There’s 0.0001 prior for 1 in 10000 intelligence level. It’s a low prior, you need a genius detector with an incredibly low false positive rate before most of your ‘geniuses’ are actually smart. A very well defined problems with very clear ‘solved’ condition (such as multiple novel mathematical proofs or novel algorithmic solution to hard problem that others try to solve) would maybe suffice, but ‘he seems smart’ certainly would not. This also goes for IQ tests themselves—while a genius would have high IQ score, high IQ scored person would most likely be someone somewhat smart slipping through the crack between what IQ test measures and what intelligence is (case example, Chris Langan, or Keith Raniere, or other high IQ ‘geniuses’ we would never suspect of being particularly smart if not for IQ tests).
Weak and/or subjective evidence of intelligence, especially given lack of statistical independence of evidence, should not get your estimate of intelligence of anyone very high.
This is rather tangential, but I’m curious, out of those who score 1 in 10000 on a standard IQ test, what percentage is actually at least, say, 1 in 5000 in actual intelligence? Do you have a citation or personal estimate?
Depends what you call “actual intelligence” as distinct from what IQ tests measure. private_messaging talks a lot in terms of observable real-world achievements, so presumably is thinking of something along those lines.
The easiest interpretation to measure would be a regression toward the mean effect. Putting a lower bound on the IQ scores in your sample means that you have a relevant fraction of people who tested higher than their average test score. I suspect that at the high end, IQ tests have few enough questions scored incorrectly that noise can let some < 1 in 5000 IQ test takers into your 1 in 10000 cutoff.
I also didn’t note the other problem: 1 in 10,000 is around IQ=155; the ceiling of most standardized (validated and normed) intelligence tests is around 1 in 1000 (IQ~=149). Tests above this tend to be constructed by people who consider themselves in this range, to see who can join their high IQ society and not substantially for any other purpose.
Would depend to how you evaluate actual intelligence. IQ test, at high range, measures reliability in solving simple problems (combined with, maybe, environmental exposure similarity to test maker when it comes to progressive matrices and other ‘continue sequence’ cases—the predictions by Solomonoff induction depend to machine and prior exposure, too). As an extreme example consider an intelligence test of very many very simple and straightforward logical questions. It will correlate with IQ but at the high range it will clearly measure something different from intelligence. All the intelligent individuals will score highly on that test, but so will a lot of people who are simply very good at simple questions.
A thought experiment: picture a class room of mind uploads, set for a half the procedural skills to read only, and teach them the algebra class. Same IQ, utterly different outcome.
I would expect that if the actual intelligence correlates with IQ to the factor of 0.9 (VERY generous assumption), the IQ could easily become non-predictive at as low as 99th percentile without creating any contradiction with the observed general correlation. edit: that would make about one out of 50 people with IQ of one in 10 000 (or one in 1000 or 1 in 1000 0000 for that matter) be intelligent at level of 1 in 5 000. That seems kind of low, but then, we mostly don’t hear of the high IQ people just for IQ alone. edit: and the high IQ organizations like Mensa and the like are hopelessly unremarkable, rather than some ultra powerful groups of super-intelligences.
In any case the point is that the higher is the percentile the more confident you must be that you have no common failure mode between parts of your test.
edit: and for the record my IQ is 148 as measured on a (crappy) test in English which is not my native tongue. I also got very high percentile ratings in programming contest, and I used to be good at chess. I have no need to rationalize something here. I feel that a lot of this sheepish innumerate assumption that you can infer one in 10 000 level performance from a test in absence of failure modes of which you are far less certain than 99.99% , comes simply from signalling—to argue against applicability of IQ test in the implausibly high percentiles lets idiots claim that you must be stupid. When you want to select one in 10 000 level of performance in running 100 meters you can’t do it by measuring performance at a standing jump.
There are longitudinal studies showing that people with 99.99th percentile performance on cognitive tests have substantially better performance (on patents, income, tenure at top universities) than those at the 99.9th or 99th percentiles. More here.
and the high IQ organizations like Mensa and the like are hopelessly unremarkable, rather than some ultra powerful groups of super-intelligences.
