PERCEPTION OF NUMBER THROUGH TOUCH.

BY J. FRANKLIN MESSENGER.

The investigation which I am now reporting began as a study of the fusion of touch sensations when more than two contacts were possible.

As the work proceeded new questions came up and the inquiry broadened so much that it seemed more appropriate to call it a study in the perception of number.

The experiments are intended to have reference chiefly to three questions: the s.p.a.ce-threshold, fusion of touch sensations, and the perception of number. I shall deny the validity of a threshold, and deny that there is fusion, and then offer a theory which attempts to explain the phenomena connected with the determination of a threshold and the problem of fusion and diffusion of touch sensations.

The first apparatus used for the research was made as follows: Two uprights were fastened to a table. These supported a cross-bar about ten inches from the table. To this bar was fastened a row of steel springs which could be pressed down in the manner of piano keys. To each of these springs was fastened a thread which held a bullet. The bullets, which were wrapped in silk to obviate temperature sensations, were thus suspended just above the fingers, two over each finger. Each thread pa.s.sed through a small ring which was held just a little above the fingers. These rings could be moved in any direction to accommodate the bullet to the position of the finger. Any number of the bullets could be let down at once. The main object at first was to learn something about the fusion of sensations when more than two contacts were given.

Special attention was given to the relation of the errors made when the fingers were near together to those made when the fingers were spread. For this purpose a series of experiments was made with the fingers close together, and then the series was repeated with the fingers spread as far as possible without the subject's feeling any strain. Each subject was experimented on one hour a week for about three months. The same kind of stimulation was given when the fingers were near together as was given when they were spread. The figures given below represent the average percentage of errors for four subjects.

Of the total number of answers given by all subjects when the fingers were close together, 70 per cent. were wrong. An answer was called wrong whenever the subject failed to judge the number correctly. In making out the figures I did not take into account the nature of the errors. Whether involving too many or too few the answer was called wrong. Counting up the number of wrong answers when the fingers were spread, I found that 28 per cent. of the total number of answers were wrong. This means simply that when the fingers were near together there were more than twice as many errors as there were when they were spread, in spite of the fact that each finger was stimulated in the same way in each case.

A similar experiment was tried using the two middle fingers only. In this case not more than four contacts could be made at once, and hence we should expect a smaller number of errors, but we should expect still to find more of them when the fingers are near together than when they are spread. I found that 49 per cent. of the answers were wrong when the fingers were near together and 20 per cent. were wrong when they were spread. It happens that this ratio is approximately the same as the former one, but I do not regard this fact as very significant. I state only that it is easier to judge in one case than in the other; how much easier may depend on various factors.

To carry the point still further I took only two bullets, one over the second phalanx of each middle finger. When the fingers were spread the two were never felt as one. When the fingers were together they were often felt as one.

The next step was to investigate the effect of bringing together the fingers of opposite hands. I asked the subject to clasp his hands in such a way that the second phalanges would be about even. I could not use the same apparatus conveniently with the hands in this position, but in order to have the contacts as similar as possible to those I had been using, I took four of the same kind of bullets and fastened them to the ends of two aesthesiometers. This enabled me to give four contacts at once. However, only two were necessary to show that contacts on fingers of opposite hands could be made to 'fuse' by putting the fingers together. If two contacts are given on contiguous fingers, they are quite as likely to be perceived as one when the fingers are fingers of opposite hands, as when they are contiguous fingers of the same hand.

These results seem to show that one of the important elements of fusion is the actual s.p.a.ce relations of the points stimulated. The reports of the subjects also showed that generally and perhaps always they located the points in s.p.a.ce and then remembered what finger occupied that place. It was not uncommon for a subject to report a contact on each of two adjacent fingers and one in between where he had no finger. A moment's reflection would usually tell him it must be an illusion, but the sensation of this illusory finger was as definite as that of any of his real fingers. In such cases the subject seemed to perceive the relation of the points to each other, but failed to connect them with the right fingers. For instance, if contacts were made on the first, second and third fingers, the first might be located on the first finger, the third on the second finger, and then the second would be located in between.

So far my attention had been given almost entirely to fusion, but the tendency on the part of all subjects to report more contacts than were actually given was so noticeable that I concluded that diffusion was nearly as common as fusion and about as easy to produce. It also seemed that the element of weight might play some part, but just what effect it had I was uncertain. I felt, too, that knowledge of the apparatus gained through sight was giving the subjects too much help.

