Learning is strange. Sometimes you get something, and sometimes you don’t. Sometimes you pound your head for hours trying to solve a problem, then later go back to it and solve it in minutes. I have two good examples:
This spring, I decided to learn to unicycle. And not just riding on smooth streets to say that I can unicycle, but riding the local mountain bike trails on one wheel. After about two and a half months of practice, I was good enough that it was worth driving to a park with good trails for a ride. I’d constantly “trip” over roots, but there were enough smooth sections for it to be fun. I went back a few times, and each time I’d make it past some section that I missed the previous ride. Then something strange happened: one day I just couldn’t ride any more. I had unplanned dismounts (UPDs) in places I could fairly consistently clear an previous rides. In addition to the normal UPDs, I had a couple crashes, the last of which twisted my ankle enough that I had to take it easy for a couple weeks to give it a chance to recover. After that day, I couldn’t really ride for a month. Not that I didn’t try. I’d ride down a smooth street, and randomly fall off my unicycle. This continued for the entire month of August. Then September began, and I decided I was starting to recover my unicycling abilities enough that it was worth a trip back to the park with mountain bike trails. For the first twenty minutes, I could barely ride. Then all of a sudden, I could ride again. I began clearing sections I hadn’t made before. I even rode good parts of the intermediate trails instead of sticking to the beginner trail. Today I went back again and was able to ride even more sections that had previously caused me to UPD, and some I hadn’t even tried before.
The second example is solving physics and math problems. Some days, I’ll look at a new problem for a couple hours without any real progress. On other days, I could look at the same problem and solve it nearly as quickly as I can write the answer. This is particularly frustrating when I know I’ve solved similar problems easily in the past, but just don’t see the solution that day.