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Various - Harvard Psychological Studies, Volume 1

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




In Fig. 1, I have represented graphically the results of these
judgments. The letters at the left, with the exception of _X_, mark
the subjects. Beginning with the most extreme judgments on either side
the center, I have erected modes to represent the number of judgments
made within each ensuing five millimeters, the number in each case
being denoted by the figure at the top of the mode. The two vertical
dot-and-dash lines represent the means of the several averages of all
the subjects, or the total averages. The short lines, dropped from
each of the horizontals, mark the individual averages of the divisions
either side the center, and at _X_ these have been concentrated into
one line. Subject _E_ obviously shows two pretty distinct fields of
choice, so that it would have been inaccurate to condense them all
into one average. I have therefore given two on each side the center,
in each case subsuming the judgments represented by the four end modes
under one average. In all, sixty judgments were made by _E_ on each
half the line. Letter _E¹_ represents the first thirty-six; _E squared_ the
full number. A comparison of the two shows how easily averages shift;
how suddenly judgments may concentrate in one region after having been
for months fairly uniformly distributed. The introduction of one more
subject might have varied the total averages by several points. Table
I. shows the various averages and mean variations in tabular form.


TABLE I.
Left. Right.
Div. M.V. Div. M.V.
_A_ 54 2.6 50 3.4
_B_ 46 4.5 49 5.7
_C_ 75 1.8 71 1.6
_D_ 62 4.4 56 4.1
_E¹_ 57 10.7 60 8.7
_F_ 69 2.6 69 1.6
_G_ 65 3.7 64 2.7
_H_ 72 3.8 67 2.1
_J_ 46 1.9 48 1.3
-- --- -- ---
Total 60 3.9 59 3.5

Golden Section = 61.1.

¹These are _E_'s general averages on 36 judgments. Fig. 1,
however, represents two averages on each side the center, for
which the figures are, on the left, 43 with M.V. 3.6; and 66
with M.V. 5.3. On the right, 49, M.V. 3.1; and 67, M.V. 2.7.
For the full sixty judgments, his total average was 63 on the
left, and 65 on the right, with mean variations of 9.8 and 7.1
respectively. The four that _E squared_ in Fig. 1 shows graphically
were, for the left, 43 with M.V. 3.6; and 68, M.V. 5.1. On the
right, 49, M.V. 3.1; and 69, M.V. 3.4.


[Illustration: FIG. 1.]

Results such as are given in Fig. 1, appear to warrant the criticism
of former experimentation. Starting with the golden section, we find
the two lines representing the total averages running surprisingly
close to it. This line, however, out of a possible eighteen chances,
only twice (subjects _D_ and _G_) falls wholly within the mode
representing the maximum number of judgments of any single subject. In
six cases (_C_ twice, _F_, _H_, _J_ twice) it falls wholly without any
mode whatever; and in seven (_A_, _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 _I¹, I squared_, etc., but not on same days. 64 65

2. Twenty at different times, but immediately before
judging on _I¹, I squared_, etc. 69 71

3. Eighteen similar judgments, but immediately after
judging on _I¹, I squared_, etc. 72 71

4. Twelve taken after all experimentation with _I¹_,
_I squared_, 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 masses. 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 mass, 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 massed 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 quantitative
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 quantitative 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 class 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 homogeneity 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 class 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 space 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 substitution 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 assumption of bilateral equivalence
underlying this is correct, then the repetition, in quantitative
terms, on one side, of what we have on the other, constitutes the
unity in the horizontal disposition of aesthetic elements; a unity
receptive to an almost infinite variety of actual visual
forms--quantitative identity 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.

[Illustration: 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_.
Secondly, four of the subjects only (_E_, _F_, _G_ and _H_) had
judgments also on the side which gave the complex filling the larger
space; to _E_, _F_ and _G_, these were secondary preferences; to _H_
they were always primary. Thirdly, the judgments on No. III. are less,
in spite of the fact that the larger component parts of No. II., might
be taken as additional weight to that side of the line, and given,
therefore, the shorter space, according to the principle of the lever.

