> And to be clear, I don't doubt that many people "can't" learn calculus in the same way I "can't" run a marathon; we don't have the desire, discipline, and free time necessary to do the work required. This does not speak in any way towards our capacities to do so, only our desire.
Your VO2max, max heart rate, and other factors appear to be significantly determined by genetics, and will absolutely contribute to your capacity to run a marathon. If it takes you a year of hard training, but it takes me a few practice runs a few weeks before, it's not fair to say we required the same amount of desire, discipline, or free time to succeed. I would instead say we had a very different capacity to run a marathon.
Are you saying that similar things could not possibly be true for learning math? Or really anything else that humans do?
I don't think any of those things contribute to whether or not I could complete a marathon, though they do contribute to how pleasant the experience would be. The same holds for learning calculus, or doing anything intellectually taxing. It's differing in difficulty for people, however it's not unachievable for anyone who isn't experiencing some kind of mental (or physical, in this marathon example) impairment.
All healthy people can learn calculus and run marathons, with varying degrees of success and effort, due to genetics and environmental factors.
I don't see how if you can agree that it requires varying degrees of effort for different people to run a marathon or learn calculus, that you then think it is impossible that some people won't be able to do those things. Just like the amount of effort required will be small for some, it will be impractically large for others. Even in the theoretical sense, there is only so much time in a day.
I also don't think "healthy" and (presumably) "not healthy" are useful categorizations. There are many people in that fuzzy in between area between "healthy" and "not healthy", for both physical and mental health.
Is it really worth so vigorously arguing the semantics of "some people are incapable of learning algebra" and "it requires an impractically large amount of effort for some people to learn algebra"?"
Yes, I think it's absolutely worth arguing the difference between "it's hard" and "it's impossible", because those are two fundamentally different things.
You can overcome difficulty, you cannot overcome (by definition) impossibility.
What you keep ignoring in what I'm saying however, is that I do think certain things are impossible for some people. I will never play in the NBA, for example, but that's a far cry from being "very good" at basketball.
Learning calculus and completing a marathon are not the point at which "healthy" (and yes, it's fuzzy, but precision is impossible on this topic) people are sometimes unable to do things. Winning a marathon and getting a Ph.D. in mathematics, I would acquiesce to your argument.
In other words, I think anyone can dabble in anything, but you do need an alignment of genetic and environmental circumstances to be in the top 1% of something. I could be argued into top 10%, but below that, it appears the data supports almost anyone being able to do almost anything, or at least well beyond whatever artificial lines we might draw to discourage people from achieving.
Your VO2max, max heart rate, and other factors appear to be significantly determined by genetics, and will absolutely contribute to your capacity to run a marathon. If it takes you a year of hard training, but it takes me a few practice runs a few weeks before, it's not fair to say we required the same amount of desire, discipline, or free time to succeed. I would instead say we had a very different capacity to run a marathon.
Are you saying that similar things could not possibly be true for learning math? Or really anything else that humans do?