Somers-Hall, (4.9), Deleuze’s Difference and Repetition, ‘4.9 Learning and the Discord of the Faculties (188–97/237–47)’, 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 4. Ideas and the Synthesis of Difference

 

4.9 Learning and the Discord of the Faculties (188–97/237–47)

 

 

Brief summary: 
For Deleuze, learning is not a matter of drawing inferences from propositions. Instead, it occurs when 1) we deal with the problematic situation in current states of affairs, then 2) gather together Idea fragments from a variety of sources to devise a ‘map’, so to speak, of the important relations in the situation, which is the Idea, and then 3) develop solutions which would change those states of affairs in ways which solve the problems. In an evolutionary sense, each bodily organ is itself like such a solution to certain problems, since for example the eye is the solution to the problem of light. Likewise, each faculty is a solution or Idea on its own. The reproductive imagination (or memory) for example could be the solution to the problem of intuitions (or perceptions) continually being lost due to the passage of time. Now, in those confusing moments while we are learning something very new, our faculties are working together discordantly, meaning that they each have their own object that is different from the other faculties’ objects. But this discordant relation of the faculties, since it is what allows us to learn, is a solution to the problem of Difference itself, which is what presents to us the many problematic situations that call for us to reconfigure our minds and workings in order to continually adapt to a complicated and changing world.

 

Summary

Previously we have been examining Deleuze’s notion of the Idea. We return now to two topics from chapter 3, namely, learning from section 3.10 and the relationship of the faculties from section 3.6. We will see that we need Ideas in Deleuze’s sense for learning, and we turn to Plato’s notion of the hypothesis. Recall again Plato’s divided line. [We also made use of the excellent diagram from the Thesis Eleven website. Many thanks!]

Of intelligible knowledge, there are two kinds: 1) mathematics and 2) knowledge of the forms. Mathematical fields like geometry use images, and they proceed deductively to a conclusion. But

The strength and the limitation of a deductive argument, however, is that its conclusion does not contain anything that is not implicitly assumed in its premises. The most it can do is simply make explicit what we have assumed at the outset. For this reason, it is essential to know that the premises of one’s argument are true, since it is from these that the argument gains its content, and validity.
(155)

[Perhaps I am mistaken, but it seems that geometry begins with hypotheses, which are uncertain, but philosophy tries to begin with certain premises by invoking Ideas or using clear and distinct concepts. And thus philosophy would be using a higher form of reasoning than geometry.] “Philosophy traditionally, according to Deleuze, has therefore attempted to show that we can convert hypotheses into categorical statements by arguing from premises that are absolutely certain, either by invoking the Ideas, or by, in Descartes’ case, positing certain concepts that are clear and distinct, and hence indubitable” (155). SH then says [I quote because I am not sure I follow the inference] “Now, as we have seen, Plato understands the Ideas by analogy with objects of empirical recollection, and Descartes’ clear and distinct ideas are fully transparent to consciousness. In both cases, therefore, we remain within the domain of consciousness and the proposition” (155).

In this procedure above, we move between two propositions directly [I suppose between premise to premise or from premises to conclusion]. Deleuze proposes a different procedure, called ‘vice-diction’, which “moves from a proposition to an Idea and then to a solution” (155). In the first stage, there is “the determination of the conditions of the problem” and in the second there is “the correlative genesis of cases of solution” (SH 156, qtg. DR 190/239). Deleuze offers two examples of learning, namely, learning to swim and learning a foreign language, which are favorite examples of Bergson. SH then quotes Bergson for the swimming example:

If we had never seen a man swim, we might say that swimming is an impossible thing, inasmuch as, to learn to swim, we must begin by holding ourselves up in the water and, consequently, already know how to swim. Reasoning, in fact, always nails us down to the solid ground. But if, quite simply, I throw myself into the water without fear, I may keep myself up well enough at first by merely struggling, and gradually adapt myself to the new environment: I shall thus have learnt to swim. So, in theory, there is a kind of absurdity in trying to know otherwise than by intelligence; but if the risk be frankly accepted, action will perhaps cut the knot that reasoning has tied and will not unloose. (Bergson 1998: 192)
(SH 156)

SH notes that we can contrast two kinds of learning here. There is the “propositional account” [learning by reasoning or intelligence, perhaps in Bergson’s terms]. But on this account, learning to swim would seem impossible or absurd, since learning to swim, that is, gaining knowledge of how to swim, already seems to presuppose that we had that knowledge in the first place. [SH then moves to Deleuze’s other sort of learning, which seems to be more dynamic, spontaneous, and interactive with the problematics involved with what is being learned. I do not follow this description very well. Let me quote it first.]

