The present paper reports the beginnings of an investigation designed to throw light on the psychological basis of our aesthetic pleasure in unequal division.  It is confined to horizontal division.  Owing to the prestige of the golden section, that is, of that division of the simple line which gives a short part bearing the same ratio to the long part that the latter bears to the whole line, experimentation of this sort has been fettered.  Investigators have confined their efforts to statistical records of approximations to, or deviations from, the golden section.  This exalts it into a possible aesthetic norm.  But such a gratuitous supposition, by limiting the inquiry to the verification of this norm, distorts the results, tempting one to forget the provisional nature of the assumption, and to consider divergence from the golden section as an error, instead of another example, merely, of unequal division.  We have, as a matter of fact, on one hand, investigations that do not verify the golden section, and, on the other hand, a series of attempts to account for our pleasure in it, as if it were, beyond dispute, the norm.  In this way the statistical inquiries have been narrowed in scope, and interpretation retarded and misdirected.  Statistically our aim should be to ascertain within how wide limits aesthetically pleasing unequal divisions fall; and an interpretative principle must be flexible enough to include persistent variations from any hypothetical norm, unless they can be otherwise accounted for.  If it is not forced on us, we have, in either case, nothing to do with the golden section.

Since Fechner, the chief investigation in the aesthetics of simple forms is that of Witmer, in 1893.[1] Only a small part of his work relates to horizontal division, but enough to show what seems to me a radical defect in statistical method, namely, that of accepting a general average of the average judgments of the several subjects, as ‘the most pleasing relation’ or ’the most pleasing proportion.’[2] Such a total average may fall wholly without the range of judgments of every subject concerned, and tells us nothing certain about the specific judgments of any one.  Even in the case of the individual subject, if he shows in the course of long experimentation that he has two distinct sets of judgments, it is not valid to say that his real norm lies between the two; much less when several subjects are concerned.  If averages are data to be psychophysically explained, they must fall well within actual individual ranges of judgment, else they correspond to no empirically determinable psychophysical processes.  Each individual is a locus of possible aesthetic satisfactions.  Since such a locus is our ultimate basis for interpretation, it is inept to choose, as ‘the most pleasing proportion,’ one that may have no correspondent empirical reference.  The normal or ideal individual, which such a norm implies, is not a psychophysical entity which may serve as a basis of explanation, but a mathematical construction.