The Principles of Psychology, Vols. 1-2

Wundt and his pupil Dietze have both tried to deter mine experimentally the maximal extent of our immediate distinct consciousness for successive impressions. Wundt found f that twelve impressions could be distin guished clearly as a united cluster, provided they were caught in a certain rhythm \)j the mind, and succeeded eacL other at intervals not smaller than 0.3 and not larger thai? 0.5 of a second. This makes the total time distinctly ap prehended to be equal to from 3.6 to 6 seconds.

Dietze ^ gives larger figures. The most favorable inter vals 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 eacli. When no grouping of the strokes beyond making couples of them by the attention was allowed — arid 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.* This would make 40 times 0.8 second, or 12 seconds, to be the maximum filled duration of which \ve 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, t 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 success ive clicks of a Savart's wheel, and of two successive snaps * Counting was of course not permitted. It would have given a sym bolic concept and no intuitive or immediate perception of the totality of the series. With counting we may of course compare together series of any length— series whose beginnings have faded from our mind, and of whose totality we retain no sensible impression at all. To count a series of clicks is an altogether different thing from merely perceiving them as dis continuous In the latter case we need only be conscious of the bits of empty duration between them ; in the former we must perform rapid acts of association between them and as many names of numbers.

f Estel in Wundt's Philosophische Studien, ir. 50. Mehner, ibid. n. 571 In Dietze's experiments even numbers of strokes were better caught than odd ones, by the ear. The rapidity of their sequence had a great influ ence on the '-esult. At more than 4 seconds apart it was impossible to per ceive series of them as units in all (cf. Wundt, Physiol. Psych n : They were simply counted as so many individual strokes. Below 021 0.11 second, according to the observer, judgment again became confusec It was found that the rate of succession most favorable for grasping long series was when the strokes were sounded at intervals of from 0.3 to 0.18 apart Series of 4, 6, 8, 16 were more easily identified than series of 10, 12, U 18. The latter could hardly be clearly grasped at all Among odd numbers, 3, 5, 7 were the series easiest caught ; next, 9, 15 ; harde .f all, 11 and 13 ; and 17 was impossible to apprehend

of an electric spark, when their interval was made as small as about -g-J-g- of a second.* 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".f 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 : $

"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] re quired by each additional click in a series for the sense of discontinuity to remain constant throughout." §

* The exact interval of the sparks was 0.00205 r. The doubleness of their snap was usually replaced by a single-seeming sound when it fell to 0.00198", the sound becoming louder \vken the sparks seemed simultaneous. The difference between these two intervals is only TTJTF7ff^ of a second; ami, as Exner remarks, our ear and brain must be wonderfully efficient organs to get distinct feelings from so slight an objective difference as this. See Pfltiger's Archiv, Bd. XI.

f Ibid. p. 407. When the sparks fell so close together that their irradi ation-circles overlapped, they appeared like one spark moving from the posi tion of the first to that of the second; and they might then follow each other as close as 0.015" without the direction of the movement ceasing to be clear. When one spark fell on the centre, the other on the margin, of the retina, the time-interval for successive apprehension had to be raised to t).076"

§ Nevertheless, multitudinous impressions may be felt as discontinuous, though separated by excessively minute intervals of time. Grtinhageu says (Pfluger's Archiv, vi. 175) that 10,000 electric shocks a second art felt as interrupted, by the tongue (I). Von WUtich (ibid. IT. 329), that between 1000 and 2000 strokes a second are felt as discrete by the finger. W. Preyer, on the other Land (Die Grenzen des Empfindungsvermogens, etc., 1868, p. 15), makes contacts appear continuous to the finger when 86.8 o) them follow in a, second. Similarly, Mach (Wiener Sitzgsb., LI. 2, 142; gives about 36. Lalanne (Comptes Rendus, LXXXII. p. 1314) found summa tion of finger contacts after 22 repetitions in a second. Such discrepan, figures are of doubtful worth. On the retina 20 to 30 impressions a second

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 differ ence which impression comes first. Thus, Exner found* the smallest perceptible interval to be, in seconds: To be conscious of a time interval at all is one thing ; to tett tvhether 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 betzveen two times which we can perceive.

