I think even geniuses have biased stupid thoughts often, even within their fields of expertise, and so the importance of rigor should not be downplayed even for them.
To use the chess analogy once more: this seems to conflict with the fact that in chess, top grandmasters’ intuitions are almost always correct (and the rare exceptions almost always involve some absurd-looking move that only gets found after the fact through post-game computer analysis). Quite often, you’ll see a chess author touting the importance of “quiet judgment” instead of “brute calculation”; that suggests extremely strongly to me that most grandmasters don’t calculate out every move—and for good reason: it would be exhausting!
Likewise, I’m given to understand many mathematicians also have this sort of intuitive judgment; of course, it takes a long time to build up the necessary background knowledge and brain connections for such judgment, but then, Jonah never claimed otherwise. From the post itself:
It took me 10,000+ hours to learn how to “see” patterns in evidence in the way that I can now. Right now, I don’t know how to communicate how to do it succinctly. It’s too much for me to do as an individual: as far as I know, nobody has ever been able to convey the relevant information to a sizable audience!
If we could find a way to quickly build up the type of judgment described above, it could very well change the way people do things forever, but alas, we’re not quite there. That’s the whole point of Jonah’s request for collaboration. (In an ideal world, I’d participate, but as a 17-year-old I doubt I’d have much to contribute and a lot of my time is used up preparing for college at this stage anyway, so… yeah. Unfortunate.)
I was not aware most grandmasters’ first instincts ended up being correct usually, interesting.
Likewise, I’m given to understand many mathematicians also have this sort of intuitive judgment; of course, it takes a long time to build up the necessary background knowledge and brain connections for such judgment, but then, Jonah never claimed otherwise. From the post itself:
I’ve been changing my position somewhat thoughout this conversation, just so it’s clear. At this point, I guess what I think is that a hard distinction between “reasoning” and “pattern recognition” doesn’t make much sense. It seems like successful pattern recognition is to a significant extent comprised of scrupulously reasoned ideas that have been internalized. If someone hypothetically refused to use explicit reasoning while being taught to recognize certain patterns, I’d expect that person to have a more difficult time learning. Reasoning about ideas in the way that is slow and deliberative eventually makes patterns easier to recognize in the way that is fast and intuitive. If someone doesn’t incorporate slow thought originated restrictions into their fast pattern matching capabilities, then they will start believing in faces that appear in the clouds, assuming that they ever learn to pattern match at all.
To use the chess analogy once more: this seems to conflict with the fact that in chess, top grandmasters’ intuitions are almost always correct (and the rare exceptions almost always involve some absurd-looking move that only gets found after the fact through post-game computer analysis). Quite often, you’ll see a chess author touting the importance of “quiet judgment” instead of “brute calculation”; that suggests extremely strongly to me that most grandmasters don’t calculate out every move—and for good reason: it would be exhausting!
Likewise, I’m given to understand many mathematicians also have this sort of intuitive judgment; of course, it takes a long time to build up the necessary background knowledge and brain connections for such judgment, but then, Jonah never claimed otherwise. From the post itself:
If we could find a way to quickly build up the type of judgment described above, it could very well change the way people do things forever, but alas, we’re not quite there. That’s the whole point of Jonah’s request for collaboration. (In an ideal world, I’d participate, but as a 17-year-old I doubt I’d have much to contribute and a lot of my time is used up preparing for college at this stage anyway, so… yeah. Unfortunate.)
I was not aware most grandmasters’ first instincts ended up being correct usually, interesting.
I’ve been changing my position somewhat thoughout this conversation, just so it’s clear. At this point, I guess what I think is that a hard distinction between “reasoning” and “pattern recognition” doesn’t make much sense. It seems like successful pattern recognition is to a significant extent comprised of scrupulously reasoned ideas that have been internalized. If someone hypothetically refused to use explicit reasoning while being taught to recognize certain patterns, I’d expect that person to have a more difficult time learning. Reasoning about ideas in the way that is slow and deliberative eventually makes patterns easier to recognize in the way that is fast and intuitive. If someone doesn’t incorporate slow thought originated restrictions into their fast pattern matching capabilities, then they will start believing in faces that appear in the clouds, assuming that they ever learn to pattern match at all.