The subjects, then, that appear not to substantiate our suggested
theory are _E_ and _H_, who in the reversed figures give the shorter
space to the less complex filling, and _F_ and _G_, who, together with
_E_ and _H_, have always secondary judgments that allot to either
complex filling a larger space than to the simple horizontal.
Consider, first, subjects _E_ and _H_. For each, the difference in
division of II. and III. is in any case very slight. Further, subject
_E_, in judgments where the complex filling _exceeds_ the horizontal
parallels in length, still gives the more complex of the two fillings
markedly the shorter space, showing, apparently, that its additional
complexity works there in accord with the theory. There was, according
to his introspection, another principle at work. As a figure, he
emphatically preferred II. to III. The filling of II. made up, he
found, by its greater interest, for lack of length. He here secured a
balance, in which the interest of the complex material compensated for
the greater _extent_ of the simpler horizontals. This accounts for its
small variation from III., and even for its occupying the smaller
space. But in judgments giving the two complex fillings the larger
space, the more interesting material _exceeded_ in extent the less
interesting. In such divisions the balance was no longer uppermost in
mind, but the desire to get as much as possible of the interesting
filling. To this end the horizontal parallels were shortened as far as
they could be without becoming insignificant. But unless some element
of balance were there (although not present to introspection) each
complex filling, when up for judgment, would have been pushed to the
same limit. It, therefore, does seem, in cases where the complex
fillings occupied a larger space than the horizontals, that the
subject, not trying consciously to secure a balance of _interests_,
was influenced more purely by the factor of complexity, and that his
judgments lend support to our theory.

Subject H was the only subject who consistently _preferred_ to have
all complex fillings occupy the larger space. Introspection invariably
revealed the same principle of procedure--he strove to get as much of
the interesting material as he could. He thought, therefore, that in
every case he moved the complex filling to that limit of the pleasing
range that he found on the simple line, which would yield him most of
the filling. Balance did not appear prominent in his introspection. A
glance, however, at the results shows that his introspection is
contradicted. For he maintains approximately the same division on the
right in all the figures, whether reversed or not, and similarly on
the left. The average on the right for all four is 67; on the left it
is 74. Comparing these with the averages on the simple line, we see
that the right averages coincide exactly, while the left but slightly
differ. I suspect, indeed, that the fillings did not mean much to _H_,
except that they were 'interesting' or 'uninteresting'; that aside
from this he was really abstracting from the filling and making the
same judgments that he would make on the simple line. Since he was
continually aware that they fell within the 'pleasing range' on the
simple line, this conclusion is the more plausible.

Perhaps these remarks account for the respective uniformities of the
judgments of _E_ and _H_, and their departure from the tendency of the
other subjects to give the more complex filling constantly the shorter
space. But subjects _F_ and _G_ also had judgments (secondary with
both of them) giving to the complex filling a larger extent than to
the parallels. With them one of two principles, I think, applies: The
judgments are either instances of abstraction from the filling, as
with _H_, or one of simpler gravity or vertical balance, as
distinguished from the horizontal equivalence which I conceive to be
at the basis of the other divisions. With _F_ it is likely to be the
latter, since the divisions of the figures under discussion do not
approach very closely those of the simple line, and because
introspectively he found that the divisions giving the complex the
larger space were 'balance' divisions, while the others were
determined with 'reference to the character of the fillings.' From _G_
I had no introspection, and the approximation of his judgments to
those he gave for the simple line make it probable that with him the
changes in the character of the filling had little significance. The
average of his judgments in which the complex filling held the greater
space is 66, while the averages on the simple line were 65 on the
left, and 64 on the right. And, in general, abstraction from filling
was easy, and to be guarded against. Subject _C_, in the course of the
work, confessed to it, quite unsolicited, and corrected himself by
giving thenceforth _all_ complex fillings much smaller space than
before. Two others noticed that it was particularly hard not to
abstract. Further, none of the four subjects mentioned (with that
possible exception of _E_) showed a sensitiveness similar to that of
the other five.

With the exception of _H_, and in accord with the constant practice of
the other five, these subjects, too, occasionally found no pleasing
division in which the complex filling preponderated in length over the
horizontals. It was uniformly true, furthermore, in every variation
introduced in the course of the investigation, involving a complex and
a simple filling, that all the nine subjects but _H_ _preferred_ the
complex in the shorter space; that five refused any divisions offering
it in the larger space; that these five showed more sensitiveness to
differences in the character of fillings; and that with one exception
(_C_) the divisions of the simple line which these subjects gave were
nearer the ends than those of the others. It surely seems plausible
that those most endowed with aesthetic sensitiveness would find a
division near the center more unequal than one nearer the end; for one
side only slightly shorter than the other would at once seem to mean
the same thing to them, and yet, because of the obvious difference in
length, be something markedly different, and they would therefore
demand a part short enough to give them sharp qualitative difference,
with, however, in some way, quantitative equivalence. When the short
part is too long, it is overcharged with significance, it strives to
be two things at once and yet neither in its fulness.

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