Harvard Psychological Studies Part 68

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 ent.i.ty which may serve as a basis of explanation, but a mathematical construction.

[1] Witmer, Lightner: 'Zur experimentellen Aesthetik einfacher raumlicher Formverhaltnisse,' _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 aesthetic 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 aesthetic, 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 aesthetics 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 aesthetic taste.' Kulpe[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 Korpera,'

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.: 'a.n.a.lytical Psychology,' Boston, 1902, p. 74.

[9] Kulpe, 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 aesthetic 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 formulae. But we cannot make experimental aesthetics 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. Kulpe'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 gla.s.s. Between the gla.s.s 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, 1 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 1 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 pa.s.s 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 _E_ represents the first thirty-six; _E_ 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 _E_ 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.

These 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 _E_ 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.

[Ill.u.s.tration: 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_, _B_ twice, _E_, _F_, _G_, _H_) within modes very near the minimum. Glancing for a moment at the individual averages, we see that none coincides with the total (although _D_ is very near), and that out of eighteen, only four (_D_ twice, _G_ twice) come within five millimeters of the general average, while eight (_B_, _C_, _J_ twice each, _F_, _H_) lie between ten and fifteen millimeters away. The two total averages (although near the golden section), are thus chiefly conspicuous in showing those regions of the line that were avoided as not beautiful. Within a range of ninety millimeters, divided into eighteen sections of five millimeters each, there are ten such sections (50 mm.) each of which represents the maximum of some one subject. The range of maximum judgments is thus about one third the whole line. From such wide limits it is, I think, a methodological error to pick out some single point, and maintain that any explanation whatever of the divisions there made interprets adequately our pleasure in unequal division. Can, above all, the golden section, which in only two cases (_D_, _G_) falls within the maximum mode; in five (_A_, _C_, _F_, _J_ twice) entirely outside all modes, and in no single instance within the maximum on both sides the center--can this seriously play the role of aesthetic norm?

I may state here, briefly, the results of several sets of judgments on lines of the same length as the first but wider, and on other lines of the same width but shorter. There were not enough judgments in either case to make an exact comparison of averages valuable, but in three successively shorter lines, only one subject out of eight varied in a constant direction, making his divisions, as the line grew shorter, absolutely nearer the ends. He himself felt, in fact, that he kept about the same absolute position on the line, regardless of the successive shortenings, made by covering up the ends. This I found to be practically true, and it accounts for the increasing variation toward the ends. Further, with all the subjects but one, two out of three pairs of averages (one pair for each length of line) bore the same relative positions to the center as in the normal line. That is, if the average was nearer the center on the left than on the right, then the same held true for the smaller lines. Not only this. With one exception, the positions of the averages of the various subjects, when considered relatively to one another, stood the same in the shorter lines, in two cases out of three. In short, not only did the pair of averages of each subject on each of the shorter lines retain the same relative positions as in the normal line, but the zone of preference of any subject bore the same relation to that of any other. Such approximations are near enough, perhaps, to warrant the statement that the absolute length of line makes no appreciable difference in the aesthetic judgment. In the wider lines the agreement of the judgments with those of the normal line was, as might be expected, still closer.

In these tests only six subjects were used. As in the former case, however, _E_ was here the exception, his averages being appreciably nearer the center than in the original line. But his judgments of this line, taken during the same period, were so much on the central tack that a comparison of them with those of the wider lines shows very close similarity. The following table will show how _E_'s judgments varied constantly towards the center:

AVERAGE.

L. R.

1. Twenty-one judgments (11 on L. and 10 on R.) during experimentation on _I, I_, etc., but not on same days. 64 65

2. Twenty at different times, but immediately before judging on _I, I_, etc. 69 71

3. Eighteen similar judgments, but immediately after judging on _I, I_, etc. 72 71

4. Twelve taken after all experimentation with _I_, _I_, etc., had ceased. 71 69

The measurements are always from the ends of the line. It looks as if the judgments in (3) were pushed further to the center by being immediately preceded by those on the shorter and the wider lines, but those in (1) and (2) differ markedly, and yet were under no such influences.

