http://www.ingber.com/smni00_jensen.txt
This is the background for an invited commentary on
The g Factor: The Science of Mental Ability by Arthur Jensen.
%A L. Ingber
%T Statistical mechanics of neocortical interactions:
Reaction time correlates of the g factor
%J Psycholoquy
%D 2000
%O URL http://www.ingber.com/smni00_g_factor.ps.gz
This is a gzipped PostScript file. (See
http://www.ingber.com/Z_gz_ps_tar_shar.txt
for some links to information on gzip and PostScript utilties.)
My commentary, along with a score of others, and Jensen's replies,
can be read on
http://www.cogsci.soton.ac.uk/cgi/psyc/ptopic?topic=intelligence-g-factor
in HTML format.
Below are ASCII-formatted versions of Jensen's Abstract to his Precis,
followed by my commentary, then his reply to my commentary. Equations in
my paper can best be viewed from the HTML or PostScript versions above.
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THE G FACTOR: THE SCIENCE OF MENTAL ABILITY
Precis of Jensen on Intelligence-g-Factor
[Praeger, 1998 xiv + 648 pp. ISBN 0-275-96103-6 ISSN 1063-2158]
Arthur R. Jensen
Graduate School of Education
University of California, Berkeley
nesnejanda@AOL.Com
Abstract
The g factor is the highest-order common factor that can be
extracted in a hierarchical factor analysis from a large battery
of diverse tests of various cognitive abilities. It is the most
important psychometric construct in the study of individual
differences in human cognitive abilities. Since its discovery by
Spearman in 1904, the g factor has become so firmly established as
a major psychological construct in terms of psychometric and
factor analytic criteria that further research along these lines
is very unlikely either to disconfirm the construct validity of g
or to add anything essentially new to our understanding of it. In
fact, g, unlike any of the primary, or first-order, factors
revealed by factor analysis, cannot be described in terms of the
knowledge content of cognitive test items, or in terms of skills,
or even in terms of theoretical cognitive processes. It is not
essentially a psychological or behavioral variable, but a
biological one, a property of the brain. But although not itself a
cognitive ability, g is what causes positive correlations among
individual differences in performance, even on cognitive tasks
that differ greatly with respect to sensory motor modality, brain
modularity, and learned cognitive skills and knowledge. The g
factor derived from conventional nonspeeded psychometric tests
shows higher correlations than any other factors independent of g
with various measures of information-processing efficiency, such
as working memory capacity, choice and discrimination reaction
times, and perceptual speed. A test's g loading is the best
predictor of its heritability and its sensitivity to inbreeding
depression. Psychometric g also has more direct biological
correlates than any other independent source of test variance, for
example brain size, brain evoked potentials, nerve conduction
velocity, and the brain's glucose metabolic rate during cognitive
activity. The ultimate arbiter among various "theories of
intelligence" must be the physical properties of the brain itself.
The current frontier of g research is the investigation of the
anatomical and physiological features of the brain that cause g.
Research has reached the point at which the only direction left in
which to go is that presaged by Spearman himself, who wrote that
the final understanding of g must "come from the most profound and
detailed direct study of the human brain in its purely physical
and chemical aspects" (1927, p.403).
Keywords
behavior genetics, cognitive modelling, evoked potentials, evolutionary
psychology, factor analysis, g factor, heritability, individual differences,
intelligence, IQ, neurometrics, psychometrics, psychophyiology, skills,
Spearman, statistics
------------------------------------------------------------------------
AUTHOR'S RATIONALE FOR SOLICITING COMMENTARY
The g factor arises from the empirical fact that scores on a large
variety of independently designed tests of extremely diverse
cognitive abilities all turn out to be positively correlated with
one another. The g factor appears to be a biological property of
the brain, highly correlated with measures of
information-processing efficiency, such as working memory capacity,
choice and discrimination reaction times, and perceptual speed. It
is highly heritable and has many biological correlates, including
brain size, evoked potentials, nerve conduction velocity, and
cerebral glucose metabolic rate during cognitive activity. It
remains to investigate and explain its neurobiological basis.
