The question of the 'span' of consciousness has often been asked and answered—sometimes a priori, sometimes by experiment. This seems the proper place for us to touch upon it; and our answer, according to the principles laid down in Chapter IX, will not be difficult. The number of things we may attend to is altogether indefinite, depending on the power of the individual intellect, on the form of the apprehension, and on what the things are. When apprehended conceptually as a connected system, their number may be very large. But however numerous the things, they can only be known in a single pulse of consciousness for which they form one complex 'object' (p. 276 ff.), so that properly speaking there is before the mind at no time a plurality of ideas, properly so called.
The 'unity of the soul' has been supposed by many philosophers, who also believed in the distinct atomic nature of 'ideas,' to preclude the presence to it of more than one objective fact, manifested in one idea, at a time. Even Dugald Stuart opines that every minimum visibile of a pictured figure
"constitutes just as distinct an object of attention to the mind as if it were separated by an interval of empty space from the rest.... It is impossible for the mind to attend to more than one of these points at once; and as the perception of the figure implies a knowledge of the relative situation of the different points with respect to each other, we must conclude that the perception of figure by the eye is the result of a number of different acts of attention. These acts of attention, however, are performed with such rapidity, that the effect, with respect to us, is the same as if the perception were instantaneous."[324]
Such glaringly artificial views can only come from fantastic metaphysics or from the ambiguity of the word 'idea,' which, standing sometimes for mental state and sometimes for thing known, leads men to ascribe to the thing, not only the unity which belongs to the mental state, but even the simplicity which is thought to reside in the Soul.
When the things are apprehended by the senses, the number of them that can be attended to at once is small, "Pluribus intentus, minor est ad singula sensus."
"By Charles Bonnet the Mind is allowed to have a distinct notion of six objects at once; by Abraham Tucker the number is limited to four; while Destutt Tracy again amplifies it to six. The opinion of the first and last of these philosophers" [continues Sir Wm. Hamilton] "seems to me correct. You can easily make the experiments for yourselves, but you must beware of grouping the objects into classes. If you throw a handful of marbles on the floor, you will find it difficult to view at once more than six, or seven at most, without confusion; but if you group them into twos, or threes, or fives, you can comprehend as many groups as you can units; because the mind considers these groups only as units—it views them as wholes, and throws their parts out of consideration."[325]
Professor Jevons, repeating this observation, by counting instantaneously beans thrown into a box, found that the number 6 was guessed correctly 120 times out of 147, 5 correctly 102 times out of 107, and 4 and 3 always right.[326] It is obvious that such observations decide nothing at all about our attention, properly so called. They rather measure in part the distinctness of our vision—especially of the primary-memory-image[327]—in part the amount of association in the individual between seen arrangements and the names of numbers.[328]
Each number-name is a way of grasping the beans as one total object. In such a total object, all the parts converge harmoniously to the one resultant concept; no single bean has special discrepant associations of its own; and so, with practice, they may grow quite numerous ere we fail to estimate them aright. But where the 'object' before us breaks into parts disconnected with each other, and forming each as it were a separate object or system, not conceivable in union with the rest, it becomes harder to apprehend all these parts at once, and the mind tends to let go of one whilst it attends to another. Still, within limits this can be done. M. Paulhan has experimented carefully on the matter by declaiming one poem aloud whilst he repeated a different one mentally, or by writing one sentence whilst speaking another, or by performing calculations on paper whilst reciting poetry.[329] He found that
"the most favorable condition for the doubling of the mind was its simultaneous application to two easy and heterogeneous operations. Two operations of the same sort, two multiplications, two recitations, or the reciting one poem and writing another, render the process more uncertain and difficult."
The attention often, but not always, oscillates during these performances; and sometimes a word from one part of the task slips into another. I myself find when I try to simultaneously recite one thing and write another that the beginning of each word or segment of a phrase is what requires the attention. Once started, my pen runs on for a word or two as if by its own momentum. M. Paulhan compared the time occupied by the same two operations done simultaneously or in succession, and found that there was often a considerable gain of time from doing them simultaneously. For instance:
"I write the first four verses of Athalie, whilst reciting eleven of Musset. The whole performance occupies 40 seconds. But reciting alone takes 22 and writing alone 31, or 53 altogether, so that there is a difference in favor of the simultaneous operations."
Or again:
"I multiply 421 312 212 by 2; the operation takes 6 seconds; the recitation of 4 verses also takes 6 seconds. But the two operations done at once only take 6 seconds, so that there is no loss of time from combining them."
Of course these time-measurements lack precision. With three systems of object (writing with each hand whilst reciting) the operation became much more difficult.
