The Fundamental Intuition

Flynn says, “There is nothing really the matter with the concept of g,” as long as one is interested in the level of individual differences in ability, as opposed to development in time within individuals or across generations. You can’t help but notice that his concession doesn’t prevent him from being ripped, in Gottfredson’s reply, for not taking g seriously enough, for not placing it at the very center of the entire discussion. It’s the price he pays for giving up too much. There is plenty, indeed practically everything, wrong with the concept of g, even in its classical context of individual differences in ability among adults at a single point in time. Explaining why requires some slightly technical concepts—bear with me.

Here is the fundamental intuition: Since at any given time tests of ability “go together,” in the sense that people who score higher on one tend, on average, to score higher on the others as well, then it must be the case that a single explanatory factor, g, must be invoked to account for their commonality. After all, if there were many abilities underlying performance on mental tests, why wouldn’t there be tests that didn’t go together with the others? The fundamental intuition states that universal positive relations among mental tests compel a single dominant explanatory construct, which has come to be called g. The fundamental intuition is wrong.

Let me try to shift your intuition a little. Suppose there were not one but two abilities underlying mental tests, call then h and i. Suppose further that these two abilities have nothing whatsoever to do with each other, that knowing your score on h tells you absolutely nothing about your score on i. Individual mental tests require various amounts of h and i. Some tests require a lot of h and a not so much i, some the reverse, some require a little of both, but tests are always positively related to whatever mix of h and i they require, and there are no tests on which untalented people do better than talented people. (I am not giving anything back to the g-men here. Positive relations between tests and abilities, whether there is one ability or many of them, is a good way to define what an ability test is, as opposed to, say, a test of attitude. Ability questions have correct answers whereas attitude questions do not, and that is why ability questions all point in the same direction.)

So anyway, we have a set of tests related variously but positively to two completely unrelated underlying abilities. What will the relations among the individual tests look like? They will all be positive. Pairs of tests that both depend highly on h or highly on i will be strongly positively related; pairs for which one depends mostly on one ability and mostly on the other will be less strongly related, but why would any pair ever be related negatively? The g-men have confused two separate statistical issues about relations among sets of tests: their much-revered positivity, and what is known in statistics as their dimensionality, which refers to the number of underlying abilities, one according to the g-men and two in my example, that is required to explain their interrelationships. The fundamental intuition is that these are one and the same issue, but they are not, in fact they have nothing at all to do with each other. Sets of all positive relations among tests can require any number of dimensions to explain them.

So the g-men want you to believe that all they need to show in order to establish the supremacy of g is that all ability tests are positively related, but that is incorrect. They need to show that interrelations among ability tests are unidimensional, and guess what? They are not. Not ever, not from the very beginning of the discussion. The giant in this field was Charles Spearman, who coined the term g and invented the statistical method called factor analysis to answer exactly this question. He started his investigation with the question of whether a single dimension could explain the positive interrelations among mental tests. It could not.

Proponents of g theory are no doubt waiting for me to explain why, if Spearman himself showed that sets of ability tests are not unidimensional, he nevertheless went on to describe g and expound the theory for the rest of his career. Can g be saved if ability is multidimensional? A description of the attempt to do so, which defines the field of intelligence between Spearman and today, requires me to get back into a few technical details.

The task of quantifying ability becomes vastly more complex if anything more than a single dimension is required to account for it. If there is only one dimension the problem is simple, because everyone can be ordered along that dimension, as if placed on a line. But if there is more than one dimension, we are not ordering them on a line but placing them on (for starters) a two-dimensional map. How do we locate people on two dimensional maps? The obvious answer is with latitude and longitude, but there is a hitch: latitude and longitude, though mathematically sufficient and perfectly convenient once you are used to them, are also arbitrary and man-made. One could define new lines that ran from northwest to southeast, or in any other direction, and they would do just as good a job of accounting mathematically for points on maps. That is why geologists are not peering at satellite photos to find great circles etched into the planet: Latitude and longitude are a useful contrivance in the interest of human convenience, not a given aspect of the natural world.

Once ability is multidimensional, g is like longitude. In a multidimensional set of interrelations among tests, one axis can be found that accounts for as much of the interrelatedness as possible, even when it is known that more dimensions are required. The g-men have defined that largest dimension as g. They haven’t discovered it, as they are fond of saying, any more than the Greenwich Meridian was discovered by the International Meridian Conference in 1884. Any set of interrelated tests has to have a largest dimension, so under this definition the existence of g is no longer a matter of empirical dispute. Rather, it has simply been defined into existence. But it has no special status. Defining multidimensional ability with a big g-factor and some number of smaller sub-factors is just one out of an infinite number of ways that ability could be aligned along dimensions.

