Various - Harvard Psychological Studies, Volume 1

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[Illustration: FIG. 8.]

[Illustration: FIG. 9.]

None of the qualitative studies that have hitherto been made on this
illusion have brought to light this significant wearing away of the
illusion.

VII.

I have already spoken of the defects of the apparatus with which the
experiments of the previous chapter were made. I shall now give an
account of some experiments that were made with an apparatus designed
to overcome these difficulties. This is shown in Fig. 10. The block
_C_ was clamped to a table, while the block _A_ could be moved back
and forth by the lever _B_, in order to bring up different lengths of
filled space for judgment. For each judgment the subject brought his
finger back to the strip _D_, and by moving his finger up along the
edge of this strip he always came into contact with the first point of
the new distance. The lever was not used in the present experiment;
but in later experiments, where the points were moved under the finger
tip, which was held stationary, this lever was very useful in
producing different rates of speed. In one series of experiments with
this apparatus the filled spaces were presented first, and in another
series the open spaces were presented first. In the previous
experiments, so far as I have reported them, the filled spaces were
always presented first.

[Illustration: FIG. 10.]

In order to enable the subject to make proper connections with the
first point in the filled space, when the open space was presented
first, a slight depression was put in the smooth surface. This
depression amounted merely to the suggestion of a groove, but it
sufficed to guide the finger.

The general results of the first series of experiments with this
apparatus were similar to those already given, but were based on a
very much larger number of judgments. They show at once that the short
filled spaces are overestimated, while the longer spaces are
underestimated. The uniformity of this law has seemed to me one of the
most significant results of this entire investigation. In the results
already reported from the experiments with the former apparatus, I
have mentioned the fact that the judgments upon the distances
fluctuate more widely when one is filled and the other open, than when
both are open. This fluctuation appeared again in a pronounced way in
the present experiments. I now set about to discover the cause of this
variation, which was so evidently outside of the limits of Weber's
law.

TABLE XI.

I. II.
Subjects. R. B. A. R. B. A.
2= 3.1 3.2 3.7 2.7 2.5 3.1
3= 4.5 4.4 4.1 4.1 4.0 3.6
4= 5.3 5.0 4.3 4.2 4.6 4.6
5= 6.0 5.1 5.8 5.9 5.2 4.3
6= 6.8 5.6 6.2 6.9 5.3 6.0
7= 7.4 7.2 6.9 7.6 7.3 6.8
8= 8.1 8.4 7.3 8.3 9.7 7.8
9= 9.3 9.0 8.5 9.5 8.9 8.7
Filled 10= 10.1 10.0 8.1 10.3 10.0 9.2
Spaces. 11= 10.5 9.3 9.7 10.6 8.7 9.6
12= 11.7 10.6 10.6 11.8 9.7 10.2
13= 12.3 10.9 10.9 11.1 10.2 9.6
14= 12.2 11.5 12.2 10.4 9.6 11.3
15= 13.6 12.3 11.9 13.1 10.1 9.6
16= 14.1 13.5 14.1 12.3 13.2 13.3
17= 14.9 12.9 14.6 14.1 12.6 13.7
18= 15.0 15.3 14.9 15.0 15.3 13.8
19= 15.2 14.6 15.2 14.1 13.9 14.2
20= 17.1 16.5 15.7 16.1 16.4 14.7

The first line of group I. reads: 'When the finger-tip was
passed over a filled space of 2 cm., the subject _R_ measured
off 3.1 cm. on the open space, the subject _B_ 3.2 cm., and
the subject _A_ 3.7.' In group II., the numbers represent the
distance measured off when both spaces were unfilled.

In my search for the cause of the variations reported previously I
first tried the plan of obliging the subject to attend more closely to
the filled space as his finger was drawn over it. In order to do this,
I held a piece of fine wire across the line of the filled space, and
after the subject had measured off the equal open space he was asked
to tell whether or not he had crossed the wire. The wire was so fine
that considerable attention was necessary to detect it. In some of the
experiments the wire was inserted early in the filled space, and in
some near the end. When it was put in near the beginning, it was
interesting to notice, as illustrating the amount of attention that
was being given to the effort of finding the wire, that the subject,
as soon as he had discovered it, would increase his speed, relax the
attention, and continue the rest of the journey more easily.

