shall understand how a perception of this kind is possible if we remember that we ourselves distin guish our right from our left by a natural feeling, and that these two parts of our own extensity do then appear to us as if they bore a different quality; in fact, this is the very reason why we cannot give a proper definition of right and left. In truth, qualitative differences exist everywhere in nature, and I do not see why two concrete directions should not be as marked in immediate perception as two colours. But the conception of an empty homo geneous medium is something far more extraordi nary, being a kind of reaction against that hetero geneity which is the very ground of our experience.
Therefore, instead of saying that animals have a special sense of direction, we may as well say that men have a special faculty of perceiving or con ceiving a space without quality. This faculty is not the faculty of abstraction: indeed, if we notice that abstraction assumes clean-cut distinctions and a kind of externality of the concepts or their symbols with regard to one another, we shall find that the faculty of abstraction already implies the intuition of a homogeneous medium. What we must say is that we have to do with two different kinds of reality, the one heterogene ous, that of sensible qualities, the other homo geneous, namely space. This latter, clearly con ceived by the human intellect, enables us to use clean-cut distinctions, to count, to abstract, and perhaps also to speak.
Now, if space is to be defined as the homogene ous, it seems that inversely every homogeneous rime, in »o an(^ unbounded medium will be space. eneousa For> homogeneity here consisting in the absence of every quality, it is hard to reducible to See n°W ^WO ^orms °f the homOgenCOUS space. could be distinguished from one another.
Nevertheless it is generally agreed to regard time as an unbounded medium, different from space but homogeneous like the latter: the homogene ous is thus supposed to take two forms, according as its contents co-exist or follow one another. It is true that, when we make time a homogeneous medium in which conscious states unfold them selves, we take it to be given all at once, which amounts to saying that we abstract it from dura tion. This simple consideration ought to warn us that we are thus unwittingly falling back upon space, and really giving up time. Moreover, we can understand that material objects, being ex terior to one another and to ourselves, derive both exteriorities from the homogeneity of a medium which inserts intervals between them and sets off their outlines: but states of consciousness, even when successive, permeate one another, and in the simplest of them the whole soul can be reflected. We may therefore surmise that time, conceived under the form of a homogeneous medium, is some spurious concept, due to the trespassing of the idea of space upon the field of pure conscious ness. At any rate we cannot finally admit two CHAP, n HOMOGENEOUS TIME AND SPACE 99 iorms of the homogeneous, time and space, without first seeking whether one of them cannot be re duced to the other. Now, externality is the dis tinguishing mark of things which occupy space, while states of consciousness are not essentially external to one another, and become so only by being spread out in time, regarded as a homogene ous medium. If, then, one of these two supposed forms of the homogeneous, namely time and space, is derived from the other, we can surmise a priori that the idea of space is the fundamental datum. But, misled by the apparent simplicity of the idea of time, the philosophers who have tried to reduce one of these ideas to the other have thought that they could make extensity out of duration. While showing how they have been misled, we shall see that time, conceived under the form of an un bounded and homogeneous medium, is nothing but the ghost of space haunting the reflective conscious ness.