Deleuze’s rather abstract analysis of the process of learning to swim or learning a language is that we do so by ‘composing the singular points of one’s own body or one’s own language with those of another shape or element, which tears us apart but also propels us into a hitherto unknown and unheard-of world of problems’ (DR 192/241). In order to escape the deductive sterility of the proposition, therefore, he claims that thinking needs to raise itself to the level of the Idea. The first stage of vice-diction is therefore that of finding other relevant cases that together specify the problem we are faced with, ‘fragments of ideal future or past events’ (DR 190/239). By ‘discovering the adjuncts’, Deleuze means this procedure of finding equivalent cases that emerge from the problem. As the Idea is an interpenetrative multiplicity, these elements must be combined to generate the Idea corresponding to the problem, just as the shades of light were passed through the convergent lens in Bergson’s example. Once we have the Idea of the problem, we can attempt to find those singular points of the Idea where it engenders solutions that are different from the present state of affairs. Deleuze gives the example of Lenin’s thought, which would involve the extraction from the present state of affairs of the Idea of the economic (abstract modes of production), and then the generation of a solution that involves a different | conjunction of singularities (just as selecting a different plane of a conic section will give us a different curve). Thus, we move from the present society to the problematic genetic principles that give rise to it, and then back to an alternative solution, or form of society. In a similar way, we do not look at the relations between parts of animals directly, as they may have different functional roles, but instead relate each to the others through the transcendental rules for their production. Thinking thus does not go from proposition to proposition. Rather, thinking becomes creative by tracing back propositions to the non-propositional field of problems that engender them.
(SH 157)

