NATURE OF THE FACTORIAL TECHNIQUE 93

is what I have called weighted summation, that is, the
computation of product-sums.

These analogous techniques have been taken over from
mathematicians, and developed by psychologists and by
physicists in almost complete independence; indeed,
during the earlier stages of their work, each was entirely
ignorant of the technical methods which the other was
adopting. The reader, therefore, may feel tempted to ask
whether they may not have been unconsciously driven to
apply very much the same devices because the material
world and the mental world are, as we know them, very
much akin in their ultimate nature, and so yield to the
same mode of analysis : both being essentially describable
in terms of patterns of relations between unknown relata.
That, however, is a question which we must postpone until
we take up the metaphysical issues.

Mathematical Arguments in Psychology.—The technical
methods that have been thus worked out may be regarded
as a special application of a branch of higher mathematics
which has received the name of the c theory of groups'
[71]; and, as I shall argue later,1 it will probably be to the
theory of groups itself that the psychologist of the future
will turn directly for his analytic technique. Here it will
be sufficient to note that, in the last resort, the apparent
reason why we can deal with intellectual processes by
methods analogous to those used in dealing with kinetic
processes is, not that the former, like the latter, are mani-
festations of one and the same physical energy, but that in
both cases the resulting changes can be expressed as the
effect of group-operations. Now, the philosopher would
consider the theory of groups, not as a branch of mathe-
matics, but as a branch of formal logic ; and, indeed, most
mathematicians would nowadays agree that their science at
its widest is to be regarded, not in the old-fashioned sense
as the science of quantity, but as the science of logical rela-
tions : c logic and mathematics differ as boy and man:
logic was the youth of mathematics; mathematics is the man-
hood of logic.'2 This suggests a conclusion of the utmost

1 See below, p. 242.

2 B, Russell, Introduction to Mathematical Philosophy, p. 194.