Molecular machines are a class of molecules typically
described as an assembly of a discrete number of molecular components
intended to produce mechanical movements in response to specific
stimuli, mimicking macromolecular devices such as switches and motors. Naturally occurring or biological molecular machines are responsible for vital living processes such as DNA replication and ATP synthesis. Kinesins and ribosomes are examples of molecular machines, and they often take the form of multi-protein complexes.
For the last several decades, scientists have attempted, with varying
degrees of success, to miniaturize machines found in the macroscopic
world.
Several
definitions describe a "molecular machine" as a class of molecules
typically described as an assembly of a discrete number of molecular
components intended to produce mechanical movements in response to
specific stimuli. The expression is often more generally applied to
molecules that simply mimic functions that occur at the macroscopic
level. A few prime requirements for a molecule to be considered a "molecular
machine" are: the presence of moving parts, the ability to consume
energy, and the ability to perform a task. Molecular machines differ from other stimuli-responsive compounds that can produce motion (such as cis-trans isomers) in their relatively larger amplitude of movement (potentially due to chemical reactions) and the presence of a clear external stimulus to regulate the movements (as compared to random thermal motion). Piezoelectric, magnetostrictive,
and other materials that produce a movement due to external stimuli on a
macro-scale are generally not included, since despite the molecular
origin of the motion the effects are not useable on the molecular scale.
This definition generally applies to synthetic molecular
machines, which have historically gained inspiration from the naturally
occurring biological molecular machines (also referred to as
"nanomachines"). Biological machines are considered to be nanoscale
devices (such as molecular proteins) in a living system that convert various forms of energy to mechanical work in order to drive crucial biological processes such as intracellular transport, muscle contractions, ATP generation and cell division.
History
What
would be the utility of such machines? Who knows? I cannot see exactly
what would happen, but I can hardly doubt that when we have some control
of the arrangement of things on a molecular scale we will get an
enormously greater range of possible properties that substances can
have, and of the different things we can do.
Biological molecular machines have been known and studied for decades
given their vital role in sustaining life, and have served as
inspiration for synthetically designed systems with similar useful
functionality. The advent of conformational analysis, or the study of conformers
to analyze complex chemical structures, in the 1950s gave rise to the
idea of understanding and controlling relative motion within molecular
components for further applications. This led to the design of
"proto-molecular machines" featuring conformational changes such as
cog-wheeling of the aromatic rings in triptycenes. By 1980, scientists could achieve desired conformations using external
stimuli and utilize this for different applications. A major example is
the design of a photoresponsive crown ether containing an azobenzene unit, which could switch between cis and trans isomers on exposure to light and hence tune the cation-binding properties of the ether. In his seminal 1959 lecture There's Plenty of Room at the Bottom, Richard Feynman alluded to the idea and applications of molecular devices designed artificially by manipulating matter at the atomic level. This was further substantiated by Eric Drexler during the 1970s, who developed ideas based on molecular nanotechnology such as nanoscale "assemblers", though their feasibility was disputed.
The
first example of an artificial molecular machine (a switchable
molecular shuttle). The positively charged ring (blue) is initially
positioned over the benzidine unit (green), but shifts to the biphenol unit (red) when the benzidine gets protonated (purple) as a result of electrochemicaloxidation or lowering of the pH.
Though these events served as inspiration for the field, the actual
breakthrough in practical approaches to synthesize artificial molecular
machines (AMMs) took place in 1991 with the invention of a "molecular
shuttle" by Sir Fraser Stoddart. Building upon the assembly of mechanically linked molecules such as catenanes and rotaxanes as developed by Jean-Pierre Sauvage in the early 1980s, this shuttle features a rotaxane with a ring that can move across an "axle" between two ends or possible binding sites (hydroquinone units). This design realized the well-defined motion of a molecular unit across the length of the molecule for the first time. In 1994, an improved design allowed control over the motion of the ring by pH variation or electrochemical methods, making it the first example of an AMM. Here the two binding sites are a benzidine and a biphenol
unit; the cationic ring typically prefers staying over the benzidine
ring, but moves over to the biphenol group when the benzidine gets
protonated at low pH or if it gets electrochemically oxidized. In 1998, a study could capture the rotary motion of a decacyclene molecule on a copper-base metallic surface using a scanning tunneling microscope. Over the following decade, a broad variety of AMMs responding to various stimuli were invented for different applications. In 2016, the Nobel Prize in Chemistry was awarded to Sauvage, Stoddart, and Bernard L. Feringa for the design and synthesis of molecular machines.
Over the past few decades, AMMs have diversified rapidly and their design principles, properties, and characterization methods have been outlined more clearly. A major starting point for the design
of AMMs is to exploit the existing modes of motion in molecules. For instance, single bonds can be visualized as axes of rotation, as can be metallocene complexes. Bending or V-like shapes can be achieved by incorporating double bonds, that can undergo cis-trans isomerization in response to certain stimuli (typically irradiation with a suitable wavelength), as seen in numerous designs consisting of stilbene and azobenzene units. Similarly, ring-opening and -closing reactions such as those seen for spiropyran and diarylethene can also produce curved shapes. Another common mode of movement is the circumrotation of rings relative
to one another as observed in mechanically interlocked molecules
(primarily catenanes). While this type of rotation can not be accessed
beyond the molecule itself (because the rings are confined within one
another), rotaxanes can overcome this as the rings can undergo
translational movements along a dumbbell-like axis. Another line of AMMs consists of biomolecules such as DNA and proteins as part of their design, making use of phenomena like protein folding and unfolding.
Some
common types of motion seen in some simple components of artificial
molecular machines. a) Rotation around single bonds and in sandwich-like
metallocenes. b) Bending due to cis-trans
isomerization. c) Translational motion of a ring (blue) between two
possible binding sites (red) along the dumbbell-like rotaxane axis
(purple). d) Rotation of interlocked rings (depicted as blue and red
rectangles) in a catenane.
AMM designs have diversified significantly since the early days of the field. A major route is the introduction of bistability
to produce molecular switches, featuring two distinct configurations
for the molecule to convert between. This has been perceived as a step
forward from the original molecular shuttle which consisted of two
identical sites for the ring to move between without any preference, in a
manner analogous to the ring flip in an unsubstituted cyclohexane. If these two sites are different from each other in terms of features like electron density, this can give rise to weak or strong recognition sites as in biological systems — such AMMs have found applications in catalysis and drug delivery.
This switching behavior has been further optimized to acquire useful
work that gets lost when a typical switch returns to its original state.
Inspired by the use of kinetic control to produce work in natural processes, molecular motors are designed to have a continuous energy influx to keep them away from equilibrium to deliver work.
