Sunday, June 25, 2006

Poetry and Math: moments and removable discontinuities

Below is one of my favorite poems.

This Much I Do Remember:

It was after dinner.
You were talking to me across the table
about something or other,
a greyhound you had seen that day
or a song you liked,

and I was looking past you
over your bare shoulder
at the three oranges lying
on the kitchen counter
next to the small electric bean grinder,
which was also orange,
and the orange and white cruets for vinegar and oil.

All of which converged
into a random still life,
so fastened together by the hasp of color,
and so fixed behind the animated
foreground of your
talking and smiling,
gesturing and pouring wine,
and the camber of your shoulders

that I could feel it being painted within me,
brushed on the wall of my skull,
while the tone of your voice
lifted and fell in its flight,
and the three oranges
remained fixed on the counter
the way stars are said
to be fixed in the universe.

Then all the moments of the past
began to line up behind that moment
and all the moments to come
assembled in front of it in a long row,
giving me reason to believe
that this was a moment I had rescued
from the millions that rush out of sight
into the darkness behind the eyes.

Even after I have forgotten what year it is,
my middle name,
and the meaning of money,
I will still carry in my pocket
the small coin of that moment,
minted in the kingdom
that we pace through every day.

--Billy Collins

A moment is such a hard thing to define. Does it have any length, or only position relative to moments before and after it?
A removable discontinuity in mathmatics and a moment in time have some similar attributes. Take the function graphed below that has a R.D. at x = 2.


We see that even thought there is a small circle marking the discontinuity at (2,4), actually the point has no dimension and thus the discontinuity has location but not length.
If you have taken math past Algebra II, the picture above is probably (I hope!) somewhat familiar, but maybe not all that interesting. Recall this part of the poem:
"Then all the moments of the past
began to line up behind that moment
and all the moments to come
assembled in front of it in a long row"

Too bad mathematics courses so rarely try to build on such beautiful connections like this.