The subjects saw the apparatus every day and knew partly what to expect, even though the eyes were closed when the contacts were made.

A more efficient apparatus seemed necessary, and, therefore, before taking up the work again in 1900, I made a new apparatus.

Not wishing the subjects to know anything about the nature of the machine or what could be done with it, I enclosed it in a box with an opening in one end large enough to allow the subject's hand to pa.s.s through, and a door in the other end through which I could operate. On the inside were movable wooden levers, adjustable to hands of different width. These were fastened by pivotal connection at the proximal end. At the outer end of each of these was an upright strip with a slot, through which was pa.s.sed another strip which extended back over the hand. This latter strip could be raised or lowered by means of adjusting screws in the upright strip. On the horizontal strip were pieces of wood made so as to slide back and forth. Through holes in these pieces plungers were pa.s.sed. At the bottom of each plunger was a small square piece of wood held and adjusted by screws.

From this piece was suspended a small thimble filled with shot and paraffine. The thimbles were all equally weighted. Through a hole in the plunger ran a thread holding a piece of lead of exactly the weight of the thimble. By touching a pin at the top this weight could be dropped into the thimble, thus doubling its weight. A screw at the top of the piece through which the plunger pa.s.sed regulated the stop of the plunger. This apparatus had three important advantages. It was entirely out of sight, it admitted of rapid and accurate adjustment, and it allowed the weights to be doubled quickly and without conspicuous effort.

For the purpose of studying the influence of weight on the judgments of number I began a series of experiments to train the subjects to judge one, two, three, or four contacts at once. For this the bare metal thimbles were used, because it was found that when they were covered with chamois skin the touch was so soft that the subjects could not perceive more than one or two with any degree of accuracy, and I thought it would take entirely too long to train them to perceive four. The metal thimbles, of course, gave some temperature sensation, but the subject needed the help and it seemed best to use the more distinct metal contacts.

In this work I had seven subjects, all of whom had had some experience in a laboratory, most of them several years. Each one took part one hour a week. The work was intended merely for training, but a few records were taken each day to see how the subjects progressed. The object was to train them to perceive one, two, three, and four correctly, and not only to distinguish four from three but to distinguish four from more than four. Hence five, six, seven, and eight at a time were often given. When the subject had learned to do this fairly well the plan was to give him one, two, three, and four in order, then to double the weight of the four and give them again to see if he would interpret the additional weight as increase in number.

This was done and the results were entirely negative. The subjects either noticed no difference at all or else merely noticed that the second four were a little more distinct than the first.

The next step was to give a number of light contacts to be compared with the same number of heavy ones--the subject, not trying to tell the exact number but only which group contained the greater number. A difference was sometimes noticed, and the subject, thinking that the only variations possible were variations of number and position, often interpreted the difference as difference in number; but the light weights were as often called more as were the heavy ones.

So far as the primary object of this part of the experiment is concerned the results are negative, but incidentally the process of training brought out some facts of a more positive nature. It was early noticed that some groups of four were much more readily recognized than others, and that some of them were either judged correctly or underestimated while others were either judged correctly or overestimated. For convenience the fingers were indicated by the letters _A B C D_, _A_ being the index finger. The thumb was not used.

Two weights were over each finger. The one near the base was called 1, the one toward the end 2. Thus _A12 B1 C2_ means two contacts on the index finger, one near the base of the second finger, and one near the end of the third finger. The possible arrangements of four may be divided into three types: (1) Two weights on each of two fingers, as _A12 B12, C12 D12_, etc., (2) four in a line across the fingers, _A1 B1 C1 D1_ or _A2 B2 C2 D2_, (3) unsymmetrical arrangements, as _A1 B2 C1 D2_, etc. Arrangements of the first type were practically never overestimated. _B12 C12_ was overestimated once and _B12 D12_ was overestimated once, but these two isolated cases need hardly be taken into account. Arrangements of the second type were but rarely overestimated--_A2 B2 C2 D2_ practically never, _A1 B1 C1 D1_ a few times. Once the latter was called eight. Apparently the subject perceived the line across the hand and thought there were two weights on each finger instead of one. Arrangements of the third type were practically never underestimated, but were overestimated in 68 per cent. of the cases.

