Now, between this succession without externality and this externality without succession a kind of endosmotic commerce goes on. Although the successive phases of our conscious life interpenetrate, some of them correspond to simultaneous oscillations of the pendulum; and since each oscillation is distinct—that is, one is no more when another is produced—we come to make the same distinctness between the successive moments of our conscious life. The oscillations of the pendulum decompose it, as it were, into mutually external parts: hence the erroneous idea of an internal homogeneous duration analogous to space, whose identical moments follow each other without interpenetrating. On the other hand, the pendular oscillations benefit by the influence they have exerted on our conscious life. Thanks to the recollection of their collective whole, which our consciousness has organized, they are preserved and then aligned; in short, we create a fourth dimension of space for them, which we call homogeneous time, and which enables the pendular movement, although produced in a certain spot, to be juxtaposited with itself indefinitely.
There is a real space, without duration, but in which phenomena appear and disappear simultaneously with our states of consciousness. There is a real duration, whose heterogeneous moments interpenetrate, but each of which can touch a state of the external world contemporaneous with it, and so be made separate from other movements. From the comparison of these two realities arises a symbolic representation of duration drawn from space. The trait common to these two terms, space and duration, is simultaneity, the intersection of time and space. This is how duration comes to get the illusory appearance of a homogeneous medium. But time is not measurable.
Neither is motion, the living symbol of time. Like duration, motion is heterogeneous and indivisible. But it is universally confused with the space through which the movable passes. The successive positions of the movable are in space, but the motion is not in space. Motion is passing from one position to another, which operation occupies duration and has reality only for a conscious spectator. Things occupy space; processes occupy duration, because they are mental syntheses and are unextended.
The synthesis which is motion is obviously not a new deploying in another homogeneous medium, of the same positions that have been perceived in space; for if it were such an act, the necessity for resynthesis would be indefinitely repeated. The synthesis which is motion is a qualitative synthesis, a gradual organization of our successive sensations with each other, a unity analogous to that of a melodic phrase. The space traversed is a quantity, indefinitely divisible; the act by which space is traversed is a quality, and indivisible. Again that endosmotic exchange takes place, as between the melodically organized perception of the series of the pendulum’s motions and its distinct objective presence at each instant. That is, we attribute to the motion the divisibility of the space traversed; and we project the act upon space, implying that outside as well as inside of consciousness the past coexists with the present. In space are only parts of space. In any point of space where the movable may be considered, there is only a position. You would search space in vain for motion.
From the fact that motion cannot be in space, Zeno concluded wrongly that motion is impossible. But those who try to answer his arguments by seeking it also in space, find it no more than he. Achilles overtakes the tortoise because each Achilles step and each tortoise step is not a space but a duration, whose nature is not addible nor divisible, and whose production therefore does not presuppose productions of parts of themselves, ad infinitum. Their development is not construction. They are entire while they are at all, and since the intersections of their terminal moments with space are not at equal distances, these intersections will coincide, or their spatial relations will be inverted, after a certain number of these simultaneities—whether of Achilles’ steps or of the tortoise’s—with points of the road have been counted; in other words, Achilles will have overtaken or outrun the tortoise after a certain number of steps.
To measure the velocity of a motion is simply to find a simultaneity; to introduce this simultaneity into calculation is to use a convenient means of foreseeing a simultaneity. Just as in duration there is nothing homogeneous except what does not lapse, to wit space in which simultaneities are aligned, so the homogeneous element of motion is that which least pertains to it, to wit the space traversed, which is immobility.
Science can work on time and motion only on condition of first eliminating the essential and qualitative element, duration from time, mobility from motion. Treatises on mechanics never define duration itself, but call two intervals of time equal when two identical bodies in circumstances identical at the commencement of each of these intervals, and subjected to identical actions and influences of every kind, have traversed the same space at the end of these intervals. There is no question, in science, of duration, but only of space and of simultaneities between outer change and certain of our psychic states. That duration does not enter into natural science is seen in the fact that if all the motions of the universe were quicker or slower, then, whereas consciousness would have an indefinable and qualitative intuition of this change, no scientific formulæ would be modified, since the same number of simultaneities would be produced again in space.
Analysis of the idea of velocity proves that mechanics has nothing to do with duration. If, on a trajectory AB, points M, N, P ... such that AM = MN = NP ... are reached at equal intervals of time, as defined above, and AM etc. are smaller than any assignable quantity, the motion is said to be uniform. The velocity of a uniform motion is therefore defined without appeal to notions other than those of space and simultaneity. By a somewhat complicated demonstration[106] the same is shown to be true of the velocity of varying motion. Mechanics necessarily works with equations, and equations always express accomplished facts. It is of the essence of duration and motion to be in formation, so that while mathematics can express any moment of duration or any position taken by a movable in space, duration and motion themselves, being mental syntheses and not things, necessarily remain outside the calculation. The movable occupies the points of a line in turn, but the motion has nothing in common with this line. The positions occupied by the movable vary with the different moments of duration; indeed, the movable creates distinct moments merely by the fact that it occupies different positions; but duration has no identical nor mutually external moments, being essentially heterogeneous and indistinct.
Only space, then, is homogeneous; only things in space are distinctly multiple. There is no succession in space. So-called “successive” states of the outer world exist each alone. Their multiplicity is real only for a consciousness capable of preserving it and then juxtapositing it with others, thus externalizing them by interrelation. They are preserved by consciousness because they give rise to facts of consciousness which connect past and present by their interpenetrating organization. But one ceases when another appears, and so consciousness perceives them in the form of a distinct multiplicity, which amounts to aligning them in the space where each existed separately. Space used in this way is just what is meant by homogeneous time.
The spatial and the temporal kind of multiplicity are just as different as space and the real time that lapses. Spatial multiplicity is always substituted for the temporal kind, in discourse; their distinction cannot be expressed in language, because language is a product of space so that terms are inevitably spatial. Even to speak of “several” conscious states interpenetrating is to characterize them numerically, and so interrelate and mutually externalize or spatialize them.[107] On the other hand, we cannot form the idea of a distinct multiplicity without considering, parallel to it, a qualitative multiplicity. Even in counting units on a homogeneous background, they organize in a dynamic, qualitative way. That is the psychological explanation of the effect of a “marked-down” price. The figures $4.98 have a quality of their own, or rather the price has, that is quite inexpressible by the formula “$5 minus 2¢.” Quantity has its quality.