This conception, which more and more shows through the reasonings of the Greek philosophers as we go from Plato to Plotinus, we may formulate thus: _The affirmation of a reality implies the simultaneous affirmation of all the degrees of reality intermediate between it and nothing._ The principle is evident in the case of number: we cannot affirm the number 10 without thereby affirming the existence of the numbers 9, 8, 7,..., etc.--in short, of the whole interval between 10 and zero. But here our mind passes naturally from the sphere of quantity to that of quality. It seems to us that, a certain perfection being given, the whole continuity of degradations is given also between this perfection, on the one hand, and the nought, on the other hand, that we think we conceive. Let us then posit the God of Aristotle, thought of thought--that is, thought _making a circle_, transforming itself from subject to object and from object to subject by an instantaneous, or rather an eternal, circular process: as, on the other hand, the nought appears to posit itself, and as, the two extremities being given, the interval between them is equally given, it follows that all the descending degrees of being, from the divine perfection down to the "absolute nothing," are realized automatically, so to speak, when we have posited God.
Let us then run through this interval from top to bottom. First of all, the slightest diminution of the first principle will be enough to precipitate Being into space and time; but duration and extension, which represent this first diminution, will be as near as possible to the divine inextension and eternity. We must therefore picture to ourselves this first degradation of the divine principle as a sphere turning on itself, imitating, by the perpetuity of its circular movement, the eternity of the circle of the divine thought; creating, moreover, its own place, and thereby place in general,[103] since it includes without being included and moves without stirring from the spot; creating also its own duration, and thereby duration in general, since its movement is the measure of all motion.[104] Then, by degrees, we shall see the perfection decrease, more and more, down to our sublunary world, in which the cycle of birth, growth and decay imitates and mars the original circle for the last time. So understood, the causal relation between God and the world is seen as an attraction when regarded from below, as an impulsion or a contact when regarded from above, since the first heaven, with its circular movement, is an imitation of God and all imitation is the reception of a form. Therefore, we perceive God as efficient cause or as final cause, according to the point of view. And yet neither of these two relations is the ultimate causal relation. The true relation is that which is found between the two members of an equation, when the first member is a single term and the second a sum of an endless number of terms. It is, we may say, the relation of the gold-piece to the small change, if we suppose the change to offer itself automatically as soon as the gold piece is presented. Only thus can we understand why Aristotle has demonstrated the necessity of a first motionless mover, not by founding it on the assertion that the movement of things must have had a beginning, but, on the contrary, by affirming that this movement could not have begun and can never come to an end. If movement exists, or, in other words, if the small change is being counted, the gold piece is to be found somewhere. And if the counting goes on for ever, having never begun, the single term that is eminently equivalent to it must be eternal. A perpetuity of mobility is possible only if it is backed by an eternity of immutability, which it unwinds in a chain without beginning or end.
Such is the last word of the Greek philosophy. We have not attempted to reconstruct it _a priori_. It has manifold origins. It is connected by many invisible threads to the soul of ancient Greece. Vain, therefore, the effort to deduce it from a simple principle.[105] But if everything that has come from poetry, religion, social life and a still rudimentary physics and biology be removed from it, if we take away all the light material that may have been used in the construction of the stately building, a solid framework remains, and this framework marks out the main lines of a metaphysic which is, we believe, the natural metaphysic of the human intellect. We come to a philosophy of this kind, indeed, whenever we follow to the end, the cinematographical tendency of perception and thought. Our perception and thought begin by substituting for the continuity of evolutionary change a series of unchangeable forms which are turn by turn, "caught on the wing," like the rings at a merry-go-round, which the children unhook with their little stick as they are passing. Now, how can the forms be passing, and on what "stick" are they strung? As the stable forms have been obtained by extracting from change everything that is definite, there is nothing left, to characterize the instability on which the forms are laid, but a negative attribute, which must be indetermination itself. Such is the first proceeding of our thought: it dissociates each change into two elements--the one stable, definable for each particular case, to wit, the Form; the other indefinable and always the same, Change in general.
