THE MOTOR POWER OF COMPLEXITY

At first the experiment was performed with the figures in a straight row, instead of in the broken line which is seen in the illustration. In counting the straight rows, the observers found it hard to keep the place in the line. A subject would become confused and count some spot twice or else he would omit it altogether. Furthermore this disturbance was found to be much greater with some figures than with others, with Card 1, for example, more than with Card 2. Therefore the device was adopted of diversifying the line, both by placing some of the figures above and some below the line and by making the distances from one figure to the next, different in the different cases. And in order to prevent the subject from associating any peculiar turn in the line with a certain number counted, it was decided to have the arrangement on the different cards different. But it was still necessary to have the intervals between figures about the same in all the cards, and therefore the row was divided into sections of six figures each and these sections were used as units, variously arranged, in constructing the other rows. For example the first unit of Card 3 is the same as the second of Card 4. Sometimes this six-figure unit is turned end for end or upside down, and thus, though the same spaces are used, the cards appear dissimilar.

The subject would be seated at the table with one hand resting lightly on the key which sets the chronoscope in motion, his eyes raised so that the table in front of him is not seen. One of the cards would then be put in the proper position in front of him (always the same), and he is told that all is ready. He looks down at the card and as soon as he begins to count the first figures in the line he presses the chronoscope key, and when he has reached the end of the line he releases the key. The time for the operation is then noted. The whole series of cards is thus gone through. An extra card of which no record is taken is used for the first few tests so that the subject may be in the proper state when the first test to be noted down is taken. Also the order of the series is changed from one experiment to the next, each card taking its turn at being first and last. It was hoped in this way to distribute among the different cards the effects of practice and fatigue, and also to guard against any expectations on the part of the subject as to the character of the next card.

The subject is told to count as fast as he can, with a reasonable feeling of certainty as to his correctness, the main object being to have a uniform principle, in counting the different series. Wrong counts were excluded, but later on the same cards given again so as to keep the tables even. Subjects were not allowed to count the figures by groups, but one by one. At first a certain amount of difficulty was found in the fact that subjects in counting would repeat the numbers to themselves, and as they seemed to be retarded by this, especially in those numbers whose corresponding names have 2 or 3 syllables, the result was that we were getting the speed with which subjects could count the numbers from 1 up to 38 or 39 and this would be practically the same whatever the figure. But all the subjects were finally trained merely to think the number, or at least to have as little vocal adjustment as possible. When this was done the subject no longer felt that it was the speed with which he could count that was being measured but the rate at which he could take in the different figures on the card, one at a time.

Between three and four hundred tests were made of the counting of the figures on the nine cards, the work being divided among seven subjects, though not in exactly equal amounts. Since the number of figures on the different cards are different, I have found the time it takes to count one figure by dividing the total time by the number of figures on a card. The following table shows the average time taken by each subject for one figure on each card, time given in thousandths of seconds. A.M.V. stands for average mean variation.

A, B, C, D, E, F, G are the different subjects, and 1, 2, 3, 4, etc., refer to the cards with the different patterns. It is seen at a glance that great differences exist between the rates with which the different subjects count. Subject G had much fewer tests than the others, and thus, not having as much training, his average is higher in comparison than it would be had he had the same training.

Now if we compare the counting of the first three or relatively simple patterns with that of the next three or comparatively complex ones, we notice at once that the simple figures are almost invariably counted in less time than the complex, there being only two exceptions. B counts 6 a little faster than 1, and G counts 6 faster than 1 and 3. Even these apparent exceptions are easily explained. As noted already, subjects are much more apt to lose their place in counting certain cards than others. This is especially true of Card 1 even after the line is broken. Now Card 6 is arranged on a different plan from the others, for it has many kinds of figures on it. This is a great help in keeping one's proper place in the counting of the series, and since wavering between two figures is avoided, the series is counted more rapidly. But B is the most rapid in counting, of all the subjects, and it is natural that any differences in the ease of keeping place should show themselves here, since the more rapid the counting the easier it is to lose the proper position. This cannot be said of G, who is a slow counter, but on the other hand it may be noted that he had only a few cases, and at first the ability to keep one's position is much less than after considerable experience. So in Cards 6 and 1 there are two conflicting principles, degree of complexity and tendency toward confusion of position. Of course both these principles are present in all the other cards, but they reach a maximum in 1 and 6, in 1 extreme simplicity with difficulty in keeping place, in 6 extreme complexity with ease in keeping place. Card 1, it will be seen, is with nearly all subjects a little slower than 2 and 3, while 6 is generally faster than 4 and 5.

