Laurent Dubois 2004

 

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” (J. B. 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 address: http://www.eskimo.com/~miyaguch/hoeflin.html

 

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: http://www.cerebrals.com/

 

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 two latter.

Power IQ tests and A.I. seemingly tend to reach two 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 (http://www.mensa.com), 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 escape such critics.

In march 2002, in response to these critics, birth of the High IQ for the Humanity project by David Udbjorg http://www.hiqh.org/: in short, the objective consist in compensating 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. He was Strongly impressed by the work of Adolphe Quetelet who 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, shows that the rotation of the factors in order to optimise 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 seven independent factors model of intelligence: word fluency, verbal comprehension, spatial visualization, numerical ability, perceptual speed, memory, reasoning.

Thurstone contribution to psychometrics 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.

 

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.

 

Guilford

 

Gardner

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

 

Sternberg

 

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:

 

 

g is the ability to see relationships between things and to manipulate those relationships to solve problems”.

http://comp.uark.edu/~todegar/PSYC2003/intelligence.html

 

 

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:

 

 

"That ability to solve problems, or create products, that are valued within one or more cultural settings".

 

 

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 children

-          IQ of maltreated babies

-          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

 

 

 

Spearman

g

 

 

 

 

 

global mental potential “energy”

 

 

Spearman

Carroll*

Factorial analysis

Product of group factors statistical relations to be confirmed

 

 

 

 

Hardware

+

Rom

(set of instructions)

 

Pure Fluidity

genotype

 

Galton

Jensen

Raw g: 

neural/neuronal speed processing factor (speed)  & neural system complexity factor  (level)

+ sensory- *short- (cash) *mid- (ram) *long- (hard) term memory

 

1st-order

Filter

 

Interface

1st Crystallization

Phenotype(?)

 

Metabolism (Breath-sugar consumption-protein-vitamins-greases…)

+

Sense (central nervous system)

 

2d-order

Filter

 

 

Software

(from other “g-loaded” entities)

 

2d Crystallization

 

(environment

[non-g + g loaded entities]

+

personality)

Gardner

9 MI

gs

Physico-math

gs

Linguistic

gs

Spatial

gs

Musical

gs

Bodily-kinaesthetic

gs

Interpersonal

gs

Intrapersonal

gs

Naturalist

gs

Existentialist

Guilford

5 contents

 

Symbolic

 

 

Semantic

(Verbal)

 

Visual

gv

 

Auditory

gu

(Rhythmic)

 

Behavioural

(Spatio-dynamical)

 

Behavioural

 

Behavioural

 

Behavioural

(olfactive-gustative-touch)

 

Behavioural

 

 

 

 

 

 

 

 

 

Common feature: “infos”,

but specific “codes”/data

 

 

Power

-          Memory 

·          Sensory

·          short (cash)

·          mid (ram)

          long (hard)

-          Persistence

-          Motivation

 

componential

 

-          Evaluation

-          Cognition

·          analytical

·          synthetical

·          hypothetico-deductive

·          inductive

·          algorithmic

[try and error]

·          dynamic

·          combinatoric

·          systematic

·          heuristic

·          conjecturo-

speculative

 

 

Contextual

-          Convergent production

·          Practical

·          Experimental

 

Experiential

-          Divergent production

(wild g)

·          pure divergence

·          producivity

·          ingenuity

·          originality

 

-          Logico-divergence

(highest quality of g)

·          autoreference

·          recursivity

·          infinity

 

 

 

 

 

-          Evanescent g

·          Artistic

·          Aesthetic

·          Emotional

 

 

 

 

 

componential

 

-          Evaluation

-          Cognition

·          analytical

·          synthetical

·          hypothetico-deductive

·          inductive

·          algorithmic

·          dynamic

·          combinatoric

·          systematic

·          heuristic

conjecturo-

speculative

 

 

Contextual

-          Convergent production

·          Practical

·          Experimental

 

Experiential

-          Divergent production

(wild g)

·          pure divergence

·          producivity

·          ingenuity

·          originality

 

-          logico-divergence

(highest quality of g)

·          autoreference

·          recursivity

·          infinity

 

 

Power

-          Memory 

·          Sensory

·          short (cash)

·          mid (ram)

          long (hard)

-          persistence

-          motivation

 

 

-          Evanescent g

·          Artistic

·          Aesthetic

·          Emotional

 

 

 

 

 

 

 

componential

 

