STUDIES IN ÆSTHETIC PROCESSES. — часть 6

The experiments of Hofbauer and Cleghorn, and many facts about the unit groups themselves, make it evident that the function of stimuli, during the movement cycle, varies with the position of the stimulus in that cycle. This offers a possible explanation of the striking peculiarities of the unit groups. The iamb [\/ _'] and the trochee [_' \/] should be quite alike for a general synthesizing process; but not only is the experiential character of the two quite unlike, but the ratio between their intervals is entirely different.

A number of measurements by different observers show that in the iambic foot the unaccented syllable is proportionately much shorter than the unaccented syllable in the trochaic foot. It is very easy to beat a simple up-and-down accompaniment to a series of simple feet of nonsense syllables; in the accompaniment the bottom of the down stroke, the limiting sensation of the movement cycle, coincides with the accented syllable of the foot. It is not an unwarranted assumption that such a fundamental accompaniment represents the fundamental movement cycle of that rhythm.

During the present investigation several observers were asked to determine at just what point in the fundamental movement the unaccented syllable occurred, when the subject gave a series of nonsense syllables. In the fundamental accompaniment the excursion of the hand and arm was at least.4 meter. Four subjects were thus tested, and the results were uniform in the case of all the simple types of unit groups.

In the case of the iamb the unaccented syllable occurs at the top of the movement, at the very beginning of the contraction phase (A, in Fig. 5).

In the case of the trochee the unaccented syllable occurs in the first third of the relaxation phase (B).

It is interesting to note that the unaccented element of the trochee comes at the earlier part of the relaxation phase, where it must intensify the relaxation process, and tend to shorten the total length of the cycle. This may be the reason for its peculiar buoyant, vigorous and non-final character. On the other hand the unaccented element of the iamb occurs at a point where it may initiate and intensify the contraction, which gives the limiting sensation; it is, therefore, more closely bound to the limiting sensation, and has the character of intensifying the beat. There is a similar contrast in the cases of the dactyl and anapæst. The accented syllable of the dactyl is longest, and the second unaccented syllable, the last in the group, is shortest. The accented syllable of the anapæst is much longer in proportion than that of the dactyl, and the unaccented syllables are very short, and hence, very close to the accented syllable, as compared with the dactyl.

In the case of the dactyl the first unaccented syllable in the movement cycle occurs at the beginning of the relaxation phase (B), in the same zone as the unaccented of the trochee. The second unaccented syllable of the dactyl appears at the beginning of the next contraction phase (A), in the zone of the unaccented syllable of the iamb. The group seems a sort of combination of the iamb and trochee, and has an element in every possible zone of the movement cycle. Like the trochee the dactyl is a non-final foot.

The unaccented syllables of the anapæst both occur at the beginning of the contraction phase (A). They are both within the zone of the unaccented syllable of the iamb. The group seems an iamb with a duplicated unaccented syllable. It is possible to form a unit group in nonsense syllables where the unaccented syllable of the iamb shall be represented not by two syllables, as in the anapæst, but by even three.

The anapæst and dactyl, if they correspond to this construction, should show a decided difference as to the possibility of prolonging the foot pause. The prolongation of the foot pause would make the dactyl but a modified trochee.

It is significant that in poetry no other types of unit groups are often recognized. The amphibrach, laid out on this scheme, would coincide with the dactyl, as there are but three possible zones for foot elements: the zone of the limiting sensation (always occupied by the accented syllable), the zone of the contraction phase (occupied by the unaccented syllables of the iamb and anapæst), and the zone of the relaxation phase (occupied by the unaccented syllable of the trochee and the middle syllable of the dactyl).

The simple sound series is fairly regular, because of its cyclic and automatic character. It is not a matter of time estimation, and the 'Taktgleichheit' is not observed with accuracy. The primary requisite for the unit groups is that they shall be alike, not that they shall be equal. The normal cycle with a heavy accent is longer than the normal cycle with a lighter accent, for the simple reason that it takes muscles longer to relax from the tenser condition. Time is not mysteriously 'lost'; the objective difference is not noticed, simply because there are no striking differences in the cycles to lead one to a time judgment. Ebhardt's notion that the motor reaction interferes with the time judgment, and that a small amount of time is needed in the rhythmic series in which to make time judgments, is a mere myth.

An unusual irregularity, like a 'lag,' is noted because of the sense of strain and because other events supervene in the interval. But such lags may be large without destroying the rhythm; indeed cæsural and verse pauses are essential to a rhythm, and in no sense rhythm-destroying. An unbroken series of unit groups is an abstraction to which most forms of apparatus have helped us. Between the extreme views of Bolton24 and Sidney Lanier,25who make regularity an essential of the rhythm of verse, and Meumann, on the other hand, who makes the meaning predominate over the rhythm, the choice would fall with Meumann, if one must choose. Bolton comes to the matter after an investigation in which regularity was a characteristic of all the series. Lanier's constructions are in musical terms, and for that very reason open to question. He points out many subtle and interesting relationships, but that verse can be formulated in terms of music is a theory which stands or falls by experimental tests.

TABLE XII.

I    saw    a    ship    a    sailing
         50   16  20  13 9 18  32 23-  132
    A    sailing    on    the    sea
    10 16  45       22     8  15  49  -68
And    it    was    full    of    pretty    things
 8   6 20 6   6  27  37  12  8  7   20   12   41    -34
    For    baby    and    for    me
     14  9  27  37  18 20  14 8  46   --

Totals of the feet: --/66/60/187
                    26/45/45/117
                    14/59/49/47/75
                    23/64/60/46--

Who    killed    Cock    Robin
 19      34       23     24 17-77
  I    said    the    sparrow
 45 21  19      3     47   29 --
With    my    bow    and    arrow
 22     36 25  49 11  38 12 23 33-42
  I    killed    Cock    Robin
  33 12  33   21  22  5  21 16 - 95

(The first stanza was measured in the Harvard Laboratory. The last is modified from Scripture's measurements of the gramophone record (1899). As the scansion of the last is in doubt with Scripture, no totals of feet are given.)

In the cases given in the above table there is an irregularity quite impossible to music.

