Apologies for my absence – academic life has recently forced me to put the blog on hold. Things have cleared up now though, and I have a backlog of things to discuss, so let’s get right to it.
Last month, Jennie Yabroff wrote an article for Newsweek discussing the new film Precious. I haven’t seen the film, but this trailer makes a fairly strong impression:
The film has received a nearly unanimous positive response from critics. The main character, Precious, begins the film as a 16 year-old illiterate middle school student, but after transferring to an alternative school, she is able to find hope with the help of a teacher who encourages her to keep a journal and write in it daily.
The theme of finding redemption through writing is certainly not new to this genre of film, as Yabroff points out. Films such as Dangerous Minds and Freedom Writers have explored this territory before, although perhaps with less success than Precious. However, Yabroff wonders if all this time spent journaling wouldn’t be better spent learning some mathematics.
In her article, Yabroff writes:
The idea that every underprivileged young adult harbors the soul of a Rimbaud is a favorite trope of popular culture. We don’t expect our bankers and lawyers to be secret Baudelaires, but we eagerly accept the idea that every poor person has a “story,” and just needs the right teacher or mentor to give it voice…
…But, contrary to what Hollywood would have us believe, the world does not reward self-expression as readily or consistently as it rewards a good head for numbers. It’s hard for any writer to support herself writing. Precious’s teacher should have known that, and given her a calculator along with that journal.
Stand and Deliver is one film that shows how mathematics can improve the lives of inner city youths, but as a general rule it does seem much more likely that a film will attempt to highlight the potential of students through writing rather than through math. Part of this bias is to be expected, since, as Yabroff points out, movies are written by writers and not mathematicians. Also, given Precious’s illiteracy, it would make more sense to build up her fundamental reading and writing skills before asking her to pick up a math book. Even so, should we be concerned that nearly every film that shows inner city youth turning their lives around does it by emphasizing words over equations?
One may be tempted to argue that it’s just harder to write a film that portrays math honestly and in a compelling way, but I think that’s only true if you’re a lazy writer or you don’t know anything about math. Especially at the high school level, the fundamental concepts could be explained in a way that’s understandable to general audience, and, dare I say it, even interesting. The end result may not seem to be as glamorous if one’s education is focused on math – given the choice, I’m guessing that kids would rather be like Kanye instead of Urkel – but this just means we need to do a better job showing kids why mathematical skills are so attractive.
I for one would love to see more movies like Stand and Deliver, especially ones that follow through and show what can be done with a background in science and math. Who knows when that will happen, though. I guess we need a character with the technical know-how of Steve Urkel, but the charm and sophistication of is suave doppelganger, Stephan Urquelle. I am confident that character is out there, and am hopeful that his (or her) time will soon come.
Sorry Steve – lose the suspenders, and then we can talk.
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.
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.
In continuing with the theme of discussing movies before I see them, I’d like to say a few words about the upcoming film District 9. You can see the trailer below, if you haven’t heard of it (although if you live in LA it’s difficult to plead ignorance, since the viral marketing has been on full blast all summer).
It’s natural to ask what a film about aliens living in South African refugee camps has to do with mathematics. Aside from the obvious (no doubt any intergalactic species must have a good working knowledge of mathematics), I’d like to point you to an aspect of the marketing campaign for the film that’s featured on the official website. If you look in the lower right, you will see a link to a site that immediately aroused my interest: Maths From Outer Space.
The purpose of this website is best summarized in its own words:
Maths From Outer Space wants to redefine what it means to be human! Our scientists have found a way to enhance the spatial and logic capabilities of the human body… In other words, we’ve found a way to make you smarter! Would you like to see if you are qualified to take part in this exciting endeavor?
From here, you can click through to take a math test. This is remarkable for a few reasons. First of all, the fact that a film like this would even incorporate a math test as part of its marketing strategy is pretty interesting. But not only that, by the end of the quiz the difficulty level of the questions went far beyond my expectations. This is a summer movie about aliens, after all, and yet their math quiz ends with questions like this:
Nothing in the quiz goes beyond the level of calculus, but even this level of sophistication is fairly surprising. After all, not even films with subject matter that focuses on mathematics give math quizzes, let alone math quizzes involving calculus.