-          Evaluation

-          Cognition

·          analytical

·          synthetical

·          hypothetico-deductive

·          inductive

·          algorithmic

·          dynamic

·          combinatoric

·          systematic

·          heuristic

conjecturo-

speculative

 

 

Contextual

-          Convergent production

·          Practical

·          Experimental

 

Experiential

-          Divergent production

(wild g)

·          pure divergence

·          producivity

·          ingenuity

·          originality

 

-          logico-divergence

(highest quality of g)

·          autoreference

·          recursivity

·          infinity

 

 

Power

-          Memory 

·          Sensory

·          short (cash)

·          mid (ram)

          long (hard)

-          persistence

-          motivation

 

 

-          Evanescent g

·          Artistic

·          Aesthetic

·          Emotional

 

 

 

 

 

 

 

 

 

 

componential

 

-          Evaluation

-          Cognition

·          analytical

·          synthetical

·          hypothetico-deductive

·          inductive

·          algorithmic

·          dynamic

·          combinatoric

·          systematic

·          heuristic

conjecturo-

speculative

 

 

Contextual

-          Convergent production

·          Practical

·          Experimental

 

Experiential

-          Divergent production

(wild g)

·          pure divergence

·          producivity

·          ingenuity

·          originality

 

-          logico-divergence

(highest quality of g)

·          autoreference

·          recursivity

·          infinity

 

 

Power

-          Memory 

·          Sensory

·          short (cash)

·          mid (ram)

          long (hard)

-          persistence

-          motivation

 

 

-          Evanescent g

·          Artistic

·          Aesthetic

·          Emotional

 

 

 

 

 

 

 

 

componential

 

-          Evaluation

-          Cognition

·          analytical

·          synthetical

·          hypothetico-deductive

·          inductive

·          algorithmic

·          dynamic

·          combinatoric

·          systematic

·          heuristic

conjecturo-

speculative

 

 

Contextual

-          Convergent production

·          Practical

·          Experimental

 

Experiential

-          Divergent production

(wild g)

·          pure divergence

·          producivity

·          ingenuity

·          originality

 

-          logico-divergence

(highest quality of g)

·          autoreference

·          recursivity

·          infinity

 

 

Power

-          Memory 

·          Sensory

·          short (cash)

·          mid (ram)

          long (hard)

-          persistence

-          motivation

 

 

-          Evanescent g

·          Artistic

·          Aesthetic

·          Emotional

 

 

mental representation

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

componential

 

-          Evaluation

-          Cognition

·          analytical

·          synthetical

·          hypothetico-deductive

·          inductive

·          algorithmic

·          dynamic

·          combinatoric

·          systematic

·          heuristic

conjecturo-

speculative

 

 

Contextual

-          Convergent production

·          Practical

·          Experimental

 

Experiential

-          Divergent production

(wild g)

·          pure divergence

·          producivity

·          ingenuity

·          originality

 

-          logico-divergence

(highest quality of g)

·          autoreference

·          recursivity

·          infinity

 

 

Power

-          Memory 

·          Sensory

·          short (cash)

·          mid (ram)

          long (hard)

-          persistence

-          motivation

 

 

-          Evanescent g

·          Artistic

·          Aesthetic

·          Emotional

 

 

empathy

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

componential

 

-          Evaluation

-          Cognition

·          analytical

·          synthetical

·          hypothetico-deductive

·          inductive

·          algorithmic

·          dynamic

·          combinatoric

·          systematic

·          heuristic

conjecturo-

speculative

 

 

Contextual

-          Convergent production

·          Practical

·          Experimental

 

Experiential

-          Divergent production

(wild g)

·          pure divergence

·          producivity

·          ingenuity

·          originality

 

-          logico-divergence

(highest quality of g)

·          autoreference

·          recursivity

·          infinity

 

 

Power

-          Memory 

·          Sensory

·          short (cash)

·          mid (ram)

          long (hard)

-          persistence

-          motivation

 

 

-          Evanescent g

·          Artistic

·          Aesthetic

·          Emotional

 

 

 

 

 

componential

 

-          Evaluation

-          Cognition

·          analytical

·          synthetical

·          hypothetico-deductive

·          inductive

·          algorithmic

·          dynamic

·          combinatoric

·          systematic

·          heuristic

conjecturo-

speculative

 

 

Contextual

-          Convergent production

·          Practical

·          Experimental

 

Experiential

-          Divergent production

(wild g)

·          pure divergence

·          producivity

·          ingenuity

·          originality

 

-          logico-divergence

(highest quality of g)