The general effect of this forcing of the attention was to increase
the apparent length of the filled space. This conclusion was reached
by comparing these results with those in which there was no compelled
attention. When the obstacle was inserted early, the space was judged
shorter than when it came at the end of the filled space. This shows
very plainly the effect of continued concentration of attention, when
that attention is directed intensely to the spot immediately under the
finger-tip. When the attention was focalized in this way, the subject
lost sight of the space as a whole. It rapidly faded out of memory
behind the moving finger-tip. But when this concentration of attention
was not required, the subject was able to hold together in
consciousness the entire collection of discrete points, and he
overestimated the space occupied by them. It must be remembered here
that I mean that the filled space with the focalized attention was
judged shorter than the filled space without such concentration of
attention, but both of these spaces were judged shorter than the
adjacent open space. This latter fact I shall attempt to explain
later. Many other simple devices were employed to oblige the subject
to fix his attention on the space as it was traversed by the finger.
The results were always the same: the greater the amount of attention,
the longer the distance seemed.

In another experiment, I tried the plan of tapping a bell as the
subject was passing over the filled space and asking him, after he had
measured off the equivalent open space, whether the sound had occurred
in the first half or in the second half of the filled space.

When the finger-tip was drawn over two adjacent open spaces, and
during the first a bell was tapped continuously, this kind of filled
space was underestimated if the distance was long and overestimated if
the distance was short. So, too, if a disagreeable odor was held to
the nostrils while the finger-tip was being drawn over one of the two
adjacent open spaces, the space thus filled by the sensations of smell
followed the law already stated. But if an agreeable perfume was used,
the distance always seemed shorter than when an unpleasant odor was
given.

In all of these experiments with spaces filled by means of other than
tactual sensations, I always compared the judgment on the filled and
open spaces with judgments on two open spaces, in order to guard
against any error due to unsymmetrical, subjective conditions for the
two spaces. It is difficult to have the subject so seat himself before
the apparatus as to avoid the errors arising from tension and flexion.
In one experiment, a piece of plush was used for the filled space and
the finger drawn over it against the nap. This filled space was judged
longer than a piece of silk of equal length. The sensations from the
plush were very unpleasant. One subject said, even, that they made him
shudder. This was of course precisely what was wanted for the
experiment. It showed that the affective tone of the sensation within
the filled space was a most important factor in producing an illusory
judgment of distance.

The overestimation of these filled spaces is evidently due in a large
measure to aesthetic motives. The space that is filled with agreeable
sensations is judged shorter than one which is filled with
disagreeable sensations. In other words, the illusions in judgments on
cutaneous space are not so much dependent on the quality of sensations
that we get from the outer world through these channels, as from the
amount of inner activity that we set over against these bare
sense-perceptions.

I have already spoken of the defects of this method of measuring off
equivalent distances as a means of getting at the quantitative amount
of the illusion. The results that have come to light thus far have,
however, amply justified the method. I had no difficulty, however, in
adapting my apparatus to the other way of getting the judgments. I had
a short curved piece of wire inserted in the handle, which could be
held across the line traversed, and thus the end of the open space
could be marked out. Different lengths were presented to the subject
as before, but now the subject passed his finger in a uniform motion
over the spaces, after which he pronounced the judgment 'greater,'
'equal,' or 'less.' The general result of these experiments was not
different from those already given. The short, filled spaces were
overestimated, while the longer ones were underestimated. The only
difference was found to be that now the transition from one direction
to the other was at a more distant point. It was, of course, more
difficult to convert these qualitative results into a quantitative
determination of the illusion.