The English school tries, in fact, to reduce relations of extensity to more or less complex Mistake of relations of succession in time. When, deriJe^rTia-*0 with our eyes shut, we run our hands t«£2ty0from" al°ng a surface, the rubbing of our cess?on°!Ti£c~ fingers against the surface, and especially «0jSeti0dura! *ne variec^ P^aY °f our joints, provide tion-" a series of sensations, which differ only by their qualities and which exhibit a certain order in time. Moreover, experience teaches us that this series can be reversed, that we can, by an IOQ TIME AND FREE WILL CHAP, n effort of a different kind (or, as we shall call it later, in an opposite direction), obtain the same sensations over again in an inverse order: relations of position in space might then be defined as reversible relations of succession in time. But such a definition involves a vicious circle, or at least a very superficial idea of time. There are, indeed, as we shall show a little later, two possible conceptions of time, the one free from all alloy, the other surreptitiously bringing in the idea of space. Pure duration is the form which the suc cession of our conscious states assumes when our ego lets itself live, when it refrains from separat ing its present state from its former states. For this purpose it need not be entirely absorbed in the passing sensation or idea; for then, on the con trary, it would no longer endure. Nor need it forget its former states: it is enough that, in recalling these states, it does not set them alongside its actual state as one point along side another, but forms both the past and the present states into an organic whole, as happens when we recall the notes of a tune, melting, so to speak, into one another. Might it not be said that, even if these notes succeed one another, yet we perceive them in one another, and that their totality may be compared to a living being whose parts, although distinct, permeate one another just because they are so closely con nected? The proof is that, if we interrupt the rhythm by dwelling longer than i<, right on one CHAP, ii DURATION, SUCCESSION AND SPACE IOI note of the tune, it is not its exaggerated length, as length, which will warn us of our mistake, but the qualitative change thereby caused in the whole of the musical phrase. We can thus con ceive of succession without distinction, and think of it as a mutual penetration, an interconnexion and organization of elements, each one of which represents the whole, and cannot be distinguished or isolated from it except by abstract thought. Such is the account of duration which would be given by a being who was ever the same and ever changing, and who had no idea of space. But, familiar with the latter idea and indeed beset by it, we introduce it unwittingly into our feeling of pure succession; we set our states of consciousness side by side in such a way as to perceive them simultaneously, no longer in one another, but alongside one another; in a word, we project time into space, we express duration in terms of extensity, and succession thus takes the form of a continuous line or a chain, the parts of which touch without penetrating one another. Note that the mental image thus shaped implies the perception, no longer successive, but simultaneous, of a before and after, and that it would be a contradiction to suppose a succession which was only a succession, and which nevertheless was contained in one and the same instant. Now, when we speak of an order of succession in duration, and of the reversi bility of this order, is the succession we are dealing with pure succession, such as we have just denned it, without any admixture of extensity, or is it succession developing in space, in such a way that we can take in at once a number of elements which are both distinct and set side by side? There is no doubt about the answer: we could not introduce order among terms without first distinguishing them and then comparing the places which they occupy; hence we must perceive them as multiple, simultaneous and distinct; in a word, we set them side by side, and if we introduce an order in what is successive, the reason is that succession is con verted into simultaneity and is projected into space. In short, when the movement of my finger along a surface or a line provides me with a series of sensations of different qualities, one of two things happens: either I picture these sensations to myself as in duration only, and in that case they succeed one another in such a way that I cannot at a given moment perceive a number of them as simultaneous and yet distinct; or else I make out an order of succession, but m that case I display the faculty not only of perceiving a suc cession of elements, but also of setting them out in line after having distinguished them: in a word, I already possess the idea of space. Hence the idea of a reversible series in duration, or even simply of a certain order of succession in time, itself implies the representation of space, and cannot be used to define it.
To give this argument a stricter form, let us imagine a straight line of unlimited length, and CHAP, n DURATION, SUCCESSION AND SPACE 103 on this line a material point A, which moves.
succession ^ this point were conscious of itself, it would feel itself change, since it moves: it would perceive a succession; but would this succession assume for it the dimensions. form Qf a ^ne p ^Q doubt it WOUld, if it could rise, so to speak, above the line which it traverses, and perceive simultaneously several points of it in juxtaposition: but by doing so it would form the idea of space, and it is in space and not in pure duration that it would see displayed the changes which it undergoes. We here put our finger on the mistake of those who regard pure duration as something similar to space, but of a simpler nature. They are fond of setting psychic states side by side, of forming a chain or a line of them, and do not imagine that they are introducing into this operation the idea of space properly so called, the idea of space in its totality, because space is a medium of three dimensions. But how can they fail to notice that, in order to perceive a line as a line, it is necessary to take up a position outside it, to take account of the void which surrounds it, and consequently to think a space of three dimensions? If our conscious point A does not yet possess the idea of space— and this is the hypothesis which we have agreed to adopt — the succession of states through which it passes cannot assume for it the form of a line; but its sensations will add themselves dynamically to one another and will organize themselves, like IO4 TIME AND FREE WILL CHAP, n the successive notes of a tune by which we allow ourselves to be lulled and soothed. In a word, pure duration might well be nothing but a suc cession of qualitative changes, which melt into and permeate one another, without precise out lines, without any tendency to externalize them selves in relation to one another, without any affiliation with number: it would be pure hetero geneity. But for the present we shall not insist upon this point; it is enough for us to have shown that, from the moment when you attribute the least homogeneity to duration, you surreptitiously introduce space.