So let’s return to Flynn. He thinks that g used to hold together, as long as our focus was on relations among tests at a single point of time, and has only come apart once he started to examine differential changes in the components of ability over time. But the coherence of g was an illusion, founded on the false intuition that positivity of relations among ability tests was sufficient evidence of unidimensionality, In fact, pace Gottfredson, it would be possible to define separate ability domains for abstract thinking and practical knowledge within a single time point, and these traits would then correspond closely to the courses of generational change that interest Flynn. Such traits would not be the correct way to divide up ability, any more than g is. They would be a plausible solution in a domain where a certain amount of indeterminacy is part of the scientific landscape, and they would be a convenient tool for studying the Flynn effect. In the same way, g is useful for many things, especially for broad-stroke prediction of outcomes like job performance. The trick is not to get hooked on any particular way of dividing up the pie, because it is a short step from there to trying to find the Greenwich Meridian at the bottom of the North Atlantic.

Actually, psychologists don’t look for lines of longitude in the seabed; they look for mental factors in the brain and genome. Flynn’s over-commitment to the reality of g leads him to be distressingly cavalier about how human ability might be represented neurologically or genetically. “General intelligence or g,” he says, “has something to do with brain quality, and good genes have a lot to do with having an above average brain.” That sounds safe enough, but wait a minute: How do we know a quality brain or a good gene when we see one? And presumably not only general intelligence but abstract reasoning ability has something to do with the brain, the environmental Flynn effect notwithstanding. When we start looking for human intelligence in the brain and the genes, what exactly should we look for? General intelligence? Specific abilities? Morality? Which way do those lines really run again?

There is nothing wrong with studying the neurology or genetics of differences in ability, but these investigations will proceed on their own neurological and genetic terms, and we should not look to them for biological vindication of the psychological expediencies that help us tame the nearly overwhelming complexity of human behavior. Literal-mindedness about the details of psychological statistics may seem harmless when the discussion is just about what goes with what and when, but history has shown us only too clearly what can happen when simplistic views of human ability make poorly informed contact with biology and genetics. I am by training a behavioral geneticist, and as such I am too well-acquainted with the ugly places oversimplified thinking about human ability and genetics can lead to let the phrase “good genes” pass without a shiver. It is best to be careful from the beginning.

Bibliographic note:

Many of the ideas discussed here were first expressed by the great psychometrician Louis Guttman (1916-1987). Responsibility for any errors of interpretation rests with me.

Eric Turkheimer is a professor of psychology at the University of Virginia.

Also from this issue

Lead Essay

  • In this month’s lead essay, famed intelligence researcher James R. Flynn draws on his new book, What Is Intelligence? Beyond the Flynn Effect, to help answer some of the puzzles surrounding the controversial issue of IQ. Flynn, who first discovered that IQ scores were rising generation after generation, notes that this improvement has been more dramatic on some parts of IQ tests than on others, challenging ideas of a unified general intelligence or “g.” Flynn argues that the fact cognitive abilities do not develop together has important implications for education. Additionally, Flynn contends that the evidence for the co-determining reciprocal influence of brain and environment should lead us to set aside simple ideas about the primacy of nurture and nature in intelligence. Once we grasp that “the brain is much more like our muscles than we had thought,” we can do more to improve cognitive performance by doing more to exercise the brain.

Response Essays

  • Linda Gottfredson, co-director of the Delaware-Johns Hopkins Project for the Study of Intelligence and Society, defends the unity of general intelligence, or g, against Flynn’s attempt to “unravel g into its component parts” by charging that “his core argument rests on logical fallacies that profoundly misinterpret the evidence.”

  • University of Virginia psychologist Eric Turkheimer contests even James Flynn’s modest accommodation with the construct of g, or general intelligence. Turkheimer argues that the “fundamental intuition” of g is that “universal positive relations among mental tests compels a single dominant explanatory construct,” but that “the fundamental intuition is wrong.” According to Turkheimer, g is not “discovered,” but is simply posited as a convenience, like the Prime Meridian. g may be useful for some purposes, but a multidimensional explanation of ability may still be correct. “The trick is not to get hooked on any particular way of dividing up the pie,” Turkheimer writes, “because it is a short step from there to trying to find the Greenwich Meridian at the bottom of the North Atlantic.”

  • Stephen J. Ceci, the Helen L. Carr Professor of Developmental Psychology at Cornell University, explains why Flynn’s work has been so important. According to Ceci, the received wisdom about the nature and effects of g, or general intelligence, led “some to argue that inequality in the distribution of wealth, prestige, and educational attainment is, in part, a consequence of unequal distribution of the intellectual capacity needed for high levels of functioning.” However, Ceci says, “[Flynn] has shown beyond doubt that general intelligence fluctuates systematically over time and this cannot be due to our having better genes than our grandparents,” and he goes on to explore the puzzles raised by this discovery.