Therefore it would seem that the apparently small exceptions are not real exceptions, but variations due to the presence of other factors than mere differences in complexity of the figures used. In observing the averages for 7, 8, and 9 we see that as a rule 7 is fastest, 8 next, and 9 the slowest. The tables are not quite so regular as for the cards just given. B and G count 8 faster than 7, and E counts 9 faster than 7. The most of these cards have on them 36, 37, 38, or 39 figures. Card 8 has 43 letters. The subjects report that the last three on this card are counted much faster. They know, as soon as they reach 40, just how many there are, and it is hard to keep from counting the rest in a group. Otherwise they do not feel any difference in counting Cards 8 and 9. Arranging the letters in words does not affect the speed of counting, so far as they can see, for in counting they do not notice the words at all.

When we average the records of all the subjects giving equal weight to each subject, though the number of tests may be different with the different men, we get the following table. Time given in thousandths of seconds.

(1) 261.38
(2) 253.49
(3) 254.54
(4) 267.46
(5) 273.08
(6) 267.22
(7) 248.19
(8) 256.01
(9) 261.15

It is seen, from looking at this table, that all divergences from the general rule have stopped. Cards 1, 2, and 3 each take less time than any of the 4, 5, 6 group, and 7 is faster than 8 and 9. So the evidence seems very strong that it takes longer to count complex than simple figures. Should one object that the difference is extremely small, a few thousandths of a second, and that thus a slight error in one test might invalidate the result, we reply that the time which is given is the time in which we count just one figure of the given pattern, and that thus of course the difference between counting two different figures must be very small. Moreover there has been a remarkable agreement of the tests taken at different times. It is not a case of finding 1, 2, and 3 counted faster one day and 4, 5, and 6 counted faster the next, but 1, 2, and 3 are counted faster nearly every time. Occasionally 1 will take longer than one of the 4, 5, 6 group. And extremely seldom is there a case where the average of 1, 2, and 3 is not less than that of 4, 5, and 6.

The experiment seems to have proven that it takes a longer time to count a row of complex figures than a similar row of simple figures. The complex figure exercises a retarding effect upon the eye as it sweeps along. There is a greater amount of sensory stimulation, consequently a greater amount of motor excitement. This motor excitement does not act in harmony with the motor activity which impels the eyes along, but has a somewhat antagonistic effect. The eye is held more by the complex figure; it is a greater effort to withdraw the gaze to look at the next figure. A certain interest, as we say, on the psychological side tends to hold one to the figure looked at. This interest is greater (other things being equal) the greater the complexity of the figure. The nervous processes involved in counting, though admittedly in very small degree, are thus inhibited by the complexity of the figure and act more slowly.

B. REACTIONS TO SIMPLE AND COMPLEX OPTICAL IMPRESSIONS

Since the preceding experiments seem to show that reactions on optical impressions are different according as the figures are more or less complex, it would seem that we ought to be able to measure by graphic methods the reactions to visual fields of varying grades of complexity and in this way to demonstrate their different motor powers.

A Porter kymograph was used on which to register the reactions. Resting on the top of the drum, and revolving with it, was a circular band of white paper, upon which were pasted the different figures to be observed. A screen was placed in front of the kymograph, thus concealing the figures; but at their level was a little square window in the screen, which, when the eye was placed in the proper position, allowed the subject to see one of the figures but nothing more. A few inches in front of this window was an eye-rest which kept the eye properly placed. A tambour received the movement from the subject and communicated it to a straw which made a scratch on the smoked paper which covered the drum.

The figures used in this experiment form two series, one, composed of geometrical figures, varying in complexity from a circle to a very complex figure consisting of many overlapping squares, triangles, etc., and the other composed of colored figures varying in complexity from a simple square of one color to a very complex mixture of various colors. The area of the visual field is about the same in all cases,—an inch square. The geometrical figures were formed of black lines on a white background. The figures used are shown in the accompanying illustrations.

The subject would be seated in front of the screen, his eye at the eye-rest a few inches in front of the window in the screen, and the forefinger of the right hand on the tambour, which is to the right of and behind the screen, and thus not seen while the eye is at the rest. Then as the drum revolves and brings a figure in front of the window, the subject observes this figure carefully, and when it is all in the field of vision he presses down with his forefinger, thus producing a curve on the drum surface. He tries to make the same finger-movement every time, whatever the figure at the window may be. But his attention is not to be too much taken up with the making of the movement, for he must be closely observing the figure. If he looks at the figure until he observes its characteristics clearly and then turns his attention from this to the finger-movement, it is evident that the optical sensation would not have much effect upon the movement. The movement must be performed while his interest in the figure is highest. Now, after a little practice, any one can accustom himself to make a certain definite movement in about the same way every time, and he can then agree that he shall make this movement as a reaction to a given stimulation. Then when the stimulus comes he makes the movement without any longer thinking of the character of the movement. It has become, to a certain extent, automatic and can look out for itself.

