Extraneous -- and so on

     Since my junior high math days, when I first heard the word "extraneous," I have loved the sound of it, the feel of my mouth when I say it, the mystery of how solving an equation can lead to extra solutions.   And then learning to check found-solutions to see if they were true solutions -- a process that has been multiply useful to me far afield from mathematics.
     My love for this math-word drew me quickly to the title of a poem by Alex Walsh, a high school student from Oberlin, Ohio, who presented her work at the poetry-with-math reading at JMM in Baltimore last Friday.   Here are her poems "Convergence" and "The Extraneous Solution" :

Convergence     by Alex Walsh

My father’s a mathematician, as
are his father and two of his brothers,
plus a sister-in-law and now
a son. I adopted trigonometric families
long before I learned to write
a sonnet, the beauty of e
to the x and its derivative lodged
deep in my brain in a way
iambic pentameter could only hope
to imitate. I found that x
was nothing compared to an alphabet
full of letters whose use I
never had to justify, but the longer
I insisted I was a poet, the more
integrals began to occupy the vacant
spaces in my mind, filling the holes
not even free verse could satisfy
as related rates transformed me
into yet another term in the infinite sequence.

The Extraneous Solution     by Alex Walsh

Ten billion possible permutations.
What was the chance I’d dial yours?

When you agreed
to be mutually exclusive,
I stopped calculating
how my every step
would affect you

but you reduced me
to my lowest terms
until I was nothing but a first-degree
polynomial, the steady slope
to your quartic variation.

In our inverse relationship,
my love grew as quickly
as yours faded into the axis.
Eventually, I stopped trying
to plot your points.

The smaller I grew,
the closer we came to our limit,
and when at last I had
all but disappeared,
you pointed to the hole
where our value should have been.

I guess we weren’t
differentiable after all.

Alex's father is an Oberlin College mathematics professor, James Walsh.  Often, family members of mathematicians write with great insight into mathematics and mathematicians.  For more of this phenomenon see, for example, my July 20, 2010 posting.