[Let us start with the examples. Deleuze discusses the swimming example in a Spinozistic context in his course lecture of 1981/03/17 and in his course lecture of 1981/03/31. The idea is that all bodies, our own and the body of water we swim in, are made up of smaller and smaller parts, ultimately of pure differential relations between vanishing terms (simplest bodies). But when we first encounter the wave, our field of differential relations and its differential relations are not at first compatible, in fact the wave’s internal relations decompose our own, and so we struggle in the water. But by learning how to modify our own workings to suit the workings of the wave, we learn to swim, and we also thereby constitute a larger composite body together. Perhaps this applies also to learning language. We must in a sense rearrange our own systems of associations and meanings in order to navigate in the other language. SH mentions the first stage of vice-diction as “finding other relevant cases that together specify the problem we are faced with, ‘fragments of ideal future or past events’ (DR 190/239)”. I am not sure what this is or how it would work in the examples. Perhaps the idea is that we need to try to direct our imagination into the future and try to figure what sorts of techniques might work were we to try them, and perhaps we might also look to similar past experiences. But I apologize that I do not know really what this sentence means. Either this or something new is what is called  ‘discovering the adjuncts’, which is when we find equivalent cases. The next sentence is then “As the Idea is an interpenetrative multiplicity, these elements must be combined to generate the Idea corresponding to the problem, just as the shades of light were passed through the convergent lens in Bergson’s example.” I am not sure what this means, but it seems one thing is that we generate an Idea that corresponds to the problem in the situation we encounter, and perhaps what is happening is we put together undetermined parts that we encounter in that situation and that we generate through finding equivalent cases. I am not sure how this works in our examples. Maybe when we first try to swim, we have these non-explicit intuitions or vague notions from memory and imagination which would somehow be applicable since they deal with a similar problematic. Perhaps we recall how oars worked when we learned how to row a boat, and we add other vague sorts of notions like observations of water-wheels, experiences while bathing, experimental thoughts about what might work- I have no idea really how this works. Then, maybe all these little undetermined Idea fragments converge as we begin successfully swimming. Or maybe the fragments converge before we successfully swim. Perhaps we have the Idea, like a light bulb going off, so to speak, then we begin successfully swimming. For, SH next says, “Once we have the Idea of the problem, we can attempt to find those singular points of the Idea where it engenders solutions that are different from the present state of affairs”. So maybe the fragments of the Idea converge as we try to adapt to the water, then we see special conceptual elements of the Idea which can generate solutions different from our current struggling not to drown. So maybe some of the singular points would be some notion about propulsion and another about staying afloat rather than sinking, and another about a mechanical rhythm of motion, and another about control of breathing. On the basis of these significant elements of the Idea, we might then figure one or another way to swim, like the different “strokes” one may use. I again am just guessing. The next sentence is: “Deleuze gives the example of Lenin’s thought, which would involve the extraction from the present state of affairs of the Idea of the economic (abstract modes of production), and then the generation of a solution that involves a different | conjunction of singularities (just as selecting a different plane of a conic section will give us a different curve).” So maybe what happened is that Lenin encountered a new sort of situation at the beginnings of the Soviet Union. There was the breakdown of the old system, as new political ideas were influencing the situation and calling for a fundamental rearrangement of social and economic relations. So maybe Lenin gathers Idea fragments somehow from the actual states of affairs and develops a sense of modes of production that could take place, and he figures out ones to actualize since they would work in that situation. Others were possible too, and they would have created a different structure to the society with its own special significant elements (like different shapes from the cone). The next sentence is: “Thus, we move from the present society to the problematic genetic principles that give rise to it, and then back to an alternative solution, or form of society”. So this seems to sum up the steps. First Lenin sees the instable current situation that resulted from demands for changes in economic relations and the breakdown of old relations, which leads him to think theoretically about the changes in modes of production and labor conditions leading up to this situation, which then lends to him devising a socialist society to successfully work with these new conditions. Then SH says, “In a similar way, we do not look at the relations between parts of animals directly, as they may have different functional roles, but instead relate each to the others through the transcendental rules for their production.” I am not sure I get this analogy. Perhaps the idea is that Lenin for example is not so concerned specifically and only with elements of the actual states of affairs, but he is concerned also with more basic relations that could be expressed in a variety of situations. Lastly SH writes, “Thinking thus does not go from proposition to proposition. Rather, thinking becomes creative by tracing back propositions to the non-propositional field of problems that engender them.” So Lenin for example did not reduce his current states of affairs to propositions from which he drew inferences, but rather on the basis of them he thought more deeply about the non-propositional problematic they are bound up in, and in this way he was able to create new social structures that solve the problems of that situation.]

So here we are “moving from one empirical state to another via an Idea” (157). We can also learn just by investigating Ideas themselves. First we note that Deleuze’s notions of problems and solutions do not apply just to matters of knowledge. We return to this point later. We for now might think of how evolution is solving problems through the ‘differenciation’ of organs. For example, the eyes are the solution to the problem of light. Each faculty also can be seen as a solution to problems, [as for example the faculty of speech is a solution to the problem of phonetic combinations:]

We can see that each of the faculties themselves is a solution to a problem [the following up to citation is Deleuze quotation]:

Take, for example, the linguistic multiplicity, regarded as a virtual system of reciprocal connections between ‘phonemes’ which is incarnated in the actual terms and relations of diverse languages: such a multiplicity renders possible speech as a faculty as well as the transcendent object of that speech, that ‘metalanguage’ which cannot be spoken in the empirical usage of a given language, but must be spoken and can be spoken only in the poetic usage of speech coextensive with virtuality. (DR 193/242–3)

