160 THE FACTORS OF THE MIND

derive a new factorial matrix and a new set of factor-
measurements admitting of a very simple and suggestive
interpretation : namely, that the new variates are composed
of a large and specifiable number (f%N) of small and equal
components, drawn by random sampling from a larger pool
of N such components, * all-or-none ' in nature : (/A being
the saturation coefficient for the^th test with the first and
only factor). These components, it is suggested, form the real
* causal background' of our tests, and " may be identified
on the bodily side " with nerve-cells or " neurone-arcs." l

In such a case, however, as I have shown elsewhere, it is
equally possible to reverse the argument, and to demon-
strate mathematically that any factorial matrix, deduced in
the first instance directly from the principles of sampling,
will itself behave as a general factor. Indeed, a formal
proof is scarcely needed : for (to put it crudely) a homo-
geneous brain, consisting merely of a very large number of
similar nerve-cells, identical in nature and in strength, would
obviously be a brain governed by a single general factor,
with no group-factors and no specific factors. In short,
there is no mathematical difference between assuming
only a single factor, varying continuously, and assuming an
infinite (or indefinitely large) number of unit-factors
forming a single homogeneous ' pool.3 A bushel of wheat
is still a bushel, whether we call it corn or insist that it is
composed of innumerable grains.2

I have discussed this point elsewhere ; and there is no
reason for repeating the arguments here, since Thomson,
it is clear, would no longer maintain that the sampling

1 G. H. Thomson, ' On the Causes of Hierarchical Order among Correla-
tion Coefficients,' Proc. Roy. Soc.9 1919, A. XCV, pp. 405 et seq.; cf. [132],
pp. 271, 302. But see below, p. 208, footnote.

2 Brit. J. Educ. Psych., IX, pp. 190 et seq., Brit. J. Psych., XXX, pp. 86
et seq. (a formal proof was appended to the original paper) and p. 209 inf.
Largely, but not entirely, the controversy between Spearman and Thomson
seems to have arisen from a difference of logical standpoint: Spearman is
interested in describing abilities extensionally, Thomson in describing them
intensionally. That seems evident if we think of the factors as logical ab-
stractions instead of picturing them as concrete entities—as neurone-arcs
in the one case, as mental energy in the other. " The difference between the
sampling theory and the two-factor theory," says Thomson, " is that the