Various - Harvard Psychological Studies, Volume 1

V >> Various >> Harvard Psychological Studies, Volume 1

Pages:
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | 52 | 53 | 54 | 55

V-shaped. Square. Oval.
S.C. D.C. S.S. S.C. D.C. S.S. S.C. D.C. S.S.
Altarpieces, 6 1 0 4 1 0 0 1 0
Mad. w. C., 0 0 0 0 0 0 0 0 0
Holy Family, 13 3 6 0 0 0 0 0 0
Adorations, 0 0 0 0 0 0 0 0 0
Crucifixions, 0 0 0 3 0 0 0 0 0
Desc. fr. Cross, 5 0 1 3 0 0 2 0 0
Annunciations, 0 1 0 0 8 0 0 0 0
Misc. Religious, 20 14 2 9 12 1 2 2 3
Allegorical, 3 2 1 3 1 0 3 1 0
Genre, 10 7 6 4 4 0 1 3 0
Landscape, 20 12 0 4 0 0 5 2 0
Port. Group, 10 7 1 0 3 0 0 0 0
Rel. Single Fig., 3 0 0 1 0 0 0 0 0
Alleg. S.F., 0 0 0 0 0 0 0 0 0
Portrait S.F., 0 0 0 0 0 0 0 0 0
Genre S.F., 1 0 0 0 0 0 0 0 0

What types are characteristic of the different kinds of pictures? In
order to answer this question we must ask first, What are the
different kinds of pictures? One answer, at least, is at once
suggested to the student on a comparison of the pictures with their
groupings according to subjects. All those which represent the Madonna
enthroned, with all variations, with or without saints, shepherds or
Holy Family, are very quiet in their action; that is, it is not really
an action at all which they represent, but an attitude--the attitude
of contemplation. This is no less true of the pictures I have called
'Adorations,' in which, indeed, the contemplative attitude is still
more marked. On the other hand, such pictures as the 'Descents,' the
'Annunciations,' and very many of the 'miscellaneous religious,'
allegorical and genre pictures, portray a definite action or event.
Taking together, for instance, in two groups of five each, the first
ten classes in the table, we find that they fall to the six types in
the following proportion:

P. D.P. Dg. V. Sq. Ov.
I. 66 13 05 13 03 0
II. 43 07 14 20 12 04

Inasmuch as II. contains also many 'contemplative' pictures, while I.
contains no 'active' ones, the contrast between the proportions of the
groups would really be sharper than the figures indicate. But as it
is, we see that the pyramid type is characteristic of the
'contemplative' pictures in a much higher degree. If the closely
allied double-pyramid type is taken with it, we have 79 per cent of
the 'contemplative' to 50 per cent, of the 'active' ones. This view is
confirmed by contrasting the 'Adoration,' the most complete example of
one group, with the genre pictures, the most complete example of the
other--and here we see that in the first all are pyramidal, and in the
second only 26 per cent. A class which might be supposed to suggest
the same treatment in composition is that of the portraits--absolute
lack of action being the rule. And we find, indeed, that no single
type is represented within it except the pyramid and double-pyramid,
with 86 per cent. of the former. Thus it is evident that for the type
of picture which expresses the highest degree of quietude,
contemplation, concentration, the pyramid is the characteristic type
of composition.

But is it not also characteristic of the 'active' pictures, since, as
we see, it has the largest representation in that class too? Perhaps
it might be said that, inasmuch as all pictures are really more
'quiet' than they are 'active,' so the type _par excellence_ is the
pyramidal--a suggestion which is certainly borne out by the table as a
whole. But setting aside for the moment the pyramid and its
sub-variety, we see that the diagonal V-shaped and square types are
much more numerous in the roughly outlined 'active' class. Taking,
again, the genre class as especially representative, we find 23 per
cent. of the diagonal type, and 25 per cent. of the V-shaped. We have
seen how closely allied are these two types, and how gradually one
passes over into the other, so that we may for the nonce take them
together as making up 47 per cent. of the whole. The type of picture
which expresses the highest degree of activity, which aims to tell a
story, has, then, for its characteristic type the V and its varieties.

The landscape picture presents a somewhat different problem. It cannot
be described as either 'active' or 'passive,' inasmuch as it does not
express either an attitude or an event. There is no definite idea to
be set forth, no point of concentration, as with the altarpieces and
the portraits, for instance; and yet a unity is demanded. An
examination of the proportions of the types shows at once the
characteristic type.