It is true that we count successive moments of duration, and that, because of its relations with Pore dura- number, time at first seems to us' to be wholly quail- a measurable magnitude, just like space, be But there is here an important distinction to be made. I say, e.g., that a minute has just elapsed, and I mean by this that a pendulum, beating the seconds, has completed sixty oscillations. If I picture these sixty oscillations to myself all at once by a single mental perception, I exclude by hypothesis the idea of a succession. I do not think of sixty strokes which succeed one another, but of sixty points on a fixed line, each one of which symbolizes, so to speak, an oscillation of the pendulum. If, on the other hand, I wish to picture these sixty oscillations in succession, but without altering the way they are produced in space, I shall CHAP, ii PURE DURATION 105 be compelled to think of each oscillation to the exclusion of the recollection of the preceding one, for space has preserved no trace of it; but by doing so I shall condemn myself to remain for ever in the present; I shall give up the attempt to think a succession or a duration. Now if, finally, I retain the recollection of the preceding oscillation together with the image of the present oscillation, one of two things will happen. Either I shall set the two images side by side, and we then fall back on our first hypothesis, or I shall per ceive one in the other, each permeating the other and organizing themselves like the notes of a tune, so as to form what we shall call a continuous or qualitative multiplicity with no resemblance to number. I shall thus get the image of pure dura tion; but I shall have entirely got rid of the idea of a homogeneous medium or a measurable quan tity. By carefully examining our consciousness we shall recognize that it proceeds in this way whenever it refrains from representing duration symbolically. When the regular oscillations of the pendulum make us sleepy, is it the last sound heard, the last movement perceived, which pro duces this effect? No, undoubtedly not, for why then should not the first have done the same? Is it the recollection of the preceding sounds or movements, set in juxtaposition to the last one?
But this same recollection, if it is later on set in juxtaposition to a single sound or movement, will remain without effect. Hence we must admit T06 TIME AND FREE WILL CHAP, n that the sounds combined with one another and acted, not by their quantity as quantity, but by the quality which their quantity exhibited, i.e. by the rhythmic organization of the whole. Could the effect of a slight but continuous stimulation be understood in any other way? If the sensa tion remained always the same, it would continue to be indefinitely slight and indefinitely bearable. But the fact is that each increase of stimulation is taken up into the preceding stimulations, and that the whole produces on us the effect of a musical phrase which is constantly on the point of ending and constantly altered in its totality by the addi tion of some new note. If we assert that it is always the same sensation, the reason is that we are thinking, not of the sensation itself, but of its objective cause situated in space. We then set it out in space in its turn, and in place of an organism which develops, in place of changes which permeate one another, we perceive one and the same sensation stretching itself out lengthwise, so to speak, and setting itself in juxtaposition to itself without limit. Pure duration, that which consciousness perceives, must thus be reckoned among the so-called intensive magnitudes, if inten sities can be called magnitudes: strictly speaking, however, it is not a quantity, and as soon as we try to measure it, we unwittingly replace it by space.
But we find it extraordinarily difficult to think of duration in its original purity; this is due, CHAP, n IS DURATION MEASURABLE? 107 no doubt, to the fact that we do not endure Time, ta dealt alone, external objects, it seems, endure Strbonoierthe as we do, and time, regarded from!?" tnis point of view, has every appearance °f a homogeneous medium. Not onlv do tne moments of this duration seem to be external to one another, like bodies in space, but the movement perceived by our senses is the, so to speak, palpable sign of a homogeneous and measurable duration. Nay more, time enters into the formulae of mechanics, into the calculations of the astronomer, and even of the physicist, under the form of a quantity. We measure the velocity of a movement, implying that time itself is a magnitude. Indeed, the analysis which we have just attempted requires to be completed, for if duration properly so-called cannot be measured, what is it that is measured by the oscillations of the pendulum? Granted that inner duration, perceived by consciousness, is nothing else but the melting of states of consciousness into one another, and the gradual growth of the ego, it will be said, notwithstanding, that the time which the astronomer introduces into his formulae, the time which our clocks divide into equal portions, this time, at least, is something different: it must be a measurable and therefore homogeneous magnitude. — It is nothing of the sort, however, and a close examina tion will dispel this last illusion.
