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 subtrajectory:.. 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.
//. 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 has a real cause, that it emanates from a force. But we must understand what we mean by this last word. In natural science force is only a function of mass and velocity: it is measured by acceleration: it is known and estimated only by the movements which it is supposed to produce in space. One with these movements, it shares their relativity. Hence the physicists, who seek the principle of absolute motion in force so denned, are led by the logic of their system back to the hypothesis of an absolute space which they had^at first desired to avoid.1 So it will be come necessary to take refuge in the metaphy sical sense of the word, and attribute the motion which we perceive in space to profound causes, analogous to those which our consciousness be lieves it discovers within the feeling of effort. But is the feeling of effort really the sense of a profound cause? Have not decisive analyses shown that there is nothing in this feeling other than the consciousness of movements already effected or begun at the periphery of the body? It is in vain, then, that we seek to found the reality of motion on a cause which is distinct from it: analysis always brings us back to motion itself.
But why seek elsewhere? So long as we apply a movement to the line along which it passes, the same point will appear to us, by turns, accord ing to the points or the axes to which we * Newton, in particular.
refer it, either at rest or in movement. But it is otherwise if we draw out of the movement the mobility which is its essence. When my eyes give me the sensation of a movement, this sensation is a reality, and something is effectually going on, whether it be that an object is changing its place before my eyes or that my eyes are moving before the object. A fortiori am I assured of the reality of the movement when I produce it after having willed to produce it, and my muscular sense brings me the consciousness of it. That is to say, I grasp the reality of movement when it appears to me, within me, as a change of state or of quality. But then how should it be otherwise when I perceive changes of quality in things? Sound differs absolutely from silence, as also one sound from another sound. Between light and darkness, between colours, between shades, the difference is absolute. The passage from one to another is also an absolutely real phenomenon. I hold then the two ends of the chain, muscular sensations within me, the sensible qualities of matter without me, and neither in the one case nor in the other do I see movement, if there be movement, as a mere relation: it is an absolute. Now, between these two extremities lie the movements of external bodies, properly so called. How are we to distinguish here between real and apparent movement? Of what object, exter nally perceived, can it be said that it moves, of what other that it remains motionless? To put CHAP, iv PERCEPTION AND MATTER 25Q such a question is to admit that the discontinuity established by common sense between objects independent of each other, having each its indi viduality, comparable to kinds of persons, is a valid distinction. For, on the contrary hypothesis, the question would no longer be how are pro duced in given parts of matter changes of posi tion, but how is effected in the whole a change of aspect, — a change of which we should then have to ascertain the nature. Let us then formulate at once our third proposition: — ///. All division of matter into independent bodies with absolutely determined outlines is an artificial division.
A body, that is, an independent material object, presents itself at first to us as a system of qualities The division oi m which resistance and colour — the data of sight and touch— occupy the centre, a11 tne rest being> ^ ^ were> suspended from them. On the °ther hand> the we w!Srif data °* signt and touch are those which most obviously have extension in space, an(j ^he essential character of space is continuity. There are intervals of silence between sounds, for the sense of hearing is not always oc cupied; between odours, between tastes, there are gaps, as though the senses of smell and taste only functioned accidentally: as soon as we open our eyes, on the contrary, the whole field of vision takes on colour; and, since solids are necessarily in contact with each other, our touch must follow 2OO MATTER AND MEMORY CHAP, iv the surface or the edges of objects without ever encountering a true interruption. How do we parcel out the continuity of material extensity, given in primary perception, into bodies of which each is supposed to have its substance and in dividuality? No doubt the aspect of this con tinuity changes from moment to moment; but why do we not purely and simply realize that the whole has changed, as with the turning of a kaleidoscope? Why, in short, do we seek, in the mobility of the whole, tracks that are supposed to be followed by bodies supposed to be in motion? A moving continuity is given to us, in which every thing changes and yet remains: whence comes it that we dissociate the two terms, permanence and change, and then represent permanence by bodies and change by homogeneous movements in space?
This is no teaching of immediate intuition; but neither is it a demand of science, for the object of science is, on the contrary, to rediscover the natural articulations of a universe we have carved artificially. _ Nay more, science, as we shall see, by an evermore complete demonstration of the reciprocal action of all material points upon each other, returns, in spite of appearances, to the idea of an universal continuity. Science and conscious ness are agreed at bottom, provided that we re gard consciousness in its most immediate data, and science in its remotest aspirations. Whence comes then the irresistible tendency to set up a material universe that is discontinuous, composed CHAP, iv PERCEPTION AND MATTER 261 of bodies which have clearly defined outlines and change their place, that is, their relation with each other?
