Somers-Hall, (5.3), Deleuze’s Difference and Repetition, ‘5.3 Merleau-Ponty and Depth (229–32/288–91, 241–4/302–5)’, summary

by Corry Shores
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[The following is summary. All boldface, underlining, and bracketed commentary are my own. Proofreading is incomplete, so please forgive my typos and other distracting mistakes. Somers-Hall is abbreviated SH and Difference and Repetition as DR.]

Summary of

Henry Somers-Hall

Deleuze’s Difference and Repetition:
An Edinburgh Philosophical Guide

Part 1
A Guide to the Text

Chapter 5. The Asymmetrical Synthesis of the Sensiblence

 

5.3 Merleau-Ponty and Depth (229–32/288–91, 241–4/302–5)

 

 

Brief summary: 

Parallel to Deleuze’s three syntheses of time are his three spatial syntheses. 1) Intensive differences are localized by being distributed into various spatial locations, and they move from place to place according to how they interrelate and interact (in thermodynamics, for example, heat moves from its location to where cold is located, normally). 2) The extensive space into which these intensities are distributed and the qualities belonging to those things in extensive space come about somehow by means of intensive depth. 3) These distributions of intensities and their explications into extensive properties and other qualities continues to remain fresh and in a perpetual state of renewal. This is because the intensive depth responsible for them returns eternally, that is, it never ceases to inject newness and variety into the system, counteracting the entropy which would otherwise cause the system to eventually die.

Summary

We will want to explain the constitution of systems, which operate in extensive space. But we need to explain also the genesis of those systems as well as the space they occupy. [For some reason,] this is not something we can do from within space or extensity. [“If we are to explain the constitution of systems, Deleuze claims, then we cannot do so within space or extensity. Rather, we need to explain the genesis of space as well as the systems it contains” (SH 170). Perhaps the idea is that since we need to explain the origins of extensive space, we cannot assume it as a concept in our explanation.] [The next points are a little complicated, so let us first run through them. 1) For Kant, the intuition of time is given to a subject. 2) But this means that the subject is in a sense outside of time, and thus we cannot give an account of how the subject emerges within time. 3) Deleuze makes a similar point about space. 4) Spatial relations and properties can likewise be (perhaps erroneously) seen as given to a subject existing outside space. 5) Deleuze, however, proposed a view of the self that is not preconstituted and pregiven, but rather is something that is produced through passive synthesis. 6) There were three syntheses of time involved in the production of the subject (at least the third one is). 7) Similarly there are three syntheses of space. 8) We noted in the last section that on account of entropy we might think there is an arrow of time directed toward the heat death of the universe, that is, from particular, ordered systems to generalized disordered ones. 9) We also saw this arrow of time with the first synthesis of habit. (See by the way James Williams’ very excellent explanation of the arrow of time in the first synthesis. The memorial past is particular and determinate but the anticipated future is general and indeterminate, thus time of the first synthesis is asymmetrical, pointing like an arrow to the future). 10) (Perhaps we are not focusing on the first spatial synthesis here, because we discussed it in the prior section. It is hard for me to characterize it.) “The second spatial synthesis will give an account of how a horizon of intensive depth constitutes the qualities and localised intensities presupposed by thermodynamics”. And this synthesis of space can be equated with the temporal synthesis of memory. 11) Just as the in the third synthesis of time there was the pure intensity of the eternal return, in the third spatial synthesis there is pure depth as intensity.]

We have already seen in Chapter 2 that for Kant the intuition of time was given to a subject. | As such, an account of the emergence of the subject within time was rendered impossible. Deleuze makes a similar point here about space. So long as space is seen purely as an ‘anticipation of perception’ (DR 231/291), the subject will be seen as given. With the subject comes the constituted realm of qualities, as well as ‘the high and the low, the right and the left, the figure and the ground’ (DR 229/288) as structures that show themselves for a subject. In Chapter 2, Deleuze introduced the notion of a passive synthesis, that is, a synthesis that constituted a subject rather than presupposing one. Just as there were three syntheses of time, so there are three spatial syntheses. When we looked at the notion of entropy in the previous section, we noted that the system of differences of intensities constituted an arrow of time. This arrow moved from particular, ordered systems to generalised, disordered systems. This directionality from the particular to the general forms a rough analogue of the first temporal synthesis of habit. The second spatial synthesis will give an account of how a horizon of intensive depth constitutes the qualities and localised intensities presupposed by thermodynamics. This synthesis can be equated with the synthesis of memory. Finally, just as there was a third synthesis of time in terms of the pure intensity of the eternal return, there is a third spatial synthesis of pure depth as intensity. In this section, I want to go through the second and third of these syntheses.
(SH 170-171)

Recall from section 1.11 “how for Merleau-Ponty, forgetfulness of the perspectivism of our experience led us to posit a world of objects” (SH 171) [I do not remember how this worked. I think the idea was that objects are phenomenally constituted perspectivally, with our own being a center of origin, but this also means that given that our perspective is limited, objects are never entirely constituted. So we need to forget the perspectivalness of object constitution in order to regard the world as being made of objects that exist fully independent of any perspectival awareness of them]. [Objects are related to one another by phenomenal implication. The red carpet has a particular way its color appears. Just by looking at it, we implicitly are aware of the lamp shining down on it to give it that particular illumination we see. And likewise, the variations in shading imply the objects interposing between the light source and the carpet. So the phenomenal constitution of any one object already carries in it implicitly spatial relations to other objects affecting its appearance. And that distance is also depth.  That might be what SH means here:] “Within this world, objects were understood in terms of their relationships with other objects, that is, the distances they held to their surroundings. As such, we cannot explain the nature of constituted objects without also explaining the possibility of these distance relations: we need an explanation of space. In this regard, Merleau-Ponty’s analysis of depth is central” (171). [If we think about our field of vision, it extends up and down and left and right. So we directly perceive height and width. However, the layers of depth all stack up in a way that appears much more two-dimensional that in fact they are. However, there are clues in the relatively two-dimensional field of vision that tell us there is also a dimension of depth away from us. For example, things further away appear smaller and less apt to come into clear focus. Painters work with a two-dimensional surface but they place visual clues in the image so that we can view spatial relations of depth in the painting.]

As he notes, traditionally depth has been considered to be different from the other dimensions of height and breadth. Whereas those dimensions are directly perceivable by us, depth is imperceptible. If we take a naive view of painting, we can see a painting as presenting a number of signs that allow us to reconstruct a three-dimensional space on the basis of the two dimensions given by its surface (lines that converge to a point in the painting are used to recreate lines that remain parallel in space itself, more boldly coloured objects are taken to be closer to the viewer, etc.). On this reading, which Merleau-Ponty notes is the foundation of Renaissance painting (Merleau-Ponty 1964: 174), depth would be a construction on the basis of extensive magnitudes that are visible to us. | ‘Depth is a third dimension derived from the other two’ (Merleau-Ponty 1964: 172).
(SH 171-172)

However, [unlike with the painters using visual clues in the two dimensions of the painted image to indicate spatial depth] Merleau-Ponty does not attempt to derive depth from the other two dimensions but rather he sees depth as “that by which the given dimensions of extensity are given to us” (172). [I cannot figure out how this works. Maybe depth is to be understood as a more basic structure, like spatial juxtaposition itself. I am not sure what else depth would be such that the other dimensions would be made possible on its basis. So maybe the idea is that when we see depth, we see a unification of many different juxtaposed layers of extensive space. On the basis of this spatial synthesis we can order the points of space in height and width as being side-by-side. Or maybe somehow depth is to be understood simply as something like spatial variation in a very general sense. The following seems to be our best description of it, “Depth thus understood is, rather, the experience of the reversibility of dimensions, of a global ‘locality’ – everything in the same place at the same time, a locality from which height, width, and depth are abstracted, of a voluminosity we express when we say that a thing is there. (Merleau-Ponty 1964: 180)”. From this I still do not understand how it works. Let me quote:]

Merleau-Ponty’s claim about this form of understanding of depth is that, while it recognises the perspectival nature of our experience, this perspectivism ultimately sees perspective as a subjective feature of our representations of an objective and pre-existing spatiality [the following up to citation is Merleau-Ponty quotation]:

What I call depth is in reality a juxtaposition of points, making it comparable to breadth. I am simply badly placed to see it. I should see it if I were in the position of a spectator looking on from the side, who can take in at a glance the series of objects spread out in front of me, whereas for me they conceal each other – or see the distance from my body to the first object, whereas for me this distance is compressed into a point . . . For God, who is everywhere, breadth is immediately equivalent to depth. (Merleau-Ponty 1962: 255)

While representation attempts to derive the field of depth from the two given dimensions, thus characterising depth itself as an axis of extended space, Merleau-Ponty reverses this procedure. That is, rather than seeing depth as derived from the given dimensions, he sees it as that by which the given dimensions of extensity are given to us. Depth is not merely breadth seen from another angle, but rather is something different in kind that, by making possible a field of autonomous but interrelated objects, also makes possible the system of extensive distances taken as foundational by representation [the following up to citation is Merleau-Ponty quotation].

