## Monday, July 12, 2010

### Poetry-application of The Fundamental Theorem of Arithmetic

Destructive effects of human greed and neglect on the earth's natural environment are echoed hauntingly in the repetitions within "We Are the Final Ones" -- a dirge-like poem I've constructed using the Fundamental Theorem of Arithmetic.  (For those unfamiliar with the theorem, brief explanation is included in paragraphs that follow the poem):

We Are the Final Ones

we breathe dirty air
oil scums our waterways
we breathe dirty air as we breathe dirty air
bees disappear
we breathe dirty air and oil scums our waterways
climate change affects the poor first
we breathe dirty air as oil scums our waterways
oil scums our waterways as we breathe dirty air
we breathe dirty air and bees disappear
glaciers melt
we breathe dirty air as we breathe dirty air and oil scums our waterways
drought is a serial killer
we breathe dirty air and climate change affects the poor first
oil scums our waterways and bees disappear
we breathe dirty air as we breathe dirty air as we breathe dirty air
What will happen to the polar bears ?

The Fundamental Theorem of Arithmetic asserts that every positve integer greater than 1 either is prime or can be factored in exactly one way into a product of powers of prime factors.  In order to recognize whether two factorizations of an integer are the same, the primes are written in increasing order.  For example, 12 = 2² x 3 and 18 = 2 x 3².
Including the title line, "We are the Final Ones" has 17 lines.  The title corresponds to 1 and subsequent lines are associated with, in order, the integers 2, 3,  . . .  17.  For each prime integer (divisible only by itself and 1), a new phrase is introduced.  For composite integers, such as 12, the poetic line is a combination of lines corresponding to its factors and their exponents.  The connector "and" represents multiplication and "as" represents exponentiation.
The first poem I encountered that's structured by this unique factorization theorem is "On the Sadness" by sculptor (and poet) Carl Andre.  I found it in  Numerals 1924-1977 by Ranier F Crone (Yale University Press, 1978);  now it also is available in the math-poetry anthology, Strange Attractors (A K Peters, 2008).  Andre's poem has 46 lines and they correspond to the integers from 47 down to 2.  Here are the first 7 lines:

47                  The door is closed
46 = 2 x 23      We are going to die if the moon changes
45 = 3² x 5      The sky is blue then we are going to die if the grass is green
44 = 2² x 11     We are going to die then we are going to die if the sea is cold
43                   The window is open
42 = 2 x 3 x 7   We are going to die if the sky is blue if men grow old
41                   Night comes slowly
. . .