https://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 https://www.ingber.com/smni00_g_factor.ps.gz This is a gzipped PostScript file. (See https://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. +=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+= 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. +=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+= 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. REFERENCES Graham, R. (1977) Covariant formulation of non-equilibrium statistical thermodynamics. Z. Physik B26:397-405. Ingber, L. (1981) Towards a unified brain theory. J. Social Biol. Struct. 4:211-224. Ingber, L. (1982) Statistical mechanics of neocortical interactions. I. Basic formulation. Physica D 5:83-107. https://www.ingber.com/smni82_basic.ps.gz Ingber, L. (1983) Statistical mechanics of neocortical interactions. Dynamics of synaptic modification. Phys. Rev. A 28:395-416. https://www.ingber.com/smni83_dynamics.ps.gz Ingber, L. (1984) Statistical mechanics of neocortical interactions. Derivation of short-term-memory capacity. Phys. Rev. A 29:3346-3358. https://www.ingber.com/smni84_stm.ps.gz Ingber, L. (1985a) Statistical mechanics of neocortical interactions. EEG dispersion relations. IEEE Trans. Biomed. Eng. 32:91-94. https://www.ingber.com/smni85_eeg.ps.gz Ingber, L. (1985b) Statistical mechanics of neocortical interactions: Stability and duration of the 7+-2 rule of short-term-memory capacity. Phys. Rev. A 31:1183-1186. https://www.ingber.com/smni85_stm.ps.gz Ingber, L. (1986) Statistical mechanics of neocortical interactions. Bull. Am. Phys. Soc. 31:868. Ingber, L. (1991) Statistical mechanics of neocortical interactions: A scaling paradigm applied to electroencephalography. Phys. Rev. A 44:4017-4060. https://www.ingber.com/smni91_eeg.ps.gz Ingber, L. 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[Invited commentary on Dynamics of the brain at global and microscopic scales: Neural networks and the EEG, by J.J. Wright and D.T.J. Liley.] https://www.ingber.com/smni96_nonlinear.ps.gz Ingber, L. (1996b) Statistical mechanics of neocortical interactions: Multiple scales of EEG, In: Frontier Science in EEG: Continuous Waveform Analysis (Electroencephal. clin. Neurophysiol. Suppl. 45), ed. R.M. Dasheiff & D.J. Vincent. Elsevier, 79-112. [Invited talk to Frontier Science in EEG Symposium, New Orleans, 9 Oct 1993.] https://www.ingber.com/smni96_eeg.ps.gz Ingber, L. (1997) Statistical mechanics of neocortical interactions: Applications of canonical momenta indicators to electroencephalography. Phys. Rev. E 55:4578-4593. https://www.ingber.com/smni97_cmi.ps.gz Ingber, L. (1998) Statistical mechanics of neocortical interactions: Training and testing canonical momenta indicators of EEG. Mathematical Computer Modelling 27:33-64. https://www.ingber.com/smni98_cmi_test.ps.gz Ingber, L. (2000) Statistical mechanics of neocortical interactions: EEG eigenfunctions of short-term memory. Behavioural and Brain Sciences (to be published). [Invited commentary on Toward a Quantitative Description of Large-Scale Neo-Cortical Dynamic Function and EEG, by P.L. Nunez.] https://www.ingber.com/smni00_eeg_stm.ps.gz Ingber, L. & Nunez, P.L. (1990) Multiple scales of statistical physics of neocortex: Application to electroencephalography. Mathematica. Computer Modelling 13:83-95. Ingber, L. & Nunez, P.L. (1995) Statistical mechanics of neocortical interactions: High resolution path-integral calculation of short- term memory. Phys. Rev. E 51:5074-5083. https://www.ingber.com/smni95_stm.ps.gz Jensen, A. (1998). The g Factor: The Science of Mental Ability. Praeger Jensen, A. (1999). Precis of: "The g Factor: The Science of Mental Ability" PSYCOLOQUY 10 (023). ftp://ftp.princeton.edu/pub/harnad/Psycoloquy/1999.volume.10/ psyc.99.10.023.intelligence-g-factor.1.jensen http://www.cogsci.soton.ac.uk/cgi/psyc/newpsy?10.023 Langouche, F., Roekaerts, D. & Tirapegui, E. (1982) Functional Integration and Semiclassical Expansions. Reidel, Dordrecht, The Netherlands. Miller, G.A. (1956) The magical number seven, plus or minus two. Psychol. Rev. 63:81-97. Mountcastle, V.B., Andersen, R.A. & Motter, B.C. (1981) The influence of attentive fixation upon the excitability of the light-sensitive neurons of the posterior parietal cortex. J. Neurosci. 1:1218-1235. Murdock, B.B., Jr. (1983) A distributed memory model for serial-order information. Psychol. Rev. 90:316-338. Nunez, P.L. (1981) Electric Fields of the Brain: The Neurophysics of EEG. Oxford University Press, London. Nunez, P.L. (1989) Towards a physics of neocortex, Vol. 2, In: Advanced Methods of Physiological System Modeling, ed. V.Z. Marmarelis. Plenum, 241-259. Nunez, P.L. (1995) Neocortical Dynamics and Human EEG Rhythms. Oxford University Press, New York, NY. Nunez, Paul L. (2000) Toward a Quantitative Description of Large Scale Neocortical Dynamic Function and EEG Behavioral and Brain Sciences 23(3) (in press). ftp://ftp.princeton.edu/pub/harnad/BBS/.WWW/bbs.nunez.html Nunez, P.L. & Srinivasan, R. (1993) Implications of recording strategy for estimates of neocortical dynamics with electroencephalography. Chaos 3:257-266. Risken, H. (1989) The Fokker-Planck Equation: Methods of Solution and Applications. Springer-Verlag, Berlin. Spearman, C. (1904). 'General intelligence, objectively determined and measured.' American Journal of Psychology, 15, 201-293. Spearman, C. (1927). The abilities of man: Their nature and measurement. New York: Macmillan. Zhang, G. & Simon, H.A. (1985) STM capacity for Chinese words and idioms: Chunking and acoustical loop hypotheses. Memory & Cognition 13:193-201. +=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+= 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 presented at the 9th Biennial Convention of the International Society for the Study of Individual Differences, Vancouver, B.C., Canada, July, 1999. 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. Journal of Educational Psychology, 1962, 123-131. Jensen, A.R. (1987a). Individual differences in the Hick paradigm. In P.A. Vernon (Ed.), Speed of information- processing and intelligence,(pp. 101-175). Norwood, NJ: Ablex. Jensen, A.R. (1987b). Process differences and individual differences in some cognitive tasks. Intelligence, 11, 107- 136. Jensen, A.R. (1998). The g factor: The science of mentalability. Westport, CT: Praeger. Jensen, A.R. (1999). Precis of: "The g Factor: The Science of Mental Ability" PSYCOLOQUY 10(23). 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 Jensen, A.R., & Figueroa, R.A. (1975). Forward and backward digit span interaction with race and IQ: Predictions from Jensen's theory. Journalof Educational Psychology, 67, 882-893. 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. +=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+= $Id: smni00_jensen.txt,v 1.9 2000/08/07 14:56:25 ingber Exp ingber $