The difference is at its minimum when the times themselves are very short. Exner, f reacting MS rapidly as possi ble 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 J^TT of a second either way from the average were at the very utmost can be felt as discrete when they fail on the same spot. The ear, which begins to fuse stimuli together into a musical tone when they follow at the rate of a little over 30 a second, can still feel 132 of them a second as discontinuous when they take the shape of '• beats' (Helmholtz, Tonempfindungen, 3d ed. p. 270).

t Pflilger's Archiv, vn. 639. Tigerstedt (Bihang till Kongl. Svenska Vetenskaps-Akad. HandI.,Bd. 8, Hitfte 2, Stockholm, 1884) revises Exnei's figures, and shows that his conclusions are exaggerated. According to Tigerstedt, two observers almost always rightly appreciated 0.05" or 0.06" of leactior.-time difference. Half the time they did it rightly when the difference sank to 0.03", though from 0.03" and O.OB" differences were often not noticed at all. Buccola found (Le Legge del Tempo nei Fenomeni del Fensiero, Milano. 1883, D. 371) that, after much practice in making rapid reactions upon a signal, he estimated directly, in figures, his own reaction -time, in 10 experiments, with an error of from 0.010" lo 0.018"; !n 6, with one of 0.005" to 0.009"; in one, with one of 0.002"; and IB 3L with one of 0.008"

correctly noticed by him at the time. The average waa 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 includ ed, 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." * Three observers in these experiments made no error when the middle interval varied -^ from the extremes. When it varied TJg-, 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 them selves. According to Feclmer's * Psy chop hy sic Law ' it ought always to bear the same ratio. Various observers, however, have found this not to be the case.f On the con trary, very interesting oscillations in the accuracy of judg ment and in the direction of the error — oscillations depen dent 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 f INDIFFERENCE- POINT;' that is to say, an interval which we judge with max imum accuracy, a time which we tend to estimate as neither longer or shorter than it really is, and away from which, f Mach, Wiener Sitzungsb., LI. 2, 133 (1865); Estel, loc. cit. p. 65, Mehner, loc. cit. p. 586; Buccola, op. cit p. 378. Fechner labors to prove that his law is only overlaid by other interfering laws in the figures re corded by these experimenters; but his case seems to me to be one of des perate infatuation with a hobby. (See Wuudt's Philosophische Studien

in both directions, errors increase their size.* This time varies from one observer to another, but its average is re markably constant, as the following table shows. f The times, noted by the ear, and the average indiffer ence-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, * Curious discrepancies exist between the German and the American ob servers with respect to the direction of the error below and above the point of indifference— differences perhaps due to the fatigue involved in the American method. The Germans lengthened intervals below it and short ened those above. With seven Americans experimented on by Stevens this was exactly reversed. The German method was to passively listen to the intervals, then judge ; the American was to reproduce them actively by movements of the hand. In Mehner's experiments there was found a second indifference-point at about 5 seconds, beyond which times were judged again too long. Glass, whose work on the subject is the latest (Philos. Studicn, IV. 423), found (when corrections were allowed for) that all times except 0.8 sec. were estimated too short. He found a series of points of greatest relative accuracy (viz., at 1.5, 2.5, 3.75, 5, 6.25, etc., secoad> respectively, and (thought that his observations roughly corrobo rated Weber's law. As 'maximum' and 'minimum' are printed inter dmnsrrably in Glass's article it is hard to follow.

f With Vierordt and his pupils the indifference point lay as higl from 1.5 sec to 4.9 sec., according to the observer (cf. Per Zeitsinn, 1808, p. 112). In. most of these experiments the time heard was actively repro duced, after a short pause, by movements of the hand, which were rocorded. Wundt gives good reasons (Physiol. Psych., n. 289, 290) for re jecting Vierorclt's figures as erroneous. Vierordt's book, it should be s nd, is full of important matter, nevertheless.

