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Physicist, Startup Founder, Blogger, Dad

Friday, May 13, 2011

One hundred thousand brains

The calculation below is from a well known theoretical physicist (slightly edited).
I occasionally read your blog and it sometimes gets me thinking in politically incorrect directions. I was just looking at your genomics slides. You are interested in the tails of the intelligence distribution, and seem to think there is a qualitative difference between +3 SD (1 in 1000) and +4 SD (1 in 30,000) ability. I suppose I share your view on this but I thought I'd check by doing a back of the envelope calculation. How many really impressive brains do I think there are in the world? By really impressive I mean capable of doing breakthrough work in a cognitively hard area like physics or math or computer science. Someone who, if I talk to them at a meeting, I can see they're doing really nontrivial things and have something to tell me. Such people are spread out over many different fields, including private industry, but let's see if we can estimate how many there are.

Let me start with physics, which is what I know best. I'd guess the top 100 departments/labs in the world each have on average 10-20 such people. The next 200 places, maybe 5-10, and so on. So maybe 5k such people in physics worldwide. If I include other departments like math, engineering, biology, etc. I'd increase this by a factor of 5 across an entire university. Adding in private industry, military research, burn outs, etc. perhaps doubles the number again. So I'd say maybe 50k in the world. Definitely not more than 100k. I might be biased, but if I set the cutoff a little higher the concentration starts to peak much more strongly in areas like physics (theory) and math departments. But let's stick with this population of 100k, who are drawn from a world population of maybe 1-2 billion people depending on what you think of the educational systems in China and India. Interestingly, this makes the population I identified right around the +4 SD level you are talking about.

I'm not so sure these people can be identified through testing early in their lives, although it's an interesting question. I'm not even sure the people identified as +4 SD on g are the same as the ones I described above, but there is probably a lot of overlap.

I do think that if these 100k people were to disappear, there would be a strongly negative effect on scientific and, eventually, technological progress worldwide. Are there another 100k people of equivalent value to the human race? [italics mine]
There are about 100k Ultra-High Net Worth (UHNW) individuals in the world, defined as having investible assets of at least $30 million USD. So it would appear that most of these brainy types fail to capture the economic returns from their contributions to society -- Zuckerberg, Brin, Page, Gates, Allen, etc. excluded ;-) Would you rather be +4 SD in brainpower, or +4 SD in net worth?

See also Out on the tail, g genomics slides.

92 comments:

David Stern said...

Publishing your results implies that what you are producing is a public good and you can't capture the full economic returns... still, I'd guess that most such people are in the upper part of the income distribution. Maybe at +2SD and above ?

LondonYoung said...

 I would do the calculation by looking at one year's worth of undergraduate degrees in the U.S. and what fraction of those graduates I think have non-trivial brains.  What fraction of MIT?  What fraction of Ohio state, etc ... 

Sam H said...

 I would settle for +1-2 SD in brainpower and +1-2 in net worth. Of course anything greater is desirable. =)

steve hsu said...

My rough guesses: +4 SD (1 in 30k) is about 100-200 freshmen each year in the US (assume some fatness in the tail; exceptional immigrants from abroad). Let's say 200. I think that's about top 5-10 percent at Caltech (avg IQ 140-5, SD around 10) or about 10-15 kids per class. The top 10 or 15 UG schools (private, all with class sizes in the 1-2k range, except for Caltech) account for about 100-150. YPS and MIT probably account for 10-25 each; H has the most, maybe 35. The remaining 50-100 are at public universities, with Berkeley having the most (maybe 5-10 per year), or at other lesser ranked privates.


A >+5 SD (not kidding) correspondent supplies this joke:

The college faculty were in their annual meeting when, suddenly, an angel
appears. Turning to the Dean, the creature said, "I will grant you one
of three boons -- infinite wisdom, infinite wealth or infinite health."
The Dean thought for a minute, then replied "Wisdom."

"So be it." and the angel disappeared.

In the silence that followed, the Dean sat thoughtfully, saying nothing and
staring off into the distance. Finally, one of the other faculty members
exclaimed, "Do you have anything to say? What words of wisdom can you
provide us?".

Quoth the Dean, "I should have taken the money."

Simfish InquilineKea said...

 The easiest way to identify them would be to get a significant fraction of them to all post online on a common place. This gets harder and harder for people beyond college though. 

The best place I can think of (right now) is College Confidential, which attracts numerous extremely strong people (namely, a very large fraction of everyone who's applying to Ivy League schools and summer programs like the Research Science Institute). However, its moderation policies have gotten significantly more repressive over the years, so this does get a lot of genuinely intelligent people banned.

I know that the CTY Talent Search program has a certain forum for people in SET (although my experience is that people develop at different rates, and some of the people with high SAT scores in 7th-8th grade didn't turn out to be exceptional). 

steve hsu said...

So, are the incentives for producing these public good results optimal for rate of progress? 

Ju Hyung Ahn said...

What about infinite health, does that mean you can't die unless you get involved in fatal accidents.
I would take that instead of wealth & wisdom.
Being "elf" in the Lord of the Rings universe can't be too bad especially in modern times where the risk of accidents are quite small.
If one is intelligent enough, one can also work on their wisdom and wealth with an abnormally long lifespan.

David Stern said...

Probably not.

Simfish InquilineKea said...

