

When you look at a line of poetry, such as the one above by Dickinson, you use the same kind of thinking to find the "foot"-the basic pattern of stressed and unstressed syllables-in the line. First, write out the pattern of the whole line, using the letter "U" to designate unstressed syllables and the letter "S" to designate stressed syllables. The first line would be written USUSUSUS. Next, can you simplify this line to find a basic repeating element that contains one stressed syllable?

If you answered, " US," or one unstressed syllable followed by one stressed syllable, you would be correct. Poets call this type of "foot" an "iamb." Other types of feet are "trochee" ( SU), "dactyl" ( SUU), "anapest" ( UUS), and the less common "spondee" ( SS) and "pyrrhus" ( UU).

If the word "iamb" sounds familiar, it might be because you have heard Shakespeare's poetry called "iambic pentameter." Remember, the footis one part of a poem's meter. The number of feet in a line is the other element. Here, knowledge of Greek and Latin roots will serve you well. The prefix "mono-" tells you that a line has one foot, or one stressed syllable. "Di" means two, "tri" means three, "tetra" means four, "penta" means five, "hexa" means six, "hepta" means seven, "octa" means eight, and so on. Using this information, I bet you can figure out how many stressed syllables are in each line of many of Shakespeare's plays. ⁴

Now, go back and look at the Dickinson poem. How many feet are in each line? The first line has four stressed syllables, and the second line has three. So, we would say that this poem alternates lines of iambic tetrameter and iambic trimeter.
Mathematical Freedom
Learning to read and write the mathematics of poetry seems like a lot of work when you first begin. You have to learn a new vocabulary of feet and metrical terms, and you have to set aside the contents of the poem to count out its rhythm. A novice musician whose world is ruled by a metronome might feel the same way.

In that metaphor, however, I think we would all agree that mastery of the forms leads to freedom of performance. Professional musicians can sight-read music when they rehearse with a new ensemble, and because they understand rhythm and time signatures, they are able to synchronize their various instruments and focus instead on the dynamics of the piece. As Irish poet William Butler Yeats wrote, "...rhythm [is] the wheel of Eternity, on which alone the transient and accidental [can] be broken, and the spirit set free."⁵ In the same way, when students first learn the language of poetry, the mathematical precision of line length and meter can free their creativity by giving them a structure to fill with meaning and truth.

So far, I have argued that poetry is mathematical, and for a young writer its mathematical structure is one of its most liberating aspects. But is that enough to call poetry and mathematics "the freest intellectual activities of human beings"? If we understand mathematical equations to be a series of numbers expressing logical relationships, distilled to their purest and yet most complex form; then we can also understand poetry to be a series of words expressing ideas, refined to similar purity and complexity. In both cases, pragmatic application is of secondary concern, even though use often follows understanding of forms.

Biological mathematician Joel Cohen explains it this way:

In addition to meanings conveyed by patterned symbols, poetry and applied mathematics have in common both economy and mystery. A few symbols convey a great deal. The symbols' full meanings and their effectiveness in creating meanings and beauty remain inexhaustible. ⁶

I love the words he chooses- economy and mystery -to describe both mathematics and poetry. They make me think of a precious stone carefully mined from a rock and then cut, faceted, polished, and honed to show off every exquisite color and flash of reflected light. The mystery unveiled by this act (How can I use these forms? What can I beautify with them? What can they teach me about the world and its Creator?) is a source of inexhaustible freedom.
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¹Cai Tianxin, "Mathematicians and Poets", Trans. Robert Berold and Gu Ye ( Notices of the AMS 58.4, April 2011): 591.

² For the sake of full disclosure, I have to admit that I have a personal stake in this discussion because I consider myself a poet, but I also take satisfaction in the order and structure of mathematics. No one wants to be a walking contradiction.

³Wallace Stevens, "Adagia," in Opus Posthumous, edited by Samuel French Morse (Knopf, 1957, reprinted, Random House, 1982).

⁵W.B. Yeats, Rosa Alchemica (1897), in Stories of Red Hanrahan, The Secret Rose, Rosa Alchemica (New York: Macmillan, 1914): 221.

⁶Joel Cohen, "A Mindful Beauty: What poetry and applied mathematics have in common" ( The American Scholar, Autumn 2009).
------------------------- Resources
Cohen, Joel. "A Mindful Beauty: What poetry and applied mathematics have in common." The American Scholar (Autumn 2009).

Growney, JoAnne. "Mathematics in Poetry." Journal of Online Mathematics and its Applications 6.1262 (October 2006).

Nemerov, Howard. "Figures of Thought." The Western Approaches. Chicago: University of Chicago Press, 1975. p. 257.

