## 30 Jan 2010

### Instantaneous Tendencies in Prigogine & Stengers Order out of Chaos / La Nouvelle Alliance

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[The following is quotation.]

Instantaneous Tendencies

in

Prigogine & Stengers

Order out of Chaos: Man's New Dialogue with Nature
La Nouvelle Alliance: Métamorphose de la science

How can a continuously varying speed be defined? How can we describe the instantaneous changes in the various quantities, such as position, velocity, and acceleration? How can we describe the state of a body at any given instant? To answer these questions, mathematicians have introduced the concept of infinitesimal quantities. An infinitesimal quantity is the result of a limiting process; it is typically the variation in a quantity occurring between two successive instants when the time elapsing between these instants tends toward zero. In this way the change is broken up into an infinite series of infinitely small changes.

At each instant the state of a moving body can be defined by its position r, by its velocity v, which expresses its "instantaneous tendency" to modify this position, and by its acceleration a, again its "instantaneous tendency," but now to modify its velocity. Instantaneous velocities and accelerations are limiting quantities that measure the ratio between two infinitesimal quantities: the variation of r (or v) during a temporal interval Δt, and this interval Δt when Δt tends to zero. Such quantities are "derivatives with respect to time," and since Leibniz they have been written as v = dr/dt and a = dv/dt. Therefore, acceleration, the derivative of a derivative,
,
becomes a "second derivative." (57-58b)

Comment décrire une vitesse qui varie de manière continue? Comment décrire l'évolution, d'instant en instant, des diverses grandeurs, positions, vitesse, accélération, qui caractérisent l'état instantané d'un mobile? Les mathématiciens ont introduit le concept de quantité infinitésimale pour répondre à de telles questions. Une quantité infinitésimale résulte d'un passage à la limite, c'est la variation d'une grandeur entre deux instants successifs lorsque l'intervalle entre ces deux instants tend vers zéro. La description infinitésimale peut ainsi décomposer le changement en une série infinie de changements infiniment petits, alors que, précédemment, on ne pouvait le décrire que comme le résultat d'un nombre fini de transitions de grandeur finie juxtaposées comme les perles d'un collier.

En chaque instant la description de l'état d'un mobile comprend non seulement sa position, que nous noterons r, mais encore sa « tendance instantanée » à changer de position, c'est-à-dire sa vitesse v en et instant, et sa tendance à modifier cette vitesse, c'est-à-dire son accélération a. Vitesse et accélération instantanées sont des « concepts limites » mesurant une variation instantanée comme le rapport entre deux quantités infinitésimales : la variation de la grandeur position ou vitesse, pendant un intervalle de temps Δt qui tend vers zéro, et cet intervalle Δt lui-même. On appelle de telles grandeurs des « dérivées par rapport au temps ». On écrit, depuis Leibniz, v = dr/dt. Quant à l'accélération, a = dv/dt =
dérivée d'une dérivée, c'est une dérivée « seconde ». (65-66bc)

Prigogine, Ilya, and Isabelle Stengers. Order out of Chaos: Man's New Dialogue with Nature. London: Heinemann, 1984.

Prigogine, Ilya, and Isabelle Stengers. La Nouvelle Alliance: Métamorphose de la science. Paris: Éditions Gallimard, 1979.

## 29 Jan 2010

### Sinking Spasms [80] Deleuze on Bacon, Painting Series. Figure at a Washbasin, 1976

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[The following is quotation. My commentary is bracketed in red.]

Sinking Spasms
Deleuze on Bacon, Painting Series

Francis Bacon

Figure at a Washbasin, 1976
Museo de Arte Contemporaneo de Caracas

Painting 26 of Deleuze's
Francis Bacon: Logique de la sensation. Tome II - Peintures
Painting [80] of the English translation
and Painting [26] of the Seuil 2002 French

it is the body that attempts to escape from itself by means of . . . . in short, a spasm: the body as plexus, and its effort or waiting for a spasm. [...] There is one painting that can guide us, the Figure at a Washbasin of 1976 [80]: clinging to the oval of the washbasin, its hands clutching the faucets, the body-Figure exerts an intense motionless effort upon itself in order to escape down the blackness of the drain. (11c)

c'est le corps qui tente de s'échapper lui-même par... Bref un spasme : le corps comme plexus, et son effort ou son attente d'un spasme. [...] Un tableau peut nous guider, « Figure au lavabo », de 1976 : accroché à l'ovale du lavabo, collé par les mains aux robinets, le corps-figure fait sur soi-même un effort intense immobile, pour s'échapper tout entier par le trou de vidange. (23cd)

The rising-descending, contraction-dilation, and systolic-diastolic oppositions cannot be identified with each other. A discharge, for example, is indeed a descent, as well as a dilation and expansion, but there is also a contraction in the discharge, as in the man at the washbasin [80] and the man on the toilet in the 1973 triptych [73]. (57a)

En effet, on ne peut pas identifier montée-descente et contraction-dilation, systole-diastole : par exemple l'écoulement est bien une descente, et aussi une dilation et expansion, mais il y a de la contraction dans l'écoulement, comme chez l'homme au lavabo et l'homme au bidet du tri triptyque de 1973. (77bc)

[Bacon's paintings cause our eyes to feel pushed-and-pulled in many directions and in many ways, all at once. The different ways can be combined but not reduced to one another. So when we look at the figure at the basin, we notice the circle confining the figure. It gives us the sense that that the space is contracting around him.

So there is a contracting motion that we sense. Yet, this is like squeezing a water balloon. The pressure of the contracting force on the figure causes its insides to try to escape somehow. The dual inward-and-outward forces are like how our hearts contract and release. So Deleuze calls them diastolic-systolic rhythms. But also in this image, Bacon is painting a moment that is no longer than a tenth of a second. And the escape has not happened yet. So the dual wrestling inward-and-outward forces cause the body to shudder-and-shake.