Unfortunately, it’s not perfect. First of all, there are some mistakes in the quiz – what is one to do when none of the options given is correct?
The “correct” answer is the first one. Perhaps if aliens had mastered the concept of the derivative, they wouldn’t have gotten trapped in the slums of Johannesburg.
Even worse is the fact that even if you answer all the questions correctly, there is no payoff. When you click to learn more about the “enrollment details,” you’re sent to a bogus link. How disappointing for the student who dreams of one day applying his math skills to uncover the secrets of advanced alien technologies.
Overall, though, I must give kudos to District 9 for its proactive stance on the integration of mathematics and film (then again, coming from a distributor called QED International, is it really a surprise?). If only more summer blockbusters would follow this lead. Perhaps other studios will take note, and next year will feature an even more seamless integration between pop entertainment and post-secondary school mathematics.
The future of summer entertainment? One can only hope so.
This past week I watched Revolutionary Road, the Oscar nominated 2008 film directed by Sam Mendes. The film stars Leonardo DiCaprio and Kate Winslet as a highly dysfunctional couple named the Wheelers, who live in 1950s suburban Connecticut. For those of you who may not have seen this feel-good picture, here’s a trailer:
The trailer doesn’t address the question of what this film has to do with mathematics. The answer lies in the character of John Giving, a “mathematician” played in the film by Michael Shannon (who turned in an Oscar-nominated performance).
We first hear of John Giving from his mother, who informs Mrs. Wheeler that her son has a brilliant mind, as evidenced by his PhD in mathematics, but that he has been institutionalized, and his doctors have suggested that it would be good for him to go out and make some friends. This introduction did not bode well for the film’s representation of the mathematically inclined, but how did the rest turn out?
Let’s explore the usual stereotypes.
- To be good at math, you must be insane.
This is probably the most common stereotype in films about mathematicians, and this film would certainly have us initially believe that it is no different. To be fair, we’re never told that Dr. Givings was ever an especially gifted mathematician, but the first facts we learn about him is that he is a mathematician, and he is insane.
But is he really? He’s certainly outspoken, and doesn’t fit in with the established conformity that has become synonymous with 1950s American life, but we’re never given any clear indication as to whether he truly did or did not belong in an asylum. Indeed, the film seems to play on the convention of the insane mathematician – Dr. Givings is told by society that he is insane, but his outspoken attitude sometimes makes him seem like the only sane one in the film.
In fact, it’s not at all clear that he is even a mathematician – perhaps he has just been given this label by a mother who yearns to take pride in her son. When Frank Wheeler asks Givings about his background as a mathematician in the book on which the film was based, Givings asserts that he is not a mathematician. “Taught it for awhile, that’s all.”
I’ve decided to give the film a pass on this stereotype. Givings may be insane, but he certainly seems more lucid than anyone else living in the suburbs. +0.
- People who are good at math are socially awkward.
Givings is awkward, but not in the way one would expect in a portrayal of a mathematician. Instead of being nervous in social situations, he seems to relish them, and is quite outspoken in his opinions. The awkwardness therefore stems from his seeming inability to keep his mouth shut.
He does create awkward situations, but not in the way you’d expect given the stereotypes about mathematicians. So I’ll give this one a pass as well.
One of two scenes featuring John Givings.
Related to the notion of social awkwardness is the idea that people who do well in math or science are not good at picking up on nonverbal cues. However, as the clip above illustrates, Givings is quite good at picking up on these cues – better than anyone else in the film, in fact. That he can observe these cues and still do mathematics is a good thing, although to be fair, Givings says that his mathematical abilities disappeared following his shock therapy treatments. +1.
