| Gould on The Bell
Curve
Fuente: The New Yorker, November 28, 1994
Curveball
The New Yorker, November 28, 1994
BY STEPHEN JAY GOULD
"THE BELL CURVE," by Richard J. Herrnstein and Charles Murray (Free Press; $30),
subtitled "Intelligence and Class Structure in American Life," provides a superb
and unusual opportunity to gain insight into he meaning of experiment as a method In
science. The primary desideratum in all experiments is reduction of confusing variables:
we bring all the buzzing and blooming confusion of the external world into our
laboratories and, holding all else constant in our artificial simplicity, try to vary just
one potential factor at a time. But many subjects defy the use of such an experimental
method -- particularly most social phenomena -- because importation into the laboratory
destroys the subject of the investigation, and then we must yearn for simplifying guides
in nature. If the external world occasionally obliges by holding some crucial factors
constant for us, we can only offer thanks for this natural boost to understanding.
So, when a book garners as much attention as "The Bell Curve," we wish to know
the causes. One might suspect the content itself startlingly new idea, or an old suspicion
newly verified by persuasive data -- but the reason might also be social acceptability, or
even just plain hype. "The Bell Curve," with its claims and supposed
documentation that race and class differences are largely caused by genetic factors and
are therefore essentially immutable, contains no new arguments and presents no compelling
data to support its anachronistic social t Darwinism, so I can only conclude that its
success in winning attention must reflect the depressing temper of our time -- a
historical moment of unprecedented ungenerosity, when a mood for slashing social programs
can be power-fully abetted by an argument that beneficiaries cannot be helped, owing to
inborn cognitive limits expressed as low I.Q. scores.
"The Bell Curve" rests on two distinctly different but sequential arguments,
which together encompass the classic corpus of biological determinism as a social
philosophy. The first argument rehashes the tenets of social Darwinism as it was
originally constituted. "Social Darwinism" has often been used as a general term
for any evolutionary argument about the biological basis of human differences, but the
initial nineteenth-century meaning referred to a specific theory of class stratification
within industrial societies, and particularly to the idea that there was a permanently
poor underclass consisting of genetically inferior people who had precipitated down into
their inevitable fate. The theory arose from a paradox of egalitarianism: as long as
people remain on top of the social heap by accident of a noble name or parental wealth,
and as long as members of despised castes cannot rise no matter what their talents, social
stratification will not reflect intellectual merit, and brilliance will be distributed
across all classes; but when true equality of opportunity is attained smart people rise
and the lower classes become rigid, retaining only the intellectually incompetent.
This argument has attracted a variety of twentieth-century champions, including the
Stanford psychologist Lewis M. Terman, who imported Alfred Binet's original test from
France, developed the Stanford-Binet I.Q. test, and gave a hereditarian interpretation to
the results (one that Binet had vigorously rejected in developing this style of test);
Prime Minister Lee Kuan Yew of Singapore, who tried to institute a eugenics pro-gram of
rewarding well-educated women for higher birth rates; and Richard Herrnstein, a co-author
of "The Bell Curve" and also the author of a 1971 Atlantic Monthly article that
presented the same argument without the documentation. The general claim is neither
uninteresting nor illogical, but it does require the validity of four shaky premises, all
asserted (but hardly discussed or de- fended) by Herrnstein and Murray. Intelligence, in
their formulation, must be depictable as a single number, capable of ranking people in
linear order, genetically based, and effectively immutable. If any of these premises are
false, their en-tire argument collapses. For example, if all are true except immutability,
then programs for early intervention in education might work to boost I.Q. permanently,
just as a pair of eyeglasses may correct a genetic defect in vision. The central argument
of "The Bell Curve" fails because most of the premises are false.
Herrnstein and Murray's second claim, the lightning rod for most commentary, extends the
argument for innate cognitive stratification to a claim that racial differences in I.Q.
are mostly determined by genetic causes -- small differences for Asian superiority over
Caucasian, but large for Caucasians over people of African descent. This argument is as
old as the study of race, and is almost surely fallacious. The last generation's
discussion centered on Arthur Jensen's 1980 book "Bias in Mental Testing" (far
more elaborate and varied than anything presented in "The Bell Curve," and
therefore still a better source for grasping the argument and its problems), and on the
cranky advocacy of William Shockley, a Nobel Prize- winning physicist. The central fallacy
in using the substantial heritability of within- group I.Q. (among whites, for example) as
an explanation of average differences between groups (whites versus blacks, for example)
is now well known and acknowledged by all, including Herrnstein and Murray, but deserves a
re- statement by example. Take a trait that is far more heritable than anyone has ever
claimed I.(2 to be but is politically uncontroversial-- body height. Suppose that I
measure the heights of adult males in a poor Indian village beset with nutritional
deprivation, and suppose the average height of adult males is five feet six inches.
