In regard to what you said about determined and directed practice, it's essentially a case of it being more about the quality, not quantity of time spent on som

In regard to what you said about determined and directed practice, it's essentially a case of it being more about the quality, not quantity of time spent on something. I realised this a number of years ago and have been utilising it ever since. Most people tend to keep going down one particular route when they're trying to achieve something and, when they hit a roadblock, they keep pushing forward. This is working harder. The alternative is to go in a completely different direction where, rather counter-intuitively, we have a chance of picking up information/experience which will get rid of the previously encountered road block. This is working smarter. If something seems too difficult, it probably is, and the reason for that is that one is missing key pieces. Doing the same thing will not find these pieces but looking in non-obvious places will (since if it was obvious, it wouldn't be difficult in the first place). I think that the mechanics behind this consist of what is basically, to borrow a term from comp sci, an impedance mismatch between our internal maps of the world and the shared maps we call physics or math or piano technique. We tend to organise things in a particular way so that we can communicate about them with each other but this shared set of symbols is never the same as an individuals' internal representation. I think that the reason all internal maps are different is because the subject (the human) is an integral part of them. In other words, one's understanding of gravity will have shared symbolism with completely subjective experiences that have nothing to do with gravity. The process of learning is essentially a mapping of one set of symbols to another. More accurately, there seem to be three levels, the experience itself, the internal symbols relating to the experience and the external shared symbols we use to communicate with each other. Based on this, I think that the categorisations in the shared map rarely make sense internally and that, as a layman, following the lines drawn by the categorisations doesn't make sense, hence the roadblocks that people encounter. To put it another way, the categorisations we have in our shared knowledge are primarily for communication purposes and are, objectively speaking, irrational. Separating math from physics from music does not make sense in real terms since they are different perspectives on the same system. Or, to put it yet another way, the map is not the territory and those who understand that are much more adept at navigating with maps.