 The thing is, once you reach such high achievement levels, it's impossible to say that "achievement X requires more genius than achievement Y". At that point, you have different kinds of genius, but you can't really compare them to any other

asdf said...

Looking at results from the Putnam as a reasonable indicator, MIT has vastly more than HYPS or Caltech.  See e.g. http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2218517#p2218517, which shows the number of people from each school to achieve each level on the most recent Putnam.  There is simply no contest.

steve hsu said...

You're talking about the situation right now, whereas I am kind of averaging over the last 20 years or so. There were times when Harvard or Caltech were better than MIT on the Putnam. Keep in mind training matters a lot for math competitions, and if for some reason a disproportionate fraction of kids who invested energy in AoPS in HS decide to go to MIT (or some other school), then would distort our perception of the real talent distribution.

Simfish InquilineKea said...

 Another thing is that Caltech is significantly more rigorous than MIT, and has a significantly more time-consuming core curriculum. So this leaves Caltech students with less time to study for competitions like the Putnam.

That being said, my general impression (from Ben Golub's posts on College Confidential and from talking to others) is that the average Caltech student is stronger than the average MIT student. That being said, it does seem that a lot of the *phenomenally* smart prefer MIT to Caltech. 

Simfish InquilineKea said...

 Also, the problem is this: http://talk.collegeconfidential.com/college-confidential-cafe/378038-scientists-low-iqs.html

We know that.... (although these were childhood IQ scores, so they're not as reliable as late-teen ones)Feynman's IQ was 126 (bio)Watson's IQ was 124 (bio)William Shockley's was 129, then 125 when tested a year later (his 2007 bio)Luis Alvarez's was below 135 (he failed to qualify for Terman study)

steve hsu said...

Caltech avg is higher than MIT's and if SD is similar then advantage in the tail goes to the former. That means the number of Putnam fellows or Nobel winners will be higher per capita at Caltech, which I believe is the case. Btw, Caltech is 5x smaller than MIT but has won the Putnam team competition more times (2x?) than MIT! Only Harvrad has more team wins than Caltech - pretty amazing for such a tiny school.

Simfish InquilineKea said...

 Oh true, good points. I do suspect that MIT's SD is higher than Caltech's, although I also suspect that their intelligence distributions aren't totally well-modeled by the bell curve (as in, I don't think there is a significant falloff at the lower end that you would see at the higher end). That being said, if we're just talking about the right end, the distribution of the low end doesn't matter much. 

Hmm, I take back my "disproportionately increase the number of people at the extreme right-end of the tail" remark - I think I did read that somewhere (with respect to impact on communities based around people who had such high z-scores), but it doesn't mathematically make sense.

LondonYoung said...

So, do we think that about 10-15 kids in each of these graduating classes meet the description above,  "capable of doing breakthrough work"?  Identify in your mind the names of these individuals that we knew (or know), and get a practical, personal, assessment of how far out in the tail people need to be.  I am actually OK with 10-15 as the cut-off ...capable of doing breakthrough work"?  Identify in your mind the names of these individuals that we knew (or know), and get a practical, personal, assessment of how far out in the tail people need to be.  I am actually OK with 10-15 as the cut-off ...

Víctor Sánchez said...

 The problem I find on these scores is that they were on Binet tests in the first half of XX. These scores are on tests that emphasize verbal ability and although all mental abilities correlates positively (g) there might be still some important differences on some persons. Einstein himself had some difficulties with language as a child, and could perfectly score "low" (120's) on a Binet test, but I would bet whatever you want that if he had taken RAPM as a child he wouldn't score at percentile 90.  Were they given later other tests (such as RAPM) they would score significantly higher, IMO. Poincare apparently failed to get a good score on one of the first versions of Stanford Binet. And definitively he hadn't a normal IQ. BTW, the IQ 160 of Einstein you can read on your link is a myth. He never took an IQ test. The opposite side of the problem, eg assuming that anybody intelligent enough to make great contributions to science must have above 4 sd, is a misconception too. 

 To sum up: I don't think that all those physicists you cite had IQ's on the 120-130 range. Probably the problem was on the testing itself. But I don't think either that they must had all above 160 IQ scores.

steve hsu said...

Look up my blog post on Roe's study of US scientists. It addresses many of these issues.

steve hsu said...

Quick summary: Harvard dominates, MIT coming on strong in recent years, Caltech punching far above its size :-)

"By a wide margin, Harvard has the best record in the Putnam competition. Through 2010, Harvard has won the team competition twenty-seven times, while its closest rival for team titles, Caltech, has won the team title ten times. MIT is in third place with six titles with three of these coming since 2003."

http://www.d.umn.edu/~jgallian/putnam.pdf 

steve hsu said...

I am interpreting here, but I think that "capable" means that given the opportunity they could make the breakthrough. They have the necessary brainpower, but of course there's luck involved to get the opportunity in the first place. In the original calculation many of these people (e.g., 5 people out of a 100-200 ranked physics department) will not have made earth-shaking breakthroughs.

I can definitely think of a dozen people in our class who seem to be as smart as researchers who actually made breakthroughs. Whether they actually will or have done so is another question. Probably half of this dozen are not even in sci/tech anymore, they are, um, allocating resources more efficiently for society's benefit ;-) Some of them might even be in the 4SD wealth category! Imagine that -- a 4/4 double winner :-)

silkop said...

How about +4 SD in happiness or +4 SD in empathy?

Víctor Sánchez said...

