THE FEELING-VALUE OF UNMUSICAL TONE-INTERVALS
BY L. E. EMERSON
Modern theories of melody start always with the presupposition that the scale must be composed of tones having the simple mathematical relation to one another of 2, 3, 4, 5, 6 (and by Meyer 7) and their multiples in order to give pleasant combinations of successive tones. But the question arises whether other tone-combinations which given together appear disharmonious may not, by their mere acoustical difference, similarity, and contrast, awake definite feelings of pleasure. And if such feeling-tones exist independently from harmony it is evident that they would enter into every melody in addition to the strictly musical feelings of harmony and that they deserve consideration as a factor of music. It would not even appear impossible that if every successive tone-distance has its particular natural feeling-character, the distances of successive harmonious tones might be only through secondary factors as habit and training preëminent among the various possibilities of combinations. A tone-consciousness, which under the guidance of experiences of harmony has been trained in our musical tone-relations, must give instinctive preference to such successions as our melodies offer. But if we artificially inhibit the conscious relation to our musical system by introducing a continuous tone-series, or at least one of steps much smaller than musical intervals, do we destroy the possibility of pleasure, and if not, do we find the pleasure in the musical interval stronger than that in other instances? That even the musical subject introduced into the realm of smallest tone-steps can easily forget and inhibit his normal standards is well known; the whole acoustical perspective seems changed by the new intervals, and the subject begins at once to build up a new temporary system of relations. The experiments in Wundt's laboratory have shown that in such cases the theoretical judgment of distances is indeed quite different from the standardized one; the octave may appear equal to the higher fifth. I wanted to study in a similar way the feeling-value in such a state of musical disorientation, when all imaginative representations of our musical intervals are inhibited.
The instrument I used was an Appun Tonmesser giving reed-tones from 128 to 512 vibrations in intervals of 4 vibrations between adjacent tones. The intervals with which I experimented varied from 4 to 88 vibrations in steps of 4. The observers were all experimental psychologists, and varied in musical discrimination from a very low to a very high degree of natural ability and skill.
The observer reported his pleasure in the progression given, in the traditional grades of 1 to 7, where 1 represents the greatest degree of pleasure, 2 means very pleasant, 3 pleasant, 4 indifferent, 5 unpleasant, 6 very unpleasant, and 7 most unpleasant of all.
The immediate problem was: What is the relation between the width of interval used and the pleasure got by hearing the motive a-b-a and b-a-b, where a is always the lower tone. The method of procedure was to take a fixed tone (460 vibrations in the first case) and get a series of observations on successive progressions b-a-b where a differed from b by 4, 8, 12 ... 56 vibrations. The greatest difference thus is approximately a musical whole tone. Then a series of observations was taken on a-b-a where a similarly differed from b by 4, 8, 12 ... 52 vibrations. The progressions were given in irregular order, that there might be no chance of the observer getting into a fixed habit of replying. The intimate relation between the pleasure in successive musical tones and the pleasure in musical harmonies suggested naturally the question whether the feeling-value of these unmusical progressions was not somehow dependent upon the affective character of the simultaneous presentation of the same tones. Therefore after a progression had been given once and judgment recorded, the two tones used were given as a "harmony," that is simultaneously, and a judgment taken as to its agreeableness. This was immediately followed by the same progression, thus giving opportunity to observe the relation between the feeling-tone of the interval as it appeared in successive and in simultaneous presentation.
The results of this part of the investigation are graphically represented in the following plates. Tables I and II indicate the feeling-value of a-b-a where a, the lower tone, is 460 vibrations, and b is from 4 to 56 vibrations in addition, and the feeling-value of b-a-b where b, the higher tone, is 460 vibrations and a is from 4 to 56 vibrations less.
PLATE VI.
The base-lines from which the vertical lines to the curves are drawn represent the feeling-tone 4, the indifference-point. Above comes 3, 2, 1 and below 5, 6, 7; each square represents a unit. The horizontal abscissæ represent the width of the interval; the arrows indicate the musical intervals. The observers are given by initials. The first evident fact for both average curves of Plate V is that the maximum pleasure does not coincide with a musical interval, but comes with an interval four or eight vibrations less than either the half or the full tone of the musical scale. While in both cases the first elevation of the curve comes before the semi-tone, b-a-b shows a decrease of pleasure as the whole step is approached while a-b-a rises again. The order a-b-a is liked better than b-a-b.
Plate VI gives the "harmony" curve for the same tone-combinations, and it is clear at the first glance that the curves for the simultaneous tones do not correspond to those for the successive ones; in many respects they are directly the opposite. The hypothesis that the pleasure in such an amusical "melody" results from the resolution of the corresponding "harmony" is thus untenable; both are highly independent of each other. Yet, here too we notice the insignificance of the musical interval, while the strong pleasure in the tones different by 4 vibrations only refers probably to the complete fusion of the tones; there arises a direct enjoyment from the four waves of sound in every second, given by the beats. The pleasure-curve of these simultaneous tones indicates of course that the inhibition of the musical dispositions and expressions holds over from the successive to the simultaneous series. The pleasure is thus clearly different from that in real harmony.
Plate VII finally gives the "melody" curve for aba and bab with changes from four to four vibrations when the interval started with is larger than a full musical step. In aba the a is 384 vibrations and b varies from 436 to 516, the variations lying thus between the musical Second and the musical Fourth. It is evident that here again no feeling-preference is given to the musical intervals.
The question arises whether such small tone-intervals of amusical character allow the construction of more complex combinations of æsthetic value. Can we have amusical micromelodies with their own completeness and feeling of end? The following experiments represent a first step into this field. We used three tones only, a, b, c in 26 different combinations, and each of the 26 variations with intervals of 4, 8 and 12 vibrations between a-b and b-c. Each of the resulting 78 "melodies" was given repeatedly to six subjects in a time-order which allowed one second for each tone. The subject had to judge on the pleasantness of the whole progression and had further to judge whether it produced a feeling of end or not.
The combinations followed in the experiments in this order: abc, cbabc, abcb, cba, abcba, cbab, bcba, cbabcb, ababc, babc, abcbab, babcba, cbcba, bcbabc, abca, acba, acb, cbac, abcab, cabc, cbacb, acbab, cab, bca, cabcb, bac. The lowest tone was varied between 200 and 444 vibrations; b and c were thus always still less distant than the next musical tone. The chief results may be shortly characterized as follows. There are hardly any judgments of indifference, the combinations are always decidedly pleasing or unpleasing. Of course a certain training in the apperception of such small-interval melodies preceded the real experiments and produced an attitude of adjustment to amusical relation. If we are in the midst of musical tone-relations and go over directly to such miniature intervals, we are seeking for the fulfilment of the habitual expectation and feel dissatisfied, or in the best case the procession is an indifferent chance combination. But as soon as a certain training with small intervals has inhibited the strictly musical expectations, a new setting of judgments with new standards comes in and a new source of pleasantness is opened. Of course even then no extreme feelings are to be expected; while the indifference-judgment 4 is lacking, the strong pleasure and displeasure, the judgments 1 and 7 are completely lacking too; three fourths of the judgments are 3 and 5. The pleasantness is decidedly more frequent than the unpleasantness, and this relation increases with the interval. The differences of four vibrations were especially with the higher tones hardly distinct for some of the subjects. Among 288 judgments in each group there were 150 pleasant and 138 unpleasant when the distances between a-b and b-c were four vibrations, 208 pleasant and 80 unpleasant when the distances were 8 vibrations, and 226 pleasant and 64 unpleasant when the distances were 12 vibrations.
The order of pleasantness expressed by the fraction of judgments of pleasantness and unpleasantness is the following: the largest number of pleasant feelings belonged to the figures cbab and bac, immediately followed by abcb; the further order downwards in affective value was: cab, cbac, babc, abca, cbcba, ababc, abc, cabc, acba, cbabcb, bcba, acb, abcba, cba, cbabc, abcab, babcba, cbacb, acbab, bcbabc, abcbab, and cabcb as least pleasant.
PLATE VII.
As to the feeling of end or æsthetic completeness the results are similar and yet independent. In a few cases the answer was "doubtful," but in the overwhelming majority a definite reply was given; and while the judgment of completeness was by far more frequent in the pleasant combinations than in the unpleasant ones, yet often the unpleasant processions appeared as complete and the pleasant ones as incomplete. Here again the feeling of completeness grows with the interval, being smallest for the figures with distances of four vibrations. But most characteristic seems the fact that the feeling of end is in no way as in music dependent upon the return to the starting-point. The combinations which involved such return to the "tonica" show in no way a preponderance of judgments of completeness. If we order the results according to the number of this æsthetic factor the figures acba, cbac, and cabc stand very low, giving in the majority of cases the suggestion of not-completeness in spite of their return to the beginning, while the figures of the type abcb, cbab, or cba, or even the complex babcba, suggest in a majority of judgments the feeling of an end. The feeling of an end comes, according to the subjective reports of the observers, with an "internal unity of meaning" of the phrase given. This unity of meaning is here evidently quite independent from any simple mathematical relation.