When I follow with my eyes on the dial of a 108 TIME AND FREE WILL CHAP. 11 clock the movement of the hand which corre- Butwhatwe spends to the oscillations of the pencaij measuring duium I do not measure duration, as time is notntime is notn- SlsimnStTet seems to be thought; I merely count tlekenTase??* simultaneities, which is very different, illustration. Outside of me, in space, there is never more than a single position of the hand and the pendulum, for nothing is left of the past positions. Within myself a process of organization or interpenetration of conscious states is going on, which constitutes true duration. It is because I endure in this way that I picture to myself what I call the past oscillations of the pendulum at the same time as I perceive the present oscillation. Now, let us withdraw for a moment the ego which thinks these so-called suc cessive oscillations: there will never be more than a single oscillation, and indeed only a single position, of the pendulum, and hence no duration. Withdraw, on the other hand, the pendulum and its oscillations; there will no longer be anything but the heterogeneous duration of the ego, without moments external to one another, with out relation to number. Thus, within our ego, there is succession without mutual externality; outside the ego, in pure space, mutual externality without succession: mutual externality, since the present oscillation is radically distinct from the previous oscillation, which no longer exists; but no succession, since succession exists solely for a conscious spectator who keeps the past in CHAP, ii IS DURATION MEASURABLE? IOQ mind and sets the two oscillations or their sym bols side by side in an auxiliary space. Now, between this succession without externality and this externality without succession, a kind of exchange takes place, very similar to what physi cists call the phenomenon of endosmosis. As the successive phases of our conscious life, although interpenetrating, correspond individually to an oscillation of the pendulum which occurs at the same time, and as, moreover, these oscillations are sharply distinguished from one another, we get into the habit of setting up the same distinc tion between the successive moments of our con scious life: the oscillations of the pendulum break it up, so to speak, into parts external to one another: hence the mistaken idea of a homo geneous inner duration, similar to space, the moments of which are identical and follow, with out penetrating, one another. But, on the other hand, the oscillations of the pendulum, which are distinct only because one has disappeared when the other appears on the scene, profit, as it were, from the influence which they have thus exercised over our conscious life. Owing to the fact that our consciousness has organized them as a whole in memory, they are first preserved and afterwards disposed in a series: in a word, we create for them a fourth dimension of space, which we call homogeneous time, and which enables the movement of the pendulum, although taking place at one spot, to be continually set in HO TIME AND FREE WILL CHAP, n juxtaposition to itself. Now, if we try to deter mine the exact part played by the real and the imaginary in this very complex process, this is what we find. There is a real space, without duration, in which phenomena appear and disap pear simultaneously with our states of conscious ness. There is a real duration, the heterogeneous moments of which permeate one another; each moment, however, can be brought into relation with a state of the external world which is contempor aneous with it, and can be separated from the other moments in consequence of this very pro cess. The comparison of these two realities gives rise to a symbolical representation of duration, derived from space. Duration thus assumes the illusory form of a homogeneous medium, and the connecting link between these two terms, space and duration, is simultaneity, which might be defined as the intersection of time and space.
