Here was my first lesson: This type of skill development is hard. When I got to the first tricky gap in the paper’s main proof argument, I faced immediate internal resistance. It was as if my mind realized the effort I was about to ask it to expend, and in response it unleashed a wave of neuronal protest, distant at first, but then as I persisted increasingly tremendous, crashing over my concentration with mounting intensity. To combat this resistance, I deployed two types of structure. The first type was time structure: “I am going to work on this for one hour,” I would tell myself. “I don’t
Here was my first lesson: This type of skill development is hard. When I got to the first tricky gap in the paper’s main proof argument, I faced immediate internal resistance. It was as if my mind realized the effort I was about to ask it to expend, and in response it unleashed a wave of neuronal protest, distant at first, but then as I persisted increasingly tremendous, crashing over my concentration with mounting intensity. To combat this resistance, I deployed two types of structure. The first type was time structure: “I am going to work on this for one hour,” I would tell myself. “I don’t care if I faint from the effort, or make no progress, for the next hour this is my whole world.” But of course I wouldn’t faint and eventually I would make progress. It took, on average, ten minutes for the waves of resistance to die down. Those ten minutes were always difficult, but knowing that my efforts had a time limit helped ensure that the difficulty was manageable. The second type of structure I deployed was information structure—a way of capturing the results of my hard focus in a useful form. I started by building a proof map that captured the dependencies between the different pieces of the proof. This was hard, but not too hard, and it got me warmed up in my efforts to understand the result. I then advanced from the maps to short self-administered quizzes that forced me to memorize the key definitions the proof used. Again, this was a relatively easy task, but it still too...
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