** Op cit p. 376. Mach's and Buccola's figures, it will be observed, are about one half of the rest-sub-multiples, therefore, observed, however, that Buccola's figure has little value, hi* observatio not being well fitted to show this particular point. as the interval of time most easy to catcli and reproduce, Odder still, both Estel and Mehuer found that multiples of this time were more accurately reproduced than the time- Intervals of intermediary length ;* 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. f 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. if 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.§

There is a certain emotional feeling accompanying the intervals of time, as is well known in music. The sense of haste goes ivith one measure of rapidity, that of delay with another ; and these two feelings harmonize with different mental moods. Vierordt listened to series of strokes per formed by a metronome at rates varying from 40 to 200 a * Estel's figures led him to think that all the multiples enjoyed this priv ilege; with Mehner, on the other hand, only the odd multiples showed diminution of the average error; thus, 0.71, 2.15, 3.55, 5, 6.4, 7.8, 9.8, and 10.65 second were respectively registered with the least error. Cf. Phil Studien, n. pp. 57, 562-565.

minute, and found that they very naturally fell into seven categories, from ' very slow ' to ' very fast.' * Each category of feeling included the intervals following each other within a certain range of speed, and no others. This is a qualita tive, not a quantitative judgment — an aesthetic 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.t

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. Although subdividing the time by beats of sensation aids our accurate knowledge of the amount of it that elapses, such subdivision does not seem at the first glance essential to our perception of its flow. Let one sit with closed eyes and, abstracting entirely from the outer world, attend exclusively to the passage of time, like one who wakes, as the poet says, " to hear time flowing in the middle of the night, and all things moving to a day of doom." There seems under such circumstances as these no variety in the material content of our thought, and what we notice appears, if anything, to be the pure series of durations budding, as it were, and growing beneath our indrawn gaze. Is this really so or not ? The question is important, for, if the experience be what it roughly seems, we have a sort of special sense for pure time — a sense to which empty duration is an adequate stimulus ; while if it be an illusion, it must be that our perception of time's flight, in the expe riences quoted, is due to the filling of the time, and to our memory of a content which it had a moment previous, and which we feel to agree or disagree with its content now.

*The number of distinguishable differences of speed between these limits is as, he takes care to remark, very much larger than 7 (Der Zeitsinn, p. that the latter alternative is the true one, and that we can no more intuit a duration than ice can intuit an extension, devoid of all sensible content. Just as with closed eyes we perceive a dark visual field in which a curdling play of ob scurest luminosity is always going on ; so, be we never so abstracted from distinct outward impressions, we are always inwardly immersed in what Wundt has somewhere called the twilight of our general consciousness. Our heart-beats, our breathing, the pulses of our attention, fragments of words or sentences that pass through our imagination, are what people this dim habitat. Now, all these processes are rhythmical, and are apprehended by us, as they occur, in their totality ; the breathing and pulses of attention, as coherent successions, each with its rise and fall ; the heart beats similarly, only relatively far more brief ; the words not separately, but in connected groups. In short, empty our minds as we may, some form of changing process remains for us to feel, and cannot be expelled. And along with the sense of the process and its rhythm goes the sense of the length of time it lasts. Awareness of change is thus the condition on which our perception of time's flow depends ; but there exists no reason to suppose that empty time's own changes are sufficient for the awareness of change to be aroused. The change must be of some concrete sort — an outward or inward sensible series, or a process of attention or voli tion.*

* I leave the text just as it was printed in the Journal of Speculative Philosophy (for 'Oct. 1886') in 1887. Since then Mtinsterberg in his masterly Beitriige zur experimentellen Psychologie (Heft 2, 1889) seems to have made it clear what the sensible changes are by which we measure the lapse of time. When the time which separates two sensible impressions is less than one third of a second, he thinks it is almost entirely the amount to which the memory -image of the first impression has faded when the second one overtakes it, which makes us feel how wide they are apart (p. 29). When the time is longer than this, we rely, he thinks, exclusively upon the feelings of muscular tension and relaxation, which we are constantly receiving although we give to them so little of our direct attention. These feelings are primarily in the muscles by which we adapt our sense-organs in attending to the signals used, some of the muscles being in the eye and ear them selves, some of them in the head, neck, etc. We here judge two timeintervals to be equal when between the beginning and end of each we feel exactlv similar relaxations and subsequent expectant tensions of these