Heritability within the village is high, which is to say that tall fathers (they may
average free feet eight inches) tend to have tall Song while short fathers (five feet four
inches on average) tend to have short sons. But this high heritability within the village
does not mean that better nutrition might not raise average height to five feet ten inches
in a few generations. Similarly, the well-documented fifteen-point average difference in
I.Q. between blacks and whites in America, with substantial heritability of I.Q. in family
lines within each group, permits no automatic conclusion that truly equal opportunity
might not raise the black average enough to equal or surpass the white mean.
Disturbing as I find the anachronism of "The Bell Curve," I am even more
distressed by its pervasive disingenuousness. The authors omit facts, misuse statistical
methods, and seem unwilling to admit the consequences of their own words.
THE ocean of publicity that has engulfed "The Bell Curve" has a basis in what
Murray and Herrnstein, in an article in The New Republic last month, call "the
flashpoint of intelligence as a public topic: the question of genetic differences between
the races." And yet, since the day of the book's publication, Murray (Herrnstein died
a month before the book appeared) has been temporizing, and denying that race is an
important subject in the book at all; he blames the press for unfairly fanning these
particular flames. In The New Republic he and Herrnstein wrote, "Here is what we hope
will be our contribution to the discussion. We put it in italics; if we could, we would
put it in neon lights: The answer doesn't much matter."
Fair enough, in the narrow sense that any individual may be a rarely brilliant member of
an averagely dumb group (and therefore not subject to judgment by the group mean), but
Murray cannot deny that "The Bell Curve" treats race as one of two major topics,
with each given about equal space; nor can he pretend that strongly stated claims about
group differences have no political impact in a society obsessed with the meanings and
consequences of ethnicity. The very first sentence of "The Bell Curve" 's
preface acknowledges that the book treats the two subjects equally: "This book is
about differences in intellectual capacity among people and groups and what those
differences mean for America's future." And Murray and Herrnstein's New Republic
article begins by identifying racial differences as the key subject of interest: "The
private dialogue about race in America is far different from the public one."
Furthermore, Herrnstein and Murray know and acknowledge the critique of extending the
substantial heritability of within-group I.Q. to explain differences between groups, so
they must construct an admittedly circumstantial case for attributing most of the
black-white mean difference to irrevocable genetics -- while properly stressing that the
average difference doesn't help in judging any particular person, because so many
individual blacks score above the white mean in I.Q. Quite apart from the rhetorical
dubiety of this old ploy in a shopworn genre -- "Some of my best friends are Group
X" -- Herrnstein and Murray violate fairness by converting a complex case that can
yield only agnosticism into a biased brief for permanent and heritable difference. They
impose this spin by turning every straw on their side into an oak, while mentioning but
downplaying the strong circumstantial case for substantial malleability and little average
genetic difference. This case includes such evidence as impressive I.Q. scores for poor
black children adopted into affluent and intellectual homes; average I.Q. increases in
some nations since the Second World War equal to the entire fifteen-point difference now
separating blacks and whites in America; and failure to find any cognitive differences
between two cohorts of children born out of wedlock to German women, reared in Germany as
Germans, but fathered by black and white American soldiers.
"THE BELL CURVE" is even more disingenuous in its argument than in its
obfuscation about race. The book is a rhetorical masterpiece of scientism, and it benefits
from the particular kind of fear that numbers impose on nonprofessional commentators. It
runs to eight hundred and forty-five pages, including more than a hundred pages of
appendixes filled with figures. So the text looks complicated, and reviewers shy away with
a knee-jerk claim that, while they suspect fallacies of argument, they really cannot
judge. In the same issue of The New Republic as Murray and Herrnstein's article, Mickey
Kaus writes, "As a lay reader of 'The Bell Curve,' I'm unable to judge fairly,"
and Leon Wieseltier adds, "Murray, too, is hiding the hardness of his politics behind
the hardness of his science. And his science, for all I know, is soft.... Or so I imagine.
I am not a scientist. I know nothing about psychometrics." And Peter Passell, in the
Times: "But this reviewer is not a biologist, and will leave the argument to
experts."
The book is in fact extraordinarily one-dimensional. It makes no attempt to survey the
range of available data, and pays astonishingly little attention to the rich and
informative history of its contentious subject. (One can only recall Santayana's dictum,
now a cliché of intellectual life: "Those who cannot remember the past are condemned
to repeat it.") Virtually all the analysis rests on a single technique applied to a
single set of data -- probably done in one computer run. (I do agree that the authors have
used the most appropriate technique and the best source of information. Still, claims as
broad as those advanced in "The Bell Curve" simply cannot be properly defended
-- that is, either supported or denied -- by such a restricted approach.) The blatant
errors and inadequacies of "The Bell Curve" could be picked up by lay reviewers
if only they would not let themselves be frightened by numbers -- for Herrnstein and
Murray do write clearly, and their mistakes are both patent and accessible.
While disclaiming his own ability to judge, Mickey Kaus, in The New Republic, does
correctly identify the authors' first two claims that are absolutely essential "to
make the pessimistic 'ethnic difference' argument work": "(1) that there is a
single, general measure of mental ability, (2) that the I.Q. tests that purport to measure
this ability . . . aren't culturally biased."
Nothing in "The Bell Curve" angered me more than the authors' failure to supply
any justification for their central claim, the sine qua non of their entire argument: that
the number known as g, the celebrated "general factor" of intelligence, first
identified by the British psychologist Charles Spearman, in 1904, captures a real property
in the head. Murray and Herrnstein simply declare that the issue has been decided, as in
this passage from their New Republic article: "Among the experts, it is by now beyond
much technical dispute that there is such a thing as a general factor of cognitive ability
on which human beings differ and that this general factor is measured reasonably well by a
variety of standardized tests, best of all by I.Q. tests designed for that purpose."
Such a statement represents extraordinary obfuscation, achievable only if one takes
"expert" to mean "that group of psychometricians working in the tradition
of g and its avatar I.Q." The authors even admit that there are three major schools
of psychometric interpretation and that only one supports their view of g and I.Q.
But this issue cannot be decided, or even understood, without discussing the key and only
rationale that has maintained g since Spearman invented it: factor analysis. The fact that
Herrnstein and Murray barely mention the factor-analytic argument forms a central
indictment of "The Bell Curve" and is an illustration of its vacuousness. How
can the authors base an eight-hundred-page book on a claim for the reality of I.Q. as
measuring a genuine, and largely genetic, general cognitive ability -- and then hardly
discuss, either pro or con, the theoretical basis for their certainty?
Admittedly, factor analysis is a difficult mathematical subject, but it can be explained
to lay readers with a geometrical formulation developed by L. L. Thurstone, an American
psychologist, in the nineteen-thirties and used by me in a full chapter on factor analysis
in my 1981 book "The Mismeasure of Man." A few paragraphs cannot suffice for
adequate explanation, so, although I offer some sketchy hints below, readers should not
question their own I.Q.s if the topic still seems arcane.
In brief, a person's performance on various mental tests tends to be positively correlated
-- that is, if you do well on one kind of test, you tend to do well on the other kinds.
This is scarcely surprising, and is subject to interpretation that is either purely
genetic (that an innate thing in the head boosts all performances) or purely environmental
(that good books and good childhood nutrition boost all performances); the positive
correlations in themselves say nothing about causes. The results of these tests can be
plotted on a multidimensional graph with an axis for each test. Spearman used factor
analysis to find a single dimension -- which he called g -- that best identifies the
common factor behind positive correlations among the tests. But Thurstone later showed
that g could be made to disappear by sit rotating the dimensions to different positions.
In one rotation Thurstone placed the dimensions near the most widely separated attributes
among the to tests, thus giving rise to the theory of multple intelligences (verbal,
mathematical, spatial, etc., with no overarching g). This theory (which I support) has
been as advocated by many prominent psychometricians, including J. P. Guilford, in the
nineteen-fifties, and Howard Gardner today. In this perspective, g cannot have inherent
reality, for it emerges in one form of mathematical representation for correlations among
tests and disappears (or greatly attenuates) in other forms, which are entirely equivalent
in amount of information explained. In any case, you can't grasp the issue at all without
a clear exposition of factor analysis -- and "The Bell Curve" cops out on this
central concept.
As for Kaus's second issue, cultural bias, the presentation of it in "The Bell
Curve" matches Arthur Jensen's and that of other hereditarians, in confusing a
technical (and proper) meaning of "bias" (I call it "S-bias," for
''statistical") with the entirely different vernacular concept (I call it
"V-bias") that provokes popular debate. All these authors sweat up and down (and
I agree with them completely) that the tests are not biased -- in the statistician's
definition. Lack of S-bias means that the same score, when it is achieved by members of
different groups, predicts the same thing, that is, a black person and a white person with
identical scores will have the same probabilities for doing anything that I.Q. is supposed
to predict.
But V-bias, the source of public concern, embodies an entirely different issue, which,
unfortunately, uses the same word. The public wants to know whether blacks average 85 and
whites 100 because society treats blacks unfairly -- that is, whether lower black scores
record biases in this social sense. And this crucial question (to which we do not know the
answer) cannot be addressed by a demonstration that S-bias doesn't exist, which is the
only issue analyzed, however correctly, in "The Bell Curve."
THE book is also suspect in its use of statistics. As I mentioned, virtually all its data
derive from one analysis -- a plotting, by a technique called multiple regression, of the
social behaviors that agitate us, such as crime, unemployment, and births out of wedlock
(known as dependent variables), against both I.Q. and parental socioeconomic status (known
as independent variables). The authors first hold I.Q. constant and consider the
relationship of social behaviors to parental socioeconomic status. They then hold
socioeconomic status constant and consider the relationship of the same social behaviors
to I.Q. In general, they find a higher correlation with I.Q. than with socioeconomic
status; for example, people with low I.Q. are more likely to drop out of high school than
people whose parents have low socioeconomic status.
But such analyses must engage two issues -- the form and the strength of the relationship
-- and Herrnstein and Murray discuss only the issue that seems to support their viewpoint,
while virtually ignoring (and in one key passage almost willfully hiding) the other. Their
numerous graphs present only the form of the relationships; that is, they draw the
regression curves of their variables against I.Q. and parental socioeconomic status. But,
in violation of all statistical norms that I've ever learned, they plot only the
regression curve and do not show the scatter of variation around the curve, so their
graphs do not show anything about the strength of the relationships -- that is, the amount
of variation in social factors explained by I.Q. and socioeconomic status. Indeed, almost
all their relationships are weak: very lithe of the variation in social factors is
explained by either independent variable (though the form of this small amount of
explanation does lie in their favored direction). In short, their own data indicate that
I.Q. is not a major factor in determining variation in nearly all the social behaviors
they study -- and so their conclusions collapse, or at least become so greatly attenuated
that their pessimism and conservative social agenda gain no significant support.
Herrnstein and Murray actually admit as much in one crucial passage, but then they hide
the pattern. They write, "It [cognitive ability] almost always explains less than 20
percent of the variance, to use the statistician's term, usually less than 10 percent and
often less than 5 percent. What this means in English is that you cannot predict what a
given person will do from his I.Q. score.... On the other hand, despite the low
association at the individual level, large differences in social behavior separate groups
of people when the groups differ intellectually on the average." Despite this
disclaimer, their remarkable next sentence makes a strong causal claim. "We will
argue that intelligence itself, not just its correlation with socioeconomic status, is
responsible for these group differences." But a few per cent of statistical
determination is not causal explanation. And the case is even worse for their key genetic
argument, since they claim a heritability of about sixty per cent for I.Q, so to isolate
the strength of genetic determination by Herrnstein and Murray's own criteria you must
nearly halve even the few per cent they claim to explain.
My charge of disingenuousness receives its strongest affirmation in a sentence tucked away
on the first page of Appendix 4, page 593: the authors state, "In the text, we do not
refer to the usual measure of goodness of fit for multiple regressions, R2, but they are
presented here for the cross-sectional analyses." Now, why would they exclude from
the text, and relegate to an appendix that very few people will read, or even consult, a
number that, by their own admission, is "the usual measure of goodness of fit"?
I can rely conclude that they did not choose admit in the main text the extreme weakness
of their vaunted relationships.