This would be a sort of resonance caused by differences that are forced together, in this case, different motional tendencies. The man's body then spasms in that instant. Notice the vibrations:

It reminds us of the vibration of a string, when we see a short moment of its movement.

The forces want to escape through some hole. In this case it is through his mouth and down the drain. Hence we also sense a downward tendency in the painting.

Note that the motions do not actualize. But we feel them. They are real. But they are virtual, in a sense. They are there as tendencies. But they do not tend outward into extensive space. They instead tend inward into an intensive depth.]

We have seen that the three fundamental elements of Bacon's painting were the armature or structure, the Figure, and the contour. [...] Now, all three of these converge on color, in color. And it is modulation - that is, the relations between colors - which at the same time explains the unity of the whole, the distribution of each element, and the way each of them acts upon the others.

Consider an example analyzed by Marc Le Bot. The 1976 Figure at a Washbasin [80]

is like a piece of wreckage washed downstream by a river of ocher color with circular eddies and a red reef, which prevent the unlimited expansion of color through a double spatial effect that confines the color locally and fixes it, in such a way that it is enhanced and accelerated. Broad flows of color in this way cross the space of Francis Bacon's pictures. If their space is comparable to a homogeneous and fluid mass in its monochromatism, but disrupted by breakwaters, their regime of signs cannot be derived from a geometry of stable measure. It is derived, in this painting, from a dynamic that makes the gaze glide from the bright ocher to the red. This is why a directional arrow can be inscribed on it. [ft1. Marc Le Bot, "Espaces," in L'Arc 73 (special issue on Francis Bacon) [Deleuze p142d] ]

This distribution can be clearly seen. There is the large, monochrome ocher shore as the background, which provides the armature. There is the contour as an autonomous power (the reef) - it is the crimson of the mattress or cushion on which the Figure is standing, a crimson that is combined with the black of the disk and contrasted with the white of the crumpled newspaper. Finally, there is the Figure, like a flow of broken tones - ochers, reds, and blues. But there are still other elements. First, there is the black blind that seems to cut across the field of ocher; then the washbasin, itself a bluish broken tone; and the long curved pipe, a white marked with manual daubs of ocher, which surrounds the mattress, the Figure, and the washbasin, and which also cuts across the field. We can see the function of these secondary yet indispensable elements. The washbasin is like a second autonomous contour which surrounds the Figure's head, just as the first surrounded its foot. And the pipe is itself a third autonomous contour, whose upper half divides the field of color in half. As for the blind, its role is all the more important insofar as, in keeping with a technique dear to Bacon, it falls between the field and the Figure, in such a way that it occupies the shallow depth that separates them and relates the entire painting to one and the same plane. It is a rich communication of colors. The Figure's broken tones incorporate not only the pure tone of the field but also the pure tone of the red cushion, adding to it bluish tones that resonate with the tone of the washbasin, a broken blue that contrasts with the pure red. (101bc; 101d-102d)

Nous avons vu que les trois éléments fondamentaux de la peinture de Bacon, c'étaient l'armature ou la structure, la Figure, le contour. [...] Or tous les trois convergent vers la couleur, dans la couleur. Et c'est la modulation, c'est-à-dire les rapports de la couleur, qui expliquent à la fois l'unité de l'ensemble, la répartition de chaque élément, et la manière dont chacun agit dans les autres.

Soit un exemple analysé par Marc le Bot : la « Figure au lavabo », de 1976, « est comme une épave charriée par un fleuve de couleur ocre, avec des remous circulaires et un récif rouge, dont le double effet spatial est sans doute de resserrer localement et de nouer un moment l'expansion illimitée de la couleur, de telle sorte qu'elle en soit relancée et accélérée. L'espace des tableaux de Francis Bacon est ainsi traversé par de larges coulées de couleurs. Si l'espace y est comparable à une masse homogène et fluide dans sa monochromie, mais rompue par des brisants, le régime des signes ne peut y relever d'une géométrie de la mesure stable. Il relève, dans ce tableau, d'une dynamique que fait glisser le regard de l'ocre clair au rouge. C'est pourquoi peut s'y inscrire une flèche de direction ». [ft141. Marc Le Bot, Espaces, in L'Arc n 73, Francis Bacon.] On voit bien la réparation : il y a la grande plage ocre monochrome comme fond, et qui donne l'armature. Il y a le contour comme puissance autonome (le récif) : c'est le pourpre du sommier ou coussin sur lequel la Figure se tient, pourpre associé au noir de la pastille et contrasté avec le blanc du journal froissé. Il y a enfin la Figure, comme une coulée de tons rompus, ocres, rouges et bleus. Mais il y a encore d'autres éléments : d'abord la persienne noire que semble couper l'aplat ocre ; et puis le lavabo, lui-même d'un bleuté rompu ; et le long tuyau incurvé, blanc marqué de taches manuelles ocres, qui entoure le sommier, la Figure et le lavabo, et qui recoupe aussi l'aplat. On voit la fonction de ces éléments secondaires et pourtant indispensables. Le lavabo est comme un second contour autonome, qui est pour la tête de la Figure, tout comme le premier était pour le pied. Et le tuyau lui-même est un troisième contour autonome, dont la branche supérieure divise en deux l'aplat. Quant à la persienne, son rôle est d'autant plus important que, suivant le procédé cher à Bacon, elle tombe entre l'aplat et la Figure, de manière à combler la profondeur maigre que les séparait, et à rapporter l'ensemble sur un seul et même plan. C'est une riche communication de couleurs les tons rompus de la Figure reprennent le ton pur de l'aplat, mais aussi le ton pur du coussin rouge, et y ajoutent des bleutés qui résonnent avec celui du lavabo, bleu rompu qui contraste avec le pur rouge. 137b; 137d-138d

Sometimes again, the field is interrupted only by a thin white bar that crosses it completely, as in the three faces of the beautiful rose-colored Triptych of 1970 [62]; and this is also the case, partially, in the Figure at a Washbasin [80], where the field is crossed by a white bar, subordinating it to the contour. (103c)

Tantôt encore, l'aplat est seulement interrompu par une mince barre blanche, qui le traverse tout entier, comme sur les trois vaces du très beau triptyque rose de 1970 ; et c'est aussi le cas, partiellement, de l'Homme au lavabo dont l'aplat ocre est traversé par une barre blance comme dépendance du contour. (139c).

