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 clichˇ 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.