Explain xkcd

Date: March 15th, 2011
From: Dan Hoey
Subject: Fairy Tales

tfogarty wrote:

  The story is called, The Ant and the Grasshopper, which isn't a
  fairy tale but one of Aesop's fables.  You can learn more about it
  here:  http://en.wikipedia.org/wiki/The_Ant_and_the_Grasshopper

So somehow the grasshopper singing/playing/not working is modeled by
"contraction to a point on a manifold that is not a 3-sphere.  Any
idea what the connection is?