Various energy sources are employed to drive molecular machines
today, but this was not the case during the early years of AMM
development. Though the movements in AMMs were regulated relative to the random
thermal motion generally seen in molecules, they could not be controlled
or manipulated as desired. This led to the addition of
stimuli-responsive moieties in AMM design, so that externally applied
non-thermal sources of energy could drive molecular motion and hence
allow control over the properties. Chemical energy (or "chemical fuels")
was an attractive option at the beginning, given the broad array of reversible chemical reactions (heavily based on acid-base chemistry) to switch molecules between different states. However, this comes with the issue of practically regulating the
delivery of the chemical fuel and the removal of waste generated to
maintain the efficiency of the machine as in biological systems. Though
some AMMs have found ways to circumvent this, more recently waste-free reactions such based on electron transfers or isomerization have gained attention (such as redox-responsive viologens). Eventually, several different forms of energy (electric, magnetic, optical and so on) have become the primary energy sources used to power AMMs,
even producing autonomous systems such as light-driven motors.
Types
Various AMMs are tabulated below along with indicative images:
Many macromolecular machines are found within cells, often in the form of multi-protein complexes. Examples of biological machines include motor proteins such as myosin, which is responsible for muscle contraction, kinesin, which moves cargo inside cells away from the nucleus along microtubules, and dynein, which moves cargo inside cells towards the nucleus and produces the axonemal beating of motile cilia and flagella.
"[I]n effect, the [motile cilium] is a nanomachine composed of perhaps
over 600 proteins in molecular complexes, many of which also function
independently as nanomachines ... Flexible linkers allow the mobile protein domains connected by them to recruit their binding partners and induce long-range allostery via protein domain dynamics." Other biological machines are responsible for energy production, for example ATP synthase which harnesses energy from proton gradients across membranes to drive a turbine-like motion used to synthesise ATP, the energy currency of a cell. Still other machines are responsible for gene expression, including DNA polymerases for replicating DNA, RNA polymerases for producing mRNA, the spliceosome for removing introns, and the ribosome for synthesising proteins. These machines and their nanoscale dynamics are far more complex than any molecular machines that have yet been artificially constructed.
Biological machines have potential applications in nanomedicine. For example, they could be used to identify and destroy cancer cells.. Molecular nanotechnology is a speculative subfield of nanotechnology regarding the possibility of engineering molecular assemblers, biological machines which could re-order matter at a molecular or atomic scale. Nanomedicine would make use of these nanorobots,
introduced into the body, to repair or detect damages and infections,
but these are considered to be far beyond current capabilities.
Research and applications
Advances in this area are inhibited by the lack of synthetic methods. In this context, theoretical modeling has emerged as a pivotal tool to understand the self-assembly or -disassembly processes in these systems.
Possible applications have been demonstrated for AMMs, including those integrated into polymeric, liquid crystal, and crystalline systems for varied functions. Homogenous catalysis is a prominent example, especially in areas like asymmetric synthesis, utilizing noncovalent interactions and biomimetic allosteric catalysis. AMMs have been pivotal in the design of several stimuli-responsive
smart materials, such as 2D and 3D self-assembled materials and nanoparticle-based systems, for versatile applications ranging from 3D printing to drug delivery.
AMMs are gradually moving from the conventional solution-phase
chemistry to surfaces and interfaces. For instance, AMM-immobilized
surfaces (AMMISs) are a novel class of functional materials consisting
of AMMs attached to inorganic surfaces forming features like
self-assembled monolayers; this gives rise to tunable properties such as
fluorescence, aggregation and drug-release activity.
Most of these "applications" remain at the proof-of-concept
level. Challenges in streamlining macroscale applications include
autonomous operation, the complexity of the machines, stability in the
synthesis of the machines and the working conditions.
The g factor is a construct developed in psychometric investigations of cognitive abilities and human intelligence. It is a variable that summarizes positive correlations
among different cognitive tasks, reflecting the assertion that an
individual's performance on one type of cognitive task tends to be
comparable to that person's performance on other kinds of cognitive
tasks. The g factor typically accounts for 40 to 50 percent of the between-individual performance differences on a given cognitive test, and composite scores ("IQ scores") based on many tests are frequently regarded as estimates of individuals' standing on the g factor. The terms IQ, general intelligence, general cognitive ability, general mental ability, and simply intelligence are often used interchangeably to refer to this common core shared by cognitive tests. However, the g factor itself is a mathematical construct indicating the level of observed correlation between cognitive tasks. The measured value of this construct depends on the cognitive tasks
that are used, and little is known about the underlying causes of the
observed correlations.
The existence of the g factor was originally proposed by the English psychologist Charles Spearman
in the early years of the 20th century. He observed that children's
performance ratings, across seemingly unrelated school subjects, were
positively correlated,
and reasoned that these correlations reflected the influence of an
underlying general mental ability that entered into performance on all
kinds of mental tests. Spearman suggested that all mental performance
could be conceptualized in terms of a single general ability factor,
which he labeled g, and many narrow task-specific ability factors. Soon after Spearman proposed the existence of g, it was challenged by Godfrey Thomson, who presented evidence that such intercorrelations among test results could arise even if no g-factor existed.
Traditionally, research on g has concentrated on psychometric investigations of test data, with a special emphasis on factor analytic approaches. However, empirical research on the nature of g has also drawn upon experimental cognitive psychology and mental chronometry, brain anatomy and physiology, quantitative and molecular genetics, and primate evolution. Research in the field of behavioral genetics has shown that the construct of g is heritable in measured populations. It has a number of other biological correlates, including brain size.
It is also a significant predictor of individual differences in many
social outcomes, particularly in education and employment.
Critics have contended that an emphasis on g is misplaced and entails a devaluation of other important abilities. Some scientists, including Stephen J. Gould, have argued that the concept of g is a merely reified construct rather than a valid measure of human intelligence.
Concept
Spearman's correlation matrix for six measures of school performance. All the correlations are positive, the positive manifold phenomenon. The bottom row shows the g loadings of each performance measure.
Classics
French
English
Math
Pitch
Music
Classics
–
French
.83
–
English
.78
.67
–
Math
.70
.67
.64
–
Pitch discrimination
.66
.65
.54
.45
–
Music
.63
.57
.51
.51
.40
–
g
.958
.882
.803
.750
.673
.646
Subtest intercorrelations in a sample of Scottish subjects who completed the WAIS-R
battery. The subtests are Vocabulary, Similarities, Information,
Comprehension, Picture arrangement, Block design, Arithmetic, Picture
completion, Digit span, Object assembly, and Digit symbol. The bottom
row shows the g loadings of each subtest.
V
S
I
C
PA
BD
A
PC
DSp
OA
DS
V
–
S
.67
-
I
.72
.59
-
C
.70
.58
.59
-
PA
.51
.53
.50
.42
-
BD
.45
.46
.45
.39
.43
-
A
.48
.43
.55
.45
.41
.44
–
PC
.49
.52
.52
.46
.48
.45
.30
-
DSp
.46
.40
.36
.36
.31
.32
.47
.23
-
OA
.32
.40
.32
.29
.36
.58
.33
.41
.14
-
DS
.32
.33
.26
.30
.28
.36
.28
.26
.27
.25
-
g
.83
.80
.80
.75
.70
.70
.68
.68
.56
.56
.48
Correlations between mental tests
In a famous research paper published in 1904, English psychologist Charles Spearman
observed that children's performance measures across seemingly
unrelated school subjects were positively correlated. The consistent
finding of universally positive correlation matrices
of mental test results (or the "positive manifold"), despite large
differences in tests' contents, has been described as "arguably the most
replicated result in all psychology".
