Whatever siren-songs Anderson (2000) may have read into 'The g Factor (Jensen, 1998; 1999) have resulted from what may be an unfortunate illusion, for which I must take the blame for not having sufficientlr repeated and emphasized that my book was about the nature of psychometric g per se, which deals entirely with variance in human abilities. It was not my intention to present a comprehensive theory of what Anderson refers to as 'mental structure.'
2. It was in a lecture I gave way back in 1977 at the University of Melbourne (Jensen, 1978) that I first spelled out the essential distinction between the structure of individual differences in ability and the what Anderson now calls a cognitive theory of mental structure. I characterized the difference as that between what we could in principle learn about intelligence by studying a single person (a province of cognitive psychology) and what we could learn only by studying the differences between individuals (a province of differential psychology). Conceptually and methodologically, these are different spheres of theory and investigation. The same word 'structure' that is used in both these spheres is itself a source of confusion. Unfortunately, I did not say enough in my book to clear up this confusion. I'll try to do so now.
3. Psychometricians and factor analysts talk about the 'structure of intellect' (or the structure of psychometric abilities, by which they mean the covariance structure, correlational structure, or factor structure of the total matrix of covariances or Pearsonian correlation coefficients among a number of tests of various mental abilities, each of which yields a distribution of scores, quantified as variance, because of individual differences in test performance. Because the correlations among the tests are not of uniform size, some pairs of tests being much more highly correlated than are other pairs in the whole correlation matrix, factor analysts speak of this phenomenon as the 'structure' of the correlation matrix. Factor analysis is a mathematical method (a set of algorithms based on matrix algebra) for elucidating this correlational structure by transforming a correlation matrix into a factor matrix, which, in the final analysis consists of a number of independent (i.e., uncorrelated or orthogonal) components or factors that will generate the pattern of correlations among the test variables within some specifiable degree of accuracy, as indicated by the residual correlation matrix (i.e., the difference between he original correlations and the correlations generated by the factors).
4. The extracted factors, then, are together referred to as the 'factor structure' of the various mental tests that were included in the analysis, and the factor composition of each test is simply its loadings on (i.e., correlation with) each of the factors. In the mental abilities domain, only one of these factors, called g (for general) is common to all of the tests, and it is typically the largest of the factors (i.e.,it accounts for a larger proportion of the total variance in all the tests than is accounted for by any other factor).
5. The g factor is especially interesting and important to behavioral and social scientists largely because of (what I have termed) 'the g nexus' (Jensen, 1998, Chapter 14), which is the phenomenon that g is related to more different nonpsychometric real-life variables that are highly significant to individuals and to society than is any other known psychological individual-difference variable that we know how to measure. The g factor also shows greater heritability than any other abilities independent of g, as well as showing correlations with various physical variables, mostly involving aspects of brain structure/function.
6. But the most important thing to note for the distinction I'm driving at here is that the g factor comes about because of (1) individual differences in many phenotyically different abilities, and (2) the all-positive but variable correlations between all those abilities. These two important phenomenon and the g to which they give rise call for an explanation in the manner of all scientific explanations of natural phenomena.
7. The g factor, which best captures these phenomena, can't just be taken for granted by psychologists any more than the other G, gravitation, can be taken for granted by physicists. In both cases there is the question of causality. An empirically testable theory is needed to explain the causal nature of the phenomenon. All scientific explanation is reductionist, in the sense that multifarious phenomena are explained in terms of some smaller number of causal factors, laws, or operating principles. The research question regarding psychometric g essentially boils down to how and why some individuals perform better than other individuals on a wide variety of mental tests as well as real-life mental challenges, in schooling, in the world of work, and in the management of their lives. On such variables, the range of individual differences in the population is large and undoubtedly real.
8. In contrast to this sphere of individual differences in mental abilities is the study of how the mind (or 'intellect,' or 'intelligence') works for any single individual. Knowledge of this kind is what we could in principle learn by studying a single person. What are the mechanisms or design features of the mind (or the brain) that permit the person to perceive, learn, remember, recall, think, reason, solve problems, and do all the other things we refer to collectively as mental abilities or 'intelligence.' A theory of intelligence in this sense is a description of the 'machinery' that can do all these things.
9. These questions were being asked long before much of anything was known about the actual workings of the brain, or the central nervous system (CNS) itself, so attempts to theorize about the structure of a 'machine' that possesses all these powers were necessarily formulated in terms of a different CNS -- the conceptual nervous system. This is essentially what cognitive psychology is all about. It formulates theories in terms of purely conceptual or hypothetical mechanisms, often called cognitive components, and these components are represented, not as neural circuits or anatomical regions, or other physiological aspects of the physical brain, but as diagrams of boxes and arrows or flow-charts showing the hypothesized connections between the components for producing a particular cognitive effect.