These facts in themselves are suggestive, but equally so was the behavior of the subject while making the answers. It would have hardly done to ask the person if certain combinations were hard to judge, for the question would serve as a suggestion to him; but it was easy to tell when a combination was difficult without asking questions. When a symmetrical arrangement was given, the subject was usually composed and answered without much hesitation. When an unsymmetrical arrangement was given he often hesitated and knit his brows or perhaps used an exclamation of perplexity before answering, and after giving his answer he often fidgeted in his chair, drew a long breath, or in some way indicated that he had put forth more effort than usual. It might be expected that the same att.i.tude would be taken when six or eight contacts were made at once, but in these cases the subject was likely either to fail to recognize that a large number was given or, if he did, he seemed to feel that it was too large for him to perceive at all and would guess at it as well as he could. But when only four were given, in a zigzag arrangement, he seemed to feel that he ought to be able to judge the number but to find it hard to do so, and knowing from experience that the larger the number the harder it is to judge he seemed to reason conversely that the more effort it takes to judge the more points there are, and hence he would overestimate the number.

The comments of the subjects are of especial value. One subject (Mr.

Dunlap) reports that he easily loses the sense of location of his fingers, and the s.p.a.ces in between them seem to belong to him as much as do his fingers themselves. When given one touch at a time and told to raise the finger touched he can do so readily, but he says he does not know which finger it is until he moves it. He feels as if he willed to move the place touched without reference to the finger occupying it. He sometimes hesitates in telling which finger it is, and sometimes he finds out when he moves a finger that it is not the one he thought it was.

Another subject (Dr. MacDougall) says that his fingers seem to him like a continuous surface, the same as the back of his hand. He usually named the outside points first. When asked about the order in which he named them, he said he named the most distinct ones first.

Once he reported that he felt six things, but that two of them were in the same places as two others, and hence he concluded there were but four. This feeling in a less careful observer might lead to overestimation of number and be called diffusion, but all cases of overestimation cannot be explained that way, for it does not explain why certain combinations are so much more likely to lead to it than others.

In one subject (Mr. Swift) there was a marked tendency to locate points on the same fingers. He made many mistakes about fingers _B_ and _C_ even when he reported the number correctly. When _B_ and _D_ were touched at the same time he would often call it _C_ and _D_, and when _C_ and _D_ were given immediately afterward he seemed to notice no difference. With various combinations he would report _C_ when _B_ was given, although _C_ had not been touched at the same time. If _B_ and _C_ were touched at the same time he could perceive them well enough.

The next part of the research was an attempt to discover whether a person can perceive any difference between one point and two points which feel like one. A simple little experiment was tried with the aesthesiometer. The subjects did not know what was being used, and were asked to compare the relative size of two objects placed on the back of the hand in succession. One of these objects was one k.n.o.b of the aesthesiometer and the other was two k.n.o.bs near enough together to lie within the threshold. The distance of the points was varied from 10 to 15 mm. Part of the time the one was given first and part of the time both were given together. The one, whether given first or second, was always given about midway between the points touched by the two. If the subject is not told to look for some specific difference he will not notice any difference between the two k.n.o.bs and the one, and he will say they are alike; but if he is told to give particular attention to the size there seems to be a slight tendency to perceive a difference. The subjects seem to feel very uncertain about their answers, and it looks very much like guess-work, but something caused the guesses to go more in one direction than in the other.

Two were called less than one .... 16% of the times given.

" " " equal to .... 48% " "

" " " greater than .... 36% " "

Approximately half of the time two were called equal to one, and if there had been no difference in the sensations half of the remaining judgments should have been that two was smaller than one, but two were called larger than one more than twice as many times as one was called larger than two. There was such uniformity in the reports of the different subjects that no one varied much from this average ratio.

This experiment seems to indicate a very slight power of discrimination of stimulations within the threshold. In striking contrast to this is the power to perceive variations of distance between two points outside the threshold. To test this the aesthesiometer was spread enough to bring the points outside the threshold. The back of the hand was then stimulated with the two points and then the distance varied slightly, the hand touched and the subject asked to tell which time the points were farther apart. A difference of 2 mm. was usually noticed, and one of from 3 to 5 mm.

was noticed always very clearly.