Henrnstein and Murray's correlation coefficients are generally low enough by themselves to
inspire lack of confidence. (Correlation coefficients measure the strength of linear
relationships between variables; the positive values run from 0.0 for no relationship to
1.0 for perfect linear relationship.) Although low figures are not atypical for large
social-science surveys involving many variables, most of Herrnstein and Murray's
correlations are very weak -- often in the 0.2 to 0.4 range. Now, 0.4 may sound
respectably strong, but -- and this is the key point -- R2 is the square of the
correlation coefficient, and the square of a umber between zero and one is less an the
number itself, so a 0.4 correlation yields an r-squared of only .16. In Appendix 4, then,
one discovers that the vast majority of the conventional measures of R2, excluded from the
main body of the text, are less than 0.1. These very low values of R2 expose the true
weakness, in any meaningful vernacular sense, of nearly all the relationships that form
the meat of "The Bell Curve."
LIKE so many conservative ideologues who rail against the largely Bogus ogre of
suffocating political correctness, Herrnstein and Murray claim that they only want a
hearing for unpopular views so that truth will out. And here, for once, I agree entirely.
As a card-carrying First Amendment (near) absolutist, I applaud the publication of
unpopular views that some people consider dangerous. I am delighted that "The Bell
Curve" was written -- so that its errors could be exposed, for Herrnstein and Murray
are right to point out the difference between public and private agendas on race, and we
must struggle to make an impact on the private agendas as well. But "The Bell
Curve" is scarcely an academic treatise in social theory and population genetics. It
is a manifesto of conservative ideology; the book's inadequate and biased treatment of
data displays its primary purpose -- advocacy. The text evokes the dreary and scary
drumbeat of claims associated with conservative think tanks: reduction or elimination of
welfare, ending or sharply curtailing affirmative action in schools and workplaces,
cutting back Head Start and other forms of preschool education, trimming programs for the
slowest learners and applying those funds to the gifted. (I would love to see more
attention paid to talented students, but not at this cruel price.)
The penultimate chapter presents an apocalyptic vision of a society with a growing
underclass permanently mired in the inevitable sloth of their low I.Q.s. They will take
over our city centers, keep having illegitimate babies (for many are too stupid to
practice birth control), and ultimately require a kind of custodial state, more to keep
them in check -- and out of high-I.Q. neighborhoods -- than to realize any hope of an
amelioration, which low I.Q. makes impossible in any case. Herrnstein and Murray actually
write, "In short, by custodial state, we have in mind a high- tech and more lavish
version of the Indian reservation for some substantial minority of the nation's
population, while the rest of America tries to go about its business."
The final chapter tries to suggest an alternative, but I have never read anything more
almost grotesquely inadequate. Herrnstein and Murray yearn romantically for the good old
days of towns and neighborhoods where all people could be given tasks of value, and
self-esteem could be found for people on all steps of the I.Q. hierarchy (so Forrest Gump
might collect clothing for the church raffle, while Mr. Murray and the other bright ones
do the planning and keep the accounts -- they have forgotten about the town Jew and the
dwellers on the other side of the tracks in many of these idyllic villages). I do believe
in this concept of neighborhood, and I will fight for its return. I grew up in such a
place in Queens. But can anyone seriously find solutions for (rather than important
palliatives of) our social ills therein?
However, if Herrnstein and Murray are wrong, and I.Q. represents not an immutable thing in
the head, grading human beings on a single scale of general capacity with large numbers of
custodial incompetents at the bottom, then the model that generates their gloomy vision
collapses, and the wonderful variousness of human abilities, properly nurtured, reemerges.
We must fight the doctrine of "The Bell Curve" both because it is wrong and
because it will, if activated, cut off all possibility of proper nurturance for everyone's
intelligence. Of course, we cannot all be rocket scientists or brain surgeons, but those
who can't might be rock musicians or professional athletes (and gain far more social
prestige and salary thereby), while others will indeed serve by standing and waiting.
I closed my chapter in "The Mismeasure of Man" on the unreality of g and the
fallacy of regarding intelligence as a single-scaled, innate thing in the head with a
marvellous quotation from John Stuart Mill, well worth repeating:
The tendency has always been strong to believe that whatever received a name must be an
entity or being, having an independent existence of its own. And if no real entity
answering to the name could be found, men did not for that reason suppose that none
existed, but imagined that it was something particularly abstruse and mysterious.
How strange that we would let a single and false number divide us, when evolution has
united all people in the recency of our common ancestry -- thus undergirding with a shared
humanity that infinite variety which custom can never stale. E pluribus unum.
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