The music-like quality of the figures was emphasized frequently in the subjective records. "I just enjoyed the progressions as music." "The elements are the same as in music." A melody of 384, 392, 400 was called a "very mournful strain"; 444, 452, 460 "Wagnerian motive; Tristan and Isolde"; and the same tones in another order "Very pleasant; expressed a pathetic resignation," or "Sounds like a little piece of music"; and so in most varied forms.
The basis of these experiments is of course by far too slender to build on them a theory, yet our results suggest at least a greater interest in the æsthetics of those tone-combinations which are excluded from our regular music. This interest is reënforced by the self-observations of all participants. They felt strongly that after all our musical pleasure in melody does not belong intrinsically to the tone-perception, but is learned and acquired like the grammar of our mother tongue. Such grammar too controls completely our internal demands for expression, and yet the learning of a different language can bring a new adjustment and a new set of psychophysical dispositions for linguistic demands. That whole apparently natural demand for the tone-combinations which give fusion and consonance can be inhibited during the listening to amusical combinations as soon as a short training in miniature intervals changes the acoustical perspective.
The development of instrumental music demanded evidently the selection of distinctly separated tones and of intervals which give harmonious combinations. The external conditions of resonant chambers may have reënforced this selective process of historical music. It is certainly different with oriental nations, which produce music not in resounding chambers but in the free air and who are singers and not players, using instruments mostly for producing a mere body of tone as a background against which the melodies move; their intervals appear to our musical ear at first bizarre, and yet there too we are readjusted to the new dispositions for satisfaction with unsuspected quickness. We have no right to identify æsthetic pleasure in successive tones with the pleasure in our conventional music with the simple mathematical relations which alone give the pleasure of fusion; but being accustomed to this system of harmonies and being trained to expect it also in the resolved form of the melody, we need indeed an inhibition of habits and a certain new training till the more modest pleasure in amusical tone progressions comes to its natural right.
ASSOCIATION, APPERCEPTION ATTENTION
CERTAINTY AND ATTENTION
BY FRANCES H. ROUSMANIERE
The results of the experiments on the feeling of certainty which I have conducted fall into two divisions—those on the nature of the feeling itself, and those on the effect of voluntarily attending to certain aspects of a total experience upon certainty in the judgments as to the constitution of that experience. The problems of the first division are: Are there different kinds of certainty? In any one kind of certainty are there degrees, and if so, are these of a limited or an unlimited number? Can certainty be analyzed into elements? The problems of the second division are: Can it be said that in the report of any experience the judgments made with the highest degree of certainty will be confined to an attended-to group, and if not, will there be more there than elsewhere? In such a report will the direction of voluntary attention toward certain aspects materially alter the distribution of the judgments of the highest order of certainty over the various aspects of any given field?
These two divisions are so distinct in problem and result as to make it seem best to describe them as independent experiments. As some interesting results on the relation of error to the different grades of certainty and to the effect of attention developed in connection with this second division of the experiment, those results are given also.
In general the same subjects took part throughout the experiments. One, an instructor in Harvard University, whom I shall call K, was not subject for the second division of the experiment. Two others, E and H, both graduate students in Harvard University, could not serve as subjects in an important part of the first division. Of those remaining, B was a student in Radcliffe College, F an instructor in Harvard University, and A, C, and D graduate students in Harvard University. These last five were my subjects for all parts of the experiment.
I. THE NATURE OF THE FEELING OF CERTAINTY
The general method here was, of course, the method of introspection. Situations were created about which the subject might be expected to make judgments with different sorts or different degrees of certainty, if such should be possible. He was then questioned as to his experience. The method has the fault of all introspective methods, viz., its results can in no case be verified. The results here are none the less suggestive, and, for the second problem, at any rate, definite enough to be convincing.
Most of the experiments were conducted in connection with visual fields. In working at the first problem which we have now to consider, however, the certainty connected with the dermal sensations and that connected with the simple reasoning process of addition were also examined. The apparatus used consisted of three sets of cards. On one set were pasted geometrical shapes cut from colored paper, and black and white letters or figures. Each of these cards was shown to a subject for a second and a half, or two seconds. After the exposure he told what he judged to be on the card, giving all that he could about the nature of his feeling of confidence (or certainty) for each judgment. On the second set of cards square pieces of tin, smooth rubber, rough rubber, cotton, felt, undressed kid, leather, eiderdown, flannel, coarse and fine sandpaper, and pricked paper were stuck, six on each card. The experimenter passed these cards so that these bits of material rubbed against the forefinger of the subject, while a curtain kept the card and the hand hidden from the subject's sight. Here, again, the subject judged of what had been on the card, just as he had done after seeing each of the first set of cards. Small sample cards, each having pasted upon it a piece of one of the substances used, were also behind the curtain, and the subject was allowed to feel of these as much as he wished while giving his report. Such sample cards were required because of the underdevelopment of the association of names of any kind with the dermal sensations. A single card with three groups of figures for addition upon it made up the third part of the apparatus. Here the subject was asked first to add the columns rapidly and to introspect as to his certainty of the correctness of the different results; then to go over the addition again, and yet a third time, and to compare his feelings of certainty in the different cases. The introspection was developed partly through the help of questions put by the experimenter, but in asking these questions great care was taken to prevent their influencing the judgment of the subject. Some observations made by the subjects during the second division of the experiment (also conducted in connection with visual fields) are, also, introduced here. Apart from this, the experiments on the feeling of certainty connected with this sense of sight were greater in number than the other experiments; and it is those that have given us most of the data for answering the second and third problems.
The subjects did not agree in their answers to the first problem. Some found not only that the certainty connected with their belief in the results of their addition seemed to be of a distinct type from that connected immediately with the sense of sight, but also that there were different sorts of certainty connected immediately with the sense of sight itself. Others found but one kind of a feeling of certainty. All agreed, however, that so far as the kind or kinds of certainty associated with them was concerned there was no difference between the sense of sight and the dermal senses, so that it would seem to be true that any distinctions which are to be found within the feeling of certainty will not be distinctions springing from the difference in the sense-organs. Within the sense of sight, however, subjects B, E, and F divided their feelings of certainty into two classes,—an absolute feeling of certainty which they felt could not be shaken, and a feeling of confidence which they would act upon but which they felt might be shaken by questioning, and which seemed different by more than degree from the feeling of certainty proper. Subjects A, C, K and H found no such marked distinction between their feeling of greatest certainty and all lesser feelings of conviction. Subject D at one time felt that the distinction into two such distinct classes, the definitely certain and the more wavering, fitted his experience, and at another time said that it seemed to him that each degree of conviction stood for an unique feeling of certainty and that any two of them were as different from each other as any other two. A second division of the feelings of certainty into two classes is to be found with subjects A, F and H. This developed in connection with the visual experiments again. The distinction here may be called one into psychological and logical certainty. The latter rests on reasoning either from the probable character of the field, or from a feeling as to its general character, to the nature of some detail. We shall notice the characteristics of these two classes later. One subject, A, further distinguished as different the feelings of certainty connected with the two methods of logical certainty just given. The others made no such distinctions. In the experiment with the columns for addition only six subjects, A, B, C, D, F, and K took part. Of these the two who had made the distinction into psychological and logical certainty with the visual experiments (subjects A and F) again made the same distinction. Subject F, however, who had had occasion to do a good deal of important work with statistics, found practically no element of logical certainty in connection with his addition, though it seemed to him that what confidence he felt in his result should be distinguished from the psychological certainty he had had as to the character of the visual fields. Subject B felt no certainty in her results except as she could so hold the process together as to have what seemed to her a simultaneous experience. When she had to judge of the results of a set of successive experiences that could not be so unified, she characterized her state of consciousness not as holding a feeling of certainty or of uncertainty, but as simply lacking any feeling of certainty. The other three subjects found no difference between the feelings of certainty and uncertainty associated with visual experiences and those associated with the process of addition. As a whole, it seems then that we must answer our first problem by saying that the case seems to be different with different individuals. With some the highest grade of certainty associated with a sense-experience is sharply distinct from the other grades, and with some again there appear at least the two general classes of psychological and logical certainty. On the other hand, there seem to be people for whom the feeling of certainty has no such sharp distinctions of kind within it.
The results as to the second problem may be more briefly and more distinctly given. No subject found any evidence that the number of the grades of certainty which he could distinguish would be limited by anything except his keenness in introspection, although in the simple tests given for the experiment, four was the greatest number of grades distinguished at any one time. Two of the subjects (B and F), who set the highest grade of certainty apart from the judgments made with lesser confidence, said that there might be degrees within that higher grade as well as among the "uncertainties." There was no evidence that logical certainty differed from psychological in respect of the grades to be found within it, and some evidence that they were alike in that respect, although logical certainty was less carefully examined. It would seem, then, that our second problem is to be answered thus: There are degrees present in some if not in all kinds of certainty, and there is no evidence that the number of these degrees is limited.