Mensa is less selective than elite colleges or workplaces for intelligence, and much less selective for other things like conscientiousness, height, social ability, family wealth, etc. Far more very high IQ people are in top academic departments, Wall Street, and Silicon Valley than in high-IQ societies more selective than Mensa. So high-IQ societies are a very unrepresentative sample, selected to be less awesome in non-IQ dimensions.
There are longitudinal studies showing that people with 99.99th percentile performance on cognitive tests
Uses other tests than IQ test, right? I do not dispute that a cognitive test can be made which would have the required reliability for detecting the 99.99th percentile. The IQ tests, however, are full of ‘continue a short sequence’ tests that are quite dubious even in principle. It is fundamentally difficult to measure up into 99.99th percentile, you need a highly reliable measurement apparatus, carefully constructed in precisely the way in which IQ tests are not. Extreme rarities like one in 10 000 should not be thrown around lightly.
Mensa is less selective than elite colleges or workplaces for intelligence
There are other societies. They all are not very selective for intelligence either, though, because they all rely on dubious tests.
and much less selective for other things like conscientiousness, height, social ability, family wealth, etc.
I would say that this makes those other places be an unrepresentative sample of the “high IQ” individuals. Even if those individuals who pass highly selective requirements on something else rarely enter mensa, they are rare (tautology on highly selective) and their relative under representation in mensa doesn’t sway mensa’s averages.
edit: for example consider the Nobel Prize winners. They all have high IQs but there is considerable spread and the IQ doesn’t seem to correlate well with the estimate of “how many others worked on this and did not succeed”.
Note: I am using “IQ” in the narrow sense of “what IQ tests measure”, not as shorthand for intelligence. The intelligence has the capacity to learn component which IQ tests do not measure but tests of mathematical aptitude (with hard problems) or verbal aptitude do.
note2: I do not believe that the correlation entirely disappears even for IQ tests past 99th percentile. My argument is that for the typical IQ tests it well could. It’s just that the further you get up the smaller fraction of the excellence is actually being measured.
Administering SATs to younger children, to raise the ceiling.
I would say that this makes those other places be an unrepresentative sample of the “high IQ” individuals.
Well Mensa is ~0 selectivity beyond the IQ threshold, and is a substitute good for other social networks, leaving it with the dregs. “Much more” is poor phrasing here, they’re not rejecting 90%. If you look at the linked papers you’ll see that a good majority of those at the 1 in 10,000 level on those childhood tests wind up with elite university/alumni or professional networks with better than Mensa IQ distributions.
Administering SATs to younger children, to raise the ceiling.
Ghmmm. I’m sure this measures a plenty of highly useful personal qualities that correlate with income. E.g. rate of learning. Or inclination to pursue intellectual work.
Well Mensa is ~0 selectivity beyond the IQ threshold, and is a substitute good for other social networks, leaving it with the dregs. “Much more” is poor phrasing here, they’re not rejecting 90%. If you look at the linked papers you’ll see that a good majority of those at the 1 in 10,000 level on those childhood tests wind up with elite university/alumni or professional networks with better than Mensa IQ distributions
Well, yes. I think we agree on all substantial points here but disagree on interpretation of my post. I referred specifically to “IQ tests” not to SAT, as lacking the rigour required for establishing 1 in 10 000 performance with any confidence, to balance on my point that e.g. ‘that guy seems smart’ shouldn’t possibly result in estimate of 1 in 10 000 , and neither could anything that relies on rather subjective estimate of the difficulty of the accomplishments in the settings where you can’t e.g. reliably estimate from number of other people who try and don’t succeed.
I referred specifically to “IQ tests” not to SAT, as lacking the rigour required for establishing 1 in 10 000 performance with any confidence, to balance on my point that e.g. ‘that guy seems smart’ shouldn’t possibly result in estimate of 1 in 10 000
Note that these studies use the same tests (childhood SAT) that Eliezer excelled on (quite a lot higher than the 1 in 10,000 level), and that I was taking into account in my estimation.
a: while that’d be fairly impressive, keep in mind that if it is quite a lot higher than 1 in 10 000 then my prior for it is quite a lot lower than 0.0001 with only minor updates up for ‘seeming clever’ , and my prior for someone being a psychopath/liar is 0.01, with updates up for talking other people into giving you money.
