Harvard Psychological Studies Part 13

[1] Bruckner, A.: 'Die Raumschwelle bei Simultanreizung,'

_Zeitschrift fur Psychologie_, 1901, Bd. 26, S. 33.

My contention is that the effects sometimes attributed to fusion and diffusion of sensations are not two different kinds of phenomena, but are identical in character and are to be explained in the same way.

Turning now to the explanation of the special experiments, we may begin with the _Vexirfehler_.[2] It seems to me that the _Vexirfehler_ is a very simple phenomenon. When a person is stimulated with two objects near together he attends first to one and then to the other and calls it two; then when he is stimulated with one object he attends to it, and expecting another one near by he hunts for it and hits upon the same one he felt before but fails to remember that it is the same one, and hence thinks it is another and says he has felt two objects. Observers agree that the expectation of two tends to bring out the _Vexirfehler_. This is quite natural. A person who expects two and receives one immediately looks about for the other without waiting to fixate the first, and therefore when he finds it again he is less likely to recognize it and more likely to think it another point and to call it two. Some observers[3] have found that the apparent distance of the two points when the _Vexirfehler_ appears never much exceeds the threshold distance. Furthermore, there being no distinct line of demarcation between one and two, there must be many sensations which are just about as much like one as they are like two, and hence they must be lumped off with one or the other group. To the mathematician one and two are far apart in the series because he has fractions in between, but we perceive only in terms of whole numbers; hence all sensations which might more accurately be represented by fractions must be cla.s.sed with the nearest whole number. A sensation is due to a combination of factors. In case of the _Vexirfehler_ one of these factors, viz., the stimulating object, is such as to suggest one, but some of the other conditions--expectation, preceding sensation, perhaps blood pressure, etc.--suggest two, so that the sensation as a whole suggests _one-plus_, if we may describe it that way, and hence the inference that the sensation was produced by two objects.

[2] Tawney, Guy A.: 'Ueber die Wahrnehmung zweier Punkte mittelst des Tastsinnes mit Rucksicht auf die Frage der Uebung und die Entstehung der Vexirfehler,' _Philos. Stud._, 1897, Bd.

XIII., S. 163.

[3] See Nichols: 'Number and s.p.a.ce,' p. 161. Henri, V., and Tawney, G.: _Philos. Stud._, Bd. XI., S. 400.

This, it seems to me, may account for the appearance of the _Vexirfehler_, but why should not the subject discover his error by studying the sensation more carefully? He cannot attend to two things at once, nor can he attend to one thing continuously, even for a few seconds. What we may call continuous attention is only a succession of attentive impulses. If he could attend to the one object continuously and at the same time hunt for the other, I see no reason why he should not discover that there is only one. But if he can have only one sensation at a time, then all he can do is to a.s.sociate that particular sensation with some idea. In the case before us he a.s.sociates it with the idea of the number two. He cannot conceive of two objects unless he conceives them as located in two different places. Sometimes a person does find that the two objects of his perception are both in the same place, and when he does so he concludes at once that there is but one object. At other times he cannot locate them so accurately, and he has no way of finding out the difference, and since he has a.s.sociated the sensation with the idea of two he still continues to call it two. If he is asked to locate the points on paper he fills out the figure just as he fills out the blind-spot, and he can draw them in just the same way that he can draw lines which he thinks he _sees_ with the blind-spot, but which really he only _infers_.

Any sensation, whether produced by one or by many objects, is one, but there may be a difference in the quality of a sensation produced by one object and that of a sensation produced by more than one object.

