IX.
The one generalization that I have thus far drawn from the investigation--namely, that the optical illusions are not reversed in passing from the field of touch, and that we therefore have a safe warrant for the conclusion that sight and touch do function alike--has contained no implicit or expressed assertion as to the origin of our notion of space. I have now reached the point where I must venture an explanation of the illusion itself.
The favorite hypothesis for the explanation of the geometrical optical illusions is the movement theory. The most generally accepted explanation of the illusion with whose tactual counterpart this paper is concerned, is that given by Wundt.[15] Wundt's explanation rests on variation in eye movements. When the eye passes over broken distances, the movement is made more difficult by reason of the frequent stoppages. The fact that the space which is filled with only one point in the middle is underestimated, is explained by Wundt on the theory that the eye has here the tendency to fix on the middle point and to estimate the distance by taking in the whole space at once without moving from this middle point. A different explanation for this illusion is offered by Helmholtz.[16] He makes use of the æsthetic factor of contrasts. Wundt insists that the fact that this illusion is still present when there are no actual eye movements does not demonstrate that the illusion is not to be referred to a motor origin. He says, "If a phenomenon is perceived with the moving eye only, the influence of movement on it is undoubtedly true. But an inference cannot be drawn in the opposite direction, that movement is without influence on the phenomenon that persists when there is no movement."[17]
[15] Wundt., W., 'Physiolog. Psych.,' 4te Aufl., Leipzig, 1893, Bd. II., S. 144.
[16] v. Helmholtz, H., 'Handbuch d. Physiol. Optik,' 2te Aufl., Hamburg u. Leipzig, 1896, S. 705.
[17] Wundt, W., _op. citat._, S. 139.
Satisfactorily as the movement hypothesis explains this and other optical illusions, it yet falls short of furnishing an entirely adequate explanation. It seems to me certain that several causes exist to produce this illusion, and also the illusion that is often associated with it, the well-known Müller-Lyer illusion. But in what degree each is present has not yet been determined by any of the quantitative studies in this particular illusion. I made a number of tests of the optical illusion, with these results: that the illusion is strongest when the attention is fixed at about the middle of the open space, that there is scarcely any illusion left when the attention is fixed on the middle of the filled space. It is stronger when the outer end-point of the open space is fixated than when the outer end of the filled space is fixated. For the moving eye, I find the illusion to be much stronger when the eye passes over the filled space first, and then over the open space, than when the process is reversed.
Now, the movement hypothesis does not, it seems to me, sufficiently explain all the fluctuations in the illusion. My experiments with the tactual illusion justify the belief that the movement theory is even less adequate to explain all of the variations there, unless the movement hypothesis is given a wider and richer interpretation than is ordinarily given to it. In the explanation of the tactual illusion which I have here been studying two other important factors must be taken into consideration. These I shall call, for the sake of convenience, the æsthetic factor and the time factor. These factors should not, however, be regarded as independent of the factor of movement. That term should be made wide enough to include these within its meaning. The importance of the time factor in the illusion for passive touch I have already briefly mentioned. I have also, in several places in the course of my experiments, called attention to the importance of the æsthetic element in our space judgments. I wish now to consider these two factors more in detail.
The foregoing discussion has pointed to the view that the space-perceiving and the localizing functions of the skin have a deep-lying common origin in the motor sensations. My experiments show that, even in the highly differentiated form in which we find them in their ordinary functioning, they plainly reveal their common origin. A formula, then, for expressing the judgments of distance by means of the resting skin might be put in this way. Let _P_ and _P'_ represent any two points on the skin, and let _L_ and _L'_ represent the local signs of these points, and _M_ and _M'_ the muscle sensations which give rise to these local signs. Then _M-M'_ will represent the distance between _P_ and _P'_, whether that distance be judged directly in terms of the localizing function of the skin or in terms of its space-perceiving function. This would be the formula for a normal judgment. In an illusory judgment, the temporal and æsthetic factors enter as disturbing elements. Now, the point which I insist on here is that the judgments of the extent of the voluntary movements, represented in the formula by _M_ and _M'_, do not depend alone on the sensations from the moving parts or other sensations of objective origin, as Dresslar would say, nor alone on the intention or impulse or innervation as Loeb and others claim, but on the sum of all the sensory elements that enter, both those of external and those of internal origin. And, furthermore, these sensations of external origin are important in judgments of space, only in so far as they are referred to sensations of internal origin. Delabarre says, "Movements are judged equal when their sensory elements are judged equal. These sensory elements need not all have their source in the moving parts. All sensations which are added from other parts of the body and which are not recognized as coming from these distant sources, are mingled with the elements from the moving member, and influence the judgment."[18] The importance of these sensations of inner origin was shown in many of the experiments in sections VI. to VIII. In the instance where the finger-tip was drawn over an open and a filled space, in the filled half the sensations were largely of external origin, while in the open half they were of internal origin. The result was that the spaces filled with sensations of internal origin were always overestimated.
The failure to recognize the importance of these inwardly initiated sensations is the chief defect in Dresslar's reasoning. He has endeavored to make our judgments in the illusion in question depend entirely on the sensations of external origin. He insists also that the illusion varies according to the variations in quantity of these external sensations. Now my experiments have shown, I think, very clearly that it is not the numerical or quantitative extent of the objective sensations which disturbs the judgment of distance, but the sensation of inner origin which we set over against these outer sensations. The piece of plush, because of the disagreeable sensations which it gives, is judged shorter than the space filled with closely crowded tacks. Dresslar seems to have overlooked entirely the fact that the feelings and emotions can be sources of illusions in the amount of movement, and hence in our judgments of space. The importance of this element has been pointed out by Münsterberg[19] in his studies of movement.
[18] Delabarre, E.B., 'Ueber Bewegungsempfindungen,' Inaug. Dissert., Freiburg, 1891.
[19] Münsterberg, H., 'Beiträge zur Experimentellen Psychol.,' Freiburg i. B., 1892, Heft 4.
