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:
x/x = xx.
(10+x+xx)1/x/xx/41/x = x.
(xx-1-1)1/x + tan(π/(x+1)) = x.
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.
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.
With the weekend close upon us, no doubt many of you are looking forward to a reprieve from the work week. The more popular among you may even have some engagements lined up. Even for those of you with “friends” or “hobbies,” however, there always comes a point when the evening begins to come to a close.
Suppose it’s late and you’re looking for a good time. Temptation runs rampant in the midnight hour of a Saturday night, especially for those of us in the fast-paced world of graduate school. But before you open that bottle, or pick up the phone to talk to live singles in your area, let me take the opportunity to inform you of a new way to spend your time during the late night wind-down: starting this weekend, you will be able to relive your childhood through the nostalgia-inducing satire that is Look Around You.
That’s right: starting this weekend, Adult Swim will begin airing the former BBC series on Sunday mornings (or late Saturday nights, depending on who you ask) at 1 a.m. The show lasted only two seasons, although I am of the firm belief that the first season was the more inspired of the two – it took it’s motivation from science videos shown to children during school on those rare days when teachers “rewarded” us by letting us watch an educational video during class time. The show’s parody of these old videos is nearly dead on, and the dry delivery with which the program makes its absurd statements only makes the show that much better. Plus, those of you with a keen eye may notice some extras who are now clearly much more famous than they were when these programs were produced.
You may be wondering what this all has to do with mathematics. The answer is that one of the educational videos is all about maths. The video is pretty fantastic, and shows that it is possible to make math funny to a general audience and a mathematical audience at the same time – something that most t-shirt designs fail to do.
The clip itself is on YouTube, but because the show is coming to Adult Swim, I’m not sure how long the video will stay up. If you haven’t seen it, take 10 minutes and watch – I promise it will be worth your time. Just make sure you have your copy book nearby.
Here’s wishing a happy weekend to you all. As for myself, I’m off to the store to buy more razor blades and Garry gum.
Recently, I found myself thinking of mathematics in an unlikely set of circumstances: while watching VH1’s latest “Celebreality” show, Brooke Knows Best. I realize that an admission like this may be embarrassing, and so it is for the sake of your edification, dear reader, that I am willing to go on the record with this deliciously shameful information.
For those of you who may not know, the titular character is the daughter of Santa with Muscles star and All-American hero, Hulk Hogan. In the show, Brooke lives in an expensive looking condo in Miami, goes to the beach, and sings her own theme song. This is about as much as I know. I swear. For those of you who are curious, the following video gives a good sense of what this show is all about.
The particular episode to which I would like to draw your attention (Episode 4) involved Brooke traveling to Panama City, Florida, to host some Spring Break parties. And I bet you thought math and spring break were incompatible.
Because of his overprotective nature (or because the producers thought it would make better television), Hulk Hogan decides that it’s a good idea to tag along on these spring break adventures. He even brings his chubby, mullet-sporting friend in tow, and the two of them cause all kinds of PG-13 hilarity. It is as if they are the love children of the love children of Abbott & Costello and Schwarzenegger & Stallone.
Hulk Hogan sees dead people.
One day, Hulk suggests that the group go visit The World’s Largest Human Maze (or, as he calls it, “The World’s Largest Human Maze in the world”). The maze in question is the Gran Maze of Panama City. Calling it the World’s Largest Human Maze is a bit deceptive, as there are hedge mazes which are larger – however, to the maze’s credit, it does not seem to refer to itself as the World’s Largest Maze in any of its information.
In any event, they go to this maze: Hulk and his buddy as one team, along with Brooke and her two roommates as another. At some point during their travels through the maze, they decide to split up and make a competition out of it: whichever team can make it through the maze first will get to plan the agenda for the rest of the day. Hulk and his friend make it through first, but only by squirming underneath the wall panels. The other team, once they learn of this deception, declares Hulk’s victory null and void.
Hulk Hogan: setting a bad example for maze solvers worldwide.
There is certainly a moral here: don’t cheat. But there is another important moral here, one I think may be lost on Hulk Hogan, even to this day. That moral is this: Hulk, you should have brushed up on your maze-solving algorithms!