Commentary is invited from psychometricians, statisticians,
geneticists, neuropsychologists, psychophysiologists, cognitive
modellers, evolutionary psychologists and other specialties
concerned with cognitive abilities, their measurement, and their
cognitive and neurobiological basis.
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STATISTICAL MECHANICS OF NEOCORTICAL INTERACTIONS:
REACTION TIME CORRELATES OF THE g FACTOR
Book Review of Jensen on Intelligence-g-Factor
ingber@ingber.com, ingber@alumni.caltech.edu
Abstract
A statistical mechanics of neuronal interactions (SMNI) is
explored as providing some substance to a physiological basis for
the g factor. Some specific elements of SMNI, previously used to
develop a theory of short-term memory (STM) and a model of
electroencephalography (EEG), are key to providing this basis.
Specifically, Hick's Law, an observed linear relationship between
reaction time (RT) and the information storage of STM, in turn
correlated to a RT-g relationship, is derived.
Keywords
short term memory; nonlinear systems; statistical models
------------------------------------------------------------------------
I. INTRODUCTION
I.I. CONTEXT OF REVIEW
1. My specific interest in reviewing "The g Factor" by Arthur Jensen (1998,
1999) is to see whether some anatomical and/or physiological processes at
the columnar level of neuronal interactions can account for the g factor.
2. From circa 1978 to the present, a series of papers on the statistical
mechanics of neocortical interactions (SMNI) has been developed to model
columns and regions of neocortex, spanning mm to cm of tissue. Most of these
papers have dealt explicitly with calculating properties of short-term
memory (STM) and scalp EEG in order to test the basic formulation of this
approach. SMNI derives aggregate behaviour of experimentally observed
columns of neurons from statistical electrical-chemical properties of
synaptic interactions. While not useful to yield insights at the single
neuron level, SMNI has demonstrated its pability to describe large-scale
properties of short-term memory and electroencephalographic (EEG)
systematics [FOOTNOTE 1].
I.II. ERRORS IN SIMPLE STATISTICAL APPROACHES
3. One must assume that Jensen faced very difficult problems in choosing
just how much technical detail to give in his broad text, e.g., discussing
the extent of the expert statistical analyses that have been brought to bear
upon the g factor. However, I do see reason to criticise some general
features of the simple statistical algorithms presented, especially those
that overlap with my own mathematical and physics expertise.
The simple approach to factor analysis initiated on page 23,
X = t + e {1}
ftp://www.cogsci.soton.ac.uk/pub/psycoloquy/1999.volume.10/Pictures/ing1.html
where e is the residual "noise" of fitting the variable X to the independent
variable t, has some serious flaws not addressed by additional material
presented thereafter. For example, in this context, I find the arguments in
the long footnote 16 on pages 101-103 unconvincing, but I agree with its
conclusion:
"But the question is mainly of scientific interest, and a really
satisfactory answer ... will become possible only as part and
parcel of a comprehensive theory of the nature of g. ... The
distribution of obtained measurements should conform to the
characteristics of the distribution dictated by theoretical
considerations."
I think it clear that any such "theoretical considerations" must themselves
be well tested against experimental evidence at each spatial-temporal scale
purported to be modelled.
4. It must be understood that a quite explicit model of the real world is
being assumed here -- that of a simple normal Gaussian process. The real
issue in many physical/biological systems is that most often the real
multivariable world is much more aptly described by something like
X = tX(X,Y) + sX(X,Y) eX {2}
ftp://www.cogsci.soton.ac.uk/pub/psycoloquy/1999.volume.10/Pictures/ing2.html
Y = tY(X,Y) + sY(X,Y) eY {3}
ftp://www.cogsci.soton.ac.uk/pub/psycoloquy/1999.volume.10/Pictures/ing3.html
When the t's and s's are constants, then simple statistics can determine
their values and cross-correlations between the s's.
