Sixteen Experimental Investigations from the Harvard Psychological Laboratory by Hugo Münsterberg (100 books to read .txt) 📕

nothing to do with the golden section.

Since Fechner, the chief investigation in the æsthetics 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 æsthetic 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.

[1] Witmer, Lightner: ‘Zur experimentellen Aesthetik einfacher

räumlicher Formverhältnisse,’ Phil. Studien, 1893, IX., S.

96-144, 209-263.

This criticism would apply to judgments of unequal division on either

side the center of a horizontal line. It would apply all the more to

any general average of judgments including both sides, for, as we

shall soon see, the judgments of individuals differ materially on the

two sides, and this difference itself may demand its explanation. And

if we should include within this average, judgments above and below

the center of a vertical line, we should have under one heading four

distinct sets of averages, each of which, in the individual cases,

might show important variations from the others, and therefore require

some variation of explanation. And yet that great leveller, the

general average, has obliterated these vital differences, and is

recorded as indicating the ‘most pleasing proportion.’[3] That such an

average falls near the golden section is immaterial. Witmer himself,

as we shall see,[4] does not set much store by this coincidence as a

starting point for explanation, since he is averse to any mathematical

interpretation, but he does consider the average in question

representative of the most pleasing division.

[2] op. cit., 212-215.

[3] Witmer: op. cit., S. 212-215.

[4] op. cit., S. 262.

I shall now, before proceeding to the details of the experiment to be

recorded, review, very briefly, former interpretative tendencies.

Zeising found that the golden section satisfied his demand for unity

and infinity in the same beautiful object.[5] In the golden section,

says Wundt,[6] there is a unity involving the whole; it is therefore

more beautiful than symmetry, according to the æsthetic principle that

that unification of spatial forms which occurs without marked effort,

which, however, embraces the greater manifold, is the more pleasing.

But to me this manifold, to be æsthetic, must be a sensible manifold,

and it is still a question whether the golden section set of relations

has an actual correlate in sensations. Witmer,[7] however, wrote, at

the conclusion of his careful researches, that scientific æsthetics

allows no more exact statement, in interpretation of the golden

section, than that it forms ‘die rechte Mitte’ between a too great and

a too small variety. Nine years later, in 1902, he says[8] that the

preference for proportion over symmetry is not a demand for an

equality of ratios, but merely for greater variety, and that ‘the

amount of unlikeness or variety that is pleasing will depend upon the

general character of the object, and upon the individual’s grade of

intelligence and æsthetic taste.’ Külpe[9] sees in the golden section

‘a special case of the constancy of the relative sensible

discrimination, or of Weber’s law.’ The division of a line at the

golden section produces ‘apparently equal differences’ between minor

and major, and major and whole. It is ‘the pleasingness of apparently

equal differences.’

[5] Zelsing, A.: ‘Aesthetische Forschungen,’ 1855, S. 172;

‘Neue Lehre von den Proportionen des menschlichen Körpera,’

1854, S. 133-174.

[6] Wundt, W.: ‘Physiologische Psychologie,’ 4te Aufl.,

Leipzig, 1893, Bd. II., S. 240 ff.

[7] op. cit., S. 262.

[8] Witmer, L.: ‘Analytical Psychology,’ Boston, 1902, p. 74.

[9] Külpe, O.: ‘Outlines of Psychology,’ Eng. Trans., London,

1895, pp. 253-255.

These citations show, in brief form, the history of the interpretation

of our pleasure in unequal division. Zeising and Wundt were alike in

error in taking the golden section as the norm. Zeising used it to

support a philosophical theory of the beautiful. Wundt and others too

hastily conclude that the mathematical ratios, intellectually

discriminated, are also sensibly discriminated, and form thus the

basis of our æsthetic pleasure. An extension of this principle would

make our pleasure in any arrangement of forms depend on the

mathematical relations of their parts. We should, of course, have no

special reason for choosing one set of relationships rather than

another, nor for halting at any intricacy of formulæ. But we cannot

make experimental æsthetics a branch of applied mathematics. A theory,

if we are to have psychological explanation at all, must be pertinent

to actual psychic experience. Witmer, while avoiding and condemning

mathematical explanation, does not attempt to push interpretation

beyond the honored category of unity in variety, which is applicable

to anything, and, in principle, is akin to Zeising’s unity and

infinity. We wish to know what actual psychophysical functionings

correspond to this unity in variety. Külpe’s interpretation is such an

attempt, but it seems clear that Weber’s law cannot be applied to the

division at the golden section. It would require of us to estimate the

difference between the long side and the short side to be equal to

that of the long side and the whole. A glance at the division shows

that such complex estimation would compare incomparable facts, since

the short and the long parts are separated, while the long part is

inclosed in the whole. Besides, such an interpretation could not apply

to divisions widely variant from the golden section.

