point of view of customary or useful knowledge from that of true knowledge. The duration wherein we see ourselves acting, and in which it is useful that we should see ourselves, is a duration whose elements are dissociated and juxtaposed. The duration wherein we act is a duration wherein 244 MATTER AND MEMORY CHAP, rv our states melt into each other. It is within this that we should try to replace ourselves by thought, in the exceptional and unique case when we speculate on the intimate nature of action, that is to say, when we are discussing human freedom. Is a method of this kind applicable to the prob lem of matter? The question is, whether, in this ' diversity of phenomena ' of which Kant spoke, that part which shows a vague tendency to wards extension could be seized by us on the hither side of the homogeneous space to which it is applied and through which we subdivide it, —just as that part which goes to make up our own inner life can be detached from time, equally ignore empty and indefinite, and brought back that extension,, ~...
concrete and to pure duration. Certainly it would beneath which be a chimerical enterprise to try to free an artificial ourselves from the fundamental con ditions of external perception. But the question is whether certain conditions, which we usually regard as fundamental, do not rather concern the use to be made of things, the practical advantage to be drawn from them, far more than the pure knowledge which we can have of them. More particularly, in regard to concrete extension, continuous, diversified and at the same time organized, we do not see why it should be bound up with the amorphous and inert space which subtends it — a space which we divide in definitely, out of which we carve figures arbitrar ily, and in which movement itself, as we have CHAP, iv DESCRIPTION OF THE METHOD 245 said elsewhere, can only appear as a multiplicity of instantaneous positions, since nothing there can ensure the coherence of past with present. It might, then, be possible, in a certain measure, to transcend space without stepping out from extensity; and here we should really have a return to the immediate, since we do indeed per ceive extensity, whereas space is merely conceived, — being a kind of mental diagram. It may be urged against this method that it arbitrarily attri butes a privileged value to immediate know ledge? But what reasons should we have for doubting any knowledge, — would the idea of doubt ing it ever occur to us, — but for the difficulties and the contradictions which reflexion discovers, but for the problems which philosophy poses? And would not immediate knowledge find in itself its justification and proof, if we could show that these difficulties, contradictions and problems are mainly the result of the symbolic diagrams which cover it up, diagrams which have for us become reality itself, and beyond which only an intense and unusual effort can succeed in pene trating?
Let us choose at once, among the results to which the application of this method may lead, those which concern our present enquiry. We must confine ourselves to mere suggestions; there can be no question here of constructing a theory of matter.
246 MATTER AND MEMORY CHAP, nr I. — Every movement, inasmuch as it is a passage from rest to rest, is absolutely indivisible.
This is not an hypothesis, but a fact, generally masked by an hypothesis.
Here, for example, is my hand, placed at the point A. I carry it to the point B, passing at one stroke through the interval between them. There are two things in this movement: an image which I see, and an act of which my muscular sense makes my consciousness aware. My consciousness gives me the [inward feeling of a single fact, for in A was rest, in B there is again rest, and between A and B is placed an indivisible or at least an undivided act, the passage from rest to Movement res*' which is movement itself. But IM^MUS my sight perceives the movement in trajectory oi the form of a line AB which is traversed, bo?y°thaf is 3Ln^ *^s ^me' ^e ^ space, may be divisible. indefinitely divided. It seems then, at first sight, that I may at will take this move ment to be multiple or indivisible, according as I consider it in space or in time, as an image which takes shape outside of me or as an act which I am myself accomplishing.
Yet, when I put aside all preconceived ideas, I soon perceive that I have no such choice, that even my sight takes in the movement from A to B as an indivisible whole, and that if it divides any thing, it is the line supposed to have been traversed, and not the movement traversing it. It is indeed CHAP, rv INDIVISIBILITY OF MOVEMENT 247 true that my hand does not go from A to B with out passing through the intermediate positions, and that these intermediate points resemble stages, as numerous as you please, all along the route; but there is, between the divisions so marked out and stages properly so called, this capital difference, that at a stage we halt, where as at these points the moving body passes. Now a passage is a movement and a halt is an immo bility. The halt interrupts the movement; the pas sage is one with the movement itself. When I see the moving body pass any point, I conceive, no doubt, that it might stop there; and even when it does not stop there, I incline to consider its passage as an arrest, though infinitely short, because I must have at least the time to think of it; but it is only my imagination which stops there, and what the moving body has to do is, on the contrary, to move. As every point of space necessarily appears to me fixed, I find it ex tremely difficult not to attribute to the moving body itself the immobility of the point with which, for a moment, I make it coincide; it seems to me, then, when I reconstitute the total movement, that the moving body has stayed an infinitely short time at every point of its trajec tory. But we must not confound the data of the senses, which perceive the movement, with the artifice of the mind, which recomposes it. The senses, left to themselves, present to us the real movement, between two real halts, as a solid 248 MATTER AND MEMORY CHAP, iv and undivided whole. The division is the work of our imagination, of which indeed the office is to fix the moving images of our ordinary experi ence, like the instantaneous flash which illumin ates a stormy landscape by night.
We discover here, at its outset, the illusion which accompanies and masks the perception of real movement. Movement visibly consists in passing from one point to another, and consequently in traversing space. Now the space which is tra versed is infinitely divisible; and as the move ment is, so to speak, applied to the line along which it passes, it appears to be one with this line and, like it, divisible. Has not the move ment itself drawn the line? Has it not traversed in turn the successive and juxtaposed points of that line? Yes, no doubt, but these points have no reality except in a line drawn, that is to say motionless; and by the very fact that you represent the movement to yourself successively in these different points, you necessarily arrest it in each of them; your successive positions are, at bottom, only so many imaginary halts. You substitute the path for the journey, and because the journey is subtended by the path you think that the two coincide. But how should a progress coincide with a thing, a move ment with an immobility?
What facilitates this illusion is that we dis tinguish moments in the course of duration, like halts in the passage of the moving body. Even CHAP, iv INDIVISIBILITY OF MOVEMENT 249 if we grant that the movement from one point to another forms an undivided whole, this move ment nevertheless takes a certain time; so that if we carve out of this duration an indivisible instant, it seems that the moving body must oc cupy, at that precise moment, a certain position, which thus stands out from the whole. The indi visibility of motion implies, then, the impossibil ity of real instants; and indeed, a very brief analysis of the idea of duration will show us both why we attribute instants to duration and why it cannot have any. Suppose a simple movement like that of my hand when it goes from A to B. This passage is given to my consciousness as an undivided whole. No doubt it endures; but this duration, which in fact coincides with the aspect which the movement has inwardly for my consciousness, is, like it, whole and undivided. Now, while it presents itself, qua movement, as a simple fact, it describes in space a trajectory which I may consider, for purposes of simplification, as a geometrical line; and the extremities of this line, considered as abstract limits, are no longer lines, but indivisible points. Now, if the line, which the moving body has described, measures for me the duration of its movement, must not the point, where the line ends, symbolize for me a terminus of this dura tion? And if this point is an indivisible of length, how shall we avoid terminating the duration of the movement by an indivisible of duration? If 25O MATTER AND MEMORY CHAP, iv the total line represents the total duration, the parts of the line must, it seems, correspond to parts of the duration, and the points of the line to moments of time. The indivisibles of duration, or moments of time, are born, then, of the need of symmetry; we come to them naturally as soon as we demand from space an integral pre sentment of duration. — But herein, precisely, lies the error. While the line AB symbolizes the duration already lapsed of the movement from A to B already accomplished, it cannot, motion less, represent the movement in its accomplish ment nor duration in its flow. And from the fact that this line is divisible into parts and that it ends in points, we cannot conclude either that the corresponding duration is com posed of separate parts or that' it is limited by instants.
The arguments of Zeno of Elea have no other origin than this illusion. They all consist in zeno trans- making time and movement coincide fers to the moving body with the line which underlies them, in the proper ties oi its attributing to them the same sub- trajectory:.. t,. hence aii the divisions as to the line, in short in difficulties and contradictions treating them like that line. In this confusion Zeno was encouraged by common sense, which usually carries over to the movement the properties of its trajectory, and also - by language, which always translates movement and duration in terms of space. But common sense and language have a right to do so CHAP, iv INDIVISIBILITY OF MOVEMENT 251 and are even bound to do so, for, since they always regard the becoming as a thing to be made use of, they have no more concern with the interior organization of movement than a workman has with the molecular structure of his tools. In holding movement to be divisible, as its trajectory is, common sense merely expresses the two facts which alone are of importance in practical life: first, that every movement de scribes a space; second, that at every point of this space the moving body might stop. But the philosopher who reasons upon the inner nature of movement is bound to restore to it the mobility which is its essence, and this is what Zeno omits to do. By the first argument (the Dichotomy) he supposes the moving body to be at rest, and then considers nothing but the stages, infinite in number, that are along the line to be traversed: we cannot imagine, he says, how the body could ever get through the interval between them. But in this way he merely proves that it is impossible to construct, d priori, movement with immobilities, a thing no man ever doubted. The sole question is whether, movement being posited as a fact, there is a sort of retrospective absurdity in assuming that an infinite number of points has been passed through. But at this we need not wonder, since movement is an undivided fact, or a series of undivided facts, whereas the trajectory is infinitely divisible. In the second argument (the Achilles) movement is 252 MATTER AND MEMORY CHAP, nr indeed given, it is even attributed to two moving bodies, but, always by the same error, there is an assumption that their movement coincides with their path, and that we may divide it, like the path itself, in any way we please. Then, instead of recognizing that the tortoise has the pace of a tortoise and Achilles the pace of Achilles, so that after a certain number of these indivisible acts or bounds Achilles will have outrun the tortoise, the contention is that we may disarticulate as we will the movement of Achilles and, as we will also, the movement of the tortoise: thus reconstructing both in an arbi trary.way, according to a law of our own which may be incompatible with the real conditions of mobility. The same fallacy appears, yet more evident, in the third argument (the Arrow) which consists in the conclusion that, because it is possible to distinguish points on the path of a moving body, we have the right to distinguish indivisible moments in the duration of its move ment. But the most instructive of Zeno's argu ments is perhaps the fourth (the Stadium) which has, we believe, been unjustly disdained, and of which the absurdity is more manifest only because the postulate masked in the three others is here frankly displayed.1 Without entering on a dis- 1 We may here briefly recall this argument. Let there be a moving body which is displaced with a certain velocity, and which passes simultaneously before two bodies, one at rest and the other moving towards it with the same velocity CHAP, iv INDIVISIBILITY OF MOVEMENT 253 cussion which would here be out of place, we will content ourselves with observing that motion, as given to spontaneous perception, is a fact which is quite clear, and that the difficulties and contra dictions pointed out by the Eleatic school concern far less the living movement itself than a dead and artificial reorganization of movement by the mind. But we now come to the conclusion of all the preceding paragraphs: as its own. During the same time that it passes a certain length of the first body, it naturally passes double that length of the other. Whence Zeno concludes that ' a duration is the double of itself.' A childish argument, it is said, because Zeno takes no account of the fact that the velocity is in the one case double that which it is in the other. — Certainly, but how, I ask, could he be aware of this? That, in the same time, a moving body passes different lengths of two bodies, of which one is at rest and the other in motion, is clear for him who makes of duration a kind of absolute, and places it either in consciousness or in something which partakes of consciousness. For while a determined portion of this absolute or conscious duration elapses, the same moving body will traverse, as it passes the two bodies, two spaces of which the one is the double of the other, without our being able to conclude from this that a duration is double itself, since duration remains independent of both spaces. But Zeno's error, in all his reasoning, is due to just this fact, that he leaves real duration on one side, and considers only its objective track in space. How then should the two lines traced by the same moving body not merit an equal consideration, qua measures of duration? And how should they not represent the same duration, even though the one is twice the other? In concluding from this that ' a duration is the double of itself,' Zeno was true to the logic of his hypo thesis; and his fourth argument is worth exactly as much as the three others.
254 MATTER AND MEMORY CHAP, rv //. There are real movements. The mathematician, expressing with greater pre cision an idea of common sense, defines position by the distance from points of reference Movement f -, •,., is relative or from axes, and movement by the only for the...,,,,.. _..
mathema- variation of the distance. Of movetician, real, u, -, for the ment, then, he only retains changes in length; and as the absolute values of the variable distance between a point and an axis, for instance, express either the displacement of the axis with regard to the point or that of the point with regard to the axis, just as we please, he attributes indifferently to the same point repose or motion. If, then, movement is no thing but a change of distance, the same object is in motion or motionless according to the points to which it is referred, and there is no absolute movement.
But things wear a very different aspect when we pass from mathematics to physics, and from the abstract study of motion to a consideration of the concrete changes occurring in the universe. Though we are free to attribute rest or motion to any material point taken by itself, it is none the less true that the aspect of the material universe changes, that the internal configuration of every real system varies, and that here we have no longer the choice between mobility and rest. Movement, whatever its inner nature, becomes an indisputable reality. We may not be able to say what parts of the whole are in motion; CHAP, iv REAL MOVEMENT 255 motion there is in the whole, none the less. Therefore it is not surprising that the same thinkers, who maintain that every particular movement is relative, speak oi the totality of movements as of an absolute. The contradiction has been pointed out in Descartes, who, after hav ing given to the thesis of relativity its most radical form by affirming that all movement is ' recip rocal,' x formulated the laws of motion as though motion were an absolute.' Leibniz and others after him have remarked this contradiction 8: it is due simply to the fact that Descartes handles motion as a physicist after having denned it as a geometer. For the geometer all movement is relative: which signifies only, in our view, that none of our mathematical symbols can express the fact that it is the moving body which is in motion rather than the axes or the points to which it is referred. And this is very natural, because these symbols, always meant for measurement, can express only distances. But that there is real motion no one can seriously deny: if there were not, nothing in the universe would change; and, above all, there would be no meaning in the consciousness which we have of our own movements. In his controversy with Descartes Henry More makes jesting allusion to this last 1 Descartes, Principes, ii, 29. 1 Principes, part ii, § 37 et seq.
* Leibniz, Specimen dynamicum (Mathem. Schriften, Gerhardt, 2nd section, vol. ii, p. 246).
256 MATTER AND MEMORY CHAF. iv point: ' When I am quietly seated, and another, going a thousand paces away, is flushed with fatigue, it is certainly he who moves and I who am at rest.' l But if there is absolute motion, is it possible to persist in regarding movement as nothing but a change of place? We should then have to make diversity of place into any real move- an absolute difference, and distinguish ment*. they,,.. -LI cannot be absolute positions in an absolute space. changes of Newton * went as far as this, followed moreover by Euler * and by others. But can this be imagined, or even conceived? A place could be absolutely distinguished from another place only by its quality or by its rela tion to the totality of space: so that space would become, on this hypothesis, either com posed of heterogeneous parts or finite. But to finite space we should give another space as boundary, and beneath heterogeneous parts of space we should imagine an homogeneous space as its foundation: in both cases it is to homogen eous and indefinite space that we should neces sarily return. We cannot, then, hinder ourselves either from holding every place to be relative, or from believing some motion to be absolute.
It may be urged that real movement is dis tinguished from relative movement in that it 1 H. Moms, Scripta PhilosopMca, 1679, vol. ii, p. 248. 8 Newton, Principia, Ed. Thomson, 1871, p. 6 et seq. 3 Euler, Theoriumotuscorpor urn solidorum, 1765, pp. 30-33.
CHAP, iv REAL MOVEMENT 257