by Daniel Smith
An important consequence follows from this analysis: movement, which is always happening in the interval, can never be measured by an abstract and homogeneous time. Consider the walk of a human, the gait of a horse, the dash of a lion, the leaping of a gazelle, or the charge of a bull. These different movements cannot be said to unfold in a homogeneous time because they are irreducible to each other—there is no common measure between them. Each movement has its own duration, its own articulations, its own divisions and subdivisions (each of us has a style of walking that is recognizable to others). The Pythagoreans discovered that even the motions of the celestial spheres are incommensurable, just as there is no common unit that can measure the sides of the square and the diagonal of a square. Abstract time is composed of common units, but real movement is not. If Achilles overtakes the tortoise, it is because his own units of movement—Achilles’ leaps and bounds—have no common measure with the small steps of the tortoise. A lion chases a gazelle: if the lion takes down the gazelle, it is because of its own running; if the gazelle escapes, it is because of its own leaps. There is no abstract time in which the chase unfolds, because there is always something unforeseen; we cannot say in advance who is going to win. The movement of the lion and the movement of the gazelle are two qualitatively different movements, two different durations; they are not composed of common units. One movement may interrupt the other, another movement might overtake it; it is with a leap that the lion will overtake the gazelle, and not with an abstract quantity displaceable in a homogeneous time. If we were to model these movements, they would take the form of non-linear equations—in other words, they would be problems without solutions. The idea toward which Bergson's first thesis is heading is the following: movement is fundamentally temporal, not spatial—that is, movement in space expresses, more profoundly, a multiplicity of different durations in time.
PARADOX AND THE SYSTEM OF JUDGMENT
What is the significance of Zeno's paradox, which claims that movement is impossible because the space traversed is infinitely divisible? From a scholarly viewpoint, Zeno's paradox is famous because it is an example of the method of exhaustion, an early version of the differential calculus, and it is clear that Zeno had a profound comprehension of the complexities and problems of Greek mathematics. At the same time, the paradox seems to flout the deliverances of experience. Zeno obviously knows that objects move, he knows that Achilles overtakes the tortoise and that the arrow reaches its target. Why, then, does he claim the opposite? The paradox seems to support the ancient image of the philosopher as someone with their head in the clouds (Thales); an archer could shoot an entire quiver of arrows into his target, and Zeno would be standing next to him with his paradox saying, “Look, I can prove to you that movement is impossible.” The paradox seems fascinating and provocative, yet somehow ridiculous. Indeed, Socrates was famous for making a claim not dissimilar to Zeno's: evil does not exist, evil is nothing. This too seems to be a claim that flies in the face of common sense, but Socrates’ argument is as instructive as Zeno's. Socrates asks his interlocutor, “You are an evil person? You want to kill?” The response: “Yes, I want to kill everyone.” Socrates: “But why do you want to kill everyone?” Response: “No reason, just because I want to, it would give me pleasure!” Socrates: “But is pleasure a good or an evil for you?” Response: “Obviously giving myself pleasure is a good thing.” And Socrates triumphs: “But now you are contradicting yourself. What you want is not to kill everyone; killing everyone is just a means. What you want is your pleasure: that is the true end of your actions. You are simply mistaken about the nature of the good.” At which point, Socrates’ interlocutors usually walk away, saying, “It's impossible to talk with you, Socrates ….” Socrates is trying to show that the evil person is mistaken: no one is voluntarily evil, since even the will of the killer is a will for the good. So find out what your good is: if it is killing, fine, but that is still a good, and you are not really seeking evil. Hence Socrates’ refrain: Evil is nothing.
Socrates’ point is that the evil person is someone who judges badly; they think they are pursuing evil when in fact they are pursuing the Good, their own good. The philosopher may have his head in the clouds, but he is none the less good because he claims to judge well. What philosophy invents, in other words, is a system of judgment. If a judgment takes the form of paradox, it is because, at its simplest level, paradox consists in saying: there is something which “is,” yet which cannot be thought; x exists, and yet it is unthinkable. This is what links Zeno and Socrates: movement and evil are actually existing things, but the problem is how to think these existing things. What Zeno tries to show is not that movement “is not”; rather, he tries to show that movement as movement is unthinkable, that movement cannot be thought without contradiction. Similarly, at bottom, what Socrates wants to show is that evil as evil cannot be thought without contradiction. A paradox announces the unthinkability of something that exists.
