Mathematical ability seems to be a high sensitivity test for this. I cannot recall ever meeting someone who I concluded was smarter than me who was not also able to solve and understand math problems I cannot. But it seems to have a surprisingly low specificity—people who are significantly better at math than me (and this includes probably everyone with a degree in a math heavy discipline) are still strangely very stupid.
Hypotheses:
The people who are better at math than me are actually smarter than me, I’m too dumb to realize it.
Intelligence has pretty significant domain variability and I happen to be especially low in mathematical intelligence relative to everything else.
My ADHD makes learning math especially hard, perhaps I’m quite good at grasping mathematical concepts but lack the discipline to pick up the procedural knowledge others have.
Lots of people of smart people compartmentalize their intelligence, they can’t or won’t apply it to areas other than math. (Don’t know if this differs from #2 except that it makes the math people sound bad instead of me)
The easiest of your hypotheses to examine is 1: can you describe (suitably anonymized, of course) three* of these stupid math wizzes and the evidence you used to infer their stupidity?
* I picked “three” because more would be (a) a pain and (b) too many for a comment.
can you describe (suitably anonymized, of course) three* of these stupid math wizzes and the evidence you used to infer their stupidity
Of course the problem is the most memorable examples are also the easiest cases.
1: Dogmatic catholic, knew for a long time without ever witnessing her doing anything clever.
2: As a nuclear physicist I assume this guy is considerably better at math than I am. But this is probably bad evidence as I only know about him because he is so stupid. But there appear to be quite a few scientists and engineers that hold superstitious and irrational beliefs: witness all the credentialed creationists.
3: Instead of just picking someone, take the Less Wrong commentariat. I suspect all but a handful of the regular commenters know more math than I do. I’m not especially smarter than anybody here. Less Wrong definitely isn’t dumb. But I don’t feel like I’m at the bottom of the barrel either. My sense is that my intellect is roughly comparably to the average Less Wrong commenter even though my math skills aren’t. I would say the same about Alicorn, for example. She seems to compare just fine though she’s said she doesn’t know a lot of math. Obviously this isn’t a case of people being good at math and being dumb, but it is a case of people being good at math while not being definitively smarter than I am.
I’m going with number 2 on this one (possibly a result of doing 4 either ‘actively’ or ‘passively’).
I have a very high error rate when doing basic math and am also quite slow (maybe even before accounting for fixing errors). People who’s ability to understand math tops out at basic calculus can still beat me on algebra tests. This effect is increased by the fact that due to mathematica and such, I have no reason to store things like the algorithm for doing polynomial long division. It takes more time and errors to rederive it on the spot.
At the higher levels of math there were people in my classes who were significantly better at it than I, and at the time it seemed like they were just better than me at math in every way. Another classmate and I (who seem to be relative peers at ‘math’) would consistently be better at “big picture” stuff, forming analogies to other problems, and just “seeing” (often actually using the visual cortex) the answer where they would just crank through math and come out with the same answer 3 pages of neat handwriting later.
As of writing this, the alternative (self serving) hypothesis has come up that maybe those that I saw as really good as math weren’t innately better than me (except for having lower error rate and possibly faster) at math, but had just put more effort into it and committed more tricks to memory. This is consistent with the fact that these were the kids that were very studious, though I don’t know how much of the variance that explains.
If you can’t ever recall meeting someone who you concluded was smarter than you who wasn’t good at X, and you didn’t use any kind of objective criteria or evaluation system to reach that conclusion, then you’re probably (consciously or otherwise) incorporating X into your definition of “smarter.”
There’s a self-promotion trap here—you have an incentive to act like the things you’re good at are the things that really matter, both because (1) that way you can credibly claim that you’re at least as smart as most people, and (2) that way you can justify your decision to continue to focus on activities that you’re good at, and which you probably enjoy.
I think the odds that you have fallen into this self-promotion trap are way higher than the odds for any of your other hypotheses.