If this difference is clear and distinct, the person a.s.signs to each sensation the number he has a.s.sociated with it. He gives it the name two when it has the quality he has a.s.sociated with that idea. But the qualities of a sensation from which the number of objects producing it is inferred are not always clear and distinct. The quality of the sensation must not be confused with any quality of the object. If we had to depend entirely on the sense of touch and always remained pa.s.sive and received sensations only when we were touched by something, there is no reason why we should not a.s.sociate the idea of one with the sensation produced by two objects and the idea of two with that produced by one object--a.s.suming that we could have any idea of number under such circ.u.mstances. The quality of a sensation from which number is inferred depends on several factors. The number itself is determined by the att.i.tude of the subject, but the att.i.tude is determined largely by a.s.sociation. A number of facts show this. When a person is being experimented on, it is very easy to confuse him and make him forget how two feel and how one feels. I have often had a subject tell me that he had forgotten and ask me to give him two distinctly that he might see how it felt. In other words, he had forgotten how to a.s.sociate his ideas and sensations. In developing the _Vexirfehler_ I found it much better, after sufficient training had been given, not to give two at all, for it only helped the subject to perceive the difference between two and one by contrast. But when one was given continually he had no such means of contrast, and having a.s.sociated the idea of two with a sensation he continued to do so. The one subject with whom I did not succeed in developing the _Vexirfehler_ to any great extent perceived the difference by comparing the sensation with one he had had some time before. I could get him, for a few times, to answer two when only one was given, but he would soon discover the difference, and he said he did it by comparing it with a sensation which he had had some time before and which he knew was two. By this means he was able to make correct a.s.sociations when otherwise he would not have done so. It has been discovered that when a subject is being touched part of the time with two and part of the time with one, and the time it takes him to make his judgments is being recorded, he will recognize two more quickly than he will one if there is a larger number of twos in the series than there is of ones. I do not see how this could be if the sensation of two is any more complex than that of one. But if both sensations are units and all the subject needs to do is to a.s.sociate the sensation with an idea, then we should expect that the a.s.sociation he had made most frequently would be made the most quickly.

If the feeling of twoness or of oneness is anything but an inference, why is it that a person can perceive two objects on two fingers which are some distance apart, but perceives the same two objects as one when the fingers are brought near together and touched in the same way? It is difficult to see how bringing the fingers together could make a sensation any less complex, but it would naturally lead a person to infer one object, because of his previous a.s.sociations. He has learned to call that _one_ which seems to occupy one place. If two contacts are made in succession he will perceive them as two because they are separated for him by the time interval and he can perceive that they occupy different places.

When two exactly similar contacts are given and are perceived as one, we cannot be sure whether the subject feels only one of the contacts and does not feel the other at all, or feels both contacts and thinks they are in the same place, which is only another way of saying he feels both as one. It is true that when asked to locate the point he often locates it between the two points actually touched, but even this he might do if he felt but one of the points. To test the matter of errors of localization I have made a few experiments in the Columbia University laboratory. In order to be sure that the subject felt both contacts I took two bra.s.s rods about four inches long, sharpened one end and rounded off the other. The subject sat with the palm of his right hand on the back of his left and his fingers interlaced. I stimulated the back of his fingers on the second phalanges with the sharp end of one rod and the blunt end of the other and asked him to tell whether the sharp point was to the right or to the left of the other. I will not give the results in detail here, but only wish to mention a few things for the purpose of ill.u.s.trating the point in question. Many of the answers were wrong. Frequently the subject would say both were on the same finger, when really they were on fingers of opposite hands, which, however, in this position were adjacent fingers. Sometimes when this happened I would ask him which finger they were on, and after he had answered I would leave the point on the finger on which he said both points were and move the other point over to the same finger, then move it back to its original position, then again over to the finger on which the other point was resting, and so on, several times. The subject would tell me that I was raising one point and putting it down again in the same place all of the time. Often a subject would tell me he felt both points on the same finger, but that he could not tell to which hand the finger belonged. When two or more fingers intervened between the fingers touched no subject ever had any difficulty in telling which was the sharp and which the blunt point, but when adjacent fingers were touched it was very common for the subject to say he could not tell which was which. This cannot be because there is more difference in the quality of the contacts in one case than in the other. If they were on the same finger it might be said that they were stimulating the same general area, but since one is on one hand and one on the other this is impossible. The subject does not think the two points are in the same place, because he feels two qualities and hence he infers two things, and he knows two things cannot be in the same place at the same time. If the two contacts were of the same quality probably they would be perceived as one on account of the absence of difference, for the absence of difference is precisely the quality of oneness.

