Gifted while female

Popular entertainment stories about prodigies tend to follow certain common threads. The prodigy is smart but poorly socialized and sometimes a bit of an asshole. If well-meaning people can talk him off that perch, we get a happy ending (“Good Will Hunting”). If on the other hand a controlling parent or guardian figure is allowed to take over, the prodigy is more likely than not to crash and burn (“Shine”).

“Gifted,” the story of a young math prodigy named Mary and her mathematically gifted family, draws on both of these story lines, setting up a competition between the controlling figure (Mary’s grandmother Evelyn) and a well-meaning person (Mary’s uncle Frank). It’s funny and watchable. Mckenna Grace and Chris Evans have great chemistry. It’s also a film about three generations of female mathematicians, written and directed by men, with the participation of four mathematical consultants, all of them male. And it’s a missed opportunity. It’s not that men should not make films about women: I believe they absolutely should. It’s not that I would have preferred a social treatise about gender and math: I get my fill of that elsewhere. But I think that it was possible to go much deeper, dig through the clichés and explore a much more interesting territory. That road was left not taken.

Mckenna Grace in “Gifted.” Photo by Wilson Webb, via IMDb.

I must start with disclosure: I was a math prodigy back in the day. I skipped a few grades, entered university at the age of 15 which was 4 years ahead of the normal schedule, and participated in math olympiads, where my highest accomplishment was being on the Polish team at the 1981 IMO in Washington. It’s not necessarily that much as prodigies go – I did not win any medals at the IMO, nor did I earn a Ph.D. by the age of 20 as some do – but then I was just a small town prodigy in backwater country and so you must calibrate your expectations accordingly. My parents couldn’t drive me to university classes or special gifted programs while I was in school. No such things were available where I lived, and in any event, my parents worked more than two full-time jobs between them, including both paid employment and maintaining a 5-person household at a time when food shortages were common and few Western style conveniences were available. Nor did they have a car.

I’m saying all this not to brag or complain, but to explain my interest in the matter and state my qualifications to discuss it. I’m aware that other folks may be less particular about such movies than myself. Public images of mathematical women continue to be scarce. Given how many Hollywood films still fail the Bechdel test, I do appreciate it when two women have a conversation that not only is not about a man, but also extends to mathematical research and female ambition. But if you’re looking for a review that only comments on the actual film and refrains from speculating on what could or might have been if someone else had made a different one, this is not it. I’m laying claim to my own territory which they have breached. I know the ground here. I talk to the birds and the snakes. I’ve learned my way around the place many times over. What about you? Are you interested in learning?

More on mathematics and madness

In popular movies, a scientist is usually brilliant but troubled. We know that he’s brilliant because we’re told so repeatedly, and we know that he’s troubled because that’s plain to see. He might spend a lot of screen time getting depressed over his lack of creative output and trying to remedy this situation by getting drunk or going out for long walks – anything that will keep him from attempting any actual work. Finally, thanks to divine inspiration, a life-changing event or some other such, he stumbles upon a Great Idea. Now that he’s made his breakthrough, the days and nights go by in a blur as the work flies off his hands, the manuscript pages practically writing themselves. Once it’s all done, the scientist has to snap out of the trance, at which point it’s not uncommon for him to collapse and have a nervous breakdown.

I don’t even want to name specific movies – that’s shooting fish in a barrel. The number increases further if you substitute a writer or artist for a scientist. If you’ve seen too many Hollywood films and don’t know better from your own experience, you could be excused for drawing the conclusion that it’s somehow the mental illness that’s responsible for our creativity. I mean, scientific discovery – not to mention art – boils down to blinding flashes of brilliance, and those come hard and fast when you’re seriously kooky, right?

And now there’s a medical study that I’m sure I’ll see quoted in support of this. According to a recent article in Science Daily, researchers at Karolinska Institutet have shown that highly creative people and people with schizophrenia have similar dopamine systems. That in turn has been linked to the capacity for what the article calls “divergent thought” (a scientist is quoted to refer to it as “thinking outside the box”, one of the most annoying phrases out there), which contributes both to creative problem solving in healthy people and abnormal thought processes in people with schizophrenia. The long suspected connection – make sure to also check the links under “related articles” – may thus have a basis in brain chemistry. Yay for the Mad Scientist!

When the truth is gone…

(Updated below: a link added.)

The main ingredients are simple: a house cat, a large box with an airtight lid, a radiation detector, a radioactive sample, and a container of poison gas such as cyanide. Start by placing the poison gas container inside the box and hooking it up to the radiation detector so that if radiation is detected, the gas container is opened and the gas is released into the box. Place the radioactive sample somewhere near the detector; the sample should be chosen so that there is, say, 50% probability that radioactive decay will be observed within an hour. Now put the cat in the box, close the box, leave the room, and shut the door behind you.

