REVISED AND EXPANDED EDITION 47
factor analysis, and multivariate thinking in general, are enor-
mously difficult for most people and hard to express without consid-
erable mathematics.
But such conventional works cannot adequately present the his-
tory of the hereditarian theory of unitary intelligence—for this no-
tion relies so crucially on both parts. We must understand why
people ever thought that a unilinear ranking could order people by
mental worth—the IQ thread, usually well treated. But we cannot
grasp or interpret the theory of unitary intelligence until we know
the basis for the prior claim that intelligence can be interpreted as a
single entity (that might then be measured by a single number like
IQ). This rationale derives from factor analysis and its supposed
validation of Spearman's g—the unitary thing in the head. But fac-
tor analysis has usually been ignored, thus precluding all possibility
of real understanding.
I resolved that I would treat factor analysis head-on—and I have
never struggled so hard to render material in a manner accessible
to general readers. I kept failing because I could not translate the
mathematics into understandable prose. Then I finally realized, in
one of those "aha" insights, that I could use Thurstone's alternative
geometrical representation of tests and axes as vectors (arrows) radi-
ating from a common point, rather than the usual algebraic formu-
lations. This approach solved my problem because most people
grasp pictures better than numbers. The resulting Chapter 7 is by
no means easy. It will never rank high in public acclaim, but I have
never been so proud of anything else I ever wrote for popular audi-
ences. I think I found the key for presenting factor analysis, and
one of the most important scientific issues of the twentieth century
cannot be understood without treating this subject. Nothing has
ever gratified me more than numerous unsolicited comments from
professional statisticians over the years, thanking me for this chap-
ter and affirming that I had indeed succeeded in conveying factor
analysis, and that I had done so accurately and understandably. I
am not nearly ready, but I will eventually chant my Nunc dimittis
in peace.
One final and peripheral point about factor analysis and Cyril
Burt: My chapter on factor analysis bears the title "The Real Error
of Cyril Burt: Factor Analysis and the Reification of Intelligence."
Burt had been charged with overt fraud in making up data for his