This is the state into which I have tried to get my subjects. Their whole attention is to be taken up with the seeing of the figures in the window, and to these figures they are to react as automatically as possible. Thus, though finger-movements are usually voluntary, all the capricious character of voluntary action will be removed here, and if the stimulus is the same in all cases, the reaction tends to assume the form of a uniform movement. There is, then, a chance to see the influence of different optical stimuli upon this action.

Six different geometrical figures were seen at each revolution of the drum and six reactions given by the subject. Between figures a white surface would occupy the field of vision. The simple and complex figures were distributed so that the subject never knew what kind of a figure would come next. The purpose of the experiment was kept as much as possible from the knowledge of the subjects; but some, knowing my general problem, surmised quite correctly my main object here.

Ten revolutions were made at each sitting, thus causing the subject to react ten times to each figure. Then a new drum paper was taken and the case with the colored figures placed upon it. This had five colored figures, and ten revolutions were made also in this case. Thus, in all, in any one day, the subject would make one hundred and ten of these finger-movements.

Since we have in all these experiments tried to find out in the different figures merely differences in the amount of the reaction, and not differences in the character of the reaction, we shall keep up this method here. Now a stronger reaction makes a higher curve, and since the drum is all the while revolving, and since the higher the curve, other things being equal, the longer it takes, the stronger reaction will also make a wider curve. So it would seem that if we wish to observe the differences in the amounts of reaction the most natural course to pursue would be to measure the heights and widths of the curves we have registered. This accordingly has been done.

In our discussion of these measurements let us, then, first, take up the curve heights, and of these, those of the geometrical figures which we call U, V, W, X, Y, Z. The height is measured from a base-line [drawn by revolving the drum after the subject has taken his finger from the tambour] to the highest point reached. These measurements are taken from two hundred reactions to each figure, divided among seven different subjects.

If we put the figures in the order of strongest reaction for the different subjects we get the following table:

It is seen from these results that, although the subjects differ, the height of the curve varies directly with the complexity of the figure. The order of the figures, which we get by measuring the height of the curves and then putting that figure with the highest curve first, with the next highest second, and so on, is exactly the same order in which we should put them if we were asked to put the most complex first, the next second, and so on. Though the individual subjects may vary somewhat from this rule, when they are all grouped together there are no exceptions.

The variations of the reactions with the different subjects may be shown very clearly in the following way, where the different figures are in the left-hand side arranged in order of descending complexity. "1st place," etc., refer to the order of arrangement of the figures by the different subjects as shown in preceding tables. Thus, Z, 3 times, 1st place, means that three subjects have in the average a higher curve for Z than for any other figure.

One can see at a glance from this, how, as the figures decrease in complexity, they take their position further on in the series. If a diagonal is drawn from the upper left-hand corner to the lower right, it will pass through or near the larger numbers in the table, thus showing that the figures belong in the ordered series in the places already shown.

Next in order let us take up the measurements of the widths of curves for the same geometrical figures which we have been considering.

If as before we take the orders for the different subjects, we get the following table:

Here, as before, in the case of the heights, it is seen that though the order is different with the different subjects, yet the general tendency is to place the most complex figures first and the simplest last. The most simple figure Y never comes in front of the fifth place except with subject C, who places it first. This exception may be ascribed to the fact that this subject, on account of his going away, did not have so many tests. In fact only one day's work of 10 reactions for each figure is recorded, and it is but natural that some variations from the standard should occur in his case.

If now, as before, we investigate where each figure occurs in the series for the different subjects we get the following table:

Here we again see the large numbers on a line from the upper left-hand to the lower right-hand corner.

Thus we get the following order from the geometrical figures as measured by the height and width of the curves:

The only difference, it is seen, is that the positions of V and X are reversed in the two series. Such a change would on our principle be fairly likely to occur, since V and X are figures near to each other in complexity and the motor effects are very similar.

In the same manner, the following tables show the reactions to the colored figures of different grades of complexity. And first, as before, is the table of the heights of the curves for the different subjects, given in millimetres. The numbers given represent the averages of all reactions made. We will call the figures, for the sake of reference, L, M, N, O, P.

Order arranged as before in a descending series according to height of curve:

This is exactly, as I should judge, the order of the complexity of the figures reacted to.

The arrangement by the individual subjects is as follows:

We see that individual differences are stronger here than in the geometrical figures, but that the same tendency to react more strongly to the complex is present in nearly every case. This can be brought to the eye more clearly if we observe the table in which is shown the position of the different figures in the series of the different subjects.

M here presents the principal exception, coming too often in the first place.

Finally we give the tables for the widths of the curves for the colored figures; and first the table of the averages of all the subjects for all the figures:

Order, arranged in a descending series according to width of curve:

Here the order is not just the same as we got from a measurement of the heights. The three complex figures have changed places somewhat, but there is no exchange of a simple and a complex.

The arrangements by the individual subjects are as follows: