Various - Harvard Psychological Studies, Volume 1

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TABLE IV.¹

4 Centimeters.

A B D E
less = gr. less = gr. less = gr. less = gr.
R. (a) 7 2 1 8 1 1 6 2 2 5 1 4
(b) 7 3 0 7 1 2 6 2 2 6 1 3
F. (a) 6 3 1 7 1 2 7 0 3 6 0 4
(b) 7 0 3 9 1 0 6 1 3 5 2 3
------- -------- -------- --------
27 8 5 31 4 5 25 5 10 22 4 14

¹In columns _A_, _B_, and _C_ the filled spaces were made up
of 4, 5 and 6 points, respectively. The total weight of the
filled space in _A_, _B_ and _C_ was always just equal to the
weight of the two points in the open space, 20 gr. In (_a_)
the filled distance was given on the right arm first, in (_b_)
on the left arm. It will be observed that this reversal made
practically no difference in the judgments and therefore was
sometimes omitted. In _D_ the filled space consisted of four
points, but here the weight of each point was 10 gr., making a
total weight of 40 gr. for the filled space, as against 20 gr.
for the open space. In _E_ the weight of each was 20 gr.,
making the total weight of the filled space 80 gr.

TABLE V.

6 Centimeters.

A B C D E
less = gr. less = gr. less = gr. less = gr. less = gr.
R. (a) 10 8 2 12 0 8 14 6 0 9 6 5 8 2 10
F. (a) 12 4 4 12 6 2 12 4 4 8 3 9 6 3 11
K. (a) 10 2 8 12 6 2 14 2 4 6 4 10 7 2 11
-------- -------- -------- -------- --------
32 14 14 36 12 12 40 12 8 23 13 24 21 7 32

TABLE VI.

8 Centimeters.

A B C D E
less = gr. less = gr. less = gr. less = gr. less = gr.
R. (a) 4 1 5 5 1 4 7 0 3 4 0 6 3 0 7
(b) 4 0 6 5 1 4 6 1 3 4 1 5 2 1 7
F. (a) 5 0 5 5 0 5 6 0 4 3 0 7 4 0 6
(b) 5 1 4 6 1 3 8 0 2 4 1 5 2 3 5
K. (a) 4 1 5 6 1 3 7 1 2 3 2 5 1 3 6
(b) 4 0 6 7 0 3 6 1 3 4 0 6 3 0 7
------- ------- ------- ------- -------
26 3 31 34 4 22 40 3 17 22 4 34 15 7 38

TABLE VII.

12 Centimeters.

A B C D E
less = gr. less = gr. less = gr. less = gr. less = gr.
R. (a) 3 6 16 8 3 14 10 8 7 6 3 16 3 4 18
F. (a) 5 7 13 10 5 10 9 6 10 6 4 15 5 1 19
K. (a) 8 2 15 8 4 13 13 9 3 3 7 15 3 0 22
-------- -------- ------- -------- ---------
16 15 44 26 12 37 32 23 20 15 14 46 11 5 59

TABLE VIII.

18 Centimeters.

A B C D E
less = gr. less = gr. less = gr. less = gr. less = gr.
R. (a) 2 0 23 0 0 25 4 4 17 3 1 21 0 1 24
(b) 3 1 21 1 0 24 5 3 17 1 6 18 0 2 23
F. (a) 1 4 20 3 0 22 8 6 11 0 5 20 2 0 23
(b) 2 3 20 2 1 22 6 7 12 1 4 20 0 3 22
K. (a) 4 2 19 4 0 21 2 7 16 0 7 18 0 0 25
(b) 1 0 24 2 6 17 8 0 17 2 6 17 1 0 24
-------- -------- -------- -------- --------
13 10 127 12 7 131 33 27 90 7 29 114 3 6 141

TABLES IV.-VIII.

The first line in column _A_ (Table IV.) signifies that out of 10
judgments, comparing an open space 4 cm., total weight 20 gr., with a
filled space of 4 points, total weight also 20 gr., the filled space
was judged less 7 times, equal 2 times, and greater once.

III.

The results of the investigation, thus far, point to the conclusion
that short filled spaces are underestimated, that long spaces are
overestimated, and that between the two there lies what might be
called an 'indifference zone.' This unexpected outcome explains, I
think, the divergent opinions of the earlier investigators of this
problem. Each theory is right in what it affirms, but wrong in what it
implicitly or openly denies.

I next set out to determine as precisely as possible how far the
factor of fusion, or what Parrish has called irradiation, enters into
the judgments. It was evident from the beginning of this whole
investigation that fusion or displacement of the points was very
common. The term 'irradiation' is, however, too specific a term to
describe a process that works in these two opposite directions. The
primary concern of these next experiments was, therefore, to devise
means for preventing fusion among the points before the subject
pronounced his judgment. With our apparatus we were able to make a
number of experiments that show, in an interesting way, the results
that follow when the sensations are not permitted to fuse. It is only
the shorter distances that concern us here. The longer distances have
already been shown to follow the law of optical illusion, that is,
that filled space is overestimated. The object of the present
experiments is to bring the shorter distances under the same law, by
showing, first, that the objective conditions as they have existed in
our experiments thus far are not parallel to those which we find in
the optical illusion. Second, that when the objective conditions are
the same, the illusion for the shorter distances follows the law just
stated.

In repeating some of the experiments reported in Tables IV.-VIII. with
varying conditions, I first tried the plan of using metallic points at
the ends of the spaces. Thus, by an apparent difference in the
temperature between the end points and the filling, the sensations
from the end points, which play the most important part in the
judgment of the length, were to a certain extent kept from fusing with
the rest. The figures in Table II. have already shown what may be
expected when the points are kept from fusing. Here, also, a marked
tendency in the direction of apparent lengthening of the distance was
at once observed. These short filled distances, which had before been
underestimated, were now overestimated. The same results follow when
metallic points are alternated with hard rubber points in the filling
itself.

This changing of the apparent temperature of the end points has, it
must be admitted, introduced another factor; and it might be objected
that it was not so much the prevention of fusion as the change in the
temperature that caused the judgments to drift towards overestimation.
I have statistics to show that this observation is in a way just.
Extremes in temperature, whether hot or cold, are interpreted as an
increase in the amount of space. This conclusion has also been
reported from a number of other laboratories. My contention at this
point is simply that there are certain conditions under which these
distances will be overestimated and that these are the very conditions
which bring the phenomenon into closer correspondence with the optical
illusion, both as to the stimuli and the subjective experience. Then,
aside from this, such an objection will be seen to be quite irrelevant
if we bear in mind that when the end points in the filled distance
were replaced by metallic points, metallic points were also employed
in the open distance. The temperature factor, therefore, entered into
both spaces alike. By approaching the problem from still another point
of view, I obtained even more conclusive evidence that it is the
fusion of the end points with the adjacent points in the short
distances that leads to the underestimation of these. I have several
series in which the end points were prevented from fusing into the
filling, by raising or lowering them in the apparatus, so that they
came in contact with the skin just after or before the intermediate
points. When the contacts were arranged in this way, the tendency to
underestimate the filled spaces was very much lessened, and with some
subjects the tendency passed over into a decided overestimation. This,
it will be seen, is a confirmation of the results in Table II.

I have already stated that the two series of experiments reported in
Section II. throughout point to the conclusion that an increase of
pressure is taken to mean an increase in the distance. I now carried
on some further experiments with short filled distances, making
variations in the place at which the pressure was increased. I found a
maximum tendency to underestimate when the central points in the
filled space were weighted more than the end points. A strong drift in
the opposite direction was noticed when the end points were heavier
than the intermediate ones. It is not so much the pressure as a whole,
as the place at which it is applied, that causes the variations in the
judgments of length. In these experiments the total weights of the
points were the same in both cases. An increase of the weight on the
end points with an equivalent diminution of the weights on the
intervening points gave the end points greater distinctness apparently
and rendered them less likely to disappear from the judgments.

At this stage in the inquiry as to the cause of the underestimation of
short distances, I began some auxiliary experiments on the problem of
the localization of cutaneous impressions, which I hoped would throw
light on the way in which the fusion or displacement that I have just
described takes place. These studies in the localization of touch
sensations were made partly with a modification of the Jastrow
aesthesiometer and partly with an attachment to the apparatus before
described (Fig. 1). In the first case, the arm upon which the
impressions were given was screened from the subject's view, and he
made a record of his judgments on a drawing of the arm. The criticism
made by Pillsbury[6] upon this method of recording the judgments in
the localization of touch sensations will not apply to my experiments,
for I was concerned only with the relative, not with the absolute
position of the points. In the case of the other experiments, a card
with a single line of numbered points was placed as nearly as possible
over the line along which the contacts had been made on the arm. The
subject then named those points on the card which seemed directly over
the points which had been touched.

[6] Pillsbury, W.B.: Amer. Journ. of Psy., 1895, Vol. VII., p.
42.

The results from these two methods were practically the same. But the
second method, although it obviously permitted the determination of
the displacements in one dimension only, was in the end regarded as
the more reliable method. With this apparatus I could be more certain
that the contacts were made simultaneously, which was soon seen to be
of the utmost importance for these particular experiments. Then, too,
by means of this aesthesiometer, all movement of the points after the
contact was made was prevented. This also was an advantage in the use
of this apparatus, here and elsewhere, which can hardly be
overestimated. With any aesthesiometer that is operated directly by the
hand, it is impossible to avoid imparting a slight motion to the
points and thus changing altogether the character of the impression.
The importance of this consideration for my work was brought forcibly
to my attention in this way. One of the results of these tests was
that when two simultaneous contacts are made differing in weight, if
only one is recognized it is invariably located in the region of the
contact with the heavier point. But now if, while the points were in
contact with the skin and before the judgment was pronounced, I gave
the lighter point a slight jar, its presence and location were thereby
revealed to the subject. Then, too, it was found to be an advantage
that the judgments were thus confined to the longitudinal displacement
only; for, as I have before insisted, it was the relative, not the
absolute position that I wished to determine, since my object in all
these experiments in localization was to determine what connection, if
any, exists between judgments upon cutaneous distances made indirectly
by means of localization, and judgments that are pronounced directly
upon the subjective experience of the distance.

In the first of these experiments, in which two points of different
weight were used, the points were always taken safely outside of the
threshold for the discrimination between two points in the particular
region of the skin operated on. An inspection of the results shown in
Figs. 2 and 3 will indicate the marked tendency of the heavier point
to attract the lighter. In Figs. 2 and 3 the heavy curves were plotted
from judgments where both heavy and light points were given together.
The dotted curve represents the localization of each point when given
alone. The height of the curves at any particular point is determined
by the number of times a contact was judged to be directly under that
point. The fact that the curves are higher over the heavy points shows
that, when two points were taken as one, this one was localized in the
vicinity of the heavier point. When points were near the threshold for
any region, it will be observed that the two points were attracted to
each other. But when the points were altogether outside the threshold,
they seemed strangely to have repelled each other. As this problem lay
somewhat away from my main interest here, I did not undertake to
investigate this peculiar fluctuation exhaustively. My chief purpose
was satisfied when I found that the lighter point is displaced toward
the heavier, in short distances. A further explanation of these
figures will be given in connection with similar figures in the next
section.

[Illustration: FIG. 2. Back of hand.]

[Illustration: FIG. 3. Forearm.]

This attraction of the heavier for the lighter points is, I think, a
sufficient explanation for the variations in judgments upon filled
distances where changes are made in the place at which the pressure is
applied. I furthermore believe that an extension of this principle
offers an explanation for the underestimation of cutaneous
line-distances, which has been frequently reported from various
laboratories. Such a straight line gives a subjective impression of
being heavier at the center. I found that if the line is slightly
concave at the center, so as to give the ends greater prominence and
thereby leave the subjective impression that the line is uniform
throughout its entire length, the line will be overestimated in
comparison with a point distance. Out of one hundred judgments on the
relative length of two hard-rubber lines of 5 cm. when pressed against
the skin, one of which was slightly concave, the concave line was
overestimated eighty-four times. For sight, a line in which the shaded
part is concentrated at the center appears longer than an objectively
equal line with the shading massed towards the ends.

IV.

In the last section, I gave an account of some experiments in the
localization of touch sensations which were designed to show how,
under varying pressure, the points in the filled distance are
displaced or fused and disappear entirely from the judgment. Our
earliest experiments, it will be remembered, yielded unmistakable
evidence that short, filled distances were underestimated; while all
of the secondary experiments reported in the last section have pointed
to the conclusion that even these shorter distances will follow the
law of the longer distances and be overestimated under certain
objective conditions, which conditions are also more nearly parallel
with those which we find in the optical illusion. I wish now to give
the results of another and longer set of experiments in the
localization of a manifold of touch sensations as we find them in this
same illusion for filled space, by which I hope to prove a direct
relation between the function of localization and the spatial
functioning proper.

These experiments were made with the same apparatus and method that
were used in the previous study in localization; but instead of two
points of different weights, four points of uniform weight were
employed. This series, therefore, will show from quite another point
of view that the fusion which takes place, even where there is no
difference in the weight, is a very significant factor in judgments of
distance on the skin.

[Illustration: Fig. 4.]

I need hardly say that here, and in all my other experiments, the
subjects were kept as far as possible in complete ignorance of the
object of the experiment. This and the other recognized laboratory
precautions were carefully observed throughout this work. Four
distances were used, 4, 8, 12 and 16 cm. At frequent intervals
throughout the tests the contact was made with only one of the points
instead of four. In this way there came to light again the interesting
fact which we have already seen in the last section, which is of great
significance for my theory--that the end points are located
differently when given alone than when they are presented
simultaneously with the other points. I give a graphic representation
of the results obtained from a large number of judgments in Figs. 4, 5
and 6. These experiments with filled spaces, like the earlier
experiments, were made on the volar side of the forearm beginning near
the wrist. In each distance four points were used, equally distributed
over the space. The shaded curve, as in the previous figures,
represents the results of the attempts to localize the points when all
four were given simultaneously. In the dotted curves, the end points
were given alone. The height of the curve at any place is determined
by the number of times a point was located immediately underneath that
particular part of the curve. In Fig. 4 the curve which was determined
by the localization of the four points when given simultaneously,
shows by its shape how the points appear massed towards the center. In
Fig. 5 the curve _AB_ shows, by its crests at _A_ and _B_, that the
end points tended to free themselves from the rest in the judgments.
But if the distance _AB_ be taken to represent the average of the
judgments upon the filled space 1, 2, 3, 4, it will be seen to be
shorter than what may be regarded as the average of the judgments upon
the corresponding open space, namely, the distance _A'B'_, determined
by the localizations of the end points alone. The comparative
regularity of the curve indicates that the subject was unable to
discriminate among the points of the filling with any degree of
certainty. The localizations were scattered quite uniformly along the
line. In these short distances the subject often judged four points as
two, or even one.

[Illustration: Fig. 5.]

[Illustration: Fig. 6.]

Turning to Fig. 6, we notice that the tendency is now to locate the
end points in the filled distance outside of the localization of these
same points when given without the intermediate points. It will also
be seen from the irregularities in these two longer curves that there
is now a clear-cut tendency to single out the individual points. The
fact that the curves here are again higher over point 4 simply
signifies that at this, the wrist end, the failure to discover the
presence of the points was less frequent than towards the elbow. But
this does not disturb the relation of the two series of judgments. As
I have before said, the first two sets of experiments described in
Section II. showed that the shorter filled distances are
underestimated, while the longer distances are overestimated, and that
between the two there is somewhat of an 'indifferent zone.' In those
experiments the judgments were made directly on the cutaneous
distances themselves. In the experiments the results of which are
plotted in these curves, the judgment of distances is indirectly
reached through the function of localization. But it will be observed
that the results are substantially the same. The longer distances are
overestimated and the shorter distances underestimated. The curves in
Figs. 4, 5 and 6 were plotted on the combined results for two
subjects. But before the combination was made the two main tendencies
which I have just mentioned were observed to be the same for both
subjects.

