A. COUNTING OF SIMPLE AND COMPLEX VISUAL OBJECTS

If every sensory stimulus has a motor reaction, then a simple figure perceived in any way ought to produce a somewhat different response from a more complex figure similarly perceived. Of course if only one figure of each kind is given it is difficult to measure in any way this difference, since it is so small. But we might make it measurable by multiplying the process. Therefore I have cut out a row of similar figures in a strip of cardboard and on another strip another series of a different pattern. Now if these rows are counted figure by figure each figure has a certain motor effect which influences the speed of counting, so that the time of counting (measured by the chronoscope) should give some indication of the comparative motor power of the figures in question.

In the accompanying illustration nine cards of various patterns are shown. Cards 1, 2, and 3 are comparatively simple patterns while 4, 5, and 6 are comparatively complex, Card 6 having the added complication of different kinds of figures on the same card. Cards 7, 8, and 9 form another group, Card 7 having the same letter throughout, Card 8 having letters composing a sentence and Card 9 a series of the letters, mostly consonants, mixed promiscuously. In order to prevent the subject from knowing the exact number, and thus, perhaps, bring in another influence at the end of the row, most of the different cards have different numbers of figures, but this difference is not great and some cards have the same number. The subject usually forgets, from one experiment to the next, the number on each card.

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.

FIG. 1

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.A.M.V.B.A.M.V.C.A.M.V.D.A.M.V.E.A.M.V.F.A.M.V.G.A.M.V.
1279.6911.47186.8713.22247.6214.89193.0812.38262.7720.20217.0012.32442.6336.51
2270.6012.47180.5511.88249.2118.00190.5111.82257.5616.03195.009.50431.0024.39
3274.439.87180.8911.57247.5915.51192.077.87259.9617.41191.5011.03434.8324.28
4286.8212.47190.3912.56255.2016.78200.5310.72267.1120.31226.4029.11445.7114.58
5290.2911.89195.4112.36262.2719.73199.899.27271.0620.86233.5020.46459.1718.92
6293.0612.21185.3311.51275.4018.13199.207.92264.5915.00220.8014.92432.1726.87
7273.3215.54192.2313.73229.2619.30185.609.83265.5619.20189.2030.31402.1321.34
8279.7713.86185.2312.69246.6618.86193.399.81277.5214.93220.7021.79388.7727.48
9285.0911.97197 0412.28269.9619.95186.309.05259.7214.27210.3411.71419.5718.22

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.