b: not having something else likewise concrete to show off (e.g. contest results of some kind and the like) will at most make me up-estimate him to bin with someone like Keith Raniere or Chris Langan (those did SAT well too), which is already the bin that he’s significantly in. Especially as he had been interested in programming, and the programming is the area where you can literally make a LOT of money in just a couple years while gaining the experience and gaining much better cred than childhood SAT. But also an area that heavily tasks general ability to think right and deal with huge amounts of learned information. My impression is that he’s a spoiled ‘math prodigy’ who didn’t really study anything beyond fairly elementary math, and my impression is that it’s his own impression except he thinks he can do advanced math with little effort using some intuition while i’m pretty damn skeptical of such stuff unless well tested.
and the programming is the area where you can literally make a LOT of money in just a couple years while gaining the experience and gaining much better cred than childhood SAT
I don’t think the childhood SAT gives that much “cred” for real-world efficacy, and I don’t conflate intelligence with “everything good a person can be.” Obviously, Eliezer is below average in the combination of conscientiousness, conformity, and so forth that causes most smart people to do more schooling. So I would expect lower performance on any given task than from a typical person of his level of intelligence. But it’s not that surprising that he would, say, continue popular blogging with significant influence on a sizable audience, rather than stop that (which he values for its effects) to work as a Google engineer to sack away a typical salary, or to do a software startup (which the stats show is pretty uncertain even for those with VC backing and previous successful startups).
‘math prodigy’ who didn’t really study anything beyond fairly elementary math, and my impression is that it’s his own impression
I agree on not having deep math knowledge, and this being reason to be skeptical of making very unusual progress in AI or FAI. However while his math scores were high, “math prodigy” isn’t quite right, since his verbal scores were even higher. There are real differences in what you expect to happen depending on the “top skill.” In the SMPY data such people often take up professions like science (or science fiction) writer (or philosopher) that use the verbal skills too, even when they have higher raw math performance than others who go to on to become hard science professors. It’s pretty mundane when such a person leans towards being a blogger rather than an engineer, especially when they are doing pretty well as the former. Eliezer has said that if not worried about x-risk he would want to become a science fiction writer, as opposed to a scientist.
Especially as he had been interested in programming, and the programming is the area where you can literally make a LOT of money in just a couple years while gaining the experience and gaining much better cred than childhood SAT.
What salary level is good enough evidence for you to consider someone clever?
Notice that your criteria for impressive cleverness excludes practically every graduate student—the vast majority make next to nothing, have few “concrete” things to show off, etc.
My impression is that he’s a spoiled ‘math prodigy’ who didn’t really study anything beyond fairly elementary math, and my impression is that it’s his own impression except he thinks he can do advanced math with little effort using some intuition while i’m pretty damn skeptical of such stuff unless well tested.
Except the interview you quoted says none of that.
JB: I can think of lots of big questions at this point, and I’ll try to get to some of those, but first I can’t resist asking: why do you want to study math?
EY: A sense of inadequacy.
[...]
[EY:] Even so, I was a spoiled math prodigy as a child—one who was merely amazingly good at math for someone his age, instead of competing with other math prodigies and training to beat them. My sometime coworker Marcello (he works with me over the summer and attends Stanford at other times) is a non-spoiled math prodigy who trained to compete in math competitions and I have literally seen him prove a result in 30 seconds that I failed to prove in an hour.
This is substantially different from EY currently being a math prodigy.
[EY:] I’ve come to accept that to some extent [Marcello and I] have different and complementary abilities—now and then he’ll go into a complicated blaze of derivations and I’ll look at his final result and say “That’s not right” and maybe half the time it will actually be wrong.
In other words, he’s no better than random chance, which is vastly different from “[thinking] he can do advanced math with little effort using some intuition.” By the same logic, you’d accept P=NP trivially.
[EY:] I’ve come to accept that to some extent [Marcello and I] have different and complementary abilities—now and then he’ll go into a complicated blaze of derivations and I’ll look at his final result and say “That’s not right” and maybe half the time it will actually be wrong.
In other words, he’s no better than random chance, which is vastly different from “[thinking] he can do advanced math with little effort using some intuition.” By the same logic, you’d accept P=NP trivially.
I don’t understand. The base rate for Marcello being right is greater than 0.5.
Maybe EY meant that, on the occasions that Eliezer objected to the final result, he was correct to object half the time. So if Eliezer objected to just 1% of the derivations, on that 1% our confidence in the result of the black box would suddenly drop down to 50% from 99.5% or whatever.
