236 THE FACTORS OF THE MIND

resemblances. But we now see that it would be equally
true, and far less misleading, to say they indicate lack of
resemblance, or difference. It would be truer still, and much
more instructive, to think of our tables of measurements,
correlations, factor-saturations and the like as comprising
a series of mutually equivalent matrices, each capable of
being transformed into the other, and to note that each of
those matrices, even if ultimately reduced to a single row or
vector, can still enumerate only relations between qualities
and not the amounts of those qualities by themselves : just
as the co-ordinates of space and time can only state the
position of a star in regard to some other object or observer,
and never its absolute position in the universe.

If, however, we adopt the commoner view—that factors
are c powers' or c abilities ' or ' mental energies/ which can
aid performance but never hinder it, and that the factor-
saturation measures the causal influence of the ability on the
test, and that factor-measurements state the amount of
ability that a person has at his disposal—then we shall be
forced, with Spearman, Thurstone, and Alexander, to
accept a far narrower view of the possibilities of factorial
work. With them we shall be compelled to reject the
whole notion of negative saturations: for with them we shall
argue that a factor, being an * ability ' or c organ,5 can only
be present or absent, never a minus quantity ; hence it can
have only positive or zero saturations (precisely zero, not
approximately zero).1 Wherever we find any negative
values, we shall start ' rotating our axes > until we are left
with positive saturations only. This will mean, paradoxic-
ally enough, that, having begun with a set of correlated tests
or traits, and having reduced them to terms of independent

1 See below, chap* xii. I have defended the acceptance of negative
saturations elsewhere ([137], p. 90) and need not repeat the arguments here.
Once again, a similar change of standpoint is discernible in physics, namely,
from concrete explanatory principles, which permitted only positive effects, to
wider and more abstract principles that would permit negative relations as well
as positive. " The concept of substance introduces ... a limited form of
analysis... in which the systems are restricted to those which furnish a set of
positive parts. . . . Though there may be such cases in physics , . ,, we
now look on it as an incidental restriction in a particular application"
(Eddington, loc. cit.9 p. 120).