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By Volkmar Weiss, German Centraly Office for Genealogy, Leipzig
Vol. 35, Mankind Quarterly, 06-01-1995, pp 373.
The Historical Perspective
From the point of view of a European reader, the much discussed book by
Herrnstein and Murray consists of two halves, which could have been published
independently in two volumes. The first half (part I. -III.) would be a volume
of supranational meaning and importance, the second one (part IV.) would be a
volume reflecting special social problems of the US from a certain political
angle and therefore would be highly controversial. It is a pity, that from the
beginning this controversial discussion of this fourth part will overshadow
the content of the first three parts, which in the long run will prove to be
as timeless and important as Darwin's Origin of the Species. Never before has
any author portrayed the relationships between IQ, education, occupation,
economy, poverty, unemployment, welfare, crime, and social structure with so
much convincing statistical data in such a well written way as done by
Herrnstein and Murray. We will restrict our comments to these strictly
scholarly parts I., II., and 111.
The two authors observe that (p. 510): "As the century progressed, the
historical mix of intellectual abilities at all levels of American society
thinned as intelligence rose to the top. The upper end of the cognitive
ability distribution has been increasingly channeled into higher education . .
. , thence into high-IQ occupations. The upshot is that the scattered
brightest of the early twentieth century have congregated, forming a new
class." However, already in 1949 (Swedish original edition even in 1944) the
sociologist Geiger came to the opposite conclusion that the intelligentsia
will never be a "class" characterized by a common purpose and goal and will
only remain a stratum. By differing in their relation to power and wealth and
striving to increase their influence in such a way, a substantial part of the
cognitive elite tends to adhere to a more or less (pseudo)egalitarian ideology
and is thriving under such conditions. The development of many countries seems
guaranteed at best when the largest number of people honestly believe that
they have already reached a maximum of equality, where in reality a maximum of
inequality exists. As long as this belief is not disturbed, such countries
enjoy social peace and, from this point of view, books as The Bell Curve are
only a nuisance, which should be suppressed, even from the point of view of a
large portion of the so-called "cognitive elite" (in German already called
lntelligenz, in Russian intelligentsia). Several times in history a surplus of
cognitive elite has been slaughtered or expelled during the next social
revolution, reestablishing in such a way the balanced polymorphism of IQ
distribution and underlying gene frequencies. History can even be understood
as the struggle between cognitive sub-elites with and without egalitarian
ideology.
The channeling of all high-IQ individuals into higher education is not
restricted to the United States alone. Parallel shifts can be observed in all
industrialized countries, even in the former communist states. For example, in
(West) Germany higher education was extended from 3% in 1900 up to about 30%
in 1990. In former East Germany this inflation of educational degrees was
stopped by governmental intervention by about 12%. Because an IQ of 125 or
more is not only a different quantity, but maybe a different quality, i.e. a
different genotype (Weiss 1992a, 1994), an extension of higher education
beyond 5 or even 10% could even cloud the emergence of the new elite. Only in
the United States there is no clouding because we have the unique situation of
IQ values available for all the educated population and a ranking of
universities (unknown, for example, in Germany). Therefore the book by
Herrnstein and Murray could only be written in the States, nowhere else could
anybody have obtained statistical data of such quality.
According to both authors (p. 34): "At mid-century America abruptly becomes
more efficient in getting the top students to college." In 1964 in East
Germany 32% of the highly gifted (IQ above 125) had fathers with higher
education, in 1970 already 66% (Weiss 1972). The underlying trend (linear in
the sixties) caused the communists to prohibit strongly the publication of all
such secret data on the growing educational stratification even within East
bloc countries (Weiss 1991). Per definition, the communist intelligentsia in
their majority had to be the offspring of workers and peasants. But this has
never been true and was becoming less and less true.
Herrnstein and Murray are aware that (p. 26):
Human society has always had some measure of cognitive stratification . . .
. This differentiation by cognitive ability did not coalesce into cognitive
classes in premodern societies for various reasons . . . . Parents could not
[not] pick the brightest of their progeny to inherit the title and the land .
. . . Stratification by cognitive ability has been weak and inconsistent until
this century because the number of very bright people was so much greater than
the specialized jobs for which intelligence is indispensable. A true cognitive
elite requires a technological society . . . . A large majority of the smart
people in . . . Elizabethan England, and Teddy Roosevelt's America were
engaged in ordinary pursuits . . . , living with everyone else . . . . Social
and economic stratification was extreme, but cognitive stratification was
minor. So it has been from the beginning of history into this century.