 Ops! we already talked about that Dr. Hsu ;) And yes, they are very high scorers, but I seriously doubt that more than 50% would have beat the WAIS ceiling of 160 by the standard scores of nowadays IQ tests because the reasons exposed before. So there is why I'm skeptical about puting the deadline at 4 sigma, since there is a clear lack of data above the 99.9 percentile on standarized IQ tests. Moreover, g seems to "max out" at 99.997 (see Jensen, although it is being questioned recently by other researchers) so some argue that measuring above 4 sigma is nearly meaningless.

asdf said...

 aren't you a 4x4 double winner from your startups?

steve hsu said...

HNW yes, UHNW no :-(

steve hsu said...

But what about 3 vs 4 SD? Standardized tests like (old) SAT and GRE had ceilings above 3 and I bet a detailed study would show some validity (see also SMPY). The avg for admits to top math and physics (theory) PhD programs is probably above 3, based on my experience. 3 on old SAT was only a little above Caltech avg.

steve hsu said...

I think the average dog is at +4SD for happiness relative to people. But I'm not sure I'd get much done in that state :-)

Given the amount of human suffering in the world +4SD in empathy would be very painful for me. I'd probably go nuts.

Sam H said...

Hsu and RKU, the smartest guys in the internet? Possibly. 

Víctor Sánchez said...

   There is a difference between 3 and 4 sd, for sure. The problem is that although some researches are getting interesting results designing tests for that sort of population there is little data right now. There is why people who achieve above 3 sd are told by psychometricians to be careful interpreting their scores. 

   Yes, the SAT has a ceiling at 4 sigma also (the newer is lower if I remember correctly, circa 150?). On the SMPY cohort three (top 1/10 000) they (the authors) estimated their average "IQ" at 186 sd16 at the beginning of the study, but when given as an adult they averaged above 3 sigma on the same SAT as yourself said, so hardly they were to test at above 5 sigma on average at a test like SB or WAIS. What I mean is that when you have a ceiling at 4 sd on nowadays IQs, the truth is that your measurement looses exactness before arriving to 4 sd. Because there are relatively little amount of individuals studied sistematically with a hard enough test, among other reasons. Another problem is the relationship between SAT on the high end and IQ at the high end, or even between IQ on different tests at the high end. I don't have read any paper with a sample of SMPY cohort three taking a formal IQ test. Would be great if you can refer me such a paper!

   Regarding the IQ average at top math and theoretical physics PhD's I haven't read any paper that puts the IQ above 3 sigma (another interesting paper you could name to me!), but a thing happens the higher the average is in this kind of groups: the lower the variance is.

steve hsu said...

 Re: math and theor. physics phds I wasn't referring to any research paper, just to SAT/GRE scores used in the admissions process.

But you are right there is not much on the high end. SMPY and Roe are the two best sources I have been able to find with relative high ceilings.

A completely open question is whether in the 3-4SD range the old SAT or "real" IQ tests like WAIS or even the IMO/Putnam have more actual validity (e.g., for predicting success as a scientist or professor).

steve hsu said...

I know many people much smarter than I am  :-( 

Max B said...

 
Quoth the Dean, "I should have taken the money."

You know unless "infinite wisdom" also comes with "infinite focus and hardwork" I'd take money too. After all you can hire guys smarter than yourself in large quantities :)

Yan Shen said...

 I'm kinda curious as to whether Steve ever competed in stuff like AIME/USAMO, Putnam, etc... Maybe one of these days he'll dish out some more biographical details! :)

steve hsu said...

You are asking about ancient history!

I was one of the top kids in Iowa but not highly ranked nationally. It wasn't a big deal back then. The top scorers tended to be from places like Bronx/Stuy and it was clear they were getting training that we weren't. There was no number theory, tricky geometry, combinatorics, etc. in what we were taught in HS. We had no teachers who could do the problems and no coaching. We just went in and took the test...

At Caltech I attended some Putnam training sessions but never actually took the test as by that time I was more interested in physics than math. My freshman year I actually planned to take it but I got food poisoning the night before. I suppose if I had practiced I might have gotten an honorable mention (top 40) as some of my friends, who I thought were roughly at my ability level, did so. But I doubt I could have been near the top. It was obvious to me that people who had trained for these things in HS and earlier still had a big advantage later on the Putnam.

At Caltech and in my later physics career I have known people who were at or near the top in these competitions and I generally find them to be quite impressive. I've actually written a physics paper with a 3x Putnam Fellow so I think I've seen the whole range of capabilities ;-) One person I know who was an IMO gold medalist (US team) told me he found his "problemist" (my terminology) ability only gave him a +1SD advantage on the Caltech curriculum, which is pretty hard stuff (if you search on the blog you can see what econ Nobelist Vernon Smith had to say about it). This is roughly consistent with my experience (although perhaps I would have guessed he would be at +1.5 to 2 SD at Caltech) because I often did as well or better in courses (at about the same level of effort) as kids who had either been at the top in US HS competition or did well on the Putnam.

In retrospect I notice I was much more interested in learning stuff than in solving tricky problems. In HS I had accelerated quite a bit (taking a lot of college math and physics courses) and kept doing so in college. At 19 (Caltech senior) I was taking grad level courses in quantum field theory and general relativity, which didn't seem like a big deal at the time but looking back I see there aren't a lot of kids doing that. I was mainly interested in learning the things I really found interesting: quantum mechanics, general relativity, quantum field theory -- the stuff I actually work on now. I don't know of anything as g loaded as this stuff, with the exception of pure math things that don't get me so excited.

