Here Is the MI-G Synthesis Dynamical Diagram

Laurent Dubois, Fontaine-L'Evêque,

rue Beaulieusart, 148,

Fontaine-L'Evêque, B-6140,

Tél. : (0032)(0)71 544185

gG Model or the MI-g synthesis

“Much work remains to be done in the factor-analytic study of cognitive abilities.

The map of abilities provided by the three-stratum theory

undoubtedly has errors of commission and omission,

with gaps to be filled in by further research,

including the development of new types of testing and assessment

and the factorial investigation of their relationship with each other

and with better established types of assessment” (Carroll, 1997)

Introduction

In the field of researches in cognitive sciences in general and A.I. in particular, it is not unreasonable to expect interesting contributions from the attempts of understanding and measuring intelligence in experimental psychology. Two main options can be distinguished: the more academically recognized theory of a general factor of intelligence subsumed under the various kinds of tests items, and the more popular but hardly scientifically verified theory of so called Multiple intelligences.

The first objective of the present work is to illustrate through a matrix the perfect compatibility of these two seemingly definitely antagonistic approaches. It will lead us, in a second time, to the drawing of a dynamical diagram susceptible of use in the A.I. framework.

From IQ to AI

High IQ communities and power tests

In January 2001, I discovered the on-line “power tests” and “High IQ communities”.

Power tests are intended to increase significantly the ceiling of the existing official and proctored intelligence scales and culture-free type IQ tests.

The main characteristics of the Power tests are their high difficulty and their consequently untimed and unproctored nature. Pioneers in this domain are people like Ron Hoeflin with the “Mega test” and Paul Cooijmans with the “Test for genius”. Currently Xavier Jouve try to make his work academically recognized. I myself developed the “Power-scale” including the “916 test”. References about these works can be found at the following adress:

High IQ communities gather people with supposed or really measured high IQ. Some exhibit learning disabilities, others didn’t adapt to the academic world but, beyond the inevitable elitism, competition and infatuation, all undoubtedly find in these societies a stimulating and sometimes comforting environment. Here is one of the most popular on-line societies:

In 2001 I create and put on line the 916 test. Initially conceived as a funny challenge to the puzzles geeks, the 916 test meets an immediate interest in the high IQ community because of the pureness and the originality of the items, especially some highly abstract verbal items that needs the mastery of an elementary language only. The test appears to be much more difficult than expected and before all its psychometric value is perfectly reliable with that of the other normed power tests and even with the classical IQ tools, essentially the RAPM and the Cattell, in the limits of the ceiling of the latter.

Power IQ tests and A.I. seemingly tend to reach to very different objectives: to develop the means to check the highest level of intelligence on the one hand, to establish the minimal conditions of emergence of intelligence on the other hand. But the will of the designers to elaborate, or discover the purest, most abstract items can be of some help to researchers in AI.

HIQH

Frequent critics against such societies and people claiming a high IQ consist in reproaching the complete uselessness of their potential and their wasting into purely intellectual masturbatory activities. Despite of its humanist objectives, a society like Mensa ( the high IQ society (over 100,000 members around the globe) founded in 1946 by the eccentric enthusiast qualified in Law Roland Berrill and the Scientist, barrister and polymath Dr Lance Ware intended to the development of intellectual faculties and performances for the improvement of humanity, did not esacape such critics.

In march 2002, birth of the High IQ for the Humanity project in short, compensate the socio-economical imbalance between developed and less developed countries aggravated by the phenomenon of "Brain Drain". Let’s note that in less than two years, almost exclusively by the mean of online interactions, HIQH has become an official NGO, a 501(c)(3) non-profit corporation
recognized by the U.S. federal government and fully exempt from federal
tax, with projects started in Nepal, Bulgaria, Kenya and Bangladesh.

As the society intended to work on the basis of an enlarged definition of intelligence, I decided to propose a synthesis of the two models of intelligence most often discussed in the high IQ forums: the “general factor of intelligence” (g) by Spearman and the “multiple intelligences” of Gardner.

As I try to highlight this compatibility through a matrix and a dynamical diagram that modelize the interactions between the man and his environment, it seems to be appropriated in the frame of lessons on cognitive sciences.

Short story of the different models of « measure » of intelligence

Here some important steps in the history of the measuring of intelligence.

Galton

Inventor of the notion of “eugenism”, the Darwin’s half-cousin thinks that “mental traits” are inheritable; he does not believe in the equivalence of intellectual potential among human beings and consider that intelligence can and has to be tested. Strongly impressed by the work of Adolphe Quetelet was the first to apply statistical methods to the study of human characteristics, and actually discovered the concept of normal distribution--the tendency for the bulk population to fall somewhere between two extremes, with numbers dropping sharply at either extreme. If plotted on a chart, these values assume a shape roughly like that of a bell.

