©By Grady M. Towers

(From The Prometheus Society's Journal, Gift of Fire Issue No. 33, September 1988)

The mathematical technique called factor analysis was invented by psychologists specifically to answer the age old question, "Is there more than one kind of intelligence?" We now know that there are two: one called fluid g, measured by culture fair tests such as the Raven Progressive Matrices or the LAIT, and another called crystallized g, measured by culture loaded tests like the Concept Mastery Test or the Miller Analogies Test. What we call g has been defined as the ability to "educe relations and correlates," or in more everyday terms, the abilities for inductive ("relations") and deductive ("correlates") reasoning. Culture fair tests measure the ability to educe relations and correlates using abstract diagrams, and other material that requires only a minimum of formal learning. Culture loaded tests measure the ability to educe relations and correlates using learned and over learned material, such as vocabulary, algorithms for arithmetic or multiplication, recognition of common objects and their uses, etc. Ordinary IQ tests measure both kinds of intelligence, but not necessarily to the same degree; they are generally biased in favor of crystallized g.

     The currently accepted relationship between these two kinds of ability is called the investment theory of intelligence. It says, in effect, that we are all born with a certain raw ability, or the eduction of relations and correlates, which can be measured with culture fair tests. As we get older, we "invest" this fluid g in certain kinds of judgment skills, such as those involved in doing a mathematical word problem, or parsing a sentence. When we are young, the theory goes, our formal educations are so much alike that we all invest our fluid g in much the same kinds of judgment skills.  That means that our fluid intelligence and our crystallized intelligence are so similar at an early age that it's almost impossible to tell them apart. After we leave school, however, we all begin to invest our fluid g abilities in different things. Measures of fluid g and crystallized g begin to draw apart. Those that invest their fluid g in school-like activities, such as accounting or law, continue to show intellectual growth on conventional (crystallized) IQ tests.  Those that put their intelligence to work in other ways, such as becoming ranchers or artists, will not show the same intellectual growth, and may even show a decline in IQ on conventional measures of intelligence. 

     Many years ago, Mensa was faced by a serious policy decision about the kind of intelligence that it wanted to select for. It turned out that three out of four prospective members who were selected using a culture fair test could not pass a culture loaded test. At the same time, it also turned out that three out of four prospective members who could pass a culture loaded test could not pass a culture fair test. In the end, Mensa chose to use culture loaded tests exclusively in selecting its members. Almost all other high IQ societies, with the exception of Four Sigma and Triple Nine, have followed suit. As a consequence, there are now three qualitatively different kinds of high IQ societies extant. One kind, represented by Four-Sigma and most of the membership of the Triple Nine Society, was recruited with the LAIT--a culture fair test--and is made up mostly of people gifted with fluid intelligence. A second kind, represented by Mensa, Intertel and ISPE, was recruited by more conventional tests, and is made up of those gifted primarily with crystallized intelligence. Some individuals, however, have joined or qualified for membership in both kinds of societies, and are about equally gifted with both kinds of ability. A large minority of Triple Nine members, as well as a majority of those in Prometheus, appear to belong in this category. 

     None of this would matter except that each kind of ability brings with it its own kind of cognitive style, its own kind of personality, and its own set of values. In fact, the contrast between persons gifted with fluid g and those gifted with crystallized g is so sharp that, with a little practice, most people find that they can learn to tell them apart at a glance. Those gifted with fluid g (LAIT) tend to be socially retiring, independent of the good opinion of others, analytical, interested in theoretical and scientific problems, and to dislike rigid systematization and routine. Those gifted primarily with crystallized g (conventional tests) tend to be sociable, quick in reactions, artistic, and to dislike logical and theoretical problems. And then there are those who are equally gifted with both kinds of ability, and tend to be mixtures of all these qualities--sometimes paradoxically so: Prometheans tend to be paradoxical.

     The discovery that there are really two kinds of intelligence was made by Raymond B. Cattell in 1940, and was repeatedly confirmed in the following years. The issue of multiple intelligence, consequently, should have been considered resolved decades ago. Nevertheless, there has been a recent resurgence of interest in these theories among some younger psychometricians who either do not understand factor analysis, or simply refuse to accept its results.  One such theorist is Howard Gardner.