These facts, together with those mentioned before, seem to me to indicate that errors of localization are largely responsible for judgments which seem to be due to fusion or diffusion of sensations.

But they are responsible only in this way, they prevent the correction of the first impression. I do not mean that a person never changes his judgment after having once made it, but a change of judgment is not necessarily a correction. Often it is just the contrary. But where a wrong judgment is made and cannot be corrected inability to localize is a prominent factor. This, however, is only a secondary factor in the perception of number. The cardinal point seems to me the following:

Any touch sensation, no matter by how many objects it is produced, is one, and number is an inference based on a temporal series of sensations. It may be that we can learn by a.s.sociation to infer number immediately from the quality of a sensation, but that means only that we recognize the sensation as one we have had before and have found it convenient to separate into parts and regard one part after the other, and we remember into how many parts we separated it. This separating into parts is a time process. What we shall regard as _one_ is a mere matter of convenience. Continuity sometimes affords a convenient basis for unity and sometimes it does not. There is no standard of oneness in the objective world. We separate things as far as convenience or time permits and then stop and call that _one_ which our own att.i.tude has determined shall be one.

That we do a.s.sociate a sensation with whatever idea we have previously connected it with, even though that idea be that of the number of objects producing it, is clearly shown by some experiments which I performed in the laboratory of Columbia University. I took three little round pieces of wood and set them in the form of a triangle. I asked the subject to pa.s.s his right hand through a screen and told him I wanted to train him to perceive one, two, three and four contacts at a time on the back of his hand, and that I would tell him always how many I gave him until he learned to do it. When it came to three I gave him two points near the knuckles and one toward the wrist and told him that was three. Then I turned the instrument around and gave him one point near the knuckles and two toward the wrist and told him that was four. As soon as he was sure he distinguished all of the points I stopped telling him and asked him to answer the number. I had four subjects, and each one learned very soon to recognize the four contacts when three were given in the manner mentioned above. I then repeated the same thing on the left hand, except that I did not tell him anything, but merely asked him to answer the number of contacts he felt. In every case the idea of four was so firmly a.s.sociated with that particular kind of a sensation that it was still called four when given on the hand which had not been trained. I gave each subject a diagram of his hand and asked him to indicate the position of the points when three were given and when four were given. This was done without difficulty. Two subjects said they perceived the four contacts more distinctly than the three, and two said they perceived the three more distinctly than the four.

It seems very evident that the sensation produced by three contacts is no more complex when interpreted as four than when interpreted as three. If that is true, then it must also be evident that the sensation produced by one contact is no more complex when interpreted as two than when interpreted as one. The converse should also be true, that the sensation produced by two contacts is no less complex when interpreted as one than when interpreted as two. Difference in number does not indicate difference in complexity. The sensation of four is not made up of four sensations of one. It is a unit as much as the sensation of one is.

There remains but one point to be elaborated. If number is not a quality of objects, but is merely a matter of att.i.tude of the subject, we should not expect to find a very clear-cut line of demarcation between the different numbers except with regard to those things which we constantly consider in terms of number. Some of our a.s.sociations are so firmly established and so uniform that we are likely to regard them as necessary. It is not so with our a.s.sociations of number and touch sensations. We have there only a vague, general notion of what the sensation of one or two is, because usually it does not make much difference to us, yet some sensations are so well established in our minds that we call them one, two or four as the case may be without hesitation. Other sensations are not so, and it is difficult to tell to which cla.s.s they belong. Just so it is easy to tell a pure yellow color from a pure orange, yet they shade into each other, so that it is impossible to tell where one leaves off and the other begins. If we could speak of a one-two sensation as we speak of a yellow-orange color we might be better able to describe our sensations. It would, indeed, be convenient if we could call a sensation which seems like one with a suggestion of two about it a two-one sensation, and one that seems nearly like two but yet suggests one a one-two sensation.

