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!

The study, by itself, might well have some value. This is a phrase I could use in a referee report on a paper addressing questions that, in my opinion, aren’t quite as pressing as the authors think. Sure, one could inquire whether schizophrenia might be to certain types of creative thought as the obsessive-compulsive disorder is to persistence, or clinical depression to feeling the blues, or cancer to normal cell growth for that matter. What’s objectionable is that this particular question is taken out of context, sensationalized and belaboured to no end, at the expense of just about every other aspect of our work and lives. People outside of science or academia can get into long and detailed arguments about how John Nash’s schizophrenia influenced his creative output. (OK, so that’s one movie there.) These are the same people who think that mathematicians do all their work on computers, that calculus and trigonometry are areas of current research, that we get paid gazillions in royalties for all those journal publications, and that if tenure track jobs start in September then you should apply in August.

There’s the schadenfreude: they think they’re so smart, but actually they’re just insane. There’s the reduction of the human element in science, a complex topic that deserves better treatment, to the lowest common denominator of weird behaviour. There’s the magical thinking that attributes creativity to weird superpowers conferred on us at a cost; this simultaneously devalues the effort we put into our work and absolves those devoid of such powers from even trying.

Then there’s the trivialization of genuine mental illness, combined with misconceptions of how the creative process really works. Suppose, for the sake of argument, that there is indeed a correlation between creative thought and schizophrenia. If we were talking about, say, athletes whose specific body type makes them well equipped to excel in certain sports and also prone to certain types of injuries, nobody would even try to suggest that it’s the injuries that help the athletes succeed. It would be absurd. And yet such claims are made about creative people all the time.

In the case of mathematicians, autism or at least Asperger’s syndrome is often implied. I suppose that people remember the card-counting sequences from Rain Man, or the stories of people with autism who could multiply five-digit numbers in their head or tell instantly how many matchsticks there are on the table, and imagine that these skills must be really useful to a mathematician. Because research mathematics is all about counting physical objects and multiplying large numbers.

But let’s go back to “divergent thoughts”, the supposed foundation of our creative achievement. It is true that we spend much of our time chasing down ideas. Let’s put it in context, though. First of all, there’s a big difference between actually getting something done and just fantasizing about it over a few beers with friends. It would be really swell if I could just think “I’d like to use X to prove Y!”, pour myself a cold one to celebrate my brilliance and wait for the paper to up and write itself. In real life, I have to sit down and do it. The calculations have to be correct, the argument logically sound. To the extent that “divergent thoughts” enter that part of the process, keeping them in check may well be more important then having them in the first place.

That’s one side of it. The other side is that a lot of work needs to be done before having a breakthrough idea becomes a possibility. That starts with getting an education. If your flashes of brilliance are based on whatever you remember from high school math classes, then chances are that you just rediscovered a first year calculus result – or that your idea has already been considered and rejected multiple times. Fast-forward to the point where we already have the background knowledge and technical chops and can start sizing up a research problem. If our “divergent thoughts” indeed originate in the most paranoid, schizophrenic, depressed corners of our mind, all that knowledge and understanding needs to be communicated over there first. Moreover, those corners need to be willing to take very specific directions from the healthy part of our mind as to what problem they are supposed to work on. Somehow, I used to think that mental illness involved losing control of mental functions.

In case you wanted to ask, yes, we do often look like a bunch of weirdos. Sometimes it’s because our behaviours and little rituals (“second clap”, anyone?) can be impenetrable to an outsider, just like someone not familiar with martial arts might not appreciate the kata or the etiquette. Sometimes it’s because focus and coherence aren’t infinitely renewable resources – the more of it we use up, the less we have left at the end of the day. And sometimes it’s just our natural tendency, possibly exacerbated further by associating with like-minded people. That’s a whole different topic and I don’t want to get into it now, so I’ll just venture a guess that there are plenty of folks with mental illnesses out there who would be more than happy to trade it for just acting weird.

If you’re interested in a more sensible take on the subject, David Auburn’s play Proof has a very neat twist on the stereotype. Katherine, the protagonist, is the daughter of a famous mathematician beset by a mental illness in his later years (I don’t recall the illness being named in the play but it might be schizophrenia). She may have inherited his mathematical talent, his mental instability, or both; we get some answers in that regard by the end of the play. There’s a Broadway production of it posted on YouTube in its entirety: here’s Part 1 of the performance, and here’s Part 2. Part 3 is embedded above. There’s a scene near the end of the play where Katherine’s father, bursting with enthusiasm and joy, tells her that he’s been working again. It starts about the 14′ mark in the embedded segment and lasts about 8 minutes. You should see it if you haven’t already.