And further (p.510):
Among the smart women, a few had professional careers of their own, but
most of them kept house, reared children, and were often the organizing forces
of their religious and social communities. People from the top of the
cognitive ability distribution lived next door to people who were not so smart
. . . They socialized with, . . . and married people less bright than
themselves as a matter of course.
They here comment that: "This was not an egalitarian utopia that we are
trying to recall."
Not a utopia, but a typical American perspective, where nearly every
immigrant had to start from the very bottom. From the point of European social
history, presumably a crude underestimation of the role the IQ played for
stratification already in traditional societies. Maybe, the engineer with the
diploma of a university of today has only the same rank as a technician in
1900 and an able smith in 1750.
Saxony is the only large European territory where we can make reliable
estimates of the absolute increase of the different social strata in modern
time (Weiss 1993). Because the quality of parish registers in Saxony was in
some places high from the beginning in 1548, the quality of genealogical
research is correspondingly high. In the 18th century parish books, data on
status and occupation of a male person are always given, even in the remotest
village. In the 16th and 17th centuries our analysis was restricted to
parishes were the genealogists have extended the data basis by means of family
reconstitution with the use of tax rolls and records of tenure of land. From
500 ancestry and pedigree files we (Weiss 1993) drew five random samples of
couples (in most cases married one), each sample comprising about 2200 couples
for the following years of marriage: 1548-1649, 16501699, 1700-1749,
1750-1814, 1815-1870. The drawn quotas are representative with respect to main
social strata and town/countryside distribution.
The upper stratum of the past, characterized by wealth, education and
power, was in many respects a cognitive elite, too. Even more interesting is
the occupational group of the "clerks," i.e. relatively poor men with jobs and
occupations, where a lot of "cognitive competence" was necessary, such as
schoolmaster, clerk, scribe, precentor, forester, or administrator. In Saxony
(where a third of all inhabitants lived in towns) this nascent cognitive elite
grew from 3% of the total urban population in 1615 to 12% in 1870, with a
first leap from about 5% to 10% in the second half of the 18th century; in the
rural population from about 2% in 1595 to 5% in 1870. From the beginning, this
occupational group was unique in their social mobility. In towns only about a
quarter of their fathers belonged to the same occupational group, another
quarter were sons of small urban craftsmen or tradesmen, and the remaining
half of the sons came from villages, especially in the 19th century, where
their fathers were schoolmasters, parsons, peasants or rural craftsmen. As
children of the countryside, these smart men entered the town with nothing
else than their above average IQ; as children of the town, they inherited no
fortune. Therefore, on the marriage market they had nothing to offer and many
had to marry wives of the same relatively humble origin or with only a small
dowry, i.e. mostly the daughters of craftsmen. But there must have been a lot
of assortative marriage with respect to IQ. Only such a marriage strategy can
explain the unique upward mobility of this occupational group in the second
generation, where about a third of their sons (and daughters by marriage)
became members of the wealthy upper stratum (Besitzund Bildungsburgertum) of
the cities, either by their own merit and earning or by marriage or in many
cases both combined. Because this group of poor "intellectuals" was always
growing, a third or more of the sons could remain in such or similar jobs as
their fathers and had a second chance of upward mobility in each following
generation. The uniqueness of this occupational group is underlined by
mentioning, for example, that more than 80% of the urban craftsmen descended
from urban craftsmen (as well as more than 80% of peasants from peasants).
Sons and daughters of the upper stratum of the towns, no more than 10% of
the total urban population, were never marrying sons and daughters of the low
stratum (with the exemption of this mentioned occupational group).
Intergenerational social mobility from the bottom to the top or vice versa,
mediated by the medium stratum, needed at least two generations. In the
countryside even the peasantry was highly stratified into full peasants,
smallholders and cotters. The marriage patterns between these three strata
were rather consistent and nobody liked to marry downward and to endanger the
economical basis of future generations. We tend to agree with Herrnstein and
Murray that these patterns of behavior primarily had nothing to do with IQ.
