Math on TV: Halls Refresh

If you’ve watched any television recently, you may have noticed the following ad for Halls Refresh. I strongly encourage you to watch it, even if you’ve seen it before, because it’s basically fantastic.


A tremendous ad, to be sure. However, if you didn’t watch closely, you may be wondering what such a sensual commercial has to do with mathematics. Watch again if you missed it – it may help to watch it full screen, although the quality gets muddy.

Did you catch it the second time? When the camera cuts to the Asian kid sitting at his desk, right before he starts to charm Mrs. Hunter, you’ll notice that he has a poster on his wall filled with mathematics. There are 5 equations on the poster, but most are probably too difficult to make out from the Youtube copy. I was fortunate enough to see this ad on television, and after a few replays I made out 4 of the 5 equations. In order, they are as follows:

  1. x/x = xx.
  2. (10+x+xx)1/x/xx/41/x = x.
  3. (xx-1-1)1/x + tan(π/(x+1)) = x.
  4. This one I didn’t get, but I can tell you it was long and involved a logarithm. Bonus points to anyone who can fill in the blank here.
  5. xx – x3 = 4(xx-1 + xx-2).

At first this poster made me a bit upset. Like other math jokes I’ve discussed before, throwing together mathematically complicated equations just for the sake of it seems lazy, when one could instead try to make some kind of joke. It’s not as if the equations above are famous, so initially it may seem like there’s nothing going on under the hood.

Upon further investigation, however, I discovered that somebody involved in the production had a sense of humor. Let’s see what happens when we look for solutions to each of the equations.

The first one is easy: since x/x = 1, we’re looking for a solution to xx = 1. This happens, of course, when x = 1.

The equations that follow are too difficult to solve by hand, but this is where we let computers do the work for us. If you graph these equations, you’ll see that the solution to the 2nd is x = 2, the solution to the 3rd is x = 3, and the solution to the 5th is x = 5. Even though I wasn’t able to read that fourth equation, I’m fairly confident that the solution to it is x = 4.

It’s not a great joke, I know, but I appreciate the fact that there is a payoff for those who are willing to dig a little bit. It’s not perfect (for example, the third equation has a second solution near x = 0.33), but it’s certainly better than many attempts. Kudos to you, Halls Refresh. This almost makes up for your use of the stereotypical nerdy Asian dude who is good at math and likes dragons.

For more surreal advertising, there’s always this classic. No math involved, unfortunately, but I’m willing to let it slide.

September 30, 2009 | 1 Comment »

Reforming Education through Geek Chic

Earlier this month, Wired published an article written by Daniel Roth, enticingly titled “Making Geeks Cool Could Reform Education.” It serves as an interesting counterpoint to the commonly used argument that the best way to reform education is to better integrate it with the most current technology, so that going to school feels less like going to school and more like playing video games (family friendly ones, of course).

Sorry, Typing of the Dead, but you’re a little too creepy.

The essay in Wired takes a slightly different approach – it profiles schools that have successfully channeled the inner geeks of their students, the argument being that the geek subculture rewards intelligence with popularity. To do this, schools must make learning seem cool. This is a feat which is easier said than done, because, as we all know, there’s no better way to convince a teenager that something is uncool than to repeatedly say how cool it is.
One way in which the schools were able to motivate students to embrace their inner geek was to surround them with older people – teachers, parents, and working professionals. One school in particular forces students to present their work to groups of outsiders. The effect here is to downplay the importance of youth culture: if students can see what their education can do for them down the road, they’re more willing to value it in the present.

Other schools have taken different measures, but the goal of curbing a focus on youth is the same. For example, at Roxbury Prep, Roth tells us that “Kids eat lunch in the classroom, they’re not allowed to talk in the halls, and they’re disciplined for using the word nerd.” Certainly social time with peers is important, but this added emphasis on academic performance appears to be paying off, because students in these schools value learning for its own sake, and are rewarded for their efforts not just by their teachers, but by their peer group as well.

Applied to mathematics, this philosophy could have a significant impact. After all, many students will tell you they hate math because they don’t see the value in it. But if students were able to interact with people who used mathematics in their everyday lives (aside from their classmates and their math teacher), one hopes they would be motivated to learn the material. Or, even better, even for students who don’t plan to make a career out of mathematics, in a culture where learning is perceived as cool, one would hope that students would take advanced mathematics just to get a taste for what it’s like.

If only…at least a man can dream. Perhaps one day we really will see the triumph of Geek Chic at all levels of education. Certainly, this is a good sign (thanks Michelle). Once we see some modern pocket protectors, I think we’ll have reached the tipping point.