Tianxin, Cai. "Mathematicians and Poets." Trans. Robert Berold and Gu Ye. Notices of the AMS 58.4 (April 2011): 590-592.

Weisstein, Eric W. "Logarithmic Spiral." MathWorld -A Wolfram Web Resource, 2013.

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Words that Count: Discovering the Mathematics of Poetry

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In a 2011 article for the American Mathematical Society, mathematician Cai Tianxin made a striking claim. He wrote, "It could be said that mathematics and poetry are the freest intellectual activities of human beings."

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Glaz thinks similar creative processes drive the acts of doing mathematics and writing poetry: "It's the combination of something that arouses curiosity and inspiration, and then there's some perspiration. And some frustration," she says. "Sometimes it doesn't work, and sometimes, happily, it works, in spite of you."

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Give Me an Epsilon and I Will Treat It Well by Ray Bobo

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Give Me an Epsilon and I Will Treat It Well by Ray Bobo

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Both require economy and precision-and each perspective can enhance the other

smithsonian.com

April is both National Poetry Month and Mathematics and Statistics Awareness Month, so a few years ago science writer Stephen Ornes dubbed it Math Poetry Month. If the words "math" and "poetry" don't intuitively make sense to you as a pair, poet and mathematician JoAnne Growney's blog Intersections-Poetry with Mathematics is a perfect place to start expanding your math-poetic horizons. The blog includes a broad range of poems with mathematical themes or built using mathematical rules.

Take "Geometry," by former U.S. Poet Laureate Rita Dove:

I prove a theorem and the house expands:
the windows jerk free to hover near the ceiling,
the ceiling floats away with a sigh.

-from "Geometry" by Rita Dove

Or "In Praise of Fractals" by Emily Grosholz, published in The Stars of Earth: New and Selected Poems (2017, Word Galaxy Press):

Euclid's geometry cannot describe,
nor Apollonius', the shape of mountains,
puddles, clouds, peninsulas or trees.
Clouds are never spheres,
nor mountains cones, nor Ponderosa pines;
bark is not smooth; and where the land and sea
so variously lie about each other
and lightly kiss, is no hyperbola.

Compared with Euclid's elementary forms,
Nature, loosening her hair, exhibits patterns
(sweetly disarrayed, afloat, uncombed)
not simply of a higher degree n
but rather of an altogether different
level of complexity:
the number of the scales of distances
describing her is almost infinite.

-from "In Praise of Fractals" by Emily Grosholz

Growney casts a wide net on her blog, which begins with the words: " Mathematical language can heighten the imagery of a poem; mathematical structure can deepen its effect." Some poems she features, like "Geometry," use mathematical themes or images; some are by mathematicians or math students. Growney has also gotten interested in the mathematics of poetic forms and poetic forms that employ mathematics.

Of course, sonnets and haiku are famous for employing strict counts on lines and syllables. But she is also interested in newer forms, often inspired by the constrained writing exercises of the French Oulipo group, which was founded by mathematicians and poets.

One such form is the " Fib," a type of poem based on the Fibonacci sequence in math. The Fibonacci sequence starts 1, 1, 2, 3, 5, 8, and so on; each term (after the first two) is the sum of the two terms before it. In a Fib poem, the first line has one syllable, the second one syllable, the third two, the fourth three, and so on. Growney, a retired math professor who sometimes teaches writing workshops, says a limited form like the Fib can help beginning poets who are having trouble starting.

Kiss
me
again
tongue and lips
like Fibonacci's
sequence, each movement a spiral,
enfold, unfold, a working through and against, again.

-from "Fibonacci Poems" by Athena Kildegaard, published in Rare Momentum

Growney grew up wanting to be a writer. "I read Little Women as a girl, and maybe it was partly the name connection, but I thought that I wanted to be a writer like Jo." She was also good at math, though, and ended up with a scholarship to study it in college. She stuck with it and earned her Ph.D. in 1970 at the University of Oklahoma. During her career as a math professor, her interest in writing continued. She took poetry classes at a nearby college when she could, discovered the math poetry anthology Against Infinity while doing a sabbatical project about mathematics and the arts, and started to see her feelings about mathematics echoed in poetry.

Mathematics and poetry, Growney says, are both "formats that can convey multiple meanings." In mathematics, a single object or idea might take different forms. A quadratic equation, for example, can be understood in terms of its algebraic expression, perhaps y=x ²+3x-7, or in terms of its graph, a parabola. Henri Poincaré, a French polymath who laid the foundations of two different fields of mathematics in the early 1900s, described mathematics as "the art of giving the same name to different things."

