# Popular Science Monthly/Volume 11/September 1877/Does it Take Time to Think?

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* DOES IT TAKE TIME TO THINK?
SOME MEASUREMENTS OF THE PERSONAL EQUATION.
By T. F. BROWNELL.
MASKELYNE, the Royal Astronomer of England, in August, 1795, had his attention called to the fact that his assistant, Mr. Kinnebrook, was making errors in recording observations. He noticed that Mr. Kinnebrook had fallen into the habit of making his records half a second later than they should be. In the following year this fault was found to have increased. All of Mr, Kinnebrook's observations were recorded as about four-fifths of a second too late. The assistant was a trained and skilled observer of long experience, but, although the fault was pointed out to him, and realized by him, it appeared impossible for him to overcome it. The same error still appeared in all his work. The two astronomers, it must be remarked, were working together observing and noting the same events, such as the transits of the same stars across hair-lines placed in the fields of vision of their telescopes or transit-instruments. After observing side by side a large number of events, and recording the times as accurately as they could to the second and fraction of a second in each case, it was found by a comparison of results that the events were almost invariably recorded by Mr. ​Kinnebrook as having taken place four-fifths of a second later than the time observed and noted by Maskelyne. All attempts by Mr. Kinnebrook to account for or to remedy what he deemed his fault were in vain. At last Maskelyne, assuming that his own observations were correct, and that the habit of his assistant arose from some defect difficult to explain, felt obliged to discharge him as incompetent for the special class of work in which he had been long engaged. At the present day astronomers, with better knowledge of the degree to which the personal element enters into all work, and especially into a class of labor so difficult as that of recording fractions of a second or hundredths of an inch, are accustomed to place as much reliance upon the observations of Mr. Kinnebrook as upon those made by the royal astronomer himself. The constant difference in the result is explained, not by the assumption of incompetency on the part of one of these astronomers, and of complete accuracy on that of the other, but by reference to what is known as the relative personal equation of the two men. It is not supposed that the records made by either of them are absolutely correct. Beyond a doubt there is in the records of each a small and constant error arising from personal characteristics. There is no reason to suppose that the amount of this error was larger with Mr. Kinnebrook than with Maskelyne. The absolute personal equation, as the error is called, is as likely to appear in the observations of one as in those of the other. The error of four-fifths of a second, which invariably appeared, does not represent a difference from the exact truth, but the constant difference between the amount of error habitual to one of these observers and the amount of error habitual to the other. But, as we do not know the personal equation of either, in this, which is the first recorded case of the kind, we can never know where the truth actually was.
By this and similar cases the attention of scientific men was called to the effect of personal characteristics in classes of work similar to that of the astronomical observatory. Examination showed that these characteristics are a constant cause of error. By numerous experiments it appeared that one who observes and records an occurrence always gives a result which differs from the exact truth. Even where the observer was trained and skilled in observing events like those in the experiment, the rule was the same. He recorded the time too early or too late. The error would appear in each experiment, and always to the same amount. If the record was too late in one, it invariably was too late. This habitual difference between the time as noted by an observer and the actual time of the happening of the occurrence is what has been termed the absolute personal equation of that observer. It represents the amount of error which he will always make. It has been found to differ with different persons for the same class of events. It also differs in the same person for events of different classes. The time required to observe and ​record the happening of a sudden and unexpected spark, for instance, is always greater than that required in the case of the expected appearance of a letter or figure thrown upon a screen. The equation also differs according as the facts are observed by the use of one of the senses or of another. The time required for some of the senses to convey intelligence to us is far greater than that required by others.
In making astronomical observations the equation requiring attention is that relating to the sense of sight. Being the value of an habitual error, it invalidates all observations, since the record of each observer is incorrect in a certain constant amount. It is, therefore, necessary to obtain the personal equation of the observer, and to add or subtract this from the results which he notes, in order to know the true time of the occurrence recorded by him. This can easily be done. To obtain the equation for observation of the transits of stars, for instance, the method is quite simple. A luminous point similar to a star is made to move with uniform velocity in a circle, and to pass across the field of a telescope. The exact time the point is upon the hair-line which divides the field of view is correctly recorded by mechanism which stops a chronometer. The observer watches the luminous point, and as soon as he sees it upon the line presses a button which stops a second chronometer. The difference between the times indicated by the two chronometers gives the personal equation of the observer for the transits of stars, recorded by pressing a button. Its amount will be very small. When the time is taken by glancing at a clock and then noting, the equation of almost all observers is so large as to demand a correction.