Since we cannot do this, we must do the best we can and describe a sensation in terms of the number it most strongly suggests. Subjects very often, as has been mentioned before, describe a sensation as 'more than one but less than two,' but when pressed for an answer will say whichever number it most resembles. A person would do the same thing if he were shown spectral colors from orange to yellow and told to name each one either orange or yellow. At one end he would be sure to say orange and at the other yellow, but in the middle of the series his answers would likely depend upon the order in which the colors were shown, just as in determining the threshold for the perception of two points by the method of minimal changes the answers in the ascending series are not the same as those in the descending series.

The experiments have shown that the sensation produced by two points, even when they are called one, is not the same as that produced by only one point, but the difference is not great enough to suggest a different number.

If the difference between one and two were determined by the distance, then the subst.i.tution of lines for k.n.o.bs of the aesthesiometer ought to make no difference. And if the sensations produced by two objects fuse when near together, then the sensations produced by lines ought to fuse as easily as those produced by k.n.o.bs.

In regard to the higher numbers difficulties will arise unless we take the same point of view and say that number is an inference from a sensation which is in itself a unit. It has been shown that four points across the ends of the fingers will be called four or less, and that four points, one on the end of each alternate finger and one at the base of each of the others, will be called four or more--usually more. In either case each contact is on a separate finger, and it is hardly reasonable to suppose there is no diffusion when they are in a straight row, but that when they are in irregular shape there is diffusion. It is more probable that the subject regards the sensation produced by the irregular arrangement as a novelty, and tries to separate it into parts. He finds both proximal and distal ends of his fingers concerned. He may discover that the area covered extends from his index to his little finger. He naturally infers, judging from past experience, that it would take a good many points to do that, and hence he overestimates the number. When a novel arrangement was given, such as moving some of the weights back on the wrist and scattering others over the fingers, very little idea of number could be gotten, yet they were certainly far enough apart to be felt one by one if a person could ever feel them that way, and the number was not so great as to be entirely unrecognizable.

THE SUBJECTIVE HORIZON.

BY ROBERT MACDOUGALL.

I.

The general nature of the factors which enter into the orientation of the main axes of our bodies, under normal and abnormal conditions, has been of much interest to the psychologist in connection with the problem of the development of s.p.a.ce and movement perception. The special points of attack in this general investigation have comprised, firstly, the separation of resident, or organic, from transient, or objective, factors; secondly, the determination of the special organic factors which enter into the mechanism of judgment and their several values; and thirdly, within this latter field, the resolution of the problem of a special mechanism of spatial orientation, the organ of the static sense.

The special problem with which we are here concerned relates to the group of factors upon which depends one's judgment that any specified object within the visual field lies within the horizontal plane of the eyes, or above or below that plane, and the several functions and values of these components. The method of procedure has been suggested by the results of preceding investigations in this general field.

The first aim of the experiments was to separate the factors of resident and transient sensation, and to determine the part played by the presence of a diversified visual field. To do so it was necessary to ascertain, for each member of the experimental group, the location of the subjective visual horizon, and the range of uncertainty in the observer's location of points within that plane. Twelve observers in all took part in the investigation. In the first set of experiments no attempt was made to change the ordinary surroundings of the observer, except in a single point, namely, the provision that there should be no extended object within range of the subject's vision having horizontal lines on a level with his eyes.

The arrangements for experimentation were as follows: A black wooden screen, six inches wide and seven feet high, was mounted between two vertical standards at right angles to the axis of vision of the observer. Vertically along the center of this screen and over pulleys at its top and bottom pa.s.sed a silk cord carrying a disc of white cardboard, 1 cm. in diameter, which rested against the black surface of the screen. From the double pulley at the bottom of the frame the two ends of the cord pa.s.sed outward to the observer, who, by pulling one or the other, could adjust the disc to any desired position. On the opposite side of the screen from the observer was mounted a vertical scale graduated in millimeters, over which pa.s.sed a light index-point attached to the silk cord, by means of which the position of the cardboard disc in front was read off. The observer was seated in an adjustable chair with chin and head rests, and a lateral sighting-tube by which the position of the eyeball could be vertically and horizontally aligned. The distance from the center of the eyeball to the surface of the screen opposite was so arranged that, neglecting the radial deflection, a displacement of 1 mm. in either direction was equal to a departure of one minute of arc from the plane of the eyes'

horizon.