Before passing to the experiments in which the open spaces were
presented first, I wish to offer an explanation for the divergent
tendencies that were exhibited through all the experiments of the last
two sections, namely, that the short filled spaces are overestimated
and the long spaces underestimated. Let us take two typical judgments,
one in which a filled space of 3 cm. is judged equal to an open space
of 4.2 cm., and then one in which the filled space is 9 cm., and is
judged equal to an open space of 7.4 cm. In the case of the shorter
distance, because of its shortness, after the finger leaves it, it is
held in a present state of consciousness for some moments, and does
not suffer the foreshortening that comes from pastness. This is,
however, only a part of the reason for its overestimation. After the
finger-tip has left the filled space, and while it is traversing the
first part of the open space, there is a dearth of sensations. The
tactual sensations are meager and faint, and muscular tensions have
not yet had time to arise. It is not until the finger has passed over
several centimeters of the distance, that the surprise of its
barrenness sets up the organic sensations of muscular strain. One
subject remarked naively at the end of some experiments of this kind,
that the process of judging was an easy and comfortable affair so long
as he was passing over the filled space, but when he set out upon the
open space he had to pay far more strict attention to the experiment.

By a careful introspection of the processes in my own case, I came to
the conclusion that it is certainly a combination of these two
illusions that causes the overestimation of the short filled
distances. In the case of the long distances, the underestimation of
the filled space is, I think, again due to a combination of two
illusions. When the finger-tip leaves the filled space, part of it,
because of its length, has already, as it were, left the specious
present, and has suffered the foreshortening effect of being relegated
to the past. And, on the other hand, after the short distance of the
open space has been traversed the sensations of muscular strain become
very pronounced, and cause a premature judgment of equality.

One subject, who was very accurate in his judgments, and for whom the
illusion hardly existed, said, when asked to explain his method of
judging, that after leaving the filled space he exerted a little more
pressure with his finger as he passed over the open space, so as to
get the same quantity of tactual sensations in both instances. The
muscular tension that was set up when the subject had passed out over
the open space a short way was very plainly noticeable in some
subjects, who were seen at this time to hold their breath.

I have thus far continually spoken of the space containing the tacks
as being the filled space, and the smooth surface as the open space.
But now we see that in reality the name should be reversed, especially
for the longer distances. The smooth surface is, after the first few
centimeters, very emphatically filled with sensations arising from the
organism which, as I have already intimated, are of the most vital
importance in our spatial judgments. Now, according to the most
generally accepted psychological theories, it is these organic
sensations which are the means whereby we measure time, and our
spatial judgments are, in the last analysis, I will not for the
present say dependent on, but at any rate fundamentally related to our
time judgments.

VIII.

In the last section I attempted to explain the overestimation of short
filled spaces, and the underestimation of long filled spaces by active
touch, as the result of a double illusion arising from the differences
in the manner and amount of attention given to the two kinds of
spaces when they are held in immediate contrast. This explanation was
of course purely theoretical. I have thus far offered no experiments
to show that this double illusion of lengthening, on the one hand, and
shortening, on the other, does actually exist. I next made some simple
experiments which seemed to prove conclusively that the phenomenon
does not exist, or at least not in so important a way, when the time
factor is not permitted to enter.

In these new experiments the filled and the open spaces were compared
separately with optical distances. After the finger-tip was drawn over
the filled path, judgment was given on it at once by comparing it
directly with an optical distance. In this way the foreshortening
effect of time was excluded. In all these experiments it was seen that
the filled space was judged longer when the judgment was pronounced on
it at once than when an interval of time was allowed, either by
drawing the finger-tip out over the open space, as in the previous
experiment, or by requiring the subject to withhold his judgment until
a certain signal was given. Any postponement of the judgment resulted
in the disappearance of a certain amount of the illusion. The
judgments that were made rapidly and without deliberation were subject
to the strongest illusion. I have already spoken of the unanimous
testimony which all who have made quantitative studies in the
corresponding optical illusions have given in this matter of the
diminution of the illusion with the lapse of time. The judgments that
were made without deliberation always exhibited the strongest tendency
to illusion.

