122 THE FACTORS OF THE MIND

(even though the critics are drawn from very different schools) as
apparently obtains among physicists in regard to the mass, distance,
or speed of movement of (say) some of the remoter stars.

It is not difficult to see why our first attempt at a serial arrange-
ment of colours broke down. Colours vary in several directions at
once ; and to arrange a set of mixed variables in a one-dimensional
scale is obviously impossible. It is like trying to state the position
of the stars by assigning a single numeral to each. If, however, we
carry out a factor-analysis for colours, we shall easily be able to
show that they can be ordered in a perfectly coherent system,
provided three bipolar factors are employed, i.e. provided we use
three independent generating relations, instead of one,

A similar confusion stultifies a good many of our first efforts at
serial arrangement in applied psychology. When a teacher is
asked to grade the pupils in his class, his judgments will often fail to
satisfy our preliminary postulates. He puts Tom above Dick
" because Tom is brighter " ; and Dick above Harry " because Dick
has learnt far more since he has been with us " ; but presently he
will decide that Harry " ought certainly to go above Tom," because
" Harry is far more intelligent, although he is rather lazy." Since
the postulate of transitivity is thus violated, must we infer that any
order of merit for school pupils is out of the question ? The answer
obviously is that " merit" denotes a complex and therefore somewhat
ambiguous relation. Once again a factor-analysis is needed to
ascertain whether the complex relation is not analysable into two
or more that are independent of each other—relative intelligence
and relative industry, for example, and possibly relative speed of
memorization. As soon as we have extracted a suitable relation the
task of satisfying the postulates is comparatively simple.

But even, when these first three postulates are satisfied,
further practical difficulties arise which suggest that the
three requirements alone are not enough to supply a satis-
factory means of grading. First, as we have seen, a single
observer and a single set of observations are seldom likely
to be conclusive. If in playing chess Tom beats Dick at
the first game and Dick beats Harry at the second, we
cannot be sure that Harry will not beat Tom at the third.
Evidently, therefore, we must repeat the trials or the tests.
But that will produce differences between the several
relations that are differences not of kind, but rather of
degree : x beating y at 19 games out of 20 is a different
relation from x beating y at only u out of 20.