The observer sat with the light at his back, and by manipulation of the cords adjusted the position of the white disc freely up and down the screen until its center was judged to be on a level with the eye.

Its position was then read off the vertical scale by the conductor (who sat hidden by an interposed screen), and the error of judgment was recorded in degrees and fractions as a positive (upward) or negative (downward) displacement. The disc was then displaced alternately upward and downward, and the judgment repeated. From the time of signalling that the point had been located until this displacement the observer sat with closed eyes. These determinations were made in series of ten, and the individual averages are in general based upon five such series, which included regularly the results of sittings on different days. In some cases twice this number of judgments were taken, and on a few occasions less. The number of judgments is attached to each series of figures in the tables. In that which follows the individual values and their general averages are given as minutes of arc for (_a_) the constant error or position of the subjective horizon, (_b_) the average deviation from the objective horizon, and (_c_) the mean variation of the series of judgments.

TABLE I.

Observer. Constant Error. Average Deviation. Mean Variation.

_A_ (100) -19.74 38.78 10.67 _C_ (90) -18.18 23.89 10.82 _D_ (100) -19.84 33.98 7.95 _E_ (50) - 4.28 72.84 6.90 _F_ (100) +46.29 46.29 2.05 _G_ (50) +14.96 35.40 8.40 _H_ (50) -27.22 27.46 5.78 _I_ (50) + 6.62 53.34 7.45 _K_ (50) + 1.08 30.26 6.59 _L_ (20) -56.70 56.70 10.39

Average: -7.70 41.89 7.69

The average subjective horizon shows a negative displacement, the exceptional minority being large. No special facts could be connected with this characteristic, either in method of judgment or in the past habits of the reactor. The average constant error is less than an eighth of a degree, and in neither direction does the extreme reach the magnitude of a single degree of arc. Since the mean variation is likewise relatively small, there is indicated in one's ordinary judgments of this kind a highly refined sense of bodily orientation in s.p.a.ce.

II.

In order to separate the resident organic factors from those presented by the fixed relations of the external world, an adaptation of the mechanism was made for the purpose of carrying on the observations in a darkened room. For the cardboard disc was subst.i.tuted a light carriage, riding upon rigid parallel vertical wires and bearing a miniature ground-gla.s.s bulb enclosing an incandescent electric light of 0.5 c.p. This was encased in a chamber with blackened surfaces, having at its center an aperture one centimeter in diameter, which was covered with white tissue paper. The subdued illumination of this disc presented as nearly as possible the appearance of that used in the preceding series of experiments. No other object than this spot of moving light was visible to the observer. Adjustment and record were made as before. The results for the same set of observers as in the preceding case are given in the following table:

TABLE II.

Subject. Constant Error. Average Deviation. Mean Variation.

_A_ (50) - 52.76 55.16 30.08 _C_ (30) - 7.40 42.00 35.31 _D_ (50) - 14.24 38.60 30.98 _E_ (50) - 43.12 86.44 30.19 _F_ (100) - 2.01 72.33 20.27 _G_ (100) - 21.89 47.47 32.83 _H_ (50) - 1.62 59.10 29.95 _I_ (50) - 32.76 41.60 24.40 _K_ (50) - 61.70 100.02 52.44 _L_ (40) -128.70 128.90 27.83