Lastly, there remains the contour. We are familiar with its ability to multiply itself, since it can include a large contour (for example, a rug) surrounding a midzied contour (a chair), which itself surrounds a small contour (a round area). Or the three contours of the Figure at a Washbasin[80]. (106a)
Reste le contour. Nous savons son pouvoir de se multiplier, puisqu'il peut y avoir un grand contour (par exemple un tapis) qui cerne un moyen contour (une chaise) qui cerne lui-même un petit contour (un rond). Ou bien les trois contours de l'« Homme au lavabo ». (142b)

[Bazin desribes the flowing motions in the painting, and the "dynamic that makes the gaze glide from the bright ocher to the red". Painters can use colors and their relations to cause our eyes to want to move from one place to another. Take for example this diagram from Paul Klee's notebooks, where he draws arrows for the movements (in his case our eyes move from red to yellow, unlike in this Bacon piece where they move from ochre to red).

Notice now how our eyes jump around the squares in Klee's Farbtafel Qu 1:

So we will look now at these motions which result from the colors and the structures they create. Our eyes begin in a sense with the ochre field. This is like a screen where the images are pinned flat to it. Deleuze says the field serves a structural role similar to an armature in sculpture.

(Lauri R. Panopoulos' Tyrone Sculpture. Thanks www.lauridolls.com)

The armature supports the structure. In Bacon's paintings, the fields are something like a two-dimensional plane, and the figures are then pinned-down upon it. Look again at the ochre 'armature' field.

Bazin says it is like the shore, held firm against the ocean waves. This field is interrupted by shapes that serve to enclose figures inside. Note that what brings-out this contour is the contrast of color.

So this white ring is one of three enclosing contours.

Another contour is the red rug which closes in on his lower body.

Note again how it is the color of the red rug that gives it this role distinct from the field. The red, Deleuze says, combines with the black circle, and is contrasted with the white of the crumpled newspaper.

And a third contour is the washbasin, which encloses the man's head.

Now we will examine the colors of the man's body. They are not monochromatic like the ochre field and the red rug. Instead, we see reds, blues, and ochers broken-up and flowing into each other.

The color is modulated in a very different way in the Figure's body. (This this entry for more on modulation). Deleuze then points-out how the colors designate the other elements of the painting. On the washbasin we see different broken blue tones, which contrast with the carpet's red. The Figure has both bluish and redish colors, as well as some of the pure tone of the field.

Look now at the black blinds.

Recall in the first place how the figure is pinned to the ochre field. There is not much spatial depth between them. Deleuze says that Bacon uses a technique to both link the figure and background onto the same plane, all while establishing their difference. In this case, the black blinds perform that function. They stand between the figure and field, all while doing so without creating a sense of spatial depth.]

Deleuze, Gilles. Francis Bacon: The Logic of Sensation. Transl. Daniel W. Smith. London/New York: Continuum, 2003.

Deleuze, Gilles. Francis Bacon: Logique de la sensation. Paris: Seuil, 2002.

Deleuze, Gilles. Francis Bacon: Logique de la sensation. Tome II - Peintures. Paris: Editions de la différence [Littératures], 1981.

Images obtained gratefully from:

Cropped images taken gratefully from:

Vibrating string image:

Armature image

Tyrone Sculpture

Paul Klee, Unendliche Naturgeschickte, (Basel : Schwabe, 1970), p.146.

### Deleuze Cinema Update: Disorderly Caddies. Jerry Lewis. The Disorderly Orderly

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There is a new Deleuze Cinema Project entry. Click on the title below.

### Modulation of Sensation: Deleuze, Bacon, Cézanne, Wagner, and Richard Pinhas

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[Other entries in this Rhythm of Sensation series]

The following is a selection (pp.117-136) from my M.Phil Thesis: The Rhythm of Sensation on the Surface of Sense: Communication in Deleuze as NonSensed and Intense. Defended and archived at the Katholieke Universiteit Leuven, 2008. It may refer back to previous sections, which are indexed here. [I am deeply grateful to the sources of the images. I am still locating some of them, thanks for your patience.]

Modulation of Sensation:
Deleuze, Bacon, Cézanne, Wagner, and Richard Pinhas

Deleuze speaks of modulations in two general senses: 1) as alterations of modalities that 2) sometimes proceeds through modules which affect those modalities. Deleuze’s references to Paul Cézanne and Richard Pinhas direct us to the examples of color modulation in Cézanne’s painting, to musical modulation in Wagner’s compositions, and to electronic sound synthesizers.

Deleuze notes that Cézanne’s modulation of color, his “principle operation,” suppresses contrasts of light and darkness.[1] It creates relief through changes of hue, and not of tone. (Colors, such as red and green, are hues, and their tonal values are the degrees of lightness or darkness, shifting chromatically from white to black). Through these changes, modulation serves as a “variable and continuous mold” that alters color, doing so by the law of Analogy:[2] this law for Cézanne is his logic of organized sensation, which we will explain first before addressing his use of color modulation.

Cézanne distinguishes representation from reproduction: a painter may only represent the sun’s intensity, he cannot make the paint shine so brightly.[3] However, the artist can surround the depiction of the sun with an arrangement of other colors organized in such a way that they invoke in us the sensation of seeing the sun. The painter, then, is not to copy the object, but to realize the sensations we have when viewing such an object, which requires that the painter break from a visually accurate rendition, and paint instead according to a “logic of organized sensations:” when Cézanne views his scene, his eyes move slowly from place-to-place. With each subtle movement, he does not so much intend to reproduce exactly what he sees; instead, he selects a color which would invoke in his viewers the same internal states that he has while viewing that part of the scenery. However, any single selected color alone does not by itself produce that internal state. Rather, it is only in its relation to its immediate surrounding colors that it can have its unique effect. Hence in this way, Cézanne modulates the color, because he makes subtle and intentional variations on the local level, so that his viewers undergo sequences of modulated internal states resembling the ones he experienced while painting.