     Gardner postulates the existence of seven different intelligences: linguistic, musical, logical-mathematical, spatial, body-kinesthetic, interpersonal, and intrapersonal. He says that he is "...convinced of the existence of an intelligence to the extent that it can be found in relative isolation in special populations (or absent in isolation in otherwise normal populations); to the extent that it may become highly developed in specific individuals or in specific cultures; and to the extent that psychometricians, experimental researchers, and/or experts in particular disciplines can posit core abilities that, in effect, define the intelligence.  (Frames of Mind, p. 9.)  In defense of his seven intelligences, Gardner offers evidence drawn from studies of  "...prodigies, gifted individuals, brain-damaged patients, idiot savants, normal children, normal adults, experts in different lines of work, and individuals from diverse cultures." (ibid.)  In short, he offers virtually no statistical or psychometric support for his thesis, but relies instead almost completely on a patchwork of anecdotes and idiosyncratic impressions.  The most troubling aspect of Gardner's work is that his theory is at least partially testable with currently available psychological instruments, and yet he makes no effort to obtain the necessary proof.  It's true that we have no test for intrapersonal intelligence or body-kinesthetic intelligence, and the only test of interpersonal intelligence available was developed for the mentally retarded (the Vineland Social Maturity Scale), but tests do exist for all the other "intelligences" Gardner postulates. Why doesn't he use them to obtain the appropriate correlations, factor analyze them, and, then show that these abilities are in fact co-equal intelligences? The obvious answer is that Gardner already knows that they aren't. He says on page 284 of Frames of Mind:

     

"And what of my use of the loaded term 'intelligence'?  As hinted at earlier, part of the motivation for using this term is my desire to put forth a more viable model of intelligence: I seek to replace the current, largely discredited notion of intelligence as a single inherited trait (or set of traits) which can be reliably assessed through an hour-long interview or a paper and pencil test. But it should be said here as well that nothing much hangs on the particular use of this term, and I would be satisfied to substitute such phrases as 'intellectual competences,' 'thought processes,'  'cognitive capacities,' 'cognitive skills,' 'forms of knowledge,' or other cognate mentalistic terminology. What is crucial is not the label but, rather, the conception: that individuals have a number of domains of potential intellectual competence which they are in the position to develop, if they are normal and if the appropriate stimulating factors are available."

  No competent psychometrician has ever claimed that an intelligence test measured all mental abilities.  No competent psychometrician has ever claimed that some of the abilities left out of intelligence tests aren't valuable.  What he would claim is that an ability must meet certain other requirements before it merits being called intelligence. In the first place, it must be a mental ability, which leaves out Gardner's body-kinesthetic intelligence. In the second place, it must be an ability. This means that it must be objectively observable under standardized conditions, and that there must be objective criterion of better-worse performance.  This seems to leave out Gardner's intrapersonal intelligence.  How can one measure a person's capacity for self-understanding?  How could you tell the difference between self-understanding and self-deception? And aren't these attributes of personality, in any event?

     The most important objection that a psychometrician would offer, however, is that Gardner is attempting to jettison the criterion of  "the indifference of the indicator".  This principle was enunciated by Charles E. Spearman in 1923, and says, in effect, that the specific content of an item in an intelligence test is unimportant, so long as all persons taking the test understand it.  No item can be without content, of course, but the principle emphasizes that the content of an item or a test is merely the vehicle for measuring g, and is unimportant in itself. That's why a test of verbal analogies can be used to estimate an individual's mathematical ability. Or why a test of number series can be used to predict a person's ability to write poetry or solve anagrams.  That’s why intelligence is conceived to be a general ability, and why it's given the symbol g.  Most of Gardner's "intelligences" are content specific, and not general abilities at all. (It may seem at first glance that the existence of fluid g and crystallized g are violations of the same principle, but this is a misunderstanding. The distinction between culture fair tests and culture loaded tests is often mistakenly thought to be the same as the distinction between nonverbal tests and verbal tests.  This, however, is simply not the case. Verbal items (or any other kind of item) can be used, in principle, to measure either fluid g or crystallized g, depending on how much prior knowledge is necessary to understand the item. The verbal items on the LAIT, for example, are very nearly pure measures of fluid g.  They make little demand on a person's verbal knowledge, but large demands on his ability to "educe relations.") The fact is that Gardner is little more than an IQ basher. His research on computational modules has merit and promises to be an important contribution to cognitive science, but it in no way disproves the existence of a general cognitive ability, nor does it justify his assertion that IO tests have been largely discredited. Nothing could be further from the truth. As with many other IQ bashers, he deliberately attempts to minimize the scope of what intelligence tests can do. He tries to present the picture that IQ tests can only predict school-like performance, and that none too well.  The reality is that a score obtained from a conventional IQ test can be used to predict performance in a profusion of activities outside the classroom, many of them bearing only the slightest resemblance to bookish or puzzle solving behavior. As evidence for this, here is a partial list of activities (and other qualities) that are positively or negatively associated with IQ.

POSITIVE CORRELATES:

• Achievement motivation

• Altruism

• Analytic style

• Anorexia nervosa

• Aptitudes: cognitive abilities; 'abstractness' of integrative complexity

• Artistic preferences and abilities

• Craftwork

• Creativity, fluency

• Dietary preferences (low-sugar, low-fat)

• Educational attainment

• Eminence, genius

• Emotional sensitivity

• Extra-curricular attainments

• Field-Independence

• Health, fitness, longevity

• Height

• Humor, sense of

• Income

• Interests, breadth and depth

• Involvement in school activities

• Leadership

• Learning ability

• Linguistic abilities (including spelling)

• Logical abilities

• Marital partner, choice of

• Media preferences (newspapers, TV channels)

• Memory

• Migration (voluntary)

• Military rank

• Moral reasoning and development

• Motor skills

• Musical preferences and abilities

• Myopia

• Occupational status

• Occupational success

• Perceptual abilities (for briefly-presented material)

• Piaget-type abilities

• Practical knowledge

• Psychotherapy, response to

• Reading ability

• Regional differences

• Social skills

• Socio-economic status of origin (parental)

• Socio-economic status (achieved)

• Sports participation

• Supermarket shopping ability

• Talking speed

• Values, attitudes

NEGATIVE CORRELATES:

• Accident-proneness

• Acquiescence

• Aging

• Alcoholism

• Authoritarianism

• Conservatism (of social views)

• Crime

• Delinquency

• Dogmatism

• Hysteria vs other neurosis

• Impulsivity

• Infant mortality

• Psychoticism

• Racial prejudice

• Reaction times

• Smoking

• Truancy

• Weight height ratio, obesity

 The data in these tables were obtained from studies using conventional (crystallized) intelligence tests. Comparable data for culture fair (fluid) intelligence tests is more meager, partly because culture fair tests haven't existed as long, and partly because much less practical use has been made of them. One useful goal that the Four Sigma and Triple Nine Societies might adopt would be to provide the same kind of validation studies for culture fair tests like the LAIT that already exist for conventional tests.  Perhaps tests of fluid intelligence would be utilized more if we knew more about them. Four Sigma and Triple Nine are in a unique position to help provide that knowledge.

     Another multiple  intelligence theorist is  Robert J. Sternberg of Yale University (Beyond  IQ; Intelligence Applied; Conceptions of Giftedness; Practical Intelligence: Nature and Origins  of  Competence in the Everyday World). Like Howard Gardner, Sternberg wants to break intelligence down into its component parts; unlike Gardner, however, Sternberg may actually have discovered one or more new kinds of intelligence. He calls his new theory the triarchic theory of intelligence because, as the term suggests, he believes that he has identified three kinds of intelligence: componential, experiential and contextual.

     Componential:  This is intelligence as conventional IQ tests measure it. It's called componential intelligence because Sternberg found a way to analyze the thought processes involved in solving IQ test items into components and metacomponents. He not only studied how a person solves an item, but also how a person chooses the strategy he does when attempting an item. People who are good at these things have high IQs, and are especially acute at analyzing arguments, or in situations calling for critical thinking. They are the typical members of the high IQ societies. 

      Experiential: This is the ability to have new insights. Traditional methods of studying intelligence concentrate on what's going on inside a person's head. Sternberg's approach to insight ability focused on finding out how experience mediated one's internal, mental world, and how one's internal world changed one's experiences. When he and his graduate student Janet E. Davidson began studying insight ability, they found that nobody knew what it was because every one had assumed that it was only one thing. Sternberg and Davidson soon discovered that there are three insight abilities, which they called selective encoding, selective combination and selective comparison. 

     Selective encoding is the ability to focus on the really critical information in a problem.  When one of Sir Alexander Fleming’s bacterial experiments was spoiled by a mold, he recognized that the mold's ability to kill the bacteria was more important than his ruined experiment.  His ability to see the implications of the accident eventually lead to the development of penicillin. 

     Selective combination is the ability to put information together to get the big picture. Many times the facts in the case may be available to everyone, but it's only the insightful person who can combine them into a meaningful new pattern. The Darwinian theory of evolution is a good example of selective combination. The facts were available to many people, but only Darwin and Wallace saw how they fit together.

     Selective comparison is the ability to see an old thing in a new way, or a new thing in an old way. When the tyrant of Syracuse suspected that his goldsmith had cheated him when making a gold crown, he asked Archimedes to find out if the crown really was made of pure gold, but forbade him to destroy it in the process.  Archimedes solved the problem when he suddenly realized that the water overflowing from his bathtub when he stepped into it demonstrated a method of measuring the volume, and thereby the density, of any irregularly shaped object. He saw that if the density of the crown was different from that of an equal weight of gold, then the crown had to be an alloy. He immediately leaped from his bathtub, and ran through the streets naked, yelling, "Eureka!, I've found it!" (Having insights tends to do that to people.)

     Contextual:  This is the ability more commonly called street smart. It's learning how to play the game, and learning how to manipulate the environment.  Most definitions of intelligence include environmental adaptability in them, but ordinary IQ tests don't measure this very well. Sternberg calls this kind of ability contextual because it involves tacit learning. This is knowledge that is not explicitly expressed or taught, but is only implied or indicated. It has to be learned directly from one's environmental context. People who are good at this tend to come out on top in almost any real world situation, even if they are not especially intelligent in terms of IQ or insight. The head of General Motors or the President of the United States are good examples of people with this kind of ability. The Psychological Corporation in San Antonio, Texas, is now developing the Sternberg Multidimensional Abilities Test.  It will be based completely on Sternberg's triarchic theory, and will provide measurements of all three intellectual abilities. Once published, studies using this test will quickly tell us if Sternberg's experiential and contextual abilities genuinely qualify as new intelligences. On the face of it, there's good reason to believe that his experiential (insight) ability has a good chance.  It is a mental ability, it is a mental ability, and it appears to meet the principle of the indifference of the indicator; all good signs. The status of Sternberg's contextual ability is harder to evaluate, but in any event, we will soon know; factor analysis will tell the tale.

DISCUSSION

       Interpreting the results of a factor analysis is a bit like attempting to read the entrails of a chicken, as the ancient Roman priests once did to discover the will of the gods. It is more difficult than actually carrying out the mathematical procedures, which are quite difficult in themselves. It takes a lot of practice, and even a skilled interpreter can easily go wrong. The trickiest part of the problem, but also the most fun, is naming the factors that the procedure reveals. Sometimes factors can't be characterized verbally at all. The safest procedure, and one often followed in the investigation of intelligence, is to assign letters to the factors discovered instead of just names. This is why the general factor is called g, and why special factors such as verbal comprehension is called v, verbal fluency called w, spatial ability called k, and so on. How does an investigator tell if he has discovered a g factor? The rule of thumb is that he has found a g when one of his factors accounts for at least twice as much variance as any other factor in the same analysis.  In the case of intelligence tests, it usually turns out that one factor alone accounts for more of the variance than all the other factors combined. What is often misunderstood by laymen, and sometimes forgotten even by experts, is that all a factor analysis can do is cut up the data in a mathematically parsimonious way. In order to detect a factor, at least two of the tests in the battery must load on that factor.  If there aren't two tests in a battery that load on verbal ability, for example, no verbal factor will be uncovered.  That's why it took so long to discover that there were two g factors, fluid and crystallized. Conventional IQ tests measure both kinds of intelligence, but the loadings on fluid g are so small that at first it took a special trick to identify it.  Once Cattell suspected its existence, he made up new tests that loaded heavily on fluid g, and used them to prove that there definitely was another form of intelligence than that measured by conventional IQ tests. A similar situation presently exists with reference to the new theories of multiple intelligence. It may be that there really is a third form of intelligence not yet confirmed simply because no test has yet been invented to measure it. As things stand now, only fluid intelligence and crystallized intelligence are definitely known to exist. I joined the high IQ societies looking for people with strong insight abilities. Instead, I found an army of logical analysts who wanted to nitpick everything to death.  I really shouldn't have been surprised at this, as this was the very quality they were originally selected for. Nevertheless, I not only felt disappointed with the high IQ societies, I also felt I didn't belong in them despite my IQ. The fact is, I don't enjoy arguments of any kind, and logical puzzles bore me.  What I do enjoy, more than I can say, are insight puzzles like this one:

     A hunter went hunting for bear. He walked five miles east of camp, but couldn't find any game. So he walked five miles north, where he saw a bear and shot it. Then he walked five miles directly back to camp. What color was the bear?