Average: - 36.62 67.16 31.43

Changes in two directions may be looked for in the results as the experimental conditions are thus varied. The first is a decrease in the certainty of judgment due to the simple elimination of certain factors upon which the judgment depends. The second is the appearance of definite types of error due to the withdrawal of certain correctives of organic tendencies which distort the judgment in specific directions. The loss in accuracy is great; the mean variation increases from 7.69 to 31.43, or more than 400 per cent. This large increase must not, however, be understood as indicating a simple reduction in the observer's capacity to locate points in the horizontal plane of the eyes. The two series are not directly comparable; for in the case of the lighted room, since the whole visual background remained unchanged, each determination must be conceived to influence the succeeding judgment, which becomes really a correction of the preceding. To make the two series strictly parallel the scenery should have been completely changed after each act of judgment. Nevertheless, a very large increase of uncertainty may fairly be granted in pa.s.sing from a field of visual objects to a single illuminated point in an otherwise dark field. It is probable that this change is largely due to the elimination of those elements of sensation depending upon the relation of the sagittal axis to the plane against which the object is viewed.

The change presented by the constant error can here be interpreted only speculatively. I believe it is a frequently noted fact that the lights in a distant house or other familiar illuminated object on land, and especially the signal lights on a vessel at sea appear higher than their respective positions by day, to the degree at times of creating the illusion that they hang suspended above the earth or water. This falls in with the experimental results set forth in the preceding table. It cannot be attributed to an uncomplicated tendency of the eyes of a person seated in such a position to seek a lower direction than the objective horizon, when freed from the corrective restraint of a visual field, as will be seen when the results of judgments made in complete darkness are cited, in which case the direction of displacement is reversed. The single illuminated spot which appears in the surrounding region of darkness, and upon which the eye of the observer is directed as he makes his judgment, in the former case restricts unconscious wanderings of the eye, and sets up a process of continuous and effortful fixation which accompanies each act of determination. I attribute the depression of the eyes to this process of binocular adjustment. The experience of strain in the act of fixation increases and decreases with the distance of the object regarded. In a condition of rest the axes of vision of the eyes tend to become parallel; and from this point onward the intensity of the effort accompanying the process of fixation increases until, when the object has pa.s.sed the near-point of vision, binocular adjustment is no longer possible. In the general distribution of objects in the visual field the nearer, for the human being, is characteristically the lower, the more distant the higher, as one looks in succession from the things at his feet to the horizon and _vice versa_. We should, therefore, expect to find, when the eyes are free to move in independence of a determinate visual field, that increased convergence is accompanied by a depression of the line of sight, decreased convergence by an elevation of it. Here such freedom was permitted, and though the fixed distance of the point of regard eliminated all large fluctuations in convergence, yet all the secondary characteristics of intense convergence were present. Those concerned in the experiment report that the whole process of visual adjustment had increased in difficulty, and that the sense of effort was distinctly greater. To this sharp rise in the general sense of strain, in cooperation with the absence of a corrective field of objects, I attribute the large negative displacement of the subjective horizon in this series of experiments.

III.

In the next set of experiments the room was made completely dark. The method of experimentation was adapted to these new conditions by subst.i.tuting for the wooden screen one of black-surfaced cardboard, which was perforated at vertical distances of five millimeters by narrow horizontal slits and circular holes alternately, making a scale which was distinctly readable at the distance of the observer.

Opposite the end of one of these slits an additional hole was punched, const.i.tuting a fixed point from which distances were reckoned on the scale. As the whole screen was movable vertically and the observer knew that displacements were made from time to time, the succession of judgments afforded no objective criterion of the range of variation in the series of determinations, nor of the relation of any individual reaction to the preceding. The method of experimentation was as follows: The observer sat as before facing the screen, the direction of which was given at the beginning of each series by a momentary illumination of the scale. In the darkness which followed the observer brought the direction of sight, with open eyes, as satisfactorily as might be into the plane of the horizontal, when, upon a simple signal, the perforated scale was instantly and noiselessly illuminated by the pressure of an electrical b.u.t.ton, and the location of the point of regard was read off the vertical scale by the observer himself, in terms of its distance from the fixed point of origin described above.