Chapter III: Preface (3)

At the beginning of the present investigation, the preponderance of testimony was found to be in favor of the view that filled space is underestimated by the skin; and this view is invariably accompanied by the conclusion, which seems quite properly to follow from it, that the skin and the eye do not function alike in our perception of space. I began my work, however, in the belief that there was lurking somewhere in the earlier experiments a radical error or oversight. I may say here, parenthetically, that I see no reason why experimental psychologists should so often be reluctant to admit that they begin certain investigations with preconceptions in favor of the theory which they ultimately defend by the results of their experiments. The conclusions of a critical research are in no wise vitiated because those conclusions were the working hypotheses with which the investigator entered upon his inquiry. I say frankly, therefore, that although my experiments developed many surprises as they advanced, I began them in the belief that the optical illusions are not reversed for touch. The uniformity of the law of sense perception is prejudiced if two senses, when affected by the same objective conditions, should report to consciousness diametrically opposite interpretations of these same objective facts. I may say at once, in advance of the evidence upon which I base the assertion, that the belief with which I began the experiments has been crystallized into a firm conviction, namely, that neither the illusion for open or filled spaces, nor any other optical illusion, is genuinely reversed for touch.

II.

I began my work on the problem in question by attempting to verify with similar apparatus the results of some of the previous investigations, in the hope of discovering just where the suspected error lay. It is unnecessary for me to give in detail the results of these preliminary series, which were quite in agreement with the general results of Parrish's experiments. Distances of six centimeters filled with points varying in number and position were, on the whole, underestimated in comparison with equal distances without intermediate point stimulations. So, too, the card with saw-toothed notches was judged shorter than the card of equal length with all but the end points cut out.

After this preliminary verification of the previous results, I was convinced that to pass from these comparatively meager statistics, gathered under limited conditions in a very special case, to the general statement that the optical illusion is reversed in the field of touch, is an altogether unwarranted procedure. When one reads the summarized conclusions of these previous investigators, one finds it there assumed or even openly asserted that the objective conditions of the tactual illusion are precisely the same as those of the optical illusion. But I contend that it is not the real analogue of the optical illusion with which these experiments have been concerned. The objective conditions are not the same in both. Although something that is very much like the optical illusion is reversed, yet I shall attempt to prove in this part of my paper, first, that the former experiments have not been made with the real counterpart of the optical illusion; second, that the optical illusion can be quite exactly reproduced on the skin; third, that where the objective conditions are the same, the filled cutaneous space is overestimated, and the illusion thus exists in the same sense for both sight and touch.

Let me first call attention to some obvious criticisms on Parrish's experiments. They were all made with one distance, namely, 6.4 centimeters; and on only one region, the forearm. Furthermore, in these experiments no attempt was made to control the factor of pressure by any mechanical device. The experimenter relied entirely on the facility acquired by practice to give a uniform pressure to the stimuli. The number of judgments is also relatively small. Again, the open and filled spaces were always given successively. This, of course, involves the comparison of a present impression with the memory of a somewhat remote past impression, which difficulty can not be completely obviated by simply reversing the order of presentation. In the optical illusion, the two spaces are presented simultaneously, and they lie adjacent to each other. It is still a debated question whether this illusion would exist at all if the two spaces were not given simultaneously and adjacent. Münsterberg[5] says of the optical illusion for the open and filled spaces, "I have the decided impression that the illusion does not arise from the fact of our comparing one half with the other, but from the fact that we grasp the line as a whole. As soon as an interval is inserted, so that the perception of the whole line as constituted of two halves vanishes, the illusion also disappears." This is an important consideration, to which I shall return again.

[5] Münsterberg, H.: 'Beiträge zur Exper. Psy.,' Freiburg i.B.,
1889, Heft II., S. 171.

Now, in my experiments, I endeavored to guard against all of these objections. In the first place, I made a far greater number of tests. Then my apparatus enabled me, firstly, to use a very wide range of distances. Where the points are set in a solid block, the experiments with long distances are practically impossible. Secondly, the apparatus enabled me to control accurately the pressure of each point. Thirdly, the contacts could be made simultaneously or successively with much precision. This apparatus (Fig. 1) was planned and made in the Harvard Laboratory, and was employed not only in our study of this particular illusion, but also for the investigation of a number of allied problems.