Binet, Simon

In 1905, in response to a request of the French government, Alfred Binet and Theophile Simon develop an intelligence scale and the notion of “mental level”, the fact that in becoming elder, the child can reproduce and understand more and more difficult situations and concepts.

Some years later, the German psychologist Wilhelm Stern will translate this notion of “mental level” in that of “mental quotient” or ratio:

.

Lewis Terman

He will adapt the test of Binet-Simon to the American society. This version named Stanford-Binet (Terman was professor at Stanford university) is one of the two most widely used intelligence scales in the world, with the Weschler intelligence scale.

This is only in 1971 that Spearman will introduce the expression “Intellectual Quotient” always in use today.

Above 16 years, one uses the expression of “deviation IQ”, i.e. the deviation of the performance to the mean.

Horn

About “intelligence scale” like the Binet-Simon: “intelligence is what is measured by the tests”!

Spearman

Discoverer of the g factor, he is the advocate of a centralized intelligence.

Thurstone

He suggests another reading of the data gathered by Spearman and, by the rotation of the factors in order to optimize their position & so maximize the variance of some tests and minimize that of others can lead, especially when orthogonality is not conserved, (oblique factors) to very different views on the structure of intelligence.

He shows that the displaying of g can be seen as a statistical artefact. He proposes a five independent factors model of intelligence: word fluency, verbal comprehension, spatial visualization, perceptual speed, memory, reasoning.

Thurstone contribution to psychometry is extremely important because he showed the possibility of a different coherent interpretation of the matrices of Spearman.

From there, it seems reasonable and even epistemologically recommended to explore neglected tracks in the attempts to understand better the ways of expression of intelligence.

Piaget

Developmental theory of intelligence.

Weschler

Author of the most widely used and recognized “intelligence scale”.

Cattell

Made the important distinction between the fluid and the crystallised intelligence, the former similar to the g and the latter to the s of Spearman.

Gardner

Distributed intelligence: physiologically and, on the other hand, inter individual relations.

Raven

The RAPM, Raven Advanced Progressive Matrices are the most widely used IQ test and probably the most culture-free tool available on the market.

Carroll

Author of a large meta-analysis of factor analytic studies of IQ tests, John Bissell Carroll is probably THE authority in psychometrics currently. He calls for further research on many aspects of human ability testing that have yet to be rigorously studied. Carroll is convinced that there are distinct cognitive ability factors in addition to the "g" factor that accounts for the greatest degree of score variation on IQ tests.

Spearman’s g factor

As it seems reasonable to think that even the most adamant opponents of Spearman’s theory will agree to admit that his definition of intelligence constitutes an excellent starting point, were it precisely to be invalidated “ab absurdo”, in the attempt to tame this fleeting matter, let us give it the privilege of the first lines of this essay:

As this and in the state of affairs, it is, at worst, a purely abstract representation, at best, a rather good approximation of the reality supposing that one knows what “intelligence” is!!! - as long as one focuses on the implicit notion of “performance” implied by this definition. One fails in satisfying our confused and intuitive perception of the richness and the complexity of the notion of intelligence.

But what is the story of this definition?

Almost in the same manner as Descartes, Spearman intends to establish experimental psychology on solid basis. Extremely critic against his predecessors in experimental psychology because of their lack of rigor and mastery of formal tools, Spearman introduced serious statistical methods (Spearman looks like conceptual and technical founders like Descartes and Newton).

But Spearman cannot escape from the contingencies of real life and has to give to himself an a priori conceptual framework most susceptible of containing the essential aspects of intelligence.

- school order determined by examinations: proficiency, efficiency in academic matters

- school order without age bias: native capacity

- impression produced upon other people: assortment by teacher in bright – mean – dull

- common sense out of school: assessed by impression produced upon other students

We can imagine more solid grounds upon which can be built a “realist” theory! We indeed don’t escape two kind of subjectivities: that of the judgements made by people giving their impressions, and that of the selection of the aspects itself. The most obvious lacuna is the absence of any reference to “creativity” and “imagination”.

But also Intelligent activities like self-knowledge, strategic games…

What makes the reputation of Spearman is his displaying of g as product of a factorial analysis. His definition is the translation of the result of a statistical operation, some people reproaching him for having simply elaborated a statistical artefact.

But Spearman himself is not satisfied with this statistical entity. He goes further and assimilates g to the expression of the “genetics”. In a sense, Spearman reinjects the product of his factorial analysis to the root of the human brain functioning. If different types of problems require different types of abilities, all types of problems require g, i.e. the “ability to see relationships between things and to manipulate those relationships to solve problems” in question.

On the other hand, Spearman cannot avoid to take into account some “specific” factors in his theory: language mastery, ability to solve logical problems, spatial representation. But these specific factors, abilities are ruled by the monarchic general factor g.

Consequently, g is both root and fruit, and its janusian, almost schizophrenic nature is synthesized in the expression “general factor of intelligence”.

On the other hand, what is the link between the highlighting of g through the factorial analysis, and the above definition of intelligence?