In the movement cycle of the simple sounds there is a perfect uniformity of the movements of the positive and negative sets of muscles from unit group to unit group. But in verse, the movements of the motor apparatus are very complicated. Certain combinations require more time for execution; but if this variation in the details of the movement does not break the series of motor cues, or so delay the movements as to produce a feeling of strain, the unit groups are felt to be alike. We have no means of judging their temporal equality, even if we cared to judge of it. It is a mistake, however, to say that time relations ('quantity') play no part in modern verse, for the phases of the movement cycle have certain duration relations which can be varied only within limits.

Extreme caution is necessary in drawing conclusions as to the nature of verse from work with scanned nonsense syllables or with mechanical clicks. It is safe to say that verse is rhythmic, and, if rhythm depends on a certain regularity of movements, that verse will show such movements. It will of course use the widest variation possible in the matter of accents, lags, dynamic forms, and lengths of sonant and element depending on emphasis. The character of the verse as it appears on the page may not be the character of the verse as it is actually read. The verses may be arbitrarily united or divided. But in any simple, rhythmic series, like verse, it seems inevitable that there shall be a pause at the end of the real verse, unless some such device as rhyme is used for the larger phrasing.

There is a variety of repetitions in poetry. There may be a vague, haunting recurrence of a word or phrase, without a definite or symmetrical place in the structure.

Repetition at once attracts attention and tends to become a structural element because of its vividness in the total effect. There are two ways in which it may enter into the rhythmic structure. It may become a well-defined refrain, usually of more than one word, repeated at intervals and giving a sense of recognition and possibly of completeness, or it may be so correlated that the verses are bound together and occur in groups or pairs. Rhyme is a highly specialized form of such recurrence.

The introduction of rhyme into verse must affect the verse in two directions.

It makes one element in the time values, viz., the verse pause, much more flexible and favors 'run on' form of verses; it is an important factor in building larger unities; it correlates verses, and contributes definite 'Gestaltqualitäten' which make possible the recognition of structure and the control of the larger movements which determine this structure. Thus it gives plasticity and variety to the verse.

On the other hand, it limits the verse form in several directions. The general dynamic relations and the individual accents must conform to the types possible with rhyme. The expressional changes of pitch, which constitute the 'melody,' or the 'inflections' of the sentences, play an important part. The dynamic and melodic phases of spoken verse which have important relations to the rhyme are not determined by the mere words. The verses may scan faultlessly, the lines may read smoothly and be without harsh and difficult combinations, and yet the total rhythmic effect may be indifferent or unpleasant. When a critic dilates on his infallible detection of an indefinable somewhat, independent of material aspects of the verse and traceable to a mystic charm of 'thought,' it may very well be that the unanalyzed thing lies in just such dynamic and melodic conditions of rhythm and rhyme.

The most primitive characteristic of music is the ensemble. Savage music is often little else than time-keeping. When the social consciousness would express itself in speech or movement in unison, some sort of automatic regulation is necessary. This is the beginning of music. The free reading of verse easily passes over into singing or chanting. When this happens, the thing most noticeable in the new form is its regulated, automatic and somewhat rigid character. It is stereotyped throughout. Not only are the intervals and accents fixed, but the pitch and quality changes are now definite, sustained and recurrent. The whole sum of the motor processes of utterance has become coördinated and regulated. Along with this precision of all the movements comes a tendency to beat a new rhythm. This accompanying rhythm is simpler and broader in character; it is a kind of long swell on which the speech movements ripple. This second rhythm may express itself in a new movement of hand, head, foot or body; when it has become more conscious, as in patting time to a dance or chant, it develops complicated forms, and a third rhythm may appear beside it, to mark the main stresses of the two processes. The negro patting time for a dance beats the third fundamental rhythm with his foot, while his hands pat an elaborate second rhythm to the primary rhythm of the dancers.

The essential character of musical rhythm, as contrasted with the rhythm of both simple sounds and of verse, is just this coördination of a number of rhythms which move side by side. This is the reason for the immense complexity and variety of musical rhythms. The processes check each other and furnish a basis for a precision and elaborateness of rhythmical movement in the individual parts which is quite impossible in a simple rhythm.

Even when the concomitant rhythms are not expressed, as in an unaccompanied solo, an accompaniment of some sort is present in the motor apparatus, and contributes its effect to the consciousness. This regulation of the movement by the coincidence of several rhythms is the cause of the striking regularity of the temporal relations. At some points in the musical series the several movement cycles may appear in the same phase, and at these points the same irregularities as in verse are possible, as in the case of pauses at the ends of periods and the irregularities of phrasing. It is evident in cases of expressional variations of tempo that a single broad rhythm is dominating and serving as a cue for the other more elaborate rhythmic processes, instead of being regulated by them.

FOOTNOTES.

1 Herbart, J.F.: 'Psychol. Untersuchungen' (Sämmt. Werk, herausgeg. von Hartenstein), Leipzig, 1850-2, Bd. VII., S. 291 ff.

2 Lotze, R.H.: 'Geschichte der Æsthetik,' München, 1863, S. 487 ff.

3 Vierordt, K.: 'Untersuchungen über d. Zeitsinn,' Tübingen, 1868.

4 von Brücke, E.W.: 'Die physiol. Grundlagen d. neuhochdeutschen Verskunst,' Wien, 1871.

5 Mach, Ernst: 'Unters. ü. d. Zeitsinn d. Ohres,' Wiener Sitz. Ber., mathem. naturw. Classe, 1865, Bd. 51, II., S. 133. Beiträge zur Physiol. d. Sinnesorgane, S. 104 ff.