Givings is certainly not your stereotypical mathematician. I worried that this film would play in to all of the stereotypes surrounding folks who do math, and so I was surprised to find that the film played with these stereotypes in a way that one doesn’t usually see. I prefer this performance to other Oscar nominated crazy mathematician roles, but I still long for the film that shows me a mathematician who’s just a normal dude (or, even better, dudette).
As many of you are no doubt aware, Pixar’s latest film opens this weekend. I have yet to see the film, so I’m sure I am spoiling nothing by telling you that part of the film involves an old man flying through the sky by means of balloons that are attached to his house.
Do not try this at with your home.
Given that I have yet to see the film, you may wonder how I could possibly hope to connect it to mathematics. Thankfully, I don’t have to – the work has been done for me by Alexis Madrigal over at Wired.com, who wrote an article discussing the feasibility of using balloons to take to the skies in one’s own home.
His assumptions are that the house weighs roughly 100,000 pounds, and that the balloons are spherically shaped with a diameter of three feet, which may seem large at first, but seems more reasonable if you look at other shots of the floating house.
How many balloons does that look like to you?
Based on these assumptions, and the weights of air and helium, Mr. Madrigal estimated that it would take roughly 105,854 balloons to lift the house.
The fun really begins in the comments section, however. The model presented in the article was quite simple and easy to understand, but perhaps overlooked some of the subtleties in the problem. Here are my favorites:
You forgot to factor in the weight of the string for the balloons. The balloons at the outer edge of the cluster would need longer strings = less overall buoyant lift/balloon once you factor the extra string weight. So you’d need more, or larger balloons.
Then there’s this one:
Actually, there’s a math error. The density of helium will be greater when in a balloon as the pressure in the balloon is greater than atmospheric pressure. This means that the lifting force per balloon is less and that you’ll need even more.
Of course, there’s also the question of how the house broke free of its foundations. The trailer makes it look as though the balloons themselves were able to uproot the house – if this is the case, one would need significantly more balloons in order to rip the house up from the ground.
Perhaps this is why the in-house estimate from Pixar for the number of balloons that would be required to make the house fly is nearly 250 times larger than the estimate given by Mr. Madgrigal. Believe it or not, the feasibility of lifting a house with balloons was brought up at Cannes, where the film premiered, to which co-director Pete Docter replied:
We have scientists at Pixar, and one of the first questions we asked them was how many balloons it would actually take to float a house. They calculated it would take 26.5m balloons. So we reckoned we would be safe from people trying it themselves.
Whether you think the number of balloons required is in the tens of millions, or just a measly 100,000 or so, both numbers are significantly more than the amount of balloons pictured on screen – which, according to a recent article by Daniel Terdiman at CNET, is closer to 10,000. This article is also good for those of you who may not be impressed with the simple calculations involved in trying to determine how many balloons would be required to lift a certain amount of weight.
Instead of analyzing the plausibility of using balloons to lift a house, the CNET article discusses the real world difficulty that comes with trying to animate upwards of 10,000 balloons so that they move together in a realistic way. The dynamics of the balloons are all highly connected – the motion of one balloon will have an effect on all the others – and modeling a system with that level of complexity is certainly no easy task. This is where mathematics flexes its muscles a bit more.
Everyone is happier with a houseful of balloons.
According to the article, the machinery at Pixar was initially only able to handle animation for about 500 balloons – to ramp this number up twenty-fold certainly must have taken some hard work and some mathematical wizardy. Producer Jonas River sums it up best:
The audience looks at (the balloon cluster) and says, “Oh, that’s pretty.” But they have no idea how much work went into it. We worked on that for over a year. (Then) the kid takes off his hat and runs his fingers through his hair. My mother will never know that took 15 people six weeks.
So, whether you’re in it to get ideas for how to build your own flying balloon contraption, or because you’re curious to see how Pixar is again pushing the boundaries of what is possible in animation, there will be something to satisfy your mathematical curiosity. The movie currently holds an impressive 98% freshness rating on Rotten Tomatoes. How much of this high rating can be explained by the film’s mathematical sophistication? Probably very little – but at least a man can hope.