Two æsthesiometers, A and B, were arranged in a framework, so that uniform stimulations could be given on both arms. The æsthesiometers were raised or lowered by means of the crank, C, and the cams, D and E. The contacts were made either simultaneously or successively, with any interval between them according to the position of the cams on the crank. The height of the æsthesiometer could be conveniently adjusted by the pins F and H. The shape of the cams was such that the descent of the æsthesiometer was as uniform as the ascent, so that the contacts were not made by a drop motion unless that was desired. The sliding rules, of which there were several forms and lengths, could be easily detached from the upright rods at _K_ and _L_. Each of the points by which the contacts were made moved easily along the sliding rule, and could be also raised or lowered for accommodation to the unevenness of the surface of the skin. These latter were the most valuable two features of the apparatus. There were two sets of points, one of hard rubber, the other of metal. This enabled me to take into account, to a certain extent, the factor of temperature. A wide range of apparent differences in temperature was secured by employing these two stimuli of such widely different conductivity. Then, as each point was independent of the rest in its movements, its weight could also be changed without affecting the rest.

In the first series of experiments I endeavored to reproduce for touch the optical illusion in its exact form. There the open and the filled spaces are adjacent to each other, and are presented simultaneously for passive functioning of the eye, which is what concerns us here in our search for the analogue of passive touch. This was by no means an easy task, for obviously the open and the filled spaces in this position on the skin could not be compared directly, owing to the lack of uniformity in the sensibility of different portions of the skin. At first, equivalents had to be established between two collinear open spaces for the particular region of the skin tested. Three points were taken in a line, and one of the end points was moved until the two adjacent open spaces were pronounced equal. Then one of the spaces was filled, and the process of finding another open space equivalent to this filled space was repeated as before. This finding of two equivalent open spaces was repeated at frequent intervals. It was found unsafe to determine an equivalent at the beginning of each sitting to be used throughout the hour.

Two sets of experiments were made with the illusion in this form. In one the contacts were made simultaneously; the results of this series are given in Table I. In the second set of experiments the central point which divided the open from the filled space touched the skin first, and then the others in various orders. The object of this was to prevent fusion of the points, and, therefore, to enable the subject to pronounce his judgments more rapidly and confidently. A record of these judgments is given in Table II. In both of these series the filled space was always taken near the wrist and the open space in a straight line toward the elbow, on the volar side of the arm. At present, I shall not undertake to give a complete interpretation of the results of these two tables, but simply call attention to two manifest tendencies in the figures. First, it will be seen that the short filled distance of four centimeters is underestimated, but that the long filled distance is overestimated. Second, in Table II., which represents the judgments when the contacts were made successively, the tendency to underestimate the short distance is less, and at the same time we notice a more pronounced overestimation of the longer filled distances. I shall give a further explanation of these results in connection with later tables.

TABLE I.

4 cm. 6 cm. 8 cm.
Filled. Open. Filled. Open. Filled. Open.

F. 5.3 4.7 7.8 7.6 9.3 10.5
F. 5.7 4.4 6.5 7.3 9.2 11.7
F. 6.0 5.6 8.2 7.3 8.7 10.8
--- --- --- --- --- ----
Av. 5.7 4.9 7.5 7.4 9.1 11.0

R. 5.7 5.1 6.7 6.8 9.3 10.2
R. 5.4 5.4 7.2 7.1 8.5 10.7
R. 4.6 4.2 8.1 8.1 9.1 11.4
--- --- --- --- --- ----
Av. 5.2 4.9 7.3 7.3 9.0 10.8

K. 5.6 5.1 6.8 6.7 8.1 9.6
K. 5.0 5.1 7.3 7.5 8.2 11.2
K. 4.9 4.9 8.2 8.1 10.1 10.1
--- --- --- --- ---- ----
Av. 5.2 5.0 7.4 7.4 8.8 10.3

TABLE II.

4 cm. 6 cm. 8 cm.
Filled. Open. Filled. Open. Filled. Open.

F. 5.1 5.0 8.0 8.3 9.2 10.3
F. 5.8 4.7 7.2 7.9 8.7 10.9
F. 5.6 5.5 6.9 9.1 9.1 11.1
--- --- --- --- --- ----
Av. 5.5 5.1 7.4 8.4 9.0 10.8

R. 6.0 4.8 8.2 7.5 9.4 10.6
R. 5.7 5.4 6.5 7.4 10.1 9.4
R. 5.0 5.2 7.7 7.8 8.6 11.2
--- --- --- --- ---- ----
Av. 5.6 5.1 7.5 7.6 9.4 10.4

K. 4.8 4.8 8.2 8.3 8.1 9.8
K. 5.1 5.3 7.1 7.7 10.0 10.8
K. 4.7 5.0 8.1 8.6 8.6 9.4
--- --- --- --- ---- ----
Av. 4.9 5.0 7.8 8.2 8.9 10.0

The first two numbers in the first line signify that when an
open distance of 4 cm. was taken, an adjacent open distance of
4.7 cm. was judged equal; but when the adjacent space was
filled, 5.3 cm. was judged equal. Each number in the column of
filled distances represents an average of five judgments. All
of the contacts in Table I. were made simultaneously; in Table
II. they were made successively.

