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.

 

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