IlyaShpitser comments on What false beliefs have you held and why were you wrong? - Less Wrong Discussion
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All of the above, but the root cause is limited aptitude. I know you don't believe that, but you probably will the day you hit your own limit.
Music is a good example. You can aspire to play the hardest and most exquisite music pieces with the best, and compose new masterpieces, but without the talent you will not progress much farther than "twinkle twinkle little star" (i'm exaggerating a bit).
Or sports. Not everyone who wants to makes it to the major leagues.
In math and sciences I have frequently observed a really motivated person learning something with extreme effort, doing the exercises, then coming to the next session with half the newly learned skills gone, and having to start nearly from scratch. As a result, the effort which is linear for many is exponential for them. Or worse.
I was in a similar situation. A couple of grad courses were easy, some harder, and one or two nearly impossible for me. I was able to do well enough on them, but it was hell. There would be no way for me to get to the level where I could do research in the area. Yet some other students just kept going, mastering the new material at the same rate as the old. (And others were forced to drop the course or the program long before.)
Think of, say, a high jumper. You can see one barely clearing 2.20 on the technique alone, with no hope of going higher, And you can see someone else doing the same height in a much more sloppy way, clearly able to do a lot better with a better technique. Brains are not much different from muscles. The limits are there, if not clearly visible.
Re your question (d), I have never tried to put enough time myself to test it, but I have tutored an aspired programmer who gave up after realizing he cannot think in the way required (see also 99.5% of programming job candidates fail the FizzBuzz test, though this seems a stretch).
You should reread what I actually said.
Sorry if I was being presumptuous. I was going by your advice to people with low math aptitude to learn more math, here and on SSC. If I confused you with someone else or grossly misrepresented your views, please disregard.
I was talking to one specific person.