During the course of my K-12 math education, I was able to watch Stand and Deliver two times during math class. The first time was in 5th or 6th grade, and during this first viewing I was less inspired by the mathematics than by the stellar performance of Lou Diamond Phillips, whose winning catch phrase “I strangled him, his body’s decomposing in my locker” has stuck with me well into my adult life.
The second time I saw the film was in high school, during the month between the AP exams and summer vacation when teachers are generally a little less rigorous with their lesson plans. Wiser now, I was able to more fully appreciate the mathematics on display in the film. I understood what it was like to sit down for an AP Test, and while I’ve never had Andy Garcia accuse me of cheating, I think I can imagine what it would feel like. Because of this, I was able to relate to the film on a deeper level.
Recently, I decided to watch this film for a third time, to see how this film compares with other films that involve mathematics. Lou Diamond Phillips was as charming as ever – but how did the math stack up?
For the uninitiated, Stand and Deliver aims to tell the true story of Jaime Escalante, a man who gained a fair amount of press in the 1980’s for developing an extremely successful advanced placement math program at an inner city school in Los Angeles. The film tells the story of the first batch of kids to study Calculus under Escalante’s tutelage, and aims to show that regardless of your background, an understanding of mathematics is not beyond your reach.
Here’s an extremely short trailer for the film. Run, Lou, run!
Most of the time when I discuss the representation of math in films, there are two main things to consider: the portrayal of mathematicians, and the portrayal of mathematics itself. For this film, Mr. Escalante is not a mathematician, however – he is instead a very good math teacher. Nevertheless, being a good math teacher means he must be good at math, and whenever someone who is good at math is presented on film, there is a danger that the character will have certain stereotypical attributes.
Thankfully, this doesn’t seem to be the case here. Let’s take a closer look at some stereotypes of mathematics.
- People who are good at math are socially awkward.
Jaime Escalante is many things in this film, but socially awkward is not one of them. He’s a charismatic dude with a comb over to match. Sure, some of the things he says may not be entirely appropriate for the classroom, but everyone seems to enjoy it. Plus, he has a stable home life with a loving wife and a son – it’s not often that people who are good at math are shown in such drama free households. +1. - To be good at math, you must be insane.
This movie shows all types of students, from the nerdy girls who work at their dad’s restaurant, to the wannabe gangsters with no aspirations for higher education. Many of the students come from less than ideal family situations. Nevertheless, there is one thing that binds them all together: their ability to learn math.
While some students are stronger than others, there isn’t one among them who is completely lost. They all learn Calculus, despite the skepticism that surrounds them. At one point Mr. Escalante opines that “students will rise to the level of expectation,” and in this case, he is correct. You don’t need to be crazy to be good at math. Having a good teacher, however, certainly helps. +1.
Real Jaime Escalante versus movie Jaime Escalante.
- Mathematics is inherently difficult and complicated, and only gifted people have a hope of doing well.
This is arguably the most harmful stereotype about mathematics. While it’s certainly true that math is difficult, and that there are those who seem to have an innate mathematical ability, it is certainly not the case that every professional mathematician (or those who use math in a technical career) are math savants. More often, they are simply people who had a few good teachers and were motivated to really understand mathematics.
Usually a film’s mathematics perspective is weighted heavily towards the savant end of the scale, which only reinforces stereotypes about people who study mathematics. Thankfully, this film really emphases the latter standard – that even if you aren’t the most naturally gifted when it comes to math, you can still succeed with enough hard work. All the students in the film work extremely hard, even the ones who may be better at math than the others. And aside from a bit involving Andy Garcia who plays a total tool, the students are all rewarded for their hard work, not only with good grades, but with a deeper understanding of math, and greater confidence about their abilities as students. As Mr. Escalante says, “Calculus is not made to be easy – it already is.” +1.
This film is very different from most films that involve math. Math isn’t presented as some mystical oracle that can only be deciphered by the borderline insane. Instead, it is presented as a difficult subject, but one that can be mastered with dedication and practice. It’s no wonder, then, that this film has secured such an enduring spot in the hearts of math teachers nationwide.
