**A Mathematician's Nightmare**

** **

** **Suppose a general store --

items with unknown values

and arbitrary prices,

rounded for ease to

whole-dollar amounts.

Each day Madame X,

keeper of the emporium,

raises or lowers each price --

exceptional bargains

and anti-bargains.

Even-numbered prices

divide by two,

while odd ones climb

by half themselves --

then half a dollar more

to keep the numbers whole.

Today I pause before

a handsome beveled mirror

priced at twenty-seven dollars.

Shall I buy or wait

for fifty-nine days

until the price is lower?

The price-changing scheme of this poem is derived from a version of the Collatz Conjecture, an unsolved problem that has stolen hours of sleep from many mathematicians. Start with any positive integer: if it is even, take half of it; if it is odd, increase it by half and round up to the next whole number. Collatz' Conjecture asserts that, regardless of the starting number, iteration of this decrease-by-half-increase-by-half process eventually leads to the number one.

"A Mathematician's Nightmare" and others of JoAnne Growney's "mathematical' poems are available in *My Dance is Mathematics*, published in 2006 by Paper Kite Press.