Thursday, June 16, 2011

High V, Low M

I sent the message below to a social scientist I know who (like many, perhaps understandably) is confused about Stephen J. Gould's status as an evolutionary theorist. Many Gould readers are surprised to learn that his main expertise was the paleontology of snails and that he struggled with higher mathematics. When I first encountered Gould's essays as a kid, I concluded that there was just no there there. He was all literary flourish and little depth.

Which brings me to an observation I've been meaning to write about. It is that high verbal ability (which Gould certainly had) is useful for appearing to be smart, or for winning arguments and impressing other people, but it's really high math ability that is useful for discovering things about the world -- that is, discovering truth or reasoning rigorously. The importance of math ability manifests in two distinct ways:

1. Powerful (deep) models of Nature (e.g., electrodynamics or evolutionary theory) are themselves mathematical. Most of the incredible progress in our understanding of the universe is just not available to people who do not understand math. For example, we can talk until we are blue in the face about the Uncertainty Principle, but there is no precise understanding without actual equations.

2. The statistical techniques used to analyze data obtained in a messy, complex world require mathematical ability to practice correctly. In almost all realistic circumstances hypothesis testing is intrinsically mathematical. It is quite easy to fool yourself statistically if you don't have strong math ability, but rather are simply following cookbook recipes.

High verbal ability is useful for more than just impressing others -- it typically implies a certain facility with concepts and relationships between ideas -- but high V alone is a dangerous thing. The most confused people I meet in the academy tend to be high V, low (modest) M types.

More on the V / M split in this longitudinal study of gifted children (SMPY / SVPY -- see esp. figure 4).

Gould on Gould (NY Review of Books, March 29 1984):
"I am hopeless at deductive sequencing... I never scored particularly well on so-called objective tests of intelligence because they stress logical reasoning ..."
This is from the email I sent to a colleague:
Gould appeals to high V low M people who do not actually understand evolutionary theory at a mathematical level. He never made any important contribution to evolutionary theory other than as a popularizer.

Note this is distinct from his deliberate obfuscation of topics like IQ in Mismeasure of Man. He wrote some incorrect things there about factor and statistical analysis, but perhaps those distortions were intentional. See The Mismeasure of Science: Stephen Jay Gould versus Samuel George Morton on Skulls and Bias.

Paul Krugman:

Now it is not very hard to find out, if you spend a little while reading in evolution, that Gould is the John Kenneth Galbraith of his subject. That is, he is a wonderful writer who is beloved by literary intellectuals and lionized by the media because he does not use algebra or difficult jargon. Unfortunately, it appears that he avoids these sins not because he has transcended his colleagues but because he does does not seem to understand what they have to say; and his own descriptions of what the field is about - not just the answers, but even the questions - are consistently misleading. His impressive literary and historical erudition makes his work seem profound to most readers, but informed readers eventually conclude that there's no there there. (And yes, there is some resentment of his fame: in the field the unjustly famous theory of "punctuated equilibrium", in which Gould and Niles Eldredge asserted that evolution proceeds not steadily but in short bursts of rapid change, is known as "evolution by jerks").

What is rare in the evolutionary economics literature, at least as far as I can tell, is references to the theorists the practitioners themselves regard as great men - to people like George Williams, William Hamilton, or John Maynard Smith. This is serious, because if you think that Gould's ideas represent the cutting edge of evolutionary theory (as I myself did until about a year and a half ago), you have an almost completely misguided view of where the field is and even of what the issues are.

John Maynard Smith:

"Gould occupies a rather curious position, particularly on his side of the Atlantic. Because of the excellence of his essays, he has come to be seen by non-biologists as the preeminent evolutionary theorist. In contrast, the evolutionary biologists with whom I have discussed his work tend to see him as a man whose ideas are so confused as to be hardly worth bothering with, but as one who should not be publicly criticized because he is at least on our side against the creationists. All this would not matter, were it not that he is giving non-biologists a largely false picture of the state of evolutionary theory."

John Tooby:

"Although Gould characterizes his critics as "anonymous" and "a tiny coterie," nearly every major evolutionary biologist of our era has weighed in in a vain attempt to correct the tangle of confusions that the higher profile Gould has inundated the intellectual world with. The point is not that Gould is the object of some criticism -- so properly are we all -- it is that his reputation as a credible and balanced authority about evolutionary biology is non-existent among those who are in a professional position to know...

These [major evolutionary biologists] include Ernst Mayr, John Maynard Smith, George Williams, Bill Hamilton, Richard Dawkins, E.O. Wilson, Tim Clutton-Brock, Paul Harvey, Brian Charlesworth, Jerry Coyne, Robert Trivers, John Alcock, Randy Thornhill, and many others."  
Richard Lewontin: 
"Steve and I taught evolution together for years and in a sense we struggled in class constantly because Steve, in my view, was preoccupied with the desire to be considered a very original and great evolutionary theorist. So he would exaggerate and even caricature certain features, which are true but not the way you want to present them. For example, punctuated equilibrium, one of his favorites. He would go to the blackboard and show a trait rising gradually and then becoming completely flat for a while with no change at all, and then rising quickly and then completely flat, etc. which is a kind of caricature of the fact that there is variability in the evolution of traits, sometimes faster and sometimes slower, but which he made into punctuated equilibrium literally. Then I would have to get up in class and say “Don’t take this caricature too seriously. It really looks like this…” and I would make some more gradual variable rates. Steve and I had that kind of struggle constantly. He would fasten on a particular interesting aspect of the evolutionary process and then make it into a kind of rigid, almost vacuous rule, because—now I have to say that this is my view—I have no demonstration of it—that Steve was really preoccupied by becoming a famous evolutionist."


See Human capital mongering: M-V-S profiles for further explanation of this figure.


David Coughlin said...

Can you get tied in knots if all you ever do is follow the string around?

MtMoru said...

Gould was probably far above average in M just not as high as you'd like. AND he was probably higher than every "psychometrician" except Schonemann and a few others. But of course everything else you say about Gould is correct. Why did Harvard hire him?