And such, also, is the essential operation of language. Forms are all that it is capable of expressing. It is reduced to taking as understood or is limited to _suggesting_ a mobility which, just because it is always unexpressed, is thought to remain in all cases the same.--Then comes in a philosophy that holds the dissociation thus effected by thought and language to be legitimate. What can it do, except objectify the distinction with more force, push it to its extreme consequences, reduce it into a system? It will therefore construct the real, on the one hand, with definite Forms or immutable elements, and, on the other, with a principle of mobility which, being the negation of the form, will, by the hypothesis, escape all definition and be the purely indeterminate. The more it directs its attention to the forms delineated by thought and expressed by language, the more it will see them rise above the sensible and become subtilized into pure concepts, capable of entering one within the other, and even of being at last massed together into a single concept, the synthesis of all reality, the achievement of all perfection. The more, on the contrary, it descends toward the invisible source of the universal mobility, the more it will feel this mobility sink beneath it and at the same time become void, vanish into what it will call the "non-being." Finally, it will have on the one hand the system of ideas, logically coördinated together or concentrated into one only, on the other a quasi-nought, the Platonic "non-being" or the Aristotelian "matter."--But, having cut your cloth, you must sew it.
With supra-sensible Ideas and an infra-sensible non-being, you now have to reconstruct the sensible world. You can do so only if you postulate a kind of metaphysical necessity in virtue of which the confronting of this All with this Zero _is equivalent_ to the affirmation of all the degrees of reality that measure the interval between them--just as an undivided number, when regarded as a difference between itself and zero, is revealed as a certain sum of units, and with its own affirmation affirms all the lower numbers. That is the natural postulate. It is that also that we perceive as the base of the Greek philosophy. In order then to explain the specific characters of each of these degrees of intermediate reality, nothing more is necessary than to measure the distance that separates it from the integral reality. Each lower degree consists in a diminution of the higher, and the _sensible_ newness that we perceive in it is resolved, from the point of view of the _intelligible_, into a new quantity of negation which is superadded to it. The smallest possible quantity of negation, that which is found already in the highest forms of sensible reality, and consequently _a fortiori_ in the lower forms, is that which is expressed by the most general attributes of sensible reality, extension and duration. By increasing degradations we will obtain attributes more and more special.
Here the philosopher's fancy will have free scope, for it is by an arbitrary decree, or at least a debatable one, that a particular aspect of the sensible world will be equated with a particular diminution of being. We shall not necessarily end, as Aristotle did, in a world consisting of concentric spheres turning on themselves. But we shall be led to an analogous cosmology--I mean, to a construction whose pieces, though all different, will have none the less the same relations between them. And this cosmology will be ruled by the same principle. The physical will be defined by the logical. Beneath the changing phenomena will appear to us, by transparence, a closed system of concepts subordinated to and coördinated with each other. Science, understood as the system of concepts, will be more real than the sensible reality. It will be prior to human knowledge, which is only able to spell it letter by letter; prior also to things, which awkwardly try to imitate it. It would only have to be diverted an instant from itself in order to step out of its eternity and thereby coincide with all this knowledge and all these things. Its immutability is therefore, indeed, the cause of the universal becoming.
Such was the point of view of ancient philosophy in regard to change and duration. That modern philosophy has repeatedly, but especially in its beginnings, had the wish to depart from it, seems to us unquestionable. But an irresistible attraction brings the intellect back to its natural movement, and the metaphysic of the moderns to the general conclusions of the Greek metaphysic. We must try to make this point clear, in order to show by what invisible threads our mechanistic philosophy remains bound to the ancient philosophy of Ideas, and how also it responds to the requirements, above all practical, of our understanding.
