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”. |
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 |
-
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 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 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 Sternberg, R.J. (1985) Beyond IQ:
A triarchic theory of human intelligence, Cambridge:Cambridge University
Press |
My Articles
(rough copy of loose ideas)
Time Travel, Logic and
Speculation
(Noesis)
Time
Travel, Logic and Speculation II
(COJ)
gG Model * MI-g
synthesis (rough copy)