Charles Murray himself admitted he did not have a talent for math and that social scientists in general were high V not as high M.

"it typically implies a certain facility with concepts and relationships between ideas" There are turgid florid BSers and then there are those who really do have a facility for expresing very subtle and complex ideas in words. The two may overlap but aren't the same. I suspect many who appear to have high V don't.

And the idea that those gifted at math are "really" the smartest doesn't correspond to the subjective judgement of smart. Fish swim, birds fly, men talk, and mathematical talent is something new. Many of the high M low V would have been judged not so smart a thousand years ago.

One fact you may not know is that those with WAIS IQs over 125 tend to have higher V than P. Mathematical ability and non-verbal intelligence aren't the same.

David Backus said...

I still think there's huge value in communicating to a broader audience, as you do in this blog.  There aren't that many people who are good at it, perhaps for the reasons you mention.  And there's always the risk that people who are good communicators (and I found SJG very entertaining) won't get the substance right.  But communication is a valuable thing, I'd love to see more people do it well.  

steve hsu said...

> ... mathematical talent is something new. Many of the high M low V would have been judged not so smart a thousand years ago. <

Yes, I agree. Part of my point is that, among the hoi polloi, "smart" is often judged on V, whereas among the cognoscenti the greatest distinctions have to do with M.

The Scientific Method is also new. A stronger statement than what I wrote in the post is that the vast majority of new conceptual space humans have been exploring in the last 200 years is off limits to people below some cutoff in math ability. This conceptual space is not only interesting, it is *useful* (See, e.g., Moore's Law :-)

I would almost assert that you cannot call yourself a serious thinker or intellectual these days without some math chops -- most of the serious and important stuff under discussion would be beyond your ken.

PS Galton, although no wrangler, was the first psychometrician. Pearson, who was stronger, was his protege. Both of these men far outdistance Gould in intellectual ability.

Liam said...

"Why did Harvard hire him?"
The same reason they hired Niall Ferguson probably.  He seems to be the SJG of economic history.

MtMoru said...

"The Scientific Method is also new." One thing you learn if your science isn't theoretical physics is that there is no scientific method.

"whereas among the cognoscenti" My guess is your own subjective judgement of smart is the same as the hoi poloi's.

Pincher said...

Stephen Jay Gould was plenty smart.  The main problem in some of his work, including this most recent revelation about his writings on Samuel Morton, was either his gross sloppiness, dishonesty, and/or hypocrisy, combined with his political bias.  Gould's errors were not caused by his lack of ability.  I have no idea what training he had in mathematics or statistics, and I suspect no one else here does, either, but whatever it was, it did not prevent him from having a major impact on the modern scholarship of evolutionary theory.

The economist Paul Krugman compared Gould's status in evolutionary theory to pop economists John Kenneth Galbraith, Lester Thurow, and Robert Reich, but that was an unfair comparison and it was one which Krugman was not fully qualified to make.  Gould was a much more formidable figure in evolutionary theory than any of those three men were in economics.  Ironically, Galbraith's son, James K. Galbraith, who is also an economist, debated Krugman in Slate on his more extreme claims about the value of non-economists discussing economics, where Galbraith wrote "This may come as a surprise to outsiders, but Krugman is not a mathematical theorist (and I have heard him admit this, to a knowing audience). Krugman's mathematics are not deep, and he has no interest in complicated manipulations of data. He owes his fame, instead, to an exceptional grace and lucidity of formal presentation. With these gifts, Paul has expanded the range of neoclassical economics in several notable directions, especially international trade theory. Krugman's professional work is mathematically literate, of course. The point is that it is also literate, and, for many economists, that is its appeal."

In other words, Krugman himself might be the best comparison in economics for what Stephen Jay Gould is in evolutionary theory: a highly competent and even on occasion original scholar with catholic interests and strong leftist politics that bleed into his scholarship.  After all, Gould has made contributions to the field of evolution, which even his worst critics in the field, like John Maynard Smith, have admitted.

I don't care for Gould or his popular work.  In fact, I don't like his influence.  But it seems to me that some of you are using some very legitimate concerns about that work to caricature the man as either a mathematical dummy or a scientist of no value, and I'm not sure why a bunch of quotes proves that.  Did Gould make math mistakes?  Yes.  Was he dishonest?  Probably.  Did he set back the popular understanding of some fields he wrote about?  Almost certainly.  But to go from that to questioning his intellectual chops in the most fundamental way strikes me as overkill.  Gould is not the Robert Reich of the evolutionary theory community. 

By the way, Francis Galton made math mistakes.  In fact, he struggled quite a bit with math while at Cambridge, suffering a nervous breakdown as a result.

TheGuyFromEarlier said...

I think this is mostly true.  It's as I've always told a friend of mine whom I discuss startup ideas with: you need a high V to really convey your vision, but you need a high M to actually create.  A high V gives you the ability to manipulate diverse ideas, while a high M gives you the ability to understand the nuts and bolts of how it is all put together.  (BTW, the y-combinator/youtube vids you've been posting are right down my alley.)  For creation in general, M is more important.  But to draw relationships between big ideas requires a strong dose of V.

With high V types, there tend to be higher levels of emotional perceptivity and the concomitant ability to convey ideas to people.  When this is combined with low M, it turns out the basis to those ideas can be pretty faulty because it's harder for that person to work out the logical underpinnings of his or her thoughts.  E.g., I have a great friend who is a high-V/low-M type, and he has an incredible ability to speak eloquently off-the-cuff.  But when I discuss issues that go against the cultural grain (like HBD) and require some level of anti-zeitgeist-logical-deduction, it's harder for him to grasp.  In other words, his understanding of the world--of human-defined constructs--is sometimes too abstracted from a realistic basis.  (That's not to say I find those concepts foolish; at our human level, they can be pretty useful, but they need to be anchored in some realism.)  

I first started building my writing chops around 8th grade when I started writing for video game websites (hah!).  I noticed essentially what you have pointed out ("literary flourish"): I could really enhance my elementary writing by loading it with adjectives and clever turns of phrase.  Needless to say, I was pretty pleased with myself.  As I got older though, I was able to tell when others were employing the same bag of tricks in their writing, but not actually saying much.  