6 Wundt, W.: 'Physiol. Psych.,' 4te Aufl., Leipzig, 1893, Bd. II., S. 83.

7 Wundt, W.: 'Physiol. Psych.,' 4te Aufl., Leipzig, 1893, II., S. 89 ff.

8 Bolton, T.L.: Amer. Jour. of Psych., 1894, VI., p. 145 et seq.

9 Meumann, E.: Phil. Stud., 1894, X., S. 249 ff.

10 Ebhardt, K.: Zeilschr. f. Psych, u. Physiol. d. Sinnesorgane, 1898, Bd. 18, S. 99.

11 Hurst, A.S., McKay, J., and Pringle, G.C.F.: Univ. of Toronto Studies, 1899, No. 3, p. 157.

12 Scripture, E.W.: Studies from the Yale Psych. Lab., 1899, VII., p. 1.

13 Marage: l'Année psychologique, 1898, V., p. 226.

14 Rousselot: La Parole, 1899.

15 Scripture, E.W.: Studies from the Yale Psych. Lab., 1899, VII., p. I.

16 Hensen: Hermann's Handbuch d. Physiol., 1879, Bd. I., Th. II., S. 187.

17 Sherrington, C.S.: Proceedings Royal Soc., 1897, p. 415.

18 Hering, H.E.: Archiv f. d. ges. Physiol. (Pflüger's), 1897, Bd. 68, S. 222; ibid., 1898, Bd. 70, S. 559.

19 Müller, R.: Phil. Stud., 1901, Bd. 17, S. 1.

20 Cleghorn, A.: Am. Journal of Physiol., 1898, I., p. 336.

21 Hofbauer: Archiv f. d. ges. Physiol. (Pflüger's), 1897, Bd. 68, S. 553.

22 Cleghorn, A.: op. cit.

23 Scripture, E.W.: 'The New Psychology,' London, 1897, p. 182.

24 Bolton, T.L.: loc. cit.

25 Lanier, S.: 'The Science of English Verse.'

STUDIES IN SYMMETRY.1

BY ETHEL D. PUFFER.

I. THE PROBLEMS OF SYMMETRY.

The problem of æsthetic satisfaction in symmetrical forms is easily linked with the well-known theory of 'sympathetic reproduction.' If there exists an instinctive tendency to imitate visual forms by motor impulses, the impulses suggested by the symmetrical form would seem to be especially in harmony with the system of energies in our bilateral organism, and this harmony may be the basis of our pleasure. But we should then expect that all space arrangements which deviate from complete symmetry, and thus suggest motor impulses which do not correspond to the natural bilateral type would fail to give æsthetic pleasure. Such, however, is not the case. Non-symmetrical arrangements of space are often extremely pleasing.

This contradiction disappears if we are able to show that the apparently non-symmetrical arrangement contains a hidden symmetry, and that all the elements of that arrangement contribute to bring about just that bilateral type of motor impulses which is characteristic of geometrical symmetry. The question whether or not this is the fact makes the leading problem of this paper, and the answer to it must throw light on the value of the theory itself.

An exhaustive treatment of our question would thus divide itself into two parts; the first dealing with real (or geometrical) symmetry, the second with apparent asymmetry; the first seeking to show that there is a real æsthetic pleasure in geometrical symmetry, and that this pleasure is indeed based on the harmony of the motor impulses suggested by symmetry, with the natural motor impulses of the human organism; the second seeking to show in what manner æsthetically pleasing but asymmetrical arrangements conform to the same principles. Within these two groups of problems two general types of investigation are seen to be required; experiment, and the analysis of æsthetic objects.

The main question, as stated above, is of course whether the theory can explain our pleasure in arrangements which are completely or partly symmetrical. It is, however, an indispensible preliminary to this question, to decide whether the pleasure in symmetrical arrangements of space is indeed immediate and original. If it were shown to be a satisfaction of expectation, bred partly from the observation of symmetrical forms in nature, partly from the greater convenience of symmetrical objects in daily use, the whole question of a psychophysical explanation would have no point. If no original æsthetic pleasure is felt, the problem would be transformed to a demand for the explanation of the various ways in which practical satisfaction is given by symmetrical objects and arrangements. The logical order, then, for our investigation would be: First, the appearance of symmetry in the productions of primitive life, as a (debatable) æsthetic phenomenon emerging from pre-æsthetic conditions; secondly, the experimental study of real symmetry; thirdly, the analysis of geometrical symmetry in art, especially in painting and architecture, by means of which the results of the preceding studies could be checked and confirmed. Having once established a theory of the æsthetic significance of real symmetry, we should next have to examine asymmetrical, beautiful objects with reference to the relation of their parts to a middle line; to isolate the elements which suggest motor impulses; to find out how far it is possible to establish a system of substitution of these psychological factors and how far such substitution takes place in works of art—i.e., to what extent a substitutional symmetry or balance is found in pleasing arrangements. These investigations, again, would fall into the two groups of experiment and analysis. The products of civilized art are too complicated to admit of the complete analysis and isolation of elements necessary to establish such a system of substitution of psychological factors as we seek. From suggestions, however, obtained from pleasing asymmetrical arrangements, first, isolated elements may be treated experimentally, and secondly, the results checked and confirmed by works of art.

With regard to the study of objects without a natural or suggested middle line, as for instance sculpture, many types of architecture, landscapes, gardens, room-arrangements, etc., we may fitly consider it as a corollary to the study of asymmetrical objects with artificial limits which do suggest a middle. If we find, by the study of them, that a system of substitution of psychological factors does obtain, the whole field can be covered by the theory already propounded, and its application extended to the minutest details. The hypothesis, having been so far confirmed, may be then easily applied to the field of asymmetrical objects without a natural middle line.

The set of problems here suggested to the student of symmetry will not be fully followed out in this paper. The experimental treatment of geometrical symmetry, the analysis of the completely symmetrical products of civilized art, and the analysis of all forms of asymmetry except asymmetry in pictures will be omitted. If, however, the fact of an original æsthetic feeling for symmetry is established by the study of primitive art, and the theory of the balance of motor impulses through the substitution of factors is established by the experimental treatment of isolated elements, and further confirmed by the analysis of pictures, the general argument may be taken as sufficiently supported. This paper, then, will contain three sections: an introductory one on symmetry in primitive art, and two main sections, one on experiments in substitutional symmetry, and one on substitutional symmetry or balance in pictures.

II. SYMMETRY IN PRIMITIVE ART.

The question which this section will attempt to answer is this: Is there in primitive art an original and immediate æsthetic feeling for symmetry? This question depends on two others which must precede it: To what extent does symmetry actually appear in primitive art? and, How far must its presence be accounted for by other than æsthetic demands?