5. Simple statistical methods can be useful even if the t's are relatively
simple quasi-linear parametrised functions. Such simple methods fail quite
miserably if the ts are highly nonlinear functions, especially if care is
not taken to use sophisticated optimisation algorithms. The most terrible
flaws often occur because, for the sake of making life easier for the
analyst, any model faithful to the real system is butchered and sacrificed,
and the s's are taken to be constants. There can be a lot of "signal" in the
(generally nonlinear) functionality of the "noise" terms, and no amount of
fancy quasi-linear statistical analysis can substitute for a proper
theory/model of the real system.
6. In general, the proper treatment of the problem is quite difficult, which
is of course no excuse for poor treatment. The solution in many disciplines
is to go a level or two deeper in some reductionist sense, to develop
plausible models at the top scale being analysed. Indeed, this was the call
I saw and responded to in the advertisement for reviewers of Jensen's (1999)
work:
"Commentary is invited from psychometricians, statisticians,
geneticists, neuropsychologists, psychophysiologists, cognitive
modellers, evolutionary psychologists and other specialties
concerned with cognitive abilities, their measurement, and their
cognitive and neurobiological basis."
In this context, the successes of SMNI and its agreement with general STM
observations are due to processing stochastic nonlinearities of the forms
described above. Attempts to avoid dealing with these nonlinearities,
derived from lower-level synaptic and neuronal activity, have not been as
successful as SMNI in detailing STM (Ingber, 1995b).
II. SMNI DESCRIPTION OF SHORT-TERM MEMORY (STM)
6. Since the early 1980s, a series of papers on the statistical mechanics of
neocortical interactions (SMNI) has been developed to model columns and
regions of neocortex, spanning mm to cm of tissue. Most of these papers have
dealt explicitly with calculating properties of short-term memory (STM) and
scalp EEG in order to test the basic formulation of this approach [FOOTNOTE
2]. This model was the first physical application of a nonlinear
multivariate calculus developed by other mathematical physicists in the late
1970s (Graham, 1977; Langouche et al, 1982).
II.I. STATISTICAL AGGREGATION
7. Studies of SMNI have detailed a physics of short-term memory and
(short-fibre contribution to) EEG phenomena (Ingber, 1984), in terms of MG
firings, where G represents E or I, ME represents contributions to columnar
firing from excitatory neurons, and MI represents contributions to columnar
firing from inhibitory neurons. About 100 neurons comprise a minicolumn
(twice that number in the visual cortex); while a macrcolumn is comprised of
around 1000 minicolumns. A mesocolumn is developed by SMNI to reflect the
convergence of short-ranged (as well as long-ranged) interactions of
macrocolumnar input on minicolumnar structures, in terms of synaptic
interactions taking place among neurons (about 10,000 synapses per neuron).
The SMNI papers give more details on this derivation.
8. In this SMNI development, a Lagrangian is explicitly defined from a
derived probability distribution of mesocolumnar firings in terms of the MG
and electric potential variables, PHIG. Several examples have been given to
illustrate how the SMNI approach is complementary to other models. For
example, a mechanical string model was first discussed as a simple analogue
of neocortical dynamics to illustrate the general ideas of top down and
bottom up interactions (Nunez, 1989; Nunez & Srinivasan, 1993). SMNI was
applied is to this simple mechanical system, illustrating how macroscopic
variables are derived from small-scale variables (Ingber & Nunez, 1990).
[See also Nunez 2000.]
II.II. STM STABILITY AND DURATION
9. To the extent that SMNI offers stochastic bounds for STM phenomena during
focused selective attention, SMNI provides a model of STM. This 7+-2 "rule"
is well verified by SMNI for acoustical STM (Ingber, 1984; Ingber, 1985b;
Ingber, 1994), transpiring on the order of tenths of a second to seconds,
limited to the retention of 7+-2 items (Miller, 1956). The 4+-2 "rule" is
also well verified by SMNI for visual or semantic STM, which typically
require longer times for rehearsal in a hypothesised articulatory loop of
individual items, with a capacity that appears to be limited to 4+-2 (Zhang
& Simon, 1985). SMNI has detailed these constraints in models of auditory
and visual cortex (Ingber, 1984; Ingber, 1985b; Ingber, 1994; Ingber &
Nunez, 1995).