In Eugene (where I live now) there is a UO math PhD who teaches at a local middle school and coaches kids for these competitions. I am pretty sure the talent pool of kids where I grew up is as strong as the one in Eugene (actually stronger because ISU had a good engineering school whereas UO is a liberal arts school), but Ames never produced a national-level competitor during my time there, whereas Eugene has produced several including an IMO gold medalist in a similar period. So it's very clear to me training matters.

Nevertheless I think anyone who can get to the national or international level in these competitions is clearly very smart, and I would tend to think these competitions are a better filter at the high end than "real" IQ tests.

Víctor Sánchez said...

 Dr. Hsu:

   I know that the political climate is not as good as it should be for doing this, but since you are a professor of physics interested in the issue you could perform some kind of experiments among your colleagues worldwide with nowadays tests. It would bring a lot more data on this matter.

steve hsu said...

g is not the same as SATV or SATM or MO (math olympiad) ability. They are all distinct, have some dependence on training, etc.

There is probably typically a 1 SD fluctuation in scores for a particular individual on different kinds of "intelligence" tests. This fluctuation may go up a lot at the high end, and if we include tests that load on training (MO).

The main issue is that different tests have different "validities" as predictors for different purposes.

Keep in mind I'm not a real "g man" -- I think of all these tests as rough predictors only. It's not clear exactly what they measure, exactly.

I do think that someone who scores +(3-4) on any of these kinds of things has a brain which is qualitatively different from that of an average person. That's the only crude assumption I need to make in order to be willing to invest time in an intelligence GWAS.

BTW, your friend might be +3 in g and +4 in MO ability, so consistent with my guess.

Sam H said...

You don't have to answer this, but I am guessing the +5 SD person is RKU. 

steve hsu said...

Nope. A whole different league.

NicolasBourbaki said...

The physicist in the quote seem to underestimate the humanities departments in their contribution. I think there's good reason to think that the smartest academics are not in the physics or math departments but actually in the philosophy departments (I'm speaking of comparing averages of course). Physics departments tend to be much less selective even at the top departments in the US than top philosophy departments because of the basic fact that humanities departments generally have far less funding and can offer far fewer places at their grad spots so they tend to select only the very best. The physics department at Caltech says for example, that it's average GRE score for incoming PhD students is 1380 for the general test. Caltech is a top ten grad physics department.

http://www.pma.caltech.edu/GSR/gre&toefl.html

UT Austin by comparison is a top 20 (ranked 19th) graduate philosophy department and its average GRE for incoming PhD students is 1486, more than 100 points higher than Caltech's. 

http://www.utexas.edu/cola/depts/philosophy/graduate-program/Admissions.php

So even though philosophy majors tend to hold their own in overall GRE standings with physics and math majors, even that raw data may underestimate their intellectual standing once they become professionals in the field. They may not just "hold their own" but may be tops. UT Austin is not alone and I've seen and heard that other top philosophy departments are similarly or even more selective. 

steve hsu said...

Not buying it.

1. Perhaps 30-50% of physics grad students (depending on department) are foreign born. Their V scores are not a good indicator of their actual verbal ability.

2. The GRE M is just way too easy and while it might be a reasonable test for philosophers' math abilities it is laughable for physics/math grad students. I would guess almost all good physics/math grad students are above the GRE M ceiling, whereas a smaller fraction of philosophy students are.

3. You need to break out the theorists, who are only (roughly) 20% of the physics population. (See Roe study for the difference in psychometric profiles.) Experimentalists often have other abilities (tinkering, building, running teams) which neither theorists nor philosophers tend to have. If you want to claim that philosophers have g similar to experimental physicists it might be true (I don't think g is really does justice to the lab abilities I listed above), but theorists are another matter.

Finally, I know (or have known) lots of philosophers as well as physics/math people and I just don't find your claim to be credible. I think we've had this conversation at least once before...

Bo said...

So if it takes ~+4sd to do nontrivial things, then are all of these sub +4sd scientists just wasting time in the wrong occupation?

It's clear that scientists below +4sd make significant contributions, but I agree that the qualitative differences between 3sd and 4sd are huge.  Would the gains to society be greater if all these +3sd scientists went into business or medicine instead?

I'm somewhere around 3.6sd based on the GRE, and I'm sure that I'll be wealthier if I abandon research and go into business.  Whether or not the world is better off is another matter.  My advisor certainly seems upset that I'm not remaining in academia.  He's probably not +4sd. either.

NicolasBourbaki said...

I've seen similar data for other top philosophy departments and their average GRE scores and if they are accurate (and I have no reason to doubt them as they are pretty consistent) then philosophy majors also score near the ceiling on the Quantitative section. A 1500 average would imply a very high Quantitative (reasonably close or matching the Caltech mean of 780) as well as a high Verbal. I am assuming also of course that the variance is roughly similar so that we will have similar proportion of those ceiling bumping among admitted students. On your first point, much of the math portion is influenced by the amount of practice and since the typical physics majors must take 5 or 6 times the math courses as a philosophy major, practice should be factored in. The verbal section is arguably the most g loaded because it has the analogies and antonyms section. If you split physicists into theorists and experimentalists, then philosophers should be split among the analytic and continental. The later I suspect will do substantially worse on the GRE, especially the Quantitative section.   