I've always felt that great writing is a combination of high V (obviously) and high M.  Great fiction writing, for example, contains self contained rules that make sense within the context of the novel and helps dictate the flow of events.  It takes a real constructive kind of intelligence (high M) to be able to truly understand those rule sets as well as a high V to envision them.  

Yan Shen said...

"I've always felt that great writing is a combination of high V
(obviously) and high M.  Great fiction writing, for example, contains
self contained rules that make sense within the context of the novel and
helps dictate the flow of events.  It takes a real constructive kind of
intelligence (high M) to be able to truly understand those rule sets as
well as a high V to envision them"

That's the stupidest thing I've ever heard. I think you're the quintessential example of someone who's good at bullshitting, but not much else. Most of what you say makes little sense and is just a mishmash of vague generalizations and fuzzy rhetoric. Whenever I read your comments, I often think to myself, "Is this guy actually saying anything substantive, or are his posts just empty rhetoric?" Sadly, the few substantive assertions you do make, such as claiming that the SAT is significantly amenable to preparation, are almost never supported by a citation of any kind, just your own personal hunch, and are in fact contradicted by the existent empirical literature.

steve hsu said...

You are right that Krugman is not very mathematical as economists go, but he understands enough (the kind of math used to model complex systems like economies or populations) to realize that Gould uses very little math in, e.g., his work on punctuated equilibrium.

Contrast this to what real evolutionary theorists (as opposed to snail collectors) work on. For example: . I flipped through Gould's 2002 book The Structure of Evolutionary Theory ("magisterial" say the high V low M admirers) and don't recall seeing many, if any, equations! It certainly makes one suspicious...

Why do you not dispute Maynard's Smith's characterization of Gould?

"... In contrast, the evolutionary biologists with whom I have discussed his work tend to see him as a man whose ideas are so confused as to be hardly worth bothering with ..."

Yes, Galton had a nervous breakdown preparing for the Tripos. Performing well on the Tripos (becoming a wrangler) is a much higher hurdle than what Gould needed to do to understand the work of real evolutionary theorists (i.e., population geneticists) like Smith or Fisher or Haldane. Real questions in evolutionary theory (kin selection, for example) simply cannot be addressed without some math.

TheGuyFromEarlier said...

Have you ever tried writing fiction before?  You create implicit rule sets that dictate when and how you say something. 

Suppose you're writing a mystery novel.  You need to dictate when a reader is given access to evidence, and how that overall pattern will parlay into an experience.  You logically choose what pieces you reveal and what pieces you don't--and when--all the while making sure it weaves perfectly into a narrative.  You manipulate time and setting and their appearances in your novel in a way that is both realistic (within the context of the novel) while also conforming to these rule sets.  The better you are at understanding these rule sets, the better you can create them so that it doesn't appear you're just throwing shit on the wall and randomly making up rules as you go. 

Also, notice a key word: "felt."  I wrote that I've always "felt" that there was a strong logical basis to great fiction writing; I did not say, "studies show there is a strong logical basis to great fiction writing."  As far as SAT prep: I stand by my skepticism, though I admit now that I might have been off.  My reason for skepticism:  have you ever ventured on, or any sort of test prep forum?  Raising scores upwards of 80-100+ points is not so uncommon.  I can think of 5-10 friends in the same situation and probably dozens from college confidential.  That said, I understand that anecdotal evidence is not the same as statistical population distributions, and I completely overlooked the fact that sometimes those rises occurred while the student was still developing mentally.   (A cursory google search: ) 

But seriously, do I need to cite a study for every pattern I notice?  My assertions may be wrong--I'm always refining my understanding-- but you're seriously a close-minded curmudgeon who is pre-limited by his lack of creativity before he even gets off the ground.

Pincher said...

"Why do you not dispute Maynard's Smith's characterization of Gould?"

Because it is one which even Maynard Smith himself made exceptions for.  The British scientist welcomed some of Gould's thinking on evolutionary paleontology, for example.  You should also know that sometimes Maynard Smith's problem with Gould was not that the American was wrong, but that he felt Gould was misrepresenting the value of Gould's own ideas on evolution and their place in evolutionary theory.

Take punctuated equilibrium, the most famous theoretical contribution to the field which Gould introduced in the 1970s.  What chapped the asses of evolutionary scientists like Maynard Smith and Richard Dawkins was not that the theory was wrong, but that Gould exaggerated its novelty.  But no one to my knowledge claims it is mathematically illiterate.  They just claim that differing rates of evolution are already incorporated in neo-Darwinism.  But even this is disputed by evolutionary biologists like Ernst Mayr, who felt Gould had made a scholarly contribution to the debate.

I don't dispute that there was a gulf between Maynard Smith and Gould's thinking on evolution or that Maynard Smith felt the need to go after Gould many times in his career.  I don't even dispute that Gould was almost always wrong or misleading in those clashes.

What I dispute is that Gould made no serious contributions to evolutionary theory, and that the reason he did not make any serious contributions to the field was because he wasn't smart enough to do so, mathematically.

I flipped through Gould's 2002 book The Structure of Evolutionary Theory ("magisterial" say the high V low M admirers) and don't recall seeing many, if any, equations! It certainly makes one suspicious...

Flip through Evolution: The First Four Billion Years and you'll see Gould's ideas are treated respectfully if briefly.  And even in The Evolution Wars: A Guide to the Debates, where Michael Ruse frequently skewers Gould, he is still treated as a serious non-orthodox Darwinian with views that must be engaged.

Gould was a vain man who exaggerated his own contributions to the debates on evolutionary theory, but he was not a stupid man nor was he someone scholars in the field could ignore.  He was not, in short, the equivalent of Lester Thurow or Robert Reich in economics, as Paul Krugman claims him to be.

"Real questions in evolutionary theory (kin selection, for example) simply cannot be addressed without some math."

The math for kin selection doesn't strike me as being high-level stuff.  Are you claiming even this was beyond Gould's ability to understand?