In the next series of experiments the illusion was approached from an entirely different point of view. The two points representing the open space were given on one arm, and the filled space on a symmetrical part of the other arm. I was now able to use a much wider range of distances, and made many variations in the weights of the points and the number that were taken for the filled distance.

However, before I began this second series, in which one of the chief variations was to be in the weights of the different points, I made a brief preliminary series of experiments to determine in a general way the influence of pressure on judgments of point distances. Only three distances were employed, four, six and twelve centimeters, and three weights, twelve, twenty and forty grams. Table III. shows that, for three men who were to serve as subjects in the main experiments that are to follow, an increase in the weight of the points was almost always accompanied by an increase in the apparent distance.

TABLE III.

Distances. 4 cm. 6 cm. 12 cm.

Weights
(Grams). 12 20 40 12 20 40 12 20 40

R. 3.9 3.2 3.0 6.2 5.6 5.3 11.4 10.4 9.3
F. 4.3 4.0 3.6 6.1 5.3 5.5 12.3 11.6 10.8
B. 4.1 3.6 3.1 6.0 5.7 5.8 12.0 10.2 9.4
P. 4.3 4.1 3.7 5.9 5.6 5.6 13.1 11.9 10.7

In the standard distances the points were each weighted to 6
grams. The first three figures signify that a two-point
distance of 4 cm., each point weighing 6 grams, was judged
equal to 3.9 cm. when each point weighed 12 grams. 3.2 cm.
when each point weighed 20 grams, etc. Each figure is the
average of five judgments.

Now the application of this principle in my criticism of Parrish's experiments, and as anticipating the direction which the following experiments will take, is this: if we take a block such as Parrish used, with only two points in it, and weight it with forty grams in applying it to the skin, it is plain that each point will receive one half of the whole pressure, or twenty grams. But if we put a pressure of forty grams upon a block of eight points, each point will receive only one eighth of the forty, or five grams. Thus, in the case of the filled space, the end points, which play the most important part in the judgment of the distance, have each only five grams' pressure, while the points in the open space have each twenty grams. We should, therefore, naturally expect that the open space would be overestimated, because of the decided increase of pressure at these significant points. Parrish should have subjected the blocks, not to the same pressure, but to a pressure proportional to the number of points in each block. With my apparatus, I was easily able to prove the correctness of my position here. It will be seen in Tables IV. to VIII. that, when the sum of the weights of the two end points in the open space was only just equal to the sum of the weights of all the points in the filled space, the filled space was underestimated just as Parrish has reported. But when the points were all of the same weight, both in the filled and the open space, the filled space was judged longer in all but the very short distances. For this latter exception I shall offer an explanation presently.

Having now given an account of the results of this digression into experiments to determine the influence of pressure upon point distances, I shall pass to the second series of experiments on the illusion in question. In this series, as has been already stated, the filled space was taken on one arm and the open on the other, and then the process was reversed in order to eliminate any error arising from a lack of symmetry between the two regions. Without, for the present, going into a detailed explanation of the statistics of this second series of experiments, which are recorded in Tables IV., V., VI., VII. and VIII., I may summarize the salient results into these general conclusions: First, the short filled distance is underestimated; second, this underestimation of the filled space gradually decreases until in the case of the filled distance of 18 cm. the judgments pass over into pronounced overestimations; third, an increase in the number of points of contact in the shorter distances increases the underestimation, while an increase in the number of points in the longer distance increases the overestimation; fourth, an increase of pressure causes an invariable increase in the apparent length of space. If a general average were made of the results given in Tables IV., V., VI., VII. and VIII., there would be a preponderance of evidence for the conclusion that the filled spaces are overestimated. But we cannot ignore the marked tendencies in the opposite direction for the long and the short distances. These anomalous results, which, it will be remembered, were also found in our first series, call for explanation. Several hypotheses were framed to explain these fluctuations in the illusion, and then some shorter series of experiments were made in different directions with as large a number of variations in the conditions as possible, in the hope of discovering the disturbing factors.

TABLE IV.

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