Dresslar says again, "The explanations heretofore given, wholly based on the differences in the time the eye uses in passing over the two spaces, must stop short of the real truth." My experiments, however, as I have already indicated, go to prove quite the contrary. In short, I do not think we have any means of distinguishing our tactual judgments of time from our similar judgments of space. When the subject is asked to measure off equal spaces, he certainly uses time as means, because when he is asked to measure off equal times he registers precisely the same illusion that he makes in his judgments of spatial distances. The fact that objectively equal times were used by Dresslar in his experiments is no reason for supposing that the subject also regarded these times as equal. What I have here asserted of active touch is true also of the resting skin. When a stylus is drawn over the skin, the subject's answer to the question, How long is the distance? is subject to precisely the same illusion as his answer to the question, How long is the time?
I can by a simple illustration show more plainly what I mean by the statement that the blending of the inner and outer sensations is necessary for the perception of space. I shall use the sense of sight for the illustration, although precisely the same reasoning would apply to the sense of touch. Suppose that I sat in an entirely passive position and gazed at a spot on an otherwise blank piece of paper before me. I am perfectly passive so far as motion on my part is concerned. I may be engaged in any manner of speculation or be in the midst of the so-called active attention to the spot; but I must be and for the present remain motionless. Now, while I am in this condition of passivity, suppose the spot be made to move slowly to one side by some force external to myself. I am immovable all the while, and yet am conscious of this movement of the spot from the first position, which I call _A_, to the new position, _A'_, where it stops. The sensation which I now have is qualitatively different from the sensation which I had from the spot in its original position. My world of experience thus far has been a purely qualitative one. I might go on to eternity having experiences of the same kind, and never dream of space, or geometry, nor should I have the unique experience of a geometrical illusion, either optical or tactual. Now suppose I set up the bodily movements of the eyes or the head, or of the whole body, which are necessary to follow the path of that point, until I overtake it and once more restore the quality of the original sensation. This circle, completed by the two processes of external activity and restoration by internal activity, forms a group of sensations which constitutes the ultimate atom in our spatial experience. I have my first spatial experience when I have the thrill of satisfaction that comes from overtaking again, by means of my own inner activity, a sensation that has escaped me through an activity not my own. A being incapable of motion, in a world of flux, would not have the spatial experience that we have. A being incapable of motion could not make the distinction between an outer change that can be corrected by an internal change, and an outer change that cannot so be restored. Such an external change incapable of restoration by internal activity we should have if the spot on the paper changed by a chemical process from black to red.
Now such a space theory is plainly not to be confused with the theory that makes the reversibility of the spatial series its primary property. It is evident that we can have a series of sensations which may be reversed and yet not give the notion of space. But we should always have space-perception if one half of the circular process above described comes from an outer activity, and the other half from an inner activity. This way of describing the reversibility of the spatial series makes it less possible to urge against it the objections that Stumpf[20] has formulated against Bain's genetic space-theory. Stumpf's famous criticism applies not only to Bain, but also to the other English empiricists and to Wundt. Bain says: "When with the hand we grasp something moving and move with it, we have a sensation of one unchanged contact and pressure, and the sensation is imbedded in a movement. This is one experience. When we move the hand over a fixed surface, we have with the feelings of movement a succession of feelings of touch; if the surface is a variable one, the sensations are constantly changing, so that we can be under no mistake as to our passing through a series of tactual impressions. This is another experience, and differs from the first not in the sense of power, but in the tactile accompaniment. The difference, however, is of vital importance. In the one case, we have an object moving and measuring time and continuous, in the other case we have coëxistence in space. The coëxistence is still further made apparent by our reversing the movement, and thereby meeting the tactile series in the inverse order. Moreover, the serial order is unchanged by the rapidity of our movements."[21]
[20] Stumpf, K., 'Ueber d. psycholog. Ursprung d. Raumvorstellung,' Leipzig, 1873, S. 54.
[21] Bain, A., 'The Senses and the Intellect,' 3d ed., New York, 1886, p. 183.
Stumpf maintained in his exhaustive criticism of this theory, first, that there are cases where all of the elements which Bain requires for the perception of space are present, and yet we have no presentation of space. Secondly, there are cases where not all of these elements are present, and where we have nevertheless space presentation. It is the first objection that concerns me here. Stumpf gives as an example, under his first objection, the singing of a series of tones, C, G, E, F. We have here the muscle sensations from the larynx, and the series of the tone-sensations which are, Stumpf claims, reversed when the muscle-sensations are reversed, etc. According to Stumpf, these are all the elements that are required by Bain, and yet we have no perception of space thereby. Henri[22] has pointed out two objections to Stumpf's criticism of Bain's theory. He says that Bain assumes, what Stumpf does not recognize, that the muscle sensations must contain three elements--resistance, time, and velocity--before they can lead to space perceptions. These three elements are not to be found in the muscle sensations of the larynx as we find them in the sensations that come from the eye or arm muscles. In addition to this, Henri claims that Bain's theory demands a still further condition. If we wish to touch two objects, _A_ and _B_, with the same member, we can get a spatial experience from the process only if we insert between the touching of _A_ and the touching of _B_ a continual series of tactual sensations. In Stumpf's instance of the singing of tones, this has been overlooked. We can go from the tone C to the tone F without inserting between the two a continuous series of musical sensations.
[22] Henri, V., 'Ueber d. Raumwahrnehmungen d. Tastsinnes,' Berlin, 1898, S. 190.
I think that all such objections to the genetic space theories are avoided by formulating a theory in the manner in which I have just stated. When one says that there must be an outer activity producing a displacement of sensation, and then an inner activity retaining that sensation, it is plain that the singing of a series of tones ascending and then descending would not be a case in point.
* * * * *
TACTUAL TIME ESTIMATION.
BY KNIGHT DUNLAP.
I. GENERAL NATURE OF THE WORK.
The experiments comprised in this investigation were made during the year 1900-1901 and the early part of the year 1901-1902. They were planned as the beginning of an attempt at the analysis of the estimation of time intervals defined by tactual stimulations. The only published work in this quarter of the field so far is that of Vierordt,[1] who investigated only the constant error of time judgment, using both auditory and tactual stimulations, and that of Meumann,[2] who in his last published contribution to the literature of the time sense gives the results of his experiments with 'filled' and 'empty' tactual intervals. The stimuli employed by Meumann were, however, not purely tactual, but electrical.
[1] Vierordt: 'Der Zeitsinn,' Tübingen, 1868.
[2] Meumann, E.: 'Beiträge zur Psychologie des Zeitbewusstseins,' III., _Phil. Studien,_ XII., S. 195-204.
