Is Intelligence Too Complex to Summarize with One Number?

Russell T. Warne

Jun 2, 2025

… the study of intelligence within the human species has followed two traditions: the scientific and the pseudoscientific. The scientific tradition recognizes the complexity of the behavioral repertoires called “intelligence” ... It further recognizes that intelligence cannot be reduced to a simple metric or number such as IQ. The pseudoscientific tradition, on the other hand, is typified by a simple-minded attempt to reduce intelligence to a single rank ordering… (Graves & Johnson, 1995, p. 280)

However, except to a small band of dedicated psychometricians, it seems obvious that to try to capture the many forms of socially expressed intelligent behavior in a single coefficient – and to rank an entire population in a linear mode, like soldiers on parade lined up by height – excludes most richly intelligent human activities. Social intelligence, emotional intelligence, the intelligent hands of the craftsman or the intelligent intuition of the scientist all elude the ‘g’ straightjacket. (Rose, 2009, p. 787)

From the time Spearman discovered g in 1904, people have been skeptical about the idea that intelligence was one entity in the mind that could be summarized by a single number. In the Introduction, I showed how psychologists in the twentieth century used factor analysis to argue about whether intelligence was one entity (as Spearman believed) or consisted of multiple mental abilities (as Thurstone claimed). For decades, psychologists repeatedly gathered data, performed factor analyses, and modified their tests, statistical methods, and theories in an effort to better understand intelligence. Though it was a slow process that lasted over half a century, it was productive in shedding light on the debate over the nature of intelligence.

This work paved the way to the general consensus that dominates psychology today: that intelligence is a general ability (like Spearman’s g) that is related to other mental abilities. The Cattell–Horn–Carroll model and the bifactor model are leading theories of intelligence that represent this compromise position. (The models are diagrammed as Figures I.5 and I.6 in the Introduction.) In a way, both the Spearman camp of psychologists – who believed that intelligence was one ability – and the Thurstone camp of psychologists – who believed in a collection of abilities – were correct. But both camps failed to recognize the entirety of human cognitive abilities and how these were all related to one another.

What is important to note about this discussion is that it was data driven. As scientists, these psychologists built, tested, and modified theories on the basis of the data they collected. Though it may have taken a while, the history of intelligence research shows that the scientific method of using data to modify beliefs does indeed help scientists get closer to the truth.

On the other hand, some people just claim – usually without any attempts to test whether their beliefs are true – that intelligence is too complex a psychological entity to summarize in a single number, like an IQ score. As can be seen in the quote above, Graves and Johnson (1995) go so far as to call the idea that intelligence can be summed up by a single number as “pseudoscience.” As I will demonstrate in the rest of this chapter, not only is intelligence a single entity which can be summarized into one score, it is also impossible for intelligence to be as multidimensional as anti-g theorists argue.

Why g Exists: The Positive Manifold

If g were a mere personal preference or an untested theory, then the opponents of g would be on strong ground in criticizing its existence. However, g is an empirical fact that emerges from the positive manifold, which occurs when almost all scores on cognitive tasks are positively correlated with one another. Spearman first noticed this in his 1904 article, where the exam grades in five school subjects (classics, French, English, mathematics, and music), and a tone discrimination test all correlated positively with one another (r = .40 to .83). Modern samples also demonstrate the positive manifold. For example, the Stanford–Binet Intelligence Scales, Fifth Edition has ten subtests that all intercorrelate (r = .46 to .69) in the norm sample (Roid, 2003, p. 165). The Wechsler tests show the same positive manifold. The subtests on the Wechsler Preschool and Primary Scale of Intelligence IV intercorrelate (r = .30 to .67 in children under age 4 and r = .25 to .67 in children ages 4 to 7; Wechsler, 2012, pp. 70–71), as do the subtests on the WISC-V (r = .09 to .71; Wechsler, 2014) and the WAIS-IV (r = 21 to .74; Wechsler, 2008, p. 62).

The positive manifold matters because this is where g comes from. Spearman’s brilliant insight in 1904 was that test scores were correlated because they were all caused by the same ability: g. He created factor analysis to demonstrate that one ability was all that was needed to explain all these positive correlations among all these abilities. In fact, it is impossible to pull a g factor out of a set of data unless the variables all intercorrelate with one another. Thus, the existence of g is dependent on the positive manifold. If there is no positive manifold, there is no g, and intelligence is not a unitary entity.

Conversely, all it takes to demolish g is to find a cognitive variable – any cognitive variable – that does not correlate with other cognitive variables. Another way to disprove the existence of g would be to find independent, non-correlating clusters of abilities because such a dataset would produce multiple factors that are unrelated to each other. Either of these scenarios would be sufficient to disprove the theory that one general ability dominates human cognition and problem solving. Despite searching for over 100 years, no one has ever found a cognitive variable that was uncorrelated with other cognitive variables or a test that consistently produces multiple factors. This is extremely strong evidence that intelligence is one entity.

Once g has been shown to exist, it is a simple matter to sum up a person’s level of g with a single score. Because g is a general problem-solving ability, creating a score is a matter of rank ordering people according to how well they solve problems. Well-designed intelligence tests require problem solving on a variety of tasks, some of which were explained in the Introduction. By tallying up how many problems of varying difficulty people can solve, it is possible to ascertain who are the most successful (and least successful) individuals in a group at problem solving. This score will be a close approximation of the relative rankings of individuals in their level of g.