But Herzog (1984) showed that in Lampertswalde, again a village in Saxony,
during 1700-1799, 4.6 children of full peasants (arithmetical mean per
marriage) inherited a total of 612 florins, which translates to 133 fl per
child, 5.4 children of millers inherited even 2165 fl., i.e., 401 fl. per
child, while 3.3 children of cotters inherited 77 fl. (only 23 fl. per child),
which was of no small importance for their chances on the marriage market.
Herrnstein and Murray seem to underestimate the possibility of upward and
downward mobility in traditional societies by personal achievement. Even in
the 16th, 17th and 18th century a small percentage of men were changing their
job several times during their lifetime (see Weiss 1993). Even peasants could
buy and sell and in such a way, at the end of the Thirty Years War, the
peasant Abraham Scheibner (Zschocken/Saxony) was able to place all his seven
children into their own property. Surely, he had luck, but, I guess, a high
IQ, too.
For the emergence of a new cognitive elite the pattern of assortative
mating with respect to IQ plays a decisive role. Assortative mating for IQ
means that mated pairs are more similar for IQ than would be expected if they
were chosen at random from the population. Herrnstein and Murray (p. 110)
state:
When the propensity to mate by cognitive ability is combined with the
educational and occupational stratification we have described, the impact on
the next generation will be larger than on the previous one, even if the
underlying propensity to mate by cognitive ability remains the same . . . . We
have been assuming that the propensity to mate by IQ has remained the same. In
reality, it has almost certainly increased and will continue to increase.
In spite of this, we should be aware of a counter-hypothesis, stating that
with respect to assortative marriage nothing essentially has changed during
the last centuries. IQ, wealth and power could always have been correlated in
such a way, that marriage patterns mediated on this basis were always
resulting indirectly in a correlation of about .50 with respect to IQ of
spouses. In other words, to prove the emergence of a new elite needs to prove
that the correlation of spouses with respect to IQ is increasing,
historically, at present and in the future. Historically this proof will be
impossible, at present difficult, in the future an everlasting challenge for
research. Assortative marriage has two consequences (Crow and Felsenstein
1968): (1) an increase in the average homozygosity, and (2) an increase in the
total population variance. For example, assortative marriage is quite high for
deafness, and it might be thought that this is a major factor in increasing
the incidence. But it has been estimated that there are at least 35 genes, any
one of which can cause deafness when homozygous, and with a small average
frequency. Thus, even with strict assortative marriage the incidence of
deafness would not be increased by more than 2% or 3%. However, for very high
IQ the situation could be quite different and would depend upon whether a
major gene locus is very important (Weiss 1992a, 1994) or not. In the case of
a major gene locus underlying general intelligence, an increase of assortative
marriage with respect to IQ would strengthen the disruptive tendencies within
industrialized societies. Both extremes, high IQ and low IQ, would be on the
increase, the percentage of the cognitive elite more by an increase caused by
assortative marriage than by a growing number of children of their own.
Furthermore, Herrnstein and Murray confirm in a convincing way that the
recent distribution of IQ is the result of natural selection in the Darwinian
sense and that the future distribution of IQ will be the result of natural
selection, too. The rise of the new elite will be impossible without a growing
number of jobs for this elite and without the will and the possibility to feed
a growing number of children of their own. It is the merit of Herrnstein and
Murray to have shown the inter-dependencies between welfare and the
proliferation of the dull. In traditional European societies this
proliferation was suppressed by a sometimes cruel policy, which nobody wishes
to be revived, and Gypsies were even persecuted. Times did change. For
example, in 1945 there were about 100,000 Gypsies living in Czechoslovakia,
and under communist rule this number grew to about 600,000. In 1980, 1,000
Gypsy women averaged 5.984 children (Kalibova and Pavlik 1988), which
contrasted dramatically with the small number of children born to Czech women,
now below replacement level. In 1980, 18.7% of all Gypsy children (2.7% of
Czech children) were in schools for mentally retarded children, 15.1% were
borderline cases of mental retardation (1.0% for Czechs), and only 0.3% were
in schools for higher education (7.1% for Czechs).
From these educational statistics we can infer an average IQ of about 85
for Gypsies in former Czechoslovakia. Statistical data from Hungary (Szabo
1991) and Romania are very similar. In the Czech Republic unemployment and
crime rate among Gypsies are sixfold to eightfold higher than among the Czech.