For those of you who may not find the film appealing, there’s always the counterpoint offered by South Park. Mr. Cartmanez may not have the heart of Mr. Escalante, but at least he has the comb over. Their teaching styles couldn’t be more different, and yet in their own way, both are successful. Somehow, though, I don’t think math teachers will find the story of Mr. Cartmanez as appropriate for their students.
In 1998, Darren Aronofsky shot to success with his independent film, Pi. The film was widely heralded as an excellent film, and earned Mr. Aronofsky the 1998 Directing Award at the Sundance Film Festival. He then went on to direct the similarly successful Requiem for a Dream, followed by the less well-received 2006 film The Fountain. His latest film, the Mickey Rourke vehicle called The Wrestler, opens soon.
The story of Pi centers on a mathematician named Max Cohen, a self professed number theorist – although he never specifies what qualifies him for this title – who spends his days analyzing the stock market and wiping the blood off of his upper lip (I know what you’re thinking, and no, he’s not a cage fighter – that would’ve made the film way better). As he comes closer to “unlocking the secrets” of the stock market (whatever that means), several interested parties begin to come out of the woodwork, all with their own self-interest at heart.
From a math perspective, how does this film stack up? Unfortunately, the answer is poorly. Those wishing to learn some math from their pop culture would be better off with an episode of Sesame Street, or perhaps some School House Rock. In fact, pretty much any math pop culture reference you can think of would probably fare better.
Let’s take a closer look at the stereotypes propagated by this film.
A trailer, for those of you fortunate enough to have not seen this film.
- Mathematicians are really good at calculating things in their heads.
One of our first introductions to Max comes early in the film, when he is leaving his apartment and a young Asian girl approaches him with a calculator. She proceeds to ask him to compute products and quotients of large numbers in his head – things like 421 x 121. Of course, since Max is a mathematician, he has no trouble computing these products. He does it just as quickly as she can type the numbers into her calculator!
As I’ve said before, this isn’t at all a realistic depiction of mathematicians. While there are certainly computational savants amongst us, it is just as common, if not more so, to encounter a mathematician who will willingly admit that he or she is no good at computation. Many mathematicians even take pride in such assertions. Mathematics is as much about doing multiplication in your head as cooking is about opening jars with your bare hands. -1.
- To be successful in math, you have to complete your Ph.D. at an extremely young age.
Max Cohen published his first paper at age 16, and completed his Ph.D. by the time he was 20. While this is certainly not unheard of in academia, the idea that you must be young to be successful is one that is especially pervasive in mathematics.
The problem with this stereotype is that it tends to discourage people from studying mathematics if they are firm in their beliefs that math is solely a young man’s game. In pop culture, most people who are good at math are portrayed as having completed their degrees at a very young age, but in reality these people are the exceptions, not the rules. In mathematics, as Aaliyah will tell you, it is becoming more and more common that age ain’t nothing but a number. -1.
Don’t subscribe to this propaganda: mathematicians enjoy a good samosa just as much as everyone else.
- People who are good at math are socially awkward.
In an early scene, Max is busy looking at numbers on his computer screen (because he’s a number theorist, remember?!) when someone comes knocking on his door. On the other side is his attractive neighbor, who not only sports a British accent, but also has brought him samosas.
Any normal person would welcome such an act with kindness and gratitude. Of course, Max is not a normal person – he is a mathematician. This must explain why he is rude to this woman, both in this scene and later on in the film, despite the fact that she is not only kind to him, but is also cute. That she puts up with his abuse is simply a testament to the power of seduction that comes with studying mathematics, whether intentional or not. -1.
- Number Theory is synonymous with numerology.
Throughout the film, Max stares at numbers. He watches stock prices fluctuate. He prints out random strings of integers from his super old computer and stares at them for long periods of time. Sometimes he even draws circles on the newspaper and shows that he is a genius at math because he can recall the formulas for the circle’s area and circumference.
