Multiple choice

I had a good chuckle at the following photo.

Here’s a thought bubble if you’d like to think about it before I reveal the answer.

You’d think that, since there are four possible answers, that you should answer 25%. However, there are two choices for 25%, so the chance of picking 25% as your answer is 2/4, or 50%. But there’s only one way to answer 50%, so the answer should be 1/4, or 25%. To quote “The King and I,” et cetera, et cetera, et cetera.

The correct answer, of course, is adding a fifth option: E) 20%.

Typographical error (perhaps)

Here’s a great typo that I saw on a paper submitted by one of my former students who aspires to be a secondary math teacher. Instead of writing “engaging one’s students,” she accidentally wrote “encaging one’s students.”

Infinite number of monkeys

From Wikipedia:

The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare.

This can be formally proven using the second Borel-Cantelli Lemma, a topic which requires measure-theoretic probability. Thus leading me to one of the driest observations that I’ve ever read in a graduate-level textbook, following the proofs of the Borel-Cantelli Lemmas:

The record of a prolonged coin-tossing game is bound to contain every conceivable book in the Morse code [using heads for dot and tails for dash], from Hamlet to eight-place logarithmic tables. It has been suggested that an army of monkeys might be trained to pound typewriters at random in the hope that ultimately great works of literature would be produced. Using a coin for the same purpose may save feeding and training expenses and free the monkeys for other monkey business.

W. Feller, An Introduction to Probability Theory and Its Applications, Volume 1 (Chapter 8.3), page 202.

25 divided by 5 is 14

A good clean joke

Q: How do you tell the difference between an introverted math professor and an extroverted math professor?

A: The extroverted math professor will look at your shoes when talking to you.

Finite simple group of order 2

I like showing this to my students around Valentine’s Day. The singers were math grad students at Northwestern.

Infraction

While I can’t take credit for this one-liner, I’m more than happy to share it.

A colleague was explaining his expectations for simplifying expressions such as

$\displaystyle \frac{\displaystyle ~~~\frac{2x}{x^2+1}~~~}{\displaystyle ~~~\frac{x}{x^2-1}~~~}$

Of course, this isn’t yet simplified, but his students were balking about doing the required work. So, on the spur of the moment, he laid down a simple rule:

Not simplifying a fraction in a fraction is an infraction.

Utterly brilliant.

Ontologically

Case Study #465 of how not to teach a class.

Me: Ontologically, what kind of object is this?

Student: It might help if I knew what “ontologically” meant.

Independence

Once in my probability class, a student asked a reasonable question — could I intuitively explain the difference between “uncorrelated” and “independent”? My expert answer: it’s like the difference between “mostly dead” and “all dead.”

Greek letters

One evening, I was watching the Philadelphia Eagles play the Chicago Bears on NBC’s Sunday Night Football telecast. The bottom of the screen showed the score: “PHI 14 CHI 7.” As my wife walked by, she innocently asked, “Why are there Greek letters on the screen?”

We’ve been fans of $\phi$ and $\chi$ ever since.