September 23, 2009 | No Comments »

Math in the Movies: Hodgepodge Edition

Most of the time I write about films where math takes a central role, but it is just as often the case that mathematics is at work in more of a supporting capacity. There are many examples of this phenomenon, even if we restrict our attention to movies that are fairly recent. To catalog each such instance would no doubt be fairly time consuming, but thankfully someone has already begun the task. It comforts me to know that I am not the only one who takes pleasure in seeing mathematics on the big screen.
Last week the Boston Globe ran an article that discusses the appearance of mathematics in a variety of recent films. In addition to mentioning the recent work on zombie dynamics, the article also discusses the link to mathematics as found in films like Casino Royale, Harry Potter and the Half Blood Prince, and The Dark Knight.

It’s a short article and worth a read, but here are some highlights:

1. The ferry scene in The Dark Knight gives a modern twist on the classic Prisoner’s Dilemma. The Dilemma is best understood by means of the following table (courtesy of Wikipedia):


Suppose two men have been arrested for a crime. Each is separated, and is asked by the authorities what happened. If one man betrays the other, the betrayer will go free while the betrayed will serve a long sentence. If both men betray, however, both will serve a moderate sentence, while if both men stay silent each will serve a short sentence.

One easily sees from the table that independent of Prisoner B’s actions, Prisoner A will receive a better payoff by betraying (it’s the difference between going free versus serving six months if Prisoner B stays silent, and serving 5 years versus serving 10 years if Prisoner B betrays). However, if both prisoners act in this way, they will both betray and end up serving 5 years, far longer than they would serve if both of them had remained silent in the first place. Therein lies the dilemma.

Of course, what happens in The Dark Knight isn’t quite so interesting. In this case, the Joker hijacks a pair of ferries and tells the passengers on each that they have the controls to blow up the other boat. If neither boat is destroyed by midnight, the Joker will destroy both.

In other words, we have the following diagram:

In this case, the strategy is clear: you want to blow up the other boat before your own boat is blown up. This strategy, of course, ignores the difficulty inherent in deciding to blow up a boat full of people – the situation is made more interesting by the fact that one of the boats is filled with convicts.

No doubt it would’ve made for a better social experiment had the Joker gone with a more traditional Prisoner’s dilemma, since here there is no advantage if both parties remain silent. One could argue that this lack of appreciation for the underlying mathematics was an early indication that the Joker’s plans would ultimately be foiled.

Criminal mastermind, or mediocre math student?

2. Even spies enjoy a bit of math here and there. The introduction to 2006’s Casino Royale uses a bit of fractal geometry, in the form of self-replicating spades:

3. 6 Degrees of Kevin Bacon is, in fact, an easier game with a celebrity other than Kevin Bacon. Surprisingly, the game is easiest when played with Dennis Hopper – in a ranking of most connected actors, Kevin Bacon came in 507th.

Sorry Kev, but even a fancy tie and a delicious last name can’t change the fact that there are actors with more connections than you.

For more links between math and the movies, I recommend taking a look at the full article. The moral here is that you can run, but you cannot hide from mathematics.

(Hat tip to Caroline for the article link.)

September 15, 2009 | No Comments »

Make Money Money, Make Money Money Money! (and Learn Math, too)

Let me begin by saying that, in response to the question Why is 9/09/09 so special?, my response is simple: it’s not.

In fact, I would argue that 09/08/09 is much more interesting. This claim has nothing to do with numerology, and everything to do with President Obama’s speech to the youth of America on the value of education. The speech made very clear the importance of taking education seriously, and hopefully convinced students that a good education benefits not only themselves, but also society at large. In case you missed the speech, the transcript can be found here.


Although the speech was about education in general, mathematics got a little bit of love too. Here’s one such example:

What you make of your education will decide nothing less than the future of this country. What you’re learning in school today will determine whether we as a nation can meet our greatest challenges in the future.

You’ll need the knowledge and problem-solving skills you learn in science and math to cure diseases like cancer and AIDS, and to develop new energy technologies and protect our environment. You’ll need the insights and critical thinking skills you gain in history and social studies to fight poverty and homelessness, crime and discrimination, and make our nation more fair and more free. You’ll need the creativity and ingenuity you develop in all your classes to build new companies that will create new jobs and boost our economy.
What a bunch of socialist propaganda. Even so, I’m glad the President decided to emphasize the importance of education today, and I hope that students were able to take something away from it.

As an addendum to this theme, I’d like to point out that while mathematics is an essential tool for fighting disease or curbing global warming, there is perhaps a more immediate benefit to studying math that was not highlighted in today’s speech; a benefit that appeals more to our self-interest than a sense of duty, but with the end result still being a knowledge of mathematics. That benefit, of course, is the almighty dollar.

Last month, the Free Exchange blog over at the Economist highlighted a paper by Joshua Goodman that analyzed the returns on learning math in high school. For some reason Mr. Goodman’s website seems to be down, so the link to the paper is broken, but you can also find the paper here.

What were his findings? While earlier authors had found that each year of schooling is correlated with an eventual earnings increase of 10-15%, Mr. Goodman found that a significant amount of this increase can be attributed to coursework in mathematics (results which were strongest for low-income black males).