And on what basis do you make this assumption about "real questions in evolutionary theory"?  Are you claiming that a paleontologist cannot make a serious scholarly contribution to evolutionary theory by reference to his own expertise, even if he has a familiarity with the math and arguments in the field?

By the way, would you say Edward Wilson doesn't understand the math?


Yan Shen said...

Take a hike. No one on here takes anything you say seriously.

Yan Shen said...

Also, be careful. Make sure you don't ever let me find out who you and where you live. Because if I ever see you, I'll rip your fucking head off and stick it up your fucking ass.

TheGuyFromEarlier said...

I'm glad you edited your statement twice now to disarm it.  When it was originally "Also, be careful. Make sure you don't ever let me find out who you and where you live. Because if I ever see you, I'll rip your fucking head off and stick it up your fucking ass." it sounded a little psychotic.  

Now it's just slightly unhinged.

MtMoru said...

Or if you're cute Yan Shen will ask you to marry him.

MtMoru said...

I wonder what Steve thinks of Tegmark's "mathematical monism".

TheGuyFromEarlier said...

I read that the 40 Year Old Virgin is based on a true story of an Asian guy who monitors IQ blogs and instantly responds to any comment about Asians, valiantly defending the honor of Asia.

Yan Shen said...

Oh come on, is that the best you can do? Even your comebacks are juvenile.

TheGuyFromEarlier said...

Be honest, Yan Shen.  How hard was it for you to wait 23 minutes before pressing enter?

Yan Shen said...

Not too hard considering I was busy fucking your mother. ;)

TheGuyFromEarlier said...

You edited again!  Good thing you didn't end at the first sentence.

RKU1 said...

Well, I actually interacted a bit with Gould back in the early 1980s, and have to admit that despite his exalted reputation at that time I was singularly unimpressed...

During that period, I think his main focus was publicly promoting the strange notion that many complex structures, notably eyes, could be best understood as having been produced by the effects of pure random chance rather than natural selection, and this frankly seemed just plain loony to me.

I pointed out to him that a complex organ such as an eye represented a single small region in a biological possibility-space of extraordinarily high dimensionality, and the notion of a species just happening to randomly wander into that region without selective pressure gradually nudging it in that direction over time was patently absurd.  I suggested that it would be quite easy to determine which species got their eyes through Gouldian random motion---they're the ones which can't see.

Gould's reply to my detailed letter seemed quite subdued, and he stated that my words (which included extremely harsh additional critiques in quite a few other areas as well) had caused him some considerable pain.  I'm sure I must still have the correspondence around somewhere...

ben_g said...

Is that really Gould's view?

"I…do not deny either the existence and
central importance of adaptation, or the production of adaptation by natural
selection. Yes, eyes are for seeing and feet are for moving. And, yes again, I know
of no scientific mechanism other than natural selection with the proven power to
build structures for such eminently workable design."

ben_g said...

"a certain facility with concepts and relationships between ideas"

That's why high V is key to innovation.  People who are high M but low V are able to work with complex tools but can't work with the big picture well enough to really change the world.

Yan Shen said...

Apparently men and women are comparable in verbal ability and there are even some suggestions that women are better verbally than men. See here.

"Verbal Abilities. Some verbal tasks show substantial mean differences
favoring females. These include synonym generation and verbal fluency (e.g.,
naming words that start with a given letter), with effect sizes ranging
from d = 0.5 to 1.2 (Gordon & Lee, 1986; Hines, 1990). On average females
score higher on college achievement tests in literature, English composition,
and Spanish (Stanley, 1993) they also excel at reading and spelling Many
more males than females are diagnosed with dyslexia and other reading disabilities
(Sutaria, 1985), and there are many more male stutterers (Yairi & Ambrose,
1992). Some memory tasks also show better performance by females, but the
size (and perhaps even the direction) of the effect varies with the type
of memory being assessed."

But, there's fairly good evidence suggesting that women lag behind men in virtually every form of nonverbal ability. Which gender innovates more?

My suspicion is that beyond some threshold, there's no real gain from being better verbally and that mathematical ability is key.

ben_g said...

With the male-female difference, I would guess that other factors like competitiveness and interests are largely responsible for the gap, though M differences probably play a role too. 

To ask a similar question to your own, Jews are higher V and similar M to white gentiles.  Who innovates more?

Yan Shen said...

Your claim is false. Jews excel in both V and M relative to whites. See here.

Cochran et al. write that according to some studies from the 1970s Ashkenazi Jews score 0.75 to 1.0 standard deviations
above the general European average. This corresponds to an IQ 112–115.
They have high verbal and mathematical scores, while their visuospatial
abilities are typically somewhat lower, by about one half a standard
deviation, than the European average.[2]

ben_g said...

My bad, that's not a very good example in that case.  The salient point though is that the significantly high V is responsible for their intellectual success.

East Asians have a higher M than whites.. Do they have a comparable V?  If so, would the "Asian creativity crisis" be at all related to lower V?

Yan Shen said...

"The salient point though is that the significantly high V is responsible for their intellectual success."

Perhaps you'll be citing some evidence?

My understanding is that the East Asian V is either comparable to that of whites or slightly lower, while their M is substantially higher. In other words, the East Asian cognitive profile relative to Europeans is similar to that of men relative to women. I'm not even sure that there's a creativity crisis, since East Asian Americans seem to be fairly over-represented on things such as the Intel Science Talent Search, IMO, IPhO, etc.

ben_g said...

[I qualified that sentence in an edit so you proly wanna update the quote]

I'll admit that my understanding of the importance of V in Jewish success is largely impressionistic.  Jews are overrepresented among intellectuals period, but especially among those intellectuals who are known for synthesizing disparate ideas and communicating complex things simply and articulately.

Also, a thought experiment: Asians are significantly higher than whites in M.  Jews are higher in M *and* V.  If the V isn't the reason for disproportionate Jewish intellectual achievement, then what do you think is?

Yan Shen said...