Once depth is understood in this way, we can no longer call it a third dimension. In the first place, if it were a dimension, it would be the first one; there are forms and definite planes only if it is stipulated how far from me their different parts are. But a first dimension that contains all the others is no longer a dimension, at least in the ordinary sense of a certain relationship according to which we make measurements. Depth thus understood is, rather, the experience of the reversibility of dimensions, of a global ‘locality’ – everything in the same place at the same time, a locality from which height, width, and depth are abstracted, of a voluminosity we express when we say that a thing is there. (Merleau-Ponty 1964: 180)

As Merleau-Ponty notes, this primordial depth here is no longer simply a ‘container’ for objects and qualities which are found within it. A consequence of this is that the genesis of quality and the genesis of space can no longer be seen as two separate projects: ‘We must seek space and its content as together’ (Merleau-Ponty 1964: 180). In ‘Eye and Mind’, he makes the claim that the enigma of depth is one of the primary inspirations of modern painting, and takes the work of Paul Klee and Paul | Cézanne as exemplary of the new project of showing ‘how the things become things, how the world becomes world’ (Merleau-Ponty 1964: 181).
(SH 172-173)

[So we are going along with this idea that somehow it is out of depth that the other dimensions are generated. Deleuze thinks this too. Again, I am not sure how this is for Deleuze, if for him this also applies in matters of perception. Merleau-Ponty does think that depth is non-extensive, but he does not equate it with intensity. Deleuze however does. Now we note how in the first “thermodynamic synthesis”, intensity was localized (perhaps because it was a matter of one particular temperature differential at some place in some system). Somehow (and I do not know how this works) in the second spatial synthesis intensity is what allows localization, since it is “a horizon that allows things and qualities to be constituted” (173). The spatial world has four features, and thus intensity is responsible for them: 1) the extensive distance between things, 2) the three dimensions of space which allows for things to have distance between them, 3) “the milieu of intensive differences recognised by thermodynamics as responsible for the appearance of qualities” (but I still do not know how that works), and 4) the qualities themselves that appear (in objects in space). The third synthesis of space is space just as an intensive quantity or pure spatium. Now, the second synthesis of space explains how intensity explicates into spatial extensity (the “how” part I still do not grasp). The next idea seems to be that this is as far as Merleau-Ponty goes, but since Deleuze sees depth as different in kind from the other dimensions and thus for him it is definable independently of extensity, then that means Deleuze goes further than Merleau-Ponty.]

This process by which a primordial depth is expressed in the form of qualities and extensions is, for Deleuze, the second spatial synthesis. ‘Depth as the (ultimate and original) heterogeneous dimension is the matrix of all extensity, including its third dimension considered to be homogeneous with the other two’ (DR 229/288). In a move that goes beyond Merleau-Ponty, he equates this non-extensive depth with intensity (‘Depth is the intensity of being, or vice-versa’ [DR, 231/290]). Now, we can note that while in the first thermodynamic synthesis, intensity was localised, in this second synthesis, intensity is rather that which allows localisation to take place – it is a horizon that allows things and qualities to be constituted. It is therefore responsible for four features of the spatial world: extensio, as the individual distances between objects; the extensum, as the three dimensions of space themselves (the frame of reference for the extensio); qualitas, as the milieu of intensive differences recognised by thermodynamics as responsible for the appearance of qualities; and quale, as these qualities themselves. Just as there were three temporal syntheses, here there are three spatial syntheses. The third synthesis of time was the pure form of time, prior to its expression in habit or memory. Deleuze describes the third spatial synthesis as ‘space as a whole, but space as an intensive quantity: the pure spatium’ (DR 230/289). While the second synthesis provides an account of the process by which intensity as depth generates the three dimensions (the explication of extensity), Deleuze notes that the fact that depth is different in kind from the dimensions it constitutes means that it is ‘definable independently of extensity’ (DR 230/289). The third spatial synthesis therefore goes beyond Merleau-Ponty’s phenomenological account by considering intensity independently of this process of the constitution of perspective.
(SH 173)

Just like with the third synthesis of time, Deleuze equates the third spatial synthesis with the eternal return (173). The eternal return is not like Plato’s doctrine of the circularity of time where the same situations repeat. [I do not follow the next points. Maybe the idea is that depth does not repeat but is prior to all things that do repeat. I will quote because I am missing the idea here:]

Just as Deleuze equated the third synthesis of time with the eternal return (2.8), in so far as it presented us with the pure field of intensity that gave rise to the two modes of temporality, the third spatial synthesis is also equated with the eternal return. Once again, as we saw in Chapter 2, Deleuze makes the point that the eternal return is not to be seen as something like the Platonic doctrine of an actual circularity of time, with a concomitant replication of a prior state of affairs. Rather than the eternal return being the claim that ‘things revolve’ (DR 241/302), | depth is precisely what is responsible for the constitution of things, and hence must be prior to them. Thus, ‘things must be dispersed within difference, and their identity must be dissolved before they become subject to eternal return and to identity in the eternal return’ (DR 241/302). If we are to think the unground from which things emerge, this unground cannot be thought in terms of things without leading to an infinite regress.
(174-175)

[I do not get the next paragraph very well. It seems the ideas are the following. For Deleuze, intensity generates extensity and the intensive differences distributed within extensity. Thermodynamics takes extensive space and its intensive distributions as givens. This means it is not aware that there is a creative and productive force that brings them about and that perhaps continues to somehow add energy or imbalance or life or something which would mean that there is not a certain heat death in the end. And maybe also the fact that intensity keeps injecting these anti-entropy factors into the world is like the eternal return, which is the continual repetition of new conditions in the world whose outcomes are not pre-calculatable.]

These three syntheses therefore explain why for Deleuze the increase in entropy proposed by thermodynamics is a transcendental illusion. Thermodynamics notes that intensive differences that we find already constituted and located in a spatial milieu tend to equalise themselves, but such an account only gives us half the picture. What is missing is the account given by the second and third syntheses whereby the extensive magnitudes thermodynamics presupposes, and with them the systems of intensive differences, are constituted. This presupposition that extensity is already constituted in effect rules out any consideration of these syntheses, thus leading to the transcendental illusion that intensive difference can only be equalised, but not constituted. The thought of depth is the thought of the eternal return because it is the thought of a field of intensity that is not cancelled by the laws of entropy. In fact, Deleuze claims that the eternal return is the thought of that which gives rise to the laws of nature, mirroring his analysis of repetition we looked at in the introduction (0.2). In the next section, we will address an issue brought up by this third synthesis. While we may have an understanding of intensity operating within extensive space (the difference in temperature between two locations, for instance), what does Deleuze mean by intensity defined independently of extension?
(SH 174)

 

Citations from:

Somers-Hall, Henry. Deleuze’s Difference and Repetition. An Edinburgh Philosophical Guide. Edinburgh: Edinburgh University, 2013.

Or if otherwise noted:

DR:
Deleuze, Gilles. Difference and Repetition, trans. Paul Patton, New York: Columbia University Press, 1994/London: Continuum, 2004.

Merleau-Ponty, Maurice (1964), ‘Eye and Mind’, trans. Carlton Dallery, in The Primacy of Perception, Evanston: Northwestern University Press, 159–90.

Merleau-Ponty, Maurice (1962), Phenomenology of Perception, trans. Colin Smith, London: Routledge & Kegan Paul.

 

 

 

 

 

 

Pt2.Ch4.Sb3 Somers-Hall’s Hegel, Deleuze, and the Critique of Representation. ‘Depth in Deleuze and Merleau-Ponty.’ summary

by Corry Shores  
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[Note: All boldface and underlining is my own. It is intended for skimming purposes. Bracketed comments are also my own explanations or interpretations.]

Henry Somers-Hall

Hegel, Deleuze, and the Critique of Representation.

Dialectics of Negation and Difference

Part 2: Responses to Representation

Chapter 4: The Virtual and the Actual

Subdivision 3: Depth in Deleuze and Merleau-Ponty

Very Brief Summary:

In his aesthetics, Merleau-Ponty creates an idea of depth that is like Bergson’s continuously integrated heterogeneous multiplicity and Deleuze’s difference as intensity. We see this depth in the way that variational lines and color in Klee and Cézanne generate the differential space of the painting. This differential generative aspect not visible in the work is like Deleuze’s virtual intensity, which explicates into extensity. Yet all objects are a mixture of virtual and actual.