* * * * * Modern, like ancient, science proceeds according to the cinematographical method. It cannot do otherwise; all science is subject to this law. For it is of the essence of science to handle _signs_, which it substitutes for the objects themselves. These signs undoubtedly differ from those of language by their greater precision and their higher efficacy; they are none the less tied down to the general condition of the sign, which is to denote a fixed aspect of the reality under an arrested form. In order to think movement, a constantly renewed effort of the mind is necessary. Signs are made to dispense us with this effort by substituting, for the moving continuity of things, an artificial reconstruction which is its equivalent in practice and has the advantage of being easily handled. But let us leave aside the means and consider only the end. What is the essential object of science? It is to enlarge our influence over things. Science may be speculative in its form, disinterested in its immediate ends; in other words we may give it as long a credit as it wants. But, however long the day of reckoning may be put off, some time or other the payment must be made. It is always then, in short, practical utility that science has in view. Even when it launches into theory, it is bound to adapt its behavior to the general form of practice. However high it may rise, it must be ready to fall back into the field of action, and at once to get on its feet.
This would not be possible for it, if its rhythm differed absolutely from that of action itself. Now action, we have said, proceeds by leaps. To act is to re-adapt oneself. To know, that is to say, to foresee in order to act, is then to go from situation to situation, from arrangement to rearrangement. Science may consider rearrangements that come closer and closer to each other; it may thus increase the number of moments that it isolates, but it always isolates moments. As to what happens in the interval between the moments, science is no more concerned with that than are our common intelligence, our senses and our language: it does not bear on the interval, but only on the extremities. So the cinematographical method forces itself upon our science, as it did already on that of the ancients.
Wherein, then, is the difference between the two sciences? We indicated it when we said that the ancients reduced the physical order to the vital order, that is to say, laws to genera, while the moderns try to resolve genera into laws. But we have to look at it in another aspect, which, moreover, is only a transposition, of the first. Wherein consists the difference of attitude of the two sciences toward change? We may formulate it by saying that _ancient science thinks it knows its object sufficiently when it has noted of it some privileged moments, whereas modern science considers the object at any moment whatever_.
The forms or ideas of Plato or of Aristotle correspond to privileged or salient moments in the history of things--those, in general, that have been fixed by language. They are supposed, like the childhood or the old age of a living being, to characterize a period of which they express the quintessence, all the rest of this period being filled by the passage, of no interest in itself, from one form to another form. Take, for instance, a falling body. It was thought that we got near enough to the fact when we characterized it as a whole: it was a movement _downward_; it was the tendency toward a _centre_; it was the _natural_ movement of a body which, separated from the earth to which it belonged, was now going to find its place again. They noted, then, the final term or culminating point ([Greek: telos, akmê]) and set it up as the essential moment: this moment, that language has retained in order to express the whole of the fact, sufficed also for science to characterize it. In the physics of Aristotle, it is by the concepts "high" and "low," spontaneous displacement and forced displacement, own place and strange place, that the movement of a body shot into space or falling freely is defined. But Galileo thought there was no essential moment, no privileged instant. To study the falling body is to consider it at it matters not what moment in its course. The true science of gravity is that which will determine, for any moment of time whatever, the position of the body in space. For this, indeed, signs far more precise than those of language are required.
We may say, then, that our physics differs from that of the ancients chiefly in the indefinite breaking up of time. For the ancients, time comprises as many undivided periods as our natural perception and our language cut out in it successive facts, each presenting a kind of individuality. For that reason, each of these facts admits, in their view, of only a _total_ definition or description. If, in describing it, we are led to distinguish phases in it, we have several facts instead of a single one, several undivided periods instead of a single period; but time is always supposed to be divided into determinate periods, and the mode of division to be forced on the mind by apparent crises of the real, comparable to that of puberty, by the apparent release of a new form.--For a Kepler or a Galileo, on the contrary, time is not divided objectively in one way or another by the matter that fills it. It has no natural articulations. We can, we ought to, divide it as we please. All moments count. None of them has the right to set itself up as a moment that represents or dominates the others. And, consequently, we know a change only when we are able to determine what it is about at any one of its moments.