One notable omission in all of this is that at no point does Max do anything even remotely resembling number theory. If anything, Max’s research would more aptly fall into the realm of financial mathematics, with maybe a splash of ergodic theory thrown into the mix.
At one point Max is so fixated on trying to find a pattern in his work that his mentor, Sol Robeson, tells him, “As soon as you discard scientific rigor, you’re no longer a mathematician; you’re a numerologist.” Coming from a film that depicts nothing BUT numerology, this is somewhat of a surprising statement. -1.
- To be good at math, you must be insane.
Let’s be honest – Max is a total whack job. Not only does he hate it when people deliver him fresh samosas, but he’s obsessive, paranoid (perhaps justifiably so), and irritable. He fantasizes about poking his brains, and at one point he shaves his head and begins drawing on his skull with indelible marker, or so we are led to believe. At least the connotations with phrenology pair nicely with the numerological gobbledygook that permeates the rest of the film.
As I’ve said before (and will no doubt say again), you can be good at math without being crazy. Being crazy is just the frosting on the cake. I kid, I kid. -1.
Wow, look at all the math in that noggin.
- The number π provides an active area of research for mathematicians.
Max’s aforementioned mentor guides Max throughout the film, and often during their discussions, Sol hearkens back to his own youth, and the amazing math he did while researching π.
Sadly, Sol is a century or two late if he expects us to believe he could make a career studying a single number. The whole idea is absurd. I have not heard of a single mathematician who has made a lucrative career studying π, and I think you’d be just as hard pressed to find one. Saying that a mathematician’s research concerns π would be like saying an English literature professor’s research concerns the word “banana.”
The only reasonable conclusion one can draw is that Sol is a fraud. This is further evidenced by the fact that he doesn’t know what density is (weight over volume? Come on, dude). Perhaps Sol was only hanging out with Max to bask in his numerological genius. No doubt his time would’ve been better spent elsewhere. -1.
In summary, this movie scores a whopping -6. This is a pretty poor showing. Sorry, Mr. Aronofsky – if it’s any consolation, I do want to see your new film. Hopefully you are more of an authority on washed up wrestlers than you are on mathematicians.
There is a joke in mathematics circles that has become well-known enough to merit its own entry on Wikipedia. This joke is referred to as the Teakettle Principle. Here’s how it goes:
A mathematician and an engineer go into the kitchen one day to make a pot of tea. Finding an empty kettle on the stove, they fill it with water, then turn on the stove and let the water boil, following the usual protocol when making tea.
The next day, the two again decide to make a pot of tea. However, upon entering the kitchen, they find that the kettle on the stove has already been filled with water! Now faced with a new problem, the engineer suggests that they simply heat the water that’s already in the kettle.
“Nonsense!” the mathematician replies. “It would be far simpler to pour the water out and replace the empty kettle on the stove top. Then we will have reduced this problem to one we have already solved!”
Ok, so the joke isn’t that funny. Its charm comes from its needling of the mathematical proclivity to reduce new problems to ones that have already been solved, sometimes even when a solution to the new problem may be readily available.
It is with this mentality that I wish to discuss Superman II with you. For you see, the problem of discussing this movie as it pertains to mathematics has already been solved in an excellent post at Overthinkingit. The name of the post is called The Math of Steel, and it thoroughly analyzes, from a mathematical perspective, the plausibility of a scene involving Superman, Niagara Falls, and a falling child. It’s really a very good example of how even superheros can benefit from a knowledge of mathematics.
Therefore, since this problem has already been solved, the problem of me discussing this film from a mathematical perspective can now also be solved, just by using the link above. You can thank the teakettle principle for that.
Ah, 1993. Andrew Wiles was on the verge of proving Fermat’s Last Theorem. Late night talk show hosts poked fun at our President’s love of McDonald’s. And on June 11th, a little film known as Jurassic Park released to audiences throughout the country.
