4. Mental Fatigue

[ABAI, Tsuru, "Mental Fatigue," New York Teachers College, Columbia University Contributions to Education, No. 54, 1912. Interpolations by THORNDIKE as found in his Educational Psychology, Vol. III, pp. 14-20. New York, Teachers College, Columbia University, 1914.]

The experiment described below was conducted with a single individual. It is a good sample for intensive study, for it has the special merit of measuring the effect of continuous exercise of a very difficult intellectual process, as free as possible from sensory or muscular work, at a stage when it was almost free from improvement by practice, over a very long period, and on four different occasions.

The first experiment was made during February and March, 1909, at Teachers College, Columbia University. The purpose of the experiment was to ascertain: (1) the amount, rate and change of the rate of fatigue in the special mental function exercised, and (2) the amount of fatigue transferred to certain other functions.

The particular function tested, was that exercised in mental multiplication of pairs of numbers like

About one thousand different combinations of figures were used. The order of the examples being made by chance, the distribution of difficult and easy examples is random. The subject of the experiment was the writer herself. . . . On February 2nd the subject made the first test in the following manner: Using an ordinary watch, the subject set a time for starting. When the hand of the watch reached the point set, the subject looked at the first example and multiplied mentally but with the original numbers in sight. The answer was written down as soon as it was obtained and the time recorded. Then the subject immediately took up the second example and repeated the same procedure. Thus she worked from 9:30 A.M. to 3:18 P.M. with a rest of forty-eight minutes for luncheon, and obtained the answers of twenty-four examples (Arai, p. 31f).

On February 4th, twenty-six such examples were done in the same manner; on February 7th, twelve; on February 15th, thirty; and on February 22nd, sixty. From the seven hours' continuous work of February 22nd, it was clear that the subject

could not, by even this long period of work, be brought to a condition of inability to do the work. The work was consequently made still more difficult, as follows:

Instead of multiplying with the original figures in sight, the subject relied on memory for the figures and multiplied them mentally with closed eyes. The method was better than the earlier one, for it not only made the task more difficult, but it helped to eliminate sensory fatigue. When the subject forgot the original figures, she looked at them again, but as the time was made longer on this account, the loss of the original figures was counted against her. But this seldom occurred as the subject was careful to commit the numbers to memory (Arai, p. 35).

Her work was to look at an example such as

4962
7584

cover it,

memorize the two numbers, then multiply mentally 4 by 4962, getting 19848, then memorize this, but keeping in mind the 4962 and the 758 to be used later, then to multiply mentally 4962 by 8, getting 39696, and perform mentally the operation of 19848

adding 396960.

Having obtained the 416808,1 she could now forget the 19848, but must not have let slip the 4962 and 75, and must remember the 416808. She then multiplied 4962 by 5, and remembered to count the 24810 as 2481000 in adding it to 416808. Having obtained 2897808, she could now forget all but it and the 4962 and 7, and the fact that the 7 counted as 7000 in multiplying. Multiplying mentally and obtaining 34734, she held it in mind and added 34734000 to 2897808, and could then write down the answer 37,631,808, look at her watch, record the time, look at the next example on the sheet, say 7267

and proceed as above.

9653

If the reader will try this work the far easier task of multiplying four-place by three-place numbers for even only an hour or two, he will appreciate that it is far more difficult and fatiguing (in the popular sense of requiring much disagreeable effort) than all but a few of life's customary intellectual labors.

1 There were only three examples in the 17th set. The score was adjusted to be what would have been for four examples done at the same speed and accuracy.

After doing 189 examples requiring about thirty-five hours (during the week February 24th to March 2nd) by this new method, the subject reached a point where practice effect was very slight, and secured in the next four days the record to be considered here.

On March 3rd, 4th, 5th, and 6th, the subject did the mental multiplication from 11 A.M. to 11 P.M. without any pauses except the two or three seconds between the examples for recording time. But the subject had taken a heavier breakfast than usual at 10 A.M. and a light supper after 11 P.M. Her health was in good condition and she slept soundly at night. The contents of her consciousness during the experiments were very simple, all desires being completely subjected to the one desire to get true fatigue curves (Arai, p. 37).

