Friday, April 25, 2008

Mathematics in Popular Culture

I have been thinking about this post for quite some time, and the impetus to do it right now is the season premiere of the Math/Crime drama ‘Numb3rs’. Also, I recently saw the Math/Gambling film 21, which somehow managed to bore me despite involving two of my favorite pursuits: mathematics and gambling.

‘Numb3rs’ is refreshing (despite the stupid title) because it is clear that they have mathematicians consulting for the show. Also, and more importantly, David Krumholz and Peter MacNicol do a great job portraying mathematicians as human beings. Far too often mathematicians are portrayed as freaks, or worse, as mentally unstable.

The list of films with this tendency is quite long: A Beautiful Mind is the most famous, but there is also Proof, Sneakers, and, bizarrely, Presumed Innocent. I’m forgetting some…

The Oscar-winning film ‘A Beautiful Mind’ is forgiven for participating in this trend, at least somewhat. It is, after all based on a true story. I am using the word ‘based’ fairly loosely – anybody who has read the biography that the film is based on knows that Nash’s schizophrenia manifested itself in a way entirely different than as was shown in the film. In the film, his insanity manifests itself primarily through vivid hallucinations. In real life, he simply became a self-centered, anti-social ass. The film was correct that he underwent electro-shock therapy. But the film overstated his ability to deal with his mental illness simply by concentrating a lot. If only mental illness were so simple!

I haven’t seen ‘Proof’. Apparently Gwyneth Paltrow plays the daughter of Anthony Hopkins’ character, and both are brilliant mathematicians. Also, apparently she suffers from vivid hallucinations, too. (BTW, hallucinations are really a cheap cinematic trick- almost as loathsome as amnesia. But I digress.)

‘Sneakers’ is a fun film that deals with cryptography in a manner that, from the mathematician’s standpoint, is laughable. The film is about the pursuit of an algorithm that allegedly can ‘break all codes’, and it does so instantly. This notion is quite absurd.

To put it simply: it is quite conceivable that two different coding schemes would translate different messages into the same coded text. The idea that the coded text could be decoded without knowing the key, so to speak, is immediately seen to be impossible. Anyway, Ben Kingsley plays the maniac mathematician in this film, though, to be fair, Robert Redford is the good guy mathematician here.

‘Presumed Innocent’ is kind of funny in that Harrison Ford’s wife is the graduate student in math – a background character for most of the film. And then it turns out she killed off Great Scacchi out of insane jealousy.

Let’s see…checking
Ah, of course Good Will Hunting features a mathematician with serious psychological issues.
Little Man Tate – serious psychological issues, though not at the level of mania.

I’ll give credit to Michael Crichton – he has likable, sane mathematicians in both the Jurassic Park series and also Sphere. I’ll forgive him for a moment for being utterly insane when it comes to environmentalism.

Anyway, ‘Good Will Hunting’ is the one that was on the tip of my mind that I could not remember.

So, about ‘21’ – the film managed to get the “Monty Hall problem” correct. The “Monty Hall problem” is as follows: you are on “Let’s make a Deal!” and Monty offers you a choice of three doors. Two of the doors have goats, but one of the three has a new car! So you pick a door. The Monty opens one of the other two doors, which has a goat, and you are offered the chance to switch your pick. What should you do?

There are three choices: switch, stay, and it doesn’t matter. It’s pretty clear that ‘stay’ isn’t the correct answer, so it really comes down to the other two.

Superficially, it looks like you now have even odds of getting the car. Indeed, Marilyn vos Savant famously blundered her answer to this problem by insisting it didn’t matter if you changed or not: with two options, you have a 50-50 chance of getting the car.

But that’s not right. When you picked the door, you only had a 1/3 chance of getting the car. And nothing has changed to improve your initial odds. Regardless of whether you picked the car or not, Monty will be able to open a door showing a goat. So the odds that you picked the car are still 1/3. So…switch.

The film 21 babbles some mumbo-jumbo about changing the variables. But the real thing here is that Monty is not acting randomly. Indeed, if Monty were acting randomly, your odds would be 50-50 when the number of choices was reduced to two. Strange how the probability becomes a function of Monty’s thinking, eh?

Anyway, 21 got that right, but screwed up too many other things. In the middle of the film, they have a big to-do about cashing in chips after Lawrence Fishburne gets on their tail. At the end of the film, this difficulty in a similar situation is simply ignored. But most annoyingly, even more annoying than all the Hollywood twists, was the fact that, when the main guy was sitting on 19, and the dealer had 10, he was shouting “Monkey! Monkey!” In this context, a “Monkey” is a face card. Why would the player want the dealer to hit 20??? Pathetic.


Christopher said...

Nice post Rick. Wasn't the realistic math guy in GWHunting the prof? :)

ilse said...

Math is hard!
*hair flip*

Jolene said...

I knew it! Ilse is a Barbie doll!

I hated Good Will Hunting, by the way.

Oh, and you forgot 21 Grams - I think you were the one who originally reminded me that Sean Penn was a math professor in it. And it fits - he was kind of messed up, what with the cheating on his wife and the stalking of the wife of his heart donor.

whispers said...

Right - 21 Grams, that's the other one I could not remember but which originally inspired this line of thought.

Stalking Naomi Watts is weird? Well sure, if you keep it up after the court order... :)

I remember at the time thinking Good Will Hunting was great, but it hasn't really stood the test of time. And I think most of my problem is with the Robin Williams character. The entire "it's not your fault" thing is pathetic.

whispers said...

Oh, and for me the funniest aspect of GWH was the postdoc named Tom, since one of my fellow grad students from Rutgers named Tom had been postdoccing at MIT when Damon and Afflect met with his supervisor Dan Kleitman. Apparently Tom blew them off and gave them no mind, so they named a sychophant after him. :)

Jolene said...

Fair enough - I suppose if you're going to stalk someone, it's at least understandable if you happen to choose Naomi Watts. Heh.

quickstrategy said...

I thought you were just about to mention the Aronofsky movie, I think it was "Pi", where the guy ... nevermind, you might not have seen it. You should.

whispers said...

I've never seen 'Pi' because I heard the premise and thought it was ludicrous. As I understand it, the general idea is that looking at really long strings of numbers is the path to enlightenment. That sounds a lot more like numerology than mathematics.

Maybe I'll see it someday if I have time to burn and it's free.

Kelly said...

My name is Kelly Clark and I am the founder of PopMatics, a teaching and learning philosophy based on the intersection of pop culture and mathematics. I am currently networking with fellow educators regarding this innovative and interactive approach to mathematics curriculum. The goal of PopMatics is to create a generation of mathematicians by capitalizing on the power of pop culture to connect complex mathematics concepts to students' daily lives. This philosophy can also be applied to all disciplines, PopLearning. I would like to send you a brief introduction to PopMatics as well as a few of the celebrity endorsements that PopMatics has recieved. Feel free to check out my website, virtual CV, and additional resources (below) to truly get a feel for the power of PopMatics and PopLearning. I look forward to hearing from you soon regarding collaboration and/or partnerships!

Kelly Clark
GoogleTalk: teachmathemagics
Facebook Group: PopMatics
LinkedIn Groups: PopMatics and PopLearning
YouTube: TeachMathemagics (be sure to check out the Algebra 1 textbook samples) (be sure to check out my blog posts) (Virtual Resume) (K-12 hybrid textbook series - proposal) (Videos about PopMatics)