2c? 2 THE MISMEASURE OF MANit as nonaccidental. But we cannot infer the cause from the corre-
lation, and the cause is certainly complex.
Spearman's g is particularly subject to ambiguity in interpreta-
tion, if only because the two most contradictory causal hypotheses
are both fully consistent with it: 1) that it reflects an inherited level
of mental acuity (some people do well on most tests because they
are born smarter); or 2) that it records environmental advantages
and deficits (some people do well on most tests because they are
well schooled, grew up with enough to eat, books in the home, and
loving parents). If the simple existence of g can be theoretically
interpreted in either a purely hereditarian or purely environmen-
talist way, then its mere presence—even its reasonable strength—
cannot justly lead to any reification at all. The temptation to reify
is powerful. The idea that we have detected something "underly-
ing" the externalities of a large set of correlation coefficients, some-
thing perhaps more real than the superficial measurements
themselves, can be intoxicating. It is Plato's essence, the abstract,
eternal reality underlying superficial appearances. But it is a temp-
tation that we must resist, for it reflects an ancient prejudice of
thought, not a truth of nature.Rotation and the nonnecessity of principal components
Another, more technical, argument clearly demonstrates why
principal components cannot be automatically reified as causal
entities. If principal components represented the only way to sim-
plify a correlation matrix, then some special status for them might
be legitimately sought. But they represent only one method among
many for inserting axes into a multidimensional space. Principal
components have a definite geometric arrangement, specified by
the criterion used to construct them—that the first principal com-
ponent shall resolve a maximal amount of information in a set of
vectors and that subsequent components shall all be mutually per-
pendicular. But there is nothing sacrosanct about this criterion;
vectors may be resolved into any set of axes placed within their
space. Principal components provide insight in some cases, but
other criteria are often more useful.
Consider the following situation, in which another scheme for
placing axes might be preferred. In Figure 6.6 I show correlations
between four mental tests, two of verbal and two of arithmetical