ACCURACY OF OUR ESTIMATE OF SHORT DURATIONS.

We must now proceed to an account of the facts of time-perception in detail as preliminary to our speculative conclusion. Many of the facts are matters of patient experimentation, others of common experience.

First of all, we note a marked difference between the elementary sensations of duration and those of space. The former have a much narrower range; the time-sense may be called a myopic organ, in comparison with the eye, for example. The eye sees rods, acres, even miles, at a single glance, and these totals it can afterward subdivide into an almost infinite number of distinctly identified parts. The units of duration, on the other hand, which the time-sense is able to take in at a single stroke, are groups of a few seconds, and within these units very few subdivisions—perhaps forty at most, as we shall presently see—can be clearly discerned. The durations we have practically most to deal with—minutes, hours, and days—have to be symbolically conceived, and constructed by mental addition, after the fashion of those extents of hundreds of miles and upward, which in the field of space are beyond the range of most men's practical interests altogether. To 'realize' a quarter of a mile we need only look out of the window and feel its length by an act which, though it may in part result from organized associations, yet seems immediately performed. To realize an hour, we must count 'now!—now!—now!—now!—' indefinitely. Each 'now' is the feeling of a separate bit of time, and the exact sum of the bits never makes a very clear impression on our mind.

How many bits can we clearly apprehend at once? Very few if they are long bits, more if they are extremely short, most if they come to us in compound groups, each including smaller bits of its own.

Hearing is the sense by which the subdivision of durations is most sharply made. Almost all the experimental work on the time-sense has been done by means of strokes of sound. How long a series of sounds, then, can we group in the mind so as not to confound it with a longer or a shorter series?

Our spontaneous tendency is to break up any monotonously given series of sounds into some sort of a rhythm. We involuntarily accentuate every second, or third, or fourth beat, or we break the series in still more intricate ways. Whenever we thus grasp the impressions in rhythmic form, we can identify a longer string of them without confusion.

Each variety of verse, for example, has its 'law'; and the recurrent stresses and sinkings make us feel with peculiar readiness the lack of a syllable or the presence of one too much. Divers verses may again be bound together in the form of a stanza, and we may then say of another stanza, "Its second verse differs by so much from that of the first stanza," when but for the felt stanza-form the two differing verses would have come to us too separately to be compared at all. But these superposed systems of rhythm soon reach their limit. In music, as Wundt[517] says, "while the measure may easily contain 12 changes of intensity of sound (as in 12/8 time), the rhythmical group may embrace 6 measures, and the period consist of 4, exceptionally of 5 [8?] groups."

Wundt and his pupil Dietze have both tried to determine experimentally the maximal extent of our immediate distinct consciousness for successive impressions.

Wundt found[518] that twelve impressions could be distinguished clearly as a united cluster, provided they were caught in a certain rhythm by the mind, and succeeded each other at intervals not smaller than 0.3 and not larger than 0.5 of a second. This makes the total time distinctly apprehended to be equal to from 3.6 to 6 seconds.

Dietze[519] gives larger figures. The most favorable intervals for clearly catching the strokes were when they came at from 0.3 second to 0.18 second apart. Forty strokes might then be remembered as a whole, and identified without error when repeated, provided the mind grasped them in five sub-groups of eight, or in eight sub-groups of five strokes each. When no grouping of the strokes beyond making couples of them by the attention was allowed—and practically it was found impossible not to group them in at least this simplest of all ways—16 was the largest number that could be clearly apprehended as a whole.[520] This would make 40 times 0.8 second, or 12 seconds, to be the maximum filled duration of which we can be both distinctly and immediately aware.

The maximum unfilled, or vacant duration, seems to lie within the same objective range. Estel and Mehner, also working in Wundt's laboratory, found it to vary from 5 or 6 to 12 seconds, and perhaps more. The differences seemed due to practice rather than to idiosyncrasy.[521]

These figures may be roughly taken to stand for the most important part of what, with Mr. Clay, we called, a few pages back, the specious present. The specious present has, in addition, a vaguely vanishing backward and forward fringe; but its nucleus is probably the dozen seconds or less that have just elapsed.

If these are the maximum, what, then, is the minimum amount of duration which we can distinctly feel?

