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

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

TABLE IV

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.

INHIBITION AND REËNFORCEMENT

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.

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

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.

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

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