And here again we have aii analogy with space. The earliest form of distinct space-perception is undoubtedly that of a movement over some one of our sensitive surfaces, and this movement is originally given as a simple whole of feeling, and is only decomposed into its elements — succes sive positions successively occupied by the moving body— when our education in discrimination is much advanced. muscles to have occurred. In reproducing intervals ourselves we try to make our feelings of this sort just what they were when we passively heard the interval. These feelings by themselves, however, can only be used when the intervals are very short, for the tension anticipatory of the terminal stimulus naturally reaches its maximum very soon. With longer intervals we take the feeling of our inspirations and expirations into account. With our expirations all the other muscular tensions in our body undergo a rhythmi cal decrease; with our inspirations the reverse takes place. When, there fore, we note a time-interval of several seconds with intent to reproduce it, what we seek is to make the earlier and later interval agree in the number and amount of these respiratory changes combined with sense-organ adjustments with which they are filled. Miinsterberg has studied care fully in his own case the variations of the respiratory factor. They are many ; but he sums up his experience by saying that whether he meas ured by inspirations that were divided by momentary pauses into six parts, or by inspirations that were continuous ; whether with sensory tension dur ing inspiration and relaxation during expiration, or by tension during both inspiration and expiration, separated by a sudden interpolated relaxation ; whether with special notice taken of the cephalic tensions, or of those in the trunk and shoulders, in all cases alike and without exception he in voluntarily endeavored, whenever he compared two times or tried to make one the same as the other, to get exactly the same respiratory conditions and conditions of tension, all the subjective conditions, in short, exactly the same during the second interval as they were during the first. Miinsterberg corroborated his subjective observations by experiments.

The observer of the time had to reproduce as exactly as possible an interval between two sharp sounds given him by an assistant. The only condition imposed upon him was that he should not modify his breathing for the purposes of measurement. It was then found that when the assistant broke in at random with his signals, the judgment of the observer was vastly less accurate than when the assistant carefully watched the observer's breathing and made both tLe beginning of the time given him and that of the time which he was to give coincide with identical phases thereof.— Finally, Miinsterberg with great plausibility tries to explain the discrepancies be tween the results of Vierordt, Estel, Mehner, Glass, etc., as due to the fact that they did not all use tlie sarne measure. Some breathe a little faster, some a little slower. Some break their inspirations into two parts, some do not, etc. The coincidence of the objective times measured with definite natural phases of breathing would very easily give periodical maxiinn of facility in measuring accurately

But a movement is a change, a process ; so we see that iu tha time-world and the space-world alike the first known things are not elements, but combinations, not separate units, but wholes already formed. The condition of being of the wholes may be the elements ; but the condition of our knowing the elements is our having already felt the wholes as wholes. In the experience of watching empty time flow — 'empty : to be taken hereafter in the relative sense just set forth — we tell it off in pulses. We say ' now ! now ! now ! : or we count ' more ! more ! more ! ' as we feel it bud. This com position out of units of duration is called the law of time's discrete flow. The discreteness is, however, merely due to the fact that our successive acts of recognition or appercep tion of what it is are discrete. The sensation is as continu ous as any sensation can be. All continuous sensations are named in beats. We notice that a certain finite ' more ' of them is passing or already past. To adopt Hodgson's image, the sensation is the measuring-tape, the perception the dividing-engine which stamps its length. As we listen to a steady sound, we take it in in discrete pulses of recog nition, calling it successively * the same! the same! the same ! ' The case stands no otherwise with time.

After a small number of beats our impression of the amount we have told off becomes quite vague. Our only way of knowing it accurately is by counting, or noticing the clock, or through some other symbolic conception.* When the times exceed hours or days, the conception is absolutely symbolic. We think of the amount we mean either solely as a name, or by running over a few salient dates therein, with no pretence of imagining the full durations that lie between them. No one has anything like a perception of the greater length of the time between now and the first century than of that between now and the tenth. To an historian,

* " Any one wishing yet further examples of this mental substitution will find one on observing how habitually he thinks of the spaces on the clock-face instead of the periods they stand for ; how, on discovering it to be half an hour later than he supposed, ne does not represent the half hour in its duration, but scarcely passes beyond the sign of it marked by the finger." (H. Spencer: Psychology, §336.) it is true, tlie longer interval will suggest a host of additional dates and events, and so appear a more multitudinous thing. And for the same reason most people will think the}* directly perceive the length of the past fortnight to exceed that of the past week. But there is properly no comparative time intuition in these cases at all. It is but dates and events. representing time ; their abundance symbolizing its length. I am sure that this is so, even where the times compared are no more than an hour or so in length, it is the same with Spaces of many miles, which we always compare with each other by the numbers which measure them.*