TABLE XV

Judgments expressed SimilarlyJudgments expressed Dissimilarly
Obs.Total Number Correct Judgements Total NumberCorrect Judgements
NumberPer Cent NumberPer Cent
A2221727756147985
B1951537849835671
Y3722777486357266

If the results of B and Y were presented alone, they would seem to indicate synergy of similarly expressed judgments. But those of A are most strongly contradictory of such a working together of such judgments. This is very surprising to me, as A had such a facility in expressing these similar judgments, especially "equal, equal, equal," that it suggested this comparison. But the apparent facile expression is here shown to have attended a diminished accuracy. No conclusion can be drawn with respect to synergic influence from the similarity of expression of judgments.

RELATION OF OBJECTIVE AND SUBJECTIVE SIMULTANEITY

Reviewing this work in combination of judgments with reference to its bearing upon the complication results, and the interval discrimination results, it seems that interference of simple mental processes going on at the same time, though it appears to be a fact, showing itself in impaired accuracy of processes combined, is yet quite inadequate to explain the whole, or indeed, any considerable part of the synchronism, as we may call the "click first" "click last" interval of Tables IV, V, and VI. The slight amount of interference of such processes as the auditory and visual perceptions, tending to proceed at the same time, would tend to a very slight displacement of one with regard to the other. It is true, for reasons already discussed, that this time-difference is so slight and so difficult of seizure that it cannot be measured, and so no measure is offered. We cannot, therefore, be certain how much of the non-detectable interval is due to this cause. But the evidence offered in the above tables of results is ample justification for the statement that interference can be responsible for only a very small part of the "click first" "click last" interval.

In the case of this interval, as in that of an interval between any disparate stimuli, a part of it must be due to the different resistance or inertia of the sense-organs. The eye is undoubtedly slower than the ear. This would at once suggest itself as the cause of the interval between the threshold mean and the visual stimulus in the results shown in Tables IV, V, and VI above. That is, vision being slower, an auditory stimulus given at the same time as a visual will appear to be earlier, and it may be given considerably later and yet appear earlier. In general, therefore, so far as this cause is active, one would expect that the interval, at which a sound must precede a visual stimulus in order to be certainly distinguished as coming before the latter, would be much shorter than the interval, at which a sound coming after a visual stimulus could be unfailingly distinguished as coming later. In other words, the centre of gravity of the "click first" "click last" interval, so far as this visual inertia is the cause of its displacement with reference to the visual stimulus time, will be after the visual stimulus.

In one case in my results, Table V, St, H middle, there is presented an extreme where not only the centre of gravity (threshold mean) is placed after the visual stimulus (letter), but the whole synchronous period ("click first" "click last" interval) is after the visual stimulus, so that a sound coming .008 sec. after the visual stimulus is distinguished with certainty as coming before it. So also St, in Table VI, one pair, the sound coming .006 sec. after is judged as coming before the visual stimulus.

But the variety of displacements of the threshold mean in different observers, and more particularly in the same observer under different experimental conditions, indicates very clearly that there are factors other than visual inertia which are quite as important, and perhaps equally responsible for this displacement. In Table VI, H, one pair, for example, the threshold mean is before the visual stimulus .011 sec. So in Table V, G, H first, and also H last, it is before the letter .005 sec. In these cases there must be some factor or factors quite as strong as this visual inertia, and counteractive to it. These are, in part, the complex attention factors which have been referred to already. Prominent among them are the rhythmic perception which is so marked in St; the movement toward the first stimulus and the "letting-go" of the breath, of A; the passive "striking" of the letter by the sound, in the case of some of the observers; and the "cocking" of the eye and the ear, of others. These all have to do with the length and place of the "click first" "click last" interval quite as much as does the visual inertia. But however this may be, of this inertia and the other factors just now named, probably each has more to do with it than does the interference of the perception processes themselves.

But after eliminating the parts played by each and all of these agencies in the determination of the interval, there will remain a period of "present time," in which there are no time-differences, and no qualitative differences which lead the subject to suspect the existence of time-differences. The mental content of this reduced synchronous period in experience is one experience. The sound was heard and the letter was seen, but they came together as aspects of one experience. In the moment of perceiving either one, it was not possible to say that the other was already a memory. In other words, the primary memory of either, whichever came first, had lasted over into the perception of the second. There had been no perceivable transformation of the first since the instant of its perception. At the moment of the inception of the second process, the first was still, to the perceiving subject, what it was at the moment of its own inception. Though change was probably going on in the physiological substrata of the mental process in question, in every minutest moment of the interval, yet a certain amount of effect of this change had to accumulate before the observer could become aware of the change, and so be aware of the passing of time or of temporal difference. This was, then, only a case of the working of the law of relativity. And the perception of time is a function of the duration and amount of change of mental process.