In order to remedy this situation, communist (sic, communist) Czechoslovakia
implemented a program of voluntary sterilization, paying Gypsy women a premium
(Fienbork, Miho, and Muller 1992, p. 103). After 1989 Gypsies were among the
first to use the new freedom of movement. On July 14, 1993 the daily Leipziger
Volkszeitung (p.16) had to write: In the northeastern quarter of Leipzig with
its 90,000 inhabitants more than a third of all police actions is dedicated to
350 Gypsy immigrants." Because socially upward mobile Gypsies are assimilated
to a certain extent and no longer designate themselves as Gypsies, and on the
contrary during each generation a few downward mobile individuals of other
populations become integrated into Gypsy tribes since centuries, these
statistics relate to some quantitatively unclear mixture of social and racial
distinctions. Therefore J.J. Kemeny (cited by Szabo 1991, p.89) has to
conclude: "The life-style of the Gypsies is the subculture of the lowest
stratum of Hungarian society."
The Bell Curve and Short Memory Capacity
Plomin et al (1994) state: "General cognitive ability (intelligence, often
indexed by IQ scores) is one of the most highly heritable behavioral
dimensions . . . . General cognitive ability . . . is a quantitative trait
with a roughly normal distribution." Herrnstein and Murray's data are based on
the Armed Forces Qualification Test (ETCHED). "It consisted the summed raw
scores of word knowledge, paragraph comprehension, arithmetic, and mathematics
knowledge subtests" (P. 570). This sum should be heavily loaded with
crystallized intelligence. "The distribution of AFQT is skewed so that the
high scores tend to be more closely bunched than the low scores. To put it
roughly, the most intelligent people who take the test have less of an
opportunity to get a high score than the least intelligent people have to get
a low score . . . . We therefore computed standardized scores corrected for
skew" (p. 572) and the ceiling effect, respectively.
Because even a minority of psychometricians (Frank 1985; Lehrl et. al.
1990; Weiss 1992a) is stubbornly claiming that IQ and especially raw scores of
subtests of fluid intelligence are not normally distributed, Herrnstein and
Murray feel needed to add (p.585):
Empirically, tests . . . , administered to a representative sample of those
for whom the test is intended, will yield scores that are spread out in a
fashion resembling a normal distribution, or a bell curve. In this sense,
tests of mental ability are not designed to produce normally distributed
scores; that's what happens . . . . It is also true, however, that tests are
usually scored and standardized under the assumption that intelligence is
normally distributed, and this has led to allegations that psychometricians
have bamboozled people into accepting that intelligence is normally
distributed.
An IQ of 140 compared with an IQ of 70 on the surface suggests a double
amount or the half of cognitive ability, respectively. However, a look of the
raw scores, i.e., of the non-normalized scores, of IQ subtest of fluid
intelligence shows that an IQ of 140 means a fourfold amount of cognitive
ability compared with an IQ of 70 (see Table 1 and Fig. 1). This relationship
holds under the condition that all subtests are elementary cognitive tasks and
the superior speed of the most intelligent is not clouded by a ceiling effect.
Since 1959, Frank (see Lehrl, Gallwitz, Blaha and Fischer 1991, for the
last updating of Frank's theory and for representative empirical results) is
claiming that general cognitive ability is limited by the channel capacity of
short-term memory. Frank and his school (Lehrl and Fischer 1990; Weiss 1992b)
are arguing that the capacity C of short-term memory (measured in bits of
information) is the product of the processing speed S of information flow (in
bits/s) and the duration time D (in s) of information in short term memory.
(By Lehrl et al. testing of processing speed S was operationalized by reading
rates, duration of information D by memory span.)
Hence:
C (bits) = S (bits/s) x D (s)
According to major gene theory of intelligence (Frank 1985), the mean of
the IQ-genotype M1M1 is 140 bits, and of the genotype M2M2 70 bits, that means
the contribution of a single M1 allele to short-term memory capacity C is
about 70 bits, of a M2 allele about 35 bits. For a heterozygote M1M2 hence 70
bits + 35 bits = 105 bits.
Does this difference between the bell curve and the distribution of short
term-memory capacity have any practical meaning? For this purpose we have
reproduced two figures, from which we can imagine the importance of the
fourfold difference in mental speed and memory capacity between high and low
IQ individuals. By this, Hernstein and Murray are not contradicted in any way,
they are essentially right. But their conclusions as to the importance of IQ
ineveryday life and work are an underestimate. Between IQ 70 (-2 standard
deviations from the mean) and IQ 140 (+2.66 standard deviations from the mean)
is not a twofold, but a fourfold difference in general cognitive ability, with
all its socioeconomic consequences.