Indeed, there are a number of procedures one can follow in order to try and solve a maze. Perhaps the most well known is the Wall Follower algorithm. In this procedure, you walk through the maze keeping either your left or right hand in contact with the wall of the maze at all times. If you do this, without removing your hand from the wall, you will eventually find the exit. Here is an example:
Solving a Maze: The Wall Follower algorithm. This maze was constructed using the Maze Maker.
Now, the astute reader may realize that unfortunately, this method will not always lead you to the end of the maze. Even in a simple example, such as the one below, it is easy to see that regardless of whether you follow your left hand or your right hand, you will merely circle the entrance and never reach the end.
Failure of the Wall Follower algorithm
So, how do we know if the Wall Follower algorithm will work? This algorithm will always lead us to the exit (provided there is one) as long as the maze itself is simply connected. Less rigorously, when the maze cannot be solved using this algorithm, it is because the maze is in separate pieces. In the example above, we see that the piece of the maze that surrounds the start is disjoint from the rest of the maze.
Why, then, does this algorithm work if the maze is simply connected? Because every simply connected maze can be continuously deformed to a circle (i.e. such mazes are homeomorphic to the circle). Once we deform the maze to a circle, it is obvious how the wall follower algorithm works: it is equivalent to simply tracing your way along a circle between two points. This video does a better job explaining what goes on:
So, had Hulk confirmed that this human maze was, in fact, simply connected, he could have used this algorithm to try and beat his daughter fair and square. However, what if the maze is not simply connected? Indeed, a zoomed in view of the maze, courtesy of Google Maps, is somewhat inconclusive. How then, could Hulk guarantee that he would eventually make his way out?
For more general mazes, we can turn to another algorithm: Tremaux’s algorithm. This algorithm will lead you to the exit even in mazes that are not simply connected. However, Tremaux’s algorithm also requires something that the Wall Follower algorithm does not: namely, you must have some way of marking your path.
The algorithm can be described according to the following rules:
Walk down the maze, drawing a line behind you.
When you come to the first intersection, choose a path at random and follow it.
When you come to a dead end, turn around and return to the last intersection.
If you are walking down a corridor that you have not been down before, and you come to an intersection you have already visited, treat the intersection as a dead end and turn around.
If you are walking down a corridor that you have been down before, and you come to an intersection (necessarily one you have already visited), then go down a path which you have not visited yet, if possible. If this is not possible, go down a path you have only been down once.
Rule 5 may look restrictive, but in fact, with this algorithm you will never need to walk down the same corridor more than twice. If the maze has a solution, this algorithm will find it. Moreover, once you have used this algorithm to find a solution, the corridors marked only once will trace out a direct path to the finish.
Solving a Maze: Tremaux’s algorithm. Notice that no corridor is traveled more than twice, and the ones traveled exactly once trace a direct path to the finish.
So there you go, Hulk. Two methods you could’ve used to try and defeat your daughter fair and square. Granted, there is no guarantee that following these procedures would have gotten you through any faster than your daughter, but they certainly wouldn’t have disqualified you from victory. Instead of being able to savor your win, you were called a cheater, and your prize was revoked.
Let this episode serve as a lesson to aspiring professional wrestlers everywhere: math can be of service, even to you.
For more on maze algorithms (both algorithms for creating mazes, or for solving them), this website offers a treasure trove of useful information. Hopefully Hulk Hogan will do his research the next time he makes such a mathematical challenge.
Hulk Hogan is ready to listen to what mathematics has to say. Are you?
You knew it had to be coming. Any self-respecting individual interested in the intersection of math with popular culture must, at some point, discuss the canonical element of said intersection: CBS’s own crime solving math show, Numb3rs. The use of the 3 is to eliminate any ambiguity surrounding the subject matter of a show called “Numbers.”