Yes, but you're comparing Jews to East Asians. That's the key issue here. Both groups are already high in M. In that case, I'm sure the additional V of Jews provides an edge. If you're comparing Jews to gentile whites, I think it would be incorrect to claim that higher V is the only reason or even the main reason why they excel.

Pincher said...


I'm not defending all or even most of Gould's ideas on evolution. I don't claim he is a major figure in the field -- the equal of, say, William Hamilton or John Maynard Smith.  I think Gould is on occasion disingenuous and probably even outright dishonest. And I have absolutely no sympathy for his political aims, which I think drive many of his scientific ideas.

I'm simply arguing that claiming Gould is ignorant about the rigorous analytical work in evolutionary theory to such a degree that he did not, and could not, contribute anything of substance in the field is a gross caricature.  Gould's ideas are frequently cited by other scholars in the field.  One can't make a similar claim in economics about the work of Robert Reich and Lester Thurow or probably even John Kenneth Galbraith.

I think a fair summary of Gould would be that he was a capable scholar whose importance in the field was exaggerated because he was both a lucid writer and a formidable energetic polemicist.  I'm actually surprised you got him to back down in your correspondence with him.  That doesn't sound like SJG at all.

Yan Shen said...

I thought East Asians excelled significantly relative to Europeans in both math and spatial ability? They average significantly higher on the SAT-M and also are substantially over-represented amongst the USA IMO team. They also seem to excel in general intelligence, as evidenced by the huge East Asian-European gap on the Ravens.

Also, what are your thoughts on the cognitive profile of men relative to women? It seems to mirror the cognitive profile of East Asians relative to Europeans. I think it's too soon to conclude what the full extent of East Asian intellectual achievement will be. See below for what I wrote about the uptick of Japanese Nobel laureates. Keep in mind that China, a country which finally opened up in 1978, 110 years after the Meiji Restoration began in 1868, has slightly more than 10x the population of Japan.

Yan Shen said...

So here's something for you to consider. East Asians excel significantly relative to whites in M. Jews in both M and V. East Asians and Jews seem to be similarly over-represented on the US IMO team. See here.

They also seem to be similarly over-represented amongst Intel Science Talent Search contestants, although as noted in this article, the rise of East Asian Americans is actually recent. How does your theory of V account for this empirical phenomenon?

The idea that immigrant parentage is a significant marker of success is
older than the contest itself. It’s the usual explanation, for example,
for the lopsided presence of Jews among the science contest finalists
going back to 1942 (it was sponsored by Westinghouse until 1998, when
Intel took over) as well as Nobel laureates for a century and in other
fields such as Hollywood and literature. Today, with the great Jewish
immigration a distant memory, it’s deemed natural that Asian immigrants
have taken the lead.
You could look back through past years’ lists of science finalists,
as I have done, to see the trend line (by counting Jewish names — it’s a
crude science, but not nearly as crude as you might think). In fact, I
was asked in 1991 by another publication to report on the question,
“What ever happened to Jewish genius?” using that year’s 40 Westinghouse
finalists. They included five Jews (down from 12 in 1965 and 18 in
1950) and 17 Asian immigrants and immigrants’ children (up from roughly
zero through the 1940s and 1950s). Q.E.D., right?

I made the requisite phone calls to aging Nobelists
teaching at Ivy League colleges. They all said Jewish genius was
history. The kids who raised their hands in class were all Asians now. Then I went back through the contest lists, year by year,
and got a big surprise. It turned out that the number of Jewish
finalists hadn’t declined at all. Mostly what it did was fluctuate
wildly: from 18 in 1950 down to five in 1954, up to nine in 1955, 15 in
1972, five in 1974 and so on. There was an overall consistency, though:
The average over the decades was about 10 Jewish finalists per year.
Today, 20 years further on, the average is still 10 per year.
Immigration has nothing to do with it.

There is a big story here, though: The rise of Asian
immigrants and their children. There were barely 10 among all the
finalists through the first 30 years. In 1974, for the first time, there
were three, then six the next year. Since then it’s been lurching
upward. In 1984 there were 13 Jews and seven Asians; in 1986, six Jews
and 11 Asians; in 2003, 12 of each.


I’m citing “Asians” specifically rather than the more general
“children of immigrants” because the increase consists almost entirely
of youngsters of Chinese and Indian origin. Those two countries each
account for between 4% and 5% of America’s total yearly immigration, but
almost all of Intel’s vaunted immigrant surge. Mexico supplies five
times as many immigrants as China or India, the Philippines and Vietnam
about the same number, and Cuba, El Salvador, Canada and South Korea
only slightly less, but those populations almost never figure in the
Intel finals.

The only other immigrant groups that show up regularly
are Russian, Moldovan, Iranian and Israeli. Virtually all of those
finalists have been Jewish, which is how I’ve counted them. There are
isolated Vietnamese, Koreans, Poles and some others, but none show a

In other words, immigration doesn’t explain the changing
demographics of the Intel science contest. Ethnicity does. Put
differently, the Intel contest is a story comprising, in roughly equal
proportions, Chinese, Indians, Jews — each accounting for 1% to 2% of
the American population — and everyone else.

5371 said...

The Krugman who wrote that was the Krugman who thought people like Barro and Prescott were thinkers and their brand of economics was legitimate. Even Krugman knows better now.

Keith Power said...

Yeah, it depends on your interpretation of "smart".

You imply a meaning of smart which is both convenient and flattering to the mathematically inclined: "It is that high verbal ability (which Gould certainly had) is useful for appearing to be smart, or for winning arguments and impressing other people, but it's really high math ability that is useful for discovering things about the world -- that is, discovering truth or reasoning rigorously.". If you define smart as a measure of understanding about the universe then of course high math ability is indispensable.

If instead you defined smart as a measure of understanding how the world - people, society - works, and how to manipulate it to achieve your goals, then high math ability is not so obviously useful. In many cases your ends could be achieved by directing others with the necessary ability. Einstein may have come up with the theory that led to the atomic bomb but others directed the chain of events that led to its construction and detonation over their enemies' heads. Presumably any major societal change that takes place as a result of deep discoveries in bioinformatics will not be directed by the techie discoverers either.

