TITLE: Encounters with Large Numbers and the Limits of Programs
AUTHOR: Eugene Wallingford
DATE: March 22, 2011  4:45 PM
DESC: 
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BODY:
Yesterday, this
<A HREF="http://xkcd.com/radiation/">
   xkcd illustration</A>
of radiation doses made the round of Twitter.  My first thought
was computational: this graph is a great way to help students
see what "order of magnitude" means and how the idea matters
to our understanding of a real-world phenomenon.

Late yesterday afternoon, one of my colleagues stopped by to
describe a Facebook conversation he had been having with a
few of our students, and in particular one of out better
students.  This student announced that he was going to write
a program to generate all possible brackets for the men's
NCAA basketball tournament.  My colleague said, "Um, there
are 2 to the 67th power brackets", to which the student
responded, "Yeah, I know, that's why I'm going to write a
program.  There are too many to do by hand."  From this
followed a discussion of just how big 2**67 is and how long
it would take a program to generate all the brackets.  Even
using a few heuristics to trim the problem down, such as
always picking a 1-seed to beat a 16-seed, the number is
astronomically large.  (Or, as
<A HREF="http://marginalrevolution.com/marginalrevolution/2006/08/the_wisdom_of_r.html">
   Richard Feynman suggests</A>,
"economically large".)

Sometimes, even good students can gain a better understanding
of a concept by encountering it in the wild.  This is perhaps
even more often true when the idea is unintuitive or beyond
our usual experience.
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