It was not generally found possible to analyze the feeling of certainty into a sum of elements, although certain characteristics seemed to be persistent in it. Here again there is marked individual variation. The general test used for the difference in degrees of confidence was the question "On which judgment would you risk more?" This satisfied every one as a true criterion for such distinctions, but subjects H and C said that for them the feeling of certainty had a much more distinct relation with the past than with the future. Perhaps for that reason, subject H proposed the test "Which judgment could I be converted from most easily and simply?" The distinctness of an image had something to do with the feeling of certainty for subject C. Beyond this, he could not characterize his feeling. Neither was he sure that the degree of certainty varied exactly with the degree of distinctness. Subject D found that all objects about which he made judgments of which he was certain were present to his mind in the form of distinct images; but did not feel that that covered all that was to be said of the feeling of certainty. The number of images present, as visual and auditory, seemed to increase the degree of certainty for him. Subject F could give no characterization of his feeling of psychological certainty. His feeling of logical certainty seemed to spring largely from a feeling of consistency between the present experience and his past experiences. With subjects A, B, and K the vividness of an image was a strong determining factor in the degree of certainty felt in any judgment, but again was not the whole story. Something they could not characterize was also present for A and B, and, as well, a feeling of more or less perfect congruence between an image and the general character of a field. (This introspection developed in connection with the visual experiments.) Among these eight subjects we have but one (K) who is satisfied with reducing certainty to a set of elements.
To my mind the most valuable thing to be gained from this division of the experiment is the suggestion that there are definite types of certainty, and that people may be classified by these. There are obviously marked individual variations as to the characteristics of this feeling. I should expect from my work this year that two pretty distinct types could be discovered. For one of these, certainty in a judgment as to an experience would rest very largely upon the vividness of an image; for the other, upon the congruence of an image with other previously accepted images, that is, the absence of conflicting images when the experience judged about is imagined part of a wide setting of past experiences. I should not expect either element of certainty to appear absolutely, without the other form. For many people one element would predominate in certain fields, as in judgments regarding sense-experiences, the other in the more logical fields. For some, again, perhaps, the two would be nearly coördinate in every experience of certainty. But for some subjects, as, I think, for subject K here, the vividness of the image would always be the determining factor, while for others, as for subject H, congruence with wider experience would be much more important. This classification of subjects according to their types of certainty might develop into a much more complicated affair. The experiments described here have gone no farther than to suggest lines along which it may perhaps run. There may be other elements equally important with these two. A set of experiments consisting of attempts to raise uncertainty to certainty would bring out the essentials of certainty from a new point of view, and would, perhaps, test this theory that individuals may be classified according to the types of their certainty, in the most satisfactory manner.
II. THE EFFECT OF VOLUNTARILY ATTENDING TO CERTAIN ASPECTS OF A TOTAL EXPERIENCE UPON CERTAINTY IN THE JUDGEMENTS CONSTITUTION OF THAT TOTAL EXPERIENCE.
As has been said, judgments as to the elements of visual fields were tested for this part of the experiment. The apparatus used was the following: The subject was seated before a low table which was shut from his view by curtains and boards. He looked down upon the table through an opening into which a camera-shutter had been fitted. This shutter was set for a two seconds' exposure and opened by means of a bulb which the subject held in his hand. Just before each exposure, the experimenter placed a card on the table below the camera-shutter. The set of twenty cards so used were alike in that the background for all was gray and the objects pasted upon the cards black letters and numerals and simple geometrical figures of chosen shapes and colors. No color was repeated on any one card. The cards were different in the choice and arrangement and in the number of objects used. The number of letters and numerals on any one card varied from two to five, the total number of objects from eight to twelve. A white card on which were pasted dark gray samples of each of the eleven shapes used, together with a card of the background of those shown in the experiment on which were pasted torn scraps of the eleven colored papers used, was always in sight at the subject's side. A camera-shutter, experiment cards and sample cards thus made up the apparatus.
The presence of the sample cards needs explanation. They stood for the attempt to place the colors and shapes on the same footing as the letters and numerals. Their presence, in the first place, and, as well, the limitation of the number of letters and numerals used, did away somewhat with the advantage that letters and numerals naturally have for ease of naming. In the second place, the use of a new color for the sample shapes and the absence of definite shape in the sample colors helped to keep the colors and shapes more distinct. With the help of these cards it seemed that we could properly hold we had a a visual field of three very nearly coördinate sets of elements.
The experiment as a whole, as conducted, had four phases which, except for one particular, were exactly alike. The subject's attention was directed toward a certain aspect of the field by (1) asking him before each exposure (or less often if that appeared unnecessary) to attend to that aspect, as, for instance, to the colors present, and (2) taking care that any questions asked should tend to strengthen rather than counteract the effect of that voluntary attention. At a given signal the subject pressed the bulb which opened the shutter. On the closing of the shutter he reported what he had seen. This report the experimenter recorded almost in the subject's own words, and later tabulated in the manner described presently. So far as giving the objects present was concerned, the report was given almost invariably without any suggestion by the experimenter as to the possibilities of the field. To help the subject distinguish the amount of confidence which he had in the judgments that such or such objects were present, however, the experimenter frequently asked such questions as, "Would you risk more on the fact that there was a square in the field than on the fact there was something blue there?" In giving his report the subject pointed to the sample cards or spoke, as he might wish. He was also allowed to be as leisurely or as rapid in giving it as he chose. A half-minute interval elapsed between the end of each report and the signal that the shutter be opened again. No persistent effort to distract the subject's attention was made then, though conversation on other topics was frequently carried on. The point in which the phases of the experiment differed was in the aspect of the field to which attention was called. In the first, this was the shapes, in the second, the colors, in the third, the letters and numerals, and in the fourth, the number of objects in the field. Fixing the attention upon the number of objects in the field served to distribute it equally over all the groups represented there. The general method of calling attention to the different aspects and of learning the effect of such attention was, as has just been said, the same for all phases.
As a preliminary to making up the tables here given, from which we are to answer our problems, the experimenter first tabulated the reports of the subjects in such a way as to show how many judgments (correct and incorrect) of each of the four grades of certainty adopted for this division of the experiment were made by each subject on each card for each group on the card (shape, color, or letter or numeral). From these tabulations the tables that follow were in turn compiled.
The number of grades of certainty adopted for this division of the experiment is obviously decidedly arbitrary. Grades of certainty there surely are. The introspection of the subjects develops that clearly, as has been stated. But there is no reason in the conditions of the case for holding to the number four, as is done here. In giving the results for which the experiment was undertaken, I shall, indeed, confine myself to studying the range of the judgments made with as high a grade of confidence as the subject believed he should ever have. This is called certainty (1) or certainty proper. But for the tributary discussion on the relation of certainty and error, the consideration of three other grades used in the report and early tabulation, is also introduced. This lowest grade (4) might better be named "as complete uncertainty as will admit of one's making any judgment." The other two are intermediate. It was at first intended to give the results with regard to the effect of voluntary attention upon the place of these grades of certainty, also, but such a discussion has been omitted because it promised to add very little more than complexity to the report. Besides this, the classification into these lower grades is too purely approximate to make the distinction there of great value. For judgments of the order certainty (1) we have the test, "Are you as certain of this as you can imagine being in an experiment of this sort?" but no such test for the other grades could be found. Yet, though he tended to omit judgments of the lower grades of certainty, each subject seemed to find four grades a convenient number to use in giving his report.
The number of experiment cards used varied with the subjects. E had so clear a memory of the cards that after as many as ten had been shown, he found difficulty in distinguishing his memory of the one which he had just seen from that of others seen earlier. Ten cards only were used in his case. A, B, D, and F showed signs of fatigue after fifteen cards which made the value of any later results questionable. C and K showed no such signs of fatigue. The same set of cards was, of course, shown any one subject for all four phases of the experiment. Those omitted were the last ten or the last five of the complete set as the case might be.
TABLE I
| % of cards where certainty (1) appears in the attended-to group. | % of cards where certainty (1) appears elsewhere than in the attended-to group only. | % of cards where certainty (1) in attended-to group only. | % of cards where certainty (1) is stronger outside than within the attended-to group. |
| A 91% | 49% | 49% | 13.3% |
| B 97 | 91 | 83 | 28 |
| C 95 | 67 | 30 | 16.6 |
| D 93.3 | 69 | 24.5 | 11.2 |
| E 96.6 | 83.3 | 13.3 | 26.6 |
| F 88.8 | 30 | 53.3 | 8.3 |
| H 91.6 | 70 | 26.6 | 10 |
Table I answers the first part of our first problem promptly. Every subject gave judgments of the order certainty (1) about groups other than that attended to, in the case of a very considerable percentage of the cards. True, again in the case of a considerable (though generally smaller) percentage of those cards, each subject confined his judgments to the group attended to. The fact of individual variation stands out again here; and, moreover, the conclusions drawn should be qualified slightly because of the fact that it was often possible for the subjects to give all the letters and numerals on the cards, and still have, as it were, some attention left over for the other, supposedly non-attended-to groups. Such reaching beyond the properly attended-to group never seemed to be possible with either shapes or colors. Aside from this, however, it is clear that judgments of the highest grade of certainty were by no means limited to the group attended to.
