What is the meaning of a piece of music?
Is it the quality that lets us recognize it upon hearing it? Does it lie in the ability to play the notes or understanding what is going in the composition? Is the meaning of a work in the emotional connection you have with it? Even then, if you are not the composer, can you ever really know the true meaning of a piece of music?
To know a piece of information and to have the ability to extract meaning from it are two very different things. A computer can know millions of variables, but it derives no meaning to itself from that information. What something means really has to do with the ways it connects to all the other things we know. The more such links, the more that thing will mean to us. Looking for one "true" meaning for anything in particular is futile. If something had only one meaning it would only be connected with one thing in our minds and would hardly mean anything at all.
Understanding this is very important for a musician. It affects the way we try to learn our music and how we try teach our students.
The worst teaching tries to shape concepts into a tower or a chain instead of trying to build cross-connected webs. The problem with chains is that they will break at their weakest links and towers easily topple. That's what happens when our mind, or a child's, wanders for just a moment.
As a way of reaching a useful conclusion, for a mathematician or a philosopher, simple straight lines are best. What we must realise is that our purpose is not the same. We need our ideas to be as cross-connected as possible if we wish to have any hope of retaining them. We think that we are helping our students effectively by showing them a simple single path and hammering away at it, but instead we are making things worse most of the time. The focus should be on building robust networks in our students' heads.
This is the problem with the so-called "miracle methods" of teaching. There is no magic shortcut to being a musician. Music comes with time, and it comes as a result of a whole organic process in which we integrate the entirety of our experience. We can help this process by helping our students look at the music from all possible angles.
We can apply this to our own practice. The greatest advantage of learning through webs of concepts instead of chains of reasoning is that the knowledge gained is long-lasting and almost impossible to forget. That should be the biggest selling point for any performing musician, since a typical fear is forgetting the music while performing in public.
Practically speaking, this concept is easy to apply. When teaching or practicing a piece, instead of following the same tired route of "learn one hand, learn the other, play both hands together and speed it up" try a more roundabout way of learning it. Start by reading up on the piece and the composer. Learn only the rhythm and clap it out. Sing all the intervals. Try playing the melody with different hands and changing the harmony. Play everything in octaves. Play everything with one hand. Play everything at half the tempo. Play with both hands what a single hand would play. Break it up into phrases and only play one phrase at a time. Play all the phrases backwards. Play it in a different key. Don't play the music, play around with the music.
The best teaching and learning needs variety. By observing all the different meanings that something has and could have, we are building webs instead of chains and ensuring that the whole thing won't come down in pieces when a single link breaks.