I wondered then what would be the result if small cards set parallel to each other were used in place of the k.n.o.bs of the aesthesiometer. I made an aesthesiometer with cards 4 mm. long in place of k.n.o.bs. These cards could be set at any angle to each other. I set them at first 10 mm. apart and parallel to each other and asked the subjects to compare the contact made by them with a contact by one card of the same size.

The point touched by the one card was always between the points touched by the two cards, and the one card was put down so that its edge would run in the same direction as the edges of the other cards.

The result of this was that:

Two were called less, 14 per cent.

" " " equal, 36 " "

" " " greater, 50 " "

I then increased the distance of the two cards to 15 mm., the other conditions remaining the same, and found that:

Two were called less, 11 per cent.

" " " equal, 50 " "

" " " greater, 39 " "

It will be noticed that the ratio in this last series is not materially different from the ratio found when the two k.n.o.bs of the aesthesiometer were compared with one k.n.o.b. The ratio found when the distance was 10 mm., however, is somewhat different. At that distance two were called greater half of the time, while at 15 mm. two were called equal to one half of the time. The explanation of the difference, I think, is found in the comments of one of my subjects. I did not ask them to tell in what way one object was larger than the other--whether longer or larger all around or what--but simply to answer 'equal,' 'greater,' or 'less.' One subject, however, frequently added more to his answers. He would often say 'larger crosswise' or 'larger lengthwise' of his hand. And a good deal of the time he reported two larger than one, not in the direction in which it really was larger, but the other way. It seems to me that when the two cards were only 10 mm. apart the effect was somewhat as it would be if a solid object 4 mm. wide and 10 mm. long had been placed on the hand.

Such an object would be recognized as having greater ma.s.s than a line 4 mm. long. But when the distance is 15 mm. the impression is less like that of a solid body but still not ordinarily like two objects.

In connection with the subject of diffusion the _Vexirfehler_ is of interest. An attempt was made to develop the _Vexirfehler_ with the aesthesiometer. Various methods were tried, but the following was most successful. I would tell the subject that I was going to use the aesthesiometer and ask him to close his eyes and answer simply 'one' or 'two.' He would naturally expect that he would be given part of the time one, and part of the time two. I carefully avoided any suggestion other than that which could be given by the aesthesiometer itself. I would begin on the back of the hand near the wrist with the points as near the threshold as they could be and still be felt as two. At each successive putting down of the instrument I would bring the points a little nearer together and a little lower down on the hand. By the time a dozen or more stimulations had been given I would be working down near the knuckles, and the points would be right together. From that on I would use only one point. It might be necessary to repeat this a few times before the illusion would persist. A great deal seems to depend on the skill of the operator. It would be noticed that the first impression was of two points, and that each stimulation was so nearly like the one immediately preceding that no difference could be noticed. The subject has been led to call a thing two which ordinarily he would call one, and apparently he loses the distinction between the sensation of one and the sensation of two. After going through the procedure just mentioned I put one k.n.o.b of the aesthesiometer down one hundred times in succession, and one subject (Mr. Meakin) called it two seventy-seven times and called it one twenty-three times. Four of the times that he called it one he expressed doubt about his answer and said it might be two, but as he was not certain he called it one.

Another subject (Mr. George) called it two sixty-two times and one thirty-eight times. A third subject (Dr. Hylan) called it two seventy-seven times and one twenty-three times. At the end of the series he was told what had been done and he said that most of his sensations of two were perfectly distinct and he believed that he was more likely to call what seemed somewhat like two one, than to call what seemed somewhat like one two. With the fourth subject (Mr.

Dunlap) I was unable to do what I had done with the others. I could get him to call one two for four or five times, but the idea of two would not persist through a series of any length. He would call it two when two points very close together were used. I could bring the k.n.o.bs within two or three millimeters of each other and he would report two, but when only one point was used he would find out after a very few stimulations were given that it was only one. After I had given up the attempt I told him what I had been trying to do and he gave what seems to me a very satisfactory explanation of his own case. He says the early sensations keep coming up in his mind, and when he feels like calling a sensation two he remembers how the first sensation felt and sees that this one is not like that, and hence he calls it one. I pa.s.s now to a brief discussion of what these experiments suggest.

It has long been known that two points near together on the skin are often perceived as one. It has been held that in order to be felt as two they must be far enough apart to have a spatial character, and hence the distance necessary for two points to be perceived has been called the 's.p.a.ce-threshold.' This threshold is usually determined either by the method of minimal changes or by the method of right and wrong cases.