What is it meant by “general factor”? It means that the performances to different kind of tests similarly loaded in g will be similar. Really it does not tell us much about what intelligence is, but rather about interindividual differences.

If probably not a simple statistical artefact, the correlations highlighted by Spearman are at first look a purely abstract representation. It has to be made more concrete. Spearman uses two ways to make his discovery more accessible: on the one hand, he assimilates g to a mental energy, on the other hand, he makes g synonymous of the ability to see relationships between things and to manipulate those relationships to solve problems. As we will see, it leads to two different interpretations of g.

His definition of intelligence allows to “materialize” it in some way.

If pertinent, the displaying of g is one of the strongest expressions of… g.

This remark itself then stays at a higher level of abstraction yet:

meta-process, & so on ad infinitum!

If the displaying of g is not an expression of… g,

Then it must be the expression of a meta-/higher factor. But then, it cannot be proved/demonstrated in our framework.

Does it make sense that the questioning

About intelligence was a product

of extra-intelligence?

Let us reason against the grain: let us suppose that g is not pertinent!

Then, the disqualification of g is the fact/power of a specific factor!

Gardner’s Multiple Intelligences

In counterpoint, here is the Howard Gardner’s definition of intelligence:

Are the Spearman and Gardner definitions really contradictory? Is the Gardner definition not simply an extension of that of Spearman?

Its merit is to underline the “relative” character of the label “intelligent” of the products of the mind.

It depends on the referential in which these products emerge.

It also emphasizes the process of “creation”, great absent in the traditional IQ tests.

Howard Gardner, professor at Harvard University, don’t believe in a “general” factor of intelligence. Rather he thinks one can distinguish 9 different types of intelligence: verbal – linguistic, logico-mathematical, spatial, bodily - kinaesthetic, musical, interpersonal, intrapersonal, naturalistic and emotional. Gardner reproaches to the education system to focus on the first three types and to completely ignore the others. Of course, testing material suffers from the same blindness!

MI empirical basis

If MI theory itself suffers from lack of experimental support, it is nevertheless not without any empirical support, even if pointed out by other people than Gardner.

- Damasio, for example, showed that brain-damaged people checked a very selective reduction of some of their capacities.

- "idiots-savants" remain unexplained cases

- in the same spirit, the case of gifted people with heterogeneous aptitudes is challenging

- Plasticity of the brain: modification of the motor and somato-sensorial cortical areas (tomography/imagery by functional magnetic resonance) in relation to shadow organs (memory of the initial arrangement of the cerebrals area supports the idea of a genetic pre-instruction)

- consideration of intelligence in an evolutive rather than crystallized/static

- g is not really invariable

- IQ of divorced parents childs

- IQ of maltreated babys

- what are special talents if they are not legitimate components of intelligence? In what are they different from the primary mental abilities?

We have with Gardner’s multiple intelligences an extension of the traditional, specific types of intelligence: mathematical-verbal-spatial, where g can express itself! The price to pay is the assimilation of g, pure abstract product of a factorial analysis with Spearman, and in such seemingly without limit, or assimilated to a statistical artefact in the head of its detractors, to a “potential energy” that diffuses differently through the different types of abilities, the variation of quantity devoted to each type explaining possible low correlations between some types of intelligence, even if the basic logical principles ruling each type must be the same.

In fact, the really fluid g is immeasurable through IQ tests, a residual fluidity only.

The most general distinction would be:

functional and conceptual intelligence

Let’s add that Gardner insist on the “distributed” character of intelligence. Physiologically, neurons are not exclusively limited to the brain. Environmentally and socially, the interactions play an important role in the development of the cognitive and creative abilities.

MI vs. g?

The key point in the apparent antagonism between MI and g is the notion of “performance”, the heart of the works of the psychometricians since Galton, Binet and Spearman to Jensen and Sternberg. It allows empirical measures and easy comparisons between testees. However it leads to make the field of intelligence too restrictive. The real contribution of Gardner, and Sternberg in some extend, is to emphasize this problem as well as to allow extension of this field by including characteristics that we all intuitively feel belonging to the essence of intelligence; e.g. “creativity”, which we all know somewhat confusedly that it is directly linked to intelligence and which the strongest weakness compared to “performance” is its unruly and free nature (wild intelligence), aleatory efficiency. Now, if we see “creative productions” as the answers to non yet formulated problems, it can more easily and obviously integrated as an essential component of intelligence!

Gardner typology is nothing more than

an extension of Thurstone primary mental abilities.

MI-g Synthesis

[the emphasis is put on g as product]

So a new framework is needed. Here below is an attempt of remodelling of the different conceptions of intelligence and of including the enlarged definition of intelligence.

The deep analysis of the matrix will be made in two steps:

- the attempt of elaborating

- the emphasis on the dynamical side through a diagram

Matrix

This matrice is itself an expression of the product.