As it held the top spot for most successful movie of all time for four years (thank you, Titanic), there is no doubt this movie has secured a place in our pop culture heritage. And while it has aged in some respects – science has advanced to the point where it can genetically engineer species that went extinct millions of years ago, but a little girl is still most impressed by the fact that cars on the island come equipped with “interactive CD-ROMs,” for instance – the film still serves up a quintessential example of the 90s summer blockbuster.
If the film is not fresh in your minds, you may be asking yourself what a movie about dinosaurs wreaking modern day havoc has to do with mathematics. In response to this, I turn your attention to the character of Dr. Ian Malcolm, played by Jeff Goldblum. Dr. Ian Malcolm is a mathematician, although he self-importantly refers to himself as a “Chaotician,” i.e. his research is in Chaos Theory.
Putting that aside for a moment, let us take a look at this portrayal of a mathematician. Does the film do a disservice to those of us in the profession, or does it raise us up, so that we can walk on mountains?
If you have lived under a rock for the past 15 years, here is a (poor quality) trailer for the film.
Let’s take a look at some of these stereotypes.
- People who are good at math are socially awkward. While Dr. Malcolm certainly has his fair share of idiosyncrasies, I believe a rational person would find it difficult to label him socially awkward. During the course of the film, he proves himself to be quite a conversationalist, and is not shy about voicing his opinions, or interacting with people he has just met.
Ian Malcolm with his stunner shades on.
Not only is Dr. Malcolm able to hold his own in a conversation, but he is also way more stylish than most portrayals of mathematicians in pop culture. Sporting both a pair of sunglasses and a leather jacket, there is no doubt that Dr. Malcolm has a keen eye for fashion, and the means to support his tastes.
Perhaps most importantly, at one point the owner of the park, John Hammond, refers to Dr. Malcolm in the following way when discussing personnel that have been brought to the island: “I bring it scientists; you bring a rock star.” While I believe this is meant to be an insult, it is more constructive to interpret this as an affirmation of the inevitability of a future utopian society in which mathematicians are given the adoration reserved today only for rock stars. The film captures the essence of this utopia quite nicely, except for the bit about the dinosaurs running around and eating people; this is not (thus far) a part of the vision.
In short, Dr. Malcolm is quite far from being socially awkward. +1.
- Male mathematicians have a crippling fear of talking to women. A strong argument could be made that this stereotype is really more of a subset of the stereotype already discussed, but because of the emphasis this film places on Dr. Malcolm’s gift of gab with women, I feel it is worth mentioning here.
In several scenes we witness how Dr. Malcolm has no reservations about spitting some serious game to females, even in front of other people. Rather than letting mathematics restrict his ability to talk to the opposite sex, Dr. Malcolm uses mathematics as an opening to get women to talk with him. In doing so, he illustrates one of the greatest unsung properties of mathematics: when used with the proper care, it is a powerful aphrodisiac. Kudos to you, Jurassic Park, for daring to shed light on this important facet of mathematics. +1.
Dr. Malcolm is looking for love.
Now, what about the bad? Unfortunately, there is plenty of bad, most of it coming from taking the good stuff too far. Let’s look back at the stereotypes already mentioned.
- People who are good at math are socially awkward. Sure, Dr. Malcolm may be socially adept, but he’s also kind of a jerk. I say this not because of his criticisms of the park, many of which seem quite valid. Instead, I base this conclusion on the fact that he’s a little full of himself. From the fact that he wears sunglasses at night (an action that would be excusable given an appropriate medical condition, but since he later loses his sunglasses, we can safely assume this is not the case), to the way he refers himself as a “Chaotician” (come on, seriously?), it is clear that Dr. Malcolm is too pompous to serve as a proper mathematics ambassador to the rest of the world.
So abrasive is this mathematician that at one point, one character refers to him by saying, “I really hate that man.” Is this what we want people to say about mathematicians? Perhaps, but only because they envy us. Certainly this does not seem to be the case here. -1.
- Male mathematicians have a crippling fear of talking to women. Although Dr. Malcolm evidences an ability to use mathematics in his courtship rituals, this commendable feat is overshadowed by the fact that he uses his forces for evil, and not for good. The only time we see him channeling the mack within is when he is putting the moves on somebody else’s girlfriend. This is, of course, a universal party foul, and one that does not reflect well upon mathematicians. Especially when the other man is a more likable character. -1.
