9 Aug 2012

Cinema & Synthesis: Time for a PreProcessed Deleuze

by Corry Shores
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The following is my presentation at the Annual Conference Dutch Association for Aesthetics at the University of Leuven, Belgium in March of 2012. Thank you Stéphane Symons and others at the Nederlands Genootschap voor Esthetica for organizing such a fruitful and interesting conference.

Corry Shores

Cinema & Synthesis:
Time for a PreProcessed Deleuze



James Williams’ recently published book, Deleuze’s Philosophy of Time, presents a compelling explanation of Deleuze’s three temporal syntheses. Williams’ process-based reading allows him to integrate the actions of each synthesis, like moving parts that fit together to make a larger machine. Yet, he devotes his conclusion to defending his decision to exclude from his analysis Deleuze’s second cinema book, The Time-Image. One of his reasons is that the cinema book portrays Bergson’s pure past as being an instantaneous crystallized doubling of the present and past, causing ‘before’ to be simultaneous with ‘after.’ Yet, if time can be instantaneous, and if ‘before’ can be simultaneous with ‘after,’ then there is no longer any need to regard the synthesis as being a process; for, a process requires the passage of time. So a process-based explanation of Deleuze’s temporality cannot apply to both Difference & Repetition and to the second cinema book. The question we ask is, would a more static or formal interpretation of Deleuze’s time synthesis work in both texts? Williams is also critical of the fact that the cinema text is “fatally attached to the more commonsense and experiential modes of exemplification and explanation we encounter in film.” This is because, instead of explicitly arguing for the simultaneity of the past and present, Deleuze rather expects us to grasp this concept merely by watching certain movie scenes.

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




[Thanks youtube / chantelle369]

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.

Photobucket

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 MankiewiczBarefoot 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.
Link

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.



Alice growing video:
http://www.youtube.com/watch?v=riAUmx_ObN0
Thanks chantelle369

28 Jul 2012

Time and Inquiry in Clifford Duffy's 'AsK'

posting by Corry Shores
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Time and Inquiry in Clifford Duffy's 'AsK'

See Clifford Duffy's 'AsK'

We are to ask ourselves what is a clock, a cock, adoodledoo? Yet we note the importance of this question really being a question, as the poem is titled 'ask,' and it has many question marks, and this question recurs in steady cycles. The affective impression is that questions themselves are under question when we ask 'what is a c(l)ock[adoodledoo]?'

Does the form of a question have something to do with the form of time, and what is the role of clock-like mechanisms in this formation?

The marquee-renewals make a cycle, like how every morning we hear cockadoodledoo from the cock at dawn. The hour hand will make 24 turns to relatively the same marking between each cockadoodledoo, and Duffy's marquee cycle will make something like 4320 cycles in that period. We know that time moves constantly forward, because it keeps moving in circles. The cycles create units of measure that allow us to put aside the continuous heterogeneous alteration through time to instead measure extending quantities of its flow. So is a c(l)ock[adoodledoo] merely a temporal homogenizer?

But why so much emphasis on the asking? What is it about asking that has something to do with time, clocks, cycles, and so forth?

The clock homogenizes. Yet what it homogenizes might be seen as a series of askings, of askings: 'what's next?' What's next, come next dawn? Another cockadoodledoo. But what is next every instant whatever? This is always for us primarily a yet-answered question. It is a sort of drama of the world's mutations.

What is the pure form of time? Putting aside time's actual passage, its form is the immanence of before and after which are in a relation of succession. They are immanent to one another, because time is always in passage from before to after, thus they cannot be structurally apart. So the c(l)ock[adoodledoo] tells us that time is passing, which means there is always a continuous flux of change. Yet the form of time, the before with after, does not change.

A question has a certain sort of temporality. Its answer comes after and is somehow brought into life through its question. When we ask a question, we have already evoked its answer, even though it is not yet explicit. The after is implicitly given with its before in the structure of the question.

So what then is a clock, a cock (adoodledoo), a Duffy marqueed poem? It is a constant reminder that each moment is an asking to be answered. The form of time and the form of a question share in common a bringing into implicit immanence the after with its before.

Clifford Duffy, 'asK'
http://recalltopoetry.blogspot.be/2012/07/ask.html

25 Jul 2012

Preview: What Is Calculus? in Ewards and Penney's Calculus

presentation of Edwards & Penney's work, by Corry Shores
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Edwards & Penney's Calculus is an incredibly-impressive, comprehensive, and understandable book. I highly recommend it.