This same table answers, also, the second part of the problem. Each subject found certainty of the highest grade sometimes stronger outside than within the group which held his attention. It is, of course, practically impossible to make absolutely certain that each subject's attention was invariably held to the group toward which it was turned, yet the percentage where certainty was stronger outside than within such groups seems large enough, in some cases, at least, as with subjects A, B, and H, to warrant our answering this second part of the problem in the negative. I should feel, however, that this was answered less definitely than was the first part of the problem. We may say, then, that the judgments made with the highest degree of certainty about a visual field will not be confined to the group attended to, and that we have strong evidence pointing toward the belief that we cannot expect there will invariably be more of such judgments within the group attended to than outside it.
TABLE II
| Label 1: % of judgments of certainty (1) given to each group in phase I (or when shapes were attended to). | Label 2: % of judgments of certainty (1) given to each group in phase II (or when colors were attended to). | Label 3: % of judgments of certainty (1) given to each group in phase III (or when letters and numerals were attended to). | Label 4: % of judgments of certainty (1) given to each group in phase IV (or when the attention was equally distributed over all the groups) | |||
| 1 | 2 | 3 | 4 | |||
| Subject | Shapes | (a) | 94% | 38% | 18% | 31% |
| A | Colors | (b) | 5 | 61 | 20 | 59 |
| Letters and Numerals | (c) | 0 | 0 | 61 | 9 | |
| Subject | (a) | 48 | 39 | 21 | 33 | |
| B | (b) | 43 | 60 | 29 | 38 | |
| (c) | 8 | 0 | 51 | 28 | ||
| Subject | (a) | 88 | 15 | 26 | 34 | |
| C | (b) | 8 | 77 | 28 | 8 | |
| (c) | 5 | 7 | 47 | 58 | ||
| Subject | (a) | 60 | 13 | 11 | 40 | |
| D | (b) | 19 | 67 | 2 | 37 | |
| (c) | 19 | 19 | 86 | 23 | ||
| Subject | (a) | 51 | 15 | 0 | 37 | |
| E | (b) | 22 | 56 | 8 | 29 | |
| (c) | 26 | 28 | 91 | 34 | ||
| Subject | (a) | 66 | 12 | 0 | 50 | |
| F | (b) | 14 | 77 | 0 | 27 | |
| (c) | 19 | 10 | 100 | 23 | ||
| Subject | (a) | 43 | 21 | 7 | 24 | |
| H | (b) | 29 | 52 | 4 | 19 | |
| (c) | 27 | 26 | 88 | 57 |
The most interesting part of this division of the experiment is brought out in Table II in answer to the problem, "Will the place of voluntary attention materially alter the distribution of judgments of the highest order of certainty among the given groups?" In every case the percentage is affected, in most cases, greatly affected. Take the case of subject A, for instance. Although, when his attention is equally distributed over the field 59% of the judgments we consider were of colors, yet when his attention was fixed on shapes and on letters and numerals this fell to 5% and 20% respectively. When it was fixed on colors, it rose, indeed, only to 61%. When, however, subject A fixed his attention upon the letters and numerals, 61% of the judgments were confined to the group attended to,—the same percentage as when colors were the attended-to group,—although, when his attention was distributed over the whole field, the percentage of these judgments about the group of letters and numerals was 9% only. When shapes were attended to, the 31% of the fourth phase of the experiment rose to 94%,—almost all of the judgments of the highest grade of certainty that were given were judgments about shapes. A similar study of the results given in the table can be made for the other subjects. The degree of change varies with the subject and with the group, but always there is some change, and often a very marked one. In this experiment the place of voluntary attention clearly did alter, and alter materially, the proportion of judgments of the highest order of certainty made about any given group.
That, indeed, would seem to me to be the answer of this experiment to the question as to the effect of voluntary attention upon certainty in one's judgments. Every subject showed a tendency to have more certainty in those judgments which were made about that aspect of the field toward which his attention was directed. Yet, on the other hand, this was a tendency only, one not strong enough to make it possible to predict beforehand exactly how great a proportion of the judgments in which he had the highest degree of confidence would be limited to that field, or even to be sure in every case that the greater proportion of those judgments would be so limited. The place of voluntary attention has an influence upon the subject-matter of the judgments made with certainty about a visual field just seen, but an influence of varying and uncertain strength.
TABLE III
| x = no judgments of that kind given. | % of mistakes in judgments of certainty (1). | % of mistakes in judgments of certainty (2). | % of mistakes in judgments of certainty (3). | % of mistakes in judgments of certainty (4). | |
| Subject (in giving shapes) | (a) | 7% | 10% | 0% | 100% |
| A (in giving colors) | (b) | 2 | 14 | 23 | 0 |
| (in giving letters and numerals) | (c) | 0 | 0 | x | x |
| Subject | (a) | 2 | 10 | 10 | 0 |
| B | (b) | 3 | 6 | 20 | 25 |
| (c) | 4 | 50 | 0 | x | |
| Subject | (a) | 1 | 8 | 10 | 0 |
| C | (b) | 4 | 14 | 14 | 0 |
| (c) | 1 | 0 | 16 | 0 | |
| Subject | (a) | 3 | 4 | 0 | 16 |
| D | (b) | 1 | 6 | 0 | 0 |
| (c) | 5 | 0 | 0 | 0 | |
| Subject | (a) | 2 | 10 | 25 | 50 |
| E | (b) | 1 | 33 | 40 | 0 |
| (c) | 0 | 0 | 0 | 0 | |
| Subject | (a) | 1 | 25 | 7 | 25 |
| F | (b) | 4 | 15 | 29 | 26 |
| (c) | 3 | 0 | 0 | x | |
| Subject | (a) | 3 | 6 | 5 | 0 |
| H | (b) | 6 | 2 | 15 | 15 |
| (c) | 4 | 0 | 0 | 20 |
TABLE IV
| General % of mistakes in judgments of certainty (1). | % of mistakes in judgments of certainty (1) about attended-to groups. | General % of mistakes in judgments not of certainty (1). | % of mistakes in judgments not of certainty (1) about attended-to groups. | |
| Subject A | 4% | 1% | 17% | 27% |
| Subject B | 3 | 2 | 10 | 7 |
| Subject C | 2 | 3 | 9 | 24 |
| Subject D | 3 | 4 | 4 | 0 |
| Subject E | 1 | 2 | 22 | 34 |
| Subject F | 3 | 1 | 21 | 23 |
| Subject H | 4 | 6 | 6 | 10 |
The results given in Tables III and IV were compiled from the same records as those of the two Tables just discussed. They give the relation of error to certainty and to attention, as that relation was developed in this experiment. No experiments were conducted with these relations of error primarily in view, but the results developed in connection with the problem of the effect of attention upon certainty in one's judgments.
Both Tables show again marked individual variation. They suggest to me, in the first place, a further line of investigation in the same field and for the same purpose as those investigations which L. William Stern outlines in an article[101] entitled Aussagestudium. This further line is the testing subjects to learn the probable relative correctness of the judgments made with different degrees of confidence. Although a comparison of the first and third columns in Table IV makes it clear that the proportion of mistakes for the highest grade of confidence is lower than for the other grades taken together, there is a very marked difference among the subjects to be noticed. The difference in the two percentages is, for instance, very slight in the cases of D and H, and very great in the case of E. It is interesting to notice with regard to E that while he has the lowest percentage of mistakes for certainty (1), he has the highest percentage for the group of certainties (2), (3), and (4). In the more detailed percentages given in Table III we see further that in certain fields and sometimes in all fields (as with subject C) judgments made with the lowest grade of confidence were invariably correct. Such Tables might be of help in a case where the evidence of eye-witnesses conflicted. We might perhaps learn that witness N made a large proportion of mistakes where he was absolutely certain, whereas witness M was seldom wrong in judgments in which he had a low degree of confidence. Even when the probity of both was unquestioned, we should not then assume that N was more probably right because he had so much more confidence in his judgments than M had in his. A much longer and more comprehensive set of experiments would be necessary before we could feel that we had at hand a table from which to work in this way.
The question of the effect of voluntary attention upon error, for answering which Table IV was compiled, brings out again the marked individual variation among these seven subjects which has shown itself in practically all parts of the experiment. Some effect seems to have been produced always, but this was sometimes to give a larger percentage of mistakes in the attended-to groups and sometimes a smaller. With A, B, and F the percentage of mistakes in certainty (1) was lower for the groups attended to than for the total number of judgments of that order. Only with subject B, however, is this true of the group of lower grades of certainties also. On the other hand, with subjects C, D, E, and H the percentage is greater for certainty (1) in the groups attended to than for certainty (1) in the collection of all the judgments of certainty (1) taken together. Here, too, in the case of subject D, the results with regard to the lower grades of certainty reverse those for certainty (1). Thus all four possibilities as to the kind of influence of voluntary attention upon certainty appear. We cannot say that the place of voluntary attention will tend to affect the percentage of error in any given way. We can only say that apparently it made some difference with each subject. It might be found by further experimenting that the character of this difference is associated with some other characteristic of either attention or the feeling of certainty, as, for instance, with the ease with which attention is held to the chosen field or with the type of the subject's certainty.
