## Thursday, February 10, 2011

### Dividing by Zero

Fairy godmothers have their magic wands and mathematician have division by zero as a way to make the impossible happen -- for example, we can show that 2 equals 3:

and multiply both sides by x-1 to get                                 x (x - 1) = 0
Now divide both sides by x to get                                           x - 1 = 0
Now substitute 0 for x and add 3 to both sides to get       0 - 1 + 3 = 0 + 3
which simplifies to give                                                               2 = 3

Here, from The Art and Poetry of Chaos:  Images from a Complex World (World Scientific, 2005), is a poem by Robin Chapman  that gives a human interpretation to our topic.

Dividing by Zero       by Robin Chapman

1.
It was a childhood puzzle
before we knew
mathematicians called it
an 'illegal operation'
and banned its computation --
flashcards of stars in columns
and rows, blue and gold,
showing 8 or 4 divisible by 4,
by 2, by 1, or  -- zero?
Nothing goes into something
how many times?

2.
Let 'something'
be the all-in-all-of-it, the whole,
and get as close as you can
to nothing, now closer yet; divide;
the result blows up,
spilling over the edges
of the longest time and farthest space.
So surely zero into one
could create the universe --
all the stars and the human race.

3.
Or let 'something' be a lemon meringue pie,
brown-curled topping, tart filling,
tender crust -- imagine it
waiting on some countertop,
owned by no one,
shared among none,
gathering dust -- but no,
the mold will divide it equally
among its cells, if nothing else.

"Nonlinear Function," another Chapman poem from The Art and Poetry of Chaos may also be found in the anthology Strange Attractors: Poems of Love and Mathematics (Eds Glaz, Growney, A K Peters, 2008).   Chapman's "The Nearest Neighbor Rules" appears in January 18's posting.  Her new poem, "The Game of Life" appears in the inaugural issue of The Journal of Humanistic Mathematics, inspired by the late Alvin White.