Mathematical ability seems to be a high sensitivity test for this. I cannot recall ever meeting someone who I concluded was smarter than me who was not also able to solve and understand math problems I cannot. But it seems to have a surprisingly low specificity—people who are significantly better at math than me (and this includes probably everyone with a degree in a math heavy discipline) are still strangely very stupid.
Hypotheses:
The people who are better at math than me are actually smarter than me, I’m too dumb to realize it.
Intelligence has pretty significant domain variability and I happen to be especially low in mathematical intelligence relative to everything else.
My ADHD makes learning math especially hard, perhaps I’m quite good at grasping mathematical concepts but lack the discipline to pick up the procedural knowledge others have.
Lots of people of smart people compartmentalize their intelligence, they can’t or won’t apply it to areas other than math. (Don’t know if this differs from #2 except that it makes the math people sound bad instead of me)
Ideas?
The easiest of your hypotheses to examine is 1: can you describe (suitably anonymized, of course) three* of these stupid math wizzes and the evidence you used to infer their stupidity?
* I picked “three” because more would be (a) a pain and (b) too many for a comment.
Of course the problem is the most memorable examples are also the easiest cases.
1: Dogmatic catholic, knew for a long time without ever witnessing her doing anything clever.
2: As a nuclear physicist I assume this guy is considerably better at math than I am. But this is probably bad evidence as I only know about him because he is so stupid. But there appear to be quite a few scientists and engineers that hold superstitious and irrational beliefs: witness all the credentialed creationists.
3: Instead of just picking someone, take the Less Wrong commentariat. I suspect all but a handful of the regular commenters know more math than I do. I’m not especially smarter than anybody here. Less Wrong definitely isn’t dumb. But I don’t feel like I’m at the bottom of the barrel either. My sense is that my intellect is roughly comparably to the average Less Wrong commenter even though my math skills aren’t. I would say the same about Alicorn, for example. She seems to compare just fine though she’s said she doesn’t know a lot of math. Obviously this isn’t a case of people being good at math and being dumb, but it is a case of people being good at math while not being definitively smarter than I am.
I suspect that “smarter” has not been defined with sufficient rigor here to make analysis possible.
I’m going with number 2 on this one (possibly a result of doing 4 either ‘actively’ or ‘passively’).
I have a very high error rate when doing basic math and am also quite slow (maybe even before accounting for fixing errors). People who’s ability to understand math tops out at basic calculus can still beat me on algebra tests. This effect is increased by the fact that due to mathematica and such, I have no reason to store things like the algorithm for doing polynomial long division. It takes more time and errors to rederive it on the spot.
At the higher levels of math there were people in my classes who were significantly better at it than I, and at the time it seemed like they were just better than me at math in every way. Another classmate and I (who seem to be relative peers at ‘math’) would consistently be better at “big picture” stuff, forming analogies to other problems, and just “seeing” (often actually using the visual cortex) the answer where they would just crank through math and come out with the same answer 3 pages of neat handwriting later.
As of writing this, the alternative (self serving) hypothesis has come up that maybe those that I saw as really good as math weren’t innately better than me (except for having lower error rate and possibly faster) at math, but had just put more effort into it and committed more tricks to memory. This is consistent with the fact that these were the kids that were very studious, though I don’t know how much of the variance that explains.
If you can’t ever recall meeting someone who you concluded was smarter than you who wasn’t good at X, and you didn’t use any kind of objective criteria or evaluation system to reach that conclusion, then you’re probably (consciously or otherwise) incorporating X into your definition of “smarter.”
There’s a self-promotion trap here—you have an incentive to act like the things you’re good at are the things that really matter, both because (1) that way you can credibly claim that you’re at least as smart as most people, and (2) that way you can justify your decision to continue to focus on activities that you’re good at, and which you probably enjoy.
I think the odds that you have fallen into this self-promotion trap are way higher than the odds for any of your other hypotheses.
If you haven’t already, you may want to check out the theory of multiple intelligences and the theory of intelligence as information processing