Of course, we all know that correlation does not imply causation, so it’s a little disingenuous to say that if you take more math classes in high school, you’ll get more money as an adult (and certainly for those of us in graduate school, it’s easy to imagine that the opposite is true). However, as pointed out on the Economist’s blog:

One reason why people who learn more mathematics earn more is because doing maths makes you smarter and more productive. According to Clancy Blair, a professor of psychology at NYU, the act of performing mathematical calculations improves reasoning, problem-solving skills, behaviour, and the ability to self-regulate. These skills are associated with the pre-frontal cortex part of the brain, which continues to develop into your early 30s.

So, while math may not make you richer, it will probably make you smarter – and this in turn can (hopefully) help you live a more comfortable lifestyle.

Then again, how could a lifestyle involving mathematics not be comfortable?

September 8, 2009 | No Comments »

Comic (but not Comical) Mathematics

A few months ago, my girlfriend and I were persuaded to subscribe to the LA Times by a very nice man at a nearby Ralph’s store who offered us $20 in groceries for the exchange. “Just try it out,” he insisted, “because you can always cancel and we’ll simply pro-rate the cost based on how long you were a subscriber.”
Fantastic, we thought. Given the current uncertainty surrounding the future of the newspaper industry, subscribing made us feel like responsible citizens – like giving blood, but with fewer personal questions beforehand.

Unfortunately, once the newspaper began to arrive, we had to face the fact that we never read it. I think I skimmed through it a couple days that first week, but after that the papers would go from our doorstep to the recycling bin. Try as we might, we simply couldn’t fit a morning newspaper routine into our lifestyle. And so, with a heavy heart, we canceled our subscription.

To be honest, I haven’t really noticed a difference. All the news I need I can easily access on the internet. The only part I do sometimes miss is rifling through the comics. Sure, you can always go to a website like comics.com and see what your favorite syndicated cartoon characters are up to, but I still prefer the layout a newspaper provides, with dozens of comics squeezed together, allowing you to read them all rapid-fire without having to wade through a list of comics and be bothered by loading times.

My father remedies this by e-mailing me comics directly. Every day I know that I can look forward to the latest adventures of Liō, but this daily standard is sometimes intermingled with other comics. For example, just the other day my father sent me the following math-themed comic:


This is the work of a man named Dave Coverly, who apparently has been named Cartoonist of the Year by the National Cartoonists Society. More of his work can be found here. Some of his cartoons are quite good. Unfortunately, the one above is not.

The above cartoon has the potential to work on multiple levels, but fails to do so. Certainly anyone can read the comic and get the joke (ha ha, the description on the sign involves math, it’s funny because the books in the bin are math books!), but the sentence on the sign doesn’t make any sense. Forget that the mathematical expression is complicated – replace it by a number, such as 1.8. Then the sign reads “Math Book Sale: Buy 2, Get 1 at 1.8!”

Huh? What is this supposed to mean? If Coverly had written 1.8 instead of (3/4 x 2B) ÷ (7π/100), I would hope that an editor would’ve said something like “Hey man, that doesn’t make any sense, why not try for a joke that isn’t so sloppy?” Instead, we get basically the same punchline, but masked by a more convoluted expression. No doubt the reader is meant to simply see that the sign involves math, chuckle inwardly, and turn the page.

It may sound like I’m just trying to pick a fight, but I don’t think this kind of thing would fly with another subject. For example, suppose the comic had a Spanish theme rather than a Math theme. In such a case, Coverly’s comic might look something like this:


This cartoon, like the last one, works on one level: it’s a Spanish book sale, and the sign describes the sale with some Spanish. It’s not hard to get the joke.

However, anyone with a basic understanding of Spanish would probably find this comic more confusing than funny, because the Spanish phrase doesn’t make sense. The phrase certainly doesn’t explain the sale, but it’s also not particularly funny in it’s own right. Why wouldn’t the sign say “half price” in Spanish? Alternatively, one could write a joke in Spanish – this would be lost on people who don’t speak Spanish, but they would still be able to appreciate the basic joke, namely that the Spanish book sale sign is partially written in Spanish.

The situation with math should be no different than the situation with Spanish, but apparently a comic like this is allowed to slide by. Perhaps our population’s mathematical illiteracy is worse than our Spanish illiteracy. Even so, I think it’s fair to call out this comic for simply being lazy. It’s not hard to get the same joke across, but enhance it so that the sign actually makes sense. Here is just one way Coverly could’ve enriched his original idea:

I feel better already.

Of course, one could argue that Parade Magazine is not the place one should go for a daily dose of mathematical humor. And indeed, you’d be correct. Of the nationally syndicated strips, Foxtrot is the only one that consistently uses math for a punchline, but such examples are few and far between. As always, for math themed comics, one is best advised to search here.

September 2, 2009 | 1 Comment »