If, then, by the original question, how many ideas or things can we attend to at once, be meant how many entirely disconnected systems or processes of conception can go on simultaneously, the answer is, not easily more than one, unless the processes are very habitual; but then two, or even three, without very much oscillation of the attention. Where, however, the processes are less automatic, as in the story of Julius Cæsar dictating four letters whilst he writes a fifth,[330] there must be a rapid oscillation of the mind from one to the next, and no consequent gain of time. Within any one of the systems the parts may be numberless, but we attend to them collectively when we conceive the whole which they form.
When the things to be attended to are small sensations, and when the effort is to be exact in noting them, it is found that attention to one interferes a good deal with the perception of the other. A good deal of fine work has been done in this field, of which I must give some account.
It has long been noticed, when expectant attention is concentrated upon one of two sensations, that the other one is apt to be displaced from consciousness for a moment and to appear subsequent; although in reality the two may have been contemporaneous events. Thus, to use the stock example of the books, the surgeon would sometimes see the blood flow from the arm of the patient whom he was bleeding, before he saw the instrument penetrate the skin. Similarly the smith may see the sparks fly before he sees the hammer smite the iron, etc. There is thus a certain difficulty in perceiving the exact date of two impressions when they do not interest our attention equally, and when they are of a disparate sort.
Professor Exner, whose experiments on the minimal perceptible succession in time of two sensations we shall have to quote in another chapter, makes some noteworthy remarks about the way in which the attention must be set to catch the interval and the right order of the sensations, when the time is exceeding small. The point was to tell whether two signals were simultaneous or successive; and, if successive, which one of them came first.
The first way of attending which he found himself to fall into, was when the signals did not differ greatly—when, e.g., they were similar sounds heard each by a different ear. Here he lay in wait for the first signal, whichever it might be, and identified it the next moment in memory. The second, which could then always be known by default, was often not clearly distinguished in itself. When the time was too short, the first could not be isolated from the second at all.
The second way was to accommodate the attention for a certain sort of signal, and the next moment to become aware in memory of whether it came before or after its mate.
"This way brings great uncertainty with it. The impression not prepared for comes to us in the memory more weak than the other, obscure as it were, badly fixed in time. We tend to take the subjectively stronger stimulus, that which we were intent upon, for the first, just as we are apt to take an objectively stronger stimulus to be the first. Still, it may happen otherwise. In the experiments from touch to sight it often seemed to me as if the impression for which the attention was not prepared were there already when the other came."
Exner found himself employing this method oftenest when the impressions differed strongly.[331]
In such observations (which must not be confounded with those where the two signals were identical and their successiveness known as mere doubleness, without distinction of which came first), it is obvious that each signal must combine stably in our perception with a different instant of time. It is the simplest possible case of two discrepant concepts simultaneously occupying the mind. Now the case of the signals being simultaneous seems of a different sort. We must turn to Wundt for observations fit to cast a nearer light thereon.
The reader will remember the reaction-time experiments of which we treated in Chapter III. It happened occasionally in Wundt's experiments that the reaction-time was reduced to zero or even assumed a negative value, which, being translated into common speech, means that the observer was sometimes so intent upon the signal that his reaction actually coincided in time with it, or even preceded it, instead of coming a fraction of a second after it, as in the nature of things it should. More will be said of these results anon. Meanwhile Wundt, in explaining them, says this:
"In general we have a very exact feeling of the simultaneity of two stimuli, if they do not differ much in strength. And in a series of experiments in which a warning precedes, at a fixed interval, the stimulus, we involuntarily try to react, not only as promptly as possible, but also in such wise that our movement may coincide with the stimulus itself. We seek to make our own feelings of touch and innervation [muscular contraction] objectively contemporaneous with the signal which we hear; and experience shows that in many cases we approximately succeed. In these cases we have a distinct consciousness of hearing the signal, reacting upon it, and feeling our reaction take place,—all at one and the same moment."[332]
In another place, Wundt adds:
"The difficulty of these observations and the comparative infrequency with which the reaction-time can be made thus to disappear shows how hard it is, when our attention is intense, to keep it fixed even on two different ideas at once. Note besides that when this happens, one always tries to bring the ideas into a certain connection, to grasp them as components of a certain complex representation. Thus in the experiments in question, it has often seemed to me that I produced by my own recording movement the sound which the ball made in dropping on the board."[333]
The 'difficulty,' in the cases of which Wundt speaks, is that of forcing two non-simultaneous events into apparent combination with the same instant of time. There is no difficulty, as he admits, in so dividing our attention between two really simultaneous impressions as to feel them to be such. The cases he describes are really cases of anachronistic perception, of subjective time-displacement, to use his own term. Still more curious cases of it have been most carefully studied by him. They carry us a step farther in our research, so I will quote them, using as far as possible his exact words:
"The conditions become more complicated when we receive a series of impressions separated by distinct intervals, into the midst of which a heterogeneous impression is suddenly brought. Then comes the question, with which member of the series do we perceive the additional impression to coincide? with that member with whose presence it really coexists, or is there some aberration?... If the additional stimulus belongs to a different sense very considerable aberrations may occur.