In this case, the faculty of speech is rendered possible by the virtual multiplicity, which gives the rules for actual speech production. If we relate the structure of speech to the Idea, we can see that it contains each of its moments. The phonemes are undetermined, but able to enter into determinable relations. These relations describe the expressiveness of the language. In turn, an individual speech act corresponds to the integration | of this field of expressions. There is a reciprocity here, however, since the multiplicity is constituted in terms of the differential relations between phonemes because it is related to the field of a given language (‘each dialectical problem is duplicated by a symbolic field in which it is expressed’ [DR 179/227]). So the constitution of the faculty of speech (the solution) in turn determines the virtual multiplicity (problem) relative to it. ‘The transcendental form of a faculty is indistinguishable from its disjointed, superior, or transcendent exercise’ (DR 143/180). In this sense, each of the faculties is an Idea as well as a relation to an Idea.
(157-158)

[I do not follow the next paragraph very well. Let me quote it first.]

We have already seen that each faculty communicates violence to the others, to the extent that they communicate in terms of objects that differ in kind. Thus, the object of sensation differed in kind from the object of memory, but yet was able to enter into a relationship with it. What is it that allows these faculties to communicate? Well, once we recognise that each of the faculties has its own transcendent object, because their objects are ‘express[ed] technically in the domain of solutions to which they give rise’ (DR 179/227), it becomes simple to explain how they can communicate with one another, yet still be distinct. On an empirical level, each faculty is distinct, as each has its own set of objects (both transcendent and empirical). While each of the faculties contains a difference between empirical and transcendental exercises, this is only the first degree of difference. The ‘second degree’ of difference is where each of these faculties is in turn the solution to the problem of pure difference [the following up to citation is Deleuze quotation]:

This harmonious Discord seemed to us to correspond to that Difference which by itself articulates or draws together. There is thus a point at which thinking, speaking, imagining, feeling, etc., are one and the same thing, but that thing affirms only the divergence of the faculties in their transcendent exercise. (DR 193–4/243)

Each faculty is therefore the expression of an Idea, Difference itself being the Idea of an Idea. In this way, each of the faculties is both the same as, and different from, the others (what Deleuze calls para-sense as opposed to common sense, because it escapes the structure of representation). While all of the faculties relate to Ideas, it is still the case that thought is in some sense superior to the other faculties. If we take speech, then we can see that it is constituted in terms of phonemes. The elements that constitute thought, however, are Ideas themselves. Thought is thus the Idea of Ideas, and relates the other faculties. Thus, ‘while the | opposition between thought and all forms of common sense remains stronger than ever, Ideas must be called “differentials” of thought, or the “Unconscious” of pure thought’ (DR 194/244).

