Tuesday, May 28, 2013

Related rates -- in fiction and poetry

     During the Memorial Day weekend I had the opportunity to read Black Rice (WSI, 2013), a novella by Burmese-American poet, artist, activist -- and friend -- Kyi May Kaung; I strongly recommend this book to you.  (My 5-star review of Kaung's book is available here at amazon.com -- follow the link and scroll down.)
     Here, in this blog, we mention topics if and only if they relate to both mathematics and poetry.  Read on and you will see!
     Midway through Black Rice, the narrator (speaking of an overflowing stream) reveals a negative attitude toward mathematics -- a strategy often used to provoke readers to experience empathy:  "Ahhh, just like me."  Here are the Burmese soldier's words:

     I had never seen streams as full before.
     They looked as if they would overflow their banks, and that catching the surplus in cups or buckets we would find the true water volume in cubic feet of all that displaced water, the true capacitty of all those streams and rivers.
     Like one of those asinine arithmetic problems in high school which I ould never figure out:  One pipe fills a bathtub at ten gallons a minute.  Another drains it at five.  At the end of eight hours how much water is there left in the bathtub?
     I was always tempted to write in my notebook -- How the Hell should I know?  And who the Hell cares?

     Kaung has a doctorate in economics and is not herself fearful of math -- as evidenced by the level and detail of the "related rates" calculus problem her novella has posed.  That problem has reminded me of a poem that was provoked by another "related rates" problem. Poet David Wagoner, in "The Calculation," deals with a situation of shifting shadows.
The Calculation     by David Wagoner

A man six feet tall stands on a curb, facing a light suspended fifteen feet above the middle of a street thirty feet wide.  He begins to walk along the curb at five m.p.h.  After he has been walking for ten seconds, at what rate is the length of his shadow increasing?
—a problem given by my calculus instructor, Penn State, 1946

Facing a streetlight under batty moths
And June bugs racheting like broken clock springs,
I stand, for the sake of a problem, on the curb—
Neither in grass nor gutter—while those wings
Switch down the light and patch my undershirt.

I turn half-right.  My shadow cuts a hedge,
Climbs through a rhododendron to a porch,
And nods on a windowsill.  How far it goes
I leave to burglars and Pythagoras.
Into the slanting glare I slant my watch,

Then walk five miles per hour, my shoes on edge
In a practiced shuffled past the sewer grid
Over the gold no-parking-or-pausing zones
And into the clear—five seconds—into dirt,
Then over a sawhorse studded with lanterns,

And at the tenth I stiffen like a stump
Whose lopped head ripples with concentric figures,
Note the location of my other head
in a garden, but keep trundling forward,
ignoring doppengängers from moon and lawn-lamp,

My eyes alert now, leveling my feet,
Seeing my shadow sweeping like a scythe
Across the stalks of daisies, barking trees,
And scraping up the blistered weatherboard
To the eaves of houses, scaling the rough shingles.

At fifteen seconds, in a vacant lot,
My head lies on a board.  I count it off.
I think back to the garden, and I guess,
Instructor, after fifteen years of sweat,
It was increasing five feet plus per second.

At the start, I could have fallen, turned around,
or crossed to the very center of confusion,
My shadow like a manhole, no one’s length,
Or the bulb itself been broken with a shot,
And all my reckoning have gone unreckoned.

But I was late because my shadow was
Pointing toward nothing like the cess of light,
Sir, and bearing your cold hypotenuse—
That cutter of corners, jaywalker of angles—
On top of my head, I walked the rest of the night.

Does Wagoner, too, claim our empathy?

"The Calculation" is found on my bookshelf in Traveling Light:  Collected and New Poems (University of Illinois Press, 1999).  It also is included in Numbers and Faces, a tiny anthology of poetry-with-mathematics that I edited for the Humanistic Mathematics Network in 2001.  Also, here is a link to a YouTube video of a 2011 reading at the Library of Congress in which Wagoner was featured (along with C. D. Wright).  He is introduced at about 6 minutes and 30 seconds into the video.


  1. I really enjoyed this post. Related rates is one of my favorite calculus topics. I wrote a little about this post and your blog on the AMS blog on math blogs: http://blogs.ams.org/blogonmathblogs/2013/06/24/the-poetry-of-calculus/