Thus, the colors he selects serve as a sort of coding of sensation that the viewer ‘interprets,’ but not as though they were symbols.[4] However, the interpretive process is just as much cerebral as sensual, hence its “logic.”[5] Painting, for Cézanne, involves more than mere sense impressions and instant associations: it also requires his conscious effort to select the right combinations of color alterations. Cézanne often used broad, ‘blocky’ paint strokes, carefully placing one patch at a time, progressing from one part of the painted object to the next, following color sequences that would be interpreted by the viewer so as to reproduce the experience of the painted scene or object. Hence his “vision was much more in his brain than in his eye.”[6]

[Note below the 'blocky' strokes in his Mont-Sainte Victoire. See also the close-up]

(Thanks

Deleuze explains that Cézanne creates depth by replacing the traditional use of value differences with his particular brand of color modulations.[7] Normally, depth is portrayed through modeling: the painter uses differences in value (lightness and darkness) to express the physical relief of the model being depicted.[8] Adding white or black to a color diminishes its intensity, which as a painting term means the degree of saturation or purity of color tone. When there are no contaminating inclusions of black or white to a color, it is in its purest hue, which means it is at its highest saturation and its greatest intensity (in this restricted painting sense of the term). In modeling, one would use variations in value to show relief: changing the amounts of shading indicates the positions of objects in reference to a light source, and creates the visual dimension of depth. Cézanne, however, uses the oppositions of warm and cool tones, in some cases, to represent light and shadow or varying distances of objects.[9] Blue has no greater tone value than yellow when both are equally saturated, yet in certain contexts, when blue is painted next to yellow, it might suggest depth or volume.[10] To modulate the color would be for Cézanne to place a patch of one saturated color beside another, with their relation bringing about an effect determined not by some pre-set system but by the circumstances of their contextualization with the other color patches. (We can see in this Cézanne landscape below how the intense green on the horizon’s center recedes into the background. What is notable about this is that normally darkened colors seem like shadows and appear as though at a distance. Here we see that the intense green has not been darkened, and yet it colors the most distant place on the horizon).

Hence, in Cézanne's paintings we often encounter seemingly out-of-place color strokes, or unrepresentative combinations of color. In his portrait below of Hortense Fiquet, for example, we see odd color-blocks used for her skin, (painting is cropped for focus).

(Thanks

However, if we attended more to the sensuous and conceptual affects that these colors have on us, we might better detect the logic of organized sensation at work in his paintings. Lawrence Gowing explains how Cézanne’s “mutations of color” were as theoretical as they were perceptual:

When one of his visitors was puzzled to find him painting a gray wall green, he explained that a sense of color was developed not only by work but by reasoning. In fact the need was both emotional and intellectual. The mutations of color with which he modulated surfaces that would have seemed to a less logical mind to require no modeling whatever were a necessity to him.

We may illustrate with the example of Cézanne's The Green Pitcher.

According to Lawrence Gowing, Cézanne began with a blank center-point of the pitcher, the point culminant, which is the part of the object which is closest to our eyes.[12] He then surrounds the culminating point with blue color-patches, and proceeds by running through the color spectrum to green (indicating the actual color of the pot) then to yellow, according to a pre-conceived ‘logic,’ in order to evoke the sensations of seeing the pitcher.[13] Norman Turner disagrees with Gowing’s claim that the color order was fixed in advance, a point which will prove relevant when describing Bacon’s continuously variative modulation. Turner argues that Cézanne does not select his colors according to an overarching and pre-determined organization, but rather he continues to each neighboring color-patch on the basis of how its immediate predecessor conditions that color change; for, each subtle transition alters the possibilities and limitations for how he may proceed. In other words, Cézanne was not so much concerned with how one color-patch associates with another one far away on the canvass, but rather more with the relation between any one patch and its immediate neighbor, in terms of the sensations unlocked in a transition from one to the other.[14] This influences the subtle sequence of quick impressions we have when our eyes move from one part of the painting to the next.

Also, to better grasp Deleuze's notion of continuous modulation, we might follow Turner and Richard Pinhas, Deleuze's student, by comparing Cézanne's color modulation to Wagner’s key modulation. Each time Cézanne modulates to the next color, he creates a general feeling, and opens possibilities for the next transition, which might not have been available for a different color. In this way, Cézanne's modulation is thought to be like musical key modulation.[15]

[We can explain the musical technique of modulation by drawing from the work of ancient Greek philosophers. Pythagoras demonstrated harmony relations between sound frequencies, by using single-stringed instruments called monochords.

(Thanks

(Thanks www.britannica.com)

For example, he demonstrated that when one string is played simultaneously with another one that is half its length, the strongest harmony is produced: this is the octave harmony. Pythagoras divided the octave into 12 smaller units, because this particular division establishes pitches with the greatest possibilities for harmonic combinations.[16] If one were to compose a song using not all twelve pitches, but instead a smaller pre-determined set, then certain harmonic relations would be excluded, and others emphasized. Different such limited sets, then, have their own feel or color to them, their own mood. Some such early Greek note patterns are called moods or modes; and both Plato and Aristotle make reference to the different sorts of emotions that these modes evoke. Both philosophers, for example, criticize the mixed Lydian (mixolydian) mode for darkening people’s moods.[17] However, one can also change from one mood to another, that is, to modulate between modes.