Brief Summary:

In Merleau-Ponty’s later aesthetics, he articulates a concept of depth in painting that is like Bergson’s heterogeneous multiplicity. Before modern painting, special dimensions were something depicted, as if the objects filled a pregiven homogeneous Euclidean space. But with Cézanne and Klee, lines and color now generate space. On account of continuous variation, parts of the painting are continuously self-differentiating while remaining intrinsically related through these differential relations. It is like Bergson’s continuous heterogeneity. This for Merleau-Ponty is the real depth of the world that the painter depicts. It is the being of the world. and it is on the basis of this depth that spatial depth can be generated. For Cézanne and Klee, depth “is that which binds objects to one another, as the ground through which they interpenetrate”. (116) This fulfills Deleuze’s three criteria for the idea: this depth is not overtly sensible, it’s elements are reciprocally determined, and it is actualized in a multiplicity of spatio-temporal relations. This depth for Deleuze is the virtual intensive spatium, which is a multiplicity of continuous differential relations. The movement from virtual to actual produces the individual entities in extensity which may take on external relations (including opposition) and have an identity, but this was impossible while being intensities. This gives us a univocal rather than an equivocal sense of being. But all objects including artworks, which tend more toward the virtual, are composites of virtual and actual. For, if the object were completely actualized, it could be no further differentiated, and if it were purely virtual, there would be nothing actual to crystallize the system’s order. And when we bring into clarity the Idea, we confuse all the differential incompossible tendencies making it up.

 

Summary

Previously we saw how Deleuze’s Idea can be viewed in terms of topological phase space; for, it is multidimensional, non-sensible and non-conceptual, and it actualizes in various spatio-temporal relationships. Section two of this chapter was about the logic of multiplicities, and section three was about this new relation to science that the concept of heterogeneous multiplicity creates.

Now the third thing we will discuss in Bergson’s thought that Deleuze emphasizes is the method of intuition. It will allow us to see what happens between the two kinds of multiplicity. Deleuze’s concept of depth will show the how things happen in the middle ground between the two tendencies, and he draws from Merleau-Ponty’s later aesthetical writings.  Here Merleau-Ponty’s concept of depth allows him to create a Bergsonian space, where space is not something fixed and external to the bodies in it. It is a generative theory of space. “Merleau-Ponty wishes to show that space and the object are generated at the same time, characterizing depth as that which brings the other dimensions into being.” (111) Deleuze takes up this concept of depth, and he considers it an intensive space. We can divide extensive space into homogeneous parts, but an intensity cannot be divided like this.

Dividing it in half leads to two quantities of water that behave similarly to the original quantity. Dividing the temperature of the system can change the nature of the system itself, however, as the behavior of the system becomes radically | altered once it passes through the various phase transitions. (111-112)

Intensity then is like Bergson’s duration, and it is unlike Euclidean space; rather it is more like virtual non-Euclidean space. Intensity is what actualizes the virtual, because it “allows the structure inherent in the virtual idea of the system to become an actual geometrical structure”. (112) The egg has extensive dimensions, but its development undergoes phase transitions, which are [somehow] alterations in intensity. “In this section we will therefore turn to Merleau-Ponty's aesthetics to clarify the role of the intensive. In order to incorporate it into our reading of Deleuze, we will first deal with two points. First, we will need to show that Merleau-Ponty's analysis is an ontological analysis, and second, that this ontology is fundamentally compatible with Deleuze's.” (112)

We begin with Merleau-Ponty’s Eye and Mind. Here he sees the artist disclosing the world in a way unlike how science does. A theory of painting for him is a metaphysics. Like with Bergson, Merleau-Ponty sees two ways of relating to the world. The scientists approach is operationalism, so she avoids dealing with the world’s properties directly and instead defines “concepts purely through our operations of measuring them, making science in this sense autonomous, since it deals simply with the correlation and analysis of data. In this approach, according to Merleau-Ponty, there is no longer any contact with the 'opacity of being,' which was present even in the early moments of modem science.”  (112) Science is abstract. It renounces metaphysical questions | in order instead to characterize its success in terms of the manipulability of the object.” (112-113) The artist, however, has a nonmanipulative approach to the world. Yet the artist’s mind is not separate from the world. The essay explores how the artist opens the world, seeing how Renaissance geometrical perspective gives way to non-geometrical renditions in modern painting, beginning with Cézanne’s developments with depth. The essay does not want to renounce science but instead to give it the metaphysics it lacks. It also tries to give the transcendental grounds for perception, which is the invisible in the visible. (113)

We now consider parallels between the structures that Merleau-Ponty and Deleuze bring out.

[1] Painting’s action within space does not define what is painted.
The artist can actualize their Idea in various media, like painting, sculpture, drawing etc. This involves a move away from the spatio-temporal. [Each variation in a line is not just another point in a space but rather a new space for new self-relations, redefinitions.]

Within such a painting, each inflection of the line forms "another aspect of the line's relationship with itself, will form an adventure, a history, a meaning of the line" (EM, 183). Furthermore, when we ask what the nature of this line is, we find that it "is no longer the apparition of an entity upon a vacant background, as it was in classical geometry. It is, as in modem geometries, the restriction, segregation, or modulation of a pre-given spatiality" (EM, 1 84). [113]

This is like Deleuze’s Idea. “While the elements of the painting have sensible form, what is painted does not.” (114) Abstract art for Merleau-Ponty does not need to relate to some particular external state of affairs. It is only when the painter gives it a name that it takes on such a relation to a particular object or event. Like Deleuze’s Idea “its actualization is possible in a variety of contexts, depending on the relation the artist gives it to the visible.” (144) Also for Merleau-Ponty [and similar to Deleuze] the work itself convolutes space rather than occupies it, in that nonEuclidean, Riemannian, topological way. So Klee in Merleau-Ponty’s analysis meets Deleuze’s three criteria for Ideas. Klee’s lines do not tell us the sensible spatial dimensions of an object, but rather give us the lines continuous self-genesis. [It is like the development of an egg through intensive space rather than through extensive space.] Both the line and its space are reciprocally determined, meeting the second criteria. And because the painting with a different name would have different particular relations to objects and events, the painting can be actualized in many different contexts, meeting the third criteria.

For Descartes, we see the geometrical forms of things under deformation, in the way they hit our retinas. So squares take on the form of rectangles, for example [depending on the angle we view them. A cup saucer will be painted as an oval.] Paintings depict these deformations, and by doing so recreates a three-dimensional space. For Descartes, we perceive a third dimension merely from the two that are present in the painting. (114-115) Also note that we could imagine God’s eye located everywhere, thus there would be no visual depth, because depth is a relation between near and far. “In order for depth to be considered in this way, objects have to be conceived of as outside one another, with solid boundaries. The Cartesian approach therefore mirrors the approach of atomism in science that Bergson attacked”  (115) Such a space is homogenous, always in itself, everywhere equal to itself, and its dimensions are interchangeable. (115)

But note how for Descartes, depth is produced through the two other dimensions in the painting. This production of space is important for Klee. “The strands of Sartre's critique of Kant, Klee's reworking of the concept of depth, and the work of Gauss and Riemann all therefore represent a move away from the classical paradigm of a homogeneous space to that of a Bergsonian interpenetrative multiplicity.”  (115) Color for Klee is important, because it does not “give rise to the classical conception of space,” but rather “gives rise to an interpenetrative space  exemplified by the late works of Cezanne.”  (115) [Recall how Cézanne creates depth with color and not shading or modeling.'] “The idea of depth created by the color field differs from that of the brass etching in that the brass etching specifies depth as a third dimension, whereas for Cezanne | and Klee, depth is that which binds objects to one another, as the ground through which they interpenetrate”. (115-116) Depth then is “the first dimension that generates the others. Even the depth of the Cartesian geometry follows from this elementary depth.” (116) Merleau-Ponty sees Klee’s color in a way that is similar to Deleuze’s intensive qualities of the virtual. “That is, color cannot be divided without being changed in nature. Thus, the primordial dimension of depth for Merleau-Ponty is an intensive dimension. It is not color that is an intensity, but that which is more general than color, but can be captured by color's intensive nature.” (116)

Merleau-Ponty’s analyses of painting show us the actualization of intensive depth. [Depth is the movement of individuation, like the painted line that continually redefines itself and the space it generates through its movement. The creation of differentiation in general is the grounds for more specific sorts of differentiations, like the relations of different positions in extensive homogeneous space.]

