24 THE FACTORS OF THE MIND

of striking regularity or simplicity : the c hierarchical '
pattern, where every row of coefficients is proportional to
every other, so that the whole set can be explained in terms
of a single factor, is the best-known instance ;1 the * bipolar '
pattern, where the entire table can be arranged in four
quadrants, two positive and two negative, is another case,2
Now, the emergence of such simple patterns, so it is com-
monly argued, can hardly be ascribed to chance ; it must
therefore constitute a significant item of evidence in favour
of some underlying factor.

No doubt, in many experimental results, the very sim-
plicity of a pattern of figures is rightly held to be suggestive
of something more than could be inferred from the figures
taken alone or individually ; and the simplicity of a formula,
at any rate in the simpler sciences, is always deemed an
added reason for its acceptance. Yet, without extraneous
information, it is seldom possible to say with certainty what:
that something is : for, strangely enough, the simplicity of a
pattern or a formula may imply either a very small number
of large causes or (what is so often ignored) a very large
number of small causes.3

1 See Appendix I, Table I.

2 A typical example is seen in conclusions drawn from the symmetrical
pattern formed by residual correlations after a factor lias been eliminated
(see Appendix I, Table V). In a research quoted by Stephenson ([97],
p. 360) a similar bipolar pattern was found in facton/ing a set of cognitive
tests, when the number of items correlated was only twelve. Not one of
the coefficients was statistically significant as judged by the ordinary
sampling error; nevertheless, Stephenson maintains that the mere presence of
the pattern (* system 5,' as he calls it) is of itself convincing evidence for the
existence of two antithetical or ' obverse ' factors. Now, as I have tried to
show elsewhere, the consistency conditions, which every table of inter-
correlations is bound to fulfil., tend inevitably to introduce such bipolar
patterns. The pattern itself, therefore, affords no evidence for any factor
other than chance, since it constitutes the most likely result where chance
alone is operative. The assumption that bipolar symmetry cannot be a
haphazard product seems analogous to the contention of a naive student who,
after calculating an average, added up all his positive residuals and found the
total to be -f- &35> ^d then, adding up all the negative residuals, found
that these came to exactly — 635 ; his exclamation was that such a remark-
able coincidence between the two figures could not possibly be produced by
accidental deviations.

3 The latter alternative arises in physics as well as in psychology, and seems