The limitation of time intervals by tactual stimulations offers, however, a rich field of variations, which promise assistance in the analytical problem of the psychology of time. The variations may be those of locality, area, intensity, rigidity, form, consecutiveness, and so on, in addition to the old comparisons of filled and empty intervals, intervals of varying length, and intervals separated by a pause and those not so separated.
To begin with, we have selected the conditions which are mechanically the simplest, namely, the comparison of two empty time intervals, both given objectively with no pause between them. We have employed the most easily accessible dermal areas, namely, that of the fingers of one or both hands, and introduced the mechanically simplest variations, namely, in locality stimulated and intensity of stimulation.
It was known from the results of nearly all who have studied the time sense experimentally, that there is in general a constant error of over- or underestimation of time intervals of moderate length, and from the results of Meumann,[3] that variations in intensity of limiting stimulation influenced the estimation decidedly, but apparently according to no exact law. The problem first at hand was then to see if variations introduced in tactual stimulations produce any regularity of effect, and if they throw any new light on the phenomena of the constant error.
[3] Meumaun, E.: 'Beiträge zur Psychologie des Zeitsinns,' II., _Phil. Studien_, IX., S. 264.
The stimulations employed were light blows from the cork tip of a hammer actuated by an electric current. These instruments, of which there were two, exactly alike in construction, were similar in principle to the acoustical hammers employed by Estel and Mehner. Each consisted essentially of a lever about ten inches in length, pivoted near one extremity, and having fastened to it near the pivot an armature so acted upon by an electromagnet as to depress the lever during the passage of an electric current. The lever was returned to its original position by a spring as soon as the current through the electromagnet ceased. A clamp at the farther extremity held a small wooden rod with a cork tip, at right angles to the pivot, and the depression of the lever brought this tip into contact with the dermal surface in proximity with which it had been placed. The rod was easily removable, so that one bearing a different tip could be substituted when desired. The whole instrument was mounted on a compact base attached to a short rod, by which it could be fastened in any desired position in an ordinary laboratory clamp.
During the course of most of the experiments the current was controlled by a pendulum beating half seconds and making a mercury contact at the lowest point of its arc. A condenser in parallel with the contact obviated the spark and consequent noise of the current interruption. A key, inserted in the circuit through the mercury cup and tapping instrument, allowed it to be opened or closed as desired, so that an interval of any number of half seconds could be interposed between successive stimulations.
In the first work, a modification of the method of right and wrong cases was followed, and found satisfactory. A series of intervals, ranging from one which was on the whole distinctly perceptible as longer than the standard to one on the whole distinctly shorter, was represented by a series of cards. Two such series were shuffled together, and the intervals given in the order so determined. Thus, when the pile of cards had been gone through, two complete series had been given, but in an order which the subject was confident was perfectly irregular. As he also knew that in a given series there were more than one occurrence of each compared interval (he was not informed that there were exactly two of each), every possible influence favored the formation each time of a perfectly fresh judgment without reference to preceding judgments. The only fear was lest certain sequences of compared intervals (_e.g._, a long compared interval in one test followed by a short one in the next), might produce unreliable results; but careful examination of the data, in which the order of the interval was always noted, fails to show any influence of such a factor.
To be more explicit with regard to the conditions of judgment; two intervals were presented to the subject in immediate succession. That is, the second stimulation marked the end of the first interval and the beginning of the second. The first interval was always the standard, while the second, or compared interval, varied in length, as determined by the series of cards, and the subject was requested to judge whether it was equal to, or longer or shorter than the standard interval.
In all of the work under Group 1, and the first work under Group 2, the standard interval employed was 5.0 seconds. This interval was selected because the minimum variation possible with the pendulum apparatus (½ sec.) was too great for the satisfactory operation of a shorter standard, and it was not deemed advisable to keep the subject's attention on the strain for a longer interval, since 5.0 sec. satisfied all the requirements of the experiment.
In all work here reported, the cork tip on the tapping instrument was circular in form, and 1 mm. in diameter. In all, except one experiment of the second group, the areas stimulated were on the backs of the fingers, just above the nails. In the one exception a spot on the forearm was used in conjunction with the middle finger.
In Groups 1 and 2 the intensity of stroke used was just sufficient to give a sharp and distinct stimulation. The intensity of the stimulation was not of a high degree of constancy from day to day, on account of variations in the electric contacts, but within each test of three stimulations the intensity was constant enough.
In experiments under Group 3 two intensities of strokes were employed, one somewhat stronger than the stroke employed in the other experiments, and one somewhat weaker--just strong enough to be perceived easily. The introduction of the two into the same test was effected by the use of an auxiliary loop in the circuit, containing a rheostat, so that the depression of the first key completed the circuit as usual, or the second key completed it through the rheostat.
At each test the subject was warned to prepare for the first stimulation by a signal preceding it at an exact interval. In experiments with the pendulum apparatus the signal was the spoken word 'now,' and the preparatory interval one second. Later, experiments were undertaken with preparatory intervals of one second and 1-4/5 seconds, to find if the estimation differed perceptibly in one case from that in the other. No difference was found, and in work thereafter each subject was allowed the preparatory interval which made the conditions subjectively most satisfactory to him.
Ample time for rest was allowed the subject after each test in a series, two (sometimes three) series of twenty to twenty-four tests being all that were usually taken in the course of the hour. Attention to the interval was not especially fatiguing and was sustained without difficulty after a few trials.
Further details will be treated as they come up in the consideration of the work by groups, into which the experiment naturally falls.
II. EXPERIMENTAL RESULTS.
1. The first group of experiments was undertaken to find the direction of the constant error for the 5.0 sec. standard, the extent to which different subjects agree and the effects of practice. The tests were therefore made with three taps of equal intensity on a single dermal area. The subject sat in a comfortable position before a table upon which his arm rested. His hand lay palm down on a felt cushion and the tapping instrument was adjusted immediately over it, in position to stimulate a spot on the back of the finger, just above the nail. A few tests were given on the first finger and a few on the second alternately throughout the experiments, in order to avoid the numbing effect of continual tapping on one spot. The records for each of the two fingers were however kept separately and showed no disagreement.
