There was strong interest in the first two posts in my sequence, and I apologize for the long delay. The reason for it is that I’ve accumulated hundreds of pages of relevant material in draft form, and have struggled with how to organize such a large body of material. I still don’t know what’s best, but since people have been asking, I decided to continue posting on the subject, even if I don’t have my thoughts as organized as I’d like. I’d greatly welcome and appreciate any comments, but I won’t have time to respond to them individually, because I already have my hands full with putting my hundreds of pages of writing in public form.
Thanks a lot for continuing your work on this sequence; it’s been really interesting and seems potentially quite valuable given the mathematical nature of many problems in AI safety.
This post of yours reminds me of http://www.paulgraham.com/taste.html When I read that essay of PG’s years ago, my reaction was something like: “This is highfalutin BS. At best, taste is when your intuition for what seems good/interesting happens to correlate highly with what actually is good/interesting according to some metric.” But when I think about this now, I realize that if this is indeed what taste is, it’s tremendously valuable, since it gives you the ability to find stuff quicker in large search spaces.
I took a few math classes in college with a great teacher who taught using the Socratic method, by asking questions. I answered a lot of his questions, and one of my classmates (who I had a lot of respect for) referred to me as a “genius”. However, I didn’t do very well on the tests my teacher administered, and ended up with a score around 79% both times I took classes he taught.
This blog post discusses a study using a construct called “clerical intelligence”; I wonder if low clerical intelligence is the sort of thing that would cause someone to be good at math “conceptually” but keep making frustrating mistakes in practice. (That’s the only reference I can find to clerical intelligence though, so perhaps it should be taken with a grain of salt.) I felt like as I’ve grown older, I’ve gotten better at thinking like a bulldozer, keeping track of my working memory, and making fewer mistakes.
I’d be interested to know whether Scott Alexander felt like he was weaker in identifying strategies to solve calculus problems or doing the actual execution. If the latter, it seems like that might work with your hypothesis that he has high mathematical ability but low clerical intelligence. (This might be hard for him to know because if your answer is wrong, without a tutor you don’t immediately know whether you chose the wrong strategy or made a small stupid mistake.)
This blog post discusses a study using a construct called “clerical intelligence”; I wonder if low clerical intelligence is the sort of thing that would cause someone to be good at math “conceptually” but keep making frustrating mistakes in practice.
Ooh! I think ‘clerical intelligence’ is the thing that my husband and I have taken to calling ‘attention to detail’ amongst ourselves. It’s also been at least occasionally studied under that name – when applying for an admin job, they gave me a test of ‘attention to detail’ that consisted of several hundred timed questions comparing a block of six numbers to another block, having to answer whether they were the same or not, with around 5-10 seconds to spend per question. I don’t think I’m outright bad at this, but it’s not effortless for me. (Luckily, I had math teachers who gave points for the work getting to the solution, not just the solution, so I could get 7⁄8 points on a complicated problem even if I substituted a + for a—somewhere and got the wrong answer).
My husband tends to use ‘attentional to detail’ to some degree also to mean what Paul Graham would call ‘taste’ or what Jonah would call ‘aesthetic discernment’. I think the causal relationship is probably that in order to develop ‘taste’–intuitions for what’s good that correspond to what’s generally agreed to be good – you need to be paying close attention to its details for a few years. Thus I have ‘taste’ for music, writing, and to some degree math, but not for fashion, since I never looked at what people were wearing.
Thanks a lot for continuing your work on this sequence; it’s been really interesting and seems potentially quite valuable given the mathematical nature of many problems in AI safety.
This post of yours reminds me of http://www.paulgraham.com/taste.html When I read that essay of PG’s years ago, my reaction was something like: “This is highfalutin BS. At best, taste is when your intuition for what seems good/interesting happens to correlate highly with what actually is good/interesting according to some metric.” But when I think about this now, I realize that if this is indeed what taste is, it’s tremendously valuable, since it gives you the ability to find stuff quicker in large search spaces.
I took a few math classes in college with a great teacher who taught using the Socratic method, by asking questions. I answered a lot of his questions, and one of my classmates (who I had a lot of respect for) referred to me as a “genius”. However, I didn’t do very well on the tests my teacher administered, and ended up with a score around 79% both times I took classes he taught.
This blog post discusses a study using a construct called “clerical intelligence”; I wonder if low clerical intelligence is the sort of thing that would cause someone to be good at math “conceptually” but keep making frustrating mistakes in practice. (That’s the only reference I can find to clerical intelligence though, so perhaps it should be taken with a grain of salt.) I felt like as I’ve grown older, I’ve gotten better at thinking like a bulldozer, keeping track of my working memory, and making fewer mistakes.
Someone on Metafilter writes:
I’d be interested to know whether Scott Alexander felt like he was weaker in identifying strategies to solve calculus problems or doing the actual execution. If the latter, it seems like that might work with your hypothesis that he has high mathematical ability but low clerical intelligence. (This might be hard for him to know because if your answer is wrong, without a tutor you don’t immediately know whether you chose the wrong strategy or made a small stupid mistake.)
Ooh! I think ‘clerical intelligence’ is the thing that my husband and I have taken to calling ‘attention to detail’ amongst ourselves. It’s also been at least occasionally studied under that name – when applying for an admin job, they gave me a test of ‘attention to detail’ that consisted of several hundred timed questions comparing a block of six numbers to another block, having to answer whether they were the same or not, with around 5-10 seconds to spend per question. I don’t think I’m outright bad at this, but it’s not effortless for me. (Luckily, I had math teachers who gave points for the work getting to the solution, not just the solution, so I could get 7⁄8 points on a complicated problem even if I substituted a + for a—somewhere and got the wrong answer).
My husband tends to use ‘attentional to detail’ to some degree also to mean what Paul Graham would call ‘taste’ or what Jonah would call ‘aesthetic discernment’. I think the causal relationship is probably that in order to develop ‘taste’–intuitions for what’s good that correspond to what’s generally agreed to be good – you need to be paying close attention to its details for a few years. Thus I have ‘taste’ for music, writing, and to some degree math, but not for fashion, since I never looked at what people were wearing.