Like all experiments, these open up further questions quite as much as they answer those toward which they are aimed. To repeat something of what has already been said, I feel that what it has established is (1) that introspection develops distinct grades of certainty in the case of every individual, (2) that the particular characteristics of the feeling of certainty vary markedly among individuals; (3) that the feelings of certainty associated with the different senses are not, as feelings of certainty, to be distinguished from each other; (4) that the judgments of the highest degree of certainty which are made about the constitution of any visual field just seen will not be confined to the group in that field toward which the attention is directed; and (5) that such fixing of the attention will, nevertheless, materially alter the subject-matter of such judgments of greatest certainty. The rather vague statement that the percentage of error is not surely less with the judgments of a group because attention is fixed on that group may perhaps be added as a sixth conclusion. The most interesting and promising of the problems which the experiments seem to me to raise are: (1) the problem, are there such definite types of the feeling of certainty that people may be classified according to their types, and, if so, what are the types and what their relation to other psychological characteristics of the individual? (2) the problem, what will be the result of careful and trained introspection as to the relation of so-called logical and psychological certainty and in what fields do these appear for different individuals? (3) the problem, how can a test for grading the probable percentage of error in the judgments of different grades of certainty made by any one person be constructed? and (4) the problem, how are such facts as those given in Table IV to be connected with the effort required for attention, the type of certainty of each subject, etc.? Other problems could, of course, be suggested, but these, I feel, mark the steps that naturally follow the experiments described here.
PLATE VIII.
INHIBITION AND REËNFORCEMENT
BY LOUIS A. TURLEY
Experiments made by Ranschburg[102] on the significance of similars in the process of learning and remembering determined that when duplicates occur within a series of stimuli, one either totally or very greatly inhibits the perception of the other according as they are contiguous or are separated by other stimuli. Dr. Yerkes,[103] in testing the effect of auditory on visual and tactual stimuli in frogs, found that if the auditory stimulus preceded another stimulus by various time-intervals, it had an alternating reënforcing and inhibitory effect. A similar result was obtained by Hofbauer[104] in a similar experiment on human subjects. The question now arises,—if the time-interval were increased between a stimulus and its duplicate in a series would the inhibitory effect gradually approach zero where all effect of the preceding stimulus ceased, to which Ranschburg's experiments point, or would the inhibitory effect be alternated with one of reënforcement as the experiments of Dr. Yerkes and Hofbauer would indicate? This problem—the effect of a stimulus on its duplicate in a succeeding series of stimuli—is the problem I undertook to solve. For this purpose, it was necessary to introduce exactly determinable time-intervals between the stimulus and its duplicate. Therefore I used—as Miss Kleinknecht[105] did for other purposes—a stroboscopic arrangement instead of simultaneous presentation which Ranschburg used.
My apparatus was Professor Münsterberg's Stereoscope without Prisms or Lenses, a description and photograph of which was published in the article by that title in Psychological Review, vol. 1; or rather, I used Professor Münsterberg's attachment to Kohl's centrifugal machine, since my apparatus was not identical, except in principle, with the "Stereoscope." The "attachment" consists of two black discs about thirty inches in diameter, mounted about eight inches apart on the disc-shaft of the centrifugal machine. The back disc is of wood. The outer three inches of its face is furnished with thirty-six equidistant strips of black tin, one end of each of which is bent so as to grip a groove in the rim of the disc, and the other end of each is gripped by tiny thumb-screws so that the strips lie along radii of the face of the disc. The front disc, slightly smaller than the back disc, is of pasteboard. Between the two discs a stationary black screen with a short narrow slit was placed so that the slit revealed only the strip on the horizontal radius of the back disc. Behind this screen an eight-candle-power electric light was placed to illuminate the back disc,—as the experiment was carried on in a darkened room. By moving this light I was enabled to vary the intensity of illumination to offset the skill of the observer.
For my purpose, a small white figure—one of the ten characters of the Arabic notation—was stuck on about the middle of each of the tin strips on the back disc; and radial slits, one millimetre wide and an inch long, were cut from one sixth of the circumference of the front disc so as to come opposite six of the strips on the back disc. Similar radial slits were cut at various intervals from the remaining five sixths of the circumference of the front disc. These were covered by small pieces of cardboard fastened to niagara clips, thus making them readily removeable. By this means any desired figure could be exposed in the same revolution with the series exposed by the six slits above mentioned.
The thirty-six strips were divided into six series of six each, indicated by chalk-marks on the disc. Each of the series was often changed in whole or in part by shifting and interchanging the strips.
The figure on which the effect of a preceding stimulus was tested occupied the fourth place in the series, since this is the place where the greatest number of errors occur, as is shown by the experiments of Ranschburg and previous investigators in the Harvard Laboratory. In my experiment, 4, 5, 6, 7, 8, and 9 occupied the fourth place in the 1st, 2d, 3d, 4th, 5th, and 6th series respectively, and the effect of a preceding stimulus was tried on each of these figures for each time-interval. The preceding stimulus in each case was a duplicate of the fourth member of a series, and was a member of some other series. Thus the fourth member of each series was at all times fixed and constant while the preceding stimulus occupied successive progressive positions round the disc. The other members of each series were chosen at random, care being taken that the fourth figure was not duplicated within its series, since it would then have taken part in inhibition within the series.
PLATE IX.
By adjusting the front disc, I exposed any one of the series desired, and by removing the cardboard blind from one of the suggestion slits, I gave a stimulus at the desired time-interval in advance of the fourth member of the series. The first interval I used was 1.11 sec. as Miss Kleinknecht had tried intervals up to 1 sec. My second interval was 1.39 sec., the third 1.8 sec., and then every .277 sec. up to 4.3 sec. In performing the experiment I exposed alternately a series without and a series with a preceding stimulus—taking from the observer three reports of each—until the six series had been seen. I then repeated this, exposing with a preceding stimulus those series that had been exposed without preceding stimulus, and without preceding stimulus those series that had been exposed with a preceding stimulus in the first instance. In this way I equalized and minimized the effects of novelty and memory.
At 1.11 sec. there was considerable inhibition in five out of six cases. In the sixth case there was slight reënforcement at this interval. With an interval of 1.39 sec., with one exception,—not the exception above mentioned,—there was a stronger inhibition than at 1.11 sec. Inhibition in all cases began to decrease from 1.39 sec. until it ceased at about 1.8 sec. The preceding stimulus then had a reënforcing effect which reached a maximum in four cases at 2.08 sec., one at 2.36 sec., and one at 2.64 sec. Then, in all cases, there was a decrease of the reënforcing effect which in three cases amounted to inhibition. In the other three cases, the preceding stimulus had no inhibitory effect for an interval greater than 1.8 sec. For one of these, Fig. 5, the preceding stimulus had a reënforcing effect for all the intervals beyond 1.8 sec. The second trough in the wave or interval of maximum inhibition was at either 2.64 sec. or 2.92 sec., except for the person for whom there was constant reënforcement beyond 1.8 sec., in which case the first interval of least reënforcement or second trough was at 3.19 sec. This was the second interval of greatest enhancement, or second crest, for four of the others. Then followed a third point of no effect or inhibition, which was 3.75 sec. or 4.03 sec. For the person for whom the preceding stimulus had least enhancing effect at 3.19 sec., the second interval of greatest reënforcement coincided with the interval of greatest inhibition for the majority of the other observers. For four of the six observers, the third interval of greatest reënforcement was 4.3 sec. In this, the observer agreed for whom the last interval of greatest reënforcement was 3.75 sec. Thus while, for this observer, the first two points of greatest reënforcement were separated by an interval of 1.11 sec., the second and third points were separated by an interval of only .55 sec. This same thing occurred in the records of two other observers, for one at this point, and for the other at another point. Of the two dissenters from the opinion of the majority that the third crest was at 4.3 sec., one was an erratic observer; and for the other, there was a slight reënforcement at 4.03 sec. and no effect at all at 4.3 sec.
Fig. 1 represents the average of the records of the six observers. The curve is based on the difference between the number of times the fourth members of the series were seen with and without preceding stimulus. The base-line represents the number of times the figure was seen without preceding stimulus, taken each day as the normal for that day. Figures above the base-line represent the greater, and those below the line, the less number of times the figure was seen with preceding stimulus, or reënforcement and inhibition, respectively. The first two points are the average of fifty-four observations; each point beyond the second is the average of 108 observations. Figs. 2, 3, 4, and 5 represent individual records constructed as Fig. 1, each point being the average of eighteen observations.