"The best way to experiment is with a number of visual impressions (which one can easily get from a moving object) for the series, and with a sound as the disparate impression. Let, e.g., an index-hand move over a circular scale with uniform and sufficiently slow velocity, so that the impressions it gives will not fuse, but permit its position at any instant to be distinctly seen. Let the clockwork which turns it have an arrangement which rings a bell once in every revolution, but at a point which can be varied, so that the observer need never know in advance just when the bell-stroke takes place. In such observations three cases are possible. The bell-stroke can be perceived either exactly at the moment to which the index points when it sounds—in this case there will be no time-displacement; or we can combine it with a later position of the index—... positive time-displacement, as we shall call it; or finally we can combine it with a position of the index earlier than that at which the sound occurred—and this we will call a negative displacement. The most natural displacement would apparently be the positive, since for apperception a certain time is always required.... But experience shows that the opposite is the case: it happens most frequently that the sound appears earlier than its real date—far less often coincident with it, or later. It should be observed that in all these experiments it takes some time to get a distinctly perceived combination of the sound with a particular position of the index, and that a single revolution of the latter is never enough for the purpose. The motion must go on long enough for the sounds themselves to form a regular series—the outcome being a simultaneous perception of two distinct series of events, of which either may by changes in its rapidity modify the result. The first thing one remarks is that the sound belongs in a certain region of the scale; only gradually is it perceived to combine with a particular position of the index. But even a result gained by observation of many revolutions may be deficient in certainty, for accidental combinations of attention have a great influence upon it. If we deliberately try to combine the bell-stroke with an arbitrarily chosen position of the index, we succeed without difficulty, provided this position be not too remote from the true one. If, again, we cover the whole scale, except a single division over which we may see the index pass, we have a strong tendency to combine the bell-stroke with this actually seen position; and in so doing may easily overlook more than 1/4 of a second of time. Results, therefore, to be of any value, must be drawn from long-continued and very numerous observations, in which such irregular oscillations of the attention neutralize each other according to the law of great numbers, and allow the true laws to appear. Although my own experiments extend over many years (with interruptions), they are not even yet numerous enough to exhaust the subject—still, they bring out the principal laws which the attention follows under such conditions."[334]
Wundt accordingly distinguishes the direction from the amount of the apparent displacement in time of the bell-stroke. The direction depends on the rapidity of the movement of the index and (consequently) on that of the succession of the bell-strokes. The moment at which the bell struck was estimated by him with the least tendency to error, when the revolutions took place once in a second. Faster than this, positive errors began to prevail; slower, negative ones almost always were present. On the other hand, if the rapidity went quickening, errors became negative; if slowing, positive. The amount of error is, in general, the greater the slower the speed and its alterations. Finally, individual differences prevail, as well as differences in the same individual at different times.[335]
Wundt's pupil von Tschisch has carried out these experiments on a still more elaborate scale,[336] using, not only the single bell-stroke, but 2, 3, 4, or 5 simultaneous impressions, so that the attention had to note the place of the index at the moment when a whole group of things was happening. The single bell-stroke was always heard too early by von Tschisch—the displacement was invariably 'negative.' As the other simultaneous impressions were added, the displacement first became zero and finally positive, i.e. the impressions were connected with a position of the index that was too late. This retardation was greater when the simultaneous impressions were disparate (electric tactile stimuli on different places, simple touch-stimuli, different sounds) than when they were all of the same sort. The increment of retardation became relatively less with each additional impression, so that it is probable that six impressions would have given almost the same result as five, which was the maximum number used by Herr von T.
Wundt explains all these results by his previous observation that a reaction sometimes antedates the signal (see above, p. 411). The mind, he supposes, is so intent upon the bell-strokes that its 'apperception' keeps ripening periodically after each stroke in anticipation of the next. Its most natural rate of ripening may be faster or slower than the rate at which the strokes come. If faster, then it hears the stroke too early; if slower, it hears it too late. The position of the index on the scale, meanwhile, is noted at the moment, early or late, at which the bell-stroke is subjectively heard. Substituting several impressions for the single bell-stroke makes the ripening of the perception slower, and the index is seen too late. So, at least, do I understand the explanations which Herren Wundt and v. Tschisch give.[337]
This is all I have to say about the difficulty of having two discrepant concepts together, and about the number of things to which we can simultaneously attend.