But g isn’t Everything

That being said, the skeptics of g are partially correct about the complexity of human cognition. Spearman and other early theorists of intelligence severely underestimated the breadth of human cognitive abilities, and no expert in the past 60 years has argued that g is the only important cognitive ability. Anyone who attacks intelligence research by arguing that “IQ isn’t everything” is attacking a straw man. Modern viewpoints take into account the complexity of human cognition while still finding a place for g. Both the Cattell–Horn–Carroll theory and the bifactor model of mental abilities recognize that g is not the entirety of mental abilities. There are other abilities in Stratum I and Stratum II that are part of both theories. These abilities are important, even if they are not as general as g.

As a result, the best-designed intelligence tests produce more than just a global IQ score. For example, the WISC-V produces a full-scale IQ score but also scores for verbal comprehension, visual-spatial ability, fluid reasoning, working memory, and processing speed. Even if two people have the same full-scale IQ score, their scores on the Stratum II abilities may be very different. These Stratum II scores often produce important information about a person’s relative cognitive strengths and weaknesses. These strengths and weaknesses matter, especially for making choices about careers or college majors. Research has shown that – in countries where students have a great deal of freedom to choose their occupations or college majors – most people gravitate towards fields that allow them to use their strengths (Makel, Kell, Lubinski, Putallaz, & Benbow, 2016; Wai et al., 2009). Even if a person has an ability above average in a particular area, if it is not their highest Stratum II ability, they are unlikely to choose a job or college major where that ability is essential. For example, a person with above-average spatial reasoning and even higher verbal ability would be more likely to become a patent lawyer (an occupation which uses both abilities, but relies more on verbal ability) than to become an engineer (which requires very little verbal ability).

This discussion of differences in Stratum II abilities is important because most people have at least one distinct Stratum II ability that they score higher on than others. For example, in one sample of over 100,000 children, 60.2% of examinees had at least one subscore on the Cognitive Abilities Test that was higher than at least one other subscore, and 3.3% of people had one Stratum II score differ by 22 IQ points or more(!) from at least one other score (Lohman, Gambrell, & Lakin, 2008). Thus, for the majority of people, planning occupational or educational goals on the sole basis of an IQ score is probably going to be ineffective; taking into consideration a person’s relative strengths and weaknesses in other abilities is important. Of course, non-cognitive variables matter, too. If a person lacks the motivation, interest, or values needed to succeed in a particular career, then it is irrelevant if intelligence tests results show that the person could do that job.

Arguments Against g that Consider the Positive Manifold

Although not in the mainstream, there are some scientists who argue that the positive manifold is not necessarily proof of g’s existence – and, therefore, an IQ score does not represent a person’s intelligence level. These theories take various forms, but generally, they are based on the claim that the brain has many modules or processes for performing different tasks and that tasks on intelligence tests require examinees to use multiple modules or cognitive processes to solve problems (e.g., Conway & Kovacs, 2018; Hampshire, Highfield, Parkin, & Owen, 2012). In this view, the positive correlations among scores on mental tasks are a result of overlapping cognitive processes or modules that are required to complete different tasks.

There are two problems with this line of argumentation. The first is that such a model requires nearly every task to draw on nearly every psychological cognitive process or module because scores on all cognitive tasks are positively correlated with one another. The result is a theory that becomes so complex that it becomes implausible (Ashton, Lee, & Visser, 2014). For example, such a theory would require reaction time tasks to draw on a person’s language-processing module – even though these tasks are so simple and performed so rapidly that language is not necessary to perform them (Jensen, 1998).

Another problem with this line of argumentation is that it does not reflect the degree to which cognitive tasks correlate with one another. If the theory were true, then similar tasks would correlate more strongly with one another than tasks that do not resemble each other. (Likewise, dissimilar tasks would be weakly correlated because they would draw on different mental processes.) But task similarity is a poor guide for how strongly tasks correlate with each other. For example, if g were an artifact of different tasks requiring the same processes or mental modules, then the digit span and backward digit span tasks should be more correlated with one another than any other pair of tasks. However, this is not what happens in real datasets. In most samples, correlations between the two digit span tasks are r ≈ .30 to 50 (e.g., Wechsler, 2008, 2014), but other dissimilar tasks (such as the similarities task and the arithmetic subtest on the WISC-V) have stronger correlations.

Conclusion

Modern theories of intelligence are based on the belief that g is related to every mental ability, either directly (in the bifactor model) or indirectly (in the Cattell–Horn–Carroll model). While the view that general intelligence is the only important mental ability was discarded long ago, g inevitably arises from the positive correlations among scores on different mental tasks. Because intelligence is one global ability, it is not hard to create one score – often called IQ – that summarizes how well a person can solve problems. While IQ is not the only important score for understanding a person’s cognitive abilities, it is a useful score for understanding general problem-solving ability.

From Chapter 2 of "In the Know: Debunking 35 Myths About Human Intelligence" by Dr. Russell Warne (2020)

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