Yet, there is a more subtle sort of modulation which we refer-to here, key modulation: of the many Greek modes, two became especially prevalent, but each of these may itself slightly vary its feeling; the note patterns may change their initial “root” note, which makes more subtle changes of mood. These different patterns are the keys, which can be modulated by using notes at the end of one melody (cadences) which are found in both keys, so to make a smoother transition.] Such modulating changes the key-feeling, but in a way which couples different moods at once during the transition. Likewise in painting, the artist may select certain dominating hues, which together have their own key-feeling, if you will, and modulate between them (the use of music terminology in describing painting is common, for example, rhythm, tone, harmony, dissonance; and vice versa: texture, color). The effect of Cézanne's color patches has little to do with the representation of their objects; rather, “it is the relationships between them – relationships of affinity and contrast, the progression of it tone to tone in a color scale, and the modulations of it scale to scale – that parallel the apprehension of the world.”[18] This is Deleuze’s philosophical interest in this sort of modulation, because he would like to explain how Bacon’s diagramming couples Figures’ movements by modulating the colors between them.

A description of Wagner’s modulation techniques is important for this discussion, because he advanced modulation from a more rigid sort to a smoother one, to a modulation synthétique continue, as Pinhas calls it; and, it is this latter sort that concerns Deleuze. [In key modulation before Wagner, a sense for the original tonal point of departure is maintained, so that the modulations may return to it for resolution. Usually in these cases, the composer uses a convenient bridging chord whose notes are found in both the prior and the latter keys, along with ambiguous notes, to serve to smoothly transition from one key to another. We might illustrate with an example in which the words in a verse serve to make this bridging transition. Wagner compares two possible lines: 1) Liebe gibt Lust zum Leben, (love gives joy to living) and, 2) die Liebe bringt Lust und Leid, (love brings joy and sorrow). In both cases, the phonetic compatibility of the substantives groups them together, superposing them through rhyme, despite their distinct occurrences. In the first case, the feelings evoked by the terms Liebe (love), Lust (joy), and Leben (living) are all compatible, just as are the phonetics of their terms. However, in the second case, the final term Leid (sorrow) ends the phrase with a sadder tone, but is still phonetically superposed to the happier feelings preceding it and overlapping it through phonetic harmony. Hence in the second line, a musician composing the music to such words would have cause and means to move to a new key feeling, perhaps a more somber minor key, and the transition can be made because the phonetics serve to bridge the two different key feelings. In the case of his Tristan und Isolde, his composition technique gives the feeling of moving continually towards other key feelings, although without ever arriving to one, and he leaves many of the chords ambiguous as to their key. His purpose is to induce the feeling of unsatisfied desire, and does so by creating expectations for resolution by modulation into another key, but yet disappoints that expectation by leaving the keys in limbo.][19] Hence in this way, Wagner advanced the technique of modulation, so that instead of limiting developmental options by striving to give the listener a sense of orientation and resolution, Wagner’s modulations progress more freely by lacking a determinate ground and finality.

A student of Deleuze, Richard Pinhas, a progressive musician and philosophy scholar, further elaborates the importance of Wagner’s innovation of the modulation synthétique continue, which led to 20th century developments in modulation, including the electronic modulation of synthesizers. [Pinhas explains that Wagner’s key-modulation technique allows for the continuous translation of melodies into other modulated forms, thus serving as an opérateur d’hétérogènes: something that couples a series of heterogeneous elements one-after-another.[20] Because Wagner’s modulations in some works never obtain a feeling of resolution, none of the modulated keys took a dominant role, and they all smeared into one continuous modulation. Younger contemporary of Wagner, Debussy, pushes modulation even further in this direction. In Wagner, we can follow the tonal progressions and tensions, even though they never resolve. Debussy, however, does not have this tonal tension, and his modulation is not even the tension of wandering unresolved key feelings; but rather, it remains within the sensuousness of one chord (one small group of pitches), which are gradually built up with more instruments playing the notes of that chord. This produces the aquatic effect: it modulates not between keys, but instead is a fluid modulation with very smooth transitions between different parts, which blurs the boundaries between them. Using this technique, Debussy continuously modulates other features of the sound, like timbre, in a modulation synthétique continue.[21] Yet this watery blurring does more to deform the sounds, to smear one into another blurry one. This function has been recently taken-over by electronic synthesizers, both digital and analog. They alter sounds, but always by degradation, taking away their fidelity from their parent sound, making them low-fi(delity), deforming the sound in a sort of perpétuelle transition.[22]] This modulatory technique of Wagner, Debussy, and electronic synthesizers operates as a diagramme modulaire, bringing about la modulation comme différence pure;[23] Deleuze is interested of course in these differences that are forced together through modulation, which likewise disorganize our faculties.

Wagner’s innovations, then, resemble the color modulation in Cézanne’s logic of organized sensations. Cézanne moves locally from one color patch to the next, without necessarily maintaining an orienting color base, moving rather through a continuous modulation from one patch to the next. Deleuze elaborates this notion of a continuous and aimless modulation, by differentiating the operations of analog and digital synthesizers, basing his distinction on an unpublished text by Pinhas.

[Deleuze notes that analogical synthesizers operate by sending the sound signal through different modules, which are discrete self-contained circuits. Each one alters the sound in its own unique way; and they may be linked and re-linked by “patch” cables, which allows for countless ways to route the sound signal through the different modules or patches.[24] (We can see Deleuze’s example in the image below of a modular analog synthesizer: features of the sound signal are modulated when sending it through different modules by means of the patch wires, with uncountable possible outcomes).

Digital synthesizers, Deleuze explains, are integral, that is to say, rather than the signal moving through a sequence of modules, it is instead processed by electrical circuitry whose different parts are already integrated with each other, and do not require manual connection with wires.

We see in the image above that the parts of a digital synthesizer’s integrated circuit are already wired together; the signal’s processing happens on a more “abstract” level through the manipulation of code.] The analog modules parallel Cézanne's use of “color patches” to modulate color: he begins with one broad stroke of uniform color, then moves to the place beside it, changing the color somewhat, thereby modulating its hue; and, he decides which change to make according the logic of organized sensations. Thus Cézanne, Wagner, and electric synthesizers are modulatory in two ways: by modulating the features of the sound or color, and doing so through a series of modules (color-patches, keys, synthesizer-patches).