[The first idea is that the faculties work discordantly, because their objects are different in kind, but they still must try to communicate despite these differences. We next seem to be building from the point we just made, which is that the faculties are solutions to problems. To this it seems we expand it to say that the faculties’ objects are also Ideas (or maybe this means something else: “each of the faculties has its own transcendent object, because their objects are ‘express[ed] technically in the domain of solutions to which they give rise’”). The next sentence I do not understand: “On an empirical level, each faculty is distinct, as each has its own set of objects (both transcendent and empirical)”. I am not sure what the “on the empirical level” means. So on the empirical level, the understanding and the imagination have their own sets of objects. Then to this we add that each faculty, on the empirical level, also has both transcendent and empirical objects. I am not sure what we would say about the faculties on the transcendental level. Perhaps first we can say this. On the empirical level they have different objects, since for example the concept of a triangle is different in kind from intuitions of triangles or of whatever else. But on the transcendental level they all have the same object, namely a problematic they are all dealing with in their own way and working together to try to solve. Then, regardless of the level, they have both a transcendental and an empirical object. The empirical object would perhaps be the specific object they have of its own kind, and the transcendental object would be the Idea each has of its own kind, which is like its own way to solve the problem. I am just making huge guesses. The next sentence is: “While each of the faculties contains a difference between empirical and transcendental exercises, this is only the first degree of difference”. So we need to distinguish empirical from transcendental exercises, but I do not know how to clearly make that distinction. Perhaps it has to do with whether their objects are empirical or transcendental. I will guess here. Maybe the idea is that insofar as the faculty is dealing with their own sort of solution, they are dealing with the empirical object, and insofar as they are dealing with the problem, they are dealing with the transcendental object. So maybe in a certain situation, our understanding is dealing with trying to find the right concept, and in that sense it’s transcendental object is the problem itself regarded in conceptual terms, and maybe it supplies the notion of triangle, which is a proposed solution and is also its empirical object. Insofar as it is dealing with that problem, its exercise is transcendental and insofar as it is dealing with the solution its exercise is empirical. Again I am just making very huge and most certainly incorrect guesses. We then note that there is a difference between these two exercises, which is the “first degree of difference”. The next sentence is: “The ‘second degree’ of difference is where each of these faculties is in turn the solution to the problem of pure difference [the following up to citation is Deleuze quotation]: This harmonious Discord seemed to us to correspond to that Difference which by itself articulates or draws together. There is thus a point at which thinking, speaking, imagining, feeling, etc., are one and the same thing, but that thing affirms only the divergence of the faculties in their transcendental exercise. (DR 193–4/243)”. I again cannot give an interpretation that I am confident in. But it seems perhaps we can say the following. If we look at a situation where our faculties are working together discordantly, we see they are dealing with a specific problem, which involves the twin exercises (empirical and transcendental) of each faculty that we mentioned above. But why would they need to work together discordantly in the first place? Perhaps this discordant exercise is itself the solution to the problem of dealing with fundamental difference in our world, which lie at the basis of all problematics that our faculties contend with. So the discordant exercise “evolved” you might say as a means for us to be able to learn how to deal with all the very complicated and challenging situations we encounter in the world, just like how the eye specifically evolved to deal with the problem of light. If the faculties only worked concordantly and only communicated the same objects, they would not be equipped with the flexibility needed to deal with our complicated and changing world. The first degree of difference is that between the transcendent and empirical exercises of the faculties, while the second degree of difference is perhaps the more basic difference that the discordantly related faculties are contending with. (Or perhaps it is another difference, like the difference between each faculty or their object, I am not sure). The next sentence is: “Each faculty is therefore the expression of an Idea, Difference itself being the Idea of an Idea”. Maybe the point here is that each faculty is a solution or an Idea, and difference, which is the problem or Idea to which each faculty is dealing, is the Idea of each facultative Idea. Then, “In this way, each of the faculties is both the same as, and different from, the others (what Deleuze calls para-sense as opposed to common sense, because it escapes the structure of representation)”. So each faculty is fundamentally a solution of its own kind, so they are different and they operate discordantly, but since they all are solutions to the same problem/Idea of Difference, they are all the same in this other sense. The final sentences seem fairly straightforward. Since the faculty of thinking deals with Ideas, it has a special place among the faculties, which also deal with Ideas but perhaps in a less explicit way. Those final sentences might be making another point, but I am not sure.]

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.

Bergson, Henri (1998), Creative Evolution, trans. Arthur Mitchell, Mineola, NY: Dover Publications.

Image credits:

Thesis Eleven.
<https://thesiseleven.wordpress.com/philosophy/platos-republic/simile-of-the-divided-line/ >

<https://osopher.files.wordpress.com/2011/02/plato-divided-line.gif?w=504&h=360>.

 

 

 

The DeComposition of Our Body's Functions. Review and philosophical application of Compound Functions in Edwards & Penney's Calculus (Section 1.4)

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

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

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The DeComposition of Our Body's Functions

Review and philosophical application of
Edwards & Penney's Calculus
Compound Functions
in
Section 1: Functions, Graphs, and Models
Subsection 4: Transcendental Functions

What Do Compound Functions Got to Do With You?

Consider if we are trying to lose weight. So we go on a diet. Over the course of a day, we begin to feel our appetite increase. So this would be one function: as time increases, our appetite increases. But then, as our appetite increases, there is a decrease in our willpower to hold strictly to the diet. So our decrease in willpower is like a function compounded on the first function. Our lives are filled with many such highly complex functional relations.

Brief Summary:

Functions can be compounded one-upon-another as if the output of one machine instantly becomes the input of another.

Points Relative to Deleuze
[Under Ongoing Revision]

We might find a composition of functions in Deleuze's account of sensation, building from his portrayal