Using factor analysis
or related statistical methods, it is possible to identify a single
common factor that can be regarded as a summary variable characterizing
the correlations between all the different tests in a test battery.
Spearman referred to this common factor as the general factor, or simply g. (By convention, g is always printed as a lower case italic.) Mathematically, the g factor is a source of variance among individuals, which means that one cannot meaningfully speak of any one individual's mental abilities consisting of g or other factors to any specified degree. One can only speak of an individual's standing on g (or other factors) compared to other individuals in a relevant population.
Different tests in a test battery may correlate with (or "load onto") the g factor of the battery to different degrees. These correlations are known as g loadings. An individual test taker's g factor score, representing their relative standing on the g factor in the total group of individuals, can be estimated using the g loadings. Full-scale IQ scores from a test battery will usually be highly correlated with g factor scores, and they are often regarded as estimates of g. For example, the correlations between g factor scores and full-scale IQ scores from David Wechsler's tests have been found to be greater than .95. The terms IQ, general intelligence, general cognitive ability, general
mental ability, or simply intelligence are frequently used
interchangeably to refer to the common core shared by cognitive tests.
The g loadings of mental tests are always positive and
usually range between .10 and .90, with a mean of about .60 and a
standard deviation of about .15. Raven's Progressive Matrices is among the tests with the highest g loadings, around .80. Tests of vocabulary and general information are also typically found to have high g loadings. However, the g loading of the same test may vary somewhat depending on the composition of the test battery.
The complexity of tests and the demands they place on mental manipulation are related to the tests' g
loadings. For example, in the forward digit span test the subject is
asked to repeat a sequence of digits in the order of their presentation
after hearing them once at a rate of one digit per second. The backward
digit span test is otherwise the same except that the subject is asked
to repeat the digits in the reverse order to that in which they were
presented. The backward digit span test is more complex than the forward
digit span test, and it has a significantly higher g loading. Similarly, the g
loadings of arithmetic computation, spelling, and word reading tests
are lower than those of arithmetic problem solving, text composition,
and reading comprehension tests, respectively.
Test difficulty and g loadings are distinct concepts that
may or may not be empirically related in any specific situation. Tests
that have the same difficulty level, as indexed by the proportion of
test items that are failed by test takers, may exhibit a wide range of g loadings. For example, tests of rote memory have been shown to have the same level of difficulty but considerably lower g loadings than many tests that involve reasoning.
Spearman's research on intelligence originated from his research on
measurement. He studied Francis Galton's theories of intelligence and
was intriuged by why Galton failed to find associations between
different performance metrics and common indicators of intelligence. Spearman posited that the tests Galton used contained substantial measurement error and were unreliable–the same person obtained a different score upon being tested again. Spearman developed procedures to correct correlation coefficients for
various influences to estimate the "true relationship", including a
procedure to disattenuate correlations.
These ideas regarding true scores, measurement error and procedures for
correcting correlations form the basis for what is now known as classical test theory.
When he applied these procedures to the data he had gathered for
measures of intelligence and what he called sensory discrimination
ability, he obtained correlations approaching 1.
The concept of "general intelligence" first arose from Spearman's
1904 paper "'General Intelligence', Objectively Determined and
Measured", where he applied his new statistical methods for correcting
correlations to tests of ability to propose a two-factor theory of
intelligence.
Based on the observation that tests of ability typically positively
correlate with each other, he proposed that these tests all measure the
same thing—general intelligence—and that individual tests measure a
combination of two factors: 'general intelligence' (g), common to all tests, and a 'specific ability' (s), specific to one test.
This concept of "general intelligence" was supposed to provide an
undisputed definition of intelligence which could be described as
"objectively determined and measured". There were several corollaries of his theory, such as the claim that it is "possible to rank order the measures in terms of their g-to-s ratio". The most important was Spearman's law of tetrad differences,
demonstrated by Spearman in 1924. It states that the pairwise products
of two sets of correlations are equal–that is, their difference is zero.
For four traits labeled 1, 2, 3, 4, this is r13⋅r24-r23r14=0. This is equivalent to the prediction that for a correlation matrix
statistically removing the common factor "g" would yield a matrix of
partial correlations that are all 0.
Early critics
The first psychologist to raise problems with Spearman's work was Cyril Burt, who noted that mental effort was not factored into his analysis. Burt marshalled a larger set of data and showed that more factors than a
single general factor were required to explain the correlations: the
law of tetrad differences was not satisfied by the data. It
was shown that correlations between certain pairs of tests were much
higher than expected on Spearman's theory that their only common factor
was general intelligence. Spearman knew about these problems as early as 1906, but attempted to
dismiss the criticism by proposing that these higher than expected
correlations were because the tests weren't meaningfully distinct.
In subsequent years, many other psychologists showed a wider array of
factors was needed to explain various sets of data: Spearman's
two-factory theory didn't explain the correlations.
Other psychologists like Thomson provided alternative
explanations for the same phenomena that he used to support the concept
with what is now known as sampling theory. Thomson accepted Spearman's data and methodology of factor analysis, but interpreted the results differently. He proposed that the mind was composed of innumerable independent
bonds or units and any test sampled some subset of these bonds.Simultaneous to Spearman's development of his theory of g was an alternative theory from Godfrey Thomson and Edward Thorndike
who proposed that the positive intercorrelation of tests (positive
manifold) was compatible with a theory of many common factors. Thorndike
argued that performance on cognitive tests drew from numerous cognitive
processes and that different cognitive tests draw from these different
processes and can produce positive correlations as observed in test
batteries.
Despite these issues, Spearman's theory garnered early support. Lewis Terman,
Stanford professor of psychology, drew upon Spearman's "general
intelligence factor" when he revised Alfred Binet's intelligence scales
to develop the Stanford-Binet Scales for American children.
The Abilities of Man
Spearman's 1927 book The Abilities of Man
attempted to provide a comprehensive account of human intelligence,
responding to his critics and compiling evidence in favor of his theory.
He now argued that general intelligence was a reflection of "mental
energy" that flowed throughout the brain, but different neural systems
served as "mental engines" that explain the specific factors.
He also refined his concept of "g", not as equivalent to as concrete
entity or synonym for intelligence, but as a magnitude that is
identified as the common factor that underlies all mental abilities, and
could be identified with tests of the tetrad equation. By now, he reluctantly accepted the existence of group factors in addition to his general factor and specific factors.
Following recognition that the arguments in his book did not
sufficiently respond to critics evidence that not all data satisfied the
tetrad condition, he put forth a different theory: that g was reflected
in every ability measure and that this was proven by the positive
correlations between tests of abilities, known as the "indifference of
the indicator".This shift between theories has been noted as transforming "g" from a
falsifiable hypothesis to an unfalsifiable result of mathematical
necessity.
