How do people find coming to terms with the idea that they are not capable of reaching a high standard at piano. How do you deal with the frustration of endless effort without result?
Interesting, I have never actually faced this. Whenever I have put in a lot of effort, I have usually seen at least some improvement. I think what matters is aggressively zoning in on the problem, boiling it down to its constituent elements, making sure that each such element is as simple as possible so that I can focus on them individually. For example, if I'm certain that there is an issue with rhythm, I will try to tap it or hum it, then record myself and listen back, until I get it right. Since there is a clear feedback loop, it is almost certain that you will notice improvement as long as you can perceive the shortcoming in the sound or physical feeling.
In other words, if you want to learn trigonometry, there's no point in trying to browbeat it into your head without knowing basic geometry such as the Pythagorean theorem. It may not be obvious that your shortcoming is, in fact, not understanding the Pythagorean theorem correctly, but if you look carefully enough, you will hopefully see it at that point, and then you can immediately correct it.
This is my philosophy while approaching new subjects in general. For the piano as well, I just keep asking questions until I'm satisfied. It might drive a teacher crazy, but *shrug*.
I have read pretty much all literature ever published on the topic of skill aquisition, and concluded that talent to a substantial extent is inherited.
The problem is that while it's arguably clear that talent is inherited, it's not well-studied what this implies for the bounds of ability for a particular individual. There's no straight line from "average linguistic ability" to "cannot read above 400 wpm". Even if someone thinks the latter is impossible for them, it's quite possible that it isn't.
I am extremely persistent, to the point that my level of persistence might be described as a form of insanity, yet it is to no avail. I cannot play advanced music, certainly not at the tempo required of advanced music.
People keep thinking of persistence as a great trait in itself, but I would argue it isn't. It's only useful if you know how to apply it. A lot of people try to study really hard, spending hours a day for years, but do not get anywhere, and this is not necessarily due to lack of ability, but is very often because they hold misapprehensions about the nature of learning the topic. One very common one in school, for example, is the idea that repeating something x times will commit it to memory. A relentlessly persistent person, who holds that idea, will be wasting almost all of their time, since the key to memory is association (I might not be completely correct about it, but I think it's a good analogy). Learning anything is full of pitfalls like this, it's not like hitting the gym x hours a day.
No amount of practice, and no type of practice seems to make any difference at all. No matter who I take advice from, no matter which practice tecniques I adopt, there is simply no result.
If you're not already, I would suggest hiring a teacher, and spending several hours practicing with them during lessons. The way you talk about "type of practice" makes it seem like you are thinking about this in terms of practice regimen and exercises. Once one set of exercises does not work, you move on to another set of exercises. The problem is that advice only works if you really understand how to apply it, and can do that consistently. It's very hard to figure out if you are applying a piece of advice correctly, and the closest you can get in a situation where you cannot understand a piece of advice is to have the person giving the advice right beside you, observing what you are doing and correcting you until you have really understood it. Be really clear in communicating when it's not working. If the teacher is any good, this will go back and forth until you understand the concept much better. You will almost always see at least a little improvement during the session. If the teacher is bad, they will often tell you to just practice it at home while you protest that it doesn't seem to be working, and from my experience this is a very frustrating and unproductive situation to be in.
It may take me 6 months or a year to bring a single line of music up to 75% of the prescribed tempo, practising extremely hard each day using only the correct, professionally recommeded practice regimen. I see others who can play the same line at 100% tempo and it takes only 2 weeks. Why is the difference so absolutely enormous?
First of all, you said you started at 32, and have been practicing for 10 years with an ineffective learning method (no offense, but there are a number of red flags for this in your write-up). This cannot compare to someone who has been learning for a decade, since they were a child, with really good teachers. When I'm playing the piano, there are so many minute changes which I have to keep making and trying out, and some which I would have never thought of which my teacher suggests. It is often those minute, almost imperceptible movements which hold the key to various aspects of technique, and beginner students often make the mistake of underestimating the complexity of this. They don't realize that certain comments by teachers, such as "hold you hand in an arch" are shorthand for executing something which is very tricky, and very difficult to do at a high level. It's a naive point of view, such as someone thinking that all of mathematics is how to solve more complicated addition problems. There are layers and layers of complexity hidden beneath, which you need to figure out. This may be easier as a child, but even as an adult, what matters is that you try to achieve those sensations and movements.
In fact, this whole idea of spending 6 months to a year to bring a single line of music up to tempo seems ridiculous to me. If you have the technique for it, you should be able to play a line of music immediately, or at least within a week or two by which time it would be memorized (which removes the cognitive overload aspect). If you can't do that, you figure out what is the exact reason why you can not learn the passage, and try to come up with solutions for that particular problem. Otherwise, again, it's like trying to beat trigonometry into your head without knowing basic facts about triangles. You can try to speed up how fast you learn all of the prerequisites for a topic, but you cannot start something from the middle of nowhere.
Also i get very, very frustrated, with experts and teachers recommending exercises and techniques, assuming that they will produce gains, because it did for them or for other students. Invariably following these exercises and strategies does not yield good results.The outcome is ALWAYS months of relentless practicing for minuscule gains that are not at all encouraging.It just boils down to innate ability.Either you have it, or you don't. Effort or strategy or persistence will never even begin to make up for it.
Well, here is where you're wrong. It's possible that certain things boil down to innate ability, but there are various aspects in your write-up where it would be clear to most pianists that your way of approach is terribly wrong. You can't really say for sure until you fix those things. There is this myth which a lot of people hold, that regardless of how they approach a subject, it will get better eventually, but this is completely false imo. You can make absolutely zero progress despite spending hundreds of hours, and this gets truer the more advanced you get in something.
Don't be too hasty to ascribe things to lack of talent. (Don't take this to mean that I think talent does not exist, I do.)