Besides consciousness and science, there is life. Beneath the principles of speculation, so carefully it is the analysed by philosophers, there are tenofe°ii^ing?s dencies of which the study has been negtiiat mark lected, and which are to be explained consciousness simply by the necessity of living, that distinct. -.. A,,, distinct. -.. A,,, bodies. is, of acting. Already the power con ferred on the individual consciousness of mani festing itself in acts requires the formation of distinct material zones, which correspond re spectively to living bodies: in this sense my own body and, by analogy with it, all other living bodies are those which I have the most right to distinguish in the continuity of the universe. But this body itself, as soon as it is constituted and distinguished, is led by its various needs to distinguish and constitute other bodies. In the humblest living being nutrition demands research, then contact, in short a series of efforts which converge towards a centre: this centre is just what is made into an object — the object which will serve as food. Whatever be the nature of matter, it may be said that life will at once establish in it a primary discontinuity, expressing the duality of the need and of that which must serve to satisfy it. But the need of food is not the only need. Others group themselves round it, all having for object the conservation of the individual or of the spe cies; and each of them leads us to distin guish, besides our own body, bodies inde pendent of it which we must seek or avoid. Our needs are, then, so many search-lights which, directed upon the continuity of sensible qualities, single out in it distinct bodies. They cannot satisfy themselves except upon the condition that they carve out, within this continuity, a body which is to be their own, and then delimit other bodies with which the first can enter into relation, as if with persons. To establish these special relations among portions thus carved out from sensible reality is just what we call living. But if this first subdivision of the real answers much less to immediate intuition than to the But, to get a fundamental needs of life, are we likely fheipJOBhicml to gain a nearer knowledge of things by we mnrt'rejtct Pushing the division yet further? In this?mSary waY we do indeed prolong the vital move-?rac5cafy merit; but we turn our back upon true needs. knowledge. That is why the rough and ready operation, which consists in decomposing the body into parts of the same nature as itself, leads us down a blind alley, where we soon feel ourselves incapable of conceiving either why this division should cease or how it could go on ad infinitum. It is nothing, in fact, but the ordinary condition of useful action, unsuitably transported into the domain of pure know ledge. We shall never explain by means of CHAP, iv PERCEPTION AND MATTER 263 particles, whatever these may be, the simple pro perties of matter: at most we can thus follow out into corpuscles as artificial as the corpus — the body itself — the actions and reactions of this body with regard to all the others. This is pre cisely the object of chemistry. It studies bodies rather than matter; and so we understand why it stops at the atom, which is still endowed with the general properties of matter. But the ma teriality of the atom dissolves more and more under the eyes of the physicist. We have no reason, for instance, for representing the atom to ourselves as a solid, rather than as liquid or gaseous, nor for picturing the reciprocal action of atoms by shocks rather than in any other way. Why do we think of a solid atom, and why of shocks? Because solids, being the bodies on which we clearly have the most hold, are those which interest us most in our relations with the external world; and because contact is the only means which appears to be at our disposal in order to make our body act upon other bodies. But very simple experiments show that there is never true contact between two neighbouring bodies l; and besides, solidity is far from being an absolutely defined state of matter.8 Solidity and shock borrow, then, their apparent clearness 1 See, on this subject, Clerk- Maxwell, Action at a Distance (Scientific Papers, Cambridge, 1890, vol. ii, pp. 313-314).
z Clerk-Maxwell, Molecular Constitution of Bodies (Scientific Papers, vol. ii, p. 618). — Van der Waals has shown, on the other hand, the continuity of liquid and gaseous states.
264 MATTER AND MEMORY CHAP, rr from the habits and necessities of practical life; — images of this kind throw no light on the inner nature of things.
Moreover, if there is a truth that science has placed beyond dispute, it is that of the reciprocal action of all parts of matter upon each other. Between the supposed molecules of bodies the forces of attraction and repulsion are at work. The influence of gravitation extends throughout interplanetary space. Something, then, exists be tween the atoms. It will be said that this some thing is no longer matter, but force. And we shall be asked to picture to ourselves, stretched between the atoms, threads which will be made more and more tenuous, until they are invisi ble and even, we are told, immaterial. But what purpose can this crude image serve? The preservation of life no doubt requires that we should distinguish, in our daily experience, between passive things and actions effected by these things in space. As it is useful to us to fix the seat of the thing at the precise point where we might touch it, its palpable outlines become for us its real limit, and we then see in its action a something, I know not what, which, being altogether different, can part company with it. But since a theory of matter is an attempt to find the reality hidden beneath these customary images which- are entirely relative to our needs, from these images it must first of all set itself free. And, indeed, we see force and matter drawing nearer together the CHAP, nr PERCEPTION AND MATTER 265 more deeply the physicist has penetrated into their effects. We see force more and more materialized, the atom more and more idealized, the two terms converging towards a common limit and the uni verse thus recovering its continuity. We may still speak of atoms; the atom may even retain its individuality for our mind which isolates it; but the solidity and the inertia of the atom dissolve either into movements or into lines of force whose reciprocal solidarity brings back to us universal continuity. To this conclusion were bound to come, though they started from very different positions, the two physicists of the last century who have most closely investigated the consti tution of matter, Lord Kelvin and Faraday. For Faraday the atom is a centre of force. He means by this that the individuality of the atom consists in the mathematical point at which cross, radiating throughout space, the indefinite lines of force which really constitute it: thus each atom occupies the whole space to which gravita tion extends and all atoms are interpenetrating.1 Lord Kelvin, moving in another order of ideas, supposes a perfect, continuous, homogeneous and incompressible fluid, filling space: what we term an atom he makes into a vortex ring, ever whirl ing in this continuity, and owing its properties to its circular form, its existence and consequently 1 Faraday, A Speculation concerning Electric Conduction (Philos. Magazine, 3rd series, vol. xxiv).