·          autoreference

·          recursivity

·          infinity

 

 

Power

-          Memory 

·          Sensory

·          short (cash)

·          mid (ram)

          long (hard)

-          persistence

-          motivation

 

 

-          Evanescent g

·          Artistic

·          Aesthetic

·          Emotional

 

 

 

 

componential

 

-          Evaluation

-          Cognition

·          analytical

·          synthetical

·          hypothetico-deductive

·          inductive

·          algorithmic

·          dynamic

·          combinatoric

·          systematic

·          heuristic

conjecturo-

speculative

 

 

Contextual

-          Convergent production

·          Practical

·          Experimental

 

Experiential

-          Divergent production

(wild g)

·          pure divergence

·          producivity

·          ingenuity

·          originality

 

-          logico-divergence

(highest quality of g)

·          autoreference

·          recursivity

·          infinity

 

 

Power

-          Memory 

·          Sensory

·          short (cash)

·          mid (ram)

          long (hard)

-          persistence

-          motivation

 

 

-          Evanescent g

·          Artistic

·          Aesthetic

·          Emotional

 

 

 

Guilford 5 operations

As sub-specifications of the 3 components of the Sternberg triarchic theory

 

+

 

Thurstone’s 7 primary mental abilities as sub-specifications

 

Analytical

-           spatial ability

-           (gsf + gsc)

-         

-perceptual speed

-numerical ability

-verbal meaning

-memory

*short (casch)

*mid (ram)

*long (hard)

-word fluency

-reasoning

 

+

 

Jensen (meta) - Binet-Simon –Weschler (+ Vernon)

 

 

     Verbal Subtests               Performance Subtests

                     gν                                     gf

 

-           Vocabulary             - Picture Completion  

-           Similarities             - Digit‑Symbol/Coding

-           Arithmetic             - Block Design          

-           Digit Span              - Matrix Reasoning

-           Information           - Picture Arrangement

-           Comprehension      - Symbol Search

-           Letter‑Number       - Object Assembly       

          Sequencing          

 

+

Guilford 6 products

 

-          unit

-          classes

-          relations

-          systems

-          transformations

-          implications

 

Carroll 8 groups factors:

 

-          Gf fluid intelligence

-          Gc crystallized intelligence

-          Gy general memory

-          Gv general visual perception

-          Gu general auditive perception

-          Gr general recuperation

-          Gs general cognitive speed

-          Gt general speed processing

 

 

Sternberg Triarchy

 

-          Componential: abstract

-          Contextual: practical

-          Experiential: creative

 

 

 

In italics, my concepts.

The computing science metaphor is for clarity.

 

This matrix is itself an expression of the product.

But it is not all. The recursive/reflexive feedback on this remark itself,

and so on ad infinitum…

 

 

 

Let us note that Arthur Jensen, the most fervent supporter of Spearman’s displaying of g doesn’t see a fundamental contradiction between his mentor and Gardner’s theories!

 

 

generator-computing

 

.

 

This matrix intends to show the levels of fitting of the different elements implied in the “development” of intelligence.

At the top of the matrix, the g factor. Now, since the definition of intelligence by Spearman himself is ambiguous, we suggest two different interpretations of g:

-          g as mental energy

-          g as a kind of pre-program, this “ability to see relationships between things and to manipulate those relationships to solve problems”.

 

 

In the second case, the pre-program has full control over the data received from the environment. In this case, g is a gift. And this gift must be more than the simple set of binary and Boolean rules, since it would look strange that not anybody, sane people, possess them; if it was not the case, they could not correctly function! But what would this additional competence consist in? In any way, the program must be initially implemented, and there is no natural way to modify it. In any case, it seems to be more than a simple mental energy.

 

In the first case precisely, we can see a rough finite amount of potential but not possibly malleable. Indeed, if g of Spearman has to be assimilated to the speed processing and the quality of the neural network, and in the extension of the memory, and especially the working memory, it cannot be submitted to the influence of the environment, which seems hardly believable at the light of the dynamical diagram designed below!

 

In short, Spearman first extracts from his matrices, by factorial analysis, a common, general factor symbolised by g. Spearman defines it as the ability to see relationships between things and to manipulate those relationships to solve problems”. After that, in order to make his discovery more “concrete”, it reinjects g to the root of the cognition and finally cements his construction by making it completely genetically determined.

 

If we continue our reading of the Matrix, we have the Gardner’s 9 types of intelligence which could constitute the 9 main specific ways/distributions of the rough potential. People have to be tested through optimal supports according to their culture, which does not prevent the items to be as culture free as possible.

