Category: Humor

Undo It

One of the basic notions of functions that’s taught in Precalculus and in Discrete Mathematics is the notion of an inverse function: if f: A \to B is a one-to-one and onto function, then there is an inverse function f^{-1}: B \to A so that

f^{-1}(f(a)) = a for all a \in A and

f(f^{-1}(b)) = b for all b \in B.

If A = B = \mathbb{R}, this is commonly taught in high school as a function that satisfies the horizontal line test.

In other words, if the function f is applied to a, the result is f(a). When the inverse function is applied to that, the answer is the original number a. Therefore, I’ll tell my class, “By applying the function f^{-1}, we uh-uh-uh-uh-uh-uh-uh-undo it.”

If I have a few country music fans in the class, this always generates a bit of a laugh.

See also the amazing duet with Carrie Underwood and Steven Tyler at the 2011 ACM awards:

Guns on university campuses

Here in Texas, public universities are trying to figure out how they’re going to comply with a recently enacted state campus-carry law so that licensed handgun owners can bring their firearms to campus. A small sampling of local news articles and websites on this topic:

And in the midst of this debate, I found the opportunity for a mathematical wisecrack.

handgun

I’ve used this wisecrack in my probability class to great effect, as the joke pedagogically illustrates the important difference between P(A \mid B) and P(A \cap B).

green line

For what it’s worth, here’s the version of the joke as I first saw it (in the book Absolute Zero Gravity):

Then there was the statistician who hated to fly because he had nightmares about terrorists with bombs. Yes, he knew that it was a million to one chance, but that wasn’t good enough. So he took a lot of trains until he realized what he had to do.

Now, whenever he flies, he packs a bomb in his own suitcase. Hey, do you know what the odds are against an airplane carrying two bombs?

green line

Two final notes:

  1. For the humor-impaired, I’m not referring to all gun owners as idiots. The only people I’m calling idiots are me and those that would slaughter innocent people (and these two sets are disjoint).
  2. Though it’s certainly an important issue, I have no interest in debating the wisdom of the campus-carry law on this blog. Rather, the point of this post was using current events to memorably illustrate mathematical ideas.

The Unsuccessful Self-Treatment of a Case of “Writer’s Block”

In 1974, Dennis Upper published his wry and classic intellectual treatise entitled The Unsuccessful Self-Treatment of a Case of “Writer’s Block” in the Journal of Applied Behavior Analysis. If you’ve never seen this before, trust me, you want to see this: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1311997/pdf/jaba00061-0143a.pdf

Postscript: In 2007, several authors were able to replicate this work in their paper A Multisite Cross-Cultural Replication of Upper’s (1974) Unsuccessful Self-Treatment of Writer’s Block: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2078566/pdf/jaba-40-04-773.pdf