10. Another interesting phenomenon of STM capacity explained by SMNI is the
primacy versus recency effect in STM serial processing (Ingber, 1985b),
wherein first-learned items are recalled most error-free, with last-learned
items still more error-free than those in the middle (Murdock, 1983). The
basic assumption is that a pattern of neuronal firing which persists for
many tau cycles, tau on the order of 10 msec, is a candidate for the storage
of the "memory" of activity that gave rise to this pattern. If several
firing patterns can simultaneously exist, then there is the capability that
several memories can be stored. The short-time probability distribution
derived for the neocortex is the primary tool in the search for such firing
patterns. The highest peaks of this probability distribution can be more
readily accessed than the others, and they sustain their patterns against
fluctuations more accurately. The more recent memories or newer patterns may
be presumed to be those having synaptic parameters which have been more
recently tuned and/or more actively rehearsed.
11. It has been noted that experimental data on velocities of propagation of
long-ranged fibres (Nunez, 1981; Nunez, 1995) and derived velocities of
propagation of information across local minicolumnar interactions (Ingber,
1982) yield comparable time scales of interactions across minicolumns of
tenths of a second. Therefore, such phenomena as STM likely are inextricably
dependent on interactions at local and global scales.
II.III. SMNI CORRELATES OF STM AND EEG
12. Previous SMNI studies have detailed that maximal numbers of attractors
lie within the physical firing space of MG. This is consistent with
experimentally observed capacities of auditory and visual short- term memory
(STM), when a "centering" mechanism is enforced by shifting background noise
in synaptic interactions, itself consistent with experimental observations
under conditions of selective attention (Mountcastle et al, 1981; Ingber,
1984; Ingber, 1985b; Ingber, 1994; Ingber & Nunez, 1995). This leads to all
attractors of the short-time distribution lying along a diagonal line in MG
space, effectively defining a narrow parabolic trough containing these most
likely firing states. This essentially collapses the 2 dimensional MG space
down to a 1 dimensional space of most importance. Thus, the predominant
physics of short-term memory and of (short-fiber contribution to) EEG
phenomena takes place in a narrow "parabolic trough" in MG space, roughly
along a diagonal line (Ingber, 1984).
13. Using the power of this formal structure, sets of EEG and evoked
potential data, collected to investigate genetic predispositions to
alcoholism, were fitted to an SMNI model to extract brain "signatures" of
short-term memory (Ingber, 1997; Ingber, 1998). These results give
quantitative support for an intuitive picture portraying neocortical
interactions as having common algebraic or physics mechanisms across quite
disparate spatial scales and functional or behavioural phenomena, i.e.,
describing interactions among neurons, columns of neurons, and regional
masses of neurons.
14. For future work, I have described how bottom-up neocortical models can
be developed into eigenfunction expansions of probability distributions
appropriate to describe short-term memory in the context of scalp EEG
(Ingber, 2000). The mathematics of eigenfunctions are similar to the
top-down eigenfunctions developed by some EEG analysts, although they have
different physical manifestations. The bottom-up eigenfunctions are at the
local mesocolumnar scale, whereas the top- down eigenfunctions are at the
global regional scale. However, these approaches have regions of substantial
overlap (Ingber & Nunez, 1990; Ingber, 1995a), and future studies may expand
top-down eigenfunctions into the bottom-up eigenfunctions, yielding a model
of scalp EEG that is ultimately expressed in terms of columnar states of
neocortical processing of attention and short-term memory.
15. An optimistic outcome of future work might be that these EEG
eigenfunctions, baselined to specific STM processes of individuals, could be
a more direct correlate to estimates of g factors.
II.IV. COMPLEXITY IN EEG
16. In Chapter 6, "Biological Correlates of g," Jensen puts these issues in
perspective: "First, psychometric tests were never intended or devised to
measure anything other than behavioural variables... at this point most
explanations are still conjectural." Most of the chapter, however, falls
back on similar too-simple statistical models of correlations between
measured variables and behavioural characteristics.
17. The sections on "Biological Correlates of g" dealing with EEG recordings
are incomplete, and appear superficial in comparison with most of the other
parts of the book. The introduction of "complexity" as a possible correlate
to IQ is based on faddish studies that do not have any theoretical or
experimental support (Nunez, 1995). If such support does emerge, it will
most likely be developed on the basis of more complete stochastic models and
much better EEG recordings.
III. SMNI STM CORRELATES OF THE G FACTOR
III.I. HIGH VS LOW G CATEGORIES
18. The outline of test categories giving rise to high versus low g loadings
on page 35 provides me with some immediate candidates for further
investigations of a physiological basis for the g factor. I think a good
working hypothesis is that these two categories are marked by having the
high g loadings more correlated than the low g loadings to statistical
interactions among the peaks of the probability distributions described
above in the context of SMNI's theory of STM. The high g categories clearly
require relatively more processing of several items of information than do
the low g categories.
19. This seems to be a correlation similar to that drawn by Spearman (1904,
1927), as described by Jensen, in having "education of relations" and
"education of correlates" more highly correlation with high g categories
than the "apprehension of experience".
III.II. MECHANISMS OF HIGH G CATEGORIES
20. From the SMNI perspective, control of selective attention generally is
highly correlated with high utilisation of STM, e.g., to tune the "centering
mechanism". This seems similar to Spearman's correlation of "mental energy"
with high g categories.
21. There are several mechanisms that could be used to distinguish how well
individuals might perform on high g category tasks. The ability to control
the "centering mechanism" is required to sustain a high degree of
statistical processes of multiple most probable states of information. The
particular balance of general chemical-electrical activity directly shapes
the distribution of most probable states. For some tasks, processing across
relatively more of these most probable states might be required; for other
tasks processing among larger focused peaks of most probable states may be
more important.
III.III. HICK'S LAW - LINEARITY OF RT VS STM INFORMATION
22. The SMNI approach to STM gives a reasonable foundation to discuss RT and
items in STM storage. These previous calculations support the intuitive
description of items in STM storage as peaks in the 10-millisecond
short-time (Ingber, 1984; Ingber, 1985b) as well as the several-second
long-time (Ingber, 1994; Ingber & Nunez, 1995) conditional probability
distribution of correlated firings of columns of neurons. These columnar
firing states of STM tasks were also correlated to EEG observations of
evoked potential activities (Ingber, 1997; Ingber, 1998). This distribution
is explicitly calculated by respecting the nonlinear synaptic interactions
among all possible combinatoric aggregates of columnar firing states
(Ingber, 1982; Ingber, 1983).
23. The RT necessary to "visit" the states under control during the span of
STM can be calculated as the mean time of "first passage" between multiple
states of this distribution, in terms of the probability P as an outer
Integral dt (sum) over refraction times of synaptic interactions during STM
time t, and an inner Integral Integral dM (sum) taken over the mesocolumnar
firing states M (Risken, 1989) which has been explicitly calculated to be
within observed STM time scales (Ingber, 1984),
RT = - Integral dt t Integral dM dP/dt {4}
ftp://www.cogsci.soton.ac.uk/pub/psycoloquy/1999.volume.10/Pictures/ing4.html
24. As demonstrated by previous SMNI STM calculations, within tenths of a
second, the conditional probability of visiting one state from another P,
can be well approximated by a short-time probability distribution expressed
in terms of the previously mentioned Lagrangian L as
P = 1/sqrt(2 pi dt g) exp(-Ldt) {5}
ftp://www.cogsci.soton.ac.uk/pub/psycoloquy/1999.volume.10/Pictures/ing5.html
where g is the determinant of the covariance matrix of the distribution P in
the space of columnar firings. This expression for RT can be approximately
rewritten as
RT = K Integral dt Integral dM P lnP {6}
ftp://www.cogsci.soton.ac.uk/pub/psycoloquy/1999.volume.10/Pictures/ing6.html
where K is a constant when the Lagrangian is approximately constant over the
time scales observed. Since the peaks of the most likely M states of P are
to a very good approximation well-separated Gaussian peaks (Ingber, 1984),
these states can be treated as independent entities under the Integral. This
last expression is essentially the "information" content weighted by the
time during which processing of information is observed.
25. The calculation of the heights of peaks corresponding to most likely
states includes the combinatoric factors of their possible columnar
manifestations, as well as the dynamics of synaptic and columnar
interactions. In the approximation that we only consider the combinatorics
of items of STM as contributing to most likely states measured by P, i.e.,
that P measures the frequency of occurrences of all possible combinations of
these items, we obtain Hick's Law, the observed linear relationship of RT
versus STM information storage, first discussed by Jensen in Chapter 8. For
example, when the bits of information are measured by the probability P
being the frequency of accessing a given number of items in STM, the bits of
information in 2, 4 and 8 states are given as approximately multiples of ln2
of items, i.e., ln2, 2ln2 and 3ln2 respectively. (The limit of taking the
logarithm of all combinations of independent items yields a constant times
the sum over pi lnpi, where pi is the frequency of occurrence of item i.)
IV. CONCLUSION
26. Jensen's book provides the motivation to explore a more fundamental
basis of the g factor. I have examined this work in the narrow focus of some
specific elements of SMNI, previously used to develop a theory of STM and a
model of EEG. I have focused on how bottom-up SMNI models can be developed
into eigenfunction expansions of probability distributions appropriate to
describe STM. This permits RT to be calculated as an expectation value over
the STM probability distribution of stored states, and in the good
approximation of such states being represented by well separated Gaussian
peaks, this yield the observed linear relationship of RT versus STM
information storage. This SMNI STM approach also suggests several other
studies that can be performed in the context of examining an underlying
basis for the g factor.
FOOTNOTES
[1] See Ingber, 1982; Ingber, 1983; Ingber, 1984; Ingber, 1991; Ingber,
1994; Ingber, 1995a; Ingber & Nunez, 1995; Ingber, 1996a; Ingber, 1997.
[2] See Ingber, 1981; Ingber, 1982; Ingber,1983; Ingber, 1984; Ingber,
1985a; Ingber, 1985b; Ingber, 1986; Ingber & Nunez, 1990; Ingber, 1991;
Ingber, 1992; Ingber, 1994; Ingber & Nunez, 1995; Ingber, 1995a; Ingber,
1995b; Ingber, 1996b; Ingber, 1997; Ingber, 1998.
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A "SIMPLEST CASES" APPROACH TO EXPLORING THE NEURAL BASIS OF G
Reply to Ingber on Jensen on Intelligence-g-Factor
Arthur R. Jensen
Educational Psychology
School of Education
University of California
Berkeley, CA 94720-1670
nesnejanda@aol.com
Abstract
Ingber (1999) proposes EEG models and methods for exploring the
brain physiology responsible for g. It could well be the case that
the more ideal measurements of g that are based on a large battery
of diverse mental tests is too broad, global, or spread through
too wide an area of the brain to allow analytical study by
neurological techniques. A successful use of the kinds of
neuroscience techniques suggested by Ingber, and probably other
techniques such as fMRI and PET, may depend upon a simplification
of the behavioral side of the equation by using highly reliable
measurements of individual differences in a number of test
paradigms, each of which isolates a single pair of simple ability
variables whose correlation is part of the g nexus.
------------------------------------------------------------------------
1. Although I am not an expert in EEG technology and neurophysiology and
therefore am not qualified to evaluate Ingber's (1999) theoretical and
methodological proposals for advancing our understanding of the neural basis
of g, I do appreciate his interest and expertise on the subject. They have
enabled me to reconsider how an experimental psychologist might best
contribute to the application of Ingber's approach to the neurological study
of psychometric g. A number of points in Ingber's commentary remind me of
certain aspects of my work as an experimental psychologist long before I
became interested in g in its own right. Had the thoughts stimulated by
Ingber's paper occurred to me at the time I wrote "The g Factor" (Jensen,
1998; 1999), I would have elaborated more on what I am about to say here.
The seeds of this idea were present in the book but they had not sprouted
until now. It might be a worthless idea in relation to Ingber's suggestions
but my lack of expertise in his specialty area makes it impossible for me to
reject the idea. It will be up to specialists in neuroscience to judge
whether or not what follows here is heading up a blind alley.
2. Because g ideally represents the highest order distillate of the
individual differences variance common to performance on many tasks
representing many apparently different abilities (therefore implying various
neural systems in different regions of the brain), it may be virtually
impossible to discover the neural basis of the covariances between all the
[n(n-1)]/2 pairs of n behavioral variables from which g is, so to speak,
"distilled" by looking for g itself. What may have to be done in order to
discover more than just correlations between psychometric g and individual
differences in some neural measure, such as evoked potential variables, is
to focus on the neurological aspect of certain well-chosen single pairs of
simple variables in the whole correlational nexus that yields g. One would
seek pairs of ability tasks on which individual differences are rather
highly correlated -- tasks that theories or models borrowed from either
cognitive psychology or cognitive neuroscience (or both) claim involve
neural processes, pathways, regions of the brain, or different "cognitive
components." The research question, then, would be: Why is there a high
correlation between performances on two tasks that factually (or
theoretically) involve different brain functions (although some functions
may be identical for both tasks)?
3. I am reminded of a study I did some 30 years ago (Jensen, 1971), which
illustrates the kind of paradigm I have in mind, although I know virtually
nothing about the neurological circuits or processes involved in the
performance since I was measuring only behavior. It was a study of
individual differences in short-term memory (STM) in which the subjects
(university undergraduates) were repeatedly tested on both auditory and
visual memory span for digits. The tests (administered by a laboratory
apparatus), as well as the recording of the subjects' responses and the
pacing of the stimuli (digits), were identical across the auditory and
visual paradigms. Through repeated testing, the reliability of the
measurements was in the high .90s. The order of administering the visual and
auditory tasks was counterbalanced.
4. I had expected to find that some individuals would perform better on
visual than on auditory STM while others would show the opposite pattern.
What I found, however, was a disattenuated correlation of unity between the
two modes of presentation. After correcting for the very slight errors of
measurement, subjects maintained the same rank order of ability on both
tasks yet the overall performance for each of the modalities differed in
their means and in their interactions with different experimental conditions
(e.g., an interposed 10 seconds delay between presentation of the digit
series and recall). So here we have two tasks with clearly different sensory
input mechanisms and pathways which result in significant mean differences
and interactions with experimental manipulations and yet show no
interactions with individual differences. Consequently, they would have
identical correlations with some other g loaded variable such as IQ with
which, in fact, they are correlated. What is the locus of the
visual/auditory STM correlation? What is the mechanism or process that makes
them perfectly correlated? If we knew that, we would have accounted for one
small bit of the g nexus. But that discovery might generalize to other
behavioral measures.
5. Another laboratory study (Jensen, 1987b), in which individual differences
could be measured with very high reliability, had similar properties. Using
the Sternberg and the Neisser reaction time (RT) paradigms, the study
involved scanning a digit series held in STM (Sternberg) and visually
scanning a series of digits presented on the screen (Neisser) to detect
either the presence or absence of a single "probe" digit. These paradigms
are identical but opposite, since the single probe digit appears either
immediately after (Sternberg) or before (Neisser) the 3-second presentation
of the digit series (consisting of 1 to 7 digits). The subject merely
presses a YES or a NO button to indicate the presence or absence of the
probe digit in the presented series and the subject's RT is measured.
