However, I instead suggest we explore the possibility that these temporal concepts can be mediated aesthetically and not merely through stated propositions. Perhaps by watching Deleuze’s cited cinema scenes, we might find it easier to see how temporal synthesis can be conceived not as a process but more as a formal status.
To help us understand
his logic of becoming, Deleuze in his book
The Logic of Sense refers us to a scene in the text of
Lewis Carroll’s
Alice in Wonderland. Here is Svankmajer’s rendition.
Svankmajer. Alice
Carroll’s text reads:
“Soon her eye fell on a little glass box that was lying under the table: she opened it, and found in it a very small cake, on which the words ‘EAT ME’ were beautifully marked in currants. ‘Well, I'll eat it,’ said Alice [….]
So she set to work, and very soon finished off the cake.
* * * * * * *
* * * * * *
* * * * * * *
[…] ‘now I'm opening out like the largest telescope that ever was! Good-bye, feet!’”
Deleuze uses this scene to illustrate the ‘pure event’ of becoming. As Alice becomes larger, she of course becomes larger than the size she just was. But in that same stroke, she is as well ‘becoming smaller’ than the sizes she is now growing into. If we are assuming she will continue her growth, then in the next moment, she will be larger; but, that coming largerness is still smaller than the even larger size that comes after that. So it is not that Alice is larger and smaller than herself. Rather, Alice is becoming larger and smaller than herself.
Certainly, she is not bigger and smaller at the same time. She is larger now; she was smaller before. But it is at the same moment that one becomes larger than one was and smaller than one becomes. This is the simultaneity of a becoming […]. becoming does not tolerate the separation or the distinction of before and after, or of past and future.[Logic of Sense]
Also in this book, Deleuze distinguishes possibility and impossibility from compossibility and incompossibility. Possibility and impossibility are matters of logic, specifically, of identity and contradiction. Compossibility and incompossibility, however, are alogical, and they concern compatibility and incompatibility.
So two incompatible states of affairs can coincide, when we are not concerned with possibility, identity, and contradiction. Thus ‘before’ and ‘after’ can coincide; so too can alternative paths of development. Deleuze elaborates this with the concept of bifurcation or forking.
There are two different senses to bifurcation. The first sort is the forking as a break in a linear progress, as described by
Stengers. She describe how for certain chemical reactions, changes in one variable can be correlated to the variations of others, but then one variable will reach a point when its path is indeterminable. It could increase or decrease, but this outcome is always left to chance.
The other sort of bifurcation we find in
Borges’ story ‘
The Garden of Forking Paths.’ It describes a Chinese monk’s unfinished manuscripts for a novel with this same title. It went unpublished because it was incomprehensible. The chapters did not proceed just sequentially. A following chapter would be like an alternate version of the same prior one: “in the third chapter the hero dies, in the fourth he is alive.”
“He believed in an infinite series of times, in a growing, dizzying net of divergent, convergent and parallel times. This network of times which approached one another, forked, broke off, or were unaware of one another for centuries, embraces all possibilities of time.” and
“In all fictional works, each time a man is confronted with several alternatives, he chooses one and eliminates the others; in [The Garden], he chooses— simultaneously—all of them. He creates, in this way, diverse futures, diverse times which themselves also proliferate and fork.” [Borges]
There is one remarkable scene in
Mankiewicz’
Barefoot Contessa, which showcases both senses of bifurcation. The soon-to-be Contessa quite abruptly switches companions, taking her down a drastically different path. But this scene was remembered by two different people, each in their own way and with their own slight variations. We will place both scenes side-by-side, listening just to the audio from one.
To illustrate the
a-logic of incompossibility, consider for example the very moment when Oedipus realizes he is the son of his wife Jocasta. Up until then, Oedipus had every reason to think that he is not her child but rather someone else’s son. But at the very shocking instant of his painful realization, he still holds onto the belief that he is not her son, while in the same stroke, he realizes that in fact he is her child. Yet, it is not impossible for both to be true. However, for him, those states of affairs are incompatible, they’re incompossible. Nonetheless, there was a moment when he was forced to place both incompatible facts together at once.
So incompossible states of affairs on the one hand, are exclusive. Either one or the other can be so, but not both.
Yet somehow they can also coincide, like ‘before’ with ‘after’ in pure becoming. As the cinematic examples will show, this is the case in the second synthesis of time as Deleuze describes it in Difference and Repetition; it is Bergson’s coincidence of the pure past with the actual present.
Let’s first examine Bergson’s expanding circuit diagram. We first consider what Bergson calls ‘after images’.
They are always a part of our perception. We look at some object, then abruptly avert our gaze to another place.
For a split-second, the image of the initial object will carry-into and overlay-upon the new scene we see. The prior object remains in our field of perception, even though it is actually no longer there. Instead, it is virtually there.