The curve in Fig. 1 is somewhat misleading in showing points of maximum reënforcement at 3.19 sec., 3.75 sec., and 4.3 sec. In no individual case was this true. The reason for the crest at 3.75 sec., or at least for its height, is that in two cases reënforcement was considerable at this interval, and there was little inhibition to offset this in the general average. At 3.19 sec., which was the second interval of greatest reënforcement, for four out of the six observers, owing to practice, the reënforcement was not great (Fig. 4), but in no case was there inhibition at this point. Thus for the lack of strong positive effect at 3.19 sec. and the lack of strong negative effect at 3.75 sec., the two crests are the same height, while the first represents the maximum effect for four and the second for two observers.
From these results, taking everything into consideration, my conclusions are:
(1) If a stimulus precedes at various time-intervals its duplicate in a series of stimuli, it will alternately inhibit and reënforce the perceiving of the duplicate stimulus.
(2) Within 4.5 sec. there are at least three points each of maximum inhibition and maximum reënforcement.
(3) The points of maximum inhibition and likewise those of maximum reënforcement are separated by intervals of from .55 sec. to 1.2 sec.—more often by one of the two extremes than by any mean.
(4) Up to 4.5 sec., as the time-interval increases, the maximum inhibition generally decreases, while the maximum enhancement correspondingly increases.
What the limit of this periodic effect is, I cannot as yet say, as up to the present I have not used time-intervals beyond 4.3 sec. But from the intensity of the effect at this interval, I do not expect the limit to be within several seconds.
THE INTERFERENCE OF OPTICAL STIMULI
BY H. KLEINKNECHT
The purpose of this investigation is the determination of the location, extent, nature, and cause of the interference of optical stimuli. Ranschburg[106] studied the phenomena carefully in using optical stimuli which were spread over the retinal field, for instance, a series of letters or figures one beside the other. But if we are to experiment on the inhibitory influence of a certain qualitative impression, we must try to eliminate the local difference; the letters or figures ought to be seen at the same spot.
This became possible by a stroboscopic arrangement, consisting of two parallel circular discs one foot apart on the same axis, whose motion was controlled by an electric current.
The discs were 60 cm. in diameter. Thirty-six radii were drawn equidistant on the farther disc, and on these were clasped black tin strips bearing letters or numbers or colors. The nearer disc was similarly divided and an opening, 3 mm. in width, was cut at each radius. This exposed the number. A cardboard placed between the discs limited the range of vision, its opening being 4 × 5 cm.
The figures were 10 mm. high, white, and placed on a dark background.
Preparatory stimuli were given to enable the subject to adjust his eye to the farther disc. They were so placed as to fall on different retinal points, thus avoiding fatigue.
Many of the tests employed by Ranschburg were used again to ascertain the influence of the change in method and with the hope that such differences might throw some light on the nature of the interference. At first there were six subjects, afterwards eight—all graduate students and trained in laboratory work. The experiment was carried on in the morning. Numbers consisting of six digits were exposed on a dark background. The time of exposure varied with the subject, but was constant throughout the experiment. The subject was asked to record the number immediately after perceiving it, but in almost every case it was read verbally (its retention being thus facilitated) and then recorded.
For the first few weeks letters were used. But since subjects found it very difficult to distinguish these, a change was made to figures. For a month and a half numbers were given for the purpose of training the subjects and of ascertaining the speed best adapted to each. This varied from 5½" to 8" a revolution, each figure being exposed from 115 to 166 sigma.
Three series of numbers were given: (1) Homogeneous, containing a repeated figure, as, 495851. (2) Heterogeneous; as, 708654. (3) Similar, that is, in construction; as, 813470 (8 and 3 being easily substituted for each other). Other similars given by Ranschburg are 9 and 0, 9 and 6, 9 and 2, and 5 and 3.
In order to determine the place of greatest interference, the repeated figures were located in all possible positions, while the preceding and succeeding figures were left unaltered, so as to obviate any new influences which might result from a change of relations. There are fifteen possible variations of the series: mabcdm, ambcdm, abmcdm, abcmdm, abcdmm, etc.
The following table, illustrative of the scheme ambmcd, will show the character of the results obtained. Only the numbers in which errors occur are here recorded, those figures which were incorrectly perceived being printed in heavy type. The dash is used when the location of the figure omitted is known, and the interrogation mark when the reply is doubtful.
| 8" V. | 8" R. | 5½" S. | 5½" M. | 5½" H | 8" E. | |
| 708025 | 70625 | 76082 | ..... | 70825 | 7082-5 | 70285 |
| 958564 | 95584 | ..... | ..... | 95864 | 985 ? 4 | 958-54 |
| 281845 | 281485 | ..... | 20861 | 28185 | 281-54 | |
| 436392 | 43632 | 43636 | 436932 | 436924 | 43632 | 43632 |
| 526273 | 526723 | 5257 | 572673 | 52763 | ..... | 52623 |
| 940469 | 94069 | 940465 | ..... | 94069 | 94640 | 940-69 |
The interference may result in permutation, substitution, or inhibition. The latter two may take several forms; as, inhibition of identicals, of similars, of dissimilars, the location of the omitted figure being known or unknown; also, substitution of an identical, similar, or dissimilar figure which precedes or follows.
The homogeneous series (540 tests) gives results as follows:
HOMOGENEOUS SERIES
| Inhibition of Identicals. | Inhibition of Similars. | Inhibition due to Location. | |||||
|---|---|---|---|---|---|---|---|
| Location of the Identicals. | Spot Known | Spot Unknown | Spot Known | Spot Unknown | Spot Known | Spot Unknown | |
| mabcdm | |||||||
| 1 | 1=6 | 1 | 1 | 4 | 5 | ||
| ambcdm | |||||||
| 2 | 2=6 | 5 | 2 | 1 | 3 | ||
| 3 | 3=6 | 2 | 3 | 5 | |||
| 4 | 4=6 | 3 | 3 | 4 | 2 | ||
| 5 | 5=6 | 6 | 15(?) | 4 | 5 | ||
| 6 | 1=5 | 1 | 2 | 1 | 2 | 1 | 3 |
| 7 | 2=5 | 5 | 3 | 3 | |||
| 8 | 3=5 | 3 | 7 | 2 | 1 | ||
| 9 | 4=5 | 2 | 21(?) | 2 | 5 | 3 | |
| 10 | 1=4 | 9 | 4 | 3 | |||
| 11 | 2=4 | 3 | 9 | 4 | 1 | 7 | |
| 12 | 3=4 | 3 | 19(?) | 1 | 2 | 4 | |
| 13 | 1=3 | [107]5+3(?) | 2 | 1 | 10 | ||
| 14 | 2=3 | 1 | 11(?) | 3 | 8 | ||
| 15 | 1=2 | 6(?) | 1 | 4 | 9 | ||
| Total | 19 | 48+75(?) | 6 | 38 | 17 | 71 | |
I. Inhibition
(1) There is considerable inhibition only when identicals are next to each other.
(2) There is but little difference in the amount of inhibition when identicals are removed two and when removed three places.
(3) The interference is greatest when 3d = 4th, 4th = 5th, and 5th = 6th figures, in which schemes it is almost equal in amount.
(4) When identicals are adjacent, it is impossible to decide whether there be inhibition or fusion, i. e., whether one be inhibited and the other appear, or whether the figure seen be a fusion of the two (unless there is an omitted figure whose location is known to the subject). Its intensity does not serve as a clue, for the perception of the number demands the full concentration of the attention.
II. Substitution
When the interference is not sufficiently great to cause inhibition, substitution may result.
(1) In the majority of cases the substituted figure is a dissimilar not occurring in the number.
(2) A preceding figure is frequently substituted.
(3) Occasionally a figure is replaced by its similar, but this is not true of the homogeneous element. (Cf. with Ranschburg.)
(4) Sometimes the next figure in the natural number series is substituted; as, 9 for 8, 6 for 5.
(5) The figures containing straight lines (4, 7, and especially 1) are less subject to illusion; likewise the smaller numbers (1, 2, 3, 4).
III. Permutation
The permutation represents the least interference.
(1) The 4th and 5th figures are most often exchanged.
(2) The figure is seldom permuted more than two places, and generally but one.
The recording of the number was most interesting. Generally the first few figures and the last were written without comment, but the 4th and 5th often called forth an expression of doubt, which was immediately followed by an exclamation at the coming of the figure into consciousness as if by "inspiration." The experience was extremely peculiar. The figure, fully as distinct as those already perceived, was always from 5″ to 10″ late, and seemed to "pop in unannounced"—to "come from nowhere." A substitution or permutation occurred without this lapse of time.
HETEROGENEOUS SERIES
(1) There are less than half as many inhibitions as in the homogeneous series, the largest number being in the 4th and 5th places.
(2) The number of substitutions is decreased by a fourth, the identicals and similars remaining the same.
(3) There are no fusions.
