Is it possible to get better at playing the piano by simply thinking about playing the piano? Oddly, the answer is yes. (Now, it's better in the long run to actually play the piano -- and that "thinking" activity must be very focused and directed -- but still, that's crazy, right?) It turns out that this phenomenon is actually quite common: by exercising the brain, humans can improve coordination skills (and even strength) in physical tasks.
This actually happened to me when I was learning to type. When I was a pre-teen, I got a job as a typist, transcribing printed magazine articles into text format for posting on a CompuServe bulletin board. Now, I'd had lessons on typing for years in school by that point -- but it never really stuck, and I remained a rapid hunt-and-peck typist, not very sure of where the keys were or how to type quickly. When I had to type page after page of text in, I was suddenly motivated to get better at the task. I began to imagine the keyboard at all times -- when I'd "speak" a thought in my mind, I'd imagine the feeling of typing it. I would not allow myself to think-speak faster than I could t-y-p-e t-h-e l-e-t-t-e-r-s o-n a k-e-y-b-o-a-r-d in my mind. (I was a weird kid, yes.) While this is arguably a little nutty and compulsive, it worked -- I got better at typing largely by thinking about typing.
If you can spare two minutes, check out this video discussing a few good examples of this phenomenon. And if you've experienced something similar to my in-brain typing tutoring, let me know in the comments!