Just as for Merleau-Ponty, depth generates the other dimensions, including Cartesian depth, for Deleuze, "extensity does not account for the individuations which occur within it" (DR, 229). That is, returning to Merleau-Ponty's analysis of the brass etchings of Descartes, extension itself both implies the already individuated in order to be generated, as Descartes sees the phenomenon of depth to be generated from the relations of bodies, and precludes the movement of individuation itself, since, from Bergson, the notion of a homogenous space renders an interpenetrative analysis impossible, as shown by the replacement of interpenetration with action at a distance in the work of Newton. Instead, Deleuze argues, "individuation and extensity must flow from a '"deeper' instance" (DR, 229). [116]

“Depth therefore forms the generative space from which extensive space | is generated.” (116-117) Deleuze calls this depth spatium. “Returning to Bergson, we can see that the spatium, as an interpenetrative multiplicity, functions for Deleuze like the multiplicity of duration.” (117) For Deleuze, “difference is that by which the given is given (DR, 222)” [117] The intensive field of depth is what gives the given. Difference is what is operating in this intensive field of depth. Intensity has a differential form [being made of a continuity of differential relations]. Actual diversity in the world is an explication of intensive difference.

For Deleuze, "difference is that by which the given is given" (DR, 222). That is, difference exists within the intensive field of depth, which is generative of extensity. In this sense, Deleuze calls it "the closest noumenon" (DR, 222). Thus, difference, as the differential form of intensity, gives rise to diversity by a process of explication. That is, as intensive force finds itself actualized within an extensive system, the unindividuated differential relations give way to relations between bodies external to one another. (117)

We will use differential calculus to understand the movement from virtual to actual. But for Deleuze and Bergson, there is not a logic of negation involved. [Negation and opposition are not a part of the intensive spatium, where multiplicities are intrinsically related differentially. They only come about in actualization into discrete entities. This is intrinsic differential relations inverted into extrinsic ones.]

Negation and opposition govern the state of the system as actualized and, therefore, for Deleuze, do indeed provide the limit case of the world in terms of the fully actual. "The negative is difference inverted, seen from below" (DR, 235). Likewise, the classical conception of identity, which requires individuation, is the result of the explication of differential relations into a spatiotemporal context. (117)

[Difference is a condition of possibility for actualization. (What is actualized are things we can understand.) So difference is transcendental. In Aristotle, being and beings were equivocal, because they had similar names but different meanings. Also note how each being is discrete from the others and externally differentiated from them. In the intensive spatium, there are no discrete beings. There is just difference, thoroughly expressed. So being is univocal, when being is difference. Also, Aristotle distinguished beings on account of oppositions between them. But since there is no opposition in the virtual, we can have a non-hierarchical understanding of being.]

In making difference the transcendental principle of his system, Deleuze has moved away from the principle of the equivocity of being put forward by Aristotle. The differential field of depth that forms the closest noumenon for Deleuze instead allows us to conceive of being as univocal. As the virtual is not defined in terms of opposition, it also allows the possibility of a nonhierarchical understanding of being, as the virtual is not to be understood in terms of opposition, which led to the theory of species and genera for Aristotle. (117)

But we need both the virtual and the actual to explain the givenness of the object [for, without the actualized object, nothing is being given, but without the virtual, nothing is giving the object.] For Merleau-Ponty, the work of art is between an actual thing and the intensive depth that generates things. Also for Deleuze, an artwork can be almost entirely virtual, displaying a “' ‘completely determined structure formed by its genetic differential elements"’ (DR, 209).” (108a) Yet for Deleuze all objects including artworks are double [expressing both virtual and actual] without the two halves resembling each other.  In Descartes, an object’s clarity and distinctness are proportional. In Deleuze’s analysis of Leibniz’s sea example, we can have a clear perception of the sea’s white noise as a whole, but all our tiny perceptions of the different small splashings of water are confused with each other. If we try to focus on one small wave, we obtain a distinct perceptions of the differential relations [between tiny waves] that make up the whole, but our perception of the whole becomes obscure. “Thus the understanding of one kind of order within the murmuring of the sea covers the other.” (118)

For Deleuze, it is the Apolline of Nietzsche's Birth of Tragedy that provides the best expression of the clear-confused, as that tied to representation, whereas the distinct-obscure is the Dionysian and properly philosophical order of the object. It is thus Apollo who gives the power of representation, of actuality, to the object, while Dionysus provides the obscure genetic and virtual conditions of the object, and of its representation. For Deleuze, "the two never unite in order to reconstitute a natural light. Rather, they compose two languages which are encoded in the language of philosophy and directed at the divergent exercises of the faculties: the disparity of style" (DR, 214) In spite of this, however, an object can never achieve pure actuality, as this would mean that it would no longer be capable of being further differentiated, nor can it be pure virtuality, as pure virtuality would be without the grain of actuality around which the order of the actualized system can crystallize. [118]

We saw also that for Bergson, pure space and pure duration are impossibilities, even though they are implied in the directions of expansion and contraction of matter/duration. So for Deleuze, everything happens somewhere between pure virtuality and pure actuality. [Recall Deleuze’s Idea. In the topographical example, instead of drawing all the vectors, we instead create a surface showing the tendencies toward equilibria in the dynamics of the systems. So all the incompossible lines of development become confused together, when the Idea as a whole comes into greater clarity. Thus] “An Idea ‘is confused in so far as it is clear’ (DR, 213).” [118] Virtuality and actuality are like two languages in philosophy that are different in kind, but everything is a matter of degree between them. (118)

Somers-Hall, Henry (2012) Hegel, Deleuze, and the Critique of Representation. Dialectics of Negation and Difference. Albany: SUNY.

Figural Studies: Lyotard's Distinction between the Figural and the Figurative (figural, figuratif)

by Corry Shores
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[May I thank the sources of these images:

olgaistefan.wordpress.com

thediagram.com

Credits found at the end.]

Figural Studies:

Lyotard's Distinction between

the Figural and the Figurative (figural, figuratif)

Paul Klee: A disguised woman, 1940

(Thank you very much olgaistefan.wordpress.com)

In Francis Bacon: The Logic of Sensation, Deleuze draws from Lyotard's distinction between the figurative and the figural [see his footnote 1 of the first chapter]. Figures in Bacon's paintings are not figurative in the sense of representing some object. We cannot look at a Bacon figure and by means of its appearance refer our minds to some definite object that the image re-presents for us.

Now let's consider something: no matter how much description we give for an object, we never seem to exhaust it of what it fully is. There is something about objects that enters into language, but in a way which cannot be fully explicated. In other words, there is always something implicit. The figural is similar to this. Perhaps it is like a non-representational presentation of what is inherent to all meaning, but which cannot be fully rendered textually or pictorially into a figuration of some sort. Hence a Bacon figure has the forces of meaning and significance powerfully expressed within it; and nevertheless, the figures do not stand for something or present anything except what they fully are and fully express to us implicitly and sensationally.

First I quote from Bill Readings' Introducing Lyotard: Art and Politics. Then I quote from Lyotard's Discourse, figure.

[Lyotard's Discours, figure] explores the nature of the distinction between discursive signification (meaning) and rhetoricity (figure). Since the figural is explicitly resistant to the rule of signification, saying what the terms 'mean' is problematic [...] Discourse is the name given by Lyotard to the process of representation by concepts. Discourse, that is, organizes the objects of knowledge as a system of concepts (units of meaning). Meanings are defined in terms of their position in the discursive network, by virtue of their opposition to all other concepts or elements in the system. Discourse thus imposes a spatial arrangement upon objects which Lyotard calls 'textual', a virtual grid of oppositions.

For Lyotard, the structural linguistics of Ferdinand de Saussure exemplify this discursivization of textual space, reducing all effects of language to meanings produced by the play between signifiers. Language is understood by Saussure as linguistic representation, in terms of the tabular system of opposed elements which make up language. In the field of figurative space, the order and proportion of Renaissance perspective performs a parallel discursive reduction of the visible to the representable. As in the costruzione legittima of Duccio's Maesta, the geometrization of perspective determines the visi-bility of objects as their relation to other objects on the spatial grid of the perspectival plane (DF: 202-208). The rule of discourse is thus the claim to order being as a structure of meanings, to identify existence with the representable by the establishment of the exclusive rule of a network of oppositions between concepts or signifiers.