From the work on the simple line, with its variations in width and length, these conclusions seem to me of interest. (1) The records offer no one division that can be validly taken to represent 'the most pleasing proportion' and from which interpretation may issue. (2) With one exception (_E_) the subjects, while differing widely from one another in elasticity of judgment, confined themselves severally to pretty constant regions of choice, which hold, relatively, for different lengths and widths of line. (3) Towards the extremities judgments seldom stray beyond a point that would divide the line into fourths, but they approach the center very closely. Most of the subjects, however, found a _slight_ remove from the center disagreeable. (4) Introspectively the subjects were ordinarily aware of a range within which judgments might give equal pleasure, although a slight disturbance of any particular judgment would usually be recognized as a departure from the point of maximum pleasingness. This feeling of potential elasticity of judgment, combined with that of certainty in regard to any particular instance, demands--when the other results are also kept in mind--an interpretative theory to take account of every judgment, and forbids it to seize on an average as the basis of explanation for judgments that persist in maintaining their aesthetic autonomy.

I shall now proceed to the interpretative part of the paper. Bilateral symmetry has long been recognized as a primary principle in aesthetic composition. We inveterately seek to arrange the elements of a figure so as to secure, horizontally, on either side of a central point of reference, an objective equivalence of lines and ma.s.ses. At one extreme this may be the rigid mathematical symmetry of geometrically similar halves; at the other, an intricate system of compensations in which size on one side is balanced by distance on the other, elaboration of design by ma.s.s, and so on. Physiologically speaking, there is here a corresponding equality of muscular innervations, a setting free of bilaterally equal organic energies. Introspection will localize the basis of these in seemingly equal eye movements, in a strain of the head from side to side, as one half the field is regarded, or the other, and in the tendency of one half the body towards a ma.s.sed horizontal movement, which is nevertheless held in check by a similar impulse, on the part of the other half, in the opposite direction, so that equilibrium results. The psychic accompaniment is a feeling of balance; the mind is aesthetically satisfied, at rest. And through whatever bewildering variety of elements in the figure, it is this simple bilateral equivalence that brings us to aesthetic rest. If, however, the symmetry is not good, if we find a gap in design where we expected a filling, the accustomed equilibrium of the organism does not result; psychically there is lack of balance, and the object is aesthetically painful. We seem to have, then, in symmetry, three aspects. First, the objective quant.i.tative equality of sides; second, a corresponding equivalence of bilaterally disposed organic energies, brought into equilibrium because acting in opposite directions; third, a feeling of balance, which is, in symmetry, our aesthetic satisfaction.

It would be possible, as I have intimated, to arrange a series of symmetrical figures in which the first would show simple geometrical reduplication of one side by the other, obvious at a glance; and the last, such a qualitative variety of compensating elements that only painstaking experimentation could make apparent what elements balanced others. The second, through its more subtle exemplification of the rule of quant.i.tative equivalence, might be called a higher order of symmetry. Suppose now that we find given, objects which, aesthetically pleasing, nevertheless present, on one side of a point of reference, or center of division, elements that actually have none corresponding to them on the other; where there is not, in short, _objective_ bilateral equivalence, however subtly manifested, but, rather, a complete lack of compensation, a striking asymmetry. The simplest, most convincing case of this is the horizontal straight line, unequally divided. Must we, because of the lack of objective equality of sides, also say that the bilaterally equivalent muscular innervations are likewise lacking, and that our pleasure consequently does not arise from the feeling of balance? A new aspect of psychophysical aesthetics thus presents itself. Must we invoke a new principle for horizontal unequal division, or is it but a subtly disguised variation of the more familiar symmetry? And in vertical unequal division, what principle governs? A further paper will deal with vertical division. The present paper, as I have said, offers a theory for the horizontal.

To this end, there were introduced, along with the simple line figures already described, more varied ones, designed to suggest interpretation. One whole cla.s.s of figures was tried and discarded because the variations, being introduced at the ends of the simple line, suggested at once the up-and-down balance of the lever about the division point as a fulcrum, and became, therefore, instances of simple symmetry. The parallel between such figures and the simple line failed, also, in the lack of h.o.m.ogeneity on either side the division point in the former, so that the figure did not appear to center at, or issue from the point of division, but rather to terminate or concentrate in the end variations. A cla.s.s of figures that obviated both these difficulties was finally adopted and adhered to throughout the work. As exposed, the figures were as long as the simple line, but of varying widths. On one side, by means of horizontal parallels, the horizontality of the original line was emphasized, while on the other there were introduced various patterns (fillings). Each figure was movable to the right or the left, behind a stationary opening 160 mm.

in length, so that one side might be shortened to any desired degree and the other at the same time lengthened, the total length remaining constant. In this way the division point (the junction of the two sides) could be made to occupy any position on the figure. The figures were also reversible, in order to present the variety-filling on the right or the left.

