The g Factor And Ulam's Challenge To Samuelson: A Social Science Proposition Both True And Non-Trivial
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The mathematician and thermonuclear bomb designer Stanislaw Ulam famously challenged economist Paul Samuelson to come with up a social science theory that was both true and nontrivial. After a few years, Samuelson replied with Ricardo's 1817 theory of comparative advantage in foreign trade: if Portugal is worse than Britain at making both steam engines and corks for wine bottles, Portugal should still concentrate on making corks because it's comparatively less bad at corks than at steam engines. (These may not be the precise examples Ricardo used in 1817, but they get his point across.)

Of course, Portugal's corkocentrism helps explain why the Portuguese Navy was such a decisive strategic element in the Age of Steam, but the advantages of having a navy that rules the waves are not considered relevant in conventional economics. 

Samuelson wrote to Ulam:

That it is logically true need not be argued before a mathematician; that is not trivial is attested by the thousands of important and intelligent men who have never been able to grasp the doctrine for themselves or to believe it after it was explained to them.

Whether Ulam, co-inventor with Edward Teller of staged radiation implosion, responded by pointing out the advantage of making nuclear weapons and not trading them is unknown. Compared to the Hussein family of Iraq and the Qaffathy family of Libya, two ruling clans that didn't find the economics of making nuclear weapons rational, the Kim family of North Korea has enjoyed a comparative advantage at avoiding violent death.

I've long thought that Spearman's 1904 g (for general) factor theory of intelligence is reasonably comparable in nontriviality.

I've always had a hard time grasping it myself. Back in 1998, I wrote a review of Arthur Jensen's magnum opus, The g Factor, that considered some of the paradoxical social and political implications:

Stephen Jay Gould's The Mismeasure of Man, a 1981 book that continues to shape the non-scientific intelligentsia's feelings about IQ, demonized g as the "rotten core" of Prof. Jensen's 1969 article documenting the white-black IQ gap. The g Factor's overwhelming vindication of g, drawing on 15 years of new research, might seem likely to end the debate. It won't, of course, for reasons good and bad. The book sheds light on crucial new issues beyond the narrow scope of g (such as racial differences in nerdishness). More depressingly, few will grasp either its strengths or its limitations due to fundamental confusions rampant among American intellectuals about how to think about humanity. 

For example, nobody noticed that Gould's assertion that human equality is a factual (rather than a moral, legal, or spiritual) reality centered on denouncing g; yet, g is the only concept that could conceivably make sense of his claim. 

Ironically, the g-ocentrists are among the last students of human nature making important discoveries within the egalitarian world-view. The one technique capable of uncovering mental equality is Jensen's: minimize the number of data points by measuring only the single most important factor (g) across only a few vast groups. Thus, Jensen, the Great Satan to egalitarian fundamentalists, delivers in Chapter 13 the most important pro-equality finding in recent decades: Men and women really do possess the same average g. Their equal average IQ's scores aren't just an artifact of IQ tests being rigged to produce this result. Jensen's finding is hugely important in itself: it's the best explanation of the splendid performance of women in many white-collar jobs. 

Still, this example also shows that g, like any successful reductionist theory, has its limits. Males and females, while similar on mean g (but not on the standard deviation of g: guys predominate among both eggheads and knuckleheads), differ on several specific cognitive talents. Men, Jensen reports in passing, tend to be better at visual-spatial skills (especially at mentally rotating 3-d objects) and at mathematical reasoning. Women are generally superior at short-term memory, perceptual speed, and verbal fluency. Since the male sex is stronger at logically manipulating objects, while the female sex prevails at social awareness, that explains why most nerds are male, while most "berms" (anti-nerds adept at interpersonal skills and fashion) are female. Beyond cognition, there are other profound sex dissimilarities in personality, motivation, and physiology. All this helps explain the sexes' different patterns in career choices. 

Because Jensen's simple, single-factor model can detect intellectual equality between men and women, it can also detect intellectual inequality between whites and blacks, if that's what the facts are. Although most responses to Jensen's equality/inequality model haven't risen above name-calling, obfuscation, guilt-by-association, and professional cowardice, there is a logical, fruitful alternative: develop a complex, multi-factor "diversity" model that rather than concentrating upon one difference among a very few groups, focuses on the many differences visible among many groups. Emphasizing the trade-offs necessary for achieving different goals, it makes toting up an overall winner look a little pointless. 

The diversity perspective has much to offer, but only when it's thoroughly understood that it's inherently less empirically egalitarian than Jensenism. The diversity model's current popularity, however, stems from the wishful thinking that it discredits racial differences, on the assumption that since Diversity and Equality are both Good Things, they must be synonyms rather than antonyms. One particularly fashionable defense of empirical equality is to combine the doctrine that there "are no such things as races" (just swarms of little ethnic groups) with Harvard professor Howard Gardner's speculations about seven "multiple intelligences." Ergo, all groups must be equal, QED. 

Let's do the math: assume, say, 100 ethnic groups and seven "intelligences." That's 700 data points. No way, no how could they all be equal — our universe doesn't work like that. The more complex your model, the less equality and the more diversity you'll perceive in the world. 

Interestingly, when I pointed this out to Gardner, he agreed with me.

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