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When I experience a creative block, I sometimes try to force my mind back
into a productive state, to think ever so hard about the problem,
and squeeze out a new idea.
The physicist Richard Feynman speaks of a similar period of "burn-out"
in his work, where he felt he was not making progress.
Except he decided to stop trying to do research entirely,
instead playing with interesting ideas in his field
without regard to where they would go.
So I got this new attitude. Now that I am burned out and I'll never accomplish anything, I've got this nice position at the university teaching classes which I rather enjoy, and just like I read the Arabian Nights for pleasure, I'm going to play with physics, whenever I want to, without worrying about any importance whatsoever.
Within a week, I was in the cafeteria and some guy, fooling around, throws a plate in the air. As the plate went up in the air I saw it wobble, and I noticed the red medallion of Cornell on the plate going around. It was pretty obvious to me that the medallion went around faster than the wobbling.
I had nothing to do, so I start to figure out the motion of the rotating plate. I discover that when the angle is very slight, the medallion rotates twice as fast as the wobble rate — two to one (Feynman mis-remembers here—the factor of 2 is the other way). It came out of a complicated equation! Then I thought, "Is there some way I can see in a more fundamental way, by looking at the forces or the dynamics, why it's two to one?"
I don't remember how I did it, but I ultimately worked out what the motion of the mass particles is, and how all the accelerations balance to make it come out two to one. I still remember going to Hans Bethe and saying, "Hey, Hans! I noticed something interesting. Here the plate goes around so, and the reason it's two to one is..." and I showed him the accelerations.
He says, "Feynman, that's pretty interesting, but what's the importance of it? Why are you doing it?"
"Hah!" I say. "There's no importance whatsoever. I'm just doing it for the fun of it." His reaction didn't discourage me; I had made up my mind I was going to enjoy physics and do whatever I liked.
I went on to work out equations of wobbles. Then I thought about how electron orbits start to move in relativity. Then there's the Dirac Equation in electrodynamics. And then quantum electrodynamics. And before I knew it (it was a very short time) I was "playing" — working, really — with the same old problem that I loved so much, that I had stopped working on when I went to Los Alamos: my thesis-type problems; all those old-fashioned, wonderful things.
It was effortless. It was easy to play with these things. It was like uncorking a bottle: Everything flowed out effortlessly. I almost tried to resist it! There was no importance to what I was doing, but ultimately there was. The diagrams and the whole business that I got the Nobel Prize for came from that piddling around with the wobbling plate.
One needs a certain amount of privilege or inconsequnce to be able to take time off from their required work, and this method will not necessarily work for them. But it can let you find your morale back to your work. And, since you're presently not making any progress anyway, you're no worse off if your excitements yield no further progress.
But you'll often discover alternative perspectives, maybe even a new derivative.