Likewise, poets create layers of meaning by utilizing words and images that have multiple interpretations and associations. Both mathematicians and poets strive for economy and precision, selecting exactly the words they need to convey their meaning.

These features of mathematics and poetry can make them daunting and frustrating for students. "If a student sees only one meaning and the intent is to exploit another meaning, it seems manipulative or unfair," says Growney. But Growney's approach to poetry can also inform our attitude towards unfamiliar mathematics. "A rule I use for poetry is you first of all read it through once without worrying about understanding," she says. "If there's something you like about it, read it again. Give yourself ten readings before you say you don't understand it."

As a professor, she used poetry in her mathematics classes to help students to connect emotionally to mathematics, learn a little bit about the history of what they were doing in class, and think of mathematics as a shared human experience. Now that she is retired, she is still active in the math poetry world, often participating in poetry events at the annual Joint Mathematics Meetings, the largest math conference in the U.S., and the Bridges conference on mathematics and the arts.

My favorite of her poems is " My Dance Is Mathematics," about Emmy Noether and women in mathematics. The poem begins with a with a poetic foreward that mathematician Hermann Weyl used to eulogize the great mathematician when she died in 1935:

Down, down, down into the darkness of the grave
Gently they go, the beautiful, the tender, the kind;
Quietly they go, the intelligent, the witty, the brave.
I know. But I do not approve. And I am not resigned.

From "Dirge without Music" by Edna St Vincent Millay; offered
by Hermann Weyl in a Memorial Address for Amalie "Emmy" Noether
on April 26, 1935 at Bryn Mawr College.

It continues:

They called you der Noether, as if mathematics
was only for men. In 1964, nearly thirty years
past your death, I saw you in a spotlight
in a World's Fair mural, "Men of Modern Mathematics."

Colleagues praised your brilliance--but after
they had called you fat and plain, rough and loud.
Some mentioned kindness and good humor
though none, in your lifetime, admitted it was you
who led the way in axiomatic algebra.
Direct and courageous, lacking self-concern,
elegant of mind, a poet of logical ideas.

At a party when you were eight years old,
you spoke up to solve a hard math puzzle.
Fearless, you set yourself apart.

I followed you and saw you choose
between mathematics and other romance.
For women only, this exclusive standard.

I heard fathers say, "Dance with Emmy--
just once, early in the evening. Old Max
is my friend; his daughter likes to dance."

If a woman's dance is mathematics,
she dances alone.

Mothers said, "Don't tease. That strange one's heart
is kind. She helps her mother with the house
and cannot help her curious mind."

Teachers said, "She's smart but stubborn,
contentious and loud, a theory builder
not persuaded by our ideas."

Students said, "She's hard to follow, bores me."
A few stood firm and built new algebras
on her exacting formulations.

In spite of Emmy's talents,
always there were reasons
not to give her rank
or permanent employment.
She's a pacifist, a woman.
She's a woman and a Jew.
Her abstract thinking
is female and abstruse.

Today, history books proclaim that Noether
is the greatest mathematician
her sex has produced. They say she was good
for a woman.

-"My Dance Is Mathematics" by JoAnne Growney

When Growney started her math poetry blog, she thought she had about a year's worth of material. Since then, far from dancing alone, she has made connections with poets and mathematicians around the world, finding more and more to share. Eight years and almost 900 posts later, she says, "I have more than I started with."

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smithsonian.com April is both National Poetry Month and Mathematics and Statistics Awareness Month, so a few years ago science writer Stephen Ornes dubbed it Math Poetry Month. If the words "math" and "poetry" don't intuitively make sense to you as a pair, poet and mathematician JoAnne Growney's blog Intersections-Poetry with Mathematics is a perfect place to start expanding your math-poetic horizons.

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Poematics: Exploring Math through Poetry

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Poematics: Exploring Math through Poetry

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Poetry: A simple solution to math anxiety (Video)

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Poetry: A simple solution to math anxiety (Video)

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Poetry: A simple solution to math anxiety | Laken Brooks | TEDxEHC

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Out of Nothing I Have Created A Strange New Universe by  Shashi Thutupalli

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Out of Nothing I Have Created A Strange New Universe by  Shashi Thutupalli

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The Intersection Between Math and Poetry (Article)

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The Intersection Between Math and Poetry (Article)

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The Intersection Between Math and Poetry

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April is designated National Poetry Month and Mathematics and Statistics Awareness Month. Aware of their intersection, science writer Stephen Ornes named April "Math Poetry Month". The two...

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Discovering Patterns in Mathematics and Poetry (eBook)

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Discovering Patterns in Mathematics and Poetry (eBook)

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