Why does paradox give such intense pleasure to philosophers? The more one insists that what they are saying is ridiculous—movement cannot be thought, evil cannot be thought—the more the philosophers will retort: fine, as you like, but tell me how you deal with this paradox. At first sight, this would not seem to be a victory for thought; thought cannot think movement, it cannot think evil, it cannot think existence, it hardly seems to be able to think anything. What, then, can thought think? It turns out that thought can think thoughts such as “Only Justice is just” (Plato)—which amounts to saying that, if existence is unthinkable, what is thinkable is pure ideality, the Idea. The more philosophers are content to think ideality, the less they are content to think existing things. What are they in the process of doing? They are accomplishing the destiny of philosophy, which is to constitute a system of judgment: that is, a means of judging everything that is, everything that exists. This is Deleuze's version of a Nietzschean theme: life is judged in terms of values that are higher than life, and existence is judged in terms of idealities that are higher than existence. One of Deleuze's constant themes can be summarized in a phrase borrowed from Artaud, to have done with judgment: that is, to have done with the system of judgment. This is why Deleuze sets philosophers such as Spinoza and Nietzsche against Socrates. They say: evil may be nothing, but then the good is nothing either. But “beyond good and evil” does not mean beyond good and bad. On the contrary, it is only by ridding ourselves of the transcendent idealities of Good and Evil that we can begin to think the existing realities of the good and the bad. As Deleuze often repeats, he wants to explore the conditions of real experience and not merely possible experience. This is the lens—or at least one of the lenses—through which we should view Deleuze's interest in Bergson. If Zeno says movement is unthinkable, Bergson's retort is to ask: What are the conditions under which the reality of movement can become thinkable? Such is the upshot of Bergson's first thesis: movement is unthinkable as long as we confuse it with the space covered.
BERGSON'S SECOND THESIS ON MOVEMENT: THE INSTANT IS AN IMMOBILE SECTION OF MOVEMENT
We can now turn to Bergson's second thesis on movement. The first thesis says that it is an illusion to reconstitute movement from moments or instants. The second thesis, developed in Creative Evolution, says that there are in fact two types of illusion: that is, two ways of reconstituting movement from privileged instants—the ancient and the modern. A common way of characterizing this difference is to say that ancient science was qualitative whereas modern science is quantitative. But Bergson has his own way of assessing the difference: whereas the ancients related movement to privileged moments, modern science related movement to any moment whatever.4 The shift from the ancient to the modern conception of movement was a fundamental revolution in thought.
For the ancients, movement had its natural articulations, as when we divide someone's life naturally into a period of childhood and a period of old age. Even though we know there is continuity in the temporality of someone's life, our perceptio
n and our language tend to isolate certain privileged moments or periods, “each presenting a kind of individuality.”5 The same holds for moving bodies, which, as Aristotle says, can be defined by their downward or upward movement, or their tendency to move toward a center. A pendulum, for instance, will eventually come to rest at a single point, and this culminating point or final term was set up as the essential moment of the movement of the pendulum, the telos toward which it was tending. From this viewpoint, Aristotle's Forms as well as Plato's Ideas “correspond to privileged or salient moments in the history of things.”6 Conceived in this way, movement expressed a “dialectic” of forms. Movement was the regulated transition from one Form or Idea to another, like the poses in a dance or the periods of a person's life. When water boils, for instance, it is not that the Form of the Cold becomes the Form of the Hot; rather, it is matter itself that passes from one form to the other, from the Form of the Cold to the Form of the Hot (10 Nov 1981). The operation through which a form is actualized or realized or “instantiated” in matter is what the Greeks called an “information”—just as a sculptor actualizes a human form in a block of marble by in-forming matter (10 Nov 1981). In themselves, the Forms are immobile—or, which amounts to the same thing, they are movements of pure thought—and it is matter that passes from one form to another. The movement of matter is physical, but the sequence of Forms is a purely logical or dialectical sequence.