The detailed results for one subject (_Mr_,) are given in Table I. The first column, under _CT_, gives the values of the different compared intervals employed. The next three columns, under _S_, _E_ and _L_, give the number of judgments of _shorter_, _equal_ and _longer_, respectively. The fifth column, under _W_, gives the number of errors for each compared interval, the judgments of _equal_ being divided equally between the categories of _longer_ and _shorter_.
In all the succeeding discussion the standard interval will be represented by _ST_, the compared interval by _CT_. _ET_ is that _CT_ which the subject judges equal to _ST_.
TABLE I.
_ST_=5.0 SEC. SUBJECT _Mr._ 60 SERIES.
_CT_ _S_ _E_ _L_ _W_ 4. 58 1 1 1.5 4.5 45 11 4 9.5 5. 32 13 15 21.5 5.5 19 16 25 27 6. 5 4 51 7 6.5 1 2 57 2
We can calculate the value of the average _ET_ if we assume that the distribution of wrong judgments is in general in accordance with the law of error curve. We see by inspection of the first three columns that this value lies between 5.0 and 5.5, and hence the 32 cases of _S_ for _CT_ 5.0 must be considered correct, or the principle of the error curve will not apply.
The method of computation may be derived in the following way: If we take the origin so that the maximum of the error curve falls on the _Y_ axis, the equation of the curve becomes
y = ke^{-[gamma]²x²}
and, assuming two points (x_{1} y_{1}) and (x_{2} y_{2}) on the curve, we deduce the formula
____________ ±D \/ log k/y_{1} x_{1} = --------------------------------- ____________ ____________ \/ log k/y_{1} ± \/ log k/y_{2}
where D = x_{1} ± x_{2}, and k = value of y when x = 0.
x_{1} and x_{2} must, however, not be great, since the condition that the curve with which we are dealing shall approximate the form denoted by the equation is more nearly fulfilled by those portions of the curve lying nearest to the _Y_ axis.
Now since for any ordinates, y_{1} and y_{2} which we may select from the table, we know the value of x_{1} ± x_{2}, we can compute the value of x_{1}, which conversely gives us the amount to be added to or subtracted from a given term in the series of _CT_'s to produce the value of the average _ET_. This latter value, we find, by computing by the formula given above, using the four terms whose values lie nearest to the _Y_ axis, is 5.25 secs.
In Table II are given similar computations for each of the nine subjects employed, and from this it will be seen that in every case the standard is overestimated.
TABLE II. _ST_= 5.0 SECS.
Subject. Average ET. No. of Series. _A_. 5.75 50 _B_. 5.13 40 _Hs_. 5.26 100 _P_. 5.77 38 _Mn_. 6.19 50 _Mr_. 5.25 60 _R_. 5.63 24 _Sh_. 5.34 100 _Sn_. 5.57 50
This overestimation of the 5.0 sec. standard agrees with the results of some of the experimenters on auditory time and apparently conflicts with the results of others. Mach[4] found no constant error. Höring[5] found that intervals over 0.5 sec. were overestimated. Vierordt,[6] Kollert,[7] Estel[8] and Glass,[9] found small intervals overestimated and long ones underestimated, the indifference point being placed at about 3.0 by Vierordt, 0.7 by Kollert and Estel and 0.8 by Glass. Mehner[10] found underestimation from 0.7 to 5.0 and overestimation above 5.0. Schumann[11] found in one set of experiments overestimation from 0.64 to 2.75 and from 3.5 to 5.0, and underestimation from 2.75 to 3.5. Stevens[12] found underestimation of small intervals and overestimation of longer ones, placing the indifference point between 0.53 and 0.87.
[4] Mach, E.: 'Untersuchungen über den Zeitsinn des Ohres,' _Sitzungsber. d. Wiener Akad._, Math.-Nat. Kl., Bd. 51, Abth. 2.
[5] Höring: 'Versuche über das Unterscheidungsvermögen des Hörsinnes für Zeitgrössen,' Tübingen, 1864.
[6] Vierordt: _op. cit._
[7] Kollert, J.: 'Untersuchungen über den Zeitsinn,' _Phil. Studien_, I., S. 79.
[8] Estel, V.: 'Neue Versuche über den Zeitsinn,' _Phil. Studien_, II., S. 39.
[9] Glass R.: 'Kritisches und Experimentelles über den Zeitsinn,' _Phil. Studien_, IV., S. 423.
[10] Mehner, Max: 'Zum Lehre vom Zeitsinn,' _Phil. Studien_, II., S. 546.
[11] Schumann, F.: 'Ueber die Schätzung kleiner Zeitgrössen,' _Zeitsch. f. Psych._, IV., S. 48.
[12] Stevens, L.T.: 'On the Time Sense,' _Mind_, XI., p. 393.
The overestimation, however, is of no great significance, for data will be introduced a little later which show definitely that the underestimation or overestimation of a given standard is determined, among other factors, by the intensity of the stimulation employed. The apparently anomalous results obtained in the early investigations are in part probably explicable on this basis.
As regards the results of _practice_, the data obtained from the two subjects on whom the greatest number of tests was made (_Hs_ and _Sh_) is sufficiently explicit. The errors for each successive group of 25 series for these two subjects are given in Table III.
TABLE III.
_ST_ = 5.0 SECONDS.
SUBJECT _Hs_. SUBJECT _Sh_. CT (1) (2) (3) (4) (1) (2) (3) (4) 4. 2.5 2.5 1.5 2.5 0. .5 0. .5 4.5 6.0 3.0 3.5 7.0 5.0 3.5 2.0 .5 5. 14.0 11.0 11.0 11.0 8.5 11.5 4.0 7.0 5.5 11.5 11.5 6.0 12.5 11.0 16.0 14.0 15.0 6. 12.0 9.0 6.5 6.0 3.5 2.0 1.5 1.0 6.5 4.0 3.5 4.0 3.5 4.0 .5 0. 0.
No influence arising from practice is discoverable from this table, and we may safely conclude that this hypothetical factor may be disregarded, although among the experimenters on auditory time Mehner[13] thought results gotten without a maximum of practice are worthless, while Meumann[14] thinks that unpracticed and hence unsophisticated subjects are most apt to give unbiased results, as with more experience they tend to fall into ruts and exaggerate their mistakes. The only stipulation we feel it necessary to make in this connection is that the subject be given enough preliminary tests to make him thoroughly familiar with the conditions of the experiment.
