It makes you distrust the people teaching you - if they're going to answer your legitimate question with circular logic, it shows that they're missing some info and not willing to admit it. So they're either lying or wrong about this thing, and who know what else they're lying or wrong about?

Similar logic puts some people off of Christianity - x is in the Bible, and we know the Bible is true because the Bible says it is true, therefore x is also true. Hmm. Someone who tries to sell you that logic is also either lying or wrong, now you can't trust either that person or the Bible.

Imagine people had refused to use the calculus because no one could really answer what an infinitesimal value really was. Sometimes you just need to make progress.

My understanding is that it was rejected by many mathematicians for precisely that reason, but that many others took up the challenge to answer the question rigorously, resulting in some major leaps in theory. On the other hand, it's good that many others were able to overlook the issue of the infinitesimals and put the techniques to lots of practical use. The lesson I take from this is that both first principles questioning and suspension of disbelief can be valuable tools for learning and discovery.

I don't think the GP (Kluny) or GGP (OscarCunningham) disagree with you on that point. If I understand them correctly, it's fine to have unresolved mysteries in your understanding, so long as you are honest about it and explicitly label it[1]. In this case, "hey, we can't quite put infinitesimals on a solid grounding (or Dirac Delta, or whatever), but it doesn't break anything else, so let's see if we can figure it out some other time."

There's a huge difference between "it's not worth our time to resolve this now" and "non-rigorous thought is okay, reality doesn't have to make sense, just do what the high-status people say, they're smarter".

[1] There's a practice in some groups to explicitly say "it works by magic" to avoid false understandings and to flag unresolved issues.

"If I understand them correctly, it's fine to have unresolved mysteries in your understanding, so long as you are honest about it and explicitly label it[1]."

Yes, exactly.

I think it's more of a rejection of the instruction, not the concept being instructed.

I had a similar experience with music instruction, everyone taught to the instrument and to the book of music, never any concepts of music theory even to the point of "What's with the sharps and flats over here by the squiggle? Why not put them where I can see them easier?" "Yeah, I don't know, it's kind of a pain, I just write them back in with pencil." "How do you write a new song?" "Oh, it's really hard, you have to be really smart like Beethoven. Don't worry about that, we have plenty of stuff to practice in the book."

Later, in self educating, I discovered key signatures, playing to those keys (and even improvising!), and that I don't have to think about sharps and flats except for accidentals and it makes so much goddamn sense, but no adult I had access to in childhood ever knew or at least none could explain something which was so fundamental, something that actually made music fun and allowed me to create a positive-feedback loop required for consistent practice.

Had I stood firmer on the grandparent's question, rejected instruction sooner (instead of just through confused burn-out), and begun to self educate sooner, I could have avoided wasting a lot of time.

A good teacher can get all of this for you. I knew all of that stuff because my mother was a violin teacher and she new musical theory in and out. Some of her first lessons are in theory before you get to sight reading so you don't have any questions like that. You had shitty teachers it sounds like and you should never reject formal education just because you had 1 bad experience.

It's funny, I "learned" piano for years as a child, but somehow missed a lot of the theory (e.g. the circle of fifths). A year ago, I got a deal on guitar lessons from a student who was looking for work for the summer. It was a crash course, pretty much taught the basic cords (G, C, D, Em, Am, etc) but we didn't have enough time to go into much theory there either. But it was enough of a crash course to start looking at the guitar and figuring out how it works, relative to my base knowledge on piano.

My partner is quite musical though (formally trained), and she's help fill in a lot of the gaps. I'm at the point now where I can fiddle around with different chord progressions and get good-sounding melodies to come out on my own. I get inversions and how they work on the guitar, etc. It's quite cool and way more interesting to me than just learning songs from a book.

If you would have rejected instruction, you would not likely be playing any music at all.

Grit is hard to come by for kids. You never find yourself interested in 'the whole field of music'. You find yourself drawn to the immediate. Seeing a piano in front of you, you might want to learn about it. You might get turned off the exact same way.

Unless your parents are directing you, childhood is a random walk through the universe of creative possibility.

Kids aren't known for being rational.