Two minor points. Firstly, don't forget the most obvious hypothesis for increased human intelligence: the genes the cause intelligence may be increasing in frequency. We have a couple of studies now suggesting this.
Secondly, I don't think it's quite right to equate what Newton did with what high schoolers today learn in terms of calculus. Newton didn't have anyone to learn it from, he derived it. That is more like what an undergraduate math major learns in a course typically called something like "real analysis" or "advanced calculus" than what a high schooler or college freshmen learns in a calculus class. Learning that the derivative of x^2 is 2x is a genuinely easier task than figuring out why.
"Secondly, I don't think it's quite right to equate what Newton did with what high schoolers today learn in terms of calculus."
Oh my claim is slightly more subtle. I'm not saying that what Newton did is similar to high schoolers learning calculus, but the difficulty of what *his contemporaries trying to learn the same thing* after he discovered it. There's a reason the Principia mostly used geometry rather than calculus intuitions.
(Though your reading of my post is consistent with the text. The article is not written very well due to time constraints, this is why elsewhere I said I'm proud of the article "on a conceptual level" but it was not "technically well-written or executed.")
i agree with this post. short & sweet. so excited about conceptual technology for math
Two minor points. Firstly, don't forget the most obvious hypothesis for increased human intelligence: the genes the cause intelligence may be increasing in frequency. We have a couple of studies now suggesting this.
Secondly, I don't think it's quite right to equate what Newton did with what high schoolers today learn in terms of calculus. Newton didn't have anyone to learn it from, he derived it. That is more like what an undergraduate math major learns in a course typically called something like "real analysis" or "advanced calculus" than what a high schooler or college freshmen learns in a calculus class. Learning that the derivative of x^2 is 2x is a genuinely easier task than figuring out why.
But overall I think your thesis is sound.
"Secondly, I don't think it's quite right to equate what Newton did with what high schoolers today learn in terms of calculus."
Oh my claim is slightly more subtle. I'm not saying that what Newton did is similar to high schoolers learning calculus, but the difficulty of what *his contemporaries trying to learn the same thing* after he discovered it. There's a reason the Principia mostly used geometry rather than calculus intuitions.
(Though your reading of my post is consistent with the text. The article is not written very well due to time constraints, this is why elsewhere I said I'm proud of the article "on a conceptual level" but it was not "technically well-written or executed.")