Time-difference in consciousness is the very simplest thing in mental life, for it is a case of the bare awareness of change. The elementary time-judgment is mere judgment of change in content of consciousness. In the experiment where one is asked to say which of two expected stimuli comes first, however, the case is already complicated. There must be a double preparation to react and to note the change characteristic of each case, and so convert it into a time-judgment. In the combination of two judgments, there is the same double expectancy, preparation to react in two ways at once. In each experiment, the preparation and shaping of expectation is the same as in reaction experiments. In all reaction work, the short reaction comes as the result of catching the attention wave at its most favorable point. If the signal to react catches the idea of reaction in the mind of the observer at the very focal point in consciousness, the shortest reaction possible under the given conditions results. So in both the combination experiment and the interval discrimination experiment, it is very necessary to catch the attention wave, equally prepared for both or all the processes, and at the highest crest of advancement. Both demand the same preparation as a compound reaction. I believe it is this inequality of balance of the attention between the various processes that is responsible for the interference which is evidenced in my results. This is my explanation of the appearance of impaired accuracy for combinations for a given observer under some conditions and the failure of any sign of impaired accuracy for the same observer under other experimental conditions, or even under the same experimental conditions at different times.
In the time-interval discrimination experiment the evenness of balance in the attention wave will make for the shortest interval discrimination, and the proportion between the two will be direct, so far as other factors do not interfere. But there are special interferences here. One of these is the fact that the two mental processes do not set off at the same moment. No matter how even the balance in attention at the moment of impact of the first of the two stimuli, the preparation for the other, not yet set off, cannot be held in equal readiness while this is going off. This discharge has already disturbed the preparation to discharge in the other direction. In the case of a given pair of stimuli of definite qualities and intensities, the relation will be one of mutual facilitation for one interval of separation and one of inhibition for another interval. In one case the first opens the path for the second, being a case similar to the summation of stimuli, and in the other, it draws all the available energy in its own direction.
THE ESTIMATION OF NUMBER
BY C. T. BURNETT
I. There are situations not a few in life in which we find ourselves estimating the number of objects in some group. Sometimes we desire to know merely whether the group is large or small. Sometimes we try to reach an absolute number that shall approximate roughly to the real number. Sometimes, again, we only care to know whether the group in question is more or less numerous than some other group that we have before us or perhaps recall in memory. The public speaker finds himself wondering whether this present scattering audience is larger than the one that last night crowded into the front seats. The farmer riding between adjoining orchards judges roughly the prospective yield by a comparative estimate of the fruit in sight. The politician too has an interest that is very notable indeed in such rough numerical estimates. He asks himself, for example, whether the voters will be more influenced by reports favorable to his party sent in from numerous small towns or by such reports from a few large centres. Or perhaps he is planning a demonstration in favor of his candidate. His problem then is so to arrange his procession that five hundred men will look like five thousand. Turning to another field, how is it that the enrolment in some institutions of learning seems larger and the size of the faculty more portentous than in other similar institutions that are really of about the same size?
These examples bring to mind our interest in rough numerical estimates and at the same time suggest the probability that we are swayed back and forth in these estimations without ever a numerical difference occurring in the objects of our judgment. These considerations lead us on, then, to an enquiry about the factors that can thus influence our estimation of number.
II. INFLUENCE OF FACTORS IN THE SAME SENSE-FIELD AS THE OBJECTS WHOSE RELATIVE NUMEROUSNESS IS IN QUESTION.
The experiments described in the following pages are concerned with the influence exerted on the judgment of a given factor by other factors presented at the same time. The object of judgment in these studies is visual number, which is to be submitted under varying conditions of the objects whose number is in question, for example, varying conditions of form, size, distribution, with the intent to discover whether this judgment is a function of these other factors as well as of the numerical. The scope of the enquiry includes both relative and absolute number.