I have already said that the illusion for passive touch was greatest
when the two spaces were presented simultaneously and adjacent.
Dresslar has mentioned in his studies on the 'Psychology of Touch,'
that the time factor cannot enter into an explanation of this
illusion; but the experiments of which I have just spoken seem to
point plainly to a very intimate relation between this illusion and
the illusions in our judgments of time. We have here presented on a
diminutive scale the illusions which we see in our daily experience in
comparing past with present stretches of time. It is a well-known
psychological experience that a filled time appears short in passing,
but long in retrospect, while an empty time appears long in passing,
but short in retrospect. Now this illusion of the open and filled
space, for the finger-tip, is at every point similar to the illusion
to which our time judgment is subject. If we pronounce judgment on a
filled space or filled time while we are still actually living in it,
it seems shorter than it really is, because, while we pay attention to
the discrete sensations of external origin, we lose sight of the
sensations of internal origin, which are the sole means whereby we
measure lapse of time, and we consequently underestimate such
stretches of time or space. But when the sensations from the outer
world which enter into such filled spaces or times exist only in
memory, the time-measuring sensations of internal origin are allowed
their full effect; and such spaces and times seem much longer than
when we are actually passing through them.

I dwell on this illusion at a length which may seem out of proportion
to its importance. My object has been to show how widely different are
the objective conditions here from what they are in the optical
illusion which has so often been called the analogue of this.
James[14] has said of this tactual illusion: 'This seems to bring
things back to the unanalyzable laws, by reason of which our feeling
of size is determined differently in the skin and in the retina even
when the objective conditions are the same.' I think that my
experiments have shown that the objective conditions are not the same;
that they differ in that most essential of all factors, namely, the
time element. Something very nearly the analogue of the optical
illusion is secured when we take very short open and filled tactual
spaces, and move over them very rapidly. Here the illusion exists in
the same direction as it does for sight, as has already been stated.
On the other hand, a phenomenon more nearly parallel to the tactual
illusion, as reported in the experiments of James and Dresslar, is
found if we take long optical distances, and traverse the open and
filled spaces continuously, without having both parts of the line
entirely in the field of view at any one moment. I made a few
experiments with the optical illusion in this form. The filled and
open spaces were viewed by the subject through a slot which was
passed over them. These experiments all pointed in the direction of an
underestimation of a filled space. Everywhere in this illusion, then,
where the objective conditions were at all similar for sight and
touch, the resulting illusion exists in the same direction for both
senses.

[14] James, William, 'Principles of Psychology,' New York, II.,
p. 250.

Throughout the previous experiments with the illusion for active touch
we saw the direct influence of the factor of time. I have yet one set
of experiments to report, which seems to me to prove beyond the
possibility of a doubt the correctness of my position. These
experiments were made with the apparatus shown in Fig. 10. The
subjects proceeded precisely as before. The finger-tip was passed over
the filled space, and then out over the open space, until an
equivalent distance was measured off. But while the subject was
drawing his fingers over the spaces, the block _A_ was moved in either
direction by means of the lever _B_. The subjects were all the while
kept ignorant of the fact that the block was being moved. They all
expressed great surprise on being told, after the experiments were
over, that the block had been moved under the finger-tip through such
long distances without their being able to detect it. The block always
remained stationary as the finger passed over one space, but was moved
either with or against the finger as it passed over the other space.

TABLE XII.

A B C D E
4 7.1 2.6 2.4 6.5
5 8.3 3.1 3.3 8.7
6 8.2 3.3 4.1 9.2
7 9.7 3.6 3.7 10.1
8 10.5 3.7 4.5 10.6
9 12.4 4.8 5.1 11.5
10 13.1 4.7 5.3 13.2
11 13.3 5.3 6.1 14.6
12 13.7 6.9 7.2 12.7
13 14.6 7.5 8.1 13.2
14 15.3 8.2 9.4 15.6
15 15.7 8.7 10.3 14.9

Column _A_ contains the filled spaces, columns _B_, _C_, _D_,
_E_ the open spaces that were judged equal. In _B_ the block
was moved with the finger, and in _C_ against the finger as it
traversed the filled space, and in _D_ and _E_ the block was
moved with and against the finger respectively as it passed
over the open space. The block was always moved approximately
one-half the distance of the filled space.