Because each patch of an analog synthesizer has circuitry components that reduce properties of the sound signal itself (according to Deleuze), analog synthesizers modulate by means of subtraction, and in this way some of the fidelity to the original sound is lost. In contrast, digital synthesizers are additive, and Deleuze makes this distinction clearer by comparing the operations of pass filters; and, although this may be one of his most technical examples, it serves to explain how we are to give a positive connotation to deformation. [We might imagine a musician playing on a drum kit, using both deep drums and cymbals. The drums produce low frequencies, and the cymbals high ones. A low-pass filter, whether analog or digital, will let the sound of the drums through, and strip away the sound of the cymbals, because a low-pass filter only lets the low frequencies pass through it. In the specific case of low-pass digital filters, the sound waves produced by the drums and cymbals are converted electronically into a code; and, in order to modify it, the digital filter must perform operations on the code. This process makes the original code more complex by adding new coded information to it, even though this new larger and more complex code will then decode into a diminished sound: when we play the output of the digital low-pass filter, we hear the drums perfectly, but the cymbals not at all. For analog low-pass filters, the sound waves of the drums and cymbals are converted into an electrical signal. Both the original sound waves and the converted electrical current oscillate in concord (they together move back-and-forth at the same frequencies): this is analogical mimicry. The analog low-pass filter, then, only lets the electrical signal through when it is moving at low frequencies, and blocks its passage when moving at higher frequencies. This results in a diminished signal, that when re-played, reproduces the sound waves for the drums, but not for the cymbals.][25] What Deleuze concludes from this distinction is that an analogical process of sound modification (modulation) enhances a sound by subtracting something from it. Whether or not that is an accurate depiction, is beside the philosophical point that this example illustrates. Deleuze calls analogical modulation an intensive subtraction, because he considers intensity at its greatest magnitude to equal a value of 0; and hence, its increases in intensity are actually falls to 0.[26] (Of course, Deleuze's statement that there is no absolute 0, which we cited previously, refers to the intensities studied in physics – for example, temperature – and perhaps has no bearing on facultative intensities). Yet, to better grasp this notion of intensity equaling zero, we will need to explore his concepts implication and explication.

Deleuze's account of implication and explication in Difference & Repetition will seem abstract unless we apply these terms to his revised doctrine of the faculties. In those cases when our faculties are disordered, we would be wrong to think that the differences between them can be measured, as if there were a homogeneous scale of values that could be used to gauge their distance from one another. However, we might still say that to greater intensities corresponds more depth: as our faculties become more disorganized, it is as though we loose stable ground and feel ourselves in freefall. However, if our faculties were to come more into accord, stability would return, and objects would become more recognizable, as we become more able to determine their spatiotemporal features. In this way, the heterogeneous intensive rhythm of sensation is made more homogeneous and extensive, and thereby, more qualitative features may be attributed to the sensed object. Yet by doing so, the original intensity diminishes, as it comes to take the form of extensity and quality.

Thus, Deleuze speaks of intensity as being implicated and inexplicable.[27] From what we have said regarding the discord of the faculties, it might seem that intensity resides implicitly in facultative disorder, and is only transcendentally sensed as the differences between faculties. We might illustrate this by considering Bacon’s 1946 Painting.

After a period of initial confusion regarding the meaning and coherence of the images, we might imagine instead that we eventually somehow become able to determine the “story” that it tells. We could then view the painting in its full extent, and explicate its meaning, its qualitative & extensive features, and its identity. When we were initially confused by the painting, we experienced the coupling of contraries that make up its matters of fact; yet, by explicating these phenomenal paradoxes into coherent descriptions, we cease to experience the painting as an event, and walk-away retaining a dull representation of it.

Thus, explication cancels intensive difference insofar as it becomes explicated. Such differences in extensive features as “the high and the low, the right and the left, the figure and the ground” flow from something deeper, in fact, from the intensive depth itself. In other words, before we are able to discern the extensive relations in our perceptions, our faculties must first be confused by the irregular ways that things are given to our senses (this is the rhythm of sensation). As our faculties establish artificial regularities – by finding a common measure to determine the extensive features of the things we perceive – what was once intensive depth then becomes extensive visual distances. It is by this means that we come to discern the ground from the figure it surrounds.[28] This will be important in contrasting Bacon’s modulation with Cézanne's; for, by merging figure and ground onto a common plane, Bacon better keeps depth from explicating into extensity.

Depth, then, is the magnitude of the faculties’ disorder.[29] Moreover, Deleuze does not consider the distances in depth to be a negative relation, but rather a positive affirmation of the difference making-up the distant faculties. He offers a mathematical example of how distance can be used to positively affirm the value of a number. He first considers a formulation that defines equal mathematical values negatively; for, it claims that, if two values cannot be different, then they must be the same. (More accurately, ‘if a b is impossible, then a = b’). Thus, the sameness of value between a and b can be established by denying the possibility of their difference. Contrariwise, his second formulation positively establishes the sameness of two unknown values by affirming that they both share the same distances to other values. (‘If a is distant from every number c which is distant from b, then a equals b’). Although, in Deleuze's case, he is not speaking of an extensive quantitative distance value, but an intensive one which cannot be given an explicit value-measure.[30] For him, the notion of equality is a matter of extensity, and quality is an issue of resemblance. However, “extensity and quality ... cover or explicate intensity. It is underneath quality and within extensity that Intensity appears upside down,” (C’est sous la qualité, c’est dans l’étendue que l’intensité apparaît la tête en bas).[31] Hence in its depth, intensive difference is not negative, but only appears to be so when explicated.

