"Binary Heart" -- linking love and mathematics

      From the xkcd webcomic by Randall Munroe -- and also shown on the cover of Strange Attractors: Poems of Love and Mathematics, we have this reminder of upcoming Valentine's Day.

"Binary Heart" by Randall Munroe,
at https://xkcd.com/99/

     Munroe's clever drawings "of romance, sarcasm, math, and language" have appeared also in previous postings in this blog (here's a link) and his website is fun to visit.
     The anthology, Strange Attractors; Poems of Love and Mathematics-- edited by Sarah Glaz and me -- was published in 2008 by AK Peters and contains more than 150 poems of math and love (including another -- "Useless" -- by Munroe.)  More about Munroe is available here.

The Nightmare of an Unsolved Problem

Back in the 1980s when I first met the Collatz conjecture in a number theory textbook it was stated this way:
     Start with any whole number  n :
          If  n  is even, reduce it by half, obtaining  n/2.
          If n is odd, increase it by half and round up to the nearest whole number, obtaining  3n/2 + 1/2 = (3n+1)/2.   Collatz' conjecture asserts that, no matter what the starting number, iteration of this increase-decrease process will each time reach the number 1.   

Math humor

      Phyllis Diller (1917-20120), outspoken and funny, pioneering female comedian, died Monday, August 20.  Her self-deprecating humor was hugely hilarious -- and it helped the rest of us also not to take ourselves too seriously.

     In honor of Phyllis Diller and humor, I first offer a link to a "poem" from a favorite math-cartoonist -- Randall Munroe offers an amusing rhyming critique of the various majors (including math) available to undergraduates --  at xkcd.com.   And, below, I share several slightly funny math jokes adapted from ones found at Math Jokes 4 Mathy Folks and shaped into 4x4 or 5x5 syllable-square poems.

Where are the Women?

Here is a small square poem about a paradox that's been on my mind recently.

               Little Women

               In school, many
               gifted math girls. 
               Later, so few
               famed math women!

Recursion

A mathematician may face a dilemma over the meaning of an ordinary term -- for words like "group" and "identity" and "random" (to name a few) have precise mathematical definitions that differ from their common meanings. Canadian poet Peter Norman's title, "Recursion," however, uses the term as it is used mathematically.  While a definition of "recursion" is widely available in mathematics texts, it was missing in my several English dictionaries -- and I found it only in the OED (though, even there,  noted as now rare or Obs.) : "a backward movement, return."   The term "return" indicates previous forward motion. In mathematical recursion (illustrated below by the Fibonacci sequence) as in Norman's poem, going backward is possible only because forward motion is known. (Interested readers will find an introduction to mathematical recursion following the poem.)

     Recursion    by Peter Norman

     I fall awake alone. Outside,
     nocturnal rain ascends.  

"Mathematical" Limericks

A dozen, a gross, and a score
Plus three times the square root of four
     Divided by seven
     Plus five times eleven
Is nine squared and not a bit more.

What can mathematics do?

For many, mathematics offers interpretive links between a mind and the truths it seeks to know,  the same role that a story plays in this poem -- "Story Water" -- by Jelaluddin Balkhi Rumi (1207 - 1273).