(4) Fewer permutations are found in this series. The 4th and 5th figures are most often permuted. In a very few cases the figure is permuted four and five places.
(5) There are an equal number of doubtful perceptions in both series.
SIMILAR SERIES
(1) There are few cases of inhibition, and even more surprising is the small number of cases in which a figure is inhibited by its similar.
(2) There are more substitutions, 6 being very often substituted for 5, generally in the 6th place and when preceded by 0 or 9, often by both. Similars are never replaced by identicals (69 by 66 or 99) as Ranschburg found in his experiments.
(3) The fusion of similars equals that of identicals in the homogeneous series.
(4) The number of permutations is the same as in the homogeneous series and less than in the heterogeneous.
(5) The doubtful perceptions have decreased by half.
That there are fewer errors in this series than in the homogeneous or heterogeneous, may be due to the fact that it was given last, especially since one subject showed marked improvement in the entire series and another during the last half. These subjects suddenly began to see six figures, while previously they had seen but five and those contained errors.
In the above 1620 tests, 9 and 0, and 8 and 3, are sometimes inhibited by and substituted for each other, but the remaining similars mentioned by Ranschburg seldom have any such effect.
It is impossible to determine definitely the nature of the interference, the greatest uncertainty existing in the homogeneous series when two identicals are adjacent. But the interference is dependent not only upon the identity or similarity of the figures of which the number is composed but also upon their location.
INHIBITIONS
| 1 | 2 | 3 | 4 | 5 | 6 | Total | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Place known | Place unknown | K. | U. | K. | U. | K. | U. | K. | U. | K. | U. | K. | U. | |
| Homogeneous | 1 | 13 | 2 | 28 | 9 | 41 | 15 | 31 | 15 | 44 | 42 | 157 | ||
| 6(?) | 14(?) | 19(?) | 21(?) | 15(?) | 75(?) | |||||||||
| Heterogeneous | 2 | 5 | 1 | 8 | 2 | 15 | 4 | 36 | 5 | 34 | 2 | 25 | 16 | 123 |
| Similar | 4 | 4 | 5 | 3 | 6 | 2 | 13 | 5 | 32 | |||||
| Total excluding(?) | 2 | 5 | 2 | 25 | 4 | 47 | 13 | 82 | 23 | 71 | 19 | 82 | 63 | 312 |
| Total of Known + Unknown | 7 | 27 | 51 | 95 | 94 | 101 | 375 | |||||||
(?) Inhibition or fusion.
SUBSTITUTIONS
| 1 | 2 | 3 | 4 | 5 | 6 | Total | |
|---|---|---|---|---|---|---|---|
| Homogeneous | 8 | 12 | 26 | 27 | 38 | 14 | 125 |
| Heterogeneous | 4 | 4 | 14 | 21 | 30 | 20 | 93 |
| Similar | 1 | 5 | 9 | 25 | 33 | 27 | 100 |
| Total | 13 | 21 | 49 | 73 | 101 | 61 | 318 |
FUSIONS [See (?) under Inhibitions]
| 1 | 2 | 3 | 4 | 5 | 6 | Total | |
|---|---|---|---|---|---|---|---|
| Homogeneous | 1 | 2 | 1 | 3 | 10 | 17 | |
| Heterogeneous | 0 | 0 | 0 | 0 | |||
| Similar | 3 | 3 | 6 | 6 | 18 | ||
| Total | 1 | 5 | 4 | 9 | 16 | 35 |
Note. There were no clear cases of fusion, but the evidence favored fusion rather than inhibition.
PERMUTATIONS
| 1 | 2 | 3 | 4 | 5 | 6 | Total | ||
|---|---|---|---|---|---|---|---|---|
| Homogeneous | (a) | 6 | 29 | 46 | 56 | 30 | 167 | |
| (b) | 5 | 21 | 45 | 68 | 35 | 174 | ||
| Heterogeneous | (a) | 15 | 25 | 60 | 62 | 28 | 190 | |
| (b) | 14 | 23 | 51 | 82 | 44 | 214 | ||
| Similar | (a) | 13 | 20 | 37 | 78 | 16 | 164 | |
| (b) | 12 | 17 | 26 | 75 | 28 | 158 | ||
| Total | (a) | 34 | 74 | 143 | 196 | 74 | 521 | |
| (b) | 31 | 61 | 122 | 225 | 107 | 546 |
(a) forward, (b) backward
Note. The permutation of an inhibited figure was not noted unless its location was known: hence the difference in the number of forward and backward permutations.
| 1 | 2 | 3 | 4 | 5 | 6 | Total | |
|---|---|---|---|---|---|---|---|
| Total Interferences | 54 | 160 | 323 | 509 | 524 | 300 | 1870 |
| % | 3% | 9% | 17% | 27% | 28% | 16% | |
| Absolute Errors (ex- | 20 | 55 | 119 | 191 | 225 | 103 | 713 |
| cluding Permutations) | 3% | 8% | 17% | 27% | 31% | 14% |
ABSOLUTE ERRORS (excluding Permutations)
| Homogeneous | Heterogeneous | Similar | |
|---|---|---|---|
| Inhibitions | 199 | 139 | 37 |
| Substitutions | 129 | 93 | 101 |
| Fusions | 17 | 18 | |
| (?) | 75 | ||
| Total | 420 | 232 | 156 |
| 52% | 29% | 19% |
Over 50% of the errors were found in the 4th and 5th places.
[Ranschburg: 90% of errors in right half—60% in 5th place, 30% in 4th, few in 6th.]
In 1620 tests, the homogeneous series contained 52% of the absolute errors, the heterogeneous 29%, and the similar 19%.
COLORS
In the hope that some light might be thrown upon the main question at issue, the writer changed the stimuli, using colors instead of numbers.
It was important that the colors should be of the same or only slightly varying intensity and that they should be easily distinguishable. In a series of preliminary experiments in which red, blue, yellow, green, brown, gray, pink, and violet were used, red was lost in 8% of the tests, and gray in 25%.
Colors 1×4 cm. in size "ran into each other," while those which were 1×1 cm. remained distinct.
Here it was found necessary to distinguish between the various factors which might cause inhibition. Three factors entered into each test—perceiving, naming, remembering.
Four subjects found difficulty in naming, especially at first. The various methods of naming are given below in detail. M. says: "The name of the color is localized in my mouth. Generally there is no movement of the tongue—an impulse only; and the name is felt in that part of the mouth where the sound would be reflected, as, red in the upper part, blue near the front, etc."
S.: "Usually there is no apparent tendency to pronounce. Occasionally, naming them over inaudibly before recording is found advantageous."
E., V., and H.: "The naming is mental, but is accompanied by a slight movement of the tongue and throat."
684 heterogeneous and 200 homogeneous tests showed that greatest inhibition occurred in the following order: 4th place (27%), 3d (26%), 5th (24%), 2d (11%), 6th (8%), 1st (4%). There was but little difference in the 3d, 4th, and 5th places.
During first tests subjects were allowed only one exposure, but later it was thought best to eliminate all omissions resulting from inability to name colors perceived, and hence they were asked to record only when able to name all colors perceived during that exposure. However several required but one exposure.
Preliminary drill was given for two weeks. Since no clear cases of fusion had been obtained in the entire number-series, the one aim of the experimenter was to ascertain whether fusion of colors, even though of heterogeneous, be possible. Eight hundred heterogeneous tests gave 927 cases of inhibition, 7 of fusion, and 18 which, though somewhat doubtful, yet gave more evidence of fusion than of inhibition. Yellow (3d place) and brown (6th place) were seen as yellowish-brown, brown and pink as pinkish-brown, etc. Gray was seen several times instead of a color and its complementary when these were in immediate succession. This was true of both red and blue. Half of the total number of substitutions was due to the displacement of yellow by brown. And a color not in the series was as likely to be substituted as one preceding or following the displaced color.
Two hundred and fifty-two homogeneous tests showed that there is greatest interference when identicals are in immediate succession, and least, when removed two places. The doubtful (fusion?) cases number one third of the inhibited. The 4th and 5th colors are permuted most often, as was found to be the case in the heterogeneous series also. The element is generally permuted but one place.
The heterogeneous color-tests show three times as much interference as the corresponding number-tests, and the homogeneous twice as much. The discrepancy in the amount of variation may be due to the experiments with the heterogeneous colors being earlier, when naturally more errors would be made.
However, a comparison of 252 homogeneous with the same number of heterogeneous tests, taken at the same time, shows that there is a much larger difference in the number of absolute errors between the heterogeneous and the homogeneous number-series than there is, proportionately, between the two series of color-tests.
Lest the want of correspondence in the results might have been due to the comparatively small number of immediately successive identicals in the color-tests, 90 homogeneous tests, equally distributed among all possible variations in the location of the identical elements, were compared with 90 heterogeneous, and it was unexpectedly found that the absolute errors as well as the permutations were almost equal in the two series. Nevertheless, the validity of a conclusion based on so few tests may well be questioned.