Víctor Sánchez said...

 Generally a person scoring high on verbal test will also score high on math ones and viceversa. That's the point about g: a general factor that is present in all mental abilities. And if I'm not wrong, many guys from SMPY highly verbal who finally got into math/physics did quite well. The same holds on IQ batteries. It is normal for a high IQ tester to get quite high on nearly all subtests. In fact, you can draw conclussions about learning disabilities if there exists some important scores discrepancies.

 In a more qualitative way of talking, high g subjects tend to be quite good at different tasks. And if they enjoy many of them, they might have what is called the "multipotentially problem", too able to do too things and finally hesitate to choose just one path. A typical problem of gifted.

 Regarding the SAT the difference between the V and the M is expected. Almost nobody get consistently perfect scores on all domains. Obtaining a perfect 1600 might be 1/5000, but attaining 800 and 750 (very high indeed, the difference with previous is almost measurement error) might be 1/1000. In the second case the correlation between both parts still remains high. It happens with all tests.

  And what Dr. Hsu states about a 1SD point variation between tests is true. In some cases might be even higher. A 50 point difference is, although, unlikely (leaving aside illness or lack of motivation). 

Víctor Sánchez said...

 In the case of physicists vs philosophers a problem with Roe data is that she didn't include philosophers, just scientists.

Víctor Sánchez said...

 I think there is an obsession with putting a clear cut-off at 3, 4 or 5 sigma. And whatever the cut-off is, the fact is that on standarized IQ tests some great physicists of XX century have been tested at 120s. Probably they had higher IQs if tested with more reliable tests of today, but be sure they wouldn't all get 160+. Other studies gives the average for Nobel Prize winners at 3 sigma. Jensen and others states that all past geniuses probably had IQs between 3 and 4 sigma by nowadays IQ tests. And the truth is that IQs above 160 are today simply not reliable, psychometrics experts say. So, the closer to 160, the closer you are not given an accurate result (may be is that the reason of the 3 sigma average for Nobel prize recipients? we don't know). 

  The problem is an obsession with huge numbers. The SMPY authors made an estimate of a IQ 186 average (!!!) for their 12 years old cohort three. When adults they scored "only" around 3.5 sigma on average. From 186 to 154, dementia praecox?? No. Obsession with ultranumbers. What I mean is that don't leave a scientist career path because you had only scored at 3.6 sigma. The truth is that it is quite probably close to the actual scientists leaders IQ, and might well be superior to some of them. Not all in life is g. Anyone telling you otherwise simply doesn't know what he is talking about or wants to fool you.

Víctor Sánchez said...

 Well, as IQ test have in fact validity up to 160. Beyond that validity falls because the inability to measure g. The same holds for SAT I think. After that point you start measuring too specific abilities, and moreover, abilities that can be trained. To sum up: both seems correct up to 4sd, not beyond.

 Regarding the International Mathematics Olympiad and alike I do not know. A very easy problem that arises using that competitions is that you are biased towards especially trained teenagers, leaving aside all potentially very high scorers that were not given special training on higher math. They could still finishing PhD in physics without having never attended such competitions.

steve hsu said...

There was an interesting old psychometrics study done by ETS that showed that taking a math intensive major had very little effect in raising GRE M relative to SAT M (taken in high school). GRE M is so easy that taking courses like real analysis doesn't raise the scores of people who can actually pass real analysis!

BTW, you didn't address the effect on the V score average from having so many physics grad students from foreign countries (esp. E. Asia).

Too bad Roe didn't test some analytic philosophers for you :-(

steve hsu said...

 I agree with your comments although I wonder how Jensen could make that claim about *all* past geniuses. If he thinks von Neumann or Gauss were only 160 I would probably have to disagree...

SMPY showed a lot of regression, but of course they were testing 12 year olds, many of whom had prepped for a widely studied test (SAT). When I was an undergrad I was paid to tutor a little kid who was trying to get into SMPY.

steve hsu said...

These are all just rough statements. We cannot really measure these things to much better than 1 SD accuracy.

Note the Fermi estimate guy doesn't think there is anything like complete overlap between his population of good scientists and the population of +4SD g scorers.

Note also that there are 30x more people at 3 than at 4. So there is a good chance that among the 3s someone will get lucky, or have some non-g type advantage (networking, creativity, lab dexterity, etc.) that gets them ahead of many of the 4s. In the Fermi calculation the correspondent only estimated that a fraction of the people even at top departments are in his "nontrivial brain" category (i.e., 50-100 people total at a top tier university).

Isn't +3.6SD at the ceiling of the GRE?

NicolasBourbaki said...

 Do you really think that the number of ESL students in physics over philosophy will depress the physics verbal score by that much? >100 points? It would be nice if someone studied top philosophers vis a vis top people in other academic disciplines regarding cognitive ability. That would be somewhat interesting but the data from the GRE from the grad departments is also interesting in its own regard. There are very few grad philosophy students. typically, top ten department receive about 300 applications for 8-12 spots. They just don't have the funding.

steve hsu said...

Well, higher Q abilities don't move the GRE average because the ceiling is so low.

Just imagine taking the equivalent of GRE V but in *Chinese*. Even if you had worked diligently on it for the last 5 years, do you think you could score as high as the *average* college graduate in China? I certainly could not.