10. Using methods of experimental psychology, we can test hypotheses about the action of the cognitive components postulated to explain an individual's performance on tasks that were specially devised to involve certain cognitive components. Questions about individual differences need never enter the picture. Experiments usually employ more than one subject only to decrease sampling error, and individual differences are assigned to the error term in the analysis of variance.
11. Anderson's (1992) own book proposes such a model of cognition and is as good an example of this kind of endeavor as I've seen in the literature. In Anderson's model, the "basic processing mechanism" (roughly analogous to the central processing unit in a computer) operates at a constant speed. In his theory, the individual differences across many different tasks that show up as g in a factor analysis are attributable to individual differences in the speed of the basic processing mechanism.
12. I have presented something quite similar to this in my discussion of information processing and g (Jensen, 1998, Chapter 8), in which the speed of information processing in the Working Memory system (pp. 248-260) comes closest to Anderson's "basic processing mechanism." But my cognitive model was not intended as a comprehensive model of all cognition, but as a mini-theory to explain the correlation between individual differences in reaction time (RT) on elementary cognitive tasks (ECTs) and individual differences in the psychometric g factor derived from untimed complex tests of reasoning and problem solving.
13. This Chapter (8 of Jensen, 1998) is my only indulgence in cognitive modeling in the whole book and admittedly had a narrow aim. But I believe that mini-models of limited phenomena, such as ECTs or even one particular ECT paradigm that can be thoroughly exploited experimentally, might be a more feasible procedure than broader cognitive models that embrace a wider range of phenomena at the expense of being less precisely testable in the laboratory. Astronomers understood the workings of our solar system long before they approached a description of our galaxy, to say nothing of the whole universe. We will probably have to follow suit and have theories of limited phenomena before we have a theory of the mind.
14. Will some kind of cognitive model, or a Conceptual Nervous System, remain the final goal of our attempt to explain mental phenomena, or are such models, however elegant, merely a stopgap until we can arrive at a true physical explanation in terms of the physiology of the central nervous system? Consider a simple analogy: A Martian with a Newtonian level IQ arrives on earth and sees many automobiles. By observing their activities carefully, the Martian develops a theory of how a car works, but without ever looking under the hood. The theory consists of positing components, represented by diagrams of various boxes, some interconnected with arrows, that apparently make the car do the things it is observed to do: there are separate components for starting, for stopping, for moving forward, for moving backward. for accelerating, for decelerating, for stopping, for turning right, and for turning left. The resulting theory really amounts to just a description of what can be observed in a car's performance. It applies to every car.
15. The Martian learns to drive, tries different cars under controlled conditions, and discovers individual differences in their rate of acceleration, maximum speed, horsepower, stopping distance as a function of speed, etc. Measures of all these variables obtained in many different cars are found to be intercorrelated. What causes these differences and their intercorrelations? An explanation in terms of the various components consists of positing differences in the workings or efficiency of certain components. In explaining differences in horsepower, the starting component seems an unlikely source of variance; neither is the turning component or the stopping component. In 'cornering', the turning component is the most plausible source of variance, and so on. But when the tests are applied to a sample of cars including everything from Rolls-Royces to the cheapest cars, the indices of performance attributed to most of these components are positively correlated with each other to varying degrees. A general performance factor is extracted from the correlations and is described as power, speed, and efficiency, but its causal mechanism(s) remain unknown.
16. Theories are possible, based on mini-theories of the workings of the separate components and their interactions, but there are too few constraints on these theories to permit a clear-cut choice between alternative, but mutually contradictory, explanations of a given phenomenon. To find the constraints needed to choose between different hypothesized models it is finally necessary to explore what goes on under the hood. By doing this, the Martian discovers three quite different "genera" of car engines. Internal combustion engines, steam engines, and electric motors; and there are three "species" of internal combustion engines: gasoline (petrol), diesel, and propane gas. Although these different types of cars all have certain mechanisms in common -- four wheels, steering wheel, accelerator, brakes, etc. -- their engines have quite different operating principles.
17. To simplify analysis, our Martian focuses on the most common type of car, those with gasoline-powered internal combustion engines. First, the Martian studies the basic working principles of these engines to get ideas of where to look for possible and testable explanations of individual differences in horse power, etc. It is discovered, for example, that the number of cylinders is strongly correlated with horsepower; the cylinder's cubic capacity is another correlate, though not as strong; and following these is the gasoline's octane level. Other variables -- reliability of spark plugs, grade of motor -- are found to increment independently the multiple correlation of all these variables with measures of different cars' horsepower and speed. Few of these variables could have been hypothesized before looking under the hood. Finally, by manipulating each of these correlated variables, those with functional significance can be separated from incidental correlates, such as the differences between radiator designs or tail pipes which may be as correlated with the manufacturer's emblem on the hood as they are correlated with any part of the machinery. Functional or causal correlates and incidental correlates are thus sorted out.