The virtual past-image inserts itself so thoroughly into the new actual-image that “we are no longer able to discern what is perception and what is memory.” Perhaps this is why fast moving objects leave a blurry trail behind them.
But just as soon as we see something, it will already begin to appear differently to us, because we move our eyes or the scene itself changes. Like before, the new image and its predecessor circulate immediately. Yet the even-older image has not gone away; it too re-imposes itself on the present perception, but in a somewhat less vivid way. Nonetheless, this enriches the object with another layer in its appearance.
With each additional moment, another new inner circuit pushes-out the former ones. So we see, then, that the past and present are perpetually crystallized together. “In truth,” writes Bergson, “every perception is already memory. Practically we perceive only the past, the pure present being the invisible progress of the past gnawing into the future.”
Yet even though all of our past is always interposed in the present in an implicit way, sometimes what we see causes one recollection to stand-out more explicitly among the rest. Often we observe something in our daily life that causes certain prior memories to flare-out before our “mind’s eye.”
And sometimes our flashbacks can be so vivid that they drown-out the actual things we see. We then begin to feel as though we are reliving that past experience.
Deleuze illustrates these recollection-circuits with the cinematic flashbacks in
Carné’s movie
The Daybreak (
Le jour se lève). The film follows events happening from sundown to dawn. During this short period, a murderer flashes back into his past. Whenever we return to the present, we hear a heavy doom-filled bass and drum beat. It gives us the feeling we are moving inevitably toward a fatal end. So during the flashbacks, the past is so vibrant that it completely covers-over the actual present things standing before him in his room. As viewers, we only see what he is remembering, and not the events still carrying-on in the present while he dreams. But because upon returning we hear that fatal march toward the end, we are reminded that even while reminiscing, we never escaped the current doomed situation.
So even though flashbacks take us away to a prior time, we should still realize that the present time caries forward simultaneously with the unfolding of the past, just as the character in the film keeps staring out his window while still calling-up distant memories.
The third synthesis is much more complex. However, our aim is to see how the cinema examples illustrate a formal rather than a process interpretation of the syntheses.
In
Difference & Repetition, Deleuze characterizes the third synthesis as the pure and empty form of time.
We will see that his treatment of
Ozu in the Cinema books portrays this temporality with still rather than with dynamic imagery. Deleuze writes:
The vase in Late Spring is interposed between the daughter’s half smile and the beginning of her tears. There is becoming, change, passage. But the form of what changes does not itself change, does not pass on. This is time, time itself, ‘a little time in its pure state’[…] everything that changes is in time, but time does not itself change […’]
The daughter has been reluctant to marry, because this would leave her widowed father all alone, creating too much drastic change in both his and her lives. Yet in this scene, she consents to her father’s wishes, and decides in fact that she will marry. Yet at that moment, Ozu shows the still life scene of the vase. This grand climactic moment of the film is substituted by a pure stillness. We feel a dramatic change, while perceiving a motionless image. The actual events coming before and after are not present in the still life, but they are both implied in the same still image, because this transition-point in the story marks the most drastically different ‘before’ and ‘after’. But the actual content of a determinate ‘before’ and ‘after’ are removed from this still image, nonetheless, this purified impression of great alteration remains. We feel in this moment the coincidence of an empty before and an empty after, that is, of the pure form of time.
But we will now consider a final image of time that shows something in continual change.
In […] Chronopolis, Kamler fashioned time out of two elements, small balls manipulated with pointed instruments, and supple sheets covering the balls. The two elements formed moments. [Deleuze, Cinema 2]
Notice Deleuze speaks here of forming moments, and not a flow of time, and also not an extending passage of time. When the two elements make contact, some new variation results in the clay. The figure, with each contact, becomes something different. But it does so by changing what it already was. What it was, and what it is becoming – its before and its after – coincide in each moment of contact.
Kamler. Chronopolis
The portrayal of time in this scene is not the extending passage of duration through which the changes happen, like how each frame of the movie-film blurs together to create the illusion of continuous motion. Rather, synthesis is found completely in each single frame alone, where the ‘before’ is synthesized simultaneously with its ‘after.’ It is not a process; it is a formal condition for time. This, I propose, is what Deleuze means by temporal synthesis.
[Thanks Edwards & Penney]
We know both the change in y and the change in x for secant line K, so we can write the formulation.
We then subtract out the two a2's in the numerator to get 2ah + h2.
Line K will continue to pas through points P and Q, pivoting around point P. As h approaches zero, secant line K moves closer to overlapping tangent line L. See this motion in the animation below.
Here lim stands for "limit", and "h → 0" stands for "h approaches zero". What the above formulation asks is "What is the limit of 2a + h as h approaches zero?" (p.55b)
we may say, more generally, that
Thus the "slope m = m(a) of the line tangent to the parabola y = x2 at the point (a, a2) is given by
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