When a physics admissions committee looks at a E Asian applicant a GRE V score which is just average (say 500 out of 800) would be considered quite good -- they'd look more at the TOEFL score, and even top TOEFL scorers might only score 500-600 on the GRE V. So, a top applicant from E Asia might have Q/V score of 800+500 (the "top" characterization would be due to other things like their course grades, letters, research accomplishments), which certainly lowers to average for the physics department relative to, say, philosophy. Comparable US applicants might be something like 800+750. Now average 1/3 of the former and 2/3 of the latter to get something like 1400 (the number you are looking at) when in fact you are talking about 1550 caliber people (once you adjust for depressed V average).

NicolasBourbaki said...

I've heard people on familiar with tests like the GRE say that verbal scores from E. Asian students are not a whole lot different from native English speakers. Speaking ability is a whole other question. This is further supported by the experience from people who have taught English to students in E. Asian countries and they tend to say that on written or other kinds of verbal assessment, the students tend to be quite competent but it may not show in their spoken skills because they have few people fluent in the language to practice that with.

steve hsu said...

I serve on admissions committees... the numbers I gave you were not made up. BTW, just to be clear by E. Asian I meant foreign nationals applying from abroad.

NicolasBourbaki said...

A 750 average Verbal for the average Native English physics grad student is HIGHLY implausible to me even at the top institutions. Do you really think that the average physics native English speaking grad student is 30-50 points higher on the verbal than the philosopher counterparts at top US philosophy grad departments? 

http://graduate-school.phds.org/rankings/philosophy/rank/_________________M______________________________________________U  

steve hsu said...

I meant the E. Asian numbers are realistic. 750V for a theory applicant at a top department is not rare, but in the overall physics applicant pool would be. Did you look at the Roe scores for theory vs expt?

Víctor Sánchez said...

Sorry Dr. Hsu. Quite a time ago I read it and was from memory. It was actualle Dr. Eysenck, and said that probably most geniuses of the past had IQ's between 3 and 4 sigma. An interesting (although I myself question it) chart is: http://hem.bredband.net/b153434/Index.htm

MtMoru said...

This whole comment thread is quite nauseating for those who know anything about psychometrics (which BTW doesn't include Arthur Jensen or Charles Murray). For an inroduction read this by Perter Schonemann: http://www.schonemann.de/pdf/89.pdf.

MtMoru said...

 "Keep in mind training matters a lot for math competitions"

It matters a lot for IQ tests too even without preparation for the specific subtests. All IQ tests are necessarily achievement tests and vice versa. It is a distinction without a difference.

And thus IQ is a personality trait as much as a measure of "mental horsepower".

MtMoru said...

 "Keep in mind training matters a lot for math competitions"

It matters a lot for IQ tests too even without preparation for the specific subtests. All IQ tests are necessarily achievement tests and vice versa. It is a distinction without a difference.

And thus IQ is a personality trait as much as a measure of "mental horsepower".

MtMoru said...

Anglo-American and French "professional philosophers" are at most second rate intellectually. That is being very kind. It's impossible to read them without getting sick. It's sort of like listening to FOX news.

BUT it is comparing apples and oranges. My experience with natural scientists: they tend to be "little bits of men abnormally developed masquerading as the whole" as Julia Flyte said of Rex Mottram.

MtMoru said...

"That's the only crude assumption I need to make in order to be willing to invest time in an intelligence GWAS."
 
Not true Steve. You would also have to assume that that qualitative difference has similar genetic causes in a large number of your cohort. Perhaps there would be more than one cluster though and therefore no genetic g.

MtMoru said...

"I don't know of anything as g loaded as this material, with the exception of pure math"

How do you know what its g loading is? Do you mean these are always the smartest people you meet? It's the hardest? It's what the fewest people are capable of doing?

Edwin said...

Actually,MIT loses out not because of a lack of talent,but due to the fact that they have too much talent.They cannot predict who is likely to win so they end up with guys scoring better than those on the team.There is a word for it,i think:"The MIT curse".

Bo said...

I hit the ceiling on math, but not on verbal. 

My non-g advantage is probably Machiavellian intelligence, so business will probably suit me better than science.

I'm not leaving science because I don't believe I can make significant contributions.  I'm leaving because I want to make money.

steve hsu said...

Still, it looks like population density of Putnam Fellows is 2x higher at Caltech.

steve hsu said...

As you know from my other comments I don't think g loading has a precise technical meaning (in this way I agree with Schoneman). I meant it in the way you interpreted it -- the smartest people, the hardest, etc. Because of the job situation in theoretical physics and math, the *majority* of people trained in these areas are/were forced into other careers, despite being the creme de la creme by any quantitative metric. If you follow their track records they've done nontrivial stuff in many other fields, including biology, computer science, defense research, finance, startups, etc. The reverse has almost never happened. So it's pretty clear which things are easy or hard even for very smart people.

PS On Schoneman, psychometrics has a vocal minority of what I call "methodological scolds" that serve a necessary purpose, but they are like people who would tell engineers that they shouldn't build bridges or cars until all of mechanical engineering can be derived from first principles of subatomic physics. As a physicist I know a crude tool when I see one: I understand the limitations of psychometrics, but am willing to overlook them in favor of practical utility (e.g., predictive power).

steve hsu said...