It will be remembered also that in these experiments, where the
judgment of distance was based directly on the cutaneous impression,
the underestimation of the short, filled distance was lessened and
even turned into an overestimation, by giving greater distinctness to
the end points, in allowing them to come in contact with the skin just
before or just after the filling. The results here are again the same
as before. The tendency to underestimate is lessened by this device.
Whenever, then, a filled space is made up of points which are
distinctly perceived as discrete--and this is shown in the longer
curves by the comparative accuracy with which the points are
located--these spaces are overestimated.

In all of these experiments on localization, the judgments were given
with open eyes, by naming the visual points under which the tactual
points seemed to lie. I have already spoken of the other method which
I also employed. This consisted in marking points on paper which
seemed to correspond in number and position to the points on the skin.
During this process the eyes were kept closed. This may appear to be a
very crude way of getting at the illusion, but from a large number of
judgments which show a surprising consistency I received the emphatic
confirmation of my previous conclusion, that filled spaces were
overestimated. These experiments were valuable also from the fact that
here the cutaneous space was estimated by the muscle sense, or active
touch, as it is called.

In the experiments so far described the filling in of the closed space
was always made by means of stationary points. I shall now give a
brief account of some experiments which I regard as very important for
the theory that I shall advance later. Here the filling was made by
means of a point drawn over the skin from one end of a two-point
distance to the other.

These experiments were made on four different parts of the skin--the
forehead, the back of the hand, the abdomen, and the leg between the
knee and the thigh. I here forsook the plan which I had followed
almost exclusively hitherto, that of comparing the cutaneous distances
with each other directly. The judgments now were secured indirectly
through the medium of visual distances. There was placed before the
subject a gray card, upon which were put a series of two-point
distances ranging from 2 to 20 cm. The two-point distances were given
on the skin, and the subject then selected from the optical distances
the one that appeared equal to the cutaneous distance. This process
furnished the judgments on open spaces. For the filled spaces,
immediately after the two-point distance was given a blunt stylus was
drawn from one point to the other, and the subject then again selected
the optical distance which seemed equal to this distance filled by the
moving point.

The results from these experiments point very plainly in one
direction. I have therefore thought it unnecessary to go into any
further detail with them than to state that for all subjects and for
all regions of the skin the filled spaces were overestimated. This
overestimation varied also with the rate of speed at which the stylus
was moved. The overestimation is greatest where the motion is slowest.

Vierordt[7] found the same result in his studies on the time sense,
that is, that the more rapid the movement, the shorter the distance
seems. But lines drawn on the skin are, according to him,
underestimated in comparison with open two-point distances. Fechner[8]
also reported that a line drawn on the skin is judged shorter than the
distance between two points which are merely touched. It will be
noticed, however, that my experiments differed from those of Vierordt
and Fechner in one essential respect. This difference, I think, is
sufficient to explain the different results. In my experiments the
two-point distance was held on the skin, while the stylus was moved
from one point to the other. In their experiments the line was drawn
without the points. This of course changes the objective conditions.
In simply drawing a line on the skin the subject rapidly loses sight
of the starting point of the movement. It follows, as it were, the
moving point, and hence the entire distance is underestimated. I made
a small number of tests of this kind, and found that the line seemed
shorter than the point distance as Fechner and Vierordt declared. But
when the point distance is kept on the skin while the stylus is being
drawn, the filling is allowed its full effect in the judgment,
inasmuch as the end points are perceived as stationary landmarks. The
subjects at first found some difficulty in withholding their judgments
until the movement was completed. Some subjects declared that they
frequently made a preliminary judgment before the filling was
inserted, but that when the moving point approached the end point,
they had distinctly the experience that the distance was widening. In
these experiments I used five sorts of motion, quick and heavy, quick
and light, slow and heavy, slow and light, and interrupted. I made no
attempt to determine either the exact amount of pressure or the exact
rate. I aimed simply at securing pronounced extremes. The slow rate
was approximately 3, and the fast approximately 15 cm. per second.