RKU1 said...

Well, please remember that the example I cited occurred some 15 years before the later admissions of Gould which you link, which admitted the critical importance of natural selection in the creation of complex organs.  Gould's earlier theories about the huge role of randomness were so patently absurd and utterly ridiculous I hardly find it too surprising that he eventually decided to backtrack from them.  I suppose it's possible that I had just totally misunderstood what Gould seemed to be saying, but this would seem inconsistent with the tone of Gould's reply to me.

steve hsu said...

High V, Low M.

I doubt he really understood (before communicating with people like you) that there are very good arguments against random walks producing functioning eyes and brains.

Matthew Carnegie said...

Interesting that Koreans and Japanese aren't overrepresented but Chinese are, despite near equal Chinese and Korean numbers. That's not something that you'd assume from the IQ data we have.

Matthew Carnegie said...

I thought East Asians excelled significantly relative to Europeans in both math and spatial ability? They average significantly higher on the SAT-M and also are substantially over-represented amongst the USA International Mathematics Olympiad team. 

My impression though is that the gap on math (to the degree it is separable from spatial ability) is much more modest than the gap in ability for spatial ability, which is where most East Asian IQ advantage comes from. Seems like that's what the data I've browsed on the WISC tells me.
They also seem to excel in general intelligence, as evidenced by the huge East Asian-European gap on the Ravens in favor of East Asians.

Raven's is both heavily correlated with g and Asians are specifically good on spatial heavy matrix reasoning tests which are similar to Raven's, so I would not be surprised if they did well on Raven's and that they would be expected to have a high G from a closely G correlated test like Raven's. 

But I would guess if you would want to avoid the confound of overestimating the size of an East Asian general factor from Raven's (or conversely, to use a parallel situation, overestimating European or Ashkenazi general factor from using the very g-loaded vocab factor) and find out if they did have a higher general factor (g).... then you'd need to take a particular set of tests put Asians and Whites through a test battery and do a PCA on individual results. If the general factor was of larger effect and/or results were higher in the Asian participents and these combined in such a way to give the Asian participents a higher absolute G, they would have a larger G.

(Although this would only be the G (general factor) for that set of tests, and might be a less interesting G than another G produced for another set of tests that was more predictive.)

Not sure if anyone's ever done this. I have a fairly dilettante knowledge of psychometrics.

Yan Shen said...

"My impression though is that the gap on math (to the degree it is
separable from spatial ability) is much more modest than the gap in
ability for spatial ability, which is where most East Asian IQ advantage
comes from"

Seems extremely unlikely given the huge degree of East Asian American over-representation on the US International Mathematics Olympiad team.

Pincher said...


"I've certainly never had any expertise in the areas of paleontology which were Gould's actual niche, so I can't comment on his prowess there.  But his work in broader evolutionary issues seems almost totally wrong-headed, ideologically motivated, and, in some important cases as we now know completely fraudulent." Ignore the issues concerning Morton's skulls, the IQ debate, etc.  They reflect evolutionary issues, but they are not directly concerned with evolutionary theory.  That Gould didn't bother to measure Morton's skulls, for example, tells us a lot about his character, but it doesn't tell us anything about his math skills or the validity of his broader ideas on evolution.  I'm sure even Steve Hsu would agree that Gould most likely had the technical competence necessary to properly measure Morton's skulls.  Let's also ignore the work Gould did in paleontology unless it directly relates to his ideas on evolutionary theory.  Instead, let's focus on the main ideas Gould is known for in evolutionary theory: 1) Punctuated equilibrium; 2) evo-devo; 3) spandrels, and let's test them against your characterization that they are either "[t]otally wrong-headed, ideologically motivated, or completely fraudulent."Punctuated equilibrium: To my knowledge, no biologist claims punctuated equilibrium is "totally wrong-headed, ideologically motivated, or completely fraudulent".  Gould and fellow paleontologist Niles Eldridge came up with the theory because they noticed large gaps in the fossil record that were inconsistent with the gradualism implicit in the neo-Darwinist theory.  Neo-Darwinists usually counter that Gould and Eldridge's idea is already incorporated in the modern evolutionary synthesis.  

Evo-devo: To my knowledge, no biologist claims evolutionary development is "totally wrong-headed, ideologically motivated, or completely fraudulent".  According to Evolution: The First Four Billion Years, Gould's work in this field would prove to be a "powerful tool for analysis of adaptive function and patterns of evolution in extinct organisms".  I've not come across any criticism of Gould's work in evo-devo.

Spandrels: The most controversial of Gould's ideas on evolution.  Also the most cited by scholars.  According to Gould and collaborator Richard Lewontin, spandrels are accidental offshoots in the form of an organism that develop only because of other selected traits.  To my knowledge, no biologist claims spandrels are "totally wrong-headed" or "completely fraudulent", but I have read the criticism that Gould and Lewontin's idea is ideologically motivated.  What Gould's critics usually claim is that spandrels are a misleading analogy that underestimates the degree to which nearly all traits are formed by natural selection.

Looking at the three items above, I would have to say that Gould's ideas on evolution hold up pretty well to the more extreme criticism of them, and that none of them have been countered by some math formula he simply didn't have knowledge of.

I might have missed some of Gould's general ideas on evolution.  Feel free to add any you think should be looked at, but try to stay away from those which aren't focused on Gould's broad ideas about evolution.

By the way, if Gould is Lysenko, who is his Stalin?

Yan Shen said...

Matthew, you seem to be skeptical of the East Asian advantage in M and even in g. Surely the huge East Asian American over-representation on the International Mathematics Olympiad, International Physics Olympiad, etc. suggests that this is almost certainly the case.

steve hsu said...

I've been told by psychometricians that there is no evidence that the principal component deduced from factor analysis over a battery of tests varies between populations. That is, g is the same for all populations for which there is extensive data, including in particular European and E. Asian populations.

Also you are confused in saying that Ravens is spatially loaded. Recognition of how a 2D pattern involves in "time" (what you call matrix reasoning) is not the same as spatial ability. The former really depends on pure logic whereas the latter involves, e.g., visualization of spatial relationships.

ben_g said...