What can be expected statistically speaking? A regression to the mean of the extreme sigma, or rather a “progression” to the positive extreme of the mean.

Let us note a little but important change in the typology of Gardner: we use the expression “Physico-mathematical” rather than “logico-mathematical” intelligence. Indeed, according to the adherence to the definition of intelligence as “That ability to solve problems”, shared by Gardner and Spearman, the same kind of “logic” must rest behind of each type of intelligence.

 

Even if indispensable in the philosophy of the project of HIQH, which has to develop new types of assessment tools, we will not explain the rest of the matrix, useless for our current purpose, with the exception of the notions of creativity to which we will make allusion below.

 

 

 

g = G  or g à G ?

 

 

Spearman must be right in stating the existence of a general factor behind the different types of mental abilities. But the question persists to know the real nature of this ability to see relationships between things and to manipulate those relationships to solve problems! And before all if it’s really predetermined because the answer to this question will determine the direction of the researches in AI and the educative options.

The question remains: if the potential is a priori determined, circumstances and particular characteristics of personality must influence the expression of a product of Genius, the best expression of g according to our theory!

It is more than probable that intelligence must be considered as output, fruit of a more or less maturation, which must take more various forms and be not immutable, contrary to what the strict advocates of genetics think.

 

 

The main idea consists in assimilating g to a mental “energ” – Spearman assimilates g to a “mental energy”- or “generator”. Indeed, as to avoid a purely “disincarnate” factor, g must be “materialized” in some way, kind of “sum”, in mathematical terms or “balance sheet” in thermodynamical terms. Now, maybe is it more proper to talk about a mental “potential”! In any case, it allows to make us conscious of the fact that this “potential” is not infinite!

As we have seen in the preliminary, the literature leads to justify two interpretations of g:  g as genetic factor and g as result of a process highlighted by the statistics which assimilate it to the product of a factor analysis.

And if, in the state of affairs, we must be satisfied with rather rough measuring tools, the supposing of the quasi-perfect adequacy between g as generator and g as product of the factor analysis constitutes precisely an epistemological abuse!

 

It is clear that the attempts of minimizing the importance of the genetic factor is vain as the importance of the combined effects of the phenotype and the sensory machinery on the one hand, and the environment and the personality on the other hand (“distribution of intelligence”), is obviously directly dependent upon the efficiency of the central nervous system.

Really, in a sense, all is on the dependence of the genetics, but does this mean that g is immutable? The functioning of the filters is conditioned by g doesn’t prevent the plasticity of the brain.

Now, a complementary reading is necessary and it is also true that the generator needs supports to express itself, g is not disincarnated; the supports? The  “filters” precisely!

Let us take advantage of the situation to underline that we can distinguish two physiologically very different ways of expression of intelligence: cognition and thought:

-          cognition: (low/basic level): cognitive tasks need important sugar consumption but anaerobic.

-          thought: (high level): thought needs O high consumption.

 

 

g à G

g is not immutable.

 

We will define G, for Genius, as the best expression of g, as the expression of a kind of “infinite intelligence at a given/precise moment”.

 

In our conception of intelligence as fruit of an evolutive process, we have “raw g” at the origin, “evolutionary g” the most part of the time, and “G”, for Genius, in conclusion, as most accomplished product in the best cases.

 

With Spearman, g and G  coincide. Genius is a gift.

In our perspective, it is not at all the case. The mental energy becomes a mental “potential”, and it is absolutely not definitely genetically determined since it is submitted to the influence of the static (unintelligent) and intelligent (other brains) environment. In other words, to take the terminology of Gardner, it is “distributed”.

 

 However, Intelligence cannot be simply assimilated to g. Intelligence is the way g is expressed. In other words, one can be more intelligent with less g!

Different levels of g can lead to an equivalent G.

Same g can lead to different G.

Lower g can lead to higher G.

 

 

In short, one observes that Spearman & Gardner’s perspectives, far from being antagonist, are perfectly complementary. “Pure g” advocates fail to take into account the very early effects of the “personality-environment” filter; the MI advocates fail in finding an underlying common feature in each type of intelligence, i.e. the common logic under the elaboration of any “specific” code-info.

g as energy, fundamental potential, as Stump/stub/stock cell that diversifies & develops with specific degrees of complexity in each type. This conception/representation allows an energy/power expenditure (thermodynamics/information-complexity theory). The degree of quality to which g is expressed can be determined in a first time according to the Kolmogorov definition of “complexity”.

 

In the perspective of researches in AI, we advocate the thesis of the “emergence” of the cognitive functions and abilities, an emergence of intelligence. This process would start with “connexionist” process to conclude with superior “symbolic” functions in a complex retroaction illustrated by the dynamical diagram here below.

 

Diagram

 

 

Thanks to the introduction of the time factor, the diagram constitutes the translation in a dynamical and more concrete structure of the Matrix. It allows us to make a connexion between the MI-g synthesis and its possible use in research in AI.

So the will to enlarge the field of testing intelligence by including Gardner’s additional types of intelligence leads us to emphasize the distributed nature of intelligence, at once physiologically and environmentally.

So, we would like to underline the essential role of a spine in the development and the functioning of intelligence. Here is a pre-treatment of the info that will determine further treatment data. In the same way, the configuration of the sense organs constitute an important factor in the filtering of the stimuli, all the more when one remembers that the nasal fossae, for example, are constituted of neurons.

 

The maturation process needs “delays”, and more specifically “time-lag delays”. Let’s note the introduction of an intermediate memory between the short- and the long-term memories: the “mid-term memory”. Indeed, we don’t that the working memory can be limited to about twenty seconds.

 

As product, G is the emergence of a process of maturation.

Let us note that with Spearman, it is not the product of one particular entity/diagram but of the correlations between the scores of multiple entities. Thus, g is a product.

But as general,  genetic factor, g must rest above, at the origin of this process. This schizophrenic nature must explain the incompleteness of the orthodox model.

 

 

If Spearman is right, it must be possible to design a perfectly culture-free test that will give, under ideal conditions of testing, a perfect measure of the intelligence of whole world population and if the distribution is really normal, it corresponds to a Bell curve. But Spearman could not ignore specific factors in testing tools. That means that in one or in another way, cultural or idiosyncratic bias cannot be avoided.

 

Creativity and logico-divergence

 

In addition to the addition of some types of mental activities to the field of testable abilities, we would like to focus on two essential ways for the different abilities to express themselves: creativity and logico-divergence.

One of the biological bases of creativity has been identified. While non creative people shut out the most part of the incoming stimuli from the surrounding environment through the process called “latent inhibition”, creative people are much more likely to take unconsciously into account the kind of stimuli that experience has shown to be irrelevant to specific needs. This low level of latent inhibition particularly contribute to original thinking when combined with high IQ and good working memory.

This is all the more interesting that not only creativity gains full credit as intellectual activity but it even surpasses more common cognitive abilities usually tested in IQ tests.

 

As for the logico-divergence, we will define it as the expression of the own limits of logic by logic itself; when and where logic reaches its limits through the notions of infinity, auto reference and recurrence that lead to stake into abyss, nest of process.

In an IQ test, it qualifies an item made of free culture-free associations that requires, to be solved, an excellent sense of observation and basic notions of logic.

 

Creativity and logico-divergence are often intimately linked and we are convinced that a program integrating them will successfully pass the Turing test.

 

 

Enlarged definition of intelligence

 

Below is an attempt of extension of the definition of intelligence going beyond the notion of “pure performance” in order to include factors such as artistic-aesthetic, sensitivity, creativity, empathy, consciousness, wisdom… The idea is the following: since it is currently impossible to elaborate a precise enough definition (both simplest and most general), the most reasonable and rigorous attitude consists in including a maximum of the probable components rather than in making the bet that intelligence can be reduced to very narrow abilities.

 

-          Ability to selectively register information? (Ability to just register info? Not so, since inanimate matter can do it as well)

-          Ability to use information (registered in sensory, short [cache], mid [ram], or long [hard] term memory)

-          Ability to search information in order to:

    . solve an existing problem (no new info)

-          Ability to produce information in order to:

    . solve an existing problem (new info)

    . formulate a new problem & solve it (two new information)

-          Faculty of wondering what the ability to selectively register, to search, to use and to create information is

-          Faculty of wondering what intelligence is

-          Faculty of being conscious of this questioning

-          Faculty of infinite auto-reflexive questioning (infinitely recursive meta-process)

 

Ability to see, memorize, use, create connections between basic homogeneous and/or heterogeneous set of codes in order to create and/or solve problems or without any precise [conscious] intention.

 

Bi-conclusions

 

The Matrix and the Diagram constitute a kind of synthesis of the four approaches of intelligence:

-          the psychometric approach: IQ testing

-          the developmental approach: Piaget (intelligence as interaction between an inner maturation and experiments with the environment)-Vygotsky (social conception of intelligence)

-          differential approach: Sternberg triarchic theory-Gardner multiple intelligence theory

-          cognitive approach: AI; model = computer; strategies of resolution of problems

 

HIQH

 

As stated in the introduction, in the politic of the High IQ for Humanity NGO, the MI-g synthesis must lead to the elaboration of enlarged testing tools and to the development of new kind of assessment. But it is not really our purpose here.

 

Beyond consciousness

 

What interests us more particularly is the conditions under which an artificial intelligence similar or superior to that of the human being can be elaborated. An AI that would propose to… the fruit of its researches, human being being auto disqualified, the equivalent of the Turing test!

As there is no particular reason that the process of natural evolution stops with the emergence of human consciousness, it is more than probable that it currently continues through the most complex known entity in the eyes of the human brain: the… human brain. It must constitute the ground of the already realized or next “qualitative jump” in the universal evolutive history!

Some searchers don’t only intend to build machines with intelligence similar to that of human beings, some of them would like to make them more intelligent. In both cases, it seems inevitable to use the finest and most performing components: the human brain anatomy.

Here are the minimal conditions:

 

-          spine: physiological distribution

 

-          five senses: physiological distribution

 

-          quantum level precision

 

-          social interactions: environmental distribution

 

This essay would deserve much longer developments.

 

 

 

Bibliography

Anderson, M. (1992) Intelligence and Development - A Cognitive Theory, 1st ed, Oxford:Blackwell Press

Carroll, J.B. (1993) Human Cognitive Abilities: A Survey of Factor-analytic Studies. New York: Cambridge University Press.

Francis Galton First Edition, Macmillan, 1883    Second Edition, Dent & Dutton (Everyman), 1907    http://www.mugu.com/galton/books/human-faculty/text/html/index.html

Gardner, H. (1993) Frames of Mind - The Theory of Multiple Intelligences, 2nd ed, New York:Basic Books

Gardner, H. (1993) INTELLIGENCE IN SEVEN STEPS http://www.newhorizons.org/future/Creating_the_Future/crfut_gardner.html

Gardner, H.; Kornhaber, M. and Wake, W. (1996) Intelligence - Multiple Perspectives, 1st ed, London:Harcourt - Brace

Goleman, D. (1996) Emotional Intelligence, 1st ed, G.B.:Bloomsbury Publishing

Gould, S.J. (1997) The Mismeasure of Man, 1st ed, G.B.:Penguin Books

Guilford, J.P. (1967) The Nature of Human Intelligence, New York: McGraw-Hill

Gustafsson, J. -E. (1984) A Unifying Model for the Structure of Intellectual Abilities, Intelligence, 8, 179-203.

Horn, J. and Cattell, R.B. (1966) Refinement and test of the theory of fluid and crystallised general intelligences. Journal of Educational Psychology, 57(5), 253-270.

Jensen, Arthur R. (2000)  IQ Tests, Psychometric and Chronometric G, and Achievement, Psycoloquy: 11,#14 http://psycprints.ecs.soton.ac.uk/archive/00000014/

Kline, P. (1994) Intelligence : The Psychometric View, 1st ed, London:Routledge

Piaget, J. (1967) The Psychology Of Intelligence, 5th ed, London:Routledge & Kegan Paul Ltd

Spearman, C. (1904) General Intelligence, objectively determined and measured. American Journal Of Psychology, 15, 201-293. http://psychclassics.yorku.ca/Spearman/

Sternberg, R.J. (1985) Beyond IQ: A triarchic theory of human intelligence, Cambridge:Cambridge University Press

Thurstone, L.L. (1938) Primary Mental Abilities, Chicago: University of Chicago Press.

Vernon. P.E. (1956) The Measurement of Abilities. London: University of London Press.

 

 

 

 

My Articles

 

ytidrusbAbsolute

Manifesto of the Manifest

(rough copy of loose ideas)

Beyond Consciousness

 

 Temporal Collision Conjecture

Time Travel, Logic and Speculation

(Noesis)

Time Travel, Logic and Speculation II 

(COJ

 

Les consciences absolues

 

 zzChess

Bishop exchange

 

POWER-SCALE   

Hyper-TesT

  Concep-T

  916

StatS

gG Model * MI-g synthesis (rough copy)

 

ZFC Axiomatic Set Theory