[EY:] I’ve come to accept that to some extent [Marcello and I] have different and complementary abilities—now and then he’ll go into a complicated blaze of derivations and I’ll look at his final result and say “That’s not right” and maybe half the time it will actually be wrong.
In other words, he’s no better than random chance, which is vastly different from “[thinking] he can do advanced math with little effort using some intuition.” By the same logic, you’d accept P=NP trivially.
If a device gives a correct diagnosis 999,999 times out of 1,000,000 and is applied to a population that has about 1 in 1,000,000 chance of being positive then a positive diagnosis by the device has approximately 50% chance of being correct. That doesn’t make it “no better than random chance”. It makes it amazingly good.
Notice that your criteria for impressive cleverness excludes practically every graduate student—the vast majority make next to nothing, have few “concrete” things to show off, etc.
It’s not criteria for cleverness, it is criteria for evidence when the prior is 0.0001 (for 1 in 10 000) . One can be clever at one in 7 billions level, and never having done anything of interest, but I can’t detect such person as clever at one in 10 000 level with any confidence without seriously strong evidence.
This is substantially different from EY currently being a math prodigy.
I meant, a childhood math prodigy.
In other words, he’s no better than random chance
If Marcello failed one time out of ten and Eliezer detected it half of the time, that would be better than chance. Without knowing failure rate of Marcello (or without knowing how the failures are detected besides being pointed out by EY), one can’t say whenever it is better than chance or not.
There’s 0.0001 prior for 1 in 10000 intelligence level. It’s a low prior, you need a genius detector with an incredibly low false positive rate before most of your ‘geniuses’ are actually smart. A very well defined problems with very clear ‘solved’ condition (such as multiple novel mathematical proofs or novel algorithmic solution to hard problem that others try to solve) would maybe suffice, but ‘he seems smart’ certainly would not. This also goes for IQ tests themselves—while a genius would have high IQ score, high IQ scored person would most likely be someone somewhat smart slipping through the crack between what IQ test measures and what intelligence is (case example, Chris Langan, or Keith Raniere, or other high IQ ‘geniuses’ we would never suspect of being particularly smart if not for IQ tests).
Weak and/or subjective evidence of intelligence, especially given lack of statistical independence of evidence, should not get your estimate of intelligence of anyone very high.
This is rather tangential, but I’m curious, out of those who score 1 in 10000 on a standard IQ test, what percentage is actually at least, say, 1 in 5000 in actual intelligence? Do you have a citation or personal estimate?
Depends what you call “actual intelligence” as distinct from what IQ tests measure. private_messaging talks a lot in terms of observable real-world achievements, so presumably is thinking of something along those lines.
The easiest interpretation to measure would be a regression toward the mean effect. Putting a lower bound on the IQ scores in your sample means that you have a relevant fraction of people who tested higher than their average test score. I suspect that at the high end, IQ tests have few enough questions scored incorrectly that noise can let some < 1 in 5000 IQ test takers into your 1 in 10000 cutoff.
I also didn’t note the other problem: 1 in 10,000 is around IQ=155; the ceiling of most standardized (validated and normed) intelligence tests is around 1 in 1000 (IQ~=149). Tests above this tend to be constructed by people who consider themselves in this range, to see who can join their high IQ society and not substantially for any other purpose.
Would depend to how you evaluate actual intelligence. IQ test, at high range, measures reliability in solving simple problems (combined with, maybe, environmental exposure similarity to test maker when it comes to progressive matrices and other ‘continue sequence’ cases—the predictions by Solomonoff induction depend to machine and prior exposure, too). As an extreme example consider an intelligence test of very many very simple and straightforward logical questions. It will correlate with IQ but at the high range it will clearly measure something different from intelligence. All the intelligent individuals will score highly on that test, but so will a lot of people who are simply very good at simple questions.
A thought experiment: picture a class room of mind uploads, set for a half the procedural skills to read only, and teach them the algebra class. Same IQ, utterly different outcome.