18. The problems of understanding cognition and individual differences in cognitive performance roughly parallel those faced by the Martian attempting to understand the workings of automobiles. The comparatively recent transition from cognitive psychology to cognitive neuroscience imposes the constraints needed to resolve the alternative models that arise in purely cognitive explanations of mental phenomena. The brain is no longer entirely a black box. Present methods of brain research can provide clues to the physiological nature of the processes that subserve certain behavioral or cognitive phenomena, at least in certain limited aspects of cognition. These are mini-theories of cognition in the sense that they attempt to explain a particular component of cognitive activity in terms of actual brain processes that can be tested empirically in both the behavioral and neurological spheres. It Both human and infrahuman models for testing hypotheses can be used.
19. An excellent example of this effort is the impressive lifework of James McGaugh and others on memory (McGaugh 2000). Other black box cognitive components can be treated similarly. At present, however, we have no comparably detailed knowledge of the neural mechanisms of perception, thinking, or problem solving. The design features and operating principles of the brain that govern these complex forms of cognition are as yet far from being understood, although something is known about the localization of such functions, or at least the important nodes or relay stations involved in their operation. It seems likely that mini-theories of limited systems will have to precede the development of theories of broader scope needed to integrate these systems to explain thinking, reasoning, problem solving, language, and the like.
20. This is nomothetic research aimed at discovering the general design features and operating principles common to all biologically normal members of a given species. As I have argued elsewhere (Jensen, 1997), this area of research is conceptually distinct from the study of individual differences. These differences, I suggest, result not from differences in the 'hard-wired' design features or operations of the nervous system, but from quantitative differences in certain aspects of the CNS and other differences in body chemistry, such as hormones, that interact with the CNS. It is these quantitative differences that are reflected in individual differences in the performance of the operating system.
21. I have not banished the word 'intelligence' from my scientific vocabulary and substituted g instead of it, contrary to Anderson's impression (par. #1). In Chapter 3 I refer to "intelligence" as an interspecies behavioral phenomenon that reflects the different design and operational features of different species. It is those features of brain design and operation that are common to all biologically normal members of a given species. On the other hand, I advise discussing intraspecies individual differences in cognition in terms of independent psychometric factors, including not only g, but all factors that can be reliably and consistently demonstrated in the psychometric abilities domain of a given species. In Homo sapiens, the g factor happens to be the largest and most ubiquitous, and that is what my book is about.
22. I find it pointless to talk about intraspecies individual differences in "intelligence" as I have defined it. I wrote: "The term 'intelligence,' then, would apply only to the whole class of processes or operating principles of the nervous system that make possible the behavioral functions that mediate the organism's adaptation to its environment, such as stimulus apprehension, perception, attention, discrimination, stimulus generalization, learning, learning-set acquisition, remembering, thinking (e.g., seeing relationships), and problem solving (Jensen, 1998, p. 46). And, in what I think may be the most important chapter of my book (Chapter 3:"The trouble with 'intelligence'"), I go on to explain why using the word 'intelligence' in this broad generic sense causes confusion in discussing individual differences in humans, as I hypothesize that all biologically normal humans possess the same intelligence in the sense in which I have defined it, but they show quantitative differences in these functions, which are best described behaviorally in terms of independent latent variables, or factors.
23. I probably should have reiterated this distinction at various points throughout the book. The fact that people have so much trouble conceptually distinguishing between intelligence as a system common to a species, on the one hand, and intraspecies variation in the behavioral performances issuing from the system, on the other hand, would seem to indicate that its most salient aspect in social perception is the conspicuous phenomenon of individual differences, so much so as to overshadow the marvelous cognitive capabilities of virtually all members of the human species. Noting this, however, does not render the individual differences, their causes, and all their correlates (the "g nexus") any less important to science or to people in general. The structure of the system that makes these human capabilities possible at all, on the one hand, and the causes of quantitative individual differences in these capabilities, on the other, should be thought of as distinct subjects for research, at least heuristically, or until further knowledge proves otherwise.
24. The next step in my argument -- yes, a hypothesis -- is that the causes of individual differences in what is summarized by g are not themselves the design features of the brain, but something else, and this could be something simpler. So discovering them could be easier than discovering the neural processes that make generic intelligence possible in the first place. Determining the basis of g, using both animals and humans as research subjects, necessarily calls for first determining correlations between measures of g and individual differences in presently measurable aspects of the brain -- anatomical, histological, and electrochemical. Then research would zero-in on the brain variables that yield consistently replicable correlations of nontrivial size to determine the particular parameters of these brain measurements that contribute most to the correlations. Discovering the products of the specific genes that are correlated with g may also provide clues to the brain variables that influence g. Brain size, with a substantial correlation of about +.40 with IQ (which is an imperfect index of g) is a good example. The correlation itself is now beyond any reasonable doubt, and it makes little difference if you control for overall body size.