If, in determining a threshold by the method of minimal changes--on the back of the hand, for example, we a.s.sume that we can begin the ascending series and find that two are perceived as one always until the distance of twenty millimeters is reached, and that in the descending series two are perceived as two until the distance of ten millimeters is reached, we might then say that the threshold is somewhere between ten and twenty millimeters. But if the results were always the same and always as simple as this, still we could not say that there is any probability in regard to the answer which would be received if two contacts 12, 15, or 18 millimeters apart were given by themselves. All we should know is that if they form part of an ascending series the answer will be 'one,' if part of a descending series 'two.'

The method of right and wrong cases is also subject to serious objections. There is no lower limit, for no matter how close together two points are they are often called two. If there is any upper limit at all, it is so great that it is entirely useless. It might be argued that by this method a distance could be found at which a given percentage of answers would be correct. This is quite true, but of what value is it? It enables one to obtain what one arbitrarily calls a threshold, but it can go no further than that. When the experiment changes the conditions change. The s.p.a.ce may remain the same, but it is only one of the elements which a.s.sist in forming the judgment, and its importance is very much overestimated when it is made the basis for determining the threshold.

Different observers have found that subjects sometimes describe a sensation as 'more than one, but less than two.' I had a subject who habitually described this feeling as 'one and a half.' This does not mean that he has one and a half sensations. That is obviously impossible. It must mean that the sensation seems just as much like two as it does like one, and he therefore describes it as half way between. If we could discover any law governing this feeling of half-way-between-ness, that might well indicate the threshold. But such feelings are not common. Sensations which seem between one and two usually call forth the answer 'doubtful,' and have a negative rather than a positive character. This negative character cannot be due to the stimulus; it must be due to the fluctuating att.i.tudes of the subject. However, if the doubtful cases could be cla.s.sed with the 'more than one but less than two' cases and a law be found governing them, we might have a threshold mark. But such a law has not been formulated, and if it had been an a.n.a.lysis of the 'doubtful' cases would invalidate it. For, since we cannot have half of a sensation or half of a place as we might have half of an area, the subject regards each stimulation as produced by one or by two points as the case may be. Occasionally he is stimulated in such a way that he can regard the object as two or as one with equal ease. In order to describe this feeling he is likely to use one or the other of the methods just mentioned.

We might say that when the sum of conditions is such that the subject perceives two points, the points are above the threshold, and when the subject perceives one point when two are given they are below the threshold. This might answer the purpose very well if it were not for the _Vexirfehler_. According to this definition, when the _Vexirfehler_ appears we should have to say that one point is above the threshold for twoness, which is a queer contradiction, to say the least. It follows that all of the elaborate and painstaking experiments to determine a threshold are useless. That is, the threshold determinations do not lead us beyond the determinations themselves.

In order to explain the fact that a person sometimes fails to distinguish between one point and two points near together, it has been suggested that the sensations fuse. This, I suppose, means either that the peripheral processes coalesce and go to the center as a single neural process, or that the process produced by each stimulus goes separately to the brain and there the two set up a single activity. Somewhat definite 'sensory circles,' even, were once believed in.

If the only fact we had to explain was that two points are often thought to be one when they are near together, 'fusion' might be a good hypothesis, but we have other facts to consider. If this one is explained by fusion, then the mistaking of one point for two must be due to diffusion of sensations. Even that might be admissible if the _Vexirfehler_ were the only phenomenon of this cla.s.s which we met. But it is also true that several contacts are often judged to be more than they actually are, and that hypothesis will not explain why certain arrangements of the stimulating objects are more likely to bring about that result than others. Still more conclusive evidence against fusion, it seems to me, is found in the fact that two points, one on each hand, may be perceived as one when the hands are brought together. Another argument against fusion is the fact that two points pressed lightly may be perceived as one, and when the pressure is increased they are perceived as two. Strong pressures should fuse better than weak ones, and therefore fusion would imply the opposite results. Bruckner[1] has found that two sensations, each too weak to be perceived by itself, may be perceived when the two are given simultaneously and sufficiently near together. This reenforcement of sensations he attributes to fusion. But we have a similar phenomenon in vision when a group of small dots is perceived, though each dot by itself is imperceptible. No one, I think, would say this is due to fusion. It does not seem to me that we need to regard reenforcement as an indication of fusion.