Against the rule of discourse in figurative and textual space, Lyotard insists upon the figural. It is crucial to understand that the figural is not simply opposed to the discursive, as another kind of space. Lyotard is not making a romantic claim that irrationality is better than reason, that desire is better than understanding. [ft 1]. If the rule of discourse is primarily the rule of representation by conceptual oppositions, the figural cannot simply be opposed to the discursive. Rather the figural opens discourse to a radical heterogeneity, a singularity, a difference which cannot be rationalized or subsumed within the rule of representation. Discours, figure evokes a difference or singularity of objects (A is not B) [ft 2] which cannot be thought under the logic of identity, as an opposition (A is defined by not being the rest of the system). This discursive system cannot deal with this singularity, cannot reduce it to an opposition within the network (Readings p.3-4). The object resists being reduced to the state of mere equivalence to its meaning within the system of signification, and the figural marks this resistance, the sense that we cannot 'say' everything about an object, that an object always in some sense remains 'other' to any discourse we may maintain about it, has a singularity in excess of any meanings we may assign to it.

The figural arises as the co-existence of incommensurable and heterogeneous spaces, of the figurative in the textual or the textual in the figurative, for example. Discours, figure itself works to move from a series of oppositions (the figurative line to the textual letter, for example) to find an irreducible difference at work in each opposed identity (the graphic letter has a plastic force, as in mediaeval manuscripts; the plastic line performs an arbitrary conceptual demarcation of space, as in modernist art). (4a)

From Lyotard's Discourse, figure:

Quant à l'espace de figure, « figural » le qualifie mieux que « figuratif » ; ce dernier terme en effet l'oppose, dans le vocabulaire de la peinture et de la critique contemporaine, à « non-figuratif » ou « abstrait » ; or le trait pertinent de cette opposition consiste dans l'analogie du représentant et du représenté, dans la possibilité offerte au spectateur de connaître le second dans le premier. Ce trait n'est pas décisif quant au problème que est le nôtre. Le figuratif n'est qu'un cas la peinture renaissante. Le terme « figuratif » indique la possibilité de dériver l'objet pictural à partir de son modèle « réel » par une translation continue. La trace sur le tableau figuratif est un trace non-arbitraire. La figurativité est donc une propriété relative au rapport de l'objet plastique avec ce qu'il représente. Elle disparaît si le tableau n'a plus pour fonction de représenter, s'il est lui-même l'objet. Il vaut alors par la seule organisation du signifiant. Celle-ci oscille entre deux pôles. (Lyotard 211c)

Paul Klee: Human Weakness, 1913

(And thank you too olgaistefan.wordpress.com)

Lyotard, Jean-François. Discours, figure. Paris: Editions Klincksieck, 1971.

Readings, Bill. Introducing Lyotard: Art and Politics. London: Routledge, 1991. Preview available here.

Images obtained gratefully from:

http://olgaistefan.wordpress.com/category/art-history/

http://thediagram.com/9_1/anthony.html

Crystals of Time. from Deleuze, Cinema 2: The Time Image

by Corry Shores
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Crystals of Time

from

Gilles Deleuze

Cinema 2: The Time Image

Cinéma 2 : L’image temps

Ch. 4 : The Crystals of Time

Ch. 4: Les cristaux de temps

To better explicate Bergson’s notion of duration, we will examine the way Deleuze characterizes the present instant as a crystallization. Bergson spoke of crystallization when describing perception, in Matter and Memory.

We might possibly have instantaneous pure sensations. But perceiving something requires some time. So consider that we are stepping out the door. Then raindrops begin falling. So we automatically open our umbrella. When we perceive the rain, we are seeing something else as well. Our mind projects images from our memory onto our sensation. This way, images from past perceptions of rain superpose upon our ongoing sensation of raindrops. These overlaid images then contract together. But this contraction is always going on. And it has been like this from the beginning of our lives. So let’s imagine if we can sensations we might have had very early on in life. We sense some object O.

That sensation sends an image to our minds. This produces memory-image A.

But just as soon as our minds receive the image, they send it back to our senses, as though the image were electricity passing around a circuit, never stopping anywhere.

The projected memory-image contracts the current sensed object-image. Together they form our first perception. In the meantime, the object has changed slightly, on account of a variety of possible reasons: it changed, or our perspective changed, our attention was interrupted, and so on. So when the past memory contracts with the current sensed object-image, their differences are forced together into the same image. This way we produce a new object-image that is slightly modified. It is partly virtual, because certain aspects of it are remnants from the past. However, that does not make it less real. For, these remnants are pieces of reality that have been preserved in our current perceptions. Hence we see then that we only perceive things by compressing the past with the present.

So the past object-image contracts with the present one, to create a new modified object-image, which we will call B’.

Like before, this image is sent to our minds, while all at the same time, the memory image is being sent back to the sensed object-image. This motion is like an electrical circuit. Just as soon as the battery sends current to the light bulb, current on the other end of the bulb already is moving back to the battery.

And then, the new modified object-image B’ contracts with previous image A to create memory image B. All the while, whatever current form of the contraction is in our memory, we send it back to the sensed-object-image. This way, our perception keeps billowing outward as new differences are contracted to the original image.

[Note that in Deleuze’s rendition, he places dashes only on the actuality side, perhaps emphasizing that the contractions involve the present instant of actuality.

]

But we must note something important. There is a continuity in our changes of perception. So we are continuously contracting whatever is in our memory to whatever we are sensing. And, every memory is already a contraction that is contracted with many other contractions. But on account of the continuity, and the fact that all our perceptions are contracted with other contractions, we really are contracting the whole body of memories into every new perception. So we do not merely contract all the similar instances of “grass” together when we see grass. In fact, we take all the images we have ever seen, and they all contract with our current perception of grass. However, we only notice those parts of our memory that resemble our current perception of grass, if even we notice any past memories at all. It all depends on how useful it is for us to notice these resemblances. Yet there is this ongoing condition of our consciousness: all of our remembered past is continually present, as the virtual which is contracted to the actual. The past is never gone from the present. And in fact, we cannot have a present perception unless we are also contracting a past image to it [otherwise it might just be a bare, instantaneous – and thus unperceived – raw sensation. But perceptions require duration, which means the continuous renewal of the past.] Hence we do not follow the traditional model of the present’s relation to the past. So we will not think that present things turn into the past, and thus the present has some priority over the past. No, because we cannot have present experiences without the past already being contracted into them. Hence in fact, the past is prerequisite for the present, and not the other way around.

So, when we perceive something, we at the same time are recalling something else. What we perceive is real, and what we recall is virtual or we might say imaginary. Also, our present perceptions manifest in our physical behavior. So if we perceive a red light while driving, we contract previous recollections of stopping, and we then automatically enact the habitual bodily behavior of hitting the brakes.

We see then that our whole body of memories continues to “billow” outward as the circuit continually widens. Bergson will use another diagram, his famous cone, to help us grasp another aspect of our consciousness. We noted that we may or may not see in our imagination the previous images that are being contracted. If someone asks us to think about red lights, we might form clear and distinct memory-images of them in our mind. But when we are distracted while driving, and then we are caught off-guard by a traffic light changed suddenly to red, we will automatically hit the brakes without noticing any memories of red lights flash into our minds. And recall also that our memories of red lights are already contracted with ever other memory we ever had. But we only notice the parts that are most useful at that moment. So when we are contemplating red lights, we notice specifically just red light images. And if we are to think about how they work, we might also notice images of electrical wires, circuit boxes, and so forth. When we are contemplating things abstractly, the images spread-out into full and distinct forms in our minds. This is even more so the case when we are dreaming, and memories are fully there for us to see and experience again in their entirety. So Bergson will depict such expansions with a wide circle. These memory-images are still contracted together, but they are given a lot of space to spread-out so they can be seen more distinctly. But when we automatically respond with a habitual behavior, like hitting the breaks, all these memories are implicit and intensely there in an instant. And they manifest fully as our habitual bodily action. So Bergson will depict such intense contractions with a point. But there are many instances in between, when our memories are more-or-less contracted. So the circle widens to varying extensions. And it becomes more-or-less distant from bodily action, depending on how abstractly we contemplate the memories. So Bergson depicts these layers of contraction with a cone [The first is the simple cone that precedes the layered one].

And the different layers of contraction are the thousands of circles in between the point and the cone’s upper base [here Bergson depicts just two of the many thousands of intermediate circular layers]:

Everything in the cone is our memory, here displayed in its full range of possible contractions. So all our memories are found in the point S where they contract into one bodily habitual action, and as well, they can all be found at the top broad circle, in expanded form. Circumstances call for different degrees of contraction, so we vary from layer-to-layer each moment, going up-and-down (‘melodically’ as Deleuze might say.)

[Here is the rendition in Deleuze’s Cinema II.