If we analyse in the same way the concept of motion, the living symbol of this seemingly homo-Two elements geneous duration, we shall be led to the™ a™ ^ make a distinction of the same kind. to?odio5£We generally say that a movement SBe M2?Se takes place in space, and when we assert S,OIindStnat motion is homogeneous and divis-SSj'SJ coenlible> it is 0* the space traversed that we are thinking, as if it were inter changeable with the motion itself. Now, if we reflect further, we shall see that the successive positions of the moving body really do occupy CHAP, n IS MOTION MEASURABLE? Ill space, but that the process by which it passes from one position to the other, a process which occupies duration and which has no reality ex cept for a conscious spectator, eludes space. We have to do here not with an object but with a progress: motion, in so far as it is a passage from one point to another, is a mental synthesis, a psychic and therefore unextended process. Space contains only parts of space, and at whatever point of space we consider the moving body, we shall get only a position. If consciousness is aware of anything more than positions, the reason is that it keeps the successive positions in mind and synthesizes them. But how does it carry out a synthesis of this kind? It cannot be by a fresh setting out of these same positions in a homo geneous medium, for a fresh synthesis would be necessary to connect the positions with one another, and so on indefinitely. We are thus com pelled to admit that we have here to do with a synthesis which is, so to speak, qualitative, a gradual organization of our successive sensations, a unity resembling that of a phrase in a melody. This is just the idea of motion which we form when we think of it by itself, when, so to speak, from motion we extract mobility. Think of what you experience on suddenly perceiving a shooting star: in this extremely rapid motion there is a natural and instinctive separation be tween the space traversed, which appears to you under the form of a line of fire, and the absolutely indivisible sensation of motion or mobility. A rapid gesture, made with one's eyes shut, will assume for consciousness the form of a purely qualitative sensation as long as there is no thought of the space traversed. In a word, there are two elements to be distinguished in motion, the space traversed and the act by which we traverse it, the successive positions and the synthesis of these positions. The first of these elements is a homogeneous quantity: the second has no reality except in a consciousness: it is a quality or an intensity, whichever you prefer. But here again we meet with a case of endosmosis, an inter mingling of the purely intensive sensation of mobility with the extensive representation of the space traversed. On the one hand we attribute to the motion the divisibility of the space which it traverses, forgetting that it is quite possible to divide an object, but not an act: and on the other hand we accustom ourselves to projecting this act itself into space, to applying it to the whole of the line which the moving body traverses, in a word, to solidifying it: as if this localizing of a progress in space did not amount to asserting that, even outside consciousness, the past co-exists along with the present!
It is to this confusion between motion and the space traversed that the paradoxes of the Eleatics are due; for the interval which separates two points is infinitely divisible, and if motion con sisted of parts like those of the interval itself, CHAP, n THE ELEATIC PARADOX 113 the interval would never be crossed. But the The common truth is that each of Achilles' steps is tlon a simple indivisible act, and that, after a &ven number of these acts, Achilles paradoxes *rf ^^ have passed the tortoise. The misthe Eieatics. take of the Eleatics arises from their identification of this series of acts, each of which is of a definite kind and indivisible, with the homo geneous space which underlies them. As this space can be divided and put together again accord ing to any law whatever, they think they are justified in reconstructing Achilles' whole move ment, not with Achilles' kind of step, but with the tortoise's kind: in place of Achilles pursuing the tortoise they really put two tortoises, regulated by each other, two tortoises which agree to make the same kind of steps or simultaneous acts, so as never to catch one another. Why does Achilles outstrip the tortoise? Because each of Achilles' steps and each of the tortoise's steps are indivisible acts in so far as they are movements, and are different magnitudes in so far as they are space: so that addition will soon give a greater length for the space traversed by Achilles than is obtained by adding together the space traversed by the tortoise and the handicap with which it started. This is what Zeno leaves out of account when he reconstructs the movement of Achilles according to the same law as the movement of the tortoise, forgetting that space alone can be divided and put together again in any way we like, and thus H4 TIME AND FREE WILL CHAP, n confusing space with motion. Hence we do not think it necessary to admit, even after the acute and profound analysis of a contemporary thinker,1 that the meeting of the two moving bodies implies a discrepancy between real and imaginary.motion, between space in itself and indefinitely divisible space, between concrete time and abstract time. Why resort to a metaphysical hypothesis, however ingenious, about the nature of space, time, and motion, when immediate intuition shows us motion within duration, and duration outside space? There is no need to assume a limit to the divisibility of concrete space; we can admit that it is infinitely divisible, provided that we make a distinction between the simultaneous positions of the two moving bodies, which are in fact in space, and their movements, which cannot occupy space, being duration rather than extent, quality and not quantity. To measure the velo city of a movement, as we shall see, is simply to ascertain a simultaneity; to introduce this velo city into calculations is simply to use a convenient means of anticipating a simultaneity. Thus mathe matics confines itself to its own province as long as it is occupied with determining the simul taneous positions of Achilles and the tortoise at a given moment, or when it admits d priori that the two moving bodies meet at a point X — a meeting which is itself a simultaneity. But it goes 1 Evellin, Infini et quantite. Paris, 1881.