If it were found that such a filling in one figure varied from one in another so that it obviously presented more than the other of some clearly distinguishable element, and yielded divisions in which it occupied constantly a shorter s.p.a.ce than the other, then we could, theoretically, shorten the divisions at will by adding to the filling in the one respect. If this were true it would be evident that what we demand is an equivalence of fillings--a shorter length being made equivalent to the longer horizontal parallels by the addition of more of the element in which the two short fillings essentially differ. It would then be a fair inference that the different lengths allotted by the various subjects to the short division of the simple line result from varying degrees of subst.i.tution of the element, reduced to its simplest terms, in which our filling varied. Unequal division would thus be an instance of bilateral symmetry.

The thought is plausible. For, in regarding the short part of the line with the long still in vision, one would be likely, from the aesthetic tendency to introduce symmetry into the arrangement of objects, to be irritated by the discrepant inequality of the two lengths, and, in order to obtain the equality, would attribute an added significance to the short length. If the a.s.sumption of bilateral equivalence underlying this is correct, then the repet.i.tion, in quant.i.tative terms, on one side, of what we have on the other, const.i.tutes the unity in the horizontal disposition of aesthetic elements; a unity receptive to an almost infinite variety of actual visual forms--quant.i.tative ident.i.ty in qualitative diversity. If presented material resists objective symmetrical arrangement (which gives, with the minimum expenditure of energy, the corresponding bilateral equivalence of organic energies) we obtain our organic equivalence in supplementing the weaker part by a contribution of energies for which it presents no obvious visual, or objective, basis. From this there results, by reaction, an objective equivalence, for the psychic correlate of the additional energies freed is an attribution to the weaker part, in order to secure this feeling of balance, of some added qualities, which at first it did not appear to have. In the case of the simple line the lack of objective symmetry that everywhere meets us is represented by an unequal division. The enhanced significance acquired by the shorter part, and its psychophysical basis, will engage us further in the introspection of the subjects, and in the final paragraph of the paper. In general, however, the phenomenon that we found in the division of the line--the variety of divisions given by any one object, and the variations among the several subjects--is easily accounted for by the suggested theory, for the different subjects merely exemplify more fixedly the shifting psychophysical states of any one subject.

In all, five sets of the corrected figures were used. Only the second, however, and the fifth (chronologically speaking) appeared indubitably to isolate one element above others, and gave uniform results. But time lacked to develop the fifth sufficiently to warrant positive statement. Certain uniformities appeared, nevertheless, in all the sets, and find due mention in the ensuing discussion. The two figures of the second set are shown in Fig. 2. Variation No. III. shows a design similar to that of No. II., but with its parts set more closely together and offering, therefore, a greater complexity. In Table II.

are given the average divisions of the nine subjects. The total length of the figure was, as usual, 160 mm. Varying numbers of judgments were made on the different subjects.

[Ill.u.s.tration: FIG. 2.]

TABLE II.

No. I. No. II. No. I. (reversed). No. II. (reversed).

L. R. L. R. R. L. R. L.

A 55 0 48 0 59 0 50 0 B 59 0 44 0 63 0 52 0 C 58 0 56 0 52 0 50 0 D 60 0 56 0 60 0 55 0 E 74 59 73 65 74 60 75 67 F 61 67 60 66 65 64 62 65 G 64 64 62 68 63 64 53 67 H 76 68 75 64 66 73 67 71 J 49 0 41 0 50 0 42 0 -- -- -- -- -- -- -- -- Total. 61 64 57 65 61 65 54 67

With the complex fillings at the left, it will be seen, firstly, that in every case the left judgment on No. III. is less than that on No.

II. With the figures reversed, the right judgments on No. III. are less than on No. II., with the exception of subjects _E_ and _H_.