]

So everything in the cone is virtual, and what lies on the plane of experience is actual. We contract our virtual pasts onto the present at point S. In this way, the virtual is continually being actualized by means of contraction. Bergson uses these metaphors: the further our memories expand, the more they evaporate; and the more they contract, the more they crystallize. There is always a “double current” moving from one tendency to the other, which is

always ready either to crystallize into uttered words or to evaporate into memories. (Bergson, Matter and Memory, 211b, emphasis mine)

consiste dans le double courant qui va de l’une à l’autre, – toujours prête, soit à se cristalliser en mots prononcés, soit à s’évaporer en souvenirs. (177)

We will now explore Deleuze’s characterization of the “crystal image” in his Cinema II text. He writes:

We have seen how, on the broader trajectories, perception and recollection, the real and the imaginary, the physical and the mental, or rather their images, continually followed each other, running behind each other and referring back to each other around a point of indiscernibility. (Deleuze 67b)

Nous avons vu comment, sur les parcours plus larges, la perception et le souvenir, le réel et l’imaginaire, le physique et le mental, ou plutôt leurs images se poursuivaient sans cesse, courant l’une derrière l’autre et renvoyant l’une à l’autre autour d’une point d’indiscernabilité. (93bc)

The simultaneous circulations and contractions of the past and present made the difference between the two indiscernible. But it is most indiscernable at the smallest circuit of the billowing contractions, and at the point nearest the plane of actual experience.

But this point of indiscernibility is precisely constituted by the smallest circle, that is, the coalescence of the actual image and the virtual image, the image with two sides, actual and virtual at the same time. (67c)

Mais ce point d’indiscernabilité, c’est précisément le plus petit cercle qui le constitue, c’est-à-dire la coalescence de l’image actuelle et de límage virtuelle, l’image biface, actuelle et virtuelle à la fois. (93c)

We will note briefly some of Deleuze’s terminology. He speaks of opsigns or what we might also call sonsigns. There are two sorts of these signs. Sometimes in cinema, we are shown objective images that give a “report.” This is like the expanded circle at the top of the cone. These report-images (or what Deleuze calls constats] give us a sense of things that we can visualize abstractly so that we can determine the relations between things in an explicit way. By this means we can also clearly see the ‘distances’ between related things, in an almost geometrical way. So it gives us “vision with depth, at a distance, tending towards abstraction.” (6bc) The other kind of opsigns are more like the point at the end of the cone, where images are contracted into a habitual bodily reaction to actual ongoing stimuli. These ‘instats’ give a “close, flat-on vision inducing involvement.” (6bc) Deleuze speaks of these signs in terms of crystallization, writing:

We gave the name opsign (and sonsign) to the actual image cut off form its motor extension: it then formed large circuits, and entered into communication with what could appear as recollection-images, dream-images and world-images. But here we see that the opsign finds its true genetic element when the actual optical image crystallizes with its own virtual image, on the small internal circuit. This is a crystal-image, which gives us the key, or rather the ‘heart’, of opsigns and their compositions. The latter are nothing other than slivers of crystal-images. (67b.c)

Nous appelions opsigne (et sonsigne) l’image actuelle coupée de son prolongement monteur : elle composait alors de grands circuits, elle entrait en communication avec ce qui pouvait apparaître comme des images-souvenir, des images-rêve, des images-monde. Mais voilà que l’opsigne trouve son véritable élément génétique quand l’image optique actuelle cristallise avec sa propre image virtuelle, sur le petit circuit intérieur. C’est une image-cristal, qui nous donne la raison, ou plutôt le « coeur » des opsignes et de leurs compositions. Ceux-ci ne sont plus que des éclats de l’image-cristal. (93-94)

In the next passage, Deleuze will refer to the “Epicurean atom.” The atoms are very small, but they have some measure of size. What makes one atom larger or smaller than another has to do with how many parts it contains. The parts extend but they themselves do not have any extension. When we combine them, we obtain extension [like Hume’s extensive parts]. So because these parts are inextensive, they are more like limits.

we have already declared on the ground of its relation to sensible bodies that the atom has size, only we placed if far below them in smallness. Further, we must consider these least indivisible points as boundary-marks, providing in themselves as primary units the measure of size for the atoms, both for the smaller and the greater, in our contemplation of these unseen bodies by means of thought. (Epicurus, line 59, page 35c, emphasis mine)

So an atom is so small as to be like a point, but it itself contains parts: inextensive limits. Deleuze writes in Cinema II:

The actual image and its virtual image thus constitute the smallest internal circuit, ultimately a peak or point, but a physical point which has distinct elements (a bit like the epicurean atom). (Deleuze, 68d)

L’image actuelle et son image virtuelle constituent donc le plus petit circuit intérieur, à la limite une pointe ou un point, mais un point physique qui n’est pas sans éléments distincts (un peu comme l’atome épicurien).

So in the instant of the current moment, the virtual past contracts with the momentary present. These images are fused together at a point. But it is a point with two sides: past and present. When the past image projects-upon and contracts-with the current one, it emerges from its virtual state and crystallizes. This produces a new actual image, which is already on its way to becoming virtual as a memory.

Distinct, but indiscernible, such are the actual and the virtual which are in continual exchange. When the virtual image becomes actual, it is then visible and limpid, as in the mirror or the solidity of finished crystal. But the actual images becomes virtual in its turn, referred elsewhere, invisible, opaque and shadowy, like a crystal barely dislodged from the earth. (68d)

Distincts, mais indiscernables, tels sont l’actuel et le virtuel qui ne cessent de s’échanger. Quand l’image virtuelle devient actuelle, elle est alors visible et limpide, comme dans le miroir ou la solidité du cristal achevé. Mais l’image actuelle devient virtuelle pour son compte, renvoyée ailleurs, invisible, opaque et ténébreuse, comme un cristal à peine dégagé de la terre. (95c)

So the crystallized image then enters into our memories. It is virtual, but it is also continually actualizing in the present. Crystals often have parallel faces and are transparent, so we might consider them as having internal mirrors facing each other. When the crystal enters our virtual memory, it then influences the way it will contract with images in the future. [See this entry on how repetition changes the mind.] So the crystal in a sense becomes more like a seed.

The crystal is no longer reducible to the external position of two mirrors face to face, but to the internal disposition of a seed in relation to the environment. What will be the seed with which we can now sow the environment [...] ? (69d)

Le cristal ne se réduit plus à la position extérieure de deux miroirs face à face, mais à la disposition interne d’un germe par rapport au milieu. Quel sera le germe capable d’ensemencer le milieu […] (96cd)

Now, consider that Deleuze interprets Spinoza as a philosopher of expressionism. There are things that we find in reality. These things are expressions of reality. Part of what we see is explicit. We see whatever facet is shown to us explicitly. And we see what it is in that moment. But the thing has other dimensions that are not limited to spatial ones. We might for example think that on the subatomic level, the object is expressing quantum mechanical principles that do not at all exhibit their strange properties to us as its super-atomic observers. Strange and incomprehensible things are going-on inside the object, and it is on account of this behavior that the object is the way it is at that moment. So the thing expresses this other dimension, but implicitly so. Now also consider that objects are changing, most times unpredictably. The changes occur as a result of a struggle of forces that are pushing-and-pulling the object in different directions of development, all at once. Certain forces prevail, often on account of pure chance, and the result is the changes the object undergoes. But at any instant, there are merely tensions and tendencies. The tendencies are implicit intensities. And the ways these intensities play-out in actuality are the explicit extensities. Consider also language. There is intensional meaning, which is like what is implied, and [for Deleuze] intension is also the tendencies for the meaning to change. And there is extensional meaning, which are the specific nameable objects that our sentences refer-to. In order to write well, it is important to communicate both on the explicit and implicit levels. And finally consider artistic creation. If the artist is too explicit, then she might as well be an illustrator for a magazine. But if she makes art where too much is implicit, as for example when there is either a mess on the canvass, or something so abstract that most people cannot relate to it, then also the art will not communicate very much. But when there is something explicit to see, but at the same time those explicit images and their relations are being push-and-pulled by implicit tendencies and suggestions in the artwork, then it will express more to the viewer. So in sum, expression for Deleuze means a mixture of explicit and implicit, virtual and actual, intensity and extensity. The crystal image as the contraction of the present actualization with virtual past would thus be expressive in this manner. At every moment, what we experience in the current instant is contracted with the virtual past, and in that way the two crystallize together. But just as soon as they crystallize, the crystal image is already moving into the virtual past. And again, just as soon as it is becoming virtual, it is also being contracted again and actualized. In this process of actualization, the virtual past is like a seed being planted in the current instant. Our experiences then are dually a seed from the past affecting how we experience the present, while at the same time a crystal from the present changing the nature of our past. Hence our experiences must have something about them which allows them to be fertilized by the past, and be crystallized with it.

The crystal is expression. Expression moves from the mirror to the seed. It is the same circuit which passes through three figures, the actual and the virtual, the limpid and the opaque, the seed and the environment. In fact, the seed is on the one hand the virtual image which will crystallize an environment which is at present [actuellement] amorphous; but on the other hand the latter must have a structure which is virtually crystalizable, in relation to which the seed now plays the role of actual image. (72c)

Le cristal est expression. L’expression va du miroir au germe. C’est le même circuit qui passe par trois figures, l’actuel et le virtuel, le limpide et l’opaque, le germe et le milieu. En effet, d’une part le germe est l’image virtuelle qui va faire cristalliser un milieu actuellement amorphe ; mais d autre part celui-ci doit avoir une structure virtuellement cristallisable, par rapport à laquelle le germe joue maintenant le rôle d’image actuelle. (100b)

So even though the crystal image has two distinct parts, one present and one past, they are contracted together into one thing. Something cannot be created in the past. So past images cannot be created in the past. Hence the past must be created in the present. This means that the present is both passing and past in the present instant, which is possible when we contract the virtual past with the current perception. The two merge. So every present perception is already a past perception, just as soon as we perceive it.

The crystal-image may well have many distinct elements, but its irreducibility consists in the indivisible unity of an actual image and ‘its’ virtual image. But what is this virtual image in coalescence with the actual one? What is a mutual image? Bergson constantly posed the question and sought the reply in time’s abyss. What is actual is always present. But then, precisely, the present changes or passes. We can always say that it becomes past when it no longer is, when a new present replaces it. But this is meaningless. [ft 18: M-E 130 ... ] It is clearly necessary for it to pass on for the new present to arrive, and it is clearly necessary for it to pass at the same time as it is present, at the moment that it is the present. Thus the image has to be present and past, still present and already present, at once and at the same time. If it was not already past at the same time as present, the present would never pass on. The past does not follow the present that it is no longer, it coexists with the present it was. The present is the actual image, and its contemporaneous past is the virtual image, the image in a mirror. [76-77] According to Bergson, ‘paramnesia’ (the illusion of déjà-vu or already having been there) simply makes this obvious point perceptible: there is a recollection of the present, contemporaneous with the present itself, as closely coupled as a role to an actor. ‘Our actual existence, then, whilst it is unrolled in time, duplicates itself along with a virtual existence, a mirror-image. Every moment of our life presents the two aspects, it is actual and virtual, perception on the one side and recollection on the other . . . Whoever becomes consciousness of the continual duplicating of his present into perception and recollection . . . will compare himself to an actor playing his part automatically, listening to himself and beholding himself playing.’ [ft 19: M-E 135-138] (77)

L’image-cristal a beau avoir beaucoup d’éléments distincts, son irréductibilité consiste dans l’unité indivisible d’une image actuelle et de « son » image virtuelle. Mais qu’est-ce qu cette image virtuelle en coalescence avec l’actuelle ? Qu’est-ce qu’une image mutuelle ? Bergson n’a cessé de poser la question, et de chercher la réponse dans l’abîme du temps. Ce Qui est actuel, c’est toujours un présent. Mais, justement, le présent change ou passe. On peut toujours dire qu’il devient passé quand il n’est plus, quand un nouveau présent le remplace. Mais cela ne veut rien dire. Il faut bien qu’il passe pour que le nouveau présent arrive, il faut bien qu’il passe en même temps qu’il est présent, au moment où il l’est. Il faut donc que l’image soit présent et passée, encore présente et déjà passée, à la fois, en même temps. Si elle n’était pas déjà passée en même temps que présente, jamais le présent ne passerait. Le passé ne succède pas ou présent qu’il n’est plus, il coexiste avec le présent qu’il a été’. Le présent, c’est l’image actuelle, et son passé contemporain, c’est l’image virtuelle, l’image en miroir. Selon Bergson, la « paramnésie » (illusion de déjà-vu, de déjà vécu) ne fait que rendre sensible cette évidence : il y a un souvenir du présent, contemporain du présent lui-même, aussi bien accolé qu’un rôle à l’acteur. « Notre existence actuelle, au fur et à mesure qu’elle se déroule dans le temps, se double ainsi d’une existence virtuelle, d’une image en miroir. Tout moment de notre vie offre donc ces deux aspects : il est actuel et virtuel, perception d’un côté et souvenir de l’autre. (…) Celui qui prendra conscience du dédoublement continuel de son présent en perception et en souvenir (…) se comparera à l’acteur qui joue automatiquement son rôle, s’écoutant et se regardant jouer. » (105-106)

The virtual memories that we contract in the present instant are different from the images we might recall in our memory. [See Matter and Memory §13 for more on this distinction] The non-contracted memory images fall along a chronological succession. But the virtual pure recollections are always present, always contracted with the current instantaneous perception. [Matter and Memory §39 and §40]. Because this virtual memory is actualizing in the present, it is not yet chronologically dated. So it is part of what Deleuze calls “the past in general.” If it were some specific past, it would be one image among a chronologically arranged sequence of other dated images. But it is a general past, for two reasons: 1) it occurs in the instantaneous, non-linear now-instant, and so it has not yet received a specified place in the past, and 2) this virtual past includes all past perceptions we ever experienced, all contracted together; hence, it is general past in this other sense, because it is always the whole collection together at once. But even though the virtual image is contracted with the actual image, they are still two different sides of the circuit, two different facets of the crystal.

Bergson calls the virtual image ‘pure recollection’, the better to distinguish it from mental images – recollection-images, dream or dreaming – with which it might be readily confused. In fact, the latter are certainly virtual images, but actualized or in the course of actualization in consciousness or psychological states. And they are necessarily actualized in relation to a new present, in relation to a different present from the one that they have been: hence these more or less broad circuits, evoking mental images in accordance with the requirements of the new present which is defined as alter than the former one, and which defines the former one as earlier according to a law of chronological succession (the recollection-image will thus be dated). In contrast, the virtual image in the pure state is defined, not in accordance with a new present in relation to which it would be (relatively) past, but in accordance with the actual present of which it is the past, absolutely and simultaneously: although it is specific it is none the less part of ‘the past in general’, in the sense that it has not yet received a date. ’ [ft 20: M-E 135] As pure virtuality, it does not have to be actualized, since it is strictly correlative with the actual image with which it forms the smallest circuit which serves as base or point for all the others. It is the virtual image which corresponds to a particular actual image, instead of being actualized, of having to be actualized in a different actual image. It is an actual-virtual circuit on the spot, and not an actualization of the virtual in accordance with a shifting actual. It is a crystal-image, and not an organic image. (77)

Si Bergson appelle l’image virtuelle « souvenir pur», c’est pour mieux la distinguer des images mentales, des images-souvenir, rêve ou rêverie, avec lesquelles on risque e la confondre. En effet, celles-ci sont bien des images virtuelles, mais actualisées ou en voie d’actualisation dans des consciences ou des états psychologiques. Et elles s’actualisent nécessairement par rapport à un nouveau présent, par rapport à un autre présent que celui qu’elles ont été : d’où ces circuits plus ou moins larges, évoquant des images mentales en fonction des exigences du nouveau présent qui se définit comme postérieur à l’ancien, et qui définit l’ancien comme antérieur d’après une loi de succession chronologique (l’image-souvenir sera donc datée). Au contraire, l’image virtuelle à l’état pur se définit, non pas en fonction d’un nouveau présent par rapport auquel elle serait (relativement) passée, mais en fonction de l’actuel présent dont elle est le passé, absolument et simultanément : particulière, elle est pourtant du « passé en général », en ce sens qu’elle n’a pas encore reçu de date. Pure virtualité, elle n’a pas à s’actualiser, puisqu’elle est strictement corrélative de l’image actuelle ou de pointe à tous les autres. Elle est l’image virtuelle qui correspond à telle image actuelle, au lieu de s’actualiser, d’avoir à s’actualiser dans une autre image actuelle. C’est un circuit sur place actuel-virtuel, et non pas une actualisation du virtuel en fonction d’un actuel en déplacement. C’est une image-cristal, et non pas une image organique. (106-107)

Our virtual images do not exist as mental states. They are always present in the current instant, even though we do not notice them all. We might only notice a small number of them at any moment. But that is merely because we do not find it useful at that moment to notice all the rest which are contracted together in the present. Now, when we do want to recall recollection-images, we do so by actualizing some part of our virtual memory. We do this by making that part of our virtual memory come before us as a perception. In a sense, we “leap” into the general past of the virtual memory.