For the purpose of this inquiry the word primitive may be taken broadly as applying to the products of savage and half-savage peoples of to-day, as well as to those of prehistoric races. The expression primitive art, also, requires a word of explanation. The primitive man seldom makes purely ornamental objects, but, on the other hand, most of his articles of daily use have an ornamental character. We have to consider primitive art, therefore, as represented in the form and ornamentation of all these objects, constituting practically an household inventory, with the addition of certain drawings and paintings which do not appear to serve a definite practical end. These last, however, constitute only a small proportion of the material.

The method of the following outline treatment will be to deduct from the object under consideration those symmetrical elements which seem to be directly traceable to non-æsthetic influences; such elements as are not thus to be accounted for must be taken as evidence of a direct pleasure in, and desire for symmetry on the part of primitive man. These possible non-æsthetic influences may be provisionally suggested to be the technical conditions of construction, the greater convenience and hence desirability of symmetrical objects for practical use, and the symmetrical character of natural forms which were imitated.

The first great group of objects is given in primitive architecture. Here is found almost complete unanimity of design, the conical, hemispherical or beehive form being well-nigh universal. The hut of the Hottentots, a cattle-herding, half-nomadic people, is a good type of this. A circle of flexible staves is stuck into the ground, bent together and fastened at the top, and covered with skins. But this is the form of shelter constructed with the greatest ease, suitable to the demands of elastic materials, boughs, twigs, reeds, etc., and giving the greatest amount of space with the least material. There are, indeed, a few examples of the rectangular form of dwelling among various primitive races, but these seem to be more or less open to explanation by the theory advanced by Mr. V. Mendeleff, of the U.S. Bureau of Ethnology. "In his opinion the rectangular form of architecture which succeeds the type under discussion, must have resulted from the circular form by the bringing together within a limited area of many houses.... This partition would naturally be built straight as a two-fold measure of economy."2 This opinion is confirmed by Mr. Cushing's observations among the Zuñi villages, where the pueblos have circular forms on the outskirts. Thus the shape of the typical primitive dwelling is seen to be fully accounted for as the product of practical considerations alone. It may therefore be dismissed as offering no especial points of interest for this inquiry.

Next in the order of primitive development are the arts of binding and weaving. The stone axe or arrow-head, for example, was bound to a wooden staff, and had to be lashed with perfect evenness,3 and when in time the material and method of fastening changed, the geometrical forms of this careful binding continued to be engraved at the juncture of blade and handle of various implements. It should be noted, however, that these binding-patterns, in spite of their superfluous character, remained symmetrical.

On the great topic of symmetry in weaving, monographs could be written. Here it is sufficient to recall4 that the absolutely necessary technique of weaving in all its various forms of interlacing, plaiting, netting, embroidering, etc., implies order, uniformity, and symmetry. The chance introduction of a thread or withe of a different color, brings out at once an ordered pattern in the result; the crowding together or pressing apart of elements, a different alternation of the woof, a change in the order of intersection, all introduce changes by the natural necessities of construction which have the effect of purpose. So far, then, as the simple weaving is concerned, the æsthetic demand for symmetry may be discounted. While it may be operative, the forms can be explained by the necessities of construction, and we have no right to assume an æsthetic motive.

The treatment of human and animal forms in weaving is, however, indicative of a direct pleasure in symmetry. The human form appears almost exclusively (much schematized) en face. When in profile, as for instance in Mexican and South American work, it is doubled—that is, two figures are seen face to face. Animal figures, on the other hand, are much used as row-ornaments in profile.5 It would seem that only the linear conception of the row or band with its suggestions of movement in one direction, justified the use of profile (e.g., in Peruvian woven stuffs), since it is almost always seen under those conditions, indicating that a limited rectangular space is felt as satisfactorily filled only by a symmetrical figure.6 Moreover, and still more confirmatory of this theory, even these row-pattern profiles are immensely distorted toward symmetry, and every 'degradation' of form, to use Professor Haddon's term, is in the direction of symmetry. (See Fig. 1.)

The shape of primitive pottery is conditioned by the following influences: The shapes of utensils preceding clay, such as skins, gourds, shells, etc., which have been imitated, the forms of basket models, and the conditions of construction (formation by the hands). For all these reasons, most of these shapes are circular. The only (in the strict sense) symmetrical shapes found are of unmistakably animal origin, and it is interesting to notice the gradual return of these to the eurhythmic form; puma, bird, frog, etc., gradually changing into head, tail and leg excrescences, and then handles and nodes (rectangular panels), upon a round bowl or jar L, as shown in the figures. In fact, in ancient American pottery,7 at least, all the symmetrical ornamentations can be traced to the opposition of head and tail, and the sides between them, of these animal forms. But beyond this there is no degradation of the broad outline of the design. The head and tail, and sides, become respectively handles and nodes—but the symmetry becomes only more and more emphasized. And as in the case of textiles, the ornaments of the rectangular spaces given by the nodes are strikingly symmetrical. Many of these are from animal motives, and nearly always heads are turned back over the body, tails exaggerated, or either or both doubled, to get a symmetrical effect. Although much of the symmetrical ornament, again, is manifestly from textile models, its symmetrical character is so carefully preserved against the suggestions of the circular form that a direct pleasure in its symmetry may be inferred. (See Figs. 2-7.)

Fig. 2.

Figs. 3. AND 4.

The subject of drawing can be here only touched upon, but the results of study go to show, in general, two main directions of primitive expression: pictorial representation, aiming at truth of life, and symbolic ornament. The drawings of Australians, Hottentots and Bushmen, and the carvings of the Esquimaux and of the prehistoric men of the reindeer period show remarkable vigor and naturalness; while the ornamentation of such tribes as the South Sea Islanders has a richness and formal beauty that compare favorably with the decoration of civilized contemporaries. But these two types of art do not always keep pace with each other. The petroglyphs of the North American Indians8 exhibit the greatest irregularity, while their tattooing is extremely regular and symmetrical. The Brazilian savage 9 draws freehand in a very lively and grotesque manner, but his patterns are regular and carefully developed. Again, not all have artistic talents in the same direction. Dr. Schurtz, in his 'Ornamentik der Aino,'10 says: "There are people who show a decided impulse for the direct imitation of nature, and especially for the representation of events of daily life, as dancing, hunting, fishing, etc. It is, however, remarkable that a real system of ornamentation is scarcely ever developed from pictorial representations of this kind; that, in fact, the people who carry out these copies of everyday scenes with especial preference, are in general less given to covering their utensils with a rich ornamentive decoration."11 Drawing and ornament, as the products of different tendencies, may therefore be considered separately.

The reason for the divergence of drawing and ornament is doubtless the original motive of ornamentation, which is found in the clan or totem ideas. Either to invoke protection or to mark ownership, the totem symbol appears on all instruments and utensils; it has been shown, indeed, that practically all primitive ornament is based on totemic motives.12 Now, since a very slight suggestion of the totem given by its recognized symbol is sufficient for the initiated, the extreme of conventionalization and degradation of patterns is allowable, and is observed to take place. The important point to be noted in this connection is, however, that all these changes are toward symmetry. The most striking examples might be indefinitely multiplied, and are to be found in the appended references (see Figs. 8 and 9).

Fig. 5.

Fig. 6.

Fig. 7.

We may distinguish here, also, between the gradual disintegration and degradation of pattern toward symmetry, as seen in the examples just given, and the deliberate distortion of figures for a special purpose. This is strikingly shown in the decorative art of the Indians of the North Pacific coast. They systematically represent their totem animals—their only decorative motives—as split in symmetrical sections, and opened out flat on the surface which is to be covered13 (see Fig. 11). Dr. Boas argues that their purpose is to get in all the received symbols, or to show the whole animal, but, however this may be, every variation introduces symmetry even where it is difficult to do so, as in the case, for instance, of bracelets, hat-brims, etc. (Fig. 10). This may in some cases be due to the symmetrical suggestions of the human body in tattooing,14 but it must be so in comparatively few.

Fig. 8.

Fig. 9.

Fig. 10.

The primitive picture has for its object not only to impart information, but to excite the very definite pleasure of recognition of a known object. All explorers agree in their accounts of the savage's delight in his own naïve efforts at picture making. All such drawings show in varying degrees the same characteristics; first of all, an entire lack of symmetry. In a really great number of examples, including drawings and picture-writing from all over the world, I have not found one which showed an attempt at symmetrical arrangement. Secondly, great life and movement, particularly in the drawings of animals. Thirdly, an emphasis of the typical characteristics, the logical marks, amounting sometimes to caricature. The primitive man draws to tell a story, as children do. He gives with real power what interests him, and puts in what he knows ought to be there, even if it is not seen, but he is so engrossed by his interest in the imitated object as to neglect entirely its relation to a background.

Fig. 11.

Now, this very antithesis of ornament and picture is enlightening as to the dawn of æsthetic feeling, and the strongest confirmation of our hypothesis of an original impulse to symmetry in art. In the ornamentation of objects the content or meaning of the design is already supplied by the merest hint of the symbol which is the practical motive of all ornamentation. The savage artist need, therefore, concern himself no more about it, and the form of his design is free to take whatever shape is demanded either by the conditions of technique and the surface to be ornamented, or by the natural æsthetic impulse. We have found that technical conditions account for only a small part of the observed symmetry in pattern, and the inference to a natural tendency to symmetry is clear. Pictorial representation, on the other hand, is enjoyed by the primitive man merely as an imitation, of which he can say, 'This is that animal'—to paraphrase Aristotle's Poetics. He is thus constrained to reproduce the form as it shows meaning, and to ignore it as form, or as his natural motor impulses would make it.

To sum up the conclusions reached by this short survey of the field of primitive art, it is clear that much of the symmetry appearing in primitive art is due (1) to the conditions of construction, as in the form of dwellings, binding-patterns, weaving and textile patterns generally; (2) to convenience in use, as in the shapes of spears, arrows, knives, two-handled baskets and jars; (3) to the imitation of animal forms, as in the shapes of pottery, etc. On the other hand (1) a very great deal of symmetrical ornament maintains itself against the suggestions of the shape to which it is applied, as the ornaments of baskets, pottery, and all rounded objects; and (2) all distortion, disintegration, degradation of pattern-motives, often so marked as all but to destroy their meaning, is in the direction of geometrical symmetry. In short it is impossible to account for more than a small part of the marked symmetry of primitive art by non-æsthetic influences, and we are therefore forced to conclude an original tendency to create symmetry, and to take pleasure in it. A strong negative confirmation of this is given, as noted above, by the utter lack of symmetry of the only branch of art in which the primitive man is fully preoccupied with meaning to the neglect of shape; and by the contrast of this with those branches of art in which attention to meaning is at its minimum.

The question put at the beginning of this section must thus be answered affirmatively. There is evidence of an original æsthetic pleasure in symmetry.

III. EXPERIMENTS IN SUBSTITUTIONAL SYMMETRY.

A. Method of Experiment.

A certain degree of original æsthetic pleasure in symmetry may be considered to have been established by the preceding section, and, without considering further the problems of real or geometrical symmetry, it may now be asked whether the pleasure aroused by the form of asymmetrical objects is not at bottom also pleasure in symmetry; whether, in other words, a kind of substitution of factors does not obtain in such objects, which brings about a psychological state similar to that produced by real symmetry.

The question what these substituted factors may be can perhaps be approached by a glance at a few pictures which are accepted as beautiful in form, although not geometrically symmetrical. Let us take, for instance, several simple pictures from among the well-known altar-pieces, all representing the same subject, the Madonna Enthroned with Infant Christ, and all of generally symmetrical outline. It seems, then, reasonable to assume that if the variations from symmetry show constantly recurring tendencies, they represent the chief factors in such a substitutional symmetry or balance, supposing it to exist. The following pictures are thus treated in detail, M. denoting Madonna; C., Child; and Cn., Central Line. The numbers refer to the collection of reproductions used exclusively in this investigation, and further described in section IV.

1. 56, Martin Schöngauer: Madonna in Rose-arbor. M. is seated exactly in Cn., C. on Right, turning to Right. M. turns to Left, and her long hair and draperies form one long unbroken line down to Left lower corner. All other details symmetrical.

2. 867, Titian: Madonna. The picture is wider than it is high. M. stands slightly to Right of Cn.; C. on Right. Both turn slightly to Left, and the drapery of M. makes a long sweep to Left. Also a deep perspective occupies the whole Left field.

3. 248, Raphael: Madonna (The Bridgewater Madonna). M. sits in Cn., turning to Left; C. lies across her lap, head to Left, but his face turned up to Right, and all the lines of his body tending sharply down to Right.

In 1, all the elements of the picture are symmetrical except the position of C. on the Right, and the long flowing line to Left. In 2, there is a slightly greater variation. The mass of the figures is to Right, and the C. entirely over against the deep perspective and the flowing line on the Left, and the direction of both faces toward that side. In 3, the greater part of C.'s figure on Left is opposed by the direction of his lines and movement to Right. Thus these three pictures, whether or not they are considered as presenting a balance, at least show several well-defined factors which detach themselves from the general symmetrical scheme. (1) Interest in C. is opposed by outward-pointing line; (2) greater mass, by outward-pointing line, deep vista, and direction of attention; and (3) again interest by direction of line and suggestion of movement.

This analysis of several æsthetically pleasing but asymmetrical arrangements of space strongly suggests that the elements of large size, deep perspective, suggested movement, and intrinsic interest are in some way equivalent in their power to arouse those motor impulses which we believe to constitute the basis of æsthetic response. It is the purpose of these experiments to follow up the lines of these suggestions, reducing them to their simplest forms and studying them under exact conditions.

But before describing the instruments and methods of this experimental treatment, I wish to speak of the articles on the 'Æsthetics of Simple Form,' published as Studies from the Harvard Psychological Laboratory, by Dr. Edgar Pierce.15 These articles, sub-entitled 'Symmetry' and 'The Functions of the Elements' seem at first sight to anticipate the discussions of this paper; but a short analysis shows that while they point in the same direction, they nevertheless deal with quite different questions and in a different manner. In the statement of his problem, indeed, Dr. Pierce is apparently treading the same path.

He says: "Can a feeling of symmetry, that is, of æsthetical equality of the two halves, remain where the two sides are not geometrically identical; and if so, what are the conditions under which this can result—what variations of one side seem æsthetically equal to the variations of the other side?" Some preliminary experiments resulted in the conclusion that an unsymmetrical and yet pleasing arrangement of a varied content rests on the pleasure in unity, thus shutting out the Golden Section choice, which depends on the pleasure in variety. That is, the choices made will not in general follow the golden section, but 'when the figure consists of two halves, the pleasure must be a feeling of æsthetical symmetry.'

The final experiments were arrangements of lines and simple figures on a square, black background in which the center was marked by a white vertical line with a blue or a red line on each side. On one side of these central lines a line was fixed; and the subject had to place on the other side lines and simple figures of different sizes and different colors, so as to balance the fixed line. The results showed that lines of greater length, or figures of greater area must be put nearer the center than shorter or smaller ones—'A short line must be farther than a long one, a narrow farther than a wide, a line farther than a square; an empty interval must be larger than one filled, and so on.' And for colors, "blue, maroon and green, the dark colors, are the farthest out; white, red and orange, the bright colors, are nearest the center. This means that a dark color must be farther out than a bright one to compensate for a form on the other side. The brightness of an object is then a constant substitute for its distance in satisfying our feeling of symmetry."

Now from these conclusions two things are clear. By his extremely emphasized central line, and his explicit question to the subjects, 'Does this balance?' the author has excluded any other point of view than that of mechanical balance. His central fulcrum is quite overpowering. Secondly, his inquiry has dealt only with size and color, leaving the questions of interest, movement, and perspective untouched. But just the purpose of this experimental study is to seek for the different and possibly conflicting tendencies in composition, and to approximate to the conditions given in pictorial art. It is evident, I think, that the two studies on symmetry will not trespass on each other's territory. The second paper of Dr. Pierce, on 'The Functions of the Elements,' deals entirely with the relation of horizontal and vertical positions of the æsthetic object and of the subject to æsthetic judgments, and has therefore no bearing on this paper.

For his apparatus Dr. Pierce used a surface of black cloth stretched over black rubber, 1 m. square. Now an investigation which is to deal with complicated and varied relations, resembling those of pictures, demands an instrument resembling them also in the shape of the background. A rectangle 600 mm. broad by 400 mm. high seemed to meet this requirement better than the square of Dr. Pierce. Other parts, also, of his instrument seemed unfitted for our purpose. The tin, 5 cm. broad and confined to the slits across the center of the square, gave not enough opportunity for movement in a vertical direction, while the scale at the back was very inconvenient for reading. To supply these lacks, a scale graduated in millimeters was attached on the lower edge of the board, between a double track in which ran slides, the positions of which could be read on the scale. To the slides were attached long strips of tin covered with black cloth. On these strips figures glued to small clamps or clasps could be slipped up or down; this arrangement of coördinates made it possible to place a figure in any spot of the whole surface without bringing the hands into the field of view. The experiments were made in a dark room, in which the apparatus was lighted by an electric globe veiled by white paper and hung above and behind the head of the subject, so as not to be seen by him and to cast no shadow: in this soft light of course the black movable strips disappeared against the black background. A gray paper frame an inch and a half wide was fitted to the black rectangle to throw it up against the black depths of the dark room—thus giving in all details the background of a picture to be composed.

The differences in method between the two sets of experiments were fundamental. In Dr. Pierce's experiments the figures were pulled from one side to the other of the half-square in question, and the subject was asked to stop them where he liked; in those of the writer the subject himself moved the slides back and forth until a position was found æsthetically satisfactory. The subject was never asked, Does this balance? He was indeed requested to abstract from the idea of balance, but to choose that position which was the most immediately pleasing for its own sake, and so far as possible detached from associations.

I have said that Dr. Pierce intentionally accentuated the center. The conditions of pictorial composition suggest in general the center only by the rectangular frame. Most of my experiments were, therefore, made without any middle line; some were repeated with a middle line of fine white silk thread, for the purpose of ascertaining the effect of the enhanced suggestion of the middle line.

But the chief difference came in the different treatment of results. Dr. Pierce took averages, whereas the present writer has interpreted individual results. Now, suppose that one tendency led the subject to place the slide at 50 and another to place it at 130 mm. from the center. The average of a large number of such choices would be 90—a position very probably disagreeable in every way. For such an investigation it was evident that interpretation of individual results was the only method possible, except where it could be conclusively shown that the subjects took one and only one point of view. They were always encouraged to make a second choice if they wished to do so, as it often happened that one would say: 'I like both of these ways very much.' Of course, individual testimony would be of the highest importance, and a general grouping into classes and indication of the majority tendency would be the only way to treat the results statistically. And indeed in carrying out the experiments this caution was found absolutely necessary. In all but one or two of the sections, the taking of averages would have made the numerical results absolutely unintelligible. Only the careful study of the individual case, comparison of various experiments on the same person to find personal tendencies, and comparison of the different tendencies, could give valuable results for the theory of symmetry.

The first question to be taken up was the influence of right and left positions on choice. A long series of experiments was undertaken with a line 80×10 mm. on one side and a line 160×10 mm. on the other, in which the positions of these were reversed, and each in turn taken as fixed and variable, with a view to determining the effect of right and left positions. No definite conclusions emerged; and in the following experiments, most of which have been made for both right and left positions, the results will be treated as if made for one side alone, and, where averages are taken, will be considered as indifferently left or right.

The experiments of Dr. Pierce were made for only one position of the fixed line—at 12 cm. distance from the center. The characteristic of the following experiments is their reference to all positions of the fixed line. For instance a fixed line, 10 cm. in length at 12 cm. distance from the center, might be balanced by a line 5 cm. in length at 20 cm. distance. But would the distance be in the same proportion for a given distance of the fixed line of say 20 or 25 cm.? It is clear that only a progressive series of positions of the fixed line would suggest the changes in points of view or tendencies of choice of the subject. Accordingly, for all the experiments the fixed line or other object was placed successively at distances of 20, 40, 60 mm., etc., from the center; or at 40, 80 mm., etc., according to the character of the object, and for each of these fixed points the subject made one or two choices. Only an understanding of the direction in which the variable series moved gave in many cases an explanation for the choice.

Each choice, it should be added, was itself the outcome of a long series of trials to find the most pleasing position. Thus, each subject made only about ten choices in an hour, each of which, as it appears in the tables, represents a large number of approximations.

B. Experiments on Size.

I have said that different tendencies or types of choice in arrangement appeared. It will be convenient in the course of explaining in detail the method of experiment, to discuss at the same time the meaning of these types of choice.

From analysis of the pictures, the simplest suggestion of balance appeared in the setting off against each other of objects of different sizes;—an apparent equivalence of a large object near the center with a small object far from the center; thus inevitably suggesting the relations of the mechanical balance, or lever, in which the heavy short arm balances the light long arm. This was also the result of Dr. Pierce's experiments for one position of his fixed line. The experiments which follow, however, differ in some significant points from this result. The instrument used was the one described in the preceding section. On one side, in the middle of the vertical strip, was placed the 'fixed' line, denoted by F., and the subject moved the 'variable' line, denoted by V., until he found the arrangement æsthetically pleasing. The experimenter alone placed F. at the given reading, and read off the position of V. After the choice F. was placed at the next interval, V. was again tried in different positions, and so on. In the following tables the successive positions of F. are given in the left column, reading downward, and the corresponding positions of V. in the right column. The different choices are placed together, but in case of any preference the second choice is indicated. The measurements are always in millimeters. Thus, F. 40, V. 60, means that F. is 40 mm. to one side of the center, and V. 60 mm. to the opposite side. F. 80×10, V. 160×10, means that the white cardboard strips 80 mm.×10 mm., etc., are used. The minus sign prefixed to a reading means that the variable was placed on the side of the fixed line. An X indicates æsthetic dislike—refusal to choose. An asterisk (*) indicates a second choice.

The following tables are specimen sets made by the subjects C, O, and D.

Now, on Dr. Pierce's theory, the variable in the first set should be nearer the center, since it is twice the size of the fixed line;—but the choices V. 120, 166, 130 for F. 40; V. 110, 104, 102, 126 for F. 80; V. 128 for F. 120; V. 196 for F. 160; V. 230, 220 for F. 200, show that other forces are at work. If these variations from the expected were slight, or if the presence of second choices did not show a certain opposition or contrast between the two positions, they might disappear in an average. But the position of F. 40, over against V. 120, 166, 130, is evidently not a chance variation. Still more striking are the variations for I. (b). Here we should expect the variable, being smaller, to be farther from the center. But for F. 40, we have V. 27, 34; for F. 80, all nearer but two; for F. 120, V. 60, 56, 48, 82, 70; for F. 160, V. 29, 74, 16, 77, 138, and for F. 200, V. 96, 36, 25, 36, 177—while several positions on the same side of the center as the constant show a point of view quite irreconcilable with mechanical balance.

II. (a) F. 2 LINES 80×10. V. SINGLE LINK 80×10.

Here the variable should supposedly be the farther out; but we have V. 58, 20 for F. 40-60; V. 48, 40, 56 for F. 60; V. 64, 70, 87 for F. 80; no larger choice for F. 100-120; indeed, from this point on everything nearer, and very much nearer. We can trace in these cases, more clearly perhaps than in the preceding, the presence of definite tendencies. O and P, from positions in accord with the mechanical theory, approach the center rapidly; while C is seldom 'mechanical,' but very slowly recedes from the center. The large number of refusals to choose assures us that the subjects demand a definitely pleasant arrangement—in other words, that every choice is the expression of a deliberate judgment.

Taking again the experiments 1. (a) and 1. (b), and grouping the results for nine subjects, C, O, A, S, H, G, D, and P, we obtain the following general types of choice. The experiments were repeated by each subject, so that we have eighteen records for each position. I should note here that preliminary experiments showed that near the frame the threshold of difference of position was 10 mm., or more, while near the center it was 4 or 5 mm.; that is, arrangements were often judged symmetrically equal which really differed by from 4 to 10 mm., according as they were near to or far from the center. In grouping types of choice, therefore, choices lying within these limits will be taken as belonging to the same type.

Exp. 1. (a) F.(80 X 10). V.(160 X 10).

¹This table is obtained by taking from the full list, not given here, of 1. (b) F. (160 X 10), V. (80 X 10), those positions of 160 X 10 where the variable 80 X 10 has been placed at or near 40, thus giving the same arrangement as for 1. (a).

