Definition of G

Form 2, © 1999 Paul Cooijmans

Remark as of 2008: This article needs revision, which may take place one day. Essentially, what needs to be incorporated better is the fact that abilities that are so useful that they are almost necessary for life go into "fixation"; that is, become possessed by almost everyone, and thus have no variance and therefore no correlation with other abilities. The abilities that do correlate positively with many other abilities are those that are not necessary, but are "making the difference" currently. They are the "cutting edge", and they will not be exactly the same abilities for each species or population.


G is the sum of evolutionary ability.

Abilities tend to correlate positively as they are naturally selected by the same criterion; survival.

The higher the correlation with G, the fewer abilities of that correlation, the less specific the ability, the less it is affected by training, and the less physical/chemical processes or body action it involves.

Abilities form a hierarchy, each characterized by its correlation with G.

Geometrically modeled, abilities are vectors, G being their sum. Higher correlations are sharper angles with G. All vectors add, but those with sharper angles are more effective, like a man pulling a train uphill is more successful if he pulls under a sharper angle with the rails.

Trainability of ability is inversely proportional to the square of the ability's correlation with G.

Hierarchy (educated guess)

.9Pattern recognition
.7Verbal, Numerical
.5Memory, Mental tempo, Perception, Emotional stability, Concentration
.4Dexterity, Sense of gravity, Kinesthetic, Sense of time, Pulchritude, Spiritual
.3Athletic (speed and strength)
.2Athletic (stamina)
.1Many specific abilities

Test construction

Make a test for various abilities. Compute for each ability its correlation with overall score. Weight the positively correlating abilities by the square of their correlation.

Initial criteria for selecting abilities:

Ad 2: The test would become too long if each specific ability were included, so one must not go beyond a degree of detail, determined by practical limitations. As highly specific abilities are expected to correlate very low, their exclusion does not affect the test.

Possible abilities:

This is a preliminary list; some of these may be too specific or not measurable, and a few may be missing. Some may only be measurable in combination with one or two other; some may have to be split up into more specific abilities. That will be sorted out in the process of test construction.

A subtest is devoted to each ability. Existing tests or test sections may be used, but care is taken to avoid ceiling problems. The subtests give standard scores on the same scale, so that a preliminary total score is obtained by summing the subtest scores. Correlations with total score are computed for each subtest. The (positively correlating) subtest scores are weighted by the square of their correlation and summed to arrive at the G score. In later tests, the weights may be implied in test construction, e.g. by the number of items devoted to each ability, or by variable item credits.

(Beyond this is more speculative)


Evolution picks abilities towards group survival. For if a group dies out, its abilities die out. "Egoistic" abilities towards individual survival that lead to the fall of a group if occurring on large scale, like terror, murder, etc., are therefore naturally not selected. This is why e.g. brutal murder is so rare it is "news", while the putting on of clothes is not. Selected is a correlating whole of abilities with a sufficient amount of "altruism" among them for group survival. This is the link between evolution and ethics.

"Criminal" abilities, that would lead to the fall of society if many would master them, correlate negatively with G, and are the result of life's random mutation on procreation level. Evolution sieves; direction is given at group level. There is always a small amount of negatively correlating abilities, kept down by natural selection. If this amount grows, correction follows in the form of stricter legislation, revolution, civil war, war, fall of the empire, dying out of the species, etc.

Abilities, so useful and common most have them in about the same amount, like breathing, eating and drinking, correlate zero with any other. An equal distribution cannot correlate. In measuring G, these are futile.

Positive correlations are found in abilities distributed unequally. These belong in a test for G. Correlation analysis shows which abilities are the most effective in "pulling the train uphill". They pull under sharp angles, while those with low positive correlations pull under less sharp angles. Abilities like terror and murder pull under blunt angles; downward. Only little downward pulling is tolerable, or downhill it goes. This is why societies have corrective schemes for the minority displaying egoistic, criminal behaviour; ability to keep those on a tight rein serves group survival, so is naturally selected. Soft attitude to crime leads to doom.

In the train image, the force of gravity is counteracting the pulling uphill. This is symbolic for what in thermodynamics and cosmology is known as "increase of entropy". Stephen Hawking explains this concept in "A Brief History of Time". Entropy is disorder; the amount of entropy in the universe is increasing, and decrease of entropy (so: increase of order) is only locally possible. Life, which is order, is on universal scale counteracted by increase of entropy, and eventually evened out by it, like flowering turbulences in the expanding gas cloud of an explosion.

In terms of abilities, G is counteracted by "e" (increase of entropy), which correlates -1 with it.

Abilities discussed

Pattern recognition originally was the ability of proteins to find molecules to combine with in the "soup" around them. To see order in a chaotic environment; the primary condition for life. It has the highest correlation with G, is unlearned, untrainable and applies to any field. It determines one's ceiling in the higher mental abilities, to wit reasoning, verbal, numerical and spatial ability.

