I was talking to friends about Deep Work, a book about doing, well, deep work, when I realized that I had two conflicting models of how to choose what to work on, and how to work on it.
The more straightforward approach is sketched by Richard Hamming in You and Your Research, which simply asks (paraphrased) “What are the important problems of your field, and if you’re not working on them, why not?” It’s an extraordinarily dense mantra, packing lots of decision power into a simple sentence: if you’re not focused on your field, then focus on your field, and if you’re not focused on the most promising area of your field, then focus on that area, and if you’re not focused on the most important problem of that area, focus on that problem. Everything else? Strip it away as much as possible, because the rocket equation is hell and we are going to Mars!
Then there’s the more playful way to find problems, which the incorrigible Richard Feynman described in Surely You’re Joking, Mr. Feynman!. Frustrated by his research problems, he decided that he would stop slaving away and just play with whatever problems caught his fancy: “Now that I am burned out and I’ll never accomplish anything… I’m going to play with physics, whenever I want to, without worrying about importance whatsoever.” He goes on to derive equations related to the physics of a spinning plate, because why not? Later, he realizes “The diagrams and the whole business that I got the Nobel Prize for came from that piddling around with the wobbling plate.” Feynman’s little anecdote is a direct repudiation of Hamming’s strategy, the triumph of play over a conscious effort to work on Important Things.
At each work’s core is a different philosophy. Hamming says “if it’s not important, you are wasting your time: by definition, how else can you do important work?”, and Feynman says “if it’s not joyful, you are wasting your time: how can you do your best work when it’s no longer important to you?”.
I flirt with both ways of thinking, but Hamming’s philosophy in particular rings in my ears. Do important work! Revel in the flow, conducting a grand symphony of gathered skills and knowledge into a masterpiece unlike any the world has seen! Though the tears, sweat, and blood blur your vision, behold your work, and see that it is good! Well, your work probably won’t actually end up being world-class, but what does it matter for a shot at glory? And never mind Hamming saying “I did sort of neglect [my wife] sometimes”, just choose a hill, the taller the better, and get ready to die on it.
You know, my current actions most closely fit a Feynman-style strategy, but I’m not even playing and learning in an effective way; instead of going to war against intractable problems, maybe I could consciously pursue a Feynman strategy and deliberately chase those “that’s funny…” moments. The problem is that it’s easier to slip into comfortable zones of thought, easier to craft trivial solutions to trivial problems, easier to wake up with the precursors of dementia and years of work even you don’t care about. And yet, gambling away the years of my life on an Important Problem is a bitter proposition, and it is gambling: Hamming getting at least six different concepts named after him is a highly unusual outcome, not participation points for years of work on the right problems.
Not that we have to choose just one: the Way of the Fox tells us we should keep a stable of models and use each one when appropriate. If we recognize Hamming’s strategy as a primarily exploitative one, and Feynman’s strategy as an exploratory one, then we can just re-use the multi-armed bandit’s mechanism; we start by exploring, and gradually exploit more and more as we get to know the exploration space. Of course, like all models this doesn’t map neatly to real life, but it does indicate that mixing strategies by varying the amount of time one spends on different approaches to problems might be a workable solution. Then the question is how one should balance exploration and exploitation efforts, especially over time, which I will leave as an exercise for the reader.
Even refusing to use a mixed strategy might not turn out badly. Wienersmith points out that it’s possible to build yourself into an expert many times within a life, so you can work your way up to working on Important Problems multiple times. But keep in mind that Important Problems are the things one cracks over a career, not right after attaining mastery, so re-training every decade is exploring too often to actually make any deep progress. However, I like to read this instead as reassuring people that they don’t just have one shot at becoming an expert: if you just went to grad school, and it turns out you utterly detest your field’s Important Problems, it’s still possible to refocus. It’s a high cost, but it’s not an infinite one. And that might be the difference between paralyzing yourself with how important the choice of field is, and making a quick partially informed decision before plunging in headfirst and learning more by actually doing things.
I still don’t have an answer at this point. These are just meditations on resolving dissonance between two different respected sources. At this end, these questions remain: who will I be, and what will I do?
 ↑ Rocketry is hard because you need to carry your fuel: for every pound of stuff you want to put into orbit (or farther), you need the fuel to boost that pound, and then the fuel to boost that fuel, and the fuel to boost that fuel, ad nauseam. This means that if you are carrying anything gratuitous and unnecessary, then you are doing rocketry wrong and you will not go to space today. Hat tip to Sam’s Ra and Kerbal Space Program for helping solidify this concept for me.
 ↑ Since I’m reading Unsong, this correspondence leapt out at me. Both the scientists are Richards. Both lived from approximately 1910-1990. Both worked in Los Alamos during the war. Both are physical scientists. This Is Not A Coincidence Because Nothing Is A Coincidence.
 ↑ For a possible follow up, Robin Hanson recently pointed out that play must be important.
 ↑ Quote: “Trying to do the impossible is definitely not for everyone. Exceptional talent is only the ante to sit down at the table. The chips are the years of your life. If wagering those chips and losing seems like an unbearable possibility to you, then go do something else. Seriously. Because you can lose.”