its individuality to its motion.1 But on either hypothesis, the nearer we draw to the ultimate elements of „ matter the better we note the van ishing of thkt discontinuity which our senses per ceived oifcthe surface. Psychological analysis has already /revealed to us that this discontinuity is relative to our needs: every philosophy of nature ends by finding it incompatible with the general properties of matter.
In truth, vortices and lines of force are never, to the mind of the physicist, more than convenient figures for illustrating his calculations. But philo sophy is bound to ask why these symbols are more convenient than others, and why they permit of further advance. Could we, working with them, get back to experience, if the notions to which they correspond did not at least point out the direction in which we may seek for a representa tion of the real? Now the direction which they indicate is obvious; they show us, pervading concrete extensity, modifications, perturbations, changes of tension or of energy, and nothing else. It is by this, above all, that they tend to unite with the purely psychological analysis of motion which we considered to begin with, an analysis which presented it to us not as a mere change of relation between objects to which it was, as it 1 Thomson, On Vortex Atoms (Proc. of the Roy. Soc. of Edin., 1867). An hypothesis of the same nature had been put forward by Graham, On the Molecular Mobility of Gases (Proc. of the Roy. Soc., 1863, p. 621 et seq.).
were, an accidental addition, but as a true and, in some sort, an independent, reality. Neither science nor consciousness, then, is opposed to this last proposition: — IV. Real movement is rather the transference of a state than of a thing.
By formulating these four propositions, we have, in reality, only been progressively narrowing the interval between the two terms So we shall,.,...-, •, see real which it IS USUal to ODDOSC to each movement as.
rather other, — qualities or sensations, and quality than ' quantity, movements. At first sight, the distance and, as such,. °.
akin to appears impassable. Qualities are consciousness. rf ** heterogeneous, movements homogene ous. Sensations, essentially indivisible, escape measurement; movements, always divisible, are distinguished by calculable differences of direction and velocity. We are fain to put qualities, in the form of sensations, in consciousness; while move ments are supposed to take place independently of us in space. These movements, compounded together, we confess, will never yield anything but movements; our consciousness, though in capable of coming into touch with them, yet by a mysterious process is said to translate them into sensations, which afterwards project themselves into space and come to overlie, we know not how, the movements they translate. Hence two differ ent worlds, incapable of communicating otherwise than by a miracle, — on the one hand that of motion in space, on the other that of consciousness with sensations. Now, certainly the difference is irre ducible (as we have shown in an earlier work *) between quality on the one hand and pure quan tity on the other. But this is just the question: do real movements present merely differences of quantity, or are they not quality itself, vibra ting, so to speak, internally, and beating time for its own existence through an often incal culable number of moments? Motion, as studied in mechanics, is but an abstraction or a sym bol, a common measure, a common denomina tor, permitting the comparison of all real move ments with each other; but these movements, regarded in themselves, are indivisibles which occupy duration, involve a before and an after, and link together the successive moments of time by a thread of variable quality which cannot be without some likeness to the continuity of our own consciousness. May we not conceive, for instance, that the irreducibility of two perceived colours is due mainly to the narrow duration into which are contracted the billions of vibrations which they execute in one of our moments? If we could stretch out this duration, that is to say, live it at a slower rhythm, should we not, as the rhythm slowed down, see these colours pale and lengthen into successive impressions, still coloured, no doubt, but nearer and nearer to coincidence 1 H. Bergson, Time and Free Will. Sonnenschein & Co.
with pure vibrations? In cases where the rhythm of the movement is slow enough to tally with the habits of our consciousness, — as in the case of the deep notes of the musical scale, for instance, — do we not feel that the quality perceived analyses itself into repeated and successive vibrations, bound together by an inner continuity? That which usually hinders this mutual approach of motion and quality is the acquired habit of attach ing movement to elements — atoms or what not, — which interpose their solidity between the move ment itself and the quality into which it contracts.
As our daily experience shows us bodies in motion, it appears to us that there ought to be, in order to sustain the elementary movements to which qualities may be reduced, diminutive bodies or corpuscles. Motion becomes then for our imagin ation no more than an accident, a series of posi tions, a change of relations; and, as it is a law of our representation that in it the stable drives away the unstable, the important and central element for us becomes the atom, between the successive positions of which movement then be comes a mere Hnk. But not only has this concep tion the inconvenience of merely carrying over to the atom all the problems raised by matter; not only does it wrongly set up as an absolute that division of matter which, in our view, is hardly anything but an outward projection of human needs; it also renders unintelligible the process by which we grasp, in perception, at one and the same time, a