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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 æsthetic 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 æsthetic 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.

 

We thus return to the simple line. I have considered a series of

judgments on it, and a series on two different figures, varying in the

degree of complexity presented, in one of their fillings. It remains

very briefly to see if the introspection on the simple line furnishes

further warrant for carrying the complexities over into the simple

line and so giving additional validity to the outlined theory of

substitution. The following phrases are from introspective notes.

 

A. Sweep wanted over long part. More attention to short.

Significance of whole in short. Certainly a concentration of interest

in the short. Short is efficacious. Long means rest; short is the

center of things. Long, an effortless activity; short, a more

strenuous activity. When complex fillings are introduced, subject is

helped out; does not have to put so much into the short division. In

simple line, subject introduces the concentration. In complex

figures the concentration is objectified. In equal division subject

has little to do with it; the unequal depends on the subject—it

calls for appreciation. Center of references is the division point,

and the eye movements to right and left begin here, and here return.

The line centers there. The balance is a horizontal affair.

 

B. Center

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