Something that confuses me.. If all groups have comparable g, why does the structure of mental ability vary between groups?  if someone read all the literature on g they wouldn't guess that people with very low IQs might have great memory abilities (hunter gatherers), or that some groups with average spatial IQs might have great verbal/logical abilities (Jews), etc.  Same question for generational differences.. e.g. the Flynn effect seems to raise certain subtests over others..

MtMoru said...

Yes indeed. g would have to vary between groups just as subtest profiles vary. There is nothing deep about the PC and it shouldn't be referred to as g. g is a vague idea which a PCA makes less vague for the purpose of publishing papers only. PCA categorizes as smartest those who are smart in the most common way. If there were someone who had very high and reliable scores on exactly those tests which were least g loaded he'd be thrown in the stupid pile merely for being so unusual.

MtMoru said...

It may surprise all of you to learn that there is no M factor for IQ tests. If the IQ test includes mathematical subtests they will not be very good predictors of ability at higher maths. The names for factors don't tell you much. They're just names. The verbal, spatial, attention factors are not the same as verbal, spatial, and attention ability. It's just that the tests most loaded with these factors are verbal, spatial, attention tests.

steve hsu said...

Ben: I should have said g is approximately the same for these populations. Inevitably there will be small differences in the exact largest eigenvector, but of course these things are only defined modulo statistical noise, etc. You get approximately the same largest eigenvector, at least that is what I am told -- I have never looked carefully at this myself.

"PCA categorizes as smartest those who are smart in the most common way."  This is correct. To me it's just a convenient way to compress the data.

Matthew Carnegie said...

Also you are confused in saying that Ravens is spatially loaded. Recognition of how a 2D pattern evolves in "time" (what you call matrix reasoning) is not the same as spatial ability. The former depends mainly on pure logic whereas the latter involves, e.g., visualization of spatial relationships.

Visuo-spatial if you would prefer. Matrix reasoning on the WISC IV (based on Raven's) does break out with visual-spatial reasoning under factor analysis:

(Yan Shen, might be interesting if you want to see how g is discovered by psychometricians.)

And visual processing is linked to matrix reasoning

Matthew Carnegie said...

It's interesting, although less interesting than something like Intel Talent Search which you've brought up, which is more applicable to the topic of basic science. I'd think advanced mathematics has a strong learned and trained component and so would not be good for determining or discussing population means also, from the population means perspective of our discussion as well. 

I would be interested to know if Korean-Americans and Japanese-Americans have the same representation gap with Chinese as described in your post on the Intel Talent Search. 

From what I can tell from - Koreans aren't near as represented as Chinese (although there are only half as many Korean Americans), but there are a couple and more than you would expect on their percentage of pop. Japanese Americans are absent, but then there's around a quarter as many as there are Chinese. Barely any Indians (the same number as Koreans). The recent White names are WASPier (Millers and Inces and Lipsons and Prices and Bartons and Carrolls) and less Jewish and generalised American than I would expect (to be sure there are a number of Jews still).

Matthew Carnegie said...

Yes, approximately is pretty much what I was going with (and guessing that the psychometricians meant by "the same g"), rather than the extremes of "exactly" or "there isn't a g factor for some populations". I hope I wasn't giving the impression of "radically different to the extent where there are a weak plurality of factors".

With testing Asians and Europeans (or indeed any pairs of ethnic groups), considering patterns of special ability, I would think there might be an issue that would be analogous to testing autistics (hereafter A), with their noted relative visuo-spatial strength (as shown in their matrix reasoning tests ability) - 

If you tested As in small proportions either against a large population of non-A people or all together and alone, then the general correlations between tests scores wouldn't change much in the first instance (if mixed with a large enough quantity of norms to wash their pattern out) or at all (if alone) and you'd get the same g factor. 

(Verbal analogy: If all our subjects own boats in many bays, but all have the same number of boats in the same bays, then a rising tide in one of bays won't affect the correlations between height in sets of boats. We'd discover the same correlation (or not!))

But test the As in 50:50 proportions with non-As and... the correlations between tests would change, and we would get a smaller "g" which correlates with performance over all tests and a more specific matrix reasoning (and related subjects) factor.

Of course, this would only be a small factor and *there would* still approximately be g.

steve hsu said...

re: IMO performance, I think high g (or, more precisely, innate math ability) is necessary but not sufficient. You need training as well. Nevertheless, anyone who succeeds at a high level in these competitions is very, very smart. On average the IMO guys will be much smarter than the Intel finalists. Trust me, I know a fair number of people from both categories. Usually the smartest Intel/Westinghouse person did a project in number theory or perhaps theoretical physics or CS and also was pretty good (if not at the very top) in IMO competitions.

steve hsu said...

PS You can ask RKU if you like, as IIRC he won the Westinghouse his year with a paper about black holes. On our BGI CGU team we have an IMO winner who was a Westinghouse finalist.

ben_g said...

Ok, so basically the importance of a g factor goes down when we sample all humans instead of particular genetic/cultural groups.  Isn't that an argument against a "general intelligence"?

g would still be the most useful single intelligence measure, especially within populations, but it's claims to significance beyond that would seem to diminish.

Shouldn't we determine the structure of intelligence by using data from all humans instead of convenient sets of them?  I bet intelligence turns out to be more complex than the g-men would have it in that case.

oasis789 said...

As a high V, not quite as high M, this post made me sad. Clearly I have nothing to contribute to the advancement of humanity, and nothing I can do will ever change that.

RKU1 said...

Well, my dataset is personal and decades out of date.  But back then it seemed to me that if you took the top 40 Intel/Westinghouse students of a given year and compared them with the top 40 IMO students, the latter group seemed at least something like 1 SD brighter or so.  And since both groups were pretty bright, that's a fairly large difference.  So my own impression is very similar to Steve's.

MtMoru said...

