ioo THE FACTORS OF THE MIND

been sharpened up until it takes the shape of an algebraic
calculus.

The student, who is already familiar with the more
technical procedures, can easily confirm this description if
he considers the nature of what corresponds to ' factors' in
modern physics. The additive * hierarchies? l of the
psychologist, i.e. the sets of figures that distinguish and
describe the psychologist's factors, would in quantum
physics be called c selective operators.' 2 When the psycho-
logist takes a mark list giving the measurements of, say, a
hundred persons for a dozen or more correlated tests, and
reduces these measurements to terms of less than half a
dozen uncorrelated factors, he is following almost exactly
the same procedure as the physicist who measures the
magnetic moments of a number of different metallic atoms,
deduces a c spectral set of selective operators,' and so obtains
the quantitative ' spectrum' of his c assembly/ The
physicist sorts his atoms into so many different kinds. In the
same way the psychologist's factors are devices for taking a
heterogeneous group of observables, and dividing the whole
set up into smaller classes which are more or less homo-
geneous. Thus, what the physicist says of his c operators'
might be applied forthwith to the psychologist's factors :
they provide " a species of spectral analysis in which a given
inhomogeneous aggregate a is resolved into a number of
parts which are (relatively) homogeneous with respect to
some variable y." 3 In plain language, then, they are
merely classificatory devices.

This standpoint may enable us to resolve in advance
many of the other heated questions that have long divided
factorists in psychology; for it now becomes evident that
these controversies, though they wear a psychological or a

1 The reader who is not yet acquainted with the peculiar use of this term
in factor-analysis may turn to Appendix I, Tables I and II, for illustrations,
and to p. 149 below for the definition and formula. This special usage is only
accidentally connected with the more familiar meaning adopted a page or
two back.

2 See chap. IX, p. 264, and Appendix II, p. 491.

8 G. Temple, The General Principles of Quantum Theory9 1934, p. 33-
Elsewhere I have offered a formal proof of the virtual identity of the physi-
cist's analysis and the psychologist's, Psycbometrika, HI, 1938, pp. 151-68.