25. The next question, then, is what is it about differences in brain size that causes individual difference in the level of g. This can be empirically investigated. Three obvious hypotheses suggest themselves, any of which could be true or false:
(1) the total number, or the average density, of cortical neurons
(2) the extent of dendritic arborization and the number of connections between neurons (as roughly indicated by the ratio of cortical gray matter to subcortical white matter)
(3) the degree of myelination of axons, which is known to covary with nerve conduction velocity, brain maturation, and decline of cognitive functions in old age (Miller, 1994).
All of these brain variables can be studied in humans and in animals. Even rats have evinced a general factor in various learning and problem-solving tasks, and as analogues of human brain functions; and experimental and genetic manipulations, research with infrahuman subjects may suggest causal hypotheses in human brain function. Other brain correlates of g, including brain chemistry (e.g., electrolytes, glucose metabolism, neurotransmitters, hormones) can be investigated in the same way, and eventually the brain variables that account for a large proportion of the g variance would be known. Agreed, this would not constitute a nomothetic explanation of intelligence, as I have defined it; but that is the aim of cognitive neuroscience. The proximal physical causes of individual differences reflected by g may then be amenable to direct influence. The heritability of g tells us that these causes exist; we will finally know what they consist of in brain development itself and how they might be beneficially influenced.
26. Anderson devotes much of his commentary to his disapproval of operationalism. On this point, however, I emphatically plead not guilty. I am not at all an operationalist. As I understand it, operationalism insists on operational definitions of ALL terms in a given area of scientific discourse, including theoretical constructs. It holds that the operational definition of a construct constitutes the sole and total meaning of that construct -- its operational definition, in other words, is both necessary and sufficient. I neither believe nor advocate this sterile position, and my occasional arguments with Lloyd Humphreys's theoretical approach to intelligence and g actually stem from my rejection of positivism and its corollary operationalism (Jensen, 1984, 1994). (However, I greatly admire Humphreys's empirical contributions.) Theoretical constructs, I believe, need not be operationally defined and, in fact, cannot be so defined, as they are not observable or directly measurable entities. General mental ability, or g, is as much a theoretical construct (or latent variable) as gravitation, or G. I have not proposed an operational definition of g. On the other hand, scientific work requires precise definitions or descriptions (call them operational definitions, if you wish) and aexplicit agreement on the measurements, indices, or other quantitative representation of the observed phenomenon it attempts to investigate empirically and explain theoretically.
27. I'm not going to read my whole book again to be sure, but I can't imagine that I ever said anything like "the g factor is intelligence," as Anderson interprets my view. Since g is a latent variable, we can at best only achieve estimates of it. Factor analysis has proven to be the best method for doing this. But the g construct certainly has surplus meaning beyond the operations of factor analysis, and that's why there is so much about g that calls for further exploration and discovery. Nor do I anywhere "reduce g to genes" -- again Anderson's words. But I think it is an important finding that the heritability estimates of various psychometric tests are related to those tests' g loadings, considering that the calculations of heritability and of tests' g loadings are based on different kinds of data that have no necessary connection between them. The fact that a connection is actually found surely adds to the Galton-Spearman conception of the construct validity of g.
28. Finally, a word on behalf of the consilience of scientific knowledge. I have read E. O. Wilson's book "Consilience" (Wilson, 1998) and liked it a lot, mainly because long before I even knew this word, I had been a consilience seeker in my personal philosophy, as a way of seeking the interrelatedness of many different things within a scientific context. This appeals to me as an absolute non-believer in anything supernatural and as one who has sought a scientifically satisfying general philosophy or world view. Therefore I am happy to find that Anderson characterizes my notion of the "g nexus" (Jensen, 1998, Chapter 14) as an example of consilience, even though it is quite limited in view of Wilson's all-embracing conception. Admittedly, the "g nexus" is at present just an idea for a broad research program, which I expect to come about as a connecting (not to say unifying) theme in the behavioral and social sciences. With or without a structural theory of intelligence per se, the g construct is there and its role in extra-psychometric variables of educational, social, economic, and personal importance can be determined and studied, even while our understanding of the physical basis of g is far from complete. Progress in understanding that most central aspect of the g nexus will accelerate along with the technical advances and discoveries being made today in brain research. More than one path will lead to the scientific understanding of g, which is clearly one of the most important constructs in human psychology.
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