Reasoning is the next step once a pattern has been recognized; mental manipulation of concepts. Reason is baked-in in the laws of physics; the hardware of the universe. We are programmed for reasoning as we perceive the logic in the world around us. This implies those with better pattern recognition become better reasoners. Reasoning is not learned from educators. The world is the paradigm. Reasoning applies to any field.

Verbal ability is an application of the previous abilities. From babyhood on we are exposed to language, so that pattern recognition and reasoning get to express themselves verbally. The first two determine our verbal ceiling, but there is a margin, dependent on the extent to which we are exposed to language and information. This is why verbal ability correlates lower with G than pattern recognition and reasoning do.

Numerical ability is similar to verbal ability, but exposure to the numerical varies more per individual than in the case of language, which is why numerical ability correlates slightly lower with G than does verbal ability.

Spatial ability is to mentally rotate a figure in two or more dimensions, and perceive distance. An application of pattern recognition and reasoning, but older than verbal and numerical ability; it was developed in predators for catching prey long before humans existed. Ability is not restricted to a species; successful genetics is reused. Humans share much DNA with other organisms. Spatial correlates lower with G than do verbal and numerical because, in humans, the latter two have "overtaken" spatial. This is why purely spatial "culture free" tests, though well-meant, are less satisfactory than one would hope.

A tendency among abilities: the closer they are to the concrete, material world, the lower the correlation with G. This is a result of the (evolutionary spoken) recent and rapid development of the brain cortex, that houses the higher mental abilities. The cortex is stacked on overnight, poorly connected to the older brain structures, suggesting extreme natural selection in favour of its abilities. Mental ability appears more successful in humans than physical ability. Obvious in the modern world, but this applies to the last 50000 years.

Memory, mental tempo, perception, emotional stability, sense of time, dexterity, sense of gravity, kinesthetic ability and athletic ability are increasingly connected to the physical and concrete. The first five are at the periphery of the purely mental, the latter ever more involve physical action.

Perception is partly dependent of quality of sensorial input; a physical matter.

Emotion stems from older parts of the brain, inaccessible for introspection. It enters the mental area, as sensorial input does. It "colours" thinking, as harmony does melody. Mental handling of emotion is matching melody to harmonic background. A genius makes anything work by virtuoso treatment of dissonant and discordant. A botcher chokes in the drivel of consonance.

Sense of time is physical-based. Not just heartbeat, but hand-clapping and feet-stamping of early man to keep warm, that evolved into rhythm and dance, are the origin of sense of time. This applies to time spans from about .07 seconds (threshold of perception) to very roughly 45 seconds. For longer periods, outside aids tend to be used (like counting, the sun, clocks, etc.). Time is perceived as an ordinal phenomenon with a strong non-linear character. In graphs, a logarithmic time scale often works best. We are short-sighted in time; our best-sensed range is about .1 to 2 seconds.

Dexterity, sense of gravity, kinesthetic and athletic ability are so sublime and useful their low (but positive) correlation with G is almost disappointing. They are needed, but appear to come a little bit short compared to mental ability, in terms of human evolution. This is the "blue collar/white collar" problem. There is temptation to say "all abilities are equal", but history and fall of communism have shown where that leads to. Mental and physical ability are not independent, but part of the same hierarchy with G on top. Although mental appears closer to G than physical, it is unfair that our current intelligence tests are purely mental. Physical ability must be included in G-testing, no matter its correlation.

Of the above abilities, only about eight occur in IQ tests, mostly not more than four or five per test. This is the result of over a century of research and test construction; these about eight (all mental) abilities have high mutual correlations and high correlations with school performance.

The model of G explained here introduces other than the traditional mental abilities in test construction, and thus widens the definition of intelligence. In this model, intelligence is not a mental, but holistic mental/physical indicator of potential to contribute to society.

The holistic G model anticipates the inflation of mental ability in the next fifty years, when silicon-based brain extensions become available to give super brain power. The Mega Test will be child's play to the man in the street. Traditional mental testing will no longer suffice to detect "giftedness". Computers themselves will, by 2025 at the latest, outscore all humans on mental tests. The definition of "g" will have to shift towards typical "human" abilities to make detection of talent possible; G will get to include a broad range of mental and physical abilities to make sure humans outscore Artificially Intelligent computers, and to make sure tests still discriminate between individuals, even though they have Extended Memory and Extended Processing Power.

IQ societies will change their entrance policy to escape the tsunami of AI computers and Extended-Brain humans, and develop admission tests according to the holistic model to measure the new G at extreme levels. The "Eric Hart" of the future may be a super intelligent expert heart surgeon who runs 800 meter in 2 minutes and moonlights as a gym bouncer.