The difference is profound. In fact, in a certain aspect it is radical. But, from the point of view from which we are regarding it, it is a difference of degree rather than of kind. The human mind has passed from the first kind of knowledge to the second through gradual perfecting, simply by seeking a higher precision. There is the same relation between these two sciences as between the noting of the phases of a movement by the eye and the much more complete recording of these phases by instantaneous photography. It is the same cinematographical mechanism in both cases, but it reaches a precision in the second that it cannot have in the first. Of the gallop of a horse our eye perceives chiefly a characteristic, essential or rather schematic attitude, a form that appears to radiate over a whole period and so fill up a time of gallop. It is this attitude that sculpture has fixed on the frieze of the Parthenon. But instantaneous photography isolates any moment; it puts them all in the same rank, and thus the gallop of a horse spreads out for it into as many successive attitudes as it wishes, instead of massing itself into a single attitude, which is supposed to flash out in a privileged moment and to illuminate a whole period.
From this original difference flow all the others. A science that considers, one after the other, undivided periods of duration, sees nothing but phases succeeding phases, forms replacing forms; it is content with a _qualitative_ description of objects, which it likens to organized beings. But when we seek to know what happens within one of these periods, at any moment of time, we are aiming at something entirely different. The changes which are produced from one moment to another are no longer, by the hypothesis, changes of quality; they are _quantitative_ variations, it may be of the phenomenon itself, it may be of its elementary parts. We were right then to say that modern science is distinguishable from the ancient in that it applies to magnitudes and proposes first and foremost to measure them. The ancients did indeed try experiments, and on the other hand Kepler tried no experiment, in the proper sense of the word, in order to discover a law which is the very type of scientific knowledge as we understand it. What distinguishes modern science is not that it is experimental, but that it experiments and, more generally, works only with a view to measure.
For that reason it is right, again, to say that ancient science applied to _concepts_, while modern science seeks _laws_--constant relations between variable magnitudes. The concept of circularity was sufficient to Aristotle to define the movement of the heavenly bodies. But, even with the more accurate concept of elliptical form, Kepler did not think he had accounted for the movement of planets. He had to get a law, that is to say, a constant relation between the quantitative variations of two or several elements of the planetary movement.
Yet these are only consequences--differences that follow from the fundamental difference. It did happen to the ancients accidentally to experiment with a view to measuring, as also to discover a law expressing a constant relation between magnitudes. The principle of Archimedes is a true experimental law. It takes into account three variable magnitudes: the volume of a body, the density of the liquid in which the body is immersed, the vertical pressure that is being exerted. And it states indeed that one of these three terms is a function of the other two.
The essential, original difference must therefore be sought elsewhere. It is the same that we noticed first. The science of the ancients is static. Either it considers in block the change that it studies, or, if it divides the change into periods, it makes of each of these periods a block in its turn: which amounts to saying that it takes no account of time. But modern science has been built up around the discoveries of Galileo and of Kepler, which immediately furnished it with a model. Now, what do the laws of Kepler say? They lay down a relation between the areas described by the heliocentric radius-vector of a planet and the _time_ employed in describing them, a relation between the longer axis of the orbit and the _time_ taken up by the course. And what was the principle discovered by Galileo? A law which connected the space traversed by a falling body with the _time_ occupied by the fall. Furthermore, in what did the first of the great transformations of geometry in modern times consist, if not in introducing--in a veiled form, it is true--time and movement even in the consideration of figures? For the ancients, geometry was a purely static science. Figures were given to it at once, completely finished, like the Platonic Ideas.