Since personal characteristics are the cause of a constant error, it follows that two observers of equal skill, using instruments of equal accuracy in observing and recording a large number of occurrences, will always differ from each other in the results obtained, and in an amount that will always be the same. This constant difference between the results given by two observers is called their relative personal equation. The four-fifths of a second between the records of Mr. Kinnebrook and Maskelyne was the value of such an equation. It is the sum or the difference of the amounts of error habitual to each. Its value may be found by experiment, or by adding together the absolute equations of each, or by subtracting one from the other in case the tendencies to error are in the same direction.
An interesting example of a personal equation was the ground of a serious criticism made about a year ago upon the trustworthiness of the observations made at Greenwich. In timing the class of observations which were criticised, the record was kept at the observatory in seconds and tenths of a second. The first record was made at the time of the observations by dots or punctures made in a tape running over a drum, the spaces between the dots representing ​corresponding lengths of time. The tape was prepared for use by being marked off by printed dots, about a third of an inch apart, into spaces representing seconds. The permanent record was prepared subsequently by reading off the results noted upon the tape. To read off the whole seconds was of course a simple matter of enumeration of spaces representing seconds. The fractious of a second, however, it was customary to estimate in tenths of a second. The estimation was made upon the position of one sharply-marked dot as referred to two other well-defined dots, one on each side of it, indicating the beginning and the end of a second, and separated about a third of an inch. It was done by inspection of the tape, by highly-trained and experienced men, to whom it had been a daily work for years. Such being the methods, an astronomer connected with another observatory selected at random from the reports of the Greenwich Observatory a large number of records, and caused the number of times each fraction of a second occurred to be counted. Theoretically, there is no reason why one fraction should appear more often than another. An examination of over 1,200 instances, however, showed that certain fractions appeared much more frequently than they theoretically should. The figure 4 or 410, and the figure 0 or 010, were found too often. Upon this fact was founded a criticism upon the accuracy of the reports. It was claimed that the frequency of these fractions was occasioned by personal characteristics in the person who estimated the fraction; and it was assumed that such were the idiosyncrasies of even the most highly-trained persons, that in making such estimations they would unconsciously tend to use certain figures rather than others; in this case it was argued that the tendency causing error was to make the record four-tenths for most fractions between threetenths and five-tenths, and where the dot was near the end of a second to record the time as a whole second. This criticism was offered in a dignified and serious way in a prominent scientific journal, and was as earnestly replied to and discussed by the observers at Greenwich in the same journal.
This example of the personal equation is quite different from that which was first briefly described. The value of the equation in this case it is impossible for us to formulate with accuracy in the present state of our knowledge. In examples like the first, the factors can be more readily observed, analyzed, and measured. The difference which appeared in the case of Maskelyne and Mr. Kinnebrook arose, without doubt, from the fact that nervous and mental actions require time for their accomplishment, and because the rate of nervous transmission and mental action in one of these observers constantly differed from that in the other. The problem of the personal equation in this aspect becomes one of physiology and psychology. As such it has been investigated with great research by specialists during the past twenty years. And, although the results obtained are in most cases only ​approximately true, the various experiments that have been made are not without some curious interest.
It is well known that the operations of the nervous system require time. The action of the different senses is not instantaneous; there is always an interval of time after a foreign body touches our skin before we know that it touches us. So also between the mental decision to make a movement and its actual execution there is a real though short interval.
Where upon sight of a star a button is to be pressed, there is, first, the action of the sense of sight which gives us knowledge of the existence of the star; and, second, action of the will causing pressure of the button. In fact, the physiological and psychical action, in all cases where excitation is followed by the giving of a signal, may be divided into six separate and successive actions. The sensation may be divided into three distinct acts. In the example supposed there is, first, the reception of the image of the star upon the retina; second, the transmission of the stimulus through the nerve from the eye to the brain; and, third, the mental perception of the existence of the star. The voluntary movement which causes the signal may also be divided into three acts. There is, first, the act of the will by which it is determined to press the button; second, the transmission of the impulse through the nerves from the brain to the hand; and, third, the excitement of the muscular fibres by which the finger is bent and the button pressed. The entire interval between the excitation and the giving of the signal, during which these six acts occur in succession, has been called the physiological time. It is really the same in amount, in most cases, with the personal equation. That portion of it which is occupied with the purely mental acts of perceiving the signal and determining the signal is called the psychical time. It is the time required to think.
Attempts have been made to measure each of these six factors, and interesting results have been obtained, though of various degrees of accuracy and trustworthiness.