The Cognitive Elite Breeds True
Many authors assert that regression to the mean levels IQ differences.
Reading on p. 26 by Herrnstein and Murray: "Over the course of a few
generations, the average intelligence in an aristocratic family fell toward
the population average. hastened by marriages that matched bride and groom by
lineage, not ability." I was afraid that again the usual misunderstanding of
regression was shared and repeated by both authors. However, in the case of
the old nobility their statement is true as in all cases where socioeconomic
status and IQ are understood as properties of the males only and where wives
are chosen according to their beauty, circumference of their breasts, dowry
and so on, regression to the mean is an unavoidable consequence.
But now very many smart women have professional careers of their own and
membership or non-membership of the cognitive elite is a property not only
shared by both husband and wife but also open to scaling of educational
degrees and occupations with respect to IQ for both sexes. What in such cases
where both married partners are members of the cognitive elite?
For the first time (beside an analog conclusion by Seligman 1992) I am
happy to read the only correct conclusion (Herrnstein and Murray, p. 357):
"Regression to the mean is a statistical conclusion, not a biological one . .
. 'Mean' referred to in 'regression to the mean' is the population's own
mean." If we consider the cognitive elite to be a subpopulation of their own,
then the regression will be only toward -and even upward - the mean of this
elite and never toward an IQ of 100 (Weiss 1982).
In 1980 (p. 114) Jensen stated:
There are several critical thresholds within the total range of IQ, each
having important educational and occupational consequences for the individual
. . . . The socially and personally most important threshold regions on the IQ
scale are those that differentiatewith high probability between persons who
because of their level of general mental ability . . . can or cannot succeed
in the academic or college graduate preparatory curriculum through high school
(about 105), and can or cannot graduate from an accredited four-year college
with grades that would qualify for admission to a professional or graduate
school (and IQ 115).
In 1970, in former East Germany, a family study, starting with 1329
mathematically gifted with an IQ higher than 130, came not only to very
similar thresholds but also from a large body of empirical data (for details
see Weiss 1992a) to the conclusion that three overlapping genotypes of IQ
(type M2M2, 68% of the total population of Germany, median IQ 94/type M1 M2,
27%, median IQ 112 / highly gifted type M1 M1, 5%, median IQ 130, mean IQ 139)
are segregating in a Mendelian manner. Twenty three years later a follow-up
(Weiss 1994) of the gifted proved Mendelian segregation among their children
(see Table 2) and among their nephews and nieces (see Table 3).
Of course, in social reality, where cognitive ability is embedded into
personality and chance plays its role in each biography, a 100% fit between a
Mendelian theory of IQ and empirical results cannot be expected. (For example,
of the 16 children (the 6.6% in the first row of Table 2) not fitting the
theory (they did not pass Abitur), one was physically and mentally disabled,
two were from broken marriages, two were midwives, two nurses, five males were
already in highly qualified technical jobs (but without Abitur), three stated
"students" in the questionnaires without further details, i.e. Abitur not
impossible.)
For all gifted individuals M1M1, the chance of their offspring belonging to
the cognitive elite is a direct function of the genotype of their respective
spouses. Of course, achievement needs education, but individuals are born with
fixed, unchangeable levels of cognitive potential. Marriages in which both
partners are M1M1 have only M1M1 children (all with Abitur, cutoff IQ with a
mean of 112, i.e. very similar to the mean of all US college graduates, of
1990; compare Figure 1 and look at the bell curve from Herrnstein and Murray
above). In marriages where the partner of the gifted subject is M1M2 half the
children would be M1M2 and consequently a quarter of all children would not
pass the Abitur (see Table 2, second row). Because n M1M2-M1M2 marriages with
100 children should segregate theoretically into 25 M1M1 (all with Abitur), 50
M1M2 and 25 M2M2 children (all without Abitur), and half of the M1M2 offspring
should attend a high school, the expected value in this marriage group
(typically middle class, both partners M1 M2) for obtaining the Abitur should
be 50"/0 (see Table 3, third row).