[13] _op. cit._, S. 558, S. 595.
[14] _op. cit._ (II.), S. 284.
2. The second group of experiments introduced the factor of a difference between the stimulation marking the end of an interval and that marking the beginning, in the form of a change in locality stimulated, from one finger to the other, either on the same hand or on the other hand. Two classes of series were given, in one of which the change was introduced in the standard interval, and in the other class in the compared interval.
In the first of these experiments, which are typical of the whole group, both of the subject's hands were employed, and a tapping instrument was arranged above the middle finger of each, as above the one hand in the preceding experiment, the distance between middle fingers being fifteen inches. The taps were given either two on the right hand and the third on the left, or one on the right and the second and third on the left, the two orders being designated as _RRL_ and _RLL_ respectively. The subject was always informed of the order in which the stimulations were to be given, so that any element of surprise which might arise from it was eliminated. Occasionally, however, through a lapse of memory, the subject expected the wrong order, in which case the disturbance caused by surprise was usually so great as to prevent any estimation.
The two types of series were taken under as similar conditions as possible, four (or in some cases five) tests being taken from each series alternately. Other conditions were the same as in the preceding work. The results for the six subjects employed are given in Table IV.
TABLE IV.
_ST_= 5.0 SECS. TWO HANDS. 15 INCHES.
Subject. Average RT. No. of Series. RRL. RLL.* (Table II.) _Hs._ 4.92 6.55 (5.26) 50 _Sh._ 5.29 5.28 (5.34) 50 _Mr._ 5.02 6.23 (5.25) 60 _Mn._ 5.71 6.71 (6.19) 24 _A._ 5.34 5.89 (5.75) 28 _Sn._ 5.62 6.43 (5.47) 60
*Transcriber's Note: Original "RRL"
From Table IV. it is apparent at a glance that the new condition involved introduces a marked change in the time judgment. Comparison with Table II. shows that in the cases of all except _Sh_ and _Sn_ the variation _RRL_ shortens the standard subjectively, and that _RLL_ lengthens it; that is, a local change tends to lengthen the interval in which it occurs. In the case of _Sh_ neither introduces any change of consequence, while in the case of _Sn_ both values are higher than we might expect, although the difference between them is in conformity with the rest of the results shown in the table.
Another set of experiments was made on subject _Mr_, using taps on the middle finger of the left hand and a spot on the forearm fifteen inches from it; giving in one case two taps on the finger and the third on the arm, and in the other one tap on the finger and the second and third on the arm; designating the orders as _FFA_ and _FAA_ respectively. Sixty series were taken, and the values found for the average _ET_ were 4.52 secs, for _FFA_ and 6.24 secs, for _FAA_, _ST_ being 5.0 secs. This shows 0.5 sec. more difference than the experiment with two hands.
Next, experiments were made on two subjects, with conditions the same as in the work corresponding to Table IV., except that the distance between the fingers stimulated was only five inches. The results of this work are given in Table V.
TABLE V.
_ST_= 5.0 SECS. TWO HANDS. 5 INCHES.
Subject RRL. RLL. No. of Series. _Sh._ 5.32 5.32 60 _Hs._ 4.40 6.80 60
It will be noticed that _Hs_ shows a slightly wider divergence than before, while _Sh_ pursues the even tenor of his way as usual.
Series were next obtained by employing the first and second fingers on one hand in exactly the same way as the middle fingers of the two hands were previously employed, the orders of stimulation being 1, 1, 2, and 1, 2, 2. The results of sixty series on Subject _Hs_ give the values of average _ET_ as 4.8 secs. for 1, 1, 2, and 6.23 sees, for 1, 2, 2, _ST_ being 5.0 secs., showing less divergence than in the preceding work.
These experiments were all made during the first year's work. They show that in most cases a change in the locality stimulated influences the estimation of the time interval, but since the details of that influence do not appear so definitely as might be desired, the ground was gone over again in a little different way at the beginning of the present year.
A somewhat more serviceable instrument for time measurements was employed, consisting of a disc provided with four rows of sockets in which pegs were inserted at appropriate angular intervals, so that their contact with fixed levers during the revolution of the disc closed an electric circuit at predetermined time intervals. The disc was rotated at a uniform speed by an electric motor.
Experiments were made by stimulation of the following localities: (1) First and third fingers of right hand; (2) first and second fingers of right hand; (3) first fingers of both hands, close together, but just escaping contact; (4) first fingers of both hands, fifteen inches apart; (5) first fingers of both hands, thirty inches apart; (6) two positions on middle finger of right hand, on same transverse line.
A standard of two seconds was adopted as being easier for the subject and more expeditious, and since qualitative and not quantitative results were desired, only one _CT_ was used in each case, thus permitting the investigation to cover in a number of weeks ground which would otherwise have required a much longer period. The subjects were, however, only informed that the objective variations were very small, and not that they were in most cases zero. Tests of the two types complementary to each other (_e.g._, _RRL_ and _RRL_) were in each case taken alternately in groups of five, as in previous work.
TABLE VI.
_ST_= 2.0 SECS.
_Subject W._
(1) CT=2.0 (3) CT=2.2 (5) CT=2.0 113 133 RRL RLL RRL RLL S 3 3 9 20 5 21 E 18 19 25 16 18 14 L 24 28 16 14 17 15
_Subject P._
(1) CT=2.0 (3)CT={1.6 (5) CT={1.6 {2.4 {2.4 113 133 RRL(1.6) RLL(2.4) RRL(1.6) RLL(2.4) S 2 16 12 16 15 10 E 38 32 32 21 26 19 L 10 2 6 15 14 21
_Subject B._
(1) CT=2.0 (2) CT=2.0 (6) CT=2.0 113 133 112 122 aab abb S 4 21 5 20 7 6 E 23 19 22 24 40 38 L 23 10 23 6 3 6
_Subject Hy._
(1) CT=2.0 (2) CT=2.4 (1a) CT=2.0 113 133 112 122 113 133 S 12 46 17 40 17 31 E 9 2 14 8 9 7 L 29 2 19 2 14 2
In the series designated as (1a) the conditions were the same as in (1), except that the subject abstracted as much as possible from the tactual nature of the stimulations and the position of the fingers. This was undertaken upon the suggestion of the subject that it would be possible to perform the abstraction, and was not repeated on any other subject.