The results of these experiments are summarized in Table I and Figure 18. The base line of Figure 18 is scaled for the number of examples done, one inch equaling forty examples, each twelve hours of rest being denoted by a quarter inch vertical line at the appropriate point on the base line.

FIG. 18. CURVE OF WORK IN MENTAL MULTIPLICATION WITH FOUR-PLACE NUMBERS.

Above each tenth of an inch along the base line a horizontal line is drawn whose height in each case denotes the time required for the four examples in question, plus an addition for each wrong figure more than two in any answer, and a subtraction for each wrong figure less than two in any answer, of three per cent of the time required for the four examples (that is, twelve per cent of the time required per example).

TABLE I-AMOUNT OF FATIGUE IN THE CASE OF MENTAL MULTIPLICATION FOUR-PLACE NUMBERS, Measured BY TIME REQUIRED (IN MINUTES), WITH ALLOWANCES FOR ERRORS, FOR SUCCESSIVE SETS OF FOUR EXAMPLES MULTIPLIED MENTALLY.*

The Amount of Fatigue.-The amount of fatigue is measurable by the increase in time required (here and through the discussion of Miss Arai's experiment "time required" means "time required for work of equal accuracy") as work continues -an allowance being made for practice, or by the increase of time required at the end of work over that required at the beginning of work after full rest. Fatigue then is shown (1) by an average increase of time for the last eight over the first eight examples on days 1, 2, 3 and 4 of 119 per cent, plus whatever correction should be applied for the practice gain, using only days 1, 2 and 3, the percentage is 135. The practice gain may be estimated by the change from day to day, especially in the first hour of the work. There was, on account of the large amount of preliminary practice, little or no practice effect observable within these four days, the times required for the first sixteen examples on successive days being 96, 95, 90 and 98 minutes; and for the first eight examples, 47, 45, 36 and 46.

Or fatigue is shown (2) by an average increase of the time required for the last eight examples of days 1, 2 and 3 over the first eight examples of days 2, 3 and 4, of 136 per cent. This figure would probably be lowered if a comparison of the last eight examples of day 4 with the eight done twelve hours later after rest could be included. There was least decrease in efficiency on the fourth day.

This, it must be remembered, by no means implies that the function was less than half as efficient at the end of the twelve hours of work as at the end of twelve hours of rest. On the contrary, the amount of percentile loss in absolute efficiency was probably very slight. For a person to be able to multiply a number like 9263 by one like 5748 without any visual, written or spoken aids, even in fifteen, or for that matter in a hundred and fifty, minutes, implies a very high degree of efficiency. That a person can exert himself to the utmost at this very difficult work for ten or twelve hours without rest and still be able to do it, even if at the expense of twice or thrice as many minutes per example as at the beginning, means that the loss in efficiency by any absolute standard has been small. For Shakespeare to have required twice as long to write "Hamlet" as he actually did require would not have meant a loss of half the efficiency of the play-writing function! For Napoleon to have taken twenty minutes instead of five to plan a series of moves at Austerlitz would not have meant that his generalship was only one-fourth as efficient!

The zero point of efficiency in the function of mental multiplication would be "just not to multiply a number like 3 by a number like 2 in, say, ten minutes." We do not, of course, know just at what point between this zero and the ability to multiply a four-place by a four-place number mentally in five minutes with only two figures in the answer wrong (as Miss Arai did at the beginning of work), we should place her ability, at the end of work, to multiply a four-place by a four-place number in eleven minutes. The reader may judge for himself. It is my impression that she could, at the end of work, certainly have multiplied a three-place by a three-place number (and probably a four-place by a three-place number) as quickly and accurately as she had multiplied a four-place by a four-place number at the beginning, and that it would be absurd to place the efficiency of her last half hour's work in each period at less than 75 per cent of the initial efficiency.