Another early criticism raised of the g theory was factor indeterminacy. In a review of Spearman's Ability of Man, Edwin Wilson pointed out that Spearman's theory did not define g uniquely because it proposed more independent factors than observed psychological tests.
and it was possible to generate a different set of factor scores for a
set of students that reproduces the same correlation matrix.
In response to these criticisms, some psychologists tried to
rescue Spearman's theory by producing batteries of tests that would
reflect g without introducing specific factor overlap that produces common factors other than g.
Invariably these attempts failed and psychologists acknowledged that
many common factors were needed to explain correlations between tests,
as many as one third as many factors as tests in a battery.
Later theories
In 1938, Louis Thurstone developed a theory of intelligence contrary to both Spearman and Thomson. He, like Thomson, proposed that there were separate factors that were unrelated to each other, but he proposed a smaller set of just seven primary mental abilities. Thurstone developed the method of multiple factor analysis to identify the number of factors needed to explain a matrix of observed correlations. His early results using orthogonal factors identified as many as 13
factors, which he believed conclusively refuted Spearman's theory,
though a reanalysis of his results showed that Spearman's g theory could
explain the data as well.
Later Thurstone abandoned the idea of completely independent factors
and posited correlated factors, analyzing test data using oblique factor
analysis but left him without a strong criticism of Spearman's theory. After the 1940s, studies using Thurstone's methods proliferated, identifying increasing numbers of mental abilities. One example was Joy Paul Guilford's
"Structure-of-Intellectual" model which proposed 3 facets of ability -
contents, products, operations - that can be composed in different ways
to obtain 150 different abilities. Lloyd Humphries argued that following Thurstone's publications,
"psychometrists and factor analysts have tended to lose sight of the
general factor in intelligence".
By 1941, Raymond Cattell, who had worked with Spearman, proposed a two common factor theory of intelligence.
Cattell's theory proposed two high level factors: Gc (crystallized
intelligence) that reflected learned knowledge and general information
and Gf (fluid intelligence) that closely resembled Spearman's
conceptualization of g.
Since proposing these factors, Cattell and his student John Horn
proposed a number of other 'general factors' or 'broad factors' like Gs
(visual inspection speed), Ga (auditory thinking), Gv (visual-spatial
reasoning), Gq (quantitative reasoning), Gr (fluency in recall). Their theory is what Arthur Jensen calls a "truncated hierarchy", as it
extracts many factors but not one unitary "general" factor on top of
the hierarchy.
Jensen
Jensen mounted defenses of the g-factor from its many critics over the course of his career. His first major work How Much Can We Boost IQ and Scholastic Achievement?
described Spearman's development of the concept of "general
intelligence" in support of what Urbach calls the "hard core of the
hereditarian program". In the dispute among psychometricians over general intelligence, Jensen fiercely argued for its existence, presenting it as a fact that no self-respecting psychometrician could deny.
In that article, Jensen presented a hierarchical model of intelligence,
where abilities operate two levels: Level I and Level II. In his later work The g Factor: The Science of Mental Ability,
Jensen offered an extensive synthesis of a large body of research to
argue that g is a legitimate scientific construct based in human biology
with far-reaching effects on human life.
In some ways, Arthur Jensen resuscitated Spearman's g theory, but his arguments reflect a marked shift from Spearman's theory of factors to its replacement with principal components.
Measurement
An
illustration of Spearman's two-factor intelligence theory. Each small
oval is a hypothetical mental test. The blue areas correspond to
test-specific variance (s), while the purple areas represent the variance attributed to g.
Factor analysis
is a family of mathematical techniques that can be used to represent
correlations between intelligence tests in terms of a smaller number of
variables known as factors. The purpose is to simplify the correlation
matrix by using hypothetical underlying factors to explain the patterns
in it. When all correlations in a matrix are positive, as they are in
the case of IQ, factor analysis will yield a general factor common to
all tests. The general factor of IQ tests is referred to as the g factor, and it typically accounts for 40 to 50 percent of the variance in IQ test batteries. The presence of correlations between many widely varying cognitive tests has often been taken as evidence for the existence of g, but mathematically the correlations do not provide any more or less support for the existence of g than for the existence of multiple factors of intelligence.
Charles Spearman developed factor analysis in order to study
correlations between tests. Initially, he developed a model of
intelligence in which variations in all intelligence test scores are
explained by only two kinds of variables: first, factors that are
specific to each test (denoted s); and second, a g factor
that accounts for the positive correlations across tests. This is known
as Spearman's two-factor theory. Later research based on more diverse
test batteries than those used by Spearman demonstrated that g alone could not account for all correlations between tests. Specifically, it was found that even after controlling for g, some tests were still correlated with each other. This led to the postulation of group factors
that represent variance that groups of tests with similar task demands
(e.g., verbal, spatial, or numerical) have in common in addition to the
shared g variance.
An illustration of John B. Carroll's three stratum theory,
an influential contemporary model of cognitive abilities. The broad
abilities recognized by the model are fluid intelligence (Gf),
crystallized intelligence (Gc), general memory and learning (Gy), broad
visual perception (Gv), broad auditory perception (Gu), broad retrieval
ability (Gr), broad cognitive speediness (Gs), and processing speed
(Gt). Carroll regarded the broad abilities as different "flavors" of g.
Through factor rotation,
it is, in principle, possible to produce an infinite number of
different factor solutions that are mathematically equivalent in their
ability to account for the intercorrelations among cognitive tests.
These include solutions that do not contain a g factor. Thus
factor analysis alone cannot establish what the underlying structure of
intelligence is. In choosing between different factor solutions,
researchers have to examine the results of factor analysis together with
other information about the structure of cognitive abilities.
There are many psychologically relevant reasons for preferring factor solutions that contain a g
factor. These include the existence of the positive manifold, the fact
that certain kinds of tests (generally the more complex ones) have
consistently larger g loadings, the substantial invariance of g factors across different test batteries, the impossibility of constructing test batteries that do not yield a g factor, and the widespread practical validity of g as a predictor of individual outcomes. The g
factor, together with group factors, best represents the empirically
established fact that, on average, overall ability differences between individuals are greater than differences among abilities within individuals, while a factor solution with orthogonal factors without g obscures this fact. Moreover, g appears to be the most heritable component of intelligence. Research utilizing the techniques of confirmatory factor analysis has also provided support for the existence of g.
A g factor can be computed from a correlation matrix of
test results using several different methods. These include exploratory
factor analysis, principal components analysis
(PCA), and confirmatory factor analysis. Different factor-extraction
methods produce highly consistent results, although PCA has sometimes
been found to produce inflated estimates of the influence of g on test scores.
While the existence of g as a statistical regularity is
well-established and uncontroversial among experts, there is no
consensus as to what causes the positive intercorrelations. Several
explanations have been proposed.
Mental energy or efficiency
Charles
Spearman reasoned that correlations between tests reflected the
influence of a common causal factor, a general mental ability that
enters into performance on all kinds of mental tasks. However, he
thought that the best indicators of g were those tests that reflected what he called the eduction of relations and correlates, which included abilities such as deduction, induction,
problem solving, grasping relationships, inferring rules, and spotting
differences and similarities. Spearman hypothesized that g was
equivalent with "mental energy". However, this was more of a
metaphorical explanation, and he remained agnostic about the physical
basis of this energy, expecting that future research would uncover the
exact physiological nature of g.
Following Spearman, Arthur Jensen maintained that all mental tasks tap into g to some degree. According to Jensen, the g
factor represents a "distillate" of scores on different tests rather
than a summation or an average of such scores, with factor analysis
acting as the distillation procedure. He argued that g
cannot be described in terms of the item characteristics or information
content of tests, pointing out that very dissimilar mental tasks may
have nearly equal g loadings. Wechsler similarly contended that g is not an ability at all but rather some general property of the brain. Jensen hypothesized that g corresponds to individual differences in the speed or efficiency of the neural processes associated with mental abilities. He also suggested that given the associations between g and elementary cognitive tasks, it should be possible to construct a ratio scale test of g that uses time as the unit of measurement.
Sampling theory
The so-called sampling theory of g, originally developed by Edward Thorndike and Godfrey Thomson,
proposes that the existence of the positive manifold can be explained
without reference to a unitary underlying capacity. According to this
theory, there are a number of uncorrelated mental processes, and all
tests draw upon different samples of these processes. The inter
correlations between tests are caused by an overlap between processes
tapped by the tests. Thus, the positive manifold arises due to a measurement problem, an
inability to measure more fine-grained, presumably uncorrelated mental
processes.
It has been shown that it is not possible to distinguish statistically between Spearman's model of g and the sampling model; both are equally able to account for inter correlations among tests. The sampling theory is also consistent with the observation that more complex mental tasks have higher g
loading, because more complex tasks are expected to involve a larger
sampling of neural elements and therefore have more of them in common
with other tasks.
Some researchers have argued that the sampling model invalidates g as a psychological concept, because the model suggests that g
factors derived from different test batteries simply reflect the shared
elements of the particular tests contained in each battery rather than a
g that is common to all tests. Similarly, high correlations
between different batteries could be due to them measuring the same set
of abilities rather than the same ability.
Critics have argued that the sampling theory is incongruent with
certain empirical findings. Based on the sampling theory, one might
expect that related cognitive tests share many elements and thus be
highly correlated. However, some closely related tests, such as forward
and backward digit span, are only modestly correlated, while some
seemingly completely dissimilar tests, such as vocabulary tests and
Raven's matrices, are consistently highly correlated. Another
problematic finding is that brain damage frequently leads to specific
cognitive impairments rather than a general impairment one might expect
based on the sampling theory.
Mutualism
The "mutualism" model of g
proposes that cognitive processes are initially uncorrelated, but that
the positive manifold arises during individual development due to mutual
beneficial relations between cognitive processes. Thus there is no
single process or capacity underlying the positive correlations between
tests. During the course of development, the theory holds, any one
particularly efficient process will benefit other processes, with the
result that the processes will end up being correlated with one another.
Thus similarly high IQs in different persons may stem from quite
different initial advantages that they had. Critics have argued that the observed correlations between the g loadings and the heritability coefficients of subtests are problematic for the mutualism theory.
Raymond Cattell, a student of Charles Spearman's, modified the unitary g factor model and divided g into two broad, relatively independent domains: fluid intelligence (Gf) and crystallized intelligence (Gc). Gf
is conceptualized as a capacity to figure out novel problems, and it is
best assessed with tests with little cultural or scholastic content,
such as Raven's matrices. Gc can be thought of as consolidated
knowledge, reflecting the skills and information that an individual
acquires and retains throughout his or her life. Gc is dependent
on education and other forms of acculturation, and it is best assessed
with tests that emphasize scholastic and cultural knowledge. Gf can be thought to primarily consist of current reasoning and problem solving capabilities, while Gc reflects the outcome of previously executed cognitive processes.
The rationale for the separation of Gf and Gc was to explain individuals' cognitive development over time. While Gf and Gc have been found to be highly correlated, they differ in the way they change over a lifetime. Gf tends to peak at around age 20, slowly declining thereafter. In contrast, Gc
is stable or increases across adulthood. A single general factor has
been criticized as obscuring this bifurcated pattern of development.
Cattell argued that Gf reflected individual differences in the efficiency of the central nervous system. Gc was, in Cattell's thinking, the result of a person "investing" his or her Gf in learning experiences throughout life.
Cattell, together with John Horn, later expanded the Gf-Gc model to include a number of other broad abilities, such as Gq (quantitative reasoning) and Gv (visual-spatial reasoning). While all the broad ability factors in the extended Gf-Gc model are positively correlated and thus would enable the extraction of a higher order g
factor, Cattell and Horn maintained that it would be erroneous to posit
that a general factor underlies these broad abilities. They argued that
g factors computed from different test batteries are not invariant and would give different values of g, and that the correlations among tests arise because it is difficult to test just one ability at a time.
However, several researchers have suggested that the Gf-Gc model is compatible with a g-centered understanding of cognitive abilities. For example, John B. Carroll's three-stratum model of intelligence includes both Gf and Gc together with a higher-order g factor. Based on factor analyses of many data sets, some researchers have also argued that Gf and g are one and the same factor and that g factors from different test batteries are substantially invariant provided that the batteries are large and diverse.
Theories of uncorrelated abilities
Several
theorists have proposed that there are intellectual abilities that are
uncorrelated with each other. Among the earliest was L.L. Thurstone who created a model of primary mental abilities
representing supposedly independent domains of intelligence. However,
Thurstone's tests of these abilities were found to produce a strong
general factor. He argued that the lack of independence among his tests
reflected the difficulty of constructing "factorially pure" tests that
measured just one ability. Similarly, J.P. Guilford
proposed a model of intelligence that comprised up to 180 distinct,
uncorrelated abilities, and claimed to be able to test all of them.
Later analyses have shown that the factorial procedures Guilford
presented as evidence for his theory did not provide support for it, and
that the test data that he claimed provided evidence against g did in fact exhibit the usual pattern of intercorrelations after correction for statistical artifacts.
Gardner's theory of multiple intelligences
More recently, Howard Gardner has developed the theory of multiple intelligences.
He posits the existence of nine different and independent domains of
intelligence, such as mathematical, linguistic, spatial, musical,
bodily-kinesthetic, meta-cognitive, and existential intelligences, and
contends that individuals who fail in some of them may excel in others.
According to Gardner, tests and schools traditionally emphasize only
linguistic and logical abilities while neglecting other forms of
intelligence.
While popular among educationalists,
Gardner's theory has been much criticized by psychologists and
psychometricians. One criticism is that the theory contradicts both
scientific and everyday usages of the word intelligence. Several researchers have argued that not all of Gardner's intelligences
fall within the cognitive sphere. For example, Gardner contends that a
successful career in professional sports or popular music reflects
bodily-kinesthetic intelligence and musical intelligence, respectively, even though one might usually talk of athletic and musical skills, talents, or abilities instead.