I have given some of the results for one subject in Table XII. These
results show at a glance how potent a factor the time element is. The
quantity of tactual sensations received by the finger-tip enters into
the judgment of space to no appreciable extent. With one subject,
after he had passed his finger over a filled space of 10 cm. the block
was moved so as almost to keep pace with the finger as it passed over
the open space. In this way the subject was forced to judge a filled
space of 10 cm. equal to only 2 cm. of the open space. And when the
block was moved in the opposite direction he was made to judge a
distance of 10 cm. equal to an open distance of 16 cm.

The criticism may be made on these experiments that the subject has
not in reality been obliged to rely entirely upon the time sense, but
that he has equated the two spaces as the basis of equivalent muscle
or joint sensation, which might be considered independent of the
sensations which yield the notion of time. I made some experiments,
however, to prove that this criticism would not be well founded. By
arranging the apparatus so that the finger-tip could be held
stationary, and the block with the open and filled spaces moved back
and forth under it, the measurement by joint and muscle sensations was
eliminated.

It will be observed that no uniform motion could be secured by simply
manipulating the lever with the hand. But uniformity of motion was not
necessary for the results at which I aimed here. Dresslar has laid
great stress on the desirability of having uniform motion in his
similar experiments. But this, it seems to me, is precisely what is
not wanted. With my apparatus, I was able to give widely different
rates of speed to the block as it passed under the finger-tip. By
giving a slow rate for the filled space and a much more rapid rate for
the open space, I found again that the subject relied hardly at all on
the touch sensations that came from the finger-tip, but almost
entirely on the consciousness of the amount of time consumed in
passing over the spaces. The judgments were made as in the previous
experiments with this apparatus. When the subject reached the point in
the open space which he judged equal to the filled space, he slightly
depressed his finger and stopped the moving block. In this way, the
subject was deprived of any assistance from arm-movements in his
judgments, and was obliged to rely on the tactual impressions received
at the finger-tip, or on his time sense. That these tactual sensations
played here also a very minor part in the judgment of the distance was
shown by the fact that these sensations could be doubled or trebled by
doubling or trebling the amount of space traversed, without
perceptibly changing the judgment, provided the rate of speed was
increased proportionately. Spaces that required the same amount of
time in traversing were judged equal.

In all these experiments the filled space was presented first. When
the open space was presented first, the results for four out of five
subjects were just reversed. For short distances the filled space was
underestimated, for long distances the filled space was overestimated.
A very plausible explanation for these anomalous results is again to
be found in the influence of the time factor. The open space seemed
longer while it was being traversed, but rapidly foreshortened after
it was left for the filled space. While on the other hand, if the
judgment was pronounced while the subject was still in the midst of
the filled space, it seemed shorter than it really was. The
combination of these two illusions is plainly again responsible for
the underestimation of the short filled spaces. The same double
illusion may be taken to explain the opposite tendency for the longer
distances.

IX.

The one generalization that I have thus far drawn from the
investigation--namely, that the optical illusions are not reversed in
passing from the field of touch, and that we therefore have a safe
warrant for the conclusion that sight and touch do function alike--has
contained no implicit or expressed assertion as to the origin of our
notion of space. I have now reached the point where I must venture an
explanation of the illusion itself.

The favorite hypothesis for the explanation of the geometrical optical
illusions is the movement theory. The most generally accepted
explanation of the illusion with whose tactual counterpart this paper
is concerned, is that given by Wundt.[15] Wundt's explanation rests on
variation in eye movements. When the eye passes over broken
distances, the movement is made more difficult by reason of the
frequent stoppages. The fact that the space which is filled with only
one point in the middle is underestimated, is explained by Wundt on
the theory that the eye has here the tendency to fix on the middle
point and to estimate the distance by taking in the whole space at
once without moving from this middle point. A different explanation
for this illusion is offered by Helmholtz.[16] He makes use of the
aesthetic factor of contrasts. Wundt insists that the fact that this
illusion is still present when there are no actual eye movements does
not demonstrate that the illusion is not to be referred to a motor
origin. He says, "If a phenomenon is perceived with the moving eye
only, the influence of movement on it is undoubtedly true. But an
inference cannot be drawn in the opposite direction, that movement is
without influence on the phenomenon that persists when there is no
movement."[17]