The modern scientific revolution—its stroke of genius—consisted in relating movement, no longer to privileged instants, but to any-instant-whatever.7 There is no longer any privilege of one instant over another instant or of one Form over another Form. In modern science, all moments are equal to each other, and equidistant from each other.8 The great idea of Descartes's geometry is that a figure refers to a trajectory which is determinable at every instant of the trajectory—which means that Descartes no longer refers to a figure or Form, but to an equation. Movement is subject to an analysis rather than a dialectic. This is the revolution, in modern science, from transcendence to immanence: rather than reconstituting movement through transcendent instants that refer to Forms outside of movement, movement is reconstituted through the immanent elements of movement itself. In Creative Evolution, Bergson provides four examples of this transformation in modern science: modern astronomy (Kepler), which determined the relation between an orbit and the time needed to traverse it; modern physics (Galileo), which determined the relation between the space traversed by a falling body and the time it takes the body to fall; modern geometry (Descartes), which determined the equation of a flat curve—that is, the position of a point on a moving straight line at any moment in its course; and modern differential and integral calculus (Newton and Leibniz), which is based on the idea of sections or cuts that can be brought infinitely close together.9 In modern science, the ancient dialectic of Forms is replaced by the mechanical succession of instants. “Modern science must be defined pre-eminently by its aspiration to take time as an independent variable,” that is, by relating movement to any-instant-whatever.”10
Now for Bergson, what remains common to these two approaches to movement—the ancient and the modern—is that they both recompose movement by means of something immobile, either through Forms that transcend movement and are actualized in matter, or through immobile cuts that are internal or immanent to movement (10 Nov 1981). In both cases, movement is sacrificed to the immobile, and duration is sacrificed to a uniform time. Put differently, one could say that for both ancient and modern science, the Whole is given: that is, the Whole is already given in advance.11 For the ancients, eternity is given to us in the Forms or Ideas, and time is a degradation of the eternal. As Plato put it in the Timaeus (37d), “Time is the mobile image of eternity.” Whence the idea of a circular time, which means that the reason for time lies outside of time in eternal Ideas, in the Forms. In modern science, the Whole is given in a different manner: not in the form of eternal Ideas outside of time, but in the form of time itself, in the sense that the following instant repeats the preceding instant. Movement is already finished, already given; it is not in process. The concept of “determinism,” as exemplified by Laplace's demon—the presumption that the whole of the future and past can be determined from knowledge of the present—is itself derived from the idea that the Whole is already given. For both ancient and modern science, the Whole is givable in principle, even if we never attain it, given our finite understanding.
Now Bergson argues that modern science, by relating movement to any-instant-whatever and making time an independent variable, should have rendered possible a new metaphysics of time that broke with the old metaphysics of the eternal—that is, a new thought of time, a thought of duration. All that was needed was for science to renounce the idea that the Whole is given or even givable. Many modern thinkers, such as Kant, had said that the Whole is neither given nor givable, but they thereby thought that the Whole is a notion devoid of meaning, or at least a notion whose function is purely practical. But this is not Bergson's thesis. Bergson insists that the Whole is a perfectly consistent notion, on the condition that we understand that the Whole is the Open. At first sight, this might seem to be a strange hypothesis uniting two seemingly contradictory notions: the Idea of a fundamental openness, and the Idea of a Whole or a Totality, which would seem to imply something closed or finished. In saying that the Whole is the Open, Bergson is saying that the Whole is duration; it is creation. Bergson is establishing an equivalence between four terms: the Whole = the Open = duration = creation (or the new).
What both ancient science and modern science miss, according to Bergson, is that movement is always taking place in the interval: by reconstituting movement through immobile cuts, even modern science fails to grasp movement adequately. What is important is not the manner in which one instant succeeds another, but rather the manner in which movement continues from one instant to another. Movement is a phenomenon of continuation, and this continuation of movement from one instant to another is irreducible to any of the instants or to any succession of instants. What Bergson calls duration is precisely this continuation of movement from one instant to another. In movement, the preceding instant is continued in the following instant, but the following instant is not merely the repetition of the preceding instant. Rather, something new and unforeseen occurs in the following moment (the lion leaps on to the gazelle and kills it). The concept of duration thus implies a metaphysics that takes as its fundamental question: How can something new be produced?12 It is this question that leads us to Bergson's third thesis.
BERGSON'S THIRD THESIS ON MOVEMENT: MOVEMENT IS A MOBILE SECTION OF DURATION
Bergson's first thesis said that movement is distinct from the space covered (space is divisible, but movement is not; it is a continuation). The second thesis said that the instant is an immobile section of movement (it is an illusion to reconstitute movement through immobile cuts, as in the cinema). Bergson's third thesis now says that movement is a mobile section of duration: that is, movement expresses a change in duration or in the Whole. What is duration? Duration is what changes, and what never ceases to change. But, then, what is change? This will be the substance of Bergson's third thesis: change is an affection of the whole. Movement is a relation between parts, but change is an affection of the Whole. More to the point: movement is merely an expression of duration—that is, any relation between parts expresses an affection of the whole. As Bergson will put it, every translation in space (movement as a relation between parts) expresses something more profound: that is, a transformation or a change in the Whole.13 Beyond the mechanism of translation, in other words, we must imagine a mechanism of transformation (17 Nov 1981). I would like to explore this third thesis briefly by proposing two sub-theses, which will attempt to explicate Bergson's claim in terms of the concept of difference of potential and the concept of relation.