Looked at from this point of view, we see the whole explanation of the existence, the amount, and the position of this synchronous period under one rubric, if only we could grant the combination of mental processes without interference. If mental processes go on together, the sole ground of the imperceptibility of short periods of time separating mental processes is in the fact that the first of these processes has not changed sufficiently to be known as different, to the perceiving subject. The minimal perceivable interval will vary from man to man, and in the same man from time to time, inversely as the amount of change per unit of time, in the process itself. The same statement could be made in terms of vividness or relative clearness. The more focal the idea or process, i. e., the more vivid or relatively clear it is, the more rapid will be the changes and the perception of those changes. Professor Münsterberg's physiological explanation of vividness,[122] as due to the facilitation of the motor discharge, has already found confirmation in the method of keenest interval discrimination as outlined above. The more rapidly the first process can get into action, the more is the discriminated interval shortened. So in Exner's experiments, where it was known which of two stimuli would come first, the interval was very much shorter than any of my results, for the motor preparation could be made very complete beforehand, as in a muscular reaction. Therefore the perceptible change, upon perception of the stimulus, occurred in a shorter time. Under any circumstances, the conditions, subjective or objective, which make for rapid maturing (and by the principle of dynamogenesis maturing means going over into action) of the mental process, make also for the shortening of the least perceptible interval.

These conditions are as various as the gamut of human experience is wide. There is nothing, from the primary temperamental characteristics to the passing wave of feeling of the present moment, which does not affect it. Most particularly, though, is it a matter of the relations existing among the elementary processes striving to go on together. Among the focal and fringe elements of a given moment of experience, no matter how carefully the practised introspectionist may strive after an ideal condition of monoideism, there is an incessant interaction. There are all sorts of hindrances and facilitations. Herein is the justification of Stern's statement that the "praesenzzeit," as he calls it, "varies with the quantity and quality of conscious content, the direction of attention, and the strength of psychical energy," and that it cannot be assigned a maximal value but rather what he calls an "optimal value." All that is included, in fact, in the complex rubrics, attention and interest, has to do with the length of this indiscriminable interval.

Time-difference in consciousness is the very simplest thing in mental life, for it is a case of the bare awareness of change. The elementary time-judgment is mere judgment of change in content of consciousness. In the experiment where one is asked to say which of two expected stimuli comes first, however, the case is already complicated. There must be a double preparation to react and to note the change characteristic of each case, and so convert it into a time-judgment. In the combination of two judgments, there is the same double expectancy, preparation to react in two ways at once. In each experiment, the preparation and shaping of expectation is the same as in reaction experiments. In all reaction work, the short reaction comes as the result of catching the attention wave at its most favorable point. If the signal to react catches the idea of reaction in the mind of the observer at the very focal point in consciousness, the shortest reaction possible under the given conditions results. So in both the combination experiment and the interval discrimination experiment, it is very necessary to catch the attention wave, equally prepared for both or all the processes, and at the highest crest of advancement. Both demand the same preparation as a compound reaction. I believe it is this inequality of balance of the attention between the various processes that is responsible for the interference which is evidenced in my results. This is my explanation of the appearance of impaired accuracy for combinations for a given observer under some conditions and the failure of any sign of impaired accuracy for the same observer under other experimental conditions, or even under the same experimental conditions at different times.

In the time-interval discrimination experiment the evenness of balance in the attention wave will make for the shortest interval discrimination, and the proportion between the two will be direct, so far as other factors do not interfere. But there are special interferences here. One of these is the fact that the two mental processes do not set off at the same moment. No matter how even the balance in attention at the moment of impact of the first of the two stimuli, the preparation for the other, not yet set off, cannot be held in equal readiness while this is going off. This discharge has already disturbed the preparation to discharge in the other direction. In the case of a given pair of stimuli of definite qualities and intensities, the relation will be one of mutual facilitation for one interval of separation and one of inhibition for another interval. In one case the first opens the path for the second, being a case similar to the summation of stimuli, and in the other, it draws all the available energy in its own direction.

THE ESTIMATION OF NUMBER

BY C. T. BURNETT

I. There are situations not a few in life in which we find ourselves estimating the number of objects in some group. Sometimes we desire to know merely whether the group is large or small. Sometimes we try to reach an absolute number that shall approximate roughly to the real number. Sometimes, again, we only care to know whether the group in question is more or less numerous than some other group that we have before us or perhaps recall in memory. The public speaker finds himself wondering whether this present scattering audience is larger than the one that last night crowded into the front seats. The farmer riding between adjoining orchards judges roughly the prospective yield by a comparative estimate of the fruit in sight. The politician too has an interest that is very notable indeed in such rough numerical estimates. He asks himself, for example, whether the voters will be more influenced by reports favorable to his party sent in from numerous small towns or by such reports from a few large centres. Or perhaps he is planning a demonstration in favor of his candidate. His problem then is so to arrange his procession that five hundred men will look like five thousand. Turning to another field, how is it that the enrolment in some institutions of learning seems larger and the size of the faculty more portentous than in other similar institutions that are really of about the same size?

These examples bring to mind our interest in rough numerical estimates and at the same time suggest the probability that we are swayed back and forth in these estimations without ever a numerical difference occurring in the objects of our judgment. These considerations lead us on, then, to an enquiry about the factors that can thus influence our estimation of number.