The results are given in Table VI., where the numerals in the headings indicate the localities and changes of stimulation, in accordance with the preceding scheme, and _'S'_, _'E'_ and _'L'_ designate the number of judgments of _shorter_, _equal_ and _longer_ respectively.
It will be observed that in several cases a _CT_ was introduced in one class which was different from the _CT_ used in the other classes with the same subject. This was not entirely arbitrary. It was found with subject _W_, for example, that the use of _CT_ = 2.0 in (3) produced judgments of shorter almost entirely in both types. Therefore a _CT_ was found, by trial, which produced a diversity of judgments. The comparison of the different classes is not so obvious under these conditions as it otherwise would be, but is still possible.
The comparison gives results which at first appear quite irregular. These are shown in Table VII. below, where the headings (1)--(3), etc., indicate the classes compared, and in the lines beneath them '+' indicates that the interval under consideration is estimated as relatively greater (more overestimated or less underestimated) in the second of the two classes than in the first,--indicating the opposite effect. Results for the first interval are given in the line denoted 'first,' and for the second interval in the line denoted 'second.' Thus, the plus sign under (1)--(3) in the first line for subject _P_ indicates that the variation _RLL_ caused the first interval to be overestimated to a greater extent than did the variation 133.
TABLE VII.
SUBJECT _P._ SUBJECT _W._ SUBJECT _B._ SUBJECT _Hy._ (1)--(3) (3)--(4) (1)--(3) (3)--(5) (2)--(1) (6)--(2) (2)--(1) First. + - + - - + - Sec. + + - + + + +
The comparisons of (6) and (2), and (1) and (3) confirm the provisional deduction from Table IV., that the introduction of a _local change_ in an interval _lengthens_ it subjectively, but the comparisons of (3) and (5), (3) and (4), and (2) and (1) show apparently that while the _amount_ of the local change influences the lengthening of the interval, it does not vary directly with this latter in all cases, but inversely in the first interval and directly in the second. This is in itself sufficient to demonstrate that the chief factors of the influence of locality-change upon the time interval are connected with the spatial localization of the areas stimulated, but a further consideration strengthens the conclusion and disposes of the apparent anomaly. It will be noticed that in general the decrease in the comparative length of the first interval produced by increasing the spatial change is less than the increase in the comparative length of the second interval produced by a corresponding change. In other words, the disparity between the results for the two types of test is greater, the greater the spatial distance introduced.
The results seem to point to the existence of two distinct factors in the so-called 'constant error' in these cases: first, what we may call the _bare constant error_, or simply the constant error, which appears when the conditions of stimulation are objectively the same as regards both intervals, and which we must suppose to be present in all other cases; and second, the particular lengthening effect which a change in locality produces upon the interval in which it occurs. These two factors may work in conjunction or in opposition, according to conditions. The bare constant error does not remain exactly the same at all times for any individual and is probably less regular in tactual time than in auditory or in optical time, according to the irregularity actually found and for reasons which will be assigned later.
3. The third group of experiments introduced the factor of variation in intensity of stimulation. By the introduction of a loop in the circuit, containing a rheostat, two strengths of current and consequently of stimulus intensity were obtained, either of which could be employed as desired. One intensity, designated as _W_, was just strong enough to be perceived distinctly. The other intensity, designated as _S_, was somewhat stronger than the intensity used in the preceding work.
In the first instance, sixty series were taken from Subject _B_, with the conditions the same as in the experiments of Group 1, except that two types of series were taken; the first two stimulations being strong and the third one weak in the first type (_SSW_), and the order being reversed in the second type (_WSS_). The results gave values of _ET_ of 5.27 secs. for _SSW_ and 5.9 secs. for _WSS_.
In order to get comprehensive qualitative results as rapidly as possible, a three-second standard was adopted in the succeeding work and only one compared interval, also three seconds, was given, although the subject was ignorant of that fact--the method being thus similar to that adopted later for the final experiments of Group 2, described above. Six types of tests were given, the order of stimulation in the different types being _SSS, WWW, SSW, WWS, SWW_ and _WSS_, the subject always knowing which order to expect. For each of the six types one hundred tests were made on one subject and one hundred and five on another, in sets of five tests of each type, the sets being taken in varied order, so that possible contrast effect should be avoided. The results were practically the same, however, in whatever order the sets were taken, no contrast effect being discernible.
The total number of judgments of _CT_, longer, equal, and shorter, is given in Table VIII. The experiments on each subject consumed a number of experiment hours, scattered through several weeks, but the relative proportions of judgments on different days was in both cases similar to the total proportions.
TABLE VIII.
_ST=CT=_ 3.0 SECS.
Subject _R_, 100. Subject _P_, 105. L E S d L E S d SSS 32 56 12 + 20 SSS 16 67 22 - 9 WWW 11 53 36 - 25 WWW 19 72 14 + 5 SSW 6 27 67 - 61 SSW 17 56 32 - 15 WWS 57 36 7 + 50 WWS 37 61 7 + 30 WSS 10 45 45 - 35 WSS 9 69 27 - 18 SWW 3 31 66 - 63 SWW 3 64 33 - 25
By the above table the absolute intensity of the stimulus is clearly shown to be an important factor in determining the constant error of judgment, since in both cases the change from _SSS_ to _WWW_ changed the sign of the constant error, although in opposite directions. But the effect of the relative intensity is more obscure. To discover more readily whether the introduction of a stronger or weaker stimulation promises a definite effect upon the estimation of the interval which precedes or follows it, the results are so arranged in Table IX. that reading downward in any pair shows the effect of a decrease in the intensity of (1) the first, (2) the second, (3) the third, and (4) all three stimulations.
TABLE IX.
Subject _R._ Subject _P._
(1) _SSS_ + 20 - 6 _WSS_ - 35 - 55 - 18 - 12
_SWW_ - 63 - 25 _WWW_ - 25 - 38 + 5 + 30
(2) _SSW_ - 61 - 15 _SWW_ - 63 - 2 - 25 + 10
_WSS_ - 35 - 18 _WWS_ + 50 + 85 + 30 - 48
(3) _SSS_ + 20 - 6 _SSW_ - 61 - 81 - 15 - 7
_WWS_ + 50 + 30 _WWW_ - 25 - 75 + 5 - 25
(4) _SSS_ + 20 - 6 _WWW_ - 15 - 35 + 5 + 11
There seems at first sight to be no uniformity about these results. Decreasing the first stimulation in the first case increases, in the second case diminishes, the comparative length of the first interval. We get a similar result in the decreasing of the second stimulation. In the case of the third stimulation only does the decrease produce a uniform result. If, however, we neglect the first pair of (3), we observe that in the other cases the effect of a _difference_ between the two stimulations is to lengthen the interval which they limit. The fact that both subjects make the same exception is, however, striking and suggestive of doubt. These results were obtained in the first year's work, and to test their validity the experiment was repeated at the beginning of the present year on three subjects, fifty series being taken from each, with the results given in Table X.
TABLE X.
_ST_ = 3.0 secs. = _CT_.
Subject _Mm._ Subject _A._ Subject _D._
S E L d S E L d S E L d SSS 24 13 13 - 11 7 30 13 + 6 10 31 9 - 1 WSS 33 9 8 - 25 20 24 6 - 14 17 27 6 - 11 SSW 19 15 16 - 3 23 16 11 - 12 10 31 9* - 1 WWW 19 12 19 0 13 26 11 - 2 1 40 9 + 8 SWW 18 30 2 - 16 23 21 6* - 17 7 38 5 - 2 WWS 13 16 21 + 8 12 30 8 - 4 15 25 10 - 5
*Transcriber's Note: Original "16" changed to "6", "19" to "9".
Analysis of this table shows that in every case a difference between the intensities of the first and second taps lengthens the first interval in comparative estimation. In the case of subject _Mm_ a difference in the intensities of the second and third taps lengthens the second interval subjectively. But in the cases of the other two subjects the difference shortens the interval in varying degrees.
The intensity difference established for the purposes of these experiments was not great, being less than that established for the work on the first two subjects, and therefore the fact that these results are less decided than those of the first work was not unexpected. The results are, however, very clear, and show that the lengthening effect of a difference in intensity of the stimulations limiting an interval has its general application only to the first interval, being sometimes reversed in the second. From the combined results we find, further, that a uniform change in the intensity of three stimulations is capable of reversing the direction of the constant error, an intensity change in a given direction changing the error from positive to negative for some subjects, and from negative to positive for others.
III. INTERPRETATION OF RESULTS.
We may say provisionally that the _change_ from a tactual stimulation of one kind to a tactual stimulation of another kind tends to lengthen subjectively the interval which the two limit. If we apply the same generalization to the other sensorial realms, we discover that it agrees with the general results obtained by Meumann[15] in investigating the effects of intensity changes upon auditory time, and also with the results obtained by Schumann[16] in investigations with stimulations addressed alternately to one ear and to the other. Meumann reports also that the change from stimulation of one sense to stimulation of another subjectively lengthens the corresponding interval.
[15] _op. cit._ (II.), S. 289-297.
[16] _op. cit._, S. 67.
What, then, are the factors, introduced by the change, which produce this lengthening effect? The results of introspection on the part of some of the subjects of our experiments furnish the clue which may enable us to construct a working hypothesis.
Many of the subjects visualize a time line in the form of a curve. In each case of this kind the introduction of a change, either in intensity or location, if large enough to produce an effect on the time estimation, produced a distortion on the part of the curve corresponding to the interval affected. All of the subjects employed in the experiments of Group 2 were distinctly conscious of the change in attention from one point to another, as the two were stimulated successively, and three of them, _Hy_, _Hs_ and _P_, thought of something passing from one point to the other, the representation being described as partly muscular and partly visual. Subjects _Mr_ and _B_ visualized the two hands, and consciously transferred the attention from one part of the visual image to the other. Subject _Mr_ had a constant tendency to make eye movements in the direction of the change. Subject _P_ detected these eye movements a few times, but subject _B_ was never conscious of anything of the kind.
All of the subjects except _R_ were conscious of more or less of a _strain_, which varied during the intervals, and was by some felt to be largely a tension of the chest and other muscles, while others felt it rather indefinitely as a 'strain of attention.' The characteristics of this tension feeling were almost always different in the second interval from those in the first, the tension being usually felt to be more _constant_ in the second interval. In experiments of the third group a higher degree of tension was felt in awaiting a light tap than in awaiting a heavy one.
Evidently, in all these cases, the effect of a _difference_ between two stimulations was to introduce certain changes in sensation _during_ the interval which they limited, owing to the fact that the subject expected the difference to occur. Thus in the third group of experiments there were, very likely, in all cases changes from sensations of high tension to sensations of lower, or vice versa. It is probable that, in the experiments of the second group, there were also changes in muscular sensations, partly those of eye muscles,
## partly of chest and arm muscles, introduced by the change of attention
from one point to another. At any rate, it is certain that there were certain sensation changes produced during the intervals by changes of locality.
If, then, we assume that the introduction of additional sensation change into an interval lengthens it, we are led to the conclusion that psychological time (as distinguished from metaphysical, mathematical, or transcendental time) is perceived simply as the quantum of change in the sensation content. That this is a true conclusion is seemingly supported by the fact that when we wish to make our estimate correspond as closely as possible with external measurements, we exclude from the content, to the best of our ability, the general complex of external sensations, which vary with extreme irregularity; and confine the attention to the more uniformly varying bodily sensations. We perhaps go even further, and inhibit certain bodily sensations, corresponding to activity of the more peripherally located muscles, that the attention may be confined to certain others. But attention to a dermal stimulation is precisely the condition which would tend to some extent to prevent this inhibition. For this reason we might well expect to find the error in estimation more variable, the 'constant error' in general greater, and the specific effects of variations which would affect the peripheral muscles, more marked in 'tactual' time than in either 'auditory' or 'optical' time. Certainly all these factors appear surprisingly large in these experiments.
It is not possible to ascertain to how great an extent subject _Sh_ inhibited the more external sensations, but certainly if he succeeded to an unusual degree in so doing, that fact would explain the absence of effect of stimulation difference in his case.
Explanation has still to be offered for the variable effect of intensity difference upon the _second_ interval. According to all subjects except _Sn_, there is a radical difference in attitude in the two intervals. In the first interval the subject is merely observant, but in the second he is more or less reproductive. That is, he measures off a length which seems equal to the standard, and if the stimulation does not come at that point he is prepared to judge the interval as 'longer,' even before the third stimulation is given. In cases, then, where the judgment with equal intensities would be 'longer,' we might expect that the actual strengthening or weakening of the final tap would make no difference, and that it would make very little difference in other cases. But even here the expectation of the intensity is an important factor in determining tension changes, although naturally much less so than in the first interval. So we should still expect the lengthening of the second interval.
We must remember, however, that, as we noticed in discussing the experiments of Group 2, there is complicated with the lengthening effect of a change the _bare constant error_, which appears even when the three stimulations are similar in all respects except temporal location. Compare _WWW_ with _SSS_, and we find that with all five subjects the constant error is decidedly changed, being even reversed in direction with three of the subjects.
Now, what determines the direction of the constant error, where there is no pause between the intervals? Three subjects reported that at times there seemed to be a slight loss of time after the second stimulation, owing to the readjustment called for by the change of attitude referred to above, so that the second interval was begun, not really at the second stimulation, but a certain period after it. This fact, if we assume it to be such, and also assume that it is present to a certain degree in all observations of this kind, explains the apparent overestimation of the first interval. Opposed to the factor of _loss of time_ there is the factor of _perspective_, by which an interval, or part of an interval, seems less in quantity as it recedes into the past. The joint effect of these two factors determines the constant error in any case where no pause is introduced between _ST_ and _CT_. It is then perfectly obvious that, as the perspective factor is decreased by diminishing the intervals compared, the constant error must receive positive increments, _i.e._, become algebraically greater; which corresponds exactly with the results obtained by Vierordt, Kollert, Estel, and Glass, that under ordinary conditions long standard intervals are comparatively underestimated, and short ones overestimated.
On the other hand, if with a given interval we vary the loss of time, we also vary the constant error. We have seen that a change in the intensity of the stimulations, although the relative intensity of the three remains constant, produces this variation of the constant error; and the individual differences of subjects with regard to sensibility, power of attention and inhibition, and preferences for certain intensities, lead us to the conclusion that for certain subjects certain intensities of stimulation make the transition from the receptive attitude to the reproductive easiest, and, therefore, most rapid.
Now finally, as regards the apparent failure of the change in _SSW_ to lengthen the second interval, for which we are seeking to account; the comparatively great loss of time occurring where the change of attitude would naturally be most difficult (that is, where it is complicated with a change of attention from a strong stimulation to the higher key of a weak stimulation) is sufficient to explain why with most subjects the lengthening effect upon the second interval is more than neutralized. The individual differences mentioned in the preceding paragraph as affecting the relation of the two factors determining the constant error, enter here of course to modify the judgments and cause disagreement among the results for different subjects.
Briefly stated, the most important points upon which this discussion hinges are thus the following: We have shown--
1. That the introduction of either a local difference or a difference of intensity in the tactual stimulations limiting an interval has, in general, the effect of causing the interval to appear longer than it otherwise would appear.
2. That the apparent exceptions to the above rule are, (_a_) that the _increase_ of the local difference in the first interval, the stimulated areas remaining unchanged, produces a slight _decrease_ in the subjective lengthening of the interval, and (_b_) that in certain cases a difference in intensity of the stimulations limiting the second interval apparently causes the interval to seem shorter than it otherwise would.
3. That the 'constant error' of time judgment is dependent upon the intensity of the stimulations employed, although the three stimulations limiting the two intervals remain of equal intensity.
To harmonize these results we have found it necessary to assume:
1. That the length of a time interval is perceived as the amount of change in the sensation-complex corresponding to that interval.
2. That the so-called 'constant error' of time estimation is determined by two mutually opposing factors, of which the first is the _loss of time_ occasioned by the change of attitude at the division between the two intervals, and the second is the diminishing effect of _perspective_.
It is evident, however, that this last assumption applies only to the conditions under which the results were obtained, namely, the comparison of two intervals marked off by three brief stimulations.
* * * * *
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 space-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 passed 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 æsthesiometers. 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 space relations of the points stimulated. The reports of the subjects also showed that generally and perhaps always they located the points in space 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 pass 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 passed 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 passed. 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 passed 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 attitude 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 spaces 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 æsthesiometer. 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 knob of the æsthesiometer and the other was two knobs 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 knobs 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 æsthesiometer 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 knobs of the æsthesiometer. I made an æsthesiometer with cards 4 mm. long in place of knobs. 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 knobs of the æsthesiometer were compared with one knob. 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 mass 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 æsthesiometer. Various methods were tried, but the following was most successful. I would tell the subject that I was going to use the æsthesiometer 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 æsthesiometer 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 knob of the æsthesiometer 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 knobs 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 pass 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 'space-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 assume 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 space may remain the same, but it is only one of the elements which assist 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 attitudes of the subject. However, if the doubtful cases could be classed 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 analysis 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 class 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. Brückner[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 reënforcement 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 reënforcement as an indication of fusion.
[1] Brückner, A.: 'Die Raumschwelle bei Simultanreizung,' _Zeitschrift für 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 classed 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 Rücksicht auf die Frage der Uebung und die Entstehung der Vexirfehler,' _Philos. Stud._, 1897, Bd. XIII., S. 163.
[3] See Nichols: 'Number and Space,' 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 associate that
## particular sensation with some idea. In the case before us he
associates 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 associated 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 assigns to each sensation the number he has associated with it. He gives it the name two when it has the quality he has associated 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 passive and received sensations only when we were touched by something, there is no reason why we should not associate the idea of one with the sensation produced by two objects and the idea of two with that produced by one object--assuming that we could have any idea of number under such circumstances. The quality of a sensation from which number is inferred depends on several factors. The number itself is determined by the attitude of the subject, but the attitude is determined largely by association. 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 associate 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 associated 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 associations 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 associate the sensation with an idea, then we should expect that the association 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 associations. 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 brass 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 illustrating 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 association 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 attitude has determined shall be one.
That we do associate 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 pass 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 associated 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 attitude 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 associations are so firmly established and so uniform that we are likely to regard them as necessary. It is not so with our associations 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 class 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 substitution of lines for knobs of the æsthesiometer 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 knobs.
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.