Total agreement with what Uncle Dave et al have said. But, I would add that it's not just during the early learning stage that we experience those perceived doldrums punctuated by spurts of rapid progress. It happens during all phases of our creative development. And, furthermore, it's not something that is limitted to music. Visual artists and writers experience the same thing.

Music is a hobby for me, but I make my living in the visual arts. Sometimes I'll go for a month or more just turning out the same old product by rote and then, bam! In one day I'll fill the whole studio with stuff that I have no idea where it came from. But, in reality, I do know where it came from. During the "doldrum" I've been absorbing ideas from a a wide variety of sources. Some have been due to intentional efforts such as studying another artist's work, but some have just been picked up subconsciously. At some point, they simply merge into a coherent executable concept. And, most importantly, inspiration feeds itself. Once you have "broken through" and created a new piece of art or written a new song or learned a new fiddle tune or finally mastered a tough bit of technique, the mental tools you need to do it again are right there and already sharpened. It's natural to turn around and write another song or learn another tune or paint another painting until the particular set of stimuli that brought on the current creative spurt are exhausted. Then we have to start collecting new bits for the next time it happens.

Bruce