The earliest experiments were made with reference to the rapidity of movement through the nerves. The first attempt to measure the velocity of nervous impulses proceeding from the brain under action of the will was made long ago by Haller. He ascertained, by reading aloud with great rapidity extracts from the "Æneid," the average number of letters which he could pronounce in one minute. Then he calculated the length of the nerve from the brain to the muscles of the tongue and mouth. Each letter he regarded as requiring a nervous impulse. He was obliged then only to multiply the number of letters spoken in each minute by the length of the nerve. This gave as a result that the rate of nervous transmission from the brain was about 150 feet a second. This experiment was defective in failing to take into account the facts that both the act of willing and that of ​muscular contraction require time. Had these been considered, the solution would have been farther from the truth than it really was. Recent investigations of more precision have not, however, given results that differ widely from that obtained by Haller. The rate as given by Helmholtz, after many experiments, is about 111 feet per second. This is now generally accepted as the most accurate statement. Slight differences in results for movements from the brain, and for those proceeding to it, have been obtained in the investigations, but the rate is regarded by the best authorities as essentially the same for both movements. If there be a difference, it arises because the rate of voluntary impulses moving from the brain outward is the more rapid of the two.
A difference also has been found to exist in the rapidity with which we perceive impressions received through the eye, and those received through the ear. This at one time was supposed to be caused by a difference in the rate of transmission in the respective nerves. The better authority now is that the disparity is occasioned either by difference of length of the two nerves, or because the mind does not so readily distinguish impressions of one kind as those of the other.
If these data are correct, it requires at least one-twelfth of a second for us to perceive a sensation in our foot. A mosquito which selects our ankle as the field of his operations has nearly a sixth of a second in which to make his escape, for it requires at least one twelfth of a second for us to find out that the mosquito is there, and another twelfth of a second for us to make up our mind to declare war upon him and to initiate hostile action.
It will be observed that the rate of nervous transmission is comparatively slow. Electricity travels at the fate of many thousand miles a second, or, more accurately, 16,000,000 times as fast as nervous action. Light moves about two-thirds as fast as electricity. If we examine movements which are comparatively sluggish, we find that a cannon-ball, when fired, moves about 900 feet a second, or nearly ten times as fast as nervous energy. A railroad-train speeding along at sixty miles an hour would be moving at about the same rate as an ordinary nervous stimulus, though in a contest the stimulus would probably win.
By further experiment it has been determined that the time required for the excitation of the muscular fibres for such acts as the supposed pressing of the button, this being the factor last in order of the entire six, is about one-hundredth of a second.
It is also declared with some precision, both by analogy to this last act and by experiment, that the time required for the reception of the impression by the sensitive membrane, which is the first and a corresponding factor of the complete physiological time, is also about one-hundredth of a second.
​There are now left undetermined only two of the factors. These are the time required for the two purely mental acts: first, of perceiving the sensation; and, second, of willing the movement which immediately follows. These two make up the psychical time. It may be obtained by first learning the entire physiological time, and then subtracting from that the value of the four known factors, the determination of which has been given. This would leave the period required for the purely mental operations of distinguishing and willing.
For the purpose of learning the physiological time for events of different orders, a large number of carefully-prepared experiments have been made by different investigators. Though the results arrived at lack much in accuracy and completeness, they are highly interesting and instructive.
For experiments relating to sight the arrangement is usually of the following nature: The patient is seated before a screen, upon which certain letters or numbers can be thrown, or before glass globes, which can be suddenly illumined by an electric spark. Upon seeing the number, letter, or illumination, as the case may be, the patient immediately gives a signal by some slight movement of the hand or foot. Nice arrangements are provided, by which both the event and the signal register themselves, giving the time exact to the thousandth of a second.
The general result of many experiments is, that the time required for ordinary persons to distinguish an appearance and to give the signal amounts to about one-fifth of a second. Exactly speaking, in the experiments of one scientist, the time required was found to be .188 of a second. In trials made by three other investigators the results have been .200, .205, and .194 of a second respectively. None of these conclusions varies much from one-fifth of a second. A comparison has also been made between cases where the event was an electric spark and others where the event was the passage of a luminous point across a line, the signal being the same in each experiment. According to one series of trials, it was found that the time required in the former case was .200 of a second and in the latter only .077 of a second. In other words, the perception and signaling of the former occupied three times as much time as in the case of the latter.
In experiments with the sense of hearing, the arrangements are generally of the same nature. The event is usually the sound of a bell or note, or of a spoken letter or number. For this sense the physiological time has been calculated to be about one-sixth of a second. Four investigators give .148, .1505, .180, and .182 of a second, as the exact results of their experiments. It will be noticed that the physiological time for the sense of hearing is shorter than for that of sight. We hear more quickly than we see.
​For the sense of touch there is a discrepancy in the results thus far given by different investigators. According to the best authority, it appears that the physiological time in this case is about one-seventh of a second, and less than that of sight or hearing. Some, however, make it somewhat larger than this, and place it midway between those of sight and hearing.
Having thus found the entire physiological time by many carefully-prepared experiments, and having previously obtained, as has been briefly pointed out, the value of four of its factors, the value of the remaining two can be readily obtained by subtracting. We should then have the time necessarily employed in purely mental acts of distinguishing or recognizing an event and willing the signal.