Ranschburg found that simultaneous homogeneous stimuli interfere with one another; while simultaneous heterogeneous stimuli clear the way for one another. On the basis of the experiments with numbers, the writer would amend the conclusion reached in the earlier research to read thus: Homogeneous optical stimuli, whether occurring simultaneously in different positions, or in immediate succession in the same positions, interfere with one another; while heterogeneous stimuli clear the way for one another.
SUBJECTIVE AND OBJECTIVE SIMULTANEITY
BY THOMAS H. HAINES
This investigation finds its starting-points in two widely separated lines of experimentation in the problems of attention. These two lines are the "scope-of-attention" experiment with the tachistoscope, and the "time-displacement" experiment with the pendulum apparatus. It seems to me these two can be brought into relation to each other to the help of each of them individually, and that an investigation taking these wide relations within its scope may reasonably be expected to throw new light upon the manner in which mental processes are related to each other when they are together in consciousness at the same time. The first of these experiments (tachistoscopic) is concerned with the number and relative clearness of the processes which go on at the same time. The second (displacement) is concerned with the conditions of the subjective displacement of one of two objectively simultaneous stimuli with reference to the other. Its problem is the essential psychological problem involved in the astronomer's error in transit observations by the eye-and-ear method, for the personal equation arising in these observations is more a matter of the reciprocal relations among the processes which are together in consciousness at the moment of observation than it is of mere reaction time. It is primarily more a matter of relative clearness, as controlled probably through interference of one with another, than it is of the more or less temperamental facility of converting ideas into action.
The psychological question at the heart of the observation-error, called the personal equation, is this,—What are the conditions which hinder such a division of attention among the parts of the complex operation of coördinating sense-stimulations, that the processes which start simultaneously may proceed to equal clearness at the same time, and so be perceived as simultaneous? The facts sought in order to answer this question are the very same as some of those, at least, demanded by the "scope-of-attention" investigation when it really opens up to its true problem. W. Wirth[108] has recently shown, in an exhaustive criticism of the tachistoscopic method, that "scope of attention" is primarily concerned with the relations of the processes present together, and that this demands a previous exhaustive study of their relative clearnesses. Earlier studies by the tachistoscopic method, as, for example those of Cattell[109] on the relatively short time for the perception of letters in words, as compared with that for separate letters, and the overlapping of processes in continuous reading, showed that the important question is, what are the processes which may go on at the same time. Leaving out a statement of the nature of the processes is equivalent to leaving out one of the dimensions when endeavoring to state the contents of a solid. The scope of attention can be defined adequately only when one knows fully what the separate processes are as well as how many there are. This analysis, which the scope-of-attention problem demands, cannot fail to be directly fruitful for the solution of the time-displacement problem. The analysis of this larger problem directly involves the former. Any attempt to investigate the time-displacement of sense-impressions from simultaneous stimuli must inevitably place the highest value upon the whole detailed analysis of any moment of attentive effort.
The present investigation, starting with the facts of time-displacement, and taking the hint offered by Gonnessiat,[110] attempts to show, by a more complete analysis, the effects of the various relations within each series,—the visual within which the sounds are to be placed, and the auditory series itself, and also relations existing between the two series. In other words, the attempt is made to strip the "displacement" experiment until nothing more remains to be coördinated than a single pair of simultaneous stimuli. This was the experiment of Exner.[111] He investigated the shortest discriminable interval marked off by various pairs of stimuli, addressed to the same sense and to different senses. From this coördination of a visual and an auditory stimulus, where the limits of the "specious present" are obtained, I make a turn into the realm of the scope of attention. By a new method, whereby impairment of accuracy of processes is made the test as to whether the processes have proceeded together, it is shown that two such perceptual processes can go on just about as well at the same time as separately. Since this test is subject to the objection that the visual and auditory processes may really be successive, though seemingly at the same time, owing to retinal inertia, the same question is removed to an entirely different plane in a further and more detailed set of experiments where the processes combined are judgments of comparison based upon one and the same visual sensation.
EXPERIMENTS IN TIME-DISPLACEMENT
The Leipsic Complication Experiment with the pendulum apparatus (for description of this see Wundt's Physiol. Psy., 5th ed., vol. 3, p. 82) was an early adaptation of the astronomers' eye-and-ear method to the purposes of psychological experimentation. Instead of localizing a visual stimulus (star on meridian) in an auditory series (clicks of a chronoscope) as in the eye-and-ear method, this adaptation localized an auditory stimulus (bell-stroke) in a visual series (successive positions of a pointer on a graduated circle). This pointer passed around to the right and to the left from the position of rest, in which it pointed vertically upward, as the pendulum, to which it was connected by clockwork, swung back and forth. By a simple adjustment the bell-stroke could be made to come at any point in the complete double swing of the pendulum, and so anywhere in the arc over which the pointer moved. This machine makes an additional problem as to the effects upon displacement of the increasing and decreasing speed. My aim being to simplify as much as possible the displacement-error and so reduce it to its elements, this feature was not only not of direct interest, but it was very desirable to dispense with it altogether. This was done by arranging the visual series so that the members were shown in perfectly regular order, i. e. with equal time-intervals, throughout the series. These equal intervals were secured by the rotation of a disc at a uniform rate.
My method also gave a more distinctly serial character to the visual stimuli, in that they were separated by blank periods. The series consisted of letters in alphabetical order. Denison's smallest white letters, about six millimetres in height, were pasted upon a disc of black cardboard, near the circumference and perpendicular to radii, so that they would appear in succession and right side up, to an observer looking through a slit at the peripheral region of the disc, as it rotated. The letters were placed in three concentric rows, so that as the disc rotated they appeared in three different places. The disc was 56.5 cm. in diameter. As a further aid in securing separate exhibitions of letters, another black disc of the same size as the one bearing the letters, with radial slits 2 mm. wide and cut in from the edge 4 cm., opposite each letter on the other disc, was mounted on the same shaft, six inches from the first, and between it and the observer. A short observation-tube was placed at the same height as the axis of the discs parallel to this axis, and opposite the slits when they were at this elevation. Looking through this, as the discs were rotated, one would see the letters right side up and in serial succession. Uniform illumination was secured by working in a dark room with artificial light. An electric lamp was hung between the discs. Uniform motion was secured by an automatic control gravity motor, connected by belt with a pulley on the disc-shaft.
The auditory stimulus, a click, adjustable to any part of the series, was made as follows: A wooden shaft, mounted on the same axle as the discs, and beyond the discs from the observer, could be rotated freely around the axle when the nut securing it was loosened. This shaft extended beyond the edge of the disc. It carried a copper wire which was in contact with the axle. A mercury cup was placed on the table, upon which the machine rested, in such position that the copper tip passed through the mercury when the discs rotated. It was thus a very simple matter to connect an electric sounder so that it would click every time the circuit was made by the copper passing through the mercury. And, by the adjustment of the wooden shaft, the click was readily placed anywhere in the visual series.
As already suggested above, the length of interval between members of the visual series, and also the time between clicks, seem to be important factors in determining the amount, and perhaps also the direction of the displacement. Bessel found his personal equation was considerably diminished when he used a clock marking half-seconds instead of one marking seconds. Wolf also diminished his error by using a clock beating one hundred times a minute instead of one beating seconds, which he was accustomed to use. Wundt found his customary negative displacement on the pendulum apparatus (coördinating the sound with a position of the index earlier than that with which it was actually simultaneous) disappeared when he had members of the visual series one thirty-sixth second apart and the auditory stimuli one second apart. It seemed important at the outset, therefore, to determine, if possible, the effects of each of these factors.
BOTH INTERVALS PROGRESSIVELY VARIED
In each experiment the observer was allowed to observe as many complications (coincidences of click and letter) as he desired, in order to assure himself of his judgment. The experimenter counted and recorded the number observed in each experiment. Experiments were made in series of ten. Six different combinations of intervals were used in this first group of experiments. The auditory intervals (time between successive clicks) and visual intervals (time between successive members of the visual series) are given at the tops of the columns in Table I. This table is a summary presentation of the results of this group. There were three observers. During each hour of experimentation with a given observer, at least one series with each of the first four time-interval combinations was tried out. "Aver. num. Trials" means the average number of complications observed in the whole number of tests averaged. "Num. Series av." means the number of series of ten experiments each averaged to give the displacement results below. "Aver. Error" is the average of all the displacements of the auditory impression, irrespective of the direction of the displacement. "Mean Displacement" is the actual mean displacement as obtained by dividing the algebraic sum of all displacements, positive and negative, by the number of experiments. The plus sign indicates a positive displacement, and the minus sign, a negative. Negative and positive are here used in the sense customary in similar experiments,—namely, the click, being heard as simultaneous with a visual impression which actually came before it, was said to be displaced negatively, and the click, being heard as simultaneous with a visual impression coming in fact later than it did, was said to be displaced positively. Average errors and mean displacements are given in the table in thousandths of seconds. Observers were asked to locate the click in the visual series in terms of one tenth the distance or time between the letters.