The virtual image (pure recollection) is not a psychological state or a consciousness: it exists outside of consciousness, in time, and we should have no more difficulty in admitting the virtual insistence of pure recollections in time than we do for the actual existence of non-perceived objects in space. [77-78] What causes our mistake is that recollection-images, and even dream-images or dreaming, haunt a consciousness which necessarily accords them a capricious or intermittent allure, since they are actualized according to the momentary needs of this consciousness. But, if we ask where consciousness is going to look for these recollection-images and these dream-images or this reverie that it evokes, according to its states, we are led back to pure virtual images of which the latter are only modes or degrees of actualization. Just as we perceive things in the place where they are, and have to place ourselves among things in order to perceive them, we go to look for recollection in the place where it is, we have to place ourselves with a leap into the past in general, into these purely virtual images which have been constantly preserved through time. It is in the past as it is in itself, as it is preserved in itself, that we go to look for our dreams or our recollection, and not the opposite. [ft 21: All these themes are dealt with in M-M, ch. III.] It is only on this condition that the recollection-image will carry the sign of the present which distinguishes it from a different image, or the dream-image, the distinctive sign of a temporal perspective: they exhaust the sign in an ‘original virtuality’. This is why, earlier, we were able to assimilate virtual images to mental images, recollection-images, dream or dreaming: these were so many incomplete solutions, but on the track of the right solution. The more or less broad, always relative, circuits, between the present and the past, refer back, on the one hand, to a small internal circuit between a present and its own past, between an actual image and its virtual image; on the other hand, they refer to deeper and deeper circuits which are themselves virtual, which each time mobilize the whole of the past, but in which the relative circuits bathe or plunge to trace an actual shape and bring in their provisional harvest. [ft22: Hence Bergson’s second great scheme, the famous cone of MM, p. 211.] (77-78)

L’ image virtuelle (souvenir pur) n’est pas un état psychologique ou une conscience : elle existe hors de la conscience, dans le temps, et nous ne devrions pas avoir plus de peine à admettre l’insistance virtuelle de souvenirs purs dans le temps que l’existence actuelle d’objets non-perçus dans l’espace. Ce qui nous trompe, c’est que les images-souvenir, et même les images-rêve ou rêverie, hantent une conscience qui leur donnent nécessairement une allure capricieuse ou intermittente, puisqu’elles s’actualisent d’après les besoins momentanés de cette conscience. Mais, si nous demandons où la conscience va chercher ces images-souvenir, ces images-rêve ou rêverie qu’elle évoque suivant ses états, nous sommes ramenés aux pures images virtuelles dont celles-ci ne sont que des modes ou des degrés d’actualisation. De même qu’on perçoit les choses là où elles sont, et qu’il faut s’installer dans les choses pour percevoir, de même nous allons chercher le souvenir là où il est, nous devons nous installer d’un saut dans le passé en général, dans ces images purement virtuelles qui n’ont pas cessé de se conserver le long du temps. C’est dans le passé tel qu’il est en soi, tel qu’il se conserve en soi, que nous allons chercher nos rêves ou nos souvenirs, et non l’inverse. C’est seulement à cette condition que l’image-souvenir portera le signe du passé qui la distingue d’une autre image, ou l’image-rêve, le signe distinctif d’une perspective temporelle : elles puisent le signe dans une « virtualité originelle». C’est pourquoi, précédemment, nous pouvions assimiler les images virtuelles à des images mentales, images-souvenir, rêve ou rêverie : c’étaient autant de solutions insuffisantes, mais sur la voie de la bonne solution. Les circuits plus ou moins larges et toujours relatifs, entre le présent et le passé, renvoient, d’une part, à un petit circuit intérieur entre un présent et son propre passé, entre un image actuelle et son image virtuelle ; d’autre part, à des circuits eux-mêmes virtuels de plus en plus profonds, qui mobilisent chaque fois tout le passé, mais dans lesquels les circuits relatifs baignent ou plongent pour se dessiner actuellement et ramener leur récolte provisoire. (107-108)

So we find both the past and the present crystallized in our current perception. Every moment, there is the tendency moving back to the past, while at the same time there is the tendency to continue-on past the present. Our experience of time is this split-tendency. But, the crystal is instantaneous. So it is not time itself. However, in a sense, we look into the crystal and see time passing through the transitions between moments. Because the past and present are contracted together in the crystal, it is one image. But, within this image lies the boundary between past and future. It is the infinitely-small inextensive present instant that is continually vanishing, like the evanescent quantities of differential calculus.

since the past is constituted not after the present that it was but at the same time, time has to split itself in two at each moment as present and past, which differ from each other in nature, or, what amounts to the same thing, it has to split the present in two heterogeneous directions, one of which is launched towards the future while the other falls into the past. Time has to split at the same time as it sets itself out or unrolls itself: it splits in two dissymmetrical jets, one of which makes all the present pass on, while the other preserves all the past.

Time consists of this split, and it is this, it is time, that we see in the crystal. The crystal-image was not time, but we see time in the crystal. We see in the crystal the perpetual foundation of time, non-chronological time, Cronos and not Chronos. This is the powerful, non-organic Life which grips the world. The visionary, the seer, is the one who sees in the crystal, and what he sees is the gushing of time as dividing in two, as splitting. Except, Bergson adds, this splitting never goes right to the end. In fact the crystal constantly exchanges the two distinct images which constitute it, the actual image of the present which passes and the virtual image of the past which is preserved: distinct and yet indiscernible, and all the more indiscernible because distinct, because we do not know which is one and which is the other. This is unequal exchange, or the point of indiscernibility, the mutual image. The crystal always lives at the limit, it is itself the “vanishing limit between the immediate past which is already no longer and the immediate future which is not yet . . . mobile mirror which endlessly reflects perception in recollection’. What we see in the crystal is therefore a dividing in two that the crystal itself constantly causes to turn on itself, that it prevents from reaching completion, because it is a perpetual self-distinguishing, a distinction in the process of being produced; which always resumes the distinct terms in itself, in order constantly to relaunch them. ‘The putting into abyss [mise-en-abyme] does not redouble the unit, as an external reflection might do; in so far as it is an internal mirroring, it can only ever split in two’, and subject it ‘to the infinite relaunch of endlessly new splitting’. (79, emphasis on ‘vanishing limit’ is mine)

puisque le passé ne se constitue pas après le présent qu’il a été, mais en même temps, il faut que le temps se dédouble à chaque instant en présent et passé, qui diffèrent l’un de l’autre en nature, ou, ce qui revient au même, dédouble le présent en deux directions hétérogènes, dont l’une s’élance vers l’avenir et l’autre tombe dans le passé. Il faut que le temps se scinde en même temps qu’il se pose ou se déroule : il se scinde en deux jets dissymétriques dont l’un fait passer tout le présent, et dont l’autre conserve tout le passé. Le temps consiste dans cette scission, et c’est elle, c’est lui qu’on voit dans le cristal. L’image-cristal n’était pas le temps, mais on voit le temps dans le cristal. On voit dans le cristal la perpétuelle fondation du temps, le temps non-chronologique, Cronos et non pas Chronos. C’est la puissante Vie non-organique qui enserre le monde. Le visionnaire, le voyant, c’est celui qui voit dans le cristal, et, ce qu’il voit, c’est le jaillissement du temps comme dédoublement, comme scission. Seulement, ajoute Bergson, cette scission ne va jamais jusqu’au bout. Le cristal en effet ne cesse d’échanger les deux images distincts qui le constituent, l’image actuelle de présent qui passe et l’image virtuelle du passé qui se conserve : distinctes et pourtant indiscernables, et d’autant plus indiscernables que distinctes, puisqu’on ne sait pas laquelle est l’une, laquelle est l’autre. C’est l’échange inégal, ou le point d’indiscernabilité, l’image mutuelle. Le cristal vit toujours à la limite, il est lui-même « limite fuyante entre le passé immédiat qui n’est déjà plus et l’avenir immédiat qui n’est pas encore (…), miroir mobile qui réfléchit sans cesse la perception en souvenir ». (108-109)

Bergson, Henri. Matière et mémoire: Essai sur la relation du corps à l'esprit. Ed. Félix Alcan. Paris: Ancienne Librairie Germer Bailliere et Cie, 1903. Available online at:http://www.archive.org/details/matireetmmoiree01berggoog

Bergson, Henri. Matter and Memory. Transl. Nancy Margaret Paul & W. Scott Palmer. Mineola,New York: Dover Publications, Inc., 2004; originally published by George Allen & Co., Ltd.,London, 1912. Available online at:http://www.archive.org/details/mattermemory00berg

Deleuze, Gilles. Cinéma 2 : L’image temps. Paris : Les éditions de minuit, 1985.

Deleuze, Gilles. Cinema 2: The Time Image. Transl. Hugh Tomlinson & Robert Galeta, London: Continuum, 1985.

Epicurus. “Letter to Herodotus.” in Epicurus: The Extant Remains. Transl. Cyril Bailey.Hildesheim: Georg Olms Verlag, 1970.