The intensive differences between disorganized faculties precede all sensations of extension and quality, but yet none of our given empirical faculties can sense this intensity. The role of the faculties is to explicate the objects they commonly detect; thus, they cannot sense intensity; for, in order to do so, they would need to raise it from the depths, elevating it to the “surface” of extensions, thereby canceling it before they can sense it. When extensities explicate intensities, the intensities become concealed. Thus, intensity can only be detected by a “transcendental exercise of sensibility,”[32] in which our faculties allow themselves to be pushed to their limits so to let the intensities flow through our bodies’ various zones and levels. Hence, the purpose of taking drugs for sensory distortion is to transcendentally sense intensity without any extensities or qualities that might explicate it, so to feel the irregular rhythm of sensational chaos. (Although it is not quite clear what Deleuze means by sensing something transcendentally, it seems that we may reference his descriptions of the way the BwO experiences its internal disorders).

Before we are able to explicate an object, we must first presume it is possible to do so. Kant explains this in terms of the object = x, which is a concept that Deleuze modifies. Kant explains that cognition is only possible by means of a concept, which enables us to unify our successive manifold of intuitions in just one act of consciousness.[33] Even in sublime experiences when these successive apprehensions could not be unified, still we presuppose the possibility for any object whatever to be unified into a concept. In other words, there is the a priori necessity that there be a sort of empty category or generic object to which any representation or concept could correspond; otherwise, the series of apprehensions would have no cause to unify. This generic object is the something in general = x, or object = x, which serves as the transcendental ground for “the unity of the consciousness in the synthesis of the manifold of all our intuitions, hence also of the concepts of objects in general.”[34] And, this original and transcendental condition is transcendental apperception, which is the “pure, original, unchanging consciousness;” whereas empirical apperceptions are the sequences of sense intuitions. Because the object = x is not empirically intuited, Kant considers it as the “transcendental object.”[35] Deleuze characterizes this something = x as a something = nothing, because it is an empty apperception. However, it becomes a lion = x when we synthesize all the particular empirical apperceptions that can turn the undetermined x into a lion: its “long hair in the wind, a roar in the air, a heavy step, a run of antelopes, well, I say it's a lion.” In this way, the diversity of empirical apperceptions becomesspecified and qualified when the faculties enter into accord regarding the series of apprehensions; and, when that synthesized image in the imagination is matched with the concept for lion, the perceived lion becomes recognized.[36]

As the a priori condition for the comprehension of empirical intuitions, the object = x is a matter of transcendental apperception; and, as non-empirical, it exemplifies Kant’s transcendental idealism. Deleuze adopts this notion of the transcendentality of the inexplicable something = x; yet, because for him it is not transcendentally “apperceived” in the mind – but rather is the underlying violent motivational force driving each empirical faculty to its limits in their effort to synchronize – the object = x exemplifies Deleuze’s transcendental empiricism.

Thus, we see that as intensity decreases, objects come more to be determined according to their extensive spatiotemporal and qualitative features, and in that way they become more explicated into extensity. Deleuze summarizes this inverse relationship with a modification of Kant’s formula, intensity = 0, which for Deleuze means that intensity is at its greatest magnitude when its numerical value is zero. However, Kant’s scale is the inverse of Deleuze's; for Kant, thenegation of intensity has the value of zero. Uncovering the difference between their formulations will explain how intensity is a fall for Deleuze, and thus why modulation produces this intensive drop.

For Kant, sensations have an intensive magnitude, which is the degree of influence on our senses, and it may diminish to 0.[37] As it rises-up from 0, its degree of intensity matches the extensive magnitudes of those objects causing its increase, so that an illuminated surface of some extensive measure causes as great a sensation as would the combination of a certain number of smaller such surfaces, themselves each of equal luminosity.[38] In other words, greater intensities correspond to greater extensities, which for Kant, provides a way to quantify them.

However, for Deleuze there is an inverse relationship between intensity’s magnitude and its measure: when its numerical measure is high, its actual magnitude (of facultative disorder) is low, and vice versa. Deleuze does not want us to take this formulation too literally, because we really have no way to quantify our intensities, not even inversely by assigning them higher numerical values. Rather, what he wants to emphasize is that the more our faculties disorganize, the more we are able to experience intensity without it being cancelled by extensive explication. This is his way to counter the Kantian notion of perception, because for Kant, when there is no phenomenal reality, intensity equals zero;[39] but for Deleuze, phenomena “appear” (flash) when intensity is at its greatest, which occurs when its numerical value equals 0; for, that happens when extensive numerical values are least a factor in sensation. Thus, we experience an increase of intensity as a fall to zero, and as a fall from stable ground.[40]

Hence, we may return finally to the falling intensive subtractions of modulation, which Deleuze exemplified with the analog synthesizer. We might also recall that, for Pinhas, electronic-synthesizer modulation causes sounds to become low-fi: by decreasing fidelity, we experience a sort of confusion as we come less to recognize the sound. Bacon’s diagramming acts as a modulator, then, in the ‘synthesizer’ sense of the term, because it is a scrambled distortion that bends an image into alternate dimensions and formations. Deleuze differentiates Bacon from Cézanne in terms of Bacon’s deformation of bodies, but also in terms of the depth these painters create. Cézanne's modulations – which use color alterations to create visual depth relations – cause in the viewer’s perception the sense that objects in the background are moving away, and those in the foreground are moving forward. (Below, in Cézanne's The Bathers, we see both a slight deformation of bodies; and, we may also notice how the modulation from the skin colors to the green causes the plants to recede into the background as the bodies seem to lift forward).

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Bacon’s diagramming, on the other hand, superposes incompatible spatial dimensions so to confuse extensions of visual depth; and, the vast expanses surrounding the deformed figures are often a monochromatic flat background rather than a three-dimensional space fading-off into the horizon. Bacon’s visual depth, then, is more shallow and superficial in the sense of extensity, and thus deeper in the sense of intensive facultative depth.[41] (Below, in Bacon’s 1982 Studies of the Human Body, we see the flat expanse which places the background at the same level of depth as the figure).