Another criticism of Gardner's theory is that many of his
purportedly independent domains of intelligence are in fact correlated
with each other. Responding to empirical analyses showing correlations
between the domains, Gardner has argued that the correlations exist
because of the common format
of tests and because all tests require linguistic and logical skills.
His critics have in turn pointed out that not all IQ tests are
administered in the paper-and-pencil format, that aside from linguistic
and logical abilities, IQ test batteries contain also measures of, for
example, spatial abilities, and that elementary cognitive tasks (for
example, inspection time and reaction time) that do not involve
linguistic or logical reasoning correlate with conventional IQ
batteries, too.
Sternberg's three classes of intelligence
Robert Sternberg, working with various colleagues, has also suggested that intelligence has dimensions independent of g.
He argues that there are three classes of intelligence: analytic,
practical, and creative. According to Sternberg, traditional
psychometric tests measure only analytic intelligence, and should be
augmented to test creative and practical intelligence as well. He has
devised several tests to this effect. Sternberg equates analytic
intelligence with academic intelligence, and contrasts it with practical
intelligence, defined as an ability to deal with ill-defined real-life
problems. Tacit intelligence is an important component of practical
intelligence, consisting of knowledge that is not explicitly taught but
is required in many real-life situations. Assessing creativity
independent of intelligence tests has traditionally proved difficult,
but Sternberg and colleagues have claimed to have created valid tests of
creativity, too.
The validation of Sternberg's theory requires that the three
abilities tested are substantially uncorrelated and have independent
predictive validity. Sternberg has conducted many experiments which he
claims confirm the validity of his theory, but several researchers have
disputed this conclusion. For example, in his reanalysis of a validation
study of Sternberg's STAT test, Nathan Brody
showed that the predictive validity of the STAT, a test of three
allegedly independent abilities, was almost solely due to a single
general factor underlying the tests, which Brody equated with the g factor.
Flynn's model
James Flynn
has argued that intelligence should be conceptualized at three
different levels: brain physiology, cognitive differences between
individuals, and social trends in intelligence over time. According to
this model, the g factor is a useful concept with respect to
individual differences but its explanatory power is limited when the
focus of investigation is either brain physiology, or, especially, the
effect of social trends on intelligence. Flynn has criticized the notion
that cognitive gains over time, or the Flynn effect, are "hollow" if
they cannot be shown to be increases in g. He argues that the
Flynn effect reflects shifting social priorities and individuals'
adaptation to them. To apply the individual differences concept of g
to the Flynn effect is to confuse different levels of analysis. On the
other hand, according to Flynn, it is also fallacious to deny, by
referring to trends in intelligence over time, that some individuals
have "better brains and minds" to cope with the cognitive demands of
their particular time. At the level of brain physiology, Flynn has
emphasized both that localized neural clusters can be affected
differently by cognitive exercise, and that there are important factors
that affect all neural clusters.
Related theories
"Indifference of the indicator"
Spearman proposed the principle of the indifference of the indicator, according to which the precise content of intelligence tests is unimportant for the purposes of identifying g, because g enters into performance on all kinds of tests. Any test can therefore be used as an indicator of g. Following Spearman, Arthur Jensen more recently argued that a g
factor extracted from one test battery will always be the same, within
the limits of measurement error, as that extracted from another battery,
provided that the batteries are large and diverse. According to this view, every mental test, no matter how distinctive, calls on g to some extent. Thus a composite score of a number of different tests will load onto g more strongly than any of the individual test scores, because the g components cumulate into the composite score, while the uncorrelated non-g
components will cancel each other out. Theoretically, the composite
score of an infinitely large, diverse test battery would, then, be a
perfect measure of g.
In contrast, L. L. Thurstone argued that a g factor extracted from a test battery reflects the average of all the abilities called for by the particular battery, and that g therefore varies from one battery to another and "has no fundamental psychological significance." Along similar lines, John Horn argued that g
factors are meaningless because they are not invariant across test
batteries, maintaining that correlations between different ability
measures arise because it is difficult to define a human action that
depends on just one ability.
To show that different batteries reflect the same g, one must administer several test batteries to the same individuals, extract g
factors from each battery, and show that the factors are highly
correlated. This can be done within a confirmatory factor analysis
framework. Wendy Johnson and colleagues have published two such studies finding correlations between g factors extracted from different
batteries between .95–1.00 for most batteries, while the correlations
ranged from .79 to .96 for the Cattell Culture Fair Intelligence Test
(the CFIT). They attributed the somewhat lower correlations with the
CFIT battery to its lack of content diversity for it contains only
matrix-type items, and interpreted the findings as supporting the
contention that g factors derived from different test batteries
are the same provided that the batteries are diverse enough. This
approach has been criticized by psychologist Lazar Stankov
in the Handbook of Understanding and Measuring Intelligence, who
concluded "Correlations between the g factors from different test
batteries are not unity."
A study authored by Scott Barry Kaufman and colleagues showed that the general factor extracted from the Woodjock-Johnson
cognitive abilities test, and the general factor extracted from the
Achievement test batteries are highly correlated, but not isomorphic.
Spearman's law of diminishing returns
A number of researchers have suggested that the proportion of variation accounted for by g may not be uniform across all subgroups within a population. Spearman's law of diminishing returns (SLODR), also termed the cognitive ability differentiation hypothesis,
predicts that the positive correlations among different cognitive
abilities are weaker among more intelligent subgroups of individuals.
More specifically, SLODR predicts that the g factor will account for a smaller proportion of individual differences in cognitive tests scores at higher scores on the g factor.
SLODR was originally proposed in 1927 by Charles Spearman, who reported that the average correlation between 12 cognitive ability
tests was .466 in 78 normal children, and .782 in 22 "defective"
children. Detterman and Daniel rediscovered this phenomenon in 1989. They reported that for subtests of both the WAIS and the WISC,
subtest intercorrelations decreased monotonically with ability group,
ranging from approximately an average intercorrelation of .7 among
individuals with IQs less than 78 to .4 among individuals with IQs
greater than 122.
SLODR has been replicated in a variety of child and adult samples
who have been measured using broad arrays of cognitive tests. The most
common approach has been to divide individuals into multiple ability
groups using an observable proxy for their general intellectual ability,
and then to either compare the average interrelation among the subtests
across the different groups, or to compare the proportion of variation
accounted for by a single common factor, in the different groups. However, as both Deary et al. (1996) and Tucker-Drob (2009) have pointed out, dividing the continuous distribution of intelligence
into an arbitrary number of discrete ability groups is less than ideal
for examining SLODR. Tucker-Drob (2009) extensively reviewed the literature on SLODR and the various methods by
which it had been previously tested, and proposed that SLODR could be
most appropriately captured by fitting a common factor model that allows
the relations between the factor and its indicators to be nonlinear in
nature. He applied such a factor model to a nationally representative
data of children and adults in the United States and found consistent
evidence for SLODR. For example, Tucker-Drob (2009) found that a general
factor accounted for approximately 75% of the variation in seven
different cognitive abilities among very low IQ adults, but only
accounted for approximately 30% of the variation in the abilities among
very high IQ adults.