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[I your author am not a mathematician; I am merely an admirer of Edwards & Penney's wonderful calculus book. Please consult the text or other references to be certain about anything in the summary below. I mean this emphatically.]

[This section introduces problems that we later discuss much further in detail.]



Summary of
Edwards & Penney
Calculus

Chapter 1. Functions, Graphs, and Models
Section 1.5. Preview: What Is Calculus?


Calculus ("the calculus") is a body of computational techniques. It revolves around two basic geometrical problems, and mathematicians have been dealing with these problems for over 2000 years. Both problems involve "the graph y = f(x) of a given function." (p.45)


Problem 1: The Tangent Problem

One problem calculus tries to solve is finding the 'line tangent' at a given point on a curve y = f(x).


Edwards and Penney then formulate the tangent problem with reference to this graph:


So let's first recall what a function is. Functions describe relationships between variables. The function describes the way that one variable varies with respect to another variable, often formulated y = f(x). So consider the function y = x2.

We have two variables, x and y. Both are varying, both increase in value. But the way that the one increases with respect to the other is further describable. As the x value increases, the y value increases to the power of two. So when x has the value of 2, y has the value of 4. And when x is 4, y is 16, and so on. Edwards and Penney offer this definition for functions.

Function:
A real-valued function f defined on a set D of real numbers is a rule that assigns to each number x in D exactly one real number, denoted by f (x).


The set D of all numbers for which f (x) is defined is called the domain (or domain of definition) of the function f. The number f (x), read "f of x," is called the value of the function f at the number (or point) x. The set of all values y = f (x) is called the range of f . That is, the range of f is the set {y: y = f (x) for some x in D). [p.2d]


So recall again the graph Edwards and Penney are using to describe the tangent problem.


Here we see that x varies with respect to y in such a way that the series of their correlated variations makes a waving curve. Now we consider a point P along the continuous variation of x's and y's correlations. a point is described with the x and y coordinate values (x, y). But the way we find y is by finding the value of the function applied to the value of x. So the y value can also be noted as f(x), and thus the coordinates for point P along the function y = f(x) would be P(x, f(x)). In the case of y = x2, we might consider the point (2, 4) for example. Thus the tangent problem:

The Tangent Problem
Given a point P(x, f(x)) on the curve y = f(x), how do we calculate the slope of the tangent line at P?

Finding the tangent gives us what is called the derivative of the function f, and later Edwards and Penney explain how we obtain derivatives. This is largely a matter of differential calculus.

Example


We are driving down a straight road. It takes us a certain amount of time (t) to go a certain distance, and the way that the distance increases as time increases can be described with the function y = f(t). If we find the slope at point (t, f(t)), then we find the velocity at time t.


Problem 2: The Area Problem

Consider this graph.



We might want to know what the area is below the curve between a and b.

The Area Problem
If f(x) ≧ 0 for x in the interval [a, b], how do we calculate the area A of the plane region that lies between the curve y = f(x) and the x-axis over the interval [a, b]?


Example

Consider this graph.

Unlike the prior example which correlated the way that distance varied with respect to time, this new graph shows how velocity varies with respect to time, given with the function y = f(t). So f(t) gives us the velocity of the car at time t. This means that the area under the curve within the time interval [a, b] gives us the distance the car travels between time a and time b.

Text summary and images from:
Edwards & Penney: Calculus. New Jersey: Prentice Hall, 2002, pp.2; 45-47.

Transcendental Equations in Edwards & Penney's Calculus


presentation of Edwards & Penney's work, by Corry Shores
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Edwards & Penney's Calculus is an incredibly-impressive, comprehensive, and understandable book. I highly recommend it.

[Search Blog Here. Index-tags are found on the bottom of the left column.]

[I your author am not a mathematician; I am merely an admirer of Edwards & Penney's wonderful calculus book. Please consult the text or other references to be certain about anything in the summary below. I mean this emphatically.]



Transcendental Equations in Edwards & Penney's Calculus


What do transcendental equations got to do with you?

Because they are all transcendental equations, see the got-to-do entries for trigonometric, exponential, and logarithmic functions.


Brief Summary

The solution to transcendental equations with the form f(x) = g(x) is the intersections of the graphs of the functions.


Points Relative to Deleuze

Again, because they are all transcendental equations, see the got-to-do entries for trigonometric, exponential, and logarithmic functions.