One careful investigator, after experiments in which the event was the sounding of a bell, and the signal was made by pressing with the foot, tabulates the result with the following precision:
| Time occupied (in seconds) by the mechanism of hearing the bell | .010 |
| By the act of perception of the sound and of willing the signal | .112 |
| By the transmission of nervous impulse through the spinal cord and nerve of the leg to the foot | .088 |
| By the mechanism of muscular contraction in moving slightly the foot | .010 |
| Total physiological time | .220 |
This is only slightly more than one-fifth of a second.
The two mental operations, it will be perceived, occupy somewhat more time than is required for the transmission of the impulse to the foot, and a little more than one-half of the entire time.
In all the tests thus far given the operation of the mind is as simple as possible. The terms of the problem are reduced to their lowest forms. Upon the simplest kind of a perception, and that expected, the patient is required to exercise his volition in the simplest way. There is no necessity of making comparison between two or more sensations, or of deciding between two or more courses of action.
But in the following experiment the mental acts required were more complex. The patient, upon receiving a slight shock given to the right foot, was to give the signal by moving the right hand, and upon receiving the shock in his left foot he was to give the signal with his left hand. He was left in ignorance upon which foot the shock was to come. It was found that under these circumstances the physiological time was prolonged one-fifteenth of a second beyond the corresponding time where the patient was informed which foot was to receive the shock. In the latter case there was no need of reflection, but in the former he was obliged first to decide which foot was touched, and then to decide upon the corresponding signal. One-fifteenth of a second represented the time required for these acts of the mind.
A similar test was made for the sense of sight. For a red light ​the signal was to be given with the right hand, for a white light with the left hand. In this case the mental action of deciding these alternatives and coördinating the corresponding act of volition required no less than .154, or nearly one-seventh of a second.
Other experiments have been made with the sense of sight, where the patient was instructed to give the signal by pronouncing the name of a vowel which was shown to him. If he had to distinguish between two vowels, the psychical time was prolonged .166 of a second beyond what it would have been for one vowel. If he was required to name one out of five, the prolongation was increased to .170 of a second.
Similar experiments with the sense of hearing, where the vowel was spoken to the patient and repeated by him, gave similar results. Where two vowels were selected from the mind occupied .056, and where five were used .086 of a second longer than if only one expected vowel were spoken.
Where two colors were shown, and the signal was given by a movement of the hand, or by the voice, the physiological time for the movement of the hand was found to be always greater than for the voice.
When the signal was the pronouncing of a vowel, as "i," the time required was less than when the patient was obliged to speak the vowel with a consonant before it, as "pi," or "ki," or "ti." The letter "p" was found to retard the patient .011 of a second, "t" twice as long, or .022 of a second, and "k" .021 of a second. A further result of these curious investigations was that the patient required three times as long to distinguish between two letters which were shown upon a screen as to distinguish between the two corresponding vowels when spoken.
In all these investigations the psychical time is made up of two periods: the first required by the mind to perceive the sensation or to distinguish the alternative, the second required for the mental act of willing the signal. An attempt has been made to measure each of these. The experiment for this purpose was so arranged that the patient was to hear several vowels, but was directed to give the signal only upon hearing a certain one of them. Under this arrangement the patient concentrated his attention upon the perception of the vowel at hearing which he was to act. He prepared himself, as far as could be, to pronounce it the moment he heard it. Before he heard it he willed to speak it on the instant that he should perceive it. There remained only the act of recognizing the vowel when it should be spoken, of distinguishing it among the other vowels. The act of volition was in this way eliminated from the physiological time, and the simplest mental act of distinguishing was calculated from the result. This result, based upon this and similar experiments, was that the mental act of distinguishing required about one twenty-third of a second of time. The whole psychical time being about one-twelfth ​of a second, the time required in ordinary cases for the remaining act of willing was easily calculated to be about one twenty-eighth of a second. If these investigations can be regarded as entirely trustworthy, they tend to show that the mind perceives somewhat more slowly than it wills.
Of the personal equation, in its widest sense, there are many examples even more suggestive and worthy of extended treatment than these which have received mathematical measurement. These examples are to be found in all human action, and in the result of all human work. Noticeably is this true in all acts and occupations which have their basis and lowest forms in acts of imitation. None the less is it true in those higher forms of art and action where close imitation is less desired than the interpretation of some pervading spirit, or the representation of some underlying essential. In the acts of painting a landscape, of copying a picture, of interpreting a symphony, of reading a poem, of acting a play, of following an argument, or in any of the common or artistic acts of men, be they mental or physical, the personal equation of the actor enters as a perceptible element in the result. The discussion of the nature and value of the personal equation where it appears in forms so subtile as in the cases last mentioned would furnish many considerations of interest and instruction, but to undertake the treatment of these forms is beyond our present purpose or opportunity.