P. D.P. Dg. V. Sq. Or.
Landscapes, 13 03 35 36 05 08

It is now necessary to ask what must be the interpretation of the use
of these types of composition. Must we consider the pyramid the
expression of passivity, the diagonal or V, of activity? But the
greatly predominating use of the second for landscapes would remain
unexplained, for at least nothing can be more reposeful than the
latter. It may aid the solution of the problem to remember that the
composition taken as a whole has to meet the demand for unity, at the
same time that it allows free play to the natural expression of the
subject. The altarpiece has to bring about a concentration of
attention to express or induce a feeling of reverence. This is
evidently brought about by the suggestion of the converging lines to
the fixation of the high point in the picture--the small area occupied
by the Madonna and Child--and by the subordination of the free play of
other elements. The contrast between the broad base and the apex gives
a feeling of solidity, of repose; and it seems not unreasonable to
suppose that the tendency to rest the eyes above the center of the
picture directly induces the associated mood of reverence or worship.
Thus the pyramidal form serves two ends; primarily that of giving
unity; and secondarily, by the peculiarity of its mass, that of
inducing the feeling-tone appropriate to the subject of the picture.

Applying this principle to the so-called 'active' pictures, we see
that the natural movement of attention between the different 'actors'
in the picture must be allowed for, while yet unity is secured. And it
is clear that the diagonal type is just fitted for this. The attention
sweeps down from the high side to the low, from which it returns
through some backward suggestion of lines or interest in the objects
of the high side. Action and reaction--movement and return of
attention--is inevitable under the conditions of this type; and this
it is which allows the free play--which, indeed, _constitutes_ and
expresses the activity belonging to the subject, just as the fixation
of the pyramid constitutes the quietude of the religious picture. Thus
it is that the diagonal composition is particularly suited to portray
scenes of grandeur, and to induce a feeling of awe in the spectator,
because only here can the eye rove in one large sweep from side to
side of the picture, recalled by the mass and interest of the side
from which it moves. The swing of the pendulum is here widest, so to
speak, and all the feeling-tones which belong to wide, free movement
are called into play. If, at the same time, the element of the deep
vista is introduced, we have the extreme of concentration combined
with the extreme of movement; and the result is a picture in the
'grand style'--comparable to high tragedy--in which all the
feeling-tones which wait on motor impulses are, as it were, while yet
in the same reciprocal relation, tuned to the highest pitch. Such a
picture is the _Finding of the Ring_, Paris Bordone (1048), in the
Venice Academy. All the mass and the interest and the suggestion of
attention is toward the right--the sweep of the downward lines and of
the magnificent perspective toward the left--and the effect of the
whole space-composition is of superb largeness of life and feeling.
With it may be compared Titian's _Presentation of the Virgin_ (107),
also in the Academy, Venice. The composition, from the figure moving
upward to one high on the right, to the downward lines, waiting groups
and deep vista on the left, is almost identical with that of the
Bordone. Neither is pure diagonal--that is, it saves itself at last by
an upward movement. Compare also the two great compositions by
Veronese, _Martyrdom of St. Mark_, etc. (1091), in the Doge's Palace,
Venice, and _Esther before Ahasuerus_ (566), in the Uffizi, Florence.
In both, the mass, direction of interest, movement and attention are
toward the left, while all the lines tend diagonally to the right,
where a vista is also suggested--the diagonal making a V just at the
end. Here, too, the effect is of magnificence and vigor.

If, then, the pyramid belongs to contemplation, the diagonal to
action, what can be said of the type of landscape? It is without
action, it is true, and yet does not express that positive quality,
that _will_ not to act, of the rapt contemplation. The landscape
uncomposed is negative; and it demands unity. Its type of composition,
then, must give it something positive besides unity. It lacks both
concentration and action; but it can gain them both from a space
composition which shall combine unity with a tendency to movement. And
this is given by the diagonal and V-shaped type. This type merely
allows free play to the natural tendency of the 'active' picture; but
it constrains the neutral, inanimate landscape. The shape itself
imparts motion to the picture: the sweep of line, the concentration of
the vista, the unifying power of the inverted triangle between two
masses, act, as it were, externally to the suggestion of the object
itself. There is always enough quiet in a landscape--the overwhelming
suggestion of the horizontal suffices for that; it is movement that is
needed for richness of effect; and, as I have shown, no type imparts
the feeling of movement so strongly as the diagonal and V-shaped type
of composition. It is worth remarking that the perfect V, which is of
course more regular, concentrated, quiet, than the diagonal, is more
frequent than the diagonal among the 'Miscellaneous Religious'
pictures (that is, it is more _needed_), since after all, as has been
said, the final aim of all space composition is just the attainment of
repose. But the landscapes need energy, not repression; and so the
diagonal type is proportionately more numerous.

