class dynamics: the law of the excluded middle story --
ask students to raise their hands in response to a yes/no question ("is
this program's runtime quadratic? all who say yes, raise your hands;
no?"). When half the class fails to raise their hands, tell this story.
There's a law in logic called "the law of the excluded middle"; it means
that either a fact is true or its negation is true. Either you are in
class today or you're not in class today. It's pretty sensible, but
there's a group of logicians called the intuitionists who don't believe in
the law of the excluded middle. Now, at one logic conference where this
famous logician (we'll call him Tom) was running a session on classical
logic vs. intuitionist logic, there's an argument raging back and forth
over the law of the excluded middle, but Tom, being an older fellow, has
tuned out and is catching a nap. All of the sudden the two main antagonist
turn to Tom and clamour for him to decide the issue. Tom wakes up with a
start, blinks a few times, and then ventures this answer into the tense
silence:
"Well.. I suppose we can all agree that either the law of the excluded
middle holds or it doesn't."
I then finish off by telling everyone that in this class we believe in
the law of the excluded middle; so, everyone must raise their hands for
some option. (P.S. I almost always give the option "it depends" as an
answer to make people who don't know comfortable giving some answer.. as
"it depends" is almost always also technically correct.)