It might be objected that a group 40-65 (2-3) would not be larger than one of 100-136 (4), but the break between 45 and 62 shows the zones not continuous. Moreover, as said above, the positions far from the center have a very large difference threshold.

I. (a) 2. F. 80:—(1) 24, (2) 50, (3) 68 70, (4) 80 85 94 95 85, (5) 102 104 110 120 124 126 125* 132, (6) 187; also V. 80:—(2) 40 40, (4) 80, (5) 120 120, (6) 160 160.

I. (a) 3. F. 120:—(1) 44 46, (2) 64 48 70 70, (3) 85 95 97 91, (4) 113 113 118, (5) 168 169 178;—44, X; also V. 120:—(1) 40 40, (3) 80 80 80, (4) 120 120, (5) 160 160.

I. (a) 4. F. 160:—(1) 25 26, (2) 40 50 57, (3) 82 85 95 100*, (4) 114 115 130, (5) 145 145 156 162, (6) 196, (7)—88*—150*—105.

I. (a) 5. F. 200:—(1) 20 23 28 36, (2) 55, (3) 108 124 130*, (4) 171 189 199 195, (5) 220 230*, (6)—46—90—110*.

On comparing the different groups, we find that in 1 and 2 there is a decided preference for a position somewhat less than half way between center and frame—more sharply marked for 1 than for 2. From 3 onward there is a decided preference for the mechanical arrangement, which would bring the larger strip nearer. Besides this, however, there are groups of variations, some very near the center, others approaching to symmetry. The maintenance of geometrical symmetry at a pretty constant ratio is to be noted; as also the presence of positions on the same side of the center as the fixed line. Before discussing the significance of these groups we may consider the results of Experiment II. (F. double line 80×10, V. single line 80×10) without giving complete lists.

We notice therein, first of all, the practical disappearance of the symmetrical choice; for F. 40-60, 60-80, 80-100, a tendency, decreasing, however, with distance from the center, to the mechanical arrangement; for F. 100-120, and all the rest, not one mechanical choice, and the positions confined almost entirely to the region 35-75. In some cases, however, the mechanical choice for (1) 40-80, (2) 60-80, was one of two, e.g., we have for (1) 20 and 138, for (3) 70 and 162; in the last two cases the mechanical being the second choice.

Now the reversals of the mechanical choice occur for Exp. I. in 1 and 2 (F. 40 and F. 80); that is, when the small fixed line is near the center, the larger variable is distant. For Exp. II. the reversals, which are much more marked, occur in all cases beyond F. 40, F. 60 and F. 80; that is, when the double constant line is far from the center, the single variable approaches. If the mechanical theory prevailed, we should have in Exp. I. the lines together in the center, and in Exp. II. both near the fringe.

From the individual testimony, based both on I. (a) and I. (b), it appears that subject M is perfectly uniform in mechanical choice when the fixed line is the small line—i.e. when it moves out, the larger is placed near the center; but when the conditions of mechanical choice would demand that, as the larger fixed line moves out, the small variable one should move out farther, he regularly chooses the reverse. Nevertheless, he insists that in just these cases he has a feeling of equilibrium.

A also takes the mechanical choice as the small fixed line goes farther from the center; but when the fixed line is large and leaves the center, he reverses the mechanical choice—evidently because it would take the small line too far out. As he says, 'he is always disturbed by too large a black space in the center.'

G almost always takes the mechanical choice;—in one whole set of experiments, in which the fixed line is the large line, he reverses regularly.

H takes for F. (80×10) the mechanical choice only for the positions F. 160 and F. 200—i.e., only when F. is very far from the center and he wishes V. (160×10) nearer. For F. (160×10) he makes six such choices out of ten, but for positions F. 160 and F. 200 he has V. 44, 65 and 20.

S takes for F. (160×10) at F. 120, V. 185 and-70; says of V. 185, which is also his choice for F. (160×10) at F. 80, 'I cannot go out further, because it is so hard to take in the whole field.' For F. (160×10) at F. 200, he has V. 130 and 60; says of V. 60, 'Very agreeable elements in connection with the relation of the two lines.'

C takes for F. (80×10) only one mechanical choice until it is at F. 120. Then always mechanical, i.e., nearer center; for F. (160×10) makes after the position F. 40 no mechanical choice, i.e., V. is nearer center.

It is evident from the above tables and individual cases that the reversals from the mechanical choice occur only when the mechanical choice would bring both lines in the center, or both near the edges, and the subjective testimony shows from what point of view this appears desirable. The subjects wish 'to take in the whole field,' they wish 'not to be disturbed by too large a black space in the center'; and when, in order to cover in some way the whole space, the small line is drawn in or the large one pushed out, they have, nevertheless, a feeling of equilibrium in spite of the reversal of mechanical balance.

Accepting for the present, without seeking a further psychological explanation, the type of 'mechanical balance,' in which amount of space is a substitute for weight, as the one most often observed, we have to seek some point of view from which this entire reversal is intelligible. For even the feeling that 'the whole field must be covered' would hardly account for an exact interchanging of positions. If size gives 'weight,' why does it not always do so? A simple answer would seem to be given by the consideration that we tend to give most attention to the center of a circumscribed space, and that any object in that center will get proportionately more attention than on the outskirts. The small line near the center, therefore, would attract attention by virtue of its centrality, and thus balance the large line, intrinsically more noticeable but farther away. Moreover, all the other moments of æsthetic pleasure, derived from the even filling of the space, would work in favor of this arrangement and against the mechanical arrangement, which would leave a large black space in the middle.

The hypothesis, then, that the demand for the filling of the whole space without large gaps anywhere enters into competition with the tendency to mechanical balance, and that this tendency is, nevertheless, reconciled with that demand through the power of a central position to confer importance, would seem to fit the facts. It is, of course, clear that neither 'mechanical balance' nor the balance of 'central' with 'intrinsic' importance have been yet accounted for on psychological grounds; it is sufficient at this point to have established the fact of some kind of balance between elements of different qualities, and to have demonstrated that this balance is at least not always to be translated into the 'mechanical' metaphor.