Probability and Coincidence

     On page 26 of my copy of the latest New Yorker is a poem by Lia Purpura entitled "Probability."  In her brief poem Purpura renders with poetic power the astonishment each of us feels when meeting a long-ago classmate at an out-of-town super market or some other unexpected event.  Take time to follow the link and read this poem.
     Recently several friends have shared with me their amazement at unexpected coincidences and I have been tempted to illustrate -- perhaps with the birthday paradox --  how likely to happen unexpected events may be.

  With more than 23 persons in a room the chances are more than 50-50

 that two of them will share a birthday (same day, maybe different years).

Many websites offer explanation of this "birthday paradox" -- here is one.

     I offer this link to some thought-provoking quotes about coincidence -- here is one of them, from Isaac Asimov:

People are entirely too disbelieving 

of coincidence. 

They are far too ready to dismiss it

and to build arcane structures  of extremely rickety substance

 in order to avoid it. 

I, on the other hand, see coincidence 
everywhere as an inevitable consequence 

of the laws of probability, 

according to which having no unusual coincidence

 is far more unusual than any coincidence 

could possibly be.

     These words are found in Asimov's essay, "The Planet that Wasn't," originally published in The Magazine of Fantasy and Science Fiction (May 1975).  
     Mathematician Joe Mazur is working on a book (FLUKE) about the nature of randomness and coincidences.