According to the superposition principle in quantum mechanics, a radioactive particle does not simply wait a while and then decay at a time chosen randomly according to a given probability distribution. Instead, it evolves into a superposition of a decayed and non-decayed state, and remains so until we check on it by performing an observation. We know that such superposed states must exist, but we never get to see them. The act of taking a measurement causes the particle to actually assume one of the two definite states, either decayed or not, with certainty. A physicist would say that the wave function of the particle collapses upon observation.

But what about the cat? If at least one of the radioactive particles decays, the poison gas is released and the cat dies. Otherwise, the cat survives. You will find out what happened once you open the box. Until then, you’re the proud owner of Schrödinger’s cat: alive and dead simultaneously, a quantum superposition of a live cat and a dead cat as dictated by the wave function of the radioactive sample.

On the other hand, if you would rather keep the kitty away from dangerous contraptions and settle for the philosophical exercise instead, you could do worse than renting A Serious Man, the latest Coen brothers movie.

The joy of political incorrectness

Thanks to my Avatar post, I guess I’m officially a part of “a bizarre cast of characters”. Then again, what else would you expect from a math professor.

James Cameron might be laughing all the way to the bank, but his record-setting 3-D film, Avatar, is receiving criticism from a bizarre cast of characters, who accuse it of being everything from a racist throwback to the source of their overwhelming depression.

The accusations range from the comical to the militantly politically correct, with voices on both sides of the right-left political divide weighing in on the blockbuster, which has earned more than $1.1-billion around the world since its release last month.

The problem with Avatar isn’t political incorrectness – it’s the shallow, schematic thinking propped up by every possible cliché. But I’ve spent enough time on that already, so instead I’m going to write about a TV series that I’m enjoying immensely even though it’s not politically correct in any conventional sense.

That would be Mad Men, of course. The male characters are all incredibly sexist, in ways that wouldn’t even be possible today; but Mad Men counters that with two basic things. First, the sexism is not romanticized or excused: it’s just there, and it’s shown for what it is. And second, the series is just so darn well written. (Warning: mild spoilers follow.)

Loving the alien, sans 3D

To follow up on the last post, this is priceless.. Except of course for this:

BACK IN SMURF MODE, JUGHEAD IS TAKEN TO THE TOP OF A FLOATING MOUNTAIN SO THAT HE CAN CATCH A DRAGON THING TO BECOME HIS RIDE. WE’RE TOLD THAT HE MUST CHOOSE ONE AND THEN FIGHT IT, AND THEN HE CHOOSES ONE AND FIGHTS IT. SINCE THERE IS NO CHANCE IN HELL THE MAIN CHARACTER WILL LOSE ANYTHING AT THIS MOMENT IN THE STORY, AND WE WERE TOLD EXACTLY WHAT WOULD HAPPEN, IT’S ABOUT AS EXCITING AS WATCHING AN EQUATION BEING SOLVED.

Any mathematician can tell you that watching equations get solved is far, far more exciting.

Via Alyssa.

The beautiful losers of Avatar

(Updated below.)

I wouldn’t have seen Avatar were it not for the reviews. I’m a sucker for a good story, not so much for special effects, and would normally have little interest in a film where the computer-generated 3D visual effects are supposed to be the main attraction. But then several reviewers disclosed a major plot device that made me want to see the movie just so that I could slam it here. Which is what I’ll be doing in this post.

Many others have already beat me to it: Aaron Bady, Annalee Newitz, Eric Repphun, Lisa Wade, to name just a few. The White Saviour angle in particular has been discussed extensively and so I won’t say much about that here. Still, there are a few things I want to add to the discussion. Note that this post is full of detailed spoilers, as are the linked articles above. Then again, if you want to be surprised by plot twists, you should see a different movie.

The men who stare at formulas

The n-category Café has a post about “Dangerous Knowledge”, the BBC documentary I reviewed here some time ago; there’s also a discussion in the comments on whether mathematicians (or academics, or creative types) are really different from “normal” people. If you came here from the link over there, welcome, and here’s hoping that you’ll enjoy this recent interview with John Nash. (Hat tip to 3QD.)

Around the 6-minute mark in the second video, Nash is asked explicitly whether his mental illness might have in some way contributed to his creativity and enabled his mathematical work. He points out in response that his work in game theory was all done before the onset of his mental problems and that he “did not develop any ideas, particularly on game theory, while being mentally irrational”. He also recalls a mistake in a published paper that he completed shortly before the breakdown and suggests that it may have been due to a malfunction of his mind.

Therein lies madness

This got me a bit puzzled: why would a comment on this post link to a BBC documentary on Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan Turing?

Given that I don’t know as much about the history of mathematics as I probably should, and that I was too tired late last night to do anything more intellectually challenging, I ended up clicking through and watching all 10 parts of the documentary.