Cognitive theorists have used these paradigms as examples of different
cognitive components being involved in the two tasks. The Sternberg memory
scan task puts a high premium on STM, whereas the Neisser visual scan task
does not. Interestingly, the RT measures derived from the two paradigms show
significant mean differences which also interact with experimental
conditions, but individual differences (corrected for attenuation) are
perfectly correlated across the two paradigms and both have the same
correlation with IQ.
6. How can this be explained, given that these tasks supposedly involve
different "cognitive components?". Of course, the Vocabulary and Block
Designs subtests of the Wechsler scales must involve extremely different
"cognitive components," yet they are highly correlated. But this is my
point: there are too many ways that Vocabulary and Block Designs differ to
allow the basis of their correlation to be easily identified. It should
probably be easier to identify the locus of the common factor if the tasks
differ in only one (or a very few) features.
7. Another equally simple paradigm is that of forward and backward digit
span (FDS and BDS). This is surprisingly different from the two previous
examples because individual differences in FDS and BDS are not very highly
correlated, even when corrected for attenuation, and FDS is only about half
as correlated with IQ as is BDS (Jensen & Figueroa, 1975). Everything is
exactly the same in FDS and BDS tests except that in BDS the subject must
recall the digits in the reverse order from that in which they were
presented by the examiner. Individuals who can consistently recall, say, 8
digits in the FDS test, are found to differ reliably in the number of digits
they can recall in BDS, and this FDS-BDS difference is positively related to
their level of g derived from test batteries that contain no tests of STM.
8. Ingber (1999) views the Hick paradigm as a tool along the lines I have
suggested. Its facets for experimental manipulation and the highly reliable
measurement of g-related individual differences are advantages similar to
those I have mentioned in connections with the STM paradigms (Jensen,
1987a). Other promising speed of information-processing paradigms that show
correlations with broad psychometric tests are inspection time (for
comprehensive references see Jensen, 1998, pp. 221-223) and -- the most
recent candidate -- the modified blink reflex (Smyth, et al., 1999).
9. We might even hearken back to Francis Galton (1822-1911) himself. His
supposedly discredited hypothesis that there is a general factor among
various modalities of sensory discrimination and the idea that this common
factor reflects general mental ability, or psychometric g, has proved to be
correct after all (Acton & Schroeder, 1999; Li et al.,1998). What is the
common cause of these correlations? We cannot rest until we know the answer
at the level of neurophysiology, unless at this point someone can prove that
the cause of these correlations does not involve the brain. Ingber sees a
technical means for pursuing research on g in the direction that the
Galton-Spearman paradigm is inevitably headed, and I hope he will continue
to bring his expertise in neuroscience to help advance this endeavour.
EDITOR'S NOTE: Owing to an enumeration error, the Ingber commentary
to which professor Jensen refers here has been reassigned thread
number 35 instead of the number 13 that it had been assigned upon
publication in 1999.
REFERENCES
Acton, G.S., & Schroeder, D.H. (1999). Color discrimination as related to
other aptitudes: An analysis of the Farnsworth-Munsell100-huetest. Paper
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Ingber, L. (1999). Statistical mechanics of neocortical interactions:
Reaction time correlates of the g factor. PSYCOLOQUY 10(68)
ftp://ftp.princeton.edu/pub/harnad/Psycoloquy/1999.volume.10/
psyc.99.10.068.intelligence-g-factor.35.ingber
http://www.cogsci.soton.ac.uk/cgi/psyc/newpsy?10.068
Jensen, A.R. (1971). Individual differences in visual and auditory memory.
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ftp://www.cogsci.soton.ac.uk/pub/psycoloquy//1999.volume.10/
psyc.99.10.023.intelligence-g-factor.1.jensen
http://www.cogsci.soton.ac.uk/cgi/psyc/newpsy?10.023
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Li, S-C, Jordanova, M., & Lindenberger, U. (1998). From good senses to good
sense: A link between tactile information processing and intelligence.
Intelligence, 26, 99-122.Smyth, M., Anderson, M., & Hammond, G. (1999). The
modified blink reflex and individual differences in speed of
processing.Intelligence,27, 13-35.
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