I have always been sure of two things: Walking is harder than playing the piano. If I ever figured out how to really play the piano I would have figured out how to live.
I want to walk as other people walk, without having to think about every aspect of placing one foot in front of the other and shifting body weight so as not to incur pain. (Most people can't see that there is a problem, but a congenital spinal anomaly leaves nothing to be taken for granted.)
But I want to play the piano, not as others do, but so as to express what I hear and how much it matters to me.
Having reached that state -- I am still working on the walk problem -- and having by now taught several cycles of students some of whom already by the age of 18 play with completely transparent (i.e., clearly audible) mastery of "the music part," as one student put it, I can address the connection between the two.
If the physical therapist shows me what walking looks like I get completely confused. My body neither looks nor feels like his; I cannot possibly imitate him. I have literally no idea what he is doing. Similarly, when a piano teacher would demonstrate a passage I was at a loss to know how to respond.
It is my intention that will ultimately make walking work, as it has been my intention to make by piano playing reflect the working of my ear that has revealed the essence not only of Schubert and Mozart, but of my students. Having learned to pay attention at the level of intention, I have learned to discern the intention of my students. The result is their increasing satisfaction with their own playing, and my increasing fascination with the complexity of the undertaking.