But the essence of the Cartesian geometry (although Descartes did not give it this form) was to regard every plane curve as described by the movement of a point on a movable straight line which is displaced, parallel to itself, along the axis of the abscissae--the displacement of the movable straight line being supposed to be uniform and the abscissa thus becoming representative of the time. The curve is then defined if we can state the relation connecting the space traversed on the movable straight line to the time employed in traversing it, that is, if we are able to indicate the position of the movable point, on the straight line which it traverses, at any moment whatever of its course. This relation is just what we call the equation of the curve. To substitute an equation for a figure consists, therefore, in seeing the actual position of the moving points in the tracing of the curve at any moment whatever, instead of regarding this tracing all at once, gathered up in the unique moment when the curve has reached its finished state.
Such, then, was the directing idea of the reform by which both the science of nature and mathematics, which serves as its instrument, were renewed. Modern science is the daughter of astronomy; it has come down from heaven to earth along the inclined plane of Galileo, for it is through Galileo that Newton and his successors are connected with Kepler. Now, how did the astronomical problem present itself to Kepler?
The question was, knowing the respective positions of the planets at a given moment, how to calculate their positions at any other moment. So the same question presented itself, henceforth, for every material system. Each material point became a rudimentary planet, and the main question, the ideal problem whose solution would yield the key to all the others was, the positions of these elements at a particular moment being given, how to determine their relative positions at any moment. No doubt the problem cannot be put in these precise terms except in very simple cases, for a schematized reality; for we never know the respective positions of the real elements of matter, supposing there are real elements; and, even if we knew them at a given moment, the calculation of their positions at another moment would generally require a mathematical effort surpassing human powers. But it is enough for us to know that these elements might be known, that their present positions might be noted, and that a superhuman intellect might, by submitting these data to mathematical operations, determine the positions of the elements at any other moment of time. This conviction is at the bottom of the questions we put to ourselves on the subject of nature, and of the methods we employ to solve them. That is why every law in static form seems to us as a provisional instalment or as a particular view of a dynamic law which alone would give us whole and definitive knowledge.
Let us conclude, then, that our science is not only distinguished from ancient science in this, that it seeks laws, nor even in this, that its laws set forth relations between magnitudes: we must add that the magnitude to which we wish to be able to relate all others is time, and that _modern science must be defined pre-eminently by its aspiration to take time as an independent variable_. But with what time has it to do?
We have said before, and we cannot repeat too often, that the science of matter proceeds like ordinary knowledge. It perfects this knowledge, increases its precision and its scope, but it works in the same direction and puts the same mechanism into play. If, therefore, ordinary knowledge, by reason of the cinematographical mechanism to which it is subjected, forbears to follow becoming in so far as becoming is moving, the science of matter renounces it equally. No doubt, it distinguishes as great a number of moments as we wish in the interval of time it considers. However small the intervals may be at which it stops, it authorizes us to divide them again if necessary. In contrast with ancient science, which stopped at certain so-called essential moments, it is occupied indifferently with any moment whatever. But it always considers moments, always virtual stopping-places, always, in short, immobilities. Which amounts to saying that real time, regarded as a flux, or, in other words, as the very mobility of being, escapes the hold of scientific knowledge. We have already tried to establish this point in a former work. We alluded to it again in the first chapter of this book. But it is necessary to revert to it once more, in order to clear up misunderstandings.
When positive science speaks of time, what it refers to is the movement of a certain mobile T on its trajectory. This movement has been chosen by it as representative of time, and it is, by definition, uniform. Let us call T_{1}, T_{2}, T_{3},...etc., points which divide the trajectory of the mobile into equal parts from its origin T_0. We shall say that 1, 2, 3,...units of time have flowed past, when the mobile is at the points T_{1}, T_{2}, T_{3},...of the line it traverses. Accordingly, to consider the state of the universe at the end of a certain time _t_, is to examine where it will be when T is at the point T_t of its course. But of the _flux_ itself of time, still less of its effect on consciousness, there is here no question; for there enter into the calculation only the points T_{1}, T_{2}, T_{3},...taken on the flux, never the flux itself. We may narrow the time considered as much as we will, that is, break up at will the interval between two consecutive divisions T_{n} and T_{n-|-1}; but it is always with points, and with points only, that we are dealing.