The square and oval types, as is seen from the table, are far less
often used. The oval, most infrequent of all, appears only among the
'active' pictures, with the exception of landscape. It usually serves
to unite a group of people among whom there is no one especially
striking--or the object of whose attention is in the center of the
picture, as in the case of the Descent from the Cross. It imparts a
certain amount of movement, but an equable and regular one, as the eye
returns in an even sweep from one side to the other.

The square type, although only three per cent. of the whole number of
pictures, suggests a point of view which has already been touched on
in the section on Primitive Art. The examples fall into two classes:
in the first, the straight lines across the picture are unrelieved by
the suggestion of any other type; in the second, the pyramid or V is
suggested in the background with more or less clearness by means of
architecture or landscape. In the first class are found, almost
exclusively, early examples of Italian, Dutch and German art; in the
second, pictures of a later period. The rigid square, in short, is
found only at an early stage in the development of composition.
Moreover, all the examples are 'story' pictures, for the most part
scenes from the lives of the saints, etc. Many of them are
double-center--square, that is, with a slight break in the middle, the
grouping purely logical, to bring out the relations of the characters.
Thus, in the _Dream of Saint Martin_, Simone Martini (325), a fresco
at Assisi, the saint lies straight across the picture with his head in
one corner. Behind him on one side, stand the Christ and angels,
grouped closely together, their heads on the same level. Compare also
the _Finding of the Cross_, Piero della Francesca (1088), a serial
picture in two parts, with their respective backgrounds all on the
same level; and most of the frescoes by Giotto at Assisi--in
particular _St. Francis before the Sultan_ (1057), in which the actors
are divided into parties, so to speak.

These are all, of course, in one sense symmetrical--in the weight of
interest, at least--but they are completely amorphous from an aesthetic
point of view. The _forms_, that is, do not count at all--only the
meanings. The story is told by a clear separation of the parts, and
as, in most stories, there are two principal actors, it merely happens
that they fall into the two sides of the picture. Interesting in
connection with this is the observation that, although the more
anecdotal the picture the more likely it is to be 'double-centered,'
the later the picture the less likely it is to be double-centered.
Thus the square and the double-center composition seem often to be
found in the same picture and to be, both, characteristic of early
composition. On the other hand, a rigid geometrical symmetry is also
characteristic, and these two facts seem to contradict each other. But
it is to be noted, first, that the rigid geometrical symmetry belongs
only to the Madonna Enthroned, and general Adoration pieces; and
secondly, that this very rigidity of symmetry in details can coexist
with variations which destroy balance. Thus, in the _Madonna
Enthroned_, Giotto (715), where absolute symmetry in detail is kept,
the Child sits far out on the right knee of the Madonna. Compare also
_Madonna_, Vitale di Bologna (157), in which the C. is almost falling
off M.'s arms to the right, her head is bent to the right, and a monk
is kneeling at the right lower corner; also _Madonna_, Ottaviano Nelli
(175)--all very early pictures. Hence, it would seem that the symmetry
of these early pictures was not dictated by a conscious demand for
symmetrical arrangement, or rather for real balance, else such
failures would hardly occur. The presence of geometrical symmetry is
more easily explained as the product, in large part, of technical
conditions: of the fact that these pictures were painted as
altarpieces to fill a space definitely symmetrical in character--often,
indeed, with architectural elements intruding into it. We may even
venture to connect the Madonna pictures with the temple images of the
classic period, to explain why it was natural to paint the object of
worship seated exactly facing the worshipper. Thus we may separate the
two classes of pictures, the one giving an object of worship, and thus
taking naturally, as has been said, the pyramidal, symmetrical shape,
and being moulded to symmetry by all other suggestions of technique;
the other aiming at nothing except logical clearness. This antithesis
of the symbol and the story has a most interesting parallel in the two
great classes of primitive art--the one symbolic, merely suggestive,
shaped by the space it had to fill, and so degenerating into the
slavishly symmetrical, the other descriptive, 'story-telling' and
without a trace of space composition. On neither side is there
evidence of direct aesthetic feeling. Only in the course of artistic
development do we find the rigid, yet often unbalanced, symmetry
relaxing into a free substitutional symmetry, and the formless
narrative crystallizing into a really unified and balanced space form.
The two antitheses approach each other in the 'balance' of the
masterpieces of civilized art--in which, for the first time, a real
feeling for space composition makes itself felt.

* * * * *

THE AESTHETICS OF UNEQUAL DIVISION.

BY ROSWELL PARKER ANGIER.

PART I.

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

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

[1] Witmer, Lightner: 'Zur experimentellen Aesthetik einfacher
raeumlicher Formverhaeltnisse,' _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.' Kuelpe[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 Koerpera,'
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] Kuelpe, 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. Kuelpe'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, 11/2 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 11/2 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.