A recent meta-analytic study by Blum and Holling also provided support for the differentiation hypothesis. As opposed to
most research on the topic, this work made it possible to study ability
and age variables as continuous predictors of the g saturation,
and not just to compare lower- vs. higher-skilled or younger vs. older
groups of testees. Results demonstrate that the mean correlation and g loadings of cognitive ability tests decrease with increasing ability, yet increase with respondent age. SLODR, as described by Charles Spearman, could be confirmed by a g-saturation decrease as a function of IQ as well as a g-saturation
increase from middle age to senescence. Specifically speaking, for
samples with a mean intelligence that is two standard deviations (i.e.,
30 IQ-points) higher, the mean correlation to be expected is decreased
by approximately .15 points. The question remains whether a difference
of this magnitude could result in a greater apparent factorial
complexity when cognitive data are factored for the higher-ability
sample, as opposed to the lower-ability sample. It seems likely that
greater factor dimensionality should tend to be observed for the case of
higher ability, but the magnitude of this effect (i.e., how much more
likely and how many more factors) remains uncertain.
Evidence of a general factor of intelligence has also been observed in non-human animals. Studies have shown that g is responsible for 47% of the variance at the species level in primates and around 55% of the individual variance observed in mice. A review and meta-analysis of general intelligence, however, found that
the average correlation among cognitive abilities was 0.18 and
suggested that overall support for g is weak in non-human animals.
Although it is not assessable using the same intelligence
measures used in humans, cognitive ability can be measured with a
variety of interactive and observational tools focusing on innovation, habit reversal, social learning, and responses to novelty. Non-human models of g such as mice are used to study genetic influences on intelligence and neurological developmental research into the mechanisms behind and biological correlates of g.
Similar to g for individuals, a new research path aims to extract a general collective intelligence factor c for groups displaying a group's general ability to perform a wide range of tasks. Definition, operationalization and statistical approach for this c factor are derived from and similar to g. Causes, predictive validity as well as additional parallels to g are investigated.
g has a number of correlates in the brain. Studies using magnetic resonance imaging (MRI) have established that g and total brain volume are moderately correlated (r~.3–.4). External head size has a correlation of ~.2 with g. MRI research on brain regions indicates that the volumes of frontal, parietal and temporal cortices, and the hippocampus are also correlated with g, generally at .25 or more, while the correlations, averaged over many studies, with overall grey matter and overall white matter have been found to be .31 and .27, respectively. Some but not all studies have also found positive correlations between g
and cortical thickness. However, the underlying reasons for these
associations between the quantity of brain tissue and differences in
cognitive abilities remain largely unknown.
Most researchers believe that intelligence cannot be localized to a single brain region, such as the frontal lobe. Brain lesion
studies have found small but consistent associations indicating that
people with more white matter lesions tend to have lower cognitive
ability. Research utilizing NMR spectroscopy
has discovered somewhat inconsistent but generally positive
correlations between intelligence and white matter integrity, supporting
the notion that white matter is important for intelligence.
Some research suggests that aside from the integrity of white
matter, also its organizational efficiency is related to intelligence.
The hypothesis that brain efficiency has a role in intelligence is
supported by functional MRI research showing that more intelligent
people generally process information more efficiently, i.e., they use
fewer brain resources for the same task than less intelligent people.
Heritability is the proportion of phenotypic variance in a trait in a
population that can be attributed to genetic factors. The heritability
of g has been estimated to fall between 40 and 80 percent using
twin, adoption, and other family study designs as well as molecular
genetic methods. Estimates based on the totality of evidence place the
heritability of g at about 50%. It has been found to increase linearly with age.
As with heritability in general, the heritability of g can
be understood in reference to a specific population at a specific place
and time, and findings for one population do not apply to a different
population that is exposed to different environmental factors. A population that is exposed to strong environmental factors can be
expected to have a lower level of heritability than a population that is
exposed to only weak environmental factors. For example, one twin study
found that genotype differences almost completely explain the variance
in IQ scores within affluent families, but make close to zero
contribution towards explaining IQ score differences in impoverished
families. Notably, heritability findings also only refer to total variation
within a population and do not support a genetic explanation for
differences between groups. It is theoretically possible for the differences between the average g of two groups to be 100% due to environmental factors even if the variance within each group is 100% heritable.
Much research points to g being a highly polygenic trait
influenced by many common genetic variants, each having only small
effects. Another possibility is that heritable differences in g are due to individuals having different "loads" of rare, deleterious mutations, with genetic variation among individuals persisting due to mutation–selection balance.
Cross-cultural studies indicate that the g factor can be
observed whenever a battery of diverse, complex cognitive tests is
administered to a human sample. In some studies, the factor structure of
IQ tests has also been found to be consistent across sexes and ethnic
groups in the U.S. and elsewhere.
Most studies suggest that there are negligible differences in the mean level of g
between the sexes, but that sex differences in cognitive abilities are
to be found in more narrow domains. For example, males generally
outperform females in spatial tasks, while females generally outperform
males in verbal tasks. Another difference that has been found in many studies is that males show more variability
in both general and specific abilities than females, with
proportionately more males at both the low end and the high end of the
test score distribution.
Differences in g between racial and ethnic groups have
been found, particularly in the U.S. between black- and
white-identifying test takers, though these differences appear to have
diminished significantly over time, and to be attributable to environmental (rather than genetic) causes. Some researchers have suggested that the magnitude of the black-white
gap in cognitive test results is dependent on the magnitude of the
test's g loading, with tests showing higher g loading producing larger gaps (see Spearman's hypothesis), while others have criticized this view as methodologically unfounded. Still others have noted that despite the increasing g loading of IQ test batteries over time, the performance gap between racial groups continues to diminish. Comparative analysis has shown that while a gap of approximately 1.1
standard deviation in mean IQ (around 16 points) between white and black
Americans existed in the late 1960s, between 1972 and 2002 black
Americans gained between 4 and 7 IQ points relative to non-Hispanic
Whites, and that "the g gap between Blacks and Whites declined virtually in tandem with the IQ gap." In contrast, Americans of East Asian descent generally slightly outscore white Americans. It has been claimed that racial and ethnic differences similar to those found in the U.S. can be observed globally, but the significance, methodological grounding, and truth of such claims have all been disputed.
An illustration of the Jensen box, an apparatus for measuring choice reaction time
Elementary cognitive tasks (ECTs) also correlate strongly with g.