This is going to be resolved by the actual studies. If the standard models used successfully in applied population genetics (e.g., to breed better crops, livestock, etc.) are wrong for human height or IQ, we will find out from adequately powered GWAS.

Víctor Sánchez said...

Nauseating is to see scientist failing to recognize other data than the one they are interested in because of personal bias. 

NicolasBourbaki said...

 Yes, I saw them but I have suspicions that they are representative of theorists and experimentalists in general. 

NicolasBourbaki said...

Modern day analytic (or "anglo-american") philosophers tend to write with other philosophers in mind and many of them tend to be quite good writers. It is true that some prose may have technical jargon (as with any technical field) but there is a distinction between difficult reading due from technicality and from being unclear or confused. I don't expect layman to just pickup a textbook on contemporary work in quantum field theory and be able to make perfectly clear sense of it no matter how intelligent the layman is. Similarly, I don't expect a layman to understand in any serious depth the actual literature in the field of contemporary philosophical discourse without an understanding of the core terminology and concepts. However some philosophical papers written by philosophers for philosophers today *are* written without much jargon and clear enough such that reasonably intelligent layman who put in the effort can easily grasp the arguments and import.   

asdf said...

My assessment as a current MIT student of the difference is that Caltech's average is higher, but MIT's top tail is higher.  I would say that it is easier to be say top 20% at MIT than at Caltech, but harder to be top 1% at MIT than at Caltech.  I suspect that current Caltech students will agree with me on this.  Of course, the situation may have been different in your time.

asdf said...

Yeah, this MIT curse is pretty well known.  For instance, on the most recent Putnam, MIT destroyed Caltech, but the actual winner is Caltech!  They picked their team correctly, MIT picked horribly wrong.  This has happened numerous times over the past decade.

steve hsu said...

Not sure why you think the top 1% at MIT (10 kids?) are better than the top 1% at Caltech (2 kids?). For example, the current Caltech senior class has a 3x Putnam Fellow. Are there 5 3x Putnam Fellows at MIT?

asdf said...

You are probably right about the Putnam fellows per capita.  However, I think if you look at where the Intel science talent search winners go, MIT and Harvard both dominate Caltech.  Additionally, for IMO team members, the only year I could find info for was 2008: http://amc.maa.org/e-exams/e9-imo/e9-1-imoarchive/2008-ia/2008imoteamannounce.shtml with 4 MIT, 1 Harvard.

I think one reason for Caltech's recent fall is that as of a few years ago, Caltech no longer offers the Axline scholarship.  If MIT and Caltech cost the same, I think most people will prefer MIT, if for no other reason than that if they decide to go into industry, finance and technology recruiting is better at MIT simply because it is bigger.

steve hsu said...

I talked to the scholarships people at Caltech during my last visit. I was shocked to learn about the Axlines and complained about it! I told them they should use the Hsu Scholarship to recruit super bright applicants... unfortunately it can only fund 1 per year.

MtMoru said...

You've misunderstood me NB. My fault.

Anglo-American philosophy is VERY easy to understand. It is sickening because Anglo-American philosphers are so, how shall I put it politely, "not that smart". The same is true of continental philosophers but with deliberate obscuration or perhaps more charitably their believing they are saying something when they are saying nothing.

There is only one philosopher deserving of the name after 1900 although even he was sometimes clueless and occasionally "continental" in the bad way.

That man was Martin Heidegger.

NicolasBourbaki said...

 I have my serious doubts that you or any non specialist could understand without serious study much of the literature on contemporary debates of many issues. But the topic is about the cognitive abilities between certain technical disciplines compared with philosophy. I think the evidence from the GRE I have presented is serious enough to warrant consideration that professional philosophers are the smartest or at LEAST comparably equivalent to any in academia. Now your personal anecdotal evidence is yours and it shouldn't be given much weight in the face of actual data. In my experience, it is physicist that tend to be far cruder in their basic reasoning skills than both mathematicians and philosophers.    

MtMoru said...

Yes he is considered a fraud by analytic philosophers. By their standards he is. 20th century French philosophy is a fraud for sure. I have come to regard him as closer to a fraud than I did 10 years ago, but as he said "intelligibility is the death of philosophy". One of the problems with analytic philosophers is that they insist without knowing it that truth must always come in the form of propositions. They also seem to think that it isn't possible to be a thinker and a bullshitter at the same time.
 
My experience ISN'T anecdotal. Philosophy departments are laughed at by natural scientists for the most part and rightly. Self-important second rate minds. 
 
"Russell, Moore, Wittgenstein, Lewis, Quine"
 
I don't know who Lewis is, but the others I can say had no insights worth reading that I hadn't had when I was 13 and read the introduction to my dictionary. Analytic philosophy is adolescent. Philosophy in general is adolescent, but there are a few exceptions.
 
If you'd like GRE bona fides, I took the old GRE once. My score was 800 verbal, 800 analytic, and 800 quantitative. That doesn't mean I'm smart, but you seem to think it does.

asdf said...

Another thing is that unlike Caltech, MIT has a substantial group of people who major in things like business or biology, and these people would not be expected to take or do particularly well on something like the Putnam.  So one should probably use a number smaller than 5x when comparing the two population sizes.

steve hsu said...

I don't deny there should be adjustments. There are biology majors at Caltech as well, though :-) I think the biggest factor is that MIT's math department is better than Caltech's, which really biases the Putnam numbers, but in the opposite direction than the effects you pointed out.

MtMoru said...