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Deleuze, then, differentiates Bacon’s and Cézanne's modulation techniques. When Cézanne modulates from one color patch to the next, he chooses each variation according to which color will replicate the experience of seeing the actual scene being painted, that is to say, according to alogic of organized sensation. Bacon’s technique, however, instead involves a logic of disorganized sensation: his diagrammed modulations are not determined rationally, but come-about through the irrational influence of chance. Also, Cézanne’s modulation would seem more like Wagner’s, where there is somewhat of a sense of key feeling for each color patch, even if they never resolve. Bacon, however, modulates color in a similar manner, yet for him, there is more deformation of bodies, which in terms of the colors in the diagrammed areas would mean something like the fidelity-lowering effect of continuous modular synthesis that Pinhas describes. Bacon’s diagram, then, deforms bodies through continuous modulation, as though it were a carnival mirror that not only altered the proportions of the figures, but their entire appearancesas well. So, by means of diagramming’s modulation, Bacon creates aesthetic analogies that force our faculties to try to organize while at the same time barring them from doing so. To witness Bacon’s paintings, it seems, would be to have an unresolving sublime experience.

Hence, we see that the importance of Bacon’s diagramming technique in Deleuze's thinking is that it exemplifies concretely the way that chaos and order interact so to produce fuller sensations, by means of the internal dissonance of our faculties and our disharmony with the world around us. It is in this way that Deleuze's theory of sensation runs counter to the phenomenological account of the organicism and harmony of perception.

[1] Gilles Deleuze, Francis Bacon: Logic of Sensation, Transl. Daniel W. Smith, (London: Continuum Books, 2003), Francis Bacon : Logique du la sensation (Paris : Les Éditions du Seuil, 2002), p.111.

[2] Logic of Sensation, p.83. Logique de la Sensation, p.111.

[3] Lawrence Gowing, “Cézanne: The Logic of Organized Sensations,” in Conversations with Cézanne, Ed. Michael Doran, (Berkeley: University of California Press, 2001), p.197.

[4] Gowing, p.197.

[5] Gowing, p.212.

[6] Norman Turner, “Cézanne, Wagner, Modulation,” The Journal of Aesthetics and Art Criticism, (Vol. 56, No. 4, Autumn, 1998), pp. 359. Quote from: Gowing, p.189.

[7] Deleuze, Logic of Sensation, p.83. Logique de la Sensation, p.111.

[8] “‘Look well at your model’ Couture advises, ‘and ask yourself where the light is greatest. ... Establish the point at which the shadow is deepest, the black most intense. It serves as a guide, as a standard for finding the different values, of your shadows and your tints,’” Turner, p.358.

[9] “One should not say model, one should say modulate” Cézanne, qtd. in Turner, p.360. “On ne devait pas dire modeler, on devrait dire moduler,” Turner, footnote 34, p.363.

[10] Gowing, p.191.

[11] Gowing, p.186.

[12] Joachim Gasquet, “What he told me...” in Conversations with Cézanne, p.121.

[13] Gowing, p.187.

[14] Turner, footnote 27, p.363.

[15] “Where it gives place to the juxtaposition of yellow and red and the alignment of the form appears to change, it may be that Cézanne thought of himself as passing to the next scale,” Gowing, p.204.

[16] Crotch, “On the Derivation of the Scale, Tuning, Temperament, the Monochord, &c,” The Musical Times and Singing Class Circular, Vol. 10, No. 224, (Oct. 1, 1861), p115.

[17] Plato, Republic, Book III, 398e. Aristotle, Politics, 1340a.

[18] Gowing, p.204.

[19] Turner, “Cézanne, Wagner, Modulation,” p.354.

[20] Richard Pinhas, “Le rythme et la modulation synthétique: Simultanéité et compossibilité des motive chez Richard Wagner,” in Les Larmes de Nietzsche: Deleuze et la musique, (Paris: Flammarion, 2001), p.165.

[21] Pinhas, p.171.

[22] Pinhas, p.176.

[23] Pinhas, p.180.

[24] Deleuze, Logic of Sensation, p.81. Logique de la Sensation, p.109.

[25] Logic of Sensation, p.81-82. Logique de la sensation, p.109-110.

[26] Logic of Sensation, p.82. Logique de la sensation, p.109-110.

[27] Difference & Repetition, p.228. Différence et répétition, p.293.

[28] Difference & Repetition, p.229-230. Différence et répétition, p.296.

[29] “The strangest alliance is formed between intensity and depth, which carries each faculty to its own limit and allows it to communicate only at the peak of its particular solitude,” Difference & Repetition, p.231. Différence et répétition, p.297-298.

[30] Deleuze, Gilles. Difference & Repetition. Transl. Paul Patton. New York:Columbia University Press, 1994, p.234. Deleuze, Gilles. Différence et répétition. Paris: Presses Universitaires de France,1968, p.301-302.

[31] Difference & Repetition, p.235. Différence et répétition, p.303.

[32] Difference & Repetition, p.236-237. Différence et répétition, p.304-305.

[33] Immanuel Kant, Critique of Pure Reason, Transls. & Eds. Paul Guyer & Allen W. Wood, (Cambridge: Cambridge University Press, 1998), p.231, A103.

[34] Critique of Pure Reason, p.232 A106.

[35] Critique of Pure Reason, p.232, A107; p.233, A108-110.

[36] Gilles Deleuze, “Cours Vincennes: synthesis and time. 28/03/1978”

[37] Critique of Pure Reason¸ p.291, B209, A168.

[38] Critique of Pure Reason¸ p.295, A176, B217.

[39] Critique of Pure Reason¸ p.291, B209, A168.

[40] Gilles Deleuze, Logic of Sensation, p.58. Logique de la sensation, p.78-79.

[41] Deleuze, Logic of Sensation, p.83. Logique de la sensation, p.112.