Where polygenic theory predicts a normal distribution of ability among
siblings of the same family (Jensen 1980, p. 80), major gene theory (Weiss
1992a) predicts that the IQ distribution of the offspring of homozygotes and
their M1 M2-spouses should be quite markedly skewed (compare Table 2, second
row). The skewedness should be in the opposite direction for M1M1-M1M2
offspring compared to M1M2-M1M2 offspring (compare Table 3, second and fourth
row). M1M2-M1M2 offspring, who are segregating according to Mendelian rules
(see above), should have a much greater variance than the offspring of
marriages where both partners are homozygotes (either M1M1 or M2M2) and are
"breeding true" (compare Table 3, first, third and fifth row), that means only
with regression to the mean of the specific type. The major gene effects
should be even more pronounced if we compare not normalized raw scores instead
of IQ values (we draw attention to Weiss 1992a, figs, 1 and 4). In 1993 in the
follow-up sample (Weiss 1994), 97% (n = 357) of the highly gifted males were
in professions typically associated with an IQ above 123, compared with 55% (n
=77) of the sons, 49% (n =220) of the brothers, 40% (n =346) of the fathers,
18% (n =570) of the male cousins, 22% (n =76) of the nephews, 14% (n =615) of
the uncles, 11% (n =2250) of the male cousins of the parents (with no evidence
for any excess on the paternal or maternal side and hence no evidence for
X-chromosome linked inheritance), 9% (n = 681) of the grandfathers, 5% (n =
1996) of the uncles of parents and 4% (n = 1290) of the great-grandfathers.
In 1903, the famous geneticist Johannsen had already confirmed
experimentally that in pure lines there is no regression toward the mean. In
the sense of genetics the cognitive elite (in contrast to the old European
nobility) is becoming more and more a pure line which breeds true, with all
its socioeconomic consequences. This is the message conveyed by Herrnstein and
Murray that should outlast the disputes of the day.
Table 1. Non-normalized raw scores in the subtests 3 + 4 + 7 + 8 + 9 of the
general cognitive ability test LPS for some selected occupations.
Mathematically sifted tested by Weiss 105
Production engineers 168
Lawyers 162
Psychologists 155
Draughtsmen 146
Clerks 132
Fitters 128
Electricians 116
Hairdressers 105
Bakers 92
Unskilled 60
Data from Horn (1962).
Table 2. Percentage obtaining the Abitur (German high school leaving
examination) among the children of gifted MIM1 (from Weiss, 1994).
* These percentages would be expected under the assumption of Mendelian
segregation and a cutoff of IQ of 112. Legend for Chart:
A - Marriage combination of proband and spouse B - Children with Abitur;
Percentage; obtained C - Children with Abitur; Percentage; expected D -
Children without Abitur; Percentage; obtained E - Children without Abitur;
Percentage expected
A B C D E
both spouses with IQ 124 and higher- M1M1 x M1M1 93.4 100 6.6 0 n =242
gifted with spouse with IQ 75.5 75 25.5 25 n = 1 84 below 124- M1M1 x M1M2
Table 3. Percentage obtaining the Abitur (German high school leaving
examination) among the nephews and nieces of highly gifted M1M1 (from Weiss,
1994).
* These percentages would be expected under the assumption of Mendelian
segregation and a cutoff of IQ of 112. Legend for Chart:
A - Sibs of probands and respective spouse B - Children with Abitur;
Percentage; obtained C - Children with Abitur; Percentage; expected D -
Children without Abitur; Percentage; obtained E - Children without Abitur;
Percentage expected
A B C D E
both spouses with IQ 124
and higher- M1M1 x M1M1 91.4 100 8.6 0 n = 70
one spouse with IQ 124
and higher; the other
with IQ below
124- M1M1 x M1M2 71.5 75 28.5 25 n = 130
both spouses with IQ
between 104 and
124 - M1M2 x M1M2 52.3 50 47.7 50 n = 107
one spouse with IQ
below 105-- M1M2 x M2M2 6.9 25 93.1 75 n = 29
both spouses with
IQ below 105 - M2M2 x M2M2 0 0 100 100 n = 12
Americans with and without a college degree as of 1990
Figure 1. Above: the "perfect" bell curve (from Herrnstein and Murray, p.
46), and Below: the bell-shaped overlapping distributions of the three
genotypes underlying general cognitive ability. In industrialized societies
the percentage of all college graduates fits closely with the sum of the
percentage of the genotype M1M2 plus the highly gifted M1M1.
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