What we retain of the movement of the mobile T are positions taken on its trajectory. What we retain of all the other points of the universe are their positions on their respective trajectories. To each _virtual stop_ of the moving body T at the points of division T_{1}, T_{2}, T_{3},...we make correspond a _virtual stop_ of all the other mobiles at the points where they are passing. And when we say that a movement or any other change has occupied a time _t_, we mean by it that we have noted a number _t_ of correspondences of this kind. We have therefore counted simultaneities; we have not concerned ourselves with the flux that goes from one to another. The proof of this is that I can, at discretion, vary the rapidity of the flux of the universe in regard to a consciousness that is independent of it and that would perceive the variation by the quite qualitative _feeling_ that it would have of it: whatever the variation had been, since the movement of T would participate in this variation, I should have nothing to change in my equations nor in the numbers that figure in them.
Let us go further. Suppose that the rapidity of the flux becomes infinite. Imagine, as we said in the first pages of this book, that the trajectory of the mobile T is given at once, and that the whole history, past, present and future, of the material universe is spread out instantaneously in space. The same mathematical correspondences will subsist between the moments of the history of the world unfolded like a fan, so to speak, and the divisions T_{1}, T_{2}, T_{3},...of the line which will be called, by definition, "the course of time." In the eyes of science nothing will have changed. But if, time thus spreading itself out in space and succession becoming juxtaposition, science has nothing to change in what it tells us, we must conclude that, in what it tells us, it takes account neither of _succession_ in what of it is specific nor of _time_ in what there is in it that is fluent. It has no sign to express what strikes our consciousness in succession and duration. It no more applies to becoming, so far as that is moving, than the bridges thrown here and there across the stream follow the water that flows under their arches.
Yet succession exists; I am conscious of it; it is a fact. When a physical process is going on before my eyes, my perception and my inclination have nothing to do with accelerating or retarding it. What is important to the physicist is the _number_ of units of duration the process fills; he does not concern himself about the units themselves and that is why the successive states of the world might be spread out all at once in space without his having to change anything in his science or to cease talking about time. But for us, conscious beings, it is the units that matter, for we do not count extremities of intervals, we feel and live the intervals themselves. Now, we are conscious of these intervals as of _definite_ intervals. Let me come back again to the sugar in my glass of water:[106] why must I wait for it to melt? While the duration of the phenomenon is _relative_ for the physicist, since it is reduced to a certain number of units of time and the units themselves are indifferent, this duration is an _absolute_ for my consciousness, for it coincides with a certain degree of impatience which is rigorously determined. Whence comes this determination? What is it that obliges me to wait, and to wait for a certain length of psychical duration which is forced upon me, over which I have no power?
If succession, in so far as distinct from mere juxtaposition, has no real efficacy, if time is not a kind of force, why does the universe unfold its successive states with a velocity which, in regard to my consciousness, is a veritable absolute? Why with this particular velocity rather than any other? Why not with an infinite velocity? Why, in other words, is not everything given at once, as on the film of the cinematograph? The more I consider this point, the more it seems to me that, if the future is bound to _succeed_ the present instead of being given alongside of it, it is because the future is not altogether determined at the present moment, and that if the time taken up by this succession is something other than a number, if it has for the consciousness that is installed in it absolute value and reality, it is because there is unceasingly being created in it, not indeed in any such artificially isolated system as a glass of sugared water, but in the concrete whole of which every such system forms part, something unforeseeable and new. This duration may not be the fact of matter itself, but that of the life which reascends the course of matter; the two movements are none the less mutually dependent upon each other. _The duration of the universe must therefore be one with the latitude of creation which can find place in it._