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paper-machine comments on The Truth About Mathematical Ability - LessWrong
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Obviously, everyone will do best if they work as hard as they can, and innate talent models can prevent people from working harder. But innate talent models are really useful at avoiding wasted effort and frustration, and so I think it's easier to make the case for the toxicity and wrongness of the inverse of the models you're describing.
In particular, I think Scott's easy response is to say "what happens when you put drive and morale into the ability bucket along with calculation ability?" (You bring up that possibility a bit with the hereditary section.) Given that Scott doesn't seem to have the drive or the morale, then you either need to claim to him that he's misdiagnosed his drive to do mathematics, which seems toxic and wrong,* or to say "yep, not a mathematician."
Also, I do work both as a research mathematician and as a industrial mathematician, and while you might be right about research mathematics, I think that equating a lot of derivation mistakes with poor industrial math ability is healthy and right. I don't want to hand off an analysis problem to someone who makes derivation mistakes, because the results can't be trusted, and I wouldn't want my accountant to be bad at calculation, and so on.
*Scott's made the comparison to sexual orientation before, and I think it fits; just like a gay guy would get fed up with people saying "you just haven't met the right girl yet!", someone who does not have the drive or talent for mathematics will get fed up with people saying "you just haven't met the right theorem yet!"
I must protest: absolutely nothing happens. Real limitations on your drive and morale don't feel from the inside like "running out of hit points", they feel like akrasia. So as long as you can choose, from the inside, to keep going, you haven't run out of drive yet.
I am reluctant to generalize to the internal experience of others, especially if the difference between my and someone else's internal experience are the cause of those externally observable drive and morale differences.
I feel like this is contentless. Suppose you and I are observing a third person, and they do not keep going. Can either of us state whether or not they could choose to keep going from the inside?
Now, if you are struggling, and say to yourself "this sucks, but I will keep going," and you do keep going for longer having said that to yourself, then great! As you point out, that's part of your overall drive, and so is irrelevant once we step outside how you get the drive you have and are instead quantifying how much drive you have.
Unfortunately, the key word there is outside: reasoning about some other system than one's self encounters no Loebian obstacles. Reasoning about one's self usually tends to involve reasoning about one's self-model, which is actually a necessarily less accurate description of your state of being than the raw data of how things feel-from-the-inside to Objectively Be.
When you are going "UUUUGGGGGH, THIS IS FUCKING IMPOSSIBLE GODDAMNIT!" you may have hit your limit for the time being. When you are frustrated and thinking, "I probably just have limited ability at maths", that's just anxiety.
I'm not sure I buy this, though. If you view the ability as learning ability, or what I call elasticity over here, then it seems like I can say "I find it more difficult than I expect to learn a foreign language; I'll downgrade my expected elasticity for foreign languages" and that might switch the EV of spending more effort on learning foreign languages from positive to negative. If there are multiple things I could do, and which thing is wisest depends on the relative elasticities, then trying to estimate those elasticities seems useful and doable without hitting the hard limit.