The mathematics involved – Cantor’s hierarchy of different-sized infinities, Boltzmann’s statistical mechanics and entropy, Gödel’s incompleteness theorem – is described remarkably well. An expert might quibble about how some of the explanations are ambiguous and imprecise, especially where it concerns Gödel’s work, but that’s a relatively small price to pay for being able to communicate the excitement, audacity and impact of mathematical ideas to a lay audience. The images and animations are, for the most part, well done and helpful. Several mathematicians and scientists (including Roger Penrose) were interviewed for the documentary, and I am guessing that experts were consulted quite extensively about the mathematical content.

That’s only one part of it, though. The movie chooses to focus on Cantor, Boltzmann, Gödel and Turing not only for their groundbreaking contributions to mathematics, but also for the mental anguish and personal tragedy in their lives. Boltzmann and Turing committed suicide, Cantor and Gödel suffered from mental illness and were hospitalized for it, and Gödel ended up starving himself to death. Now, I understand that these are undisputed historical facts. I also understand that troubled characters make for a more interesting movie. But I’m tired of watching the media portray mathematicians as socially challenged and mentally unstable, not to mention poorly dressed. You’d never know that it is quite possible for a great mathematician to be a well adjusted and fully functional human being, to have a long, happy and accomplished life, or to face and overcome adversity without developing a mental illness.

Moon

The movie, set in a not necessarily very distant future, starts with a voice-over monologue, advertisement style. You see, back in the old days we used to rely on fossil fuels for our energy. That caused smog and pollution, affecting our health and that of the planet. (We get some impressive shots of smog in Los Angeles.) Thankfully, those times are long gone. Our skies are clear, our water is fresh, and we have enough clean energy to convert deserts into farmlands. You may ask yourself, how did we get there? Part of it, the voice-over informs us, has to do with the mining of something called Helium 3 on the far side of the moon and using it as fusion fuel. The rest of the answer will be forthcoming shortly. You might not like it.

With the opening credits still running, we meet Sam Bell (Sam Rockwell), the sole operator of one such Helium 3 mining station on the moon. He’s almost at the end of a 3-year contract, the true nature of which will be revealed gradually over the course of the movie. He is not doing well. He looks pale and disheveled, he has been talking to himself, and his mental state is so fragile that he starts to experience hallucinations. Or does he see dead people?

The Monty Hall problem

On a plane flight back from a recent trip, I watched the movie 21. The plot, advertised as “based on a true story”, is roughly as follows. (In case you have not seen the movie and would like to, I will try to avoid major spoilers.)

Ben Campbell, an idealistic and somewhat naive MIT student, impresses a math professor (Kevin Spacey) by answering correctly a couple of tricky questions in class. Soon afterwards, the professor asks Ben to join his card-counting blackjack team in return for a share of the profits. The team travels to Las Vegas on weekends, plays blackjack at major casinos, and wins millions of dollars by placing themselves strategically at the right tables and employing the card-counting techniques taught by the professor. Ben refuses at first (“and if you tell anybody, I’ll make sure that you won’t graduate”), but there’s no other way that he can pay for his dream med school, and he’s attracted to a female student on the team, and besides, if he didn’t join the team, there would be no movie, so guess what happens.

That’s about the first quarter of the movie, and I’ll leave it there, because this is already enough to raise serious questions about just how close to a “true story” we are here.

My first question was, has there really been an MIT math professor who made a fortune off a team of student card players? Wouldn’t that be serious professional misconduct, and would an MIT professor (not a bad job) really take this sort of risk? As it turns out, the movie is somewhat loosely based on the adventures of a real-life MIT card counting team (one of several that MIT has had over the years). However, the teams were all entirely composed of, and run by, the students. There were no professors involved, and the Spacey character is completely fictional.

Which also preempted my follow-up question. There’s a classroom scene where the Spacey character asks his students what applications of Newton’s method they know. A student suggests, “Nonlinear equations?…” Spacey responds along the lines of “Yeah, that’s very clever, because this course is called Nonlinear Equations. Why don’t you tell me something I don’t already know.” My impression was that Spacey’s demeanor, and this exchange in particular, was a little bit too snarky. A professor is not supposed to do that if he (or, especially, she) wants to get good student evaluations.

The user comments on IMDB include several reviews by authors who appear to be well familiar with casinos, blackjack and card counting, and are not entirely happy with the treatment of the subject. I’ve never played blackjack, or been to a casino, but their criticism makes sense to me.

But here’s the reason why I’m writing this post. How exactly does Ben manage to impress Spacey’s character? Spacey asks him the following question:

You’re on a game show. The host asks you to choose one of three doors. Behind one of them there’s a car, behind each of the other two there’s a goat. You pick one door, say Door 1. The host, who knows where the car is and is not allowed to reveal that information, opens Door 3, behind which there is a goat. He then asks you if you want to choose Door 2 instead of 1. Is it to your advantage to switch?

In case you’d like to think about it, the rest of post is behind the cut.