This paper, as I said, reports but the beginnings of an investigation

into unequal division, confined as it is to results obtained from the

division of a simple horizontal line, and to variations introduced as

hints towards interpretation. The tests were made in a partially

darkened room. The apparatus rested on a table of ordinary height, the

part exposed to the subject consisting of an upright screen, 45 cm.

high by 61 cm. broad, covered with black cardboard, approximately in

the center of which was a horizontal opening of considerable size,

backed by opal glass. Between the glass and the cardboard, flush with

the edges of the opening so that no stray light could get through, a

cardboard slide was inserted from behind, into which was cut the

exposed figure. A covered electric light illuminated the figure with a

yellowish-white light, so that all the subject saw, besides a dim

outline of the apparatus and the walls of the room, was the

illuminated figure. An upright strip of steel, 1½ mm. wide, movable in

either direction horizontally by means of strings, and controlled by

the subject, who sat about four feet in front of the table, divided

the horizontal line at any point. On the line, of course, this

appeared as a movable dot. The line itself was arbitrarily made 160

mm. long, and 1½ mm. wide. The subject was asked to divide the line

unequally at the most pleasing place, moving the divider from one end

slowly to the other, far enough to pass outside any pleasing range,

or, perhaps, quite off the line; then, having seen the divider at all

points of the line, he moved it back to that position which appealed

to him as most pleasing. Record having been made of this, by means of

a millimeter scale, the subject, without again going off the line,

moved to the pleasing position on the other side of the center. He

then moved the divider wholly off the line, and made two more

judgments, beginning his movement from the other end of the line.

These four judgments usually sufficed for the simple line for one

experiment. In the course of the experimentation each of nine subjects

gave thirty-six such judgments on either side the center, or

seventy-two in all.

In Fig. 1, I have represented graphically the results of these

judgments. The letters at the left, with the exception of X, mark

the subjects. Beginning with the most extreme judgments on either side

the center, I have erected modes to represent the number of judgments

made within each ensuing five millimeters, the number in each case

being denoted by the figure at the top of the mode. The two vertical

dot-and-dash lines represent the means of the several averages of all

the subjects, or the total averages. The short lines, dropped from

each of the horizontals, mark the individual averages of the divisions

either side the center, and at X these have been concentrated into

one line. Subject E obviously shows two pretty distinct fields of

choice, so that it would have been inaccurate to condense them all

into one average. I have therefore given two on each side the center,

in each case subsuming the judgments represented by the four end modes

under one average. In all, sixty judgments were made by E on each

half the line. Letter E¹ represents the first thirty-six; E² the

full number. A comparison of the two shows how easily averages shift;

how suddenly judgments may concentrate in one region after having been

for months fairly uniformly distributed. The introduction of one more

subject might have varied the total averages by several points. Table

I. shows the various averages and mean variations in tabular form.

TABLE I.

Left. Right.

Div. M.V. Div. M.V.

A 54 2.6 50 3.4

B 46 4.5 49 5.7

C 75 1.8 71 1.6

D 62 4.4 56 4.1

E¹ 57 10.7 60 8.7

F 69 2.6 69 1.6

G 65 3.7 64 2.7

H 72 3.8 67 2.1

J 46 1.9 48 1.3

— – — –

Total 60 3.9 59 3.5

Golden Section = 61.1.

¹These are E‘s general averages on 36 judgments. Fig. 1,

however, represents two averages on each side the center, for

which the figures are, on the left, 43 with M.V. 3.6; and 66

with M.V. 5.3. On the right, 49, M.V. 3.1; and 67, M.V. 2.7.

For the full sixty judgments, his total average was 63 on the

left, and 65 on the right, with mean variations of 9.8 and 7.1

respectively. The four that E² in Fig. 1 shows graphically

were, for the left, 43 with M.V. 3.6; and 68, M.V. 5.1. On the

right, 49, M.V. 3.1; and 69, M.V. 3.4.

[Illustration: FIG. 1.]

Results such as are given in Fig. 1, appear to warrant the criticism

of former experimentation. Starting with the golden section, we find

the two lines representing the total averages running surprisingly

close to it. This line, however, out of a possible eighteen chances,

only twice (subjects D and G) falls wholly within the mode

representing the maximum number of judgments of any single subject. In

six cases (C twice, F, H, J twice) it falls wholly without any

mode whatever; and in seven (A,