An Obsessive Digression
For the past two weeks, I’ve been trying to prove a bothersome theorem. It’s not particularly flashy, but I need it for a paper. More importantly, it felt like it should be easy and I took it personally that it’s not.
Predictably, I began to obsess about this proof — by which I mean I took to returning to the proof again and again during breaks in my working day. It became a staple during my commutes to and from work, and began to hijack blocks of time from my otherwise carefully constructed schedules.
Earlier this week, the weather was nice, so while waiting out the traffic at home in the morning I sat outside in my backyard with my grid notebook (something about grid rule aids mathematical thinking) and, as I had been doing, noodled on the theorem.
Except this time: something shook loose.
I scribbled notes for an hour, drove to campus, and set about trying to formalize my new idea.
It didn’t work.
But now I had the scent. Long story short, six hours later I had a proof that seems to work for a more or less reasonable version of the problem (time will tell).
I started that day with a pretty elaborate time block schedule. It was ignored; as was my e-mail inbox; as were several pretty important administrative obligations. But the important thing is that I think I finally tamed that damnable theorem.
Obsession as Productivity Tool
In my work as a theoretician, (bounded) obsession of this type plays an important role in productivity.
A main theorem in this 2014 paper, for example, was finally proved on the metro, whereas the main theorem in this 2013 paper was cracked on a speaking trip to Canada (I started working on it when I arrived at the airport in D.C. and had the key points nailed down by the time my limo arrived at the hotel in Waterloo) . In an interesting coincidence, the breakthroughs in this 2014 paper and this 2011 paper both happened while stuck at home during (different) snow storms.
In all cases, if I hadn’t allowed the relevant problem to evolve into an obsession, I might not have solved it. They required lots of hours of deep thinking under lots of conditions: both products of obsession.
With this in mind, my contention in this post is that this trick of the theoretician is relevant in many more fields.
Important things are hard to do. Obsession supports hard accomplishment.
The challenge, of course, is keeping the obsessions under control (a somewhat oxymoronic task), and learning when to unobsess when progress stalls too much (at best, 1 in 3 of my obsessions yield theorems).
In the final accounting, however, obsession remains a tool that’s not talked about much but should be, as it often plays a key role in elite level knowledge work.