Summary of
Edwards & Penney
Calculus

Chapter 1: Functions, Graphs, and Models
Section 1.4: Transcendental Functions

Subsection 5: Transcendental Equations


We previously examined trigonometric, exponential, and logarithmic functions. These are all types of transcendental functions. Equations that include transcendental functions within them may have infinitely many solutions. Yet they might also have just a finite number of solutions. Edwards and Penney note one approach to dealing with transcendental equations. We might render them as

f(x) = g(x)

"where both the functions f and g are readily graphed." (p.40d) Wherever graphs y = f(x) and y = g(x) intersect are the solutions to the equation.


Example

Consider these graphs


There is a single point where graphs y = x and y = cos x. This means that the equation x = cos x has only one solution. The graphs also tell us that the solution lies within the interval (0, 1).

Text summary and images from:
Edwards & Penney: Calculus. New Jersey: Prentice Hall, 2002, pp.40-41.

Deleuze Cinema Update: Final Judgment. Orson Welles. The Stranger


by Corry Shores
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There is a new Deleuze Cinema Project entry. Click on the link below.

The Nature of Logarithmic Functions. Logarithmic Functions in Edwards & Penney's Calculus

Edwards & Penney's Calculus is an incredibly-impressive, comprehensive, and understandable book. I highly recommend it.

[Search Blog Here. Index-tags are found on the bottom of the left column.]

[I your author am not a mathematician; I am merely an admirer of Edwards & Penney's wonderful calculus book. Please consult the text or other references to be certain about anything in the summary below. I mean this emphatically.]


The Nature of Logarithmic Functions
Logarithmic Functions in Edwards & Penney's Calculus


What do logarithmic functions got to do with you?

In the natural world around us, things often expand or tapper off in a steady way. Consider how sound reverberations taper off or how logarithmic spirals expand:

(Thanks wikipedia )

Logarithms can help us study many phenomena in the natural world around us.


Brief Summary

y = logax if ay = x


Points Relative to Deleuze

Deleuze writes:

Since intensity is already difference, it refers to a series of other differences that it affirms by affirming itself. It is said that in general there are no reports of null frequencies, no effectively null potentials, no absolutely null pressure, as though on a line with logarithmic gradations where zero lies at the end of an infinite series of smaller and smaller fractions. (Difference and Repetition 234c)

As a sound tapers off seemingly to nothing, it is perhaps undergoing an infinite series of lowering variations. The diminishing wave is not so much being negated as it is being constituted by infinitesimal differential relations.


Summary of
Edwards & Penney
Calculus

Chapter 1: Functions, Graphs, and Models
Section 1.4: Transcendental Functions

Subsection 4: Logarithmic Functions


Before we examine logarithmic functions, first recall exponential functions. In an exponential function, a constant base is raised to a variable power. A logarithmic function is an inverse to an exponential function. So consider this formulation for logarithmic functions:

y = logax if ay = x

Here we have a, y, and x. a is the base, y is an exponential power of a, and x is the value of a raised to the power of y. "The base a logarithm of the positive number x is the power to which a must be raised to get x." (p.39c)

Base 10 is the common logarithm: log10x

Later we discuss the natural logarithm e, which is a special irrational number.

lnx = logex

e = 2.71828182845904523536 . . . .

Edwarts and Penny graph y = lnx and y = log10x.


Both graphs rise slowly and steadily as they move to the right, and also, both graphs cross through point (1, 0). Logarithmic functions cannot have negative numbers or zero in their domains, because exponential functions cannot take on zero or negative values. The function log x = log10x increases slowly as x increases. We see this in the graph and also in the fact that log10100,000 = 5 and log101,000,000 = 6. Consider how on the contrary in exponential function ax (with a > 1) growth increases more rapidly than any other powerfunction as x → ∞. The f0llowing example shows how logarithmic functions increase slower than power functions.


Example



This table compares the rate of growth in the power function


with the rate of growth for the logarithmic function g(x) = logx. Here are graphs displaying these values.



As we can see in both the table and the graph, when x > 100,000, logx is smaller than



The graph below shows us the values when x is much smaller.


Here we see that logx at the lower values begins smaller than




but when x nears 5, the growth of logx overtakes


Then much later in their development,


overtakes logx when x = 100,000. Then, when x = 1050,


equals 5,000,000,000, while logx only equals 50.



Deleuze, Gilles. Difference & Repetition. Transl. Paul Patton. New York: Columbia University Press, 1994.

Text summary and images from:
Edwards & Penney: Calculus. New Jersey: Prentice Hall, 2002, pp.39-40.

Shell image from:
http://en.wikipedia.org/wiki/File:NautilusCutawayLogarithmicSpiral.jpg