The smallest figure experimentally ascertained was by Exner, who distinctly heard the doubleness of two successive clicks of a Savart's wheel, and of two successive snaps of an electric spark, when their interval was made as small as about 1/500 of a second.[522]

With the eye, perception is less delicate. Two sparks, made to fall beside each other in rapid succession on the centre of the retina, ceased to be recognized as successive by Exner when their interval fell below 0.044''.[523]

Where, as here, the succeeding impressions are only two in number, we can easiest perceive the interval between them. President Hall, who experimented with a modified Savart's wheel, which gave clicks in varying number and at varying intervals, says:[524]

"In order that their discontinuity may be clearly perceived, four or even three clicks or beats must be farther apart than two need to be. When two are easily distinguished, three or four separated by the same interval ... are often confidently pronounced to be two or three respectively. It would be well if observations were so directed as to ascertain, at least up to ten or twenty, the increase [of interval] required by each additional click in a series for the sense of discontinuity to remain constant throughout."[525]

Where the first impression falls on one sense, and the second on another, the perception of the intervening time tends to be less certain and delicate, and it makes a difference which impression comes first. Thus, Exner found[526] the smallest perceptible interval to be, in seconds:

To be conscious of a time interval at all is one thing; to tell whether it be shorter or longer than another interval is a different thing. A number of experimental data are on hand which give us a measure of the delicacy of this latter perception. The problem is that of the smallest difference between two times which we can perceive.

The difference is at its minimum when the times themselves are very short. Exner,[527] reacting as rapidly as possible with his foot, upon a signal seen by the eye (spark), noted all the reactions which seemed to him either slow or fast in the making. He thought thus that deviations of about 1/100 of a second either way from the average were correctly noticed by him at the time. The average was here 0.1840''. Hall and Jastrow listened to the intervals between the clicks of their apparatus. Between two such equal intervals of 4.27'' each, a middle interval was included, which might be made either shorter or longer than the extremes. "After the series had been heard two or even three times, no impression of the relative length of the middle interval would often exist, and only after hearing the fourth and last [repetition of the series] would the judgment incline to the plus or minus side. Inserting the variable between two invariable and like intervals greatly facilitated judgment, which between two unlike terms is far less accurate."[528] Three observers in these experiments made no error when the middle interval varied 1/60 from the extremes. When it varied 1/120, errors occurred, but were few. This would make the minimum absolute difference perceived as large as 0.355''.

This minimum absolute difference, of course, increases as the times compared grow long. Attempts have been made to ascertain what ratio it bears to the times themselves. According to Fechner's 'Psychophysic Law' it ought always to bear the same ratio. Various observers, however, have found this not to be the case.[529] On the contrary, very interesting oscillations in the accuracy of judgment and in the direction of the error—oscillations dependent upon the absolute amount of the times compared—have been noticed by all who have experimented with the question. Of these a brief account may be given.

In the first place, in every list of intervals experimented with there will be found what Vierordt calls an 'indifference-point;' that is to say, an interval which we judge with maximum accuracy, a time which we tend to estimate as neither longer or shorter than it really is, and away from which, in both directions, errors increase their size.[530] This time varies from one observer to another, but its average is remarkably constant, as the following table shows.[531]

The times, noted by the ear, and the average indifference-points (given in seconds) were, for—

The odd thing about these figures is the recurrence they show in so many men of about three fourths of a second, as the interval of time most easy to catch and reproduce, Odder still, both Estel and Mehner found that multiples of this time were more accurately reproduced than the time-intervals of intermediary length;[537] and Glass found a certain periodicity, with the constant increment of 1.25 sec., in his observations. There would seem thus to exist something like a periodic or rhythmic sharpening of our time-sense, of which the period differs somewhat from one observer to the next.

Our sense of time, like other senses, seems subject to the law of contrast. It appeared pretty plainly in Estel's observations that an interval sounded shorter if a long one had immediately preceded it, and longer when the opposite was the case.

Like other senses, too, our sense of time is sharpened by practice. Mehner ascribes almost all the discrepancies between other observers and himself to this cause alone.[538]

Tracts of time filled (with clicks of sound) seem longer than vacant ones of the same duration, when the latter does not exceed a second or two.[539] This, which reminds one of what happens with spaces seen by the eye, becomes reversed when longer times are taken. It is, perhaps, in accordance with this law that a loud sound, limiting a short interval of time, makes it appear longer, a slight sound shorter. In comparing intervals marked out by sounds, we must take care to keep the sounds uniform.[540]

There is a certain emotional feeling accompanying the intervals of time, as is well known in music. The sense of haste goes with one measure of rapidity, that of delay with another; and these two feelings harmonize with different mental moods. Vierordt listened to series of strokes performed by a metronome at rates varying from 40 to 200 a minute, and found that they very naturally fell into seven categories, from 'very slow' to 'very fast.'[541] Each category of feeling included the intervals following each other within a certain range of speed, and no others. This is a qualitative, not a quantitative judgment—an æsthetic judgment, in fact. The middle category, of speed that was neutral, or, as he calls it, 'adequate,' contained intervals that were grouped about 0.62 second, and Vierordt says that this made what one might almost call an agreeable time.[542]

The feeling of time and accent in music, of rhythm, is quite independent of that of melody. Tunes with marked rhythm can be readily recognized when simply drummed on the table with the finger-tips.