I would expect that if the actual intelligence correlates with IQ to the factor of 0.9 (VERY generous assumption), the IQ could easily become non-predictive at as low as 99th percentile without creating any contradiction with the observed general correlation. edit: that would make about one out of 50 people with IQ of one in 10 000 (or one in 1000 or 1 in 1000 0000 for that matter) be intelligent at level of 1 in 5 000. That seems kind of low, but then, we mostly don’t hear of the high IQ people just for IQ alone. edit: and the high IQ organizations like Mensa and the like are hopelessly unremarkable, rather than some ultra powerful groups of super-intelligences.
In any case the point is that the higher is the percentile the more confident you must be that you have no common failure mode between parts of your test.
edit: and for the record my IQ is 148 as measured on a (crappy) test in English which is not my native tongue. I also got very high percentile ratings in programming contest, and I used to be good at chess. I have no need to rationalize something here. I feel that a lot of this sheepish innumerate assumption that you can infer one in 10 000 level performance from a test in absence of failure modes of which you are far less certain than 99.99% , comes simply from signalling—to argue against applicability of IQ test in the implausibly high percentiles lets idiots claim that you must be stupid. When you want to select one in 10 000 level of performance in running 100 meters you can’t do it by measuring performance at a standing jump.
There are longitudinal studies showing that people with 99.99th percentile performance on cognitive tests have substantially better performance (on patents, income, tenure at top universities) than those at the 99.9th or 99th percentiles. More here.
Mensa is less selective than elite colleges or workplaces for intelligence, and much less selective for other things like conscientiousness, height, social ability, family wealth, etc. Far more very high IQ people are in top academic departments, Wall Street, and Silicon Valley than in high-IQ societies more selective than Mensa. So high-IQ societies are a very unrepresentative sample, selected to be less awesome in non-IQ dimensions.
Uses other tests than IQ test, right? I do not dispute that a cognitive test can be made which would have the required reliability for detecting the 99.99th percentile. The IQ tests, however, are full of ‘continue a short sequence’ tests that are quite dubious even in principle. It is fundamentally difficult to measure up into 99.99th percentile, you need a highly reliable measurement apparatus, carefully constructed in precisely the way in which IQ tests are not. Extreme rarities like one in 10 000 should not be thrown around lightly.
There are other societies. They all are not very selective for intelligence either, though, because they all rely on dubious tests.
I would say that this makes those other places be an unrepresentative sample of the “high IQ” individuals. Even if those individuals who pass highly selective requirements on something else rarely enter mensa, they are rare (tautology on highly selective) and their relative under representation in mensa doesn’t sway mensa’s averages.
edit: for example consider the Nobel Prize winners. They all have high IQs but there is considerable spread and the IQ doesn’t seem to correlate well with the estimate of “how many others worked on this and did not succeed”.
Note: I am using “IQ” in the narrow sense of “what IQ tests measure”, not as shorthand for intelligence. The intelligence has the capacity to learn component which IQ tests do not measure but tests of mathematical aptitude (with hard problems) or verbal aptitude do.
note2: I do not believe that the correlation entirely disappears even for IQ tests past 99th percentile. My argument is that for the typical IQ tests it well could. It’s just that the further you get up the smaller fraction of the excellence is actually being measured.
Administering SATs to younger children, to raise the ceiling.
Well Mensa is ~0 selectivity beyond the IQ threshold, and is a substitute good for other social networks, leaving it with the dregs. “Much more” is poor phrasing here, they’re not rejecting 90%. If you look at the linked papers you’ll see that a good majority of those at the 1 in 10,000 level on those childhood tests wind up with elite university/alumni or professional networks with better than Mensa IQ distributions.
Ghmmm. I’m sure this measures a plenty of highly useful personal qualities that correlate with income. E.g. rate of learning. Or inclination to pursue intellectual work.
Well, yes. I think we agree on all substantial points here but disagree on interpretation of my post. I referred specifically to “IQ tests” not to SAT, as lacking the rigour required for establishing 1 in 10 000 performance with any confidence, to balance on my point that e.g. ‘that guy seems smart’ shouldn’t possibly result in estimate of 1 in 10 000 , and neither could anything that relies on rather subjective estimate of the difficulty of the accomplishments in the settings where you can’t e.g. reliably estimate from number of other people who try and don’t succeed.
Note that these studies use the same tests (childhood SAT) that Eliezer excelled on (quite a lot higher than the 1 in 10,000 level), and that I was taking into account in my estimation.
Sources?