"how shall we say, bluff and bullshit"

Nope.

"Professional philosophers" make their living by teaching. Their students have no future except to try to become teachers themselves. Yet amazingly some "professional philosophers" specialize in ethics.

"contemporary philosophers on who the most important philosopher of the last 200 years is"

I saw this and it proves my point. The contemporary "philosophers" were analytic "philosophers", that is, not philosophers. Reading Lewis's wiki it's easy to see he had nothing interesting to say and that he was a fool.

"and since you claimed to easily understand the problems in philosophy today, can you answer some of my questions regarding, say, the slingshot argument (since you mentioned truth), two-dimensional semantics, rational decision making, formal learning theory, sortals, properties, anomalous monism, causal modeling, tropes, and hypertasks"

You're too stupid to actually read what I wrote? Go back and read it. All of this IS bullshit and VERY easy to understand. It's like doing a crossword and equally as trivial. "the problems in philosophy today" aren't problems.

MtMoru said...

BTW Nick, you don't know what "anecdotal" means.

NicolasBourbaki said...

I see that the "anecdotal" wasn't on your GRE prep test. For someone that got "800" on the Verbal of the GRE (good one!), you sure do seem to have difficulties with words far easier than those found on the GRE.

http://en.wikipedia.org/wiki/Anecdotal_evidence
The expression anecdotal evidence refers both to evidence that is factually unreliable, as well as evidence that may be true but cherry-picked or otherwise unrepresentative of typical cases.[1] In other words, there are two distinct meanings:(1) Evidence in the form of an anecdote or hearsay is called anecdotal if there is doubt about its veracity; the evidence itself is considered untrustworthy.(2) Evidence, which may itself be true and verifiable, used to deduce a conclusion which does not follow from it, usually by generalizing from an insufficient amount of evidence.Generalizing from your own experience of what scientists said *is* anecdotal evidence. Your blind denials cannot avoid the reality of the meaning as it is used in the English language.

NicolasBourbaki said...

"Nope"

This sounds like a blind denial to me. BTW, have you wikied 'David Lewis' yet? I hope you at least now know who he is. His philosophical ideas of course, may take a little longer to get familiar with but with your perfect GRE score (*wink*), I suspect you will certainly master them far better than even Lewis himself. 

"You're too stupid to actually read what I wrote?"

Wow, you really lost it. I think I've done enough to humiliate and expose the fraud you are. Thanks for the laughs and your brilliant answers to my questions about philosophical topics. You have indeed proved yourself far more intelligent than those second rate minds in the philosophy department.  

Jonathan Inbal said...

 the ceiling on math for the GRE is barely +1 SD...

Edwin said...

Here is a link to last year's Putnam exam Results
Defence lawyers condemned the charges yesterday, saying it was impossible to predict earthquakes. Seismologists have long concurred, saying no big earthquake has been foretold.Read more: http://www.smh.com.au/world/italian-scientists-arrested-over-deadly-quake-20110526-1f6ec.html#ixzz1NQck9N5a

Edwin said...

http://math.caltech.edu/2010PutnamResults.pdf

steve hsu said...

So even though it was a banner year for MIT, Caltech still beat them in the team competition and outperformed on a per-capita basis. It looks like among the top 20 scorers 7 were from MIT and 4 were from Caltech. Adjusting for the sizes of the schools we get something roughly consistent with the historical result that Caltech has 2x as many top performers (e.g., Putnam Fellows) per capita as MIT. The school that did worse than their historical trend is Harvard, and this year might be the first year ever for Stanford to have a Putnam Fellow.

MtMoru said...

If you were a VIP Nick I'd be happy to fax you my GREs.

All of the specific pseudoproblems you listed would take some time and length for me to "explain", but this doesn't mean they're not easy to explain. Hardly.

I will say on anaomolous monism and other mind-body problem ideas that the problem with the mind body-problem is that there is no problem. The reason is that "body" or "the physical" as used by pseudo-philosophers is unanlyzed and unltimately incoherent. You should read Berkeley more sympathetically than you have.

Analytic "philosophy" is to linguistics, mathematics, mathematical logic

as

a cargo cult is to an industrialized country.

NicolasBourbaki said...

You don't have to b e a VIP to fax anyone the GRE report. If you really wanted to prove it (and as we both know, you cannot) you would email a photocopy to a impartial third party (perhaps the blog writer, Hsu) but as we both know and everyone following this so far can see, your claims are, how shall we say, not credible. Your refusal to do so constitute prima facie proof of your lying to everyone about your self proclaimed abilities. 

Your avoidance of the philosophical issues after cursory google searches adds to your credibility deficit as well as for your claims of intellectual superiority. You have not shown any understanding of any philosophical problems of the last 100 years despite your claims to have understood them well and refuted them and you have not shown your superiority to the philosophers.  In fact, it's pretty obvious you are just bluffing and bullshitting. 

Víctor Sánchez said...

This discussion leads to nowhere. Please finish it.

NicolasBourbaki said...

It's been finished. Unless you have something substantial to add, you are just adding to the substantial fluff already contributed by "mtmoru". 

Víctor Sánchez said...

I made that comment just one hour after your last post, so wasn't finished for sometime. I do not have anything to add since there is never nothing to add to such kind of discussions. I politely asked you to finish your replies to a troll like MtMoru (was not obvius it was just a loss of time?), so save your rudeness.

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