Since premiering in January of 2005, Numb3rs has been a consistent performer for CBS, in spite of (or because of, depending on your assumptions about the makeup of the show’s audience) its Friday night time slot. For those of you who may have never seen the show, the following synopsis should help give you some perspective:
Body counts, multiple criminal masterminds, and perpetrators who are likely to act again … this is the world of NUMB3RS. FBI agent Don Eppes (Rob Morrow) couldn’t be more different from his younger brother, Charlie (David Krumholtz), a brilliant math professor at a California university. Don deals in hard facts and evidence, whereas Charlie thrives in a world of mathematical probability and equations. But despite their disparate lives and career paths, Don and Charlie often combine their areas of expertise to solve a wide range of challenging crimes in Los Angeles. (Courtesy of the Numb3rs Season 2 DVD Box)
Indeed, mathematicians would be nowhere without their probabilities, or their equations. Startlingly, one could replace the word “equations” by the word “witchcraft” without at all effecting the tone of the above synopsis.
Let’s take a look at the man who provides the center for the show, Professor Charlie Eppes.
When you’re this good at math, you get to wear blazers made entirely of gold.
Watch a few episodes of Numb3rs (or read thisWikipedia entry), and you will likely learn the following about this darling mathematician:
1. Charlie graduated from Princeton when he was 16, and is a young math prodigy. 2. Charlie enjoys chess. 3. Charlie loves blackboards. 4. Charlie has a beautiful girlfriend (a former graduate student, no less) named Amita Ramanujan, who may or may not be related to this famous (and awesome) mathematician.
5. Charlie enjoys socializing, and appears to shower regularly. 6. Charlie loves to explain mathematical concepts using real world examples, such as vacuums or spiders (see below).
Spiders love math.
What are we to make of these observations? While some play in to stereotypes of mathematicians, others fly in the face of those very same stereotypes.
For the record, let it be known that you don’t have to graduate from college when you’re 16 to be a good mathematician (although it certainly doesn’t hurt). Moreover, not all mathematicians are good at, or even enjoy chess.
By and large, though, we do enjoy a good blackboard.
Points 4 and 5 signify a departure from the math nerd we all know and love. A sexy, brilliant mathematician with an equally sexy, brilliant mathematician? Neither of them even wear glasses! Not to mention the fact that Charlie has more charm than most of the other characters on the show. Is he a mathematician, or a rock star? Or, even better, is he merely a prophet for the future, in which mathematicians and rock stars will be one and the same?
Of course, when you are centering your show on a mathematician, you had better make that mathematician marketable. So in a sense, avoiding certain stereotypes becomes a necessity. Still, having a positive mathematics role model like Charlie Eppes certainly can’t be bad for the math community. In fact, if the below video is any indication, people LOVE mathematicians.
Turn up the volume and press play. You won’t be disappointed.
This is not to say that Charlie is the only character who displays certain stereotypical idiosyncrasies. In fact, Charlie’s friend and colleague Larry Fleinhardt exhibits behaviors stereotypical of mathematics savants, including a certain social awkwardness, as well as an aversion to any food that is not white. However, since Professor Fleinhardt is technically a Physicist, I will throw him to the Physics camp for interpretation.
Mathematicians may be portrayed relatively favorably, but what about the math itself? Is it legit? Well, it’s hard to say, really, since when all is said and done, there’s not a whole lot of math on display. Certainly there are a lot of scenes with people waving their hands and discussing math, or scenes with chalkboards that have math on them, but these scenes are often placeholders in between scenes with guns or explosions or good looking government employees (here I use “or” in the inclusive, mathematical sense of the word). This, however, is expected, again because of the mass market nature of the program. Overall, I think you’d find it difficult to do math any better after having watched an episode of Numb3rs. On the plus side, they do emphasize that the story lines are based on actual cases, so viewers can take comfort in the fact that even out in the real world, math is helping to bring in the bad guys.
The show certainly doesn’t do any damage to math’s reputation. By making a protagonist who is smart and has a winning smile, the creators seem to be doing their part to show that math needn’t be as scary as it’s made out to be. While there are plenty of moments where it can be hard to suspend your disbelief (he may be smart, but I don’t think even DoogieHowser can solve the Riemann Hypothesis, contrary to what Prime Suspect would have us believe), as an overall ambassador to the universe of mathematics, the show gets a pass. If nothing else, it teaches America that not all mathematicians are completely socially inept, even if we do live at home and put the moves on a few of our advisees.