Also,
a: while that’d be fairly impressive, keep in mind that if it is quite a lot higher than 1 in 10 000 then my prior for it is quite a lot lower than 0.0001 with only minor updates up for ‘seeming clever’ , and my prior for someone being a psychopath/liar is 0.01, with updates up for talking other people into giving you money.
b: not having something else likewise concrete to show off (e.g. contest results of some kind and the like) will at most make me up-estimate him to bin with someone like Keith Raniere or Chris Langan (those did SAT well too), which is already the bin that he’s significantly in. Especially as he had been interested in programming, and the programming is the area where you can literally make a LOT of money in just a couple years while gaining the experience and gaining much better cred than childhood SAT. But also an area that heavily tasks general ability to think right and deal with huge amounts of learned information. My impression is that he’s a spoiled ‘math prodigy’ who didn’t really study anything beyond fairly elementary math, and my impression is that it’s his own impression except he thinks he can do advanced math with little effort using some intuition while i’m pretty damn skeptical of such stuff unless well tested.
I don’t think the childhood SAT gives that much “cred” for real-world efficacy, and I don’t conflate intelligence with “everything good a person can be.” Obviously, Eliezer is below average in the combination of conscientiousness, conformity, and so forth that causes most smart people to do more schooling. So I would expect lower performance on any given task than from a typical person of his level of intelligence. But it’s not that surprising that he would, say, continue popular blogging with significant influence on a sizable audience, rather than stop that (which he values for its effects) to work as a Google engineer to sack away a typical salary, or to do a software startup (which the stats show is pretty uncertain even for those with VC backing and previous successful startups).
I agree on not having deep math knowledge, and this being reason to be skeptical of making very unusual progress in AI or FAI. However while his math scores were high, “math prodigy” isn’t quite right, since his verbal scores were even higher. There are real differences in what you expect to happen depending on the “top skill.” In the SMPY data such people often take up professions like science (or science fiction) writer (or philosopher) that use the verbal skills too, even when they have higher raw math performance than others who go to on to become hard science professors. It’s pretty mundane when such a person leans towards being a blogger rather than an engineer, especially when they are doing pretty well as the former. Eliezer has said that if not worried about x-risk he would want to become a science fiction writer, as opposed to a scientist.
Hey, Raniere was smart enough to get his own cult going.
Or old enough and disillusioned enough not to fight the cultist’s desire to admire someone.
What salary level is good enough evidence for you to consider someone clever?
Notice that your criteria for impressive cleverness excludes practically every graduate student—the vast majority make next to nothing, have few “concrete” things to show off, etc.
Except the interview you quoted says none of that.
[...]
This is substantially different from EY currently being a math prodigy.
In other words, he’s no better than random chance, which is vastly different from “[thinking] he can do advanced math with little effort using some intuition.” By the same logic, you’d accept P=NP trivially.
I don’t understand. The base rate for Marcello being right is greater than 0.5.
Maybe EY meant that, on the occasions that Eliezer objected to the final result, he was correct to object half the time. So if Eliezer objected to just 1% of the derivations, on that 1% our confidence in the result of the black box would suddenly drop down to 50% from 99.5% or whatever.
Yes, but that’s not “no better than random chance.”
Sure. I was suggesting a way in which an objection which is itself only 50% correct could be useful, contra Dmytry.
Oh, right. The point remains that even a perfect Oracle isn’t an efficient source of math proofs.
You do not understand how basic probability works. I recommend An Intuitive Explanation of Bayes’ Theorem.
If a device gives a correct diagnosis 999,999 times out of 1,000,000 and is applied to a population that has about 1 in 1,000,000 chance of being positive then a positive diagnosis by the device has approximately 50% chance of being correct. That doesn’t make it “no better than random chance”. It makes it amazingly good.
It’s not criteria for cleverness, it is criteria for evidence when the prior is 0.0001 (for 1 in 10 000) . One can be clever at one in 7 billions level, and never having done anything of interest, but I can’t detect such person as clever at one in 10 000 level with any confidence without seriously strong evidence.
I meant, a childhood math prodigy.
If Marcello failed one time out of ten and Eliezer detected it half of the time, that would be better than chance. Without knowing failure rate of Marcello (or without knowing how the failures are detected besides being pointed out by EY), one can’t say whenever it is better than chance or not.