In summary, this film really doesn’t do much for the perception of mathematicians one way or the other. While Dr. Malcolm is more suave and sophisticated than most people come to expect from their mathematicians, he is also in love with the sound of his own voice, and potentially a home wrecker. In the end, some may be able to look past the character’s shortcomings, and some may not. However, I suppose that any man who can serve as the inspiration for the following video can’t be all bad.
Does the situation improve in the 1997 follow-up, The Lost World? Perhaps, although I don’t really want to sit through the film to find out.
Winning them the Oscar for Best Original Screenplay in 1998, Good Will Hunting propelled Matt Damon and Ben Affleck to the Hollywood A-list (no doubt Phantoms would have done this for Ben Affleck, had it not been for the success of Good Will Hunting only months earlier). I will not summarize the plot, except to say that in this film, Matt Damon is a math superstar. For those wanting more in the way of plot summary, this trailer may help to refresh your memory:
There are a number of films that center around math geniuses, and for the most part they have met with some degree of critical and commercial success. Our purpose here is not to critique these films, but to answer a simple question: In what ways do these films perpetuate stereotypes about mathematics and mathematicians, and in what ways do these films rise above those same stereotypes? Here we use a rather crude scoring system, whereby each perpetuated stereotype corresponds to a loss of one point, while each stereotype that is overturned corresponds to a gain of one point.
Let’s start with the good. - People who are good at math are socially awkward. Will Hunting certainly runs counter to this statement. He has several close friends, enjoys going out for drinks, and lands a smoking British girlfriend. Will also really likes punching people (see below), a pastime I think it’s safe to say is not shared by most people who study math.
Watch out! This clip, and the one below, may contain objectionable language.
While Will Hunting is not socially awkward, not everyone in the film can escape the same fate. Fields medal winning, ascot adoring math professor Gerald Lambeau seems relatively well adjusted, but his teaching assistant Tom is painfully awkward – almost awkward enough to overshadow the non-awkwardness of the rest of the mathematically inclined cast. Perhaps he simply got lost in Matt Damon’s eyes.
Overall, the film does a good job of showing that not everyone who is good at math is a social outcast. +1.
- Mathematicians are single-minded of purpose, and have no interest in anything besides mathematics. Will Hunting provides a strong counter-example for this assertion as well. The movie shows us that Will is not just a math prodigy, but is basically an all-around smart dude. Very little time is spent showing the audience how Will does math – understandably so, since I can imagine few things less cinematic than watching someone think about math problems. Because of this, we see the other aspects of his character, and learn that his realm of interests extends far beyond what can be found in a collection of math books. +1.
Among other activities, Will enjoys schooling Harvard punks. He also enjoys eating caramels.
- To be good at math, you must be insane. While he certainly has some issues, I don’t think anyone would assert that Will has any significant mental disorders. This film shows that you don’t have to be crazy to enjoy math – although it couldn’t hurt, I suppose. +1.
What about the not so good?
- It is important to do math on windows, mirrors, or other unconventional writing surfaces. I get it. Watching people sit at a desk and write things down is boring. Nobody wants to watch that. But if you go to a mathematician’s office, I doubt you will find writing on the window, or on the mirror of their bathroom at home. That’s what blackboards are for. -1.
Dude must’ve run out of chalk.
Other than that, the film does a fairly good job. It is understandable vague when it comes to the supposedly insanely difficult problems Prof. Lambeau gives his students throughout the film, although the brevity of their solutions seems to suggest that really they weren’t so bad in the first place. The film does earn points, however, for featuring Parseval’s identity in the first classroom scene.
In conclusion, the film earns two points here, for its portrayal of math students as real people with varied interests, even if they do enjoy writing equations on non standard surfaces. One wonders if the sequel will be able to compete.
Sorry Steve – lose the suspenders, and then we can talk.