ECTs are, as the name suggests, simple tasks that apparently require
very little intelligence, but still correlate strongly with more
exhaustive intelligence tests. Determining whether a light is red or
blue and determining whether there are four or five squares drawn on a
computer screen are two examples of ECTs. The answers to such questions
are usually provided by quickly pressing buttons. Often, in addition to
buttons for the two options provided, a third button is held down from
the start of the test. When the stimulus is given to the subject, they
remove their hand from the starting button to the button of the correct
answer. This allows the examiner to determine how much time was spent
thinking about the answer to the question (reaction time, usually
measured in small fractions of second), and how much time was spent on
physical hand movement to the correct button (movement time). Reaction
time correlates strongly with g, while movement time correlates less strongly. ECT testing has allowed quantitative examination of hypotheses
concerning test bias, subject motivation, and group differences. By
virtue of their simplicity, ECTs provide a link between classical IQ
testing and biological inquiries such as fMRI studies.
Working memory
One theory holds that g is identical or nearly identical to working memory capacity. Among other evidence for this view, some studies have found factors representing g and working memory to be perfectly correlated. However, in a meta-analysis the correlation was found to be considerably lower. One criticism that has been made of studies that identify g with working memory is that "we do not advance understanding by showing that one mysterious concept is linked to another."
Piagetian tasks
Psychometric
theories of intelligence aim at quantifying intellectual growth and
identifying ability differences between individuals and groups. In
contrast, Jean Piaget's theory of cognitive development
seeks to understand qualitative changes in children's intellectual
development. Piaget designed a number of tasks to verify hypotheses
arising from his theory. The tasks were not intended to measure
individual differences, and they have no equivalent in psychometric
intelligence tests. For example, in one of the best-known Piagetian conservation tasks
a child is asked if the amount of water in two identical glasses is the
same. After the child agrees that the amount is the same, the
investigator pours the water from one of the glasses into a glass of
different shape so that the amount appears different although it remains
the same. The child is then asked if the amount of water in the two
glasses is the same or different.
Notwithstanding the different research traditions in which
psychometric tests and Piagetian tasks were developed, the correlations
between the two types of measures have been found to be consistently
positive and generally moderate in magnitude. A common general factor
underlies them. It has been shown that it is possible to construct a
battery consisting of Piagetian tasks that is as good a measure of g as standard IQ tests.
The traditional view in psychology is that there is no meaningful relationship between personality and intelligence, and that the two should be studied separately. Intelligence can be understood in terms of what an individual can do, or what his or her maximal performance is, while personality can be thought of in terms of what an individual will typically
do, or what his or her general tendencies of behavior are. Large-scale
meta-analyses have found that there are hundreds of connections >.20
in magnitude between cognitive abilities and personality traits across
the Big Five. This is despite the fact that correlations with the global Big Five factors themselves being small, except for Openness (.26). More interesting relations emerge at other levels (e.g., .23 for the
activity facet of extraversion with general mental ability, -.29 for the
uneven-tempered facet of neuroticism, .32 for the industriousness
aspect of conscientiousness, .26 for the compassion aspect of
agreeableness).
The associations between intelligence and personality have
generally been interpreted in two main ways. The first perspective is
that personality traits influence performance on intelligence tests.
For example, a person may fail to perform at a maximal level on an IQ
test due to his or her anxiety and stress-proneness. The second
perspective considers intelligence and personality to be conceptually
related, with personality traits determining how people apply and
invest their cognitive abilities, leading to knowledge expansion and
greater cognitive differentiation. Other theories (e.g., Cybernetic Trait Complexes Theory) view
personality and cognitive ability as intertwined parameters of
individuals that co-evolved and are also co-influenced during
development (e.g., by early life starvation).
Creativity
Some researchers believe that there is a threshold level of g below which socially significant creativity
is rare, but that otherwise there is no relationship between the two.
It has been suggested that this threshold is at least one standard
deviation above the population mean. Above the threshold, personality
differences are believed to be important determinants of individual
variation in creativity.
Others have challenged the threshold theory. While not disputing
that opportunity and personal attributes other than intelligence, such
as energy and commitment, are important for creativity, they argue that g is positively associated with creativity even at the high end of the ability distribution. The longitudinal Study of Mathematically Precocious Youth
has provided evidence for this contention. It has shown that
individuals identified by standardized tests as intellectually gifted in
early adolescence accomplish creative achievements (for example,
securing patents or publishing literary or scientific works) at several
times the rate of the general population, and that even within the top 1
percent of cognitive ability, those with higher ability are more likely
to make outstanding achievements. The study has also suggested that the
level of g acts as a predictor of the level of achievement, while specific cognitive ability patterns predict the realm of achievement.
Criticism
Connection with eugenics and racialism
Research
on the G-factor, as well as other psychometric values, has been widely
criticized for not properly taking into account the eugenicist background of its research practices. The reductionism of the G-factor has been attributed to having evolved from pseudoscientific theories about race and intelligence. Spearman's g and the concept of inherited, immutable intelligence were a boon for eugenicists and pseudoscientists alike.
Joseph L. Graves Jr. and Amanda Johnson have argued that g "...is to the psychometricians what Huygens' ether was to early physicists: a nonentity taken as an article of faith instead of one in need of verification by real data."
Some scientists have described the g factor, and psychometrics, as forms of pseudoscience.
Conceptual critiques
Paleontologist and biologist Stephen Jay Gould presented a critique in his 1981 book The Mismeasure of Man. He argued that psychometricians fallaciously reified the g
factor into an ineluctable "thing" that provided a convenient
explanation for human intelligence, grounded only in mathematical theory
rather than the rigorous application of mathematical theory to
biological knowledge. An example is provided in the work of Cyril Burt, published
posthumously in 1972: "The two main conclusions we have reached seem
clear and beyond all question. The hypothesis of a general factor
entering into every type of cognitive process, tentatively suggested by
speculations derived from neurology and biology, is fully borne out by
the statistical evidence; and the contention that differences in this
general factor depend largely on the individual's genetic constitution
appears incontestable.The concept of an innate, general cognitive
ability, which follows from these two assumptions, though admittedly
sheerly an abstraction, is thus wholly consistent with the empirical
facts."
Several researchers have criticized Gould's arguments. For
example, they have rejected the accusation of reification, maintaining
that the use of extracted factors such as g as potential causal
variables whose reality can be supported or rejected by further
investigations constitutes a normal scientific practice that in no way
distinguishes psychometrics from other sciences. Critics have also
suggested that Gould did not understand the purpose of factor analysis,
and that he was ignorant of relevant methodological advances in the
field. While different factor solutions may be mathematically equivalent
in their ability to account for intercorrelations among tests,
solutions that yield a g factor are psychologically preferable
for several reasons extrinsic to factor analysis, including the
phenomenon of the positive manifold, the fact that the same g can emerge from quite different test batteries, the widespread practical validity of g, and the linkage of g to many biological variables.
John Horn and John McArdle have argued that the modern g theory, as espoused by, for example, Arthur Jensen, is unfalsifiable, because the existence of a common factor like g follows tautologically from positive correlations among tests. They contrasted the modern hierarchical theory of g with Spearman's original two-factor theory which was readily falsifiable (and indeed was falsified).