The vocab subtest is the most g loaded and the most reliable for the WISC and the WAIS. If there were a self-described IQ test consiting only of this Wechsler subtest it would be better than RPM. Further vocab has no Flynn effect but RPM does in a huge way. So why not say that whichever group has the highest vocab score is smartest? That's a problem for E Asian supremacists like Yan Shen.

Ju Hyung Ahn said...

alright d00d now you're just making shit up, block design is the most g-loaded in the WAIS test not vocabulary.
"If there were a self-described IQ test consiting only of this Wechsler subtest it would be better than RPM"
Tell me how you're going to go to do because g-loading of vocabulary of .71 while Raven's is .80.  I'm not against speculative ideas but let's base it on factual data.  You could say you could make more g-loaded test than Raven's if you use only block design section of WAIS since its g-loading is about .88.

MtMoru said...

You are the one who is eether making "shit" up or doesn't understand what he's reading.

Ju Hyung Ahn said...

What is there to misunderstand here?  I pointed out your obvious error in stating "The vocab subtest is the g loaded...for the WISC and the WAIS."  and you think a test that is less g-loaded is better indicator of g because it has higher reliability and less prone to Flynn effects.  Don't get angry when you misquoted data and check g-loadings on vocab and block design subtest of WAIS.

MtMoru said...

As I suspected you did not understand what you were reading.
1. Only 48 participants
2. Schmid-Leiman hierarchical factor analysis

From Carnegie's post

MtMoru said...

Here's another though the source isn't given.

Vocab is acquired and may be willfully increased? If yes then what is g really?

Ju Hyung Ahn said...

You're citing studies of WISC to also draw that vocabulary section of WAIS is also the most g-loaded.  In addition, your sources also show that vocab isn't the most reliable subtest of WISC, but I don't feel like nitpicking here.  Here's another study of WAIS (as opposed to WISC) that shows that vocab is far from being the most g-loaded in WAIS.  It is based on Spanish version of WAIS-III, but with thumping 703 females and 666 men (aged 15–94) sample.

Colom, R., Abad, F. J., Garcia, L. F., & Juan-Espinosa, M. (2002). Education, Wechsler’s full scale IQ, and g. Intelligence, 30, 449–462.

Variation of the tables available @  - Table 1
It is explicitly stated within the article that subtest 1 is the vocabulary section.  Refer to footnote 2 in page 435.

Ju Hyung Ahn said...

I must admit that I wasn't aware of the recent WISC-IV study.  I think it is certainly debatable for both sides, especially with the scarce number of resources available.

MtMoru said...

"It is based on Spanish version." Your sources are crap or prove that g loading varies from one population to another.

This isn't new info. The vocab subtest has been most g loaded and most reliable forever for the WISC AND the WAIS. You may find studies where it isn't, but they are outliers. Of course if reliability is only for one-month it's meaningless. 

Furthermore, contra the bias of E Asian supremacists those with the highest full scale IQs  score higher on the verbal subtests than on any others. The verbal subtests are the best at discriminating between smart and not.

Vocab, information, and arithmetic have not been affected by the Flynn effect.

Yan Shen said...

"Furthermore, contra the bias of E Asian supremacists those with the
highest full scale IQs  score higher on the verbal subtests than on any
others. The verbal subtests are the best at discriminating between smart
and not."

Does this mean that women are "smarter than men? :)

Ju Hyung Ahn said...

and your sources prove that vocab is better indicator of g than other subtests for children but NOT adults

MtMoru said...

Another source with flaws just to show I'm not making it up.

MtMoru said...

I don't really have a dog in this fight. I think it's weird that the vocab subtest is so g loaded.

"Does that mean women are smarter than men?" Verbal IQ above a threshold of, say, full scale IQ 125 may be higher in men. Women are more fluent, talkative, but do they score higher on verbal intelligence tests? Elite verbal games competitors are always men.

I was just paraphrasing the consistent result that the subtest score profile of those in the top 5% for full scale Wechsler IQ is like that of Ashkenazi Jews.

David Coughlin said...

Apropos of nothing, I have a comment on the power of memes.  I think that I recall you mentioning wranglers before, but I didn't recall it when I read about studying for the Tripos in a comment here.  Then, a day later, after Space Systems announces that the layoffs are coming, I'm trolling the corporate jobs database and up pops a couple of jobs in Cambridgeshire.  One of my favorite professors ever [Adriana Pesci, one of the few people who consistently connected with the question I was asking, not the question they were prepared to answer] is teaching at Cambridge [her husband is an illustrious complex (bio)systems physicist].  So, I look her up and surf the PhD opportunities at Cambridge.  While reading the DAMTP site, bam, there it is, Part III of the Tripos.  Twice in two days cements it in my brain.

It would be insane to try and do it while working a full-time-with-travel job, but that doesn't keep my mind from tracking back to it.  If I learned anything about my OR degree, it is that I have a limit.  That if I take even two graduate courses, then I need them to progress on track because I have no reserve capacity to catch up.  But that doesn't mitigate my [almost primal] want to take a shot at it.

RKU1 said...

Actually, my phrasing was poor.  I'd been describing the top 40 or so students on the American MO qualification/filtering exam for the IMO.  And back in those Olden Days, the AMO/IMO had little visibility, and my impression was that it seemed to attract comparable numbers of raw participants as the Intel/Westinghouse competition, or perhaps considerably fewer.  I don't even think that Physics or Chemistry International Olympiads had been established at that point, or if they had, their visibility was lower still.

Dawg_from_Hell 2010 said...

Btw, Dr. Hsu, what kind of  career/education would a person with the following cognitive profile be suitable for:

1. V: + 2.5 to +3 SDs
2. M: + 2.5 to +3 SDs
3. Spatial: -0.5 to +0.5 SDs
4. Long term memory (just an estimate based on people I know):  -0.5 to 0 SDs



Dingo Hammer said...

There is another explanation. Gould was making money selling books. Like so many others that preach to the converted, i.e. talk radio personalities, the accuracy of the message doesn't matter. What matters is that they say what their audience wants to hear.

Crystal N Woods said...

Absolutely if you start trying to connect different bits of it.

Maria Smith said...

great idea for us

data justification

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