Although inapplicable to the real world, these last—which are constructions in which the mind is submitted to no other laws than agreement with itself—are brilliant examples of the power of abstraction, when it attains its highest degree of development.
SECTION III. THE CONCEPT OF TIME.
In evolving the idea of time, as in that of space, we must first examine the concrete fact which is its starting-point, i. e., real duration; next the concept which is extracted from it, time in abstracto—and this must be followed in the successive stages of its development.
I.
Real, concrete duration is a quality known by itself, included among internal and external sensations, as later on in the representations which psychology, in what concerns it, must accept as an ultimate datum.
What is this concrete duration, furnished by experience? It might strictly be said to be the present; yet this answer is somewhat theoretical, for it must be admitted that what we term “the present” has vague and fluctuating limits. Moreover, its clear and precise distinction from what has preceded and what is to follow it—the past and the future—is a somewhat late production. Of this we have objective witness (see Ch. II.) in primitive languages, during the period in which the value of the verbs was undetermined. Take again the fact, as frequently observed, that children even at the age of three, or older, having vague notions of past and future, make a general confusion, and do not distinguish between “yesterday” and last week, between “to-morrow” and next week (Sully).
Still, we must admit that the present has the privilege of appearing in consciousness as the typical duration, the standard, the measure to which everything must be referred. Nor can this be otherwise, seeing that (as is too often forgotten) we live only in the present; that the past and the future have no existence for us, are only known to us under the condition of becoming present, of occupying actual consciousness. The present is the only psychical element, which, consciously or unconsciously, gives a content and reality to duration.
It is essential to rid ourselves of the opinion accredited by many authors, that the present is only an elusive moment, a transition, a passage, a flash, a mathematical point, a zero, a nullity; on the contrary—it alone has duration, is now long, now short. It is even possible, to some extent, to determine its limits, and to transcend this vague description. Here we are aided by the labors of the psycho-physicists. We may say that this study, long restricted to metaphysical dissertations, entered upon a positive phase with Czermak, who (in 1857) opened out a new line, in which he has been followed by many others. The numerous researches and experiments made upon the “sense of time” may be omitted without prejudice to our subject, while the discussion of them would deter us from our principal aims. We must, however, give a rapid summary of those which relate either to the actual perception of duration, or to the reproduction in memory of past duration.[105]
1. This present, declared to be inapprehensible, has however been determined as regards its minimum duration. For the discrimination period between two different sensations (taken as the type of the briefest and simplest psychical act), Kries and Auerbach found durations varying between 0·01 and 0·07 second with an average of 0·03 second. At a later period, Exner, experimenting with Savart’s wheel, stated that the interval at which two successive taps can be perceived separately may be reduced to 0·05 second: as also for the sound produced by two electric sparks. For the eye, the minimum perceptible interval between two impressions falling on the yellow spot, is 0·044 second. Below this, one of the conditions necessary to consciousness—an adequate duration—is wanting.
Certain experiments contributed by Wundt and his pupils throw light also upon the maximum duration that can be apprehended by consciousness. They made use, almost exclusively, of auditory sensations, which are more closely allied than any others to the sense of time. Wundt finds that twelve impressions equivalent to a duration varying from 3·6 to 6 seconds can be clearly perceived to form a group. Dietze admits the continuous perception of 40 beats of the metronome, provided the mind arranges them spontaneously in 5 sub groups of 8, or 8 sub-groups of 5. Total duration: 12 seconds. Others vary in their conclusions from 6 to 12 seconds and even more.[106] James is inclined to think that the actual present may extend to a minute.