> This used to get on my nerves, how can people be so stupid? Why won't they just think for a moment!? But recently I've been focussing some effort on learning a language (Spanish) and realise that in that this case the first-principles style of learning that works so well for physics and maths is largely useless

I had the exact same experience. I'm an Engineer, and my entire life I've only been able to learn (and self-teach) by reasoning through first principles. When I can't reason it through, I don't want to learn it "just because"

I never put any effort into learning a language, and always thought it was "dumb". In high school I could say hello and count to 10 in a couple of languages, but that was it.

When I was 27 I started traveling through Central and South America, and wanted to learn Spanish. I honestly didn't know if I was capable, or if my brain and learning style would allow for it.

For the first couple of months I was frustrated and always saying things like "but that doesn't make any sense", "It should be like this" etc.

After a few months, I just stopped trying to reason it through and started going with it, like you said. After about a year and a half I stopped translating into English in my head, I started dreaming in Spanish, and I can now guess words and verb conjugations without consciously realizing I even know that given word. It first started happening when I was a little drunk, which is a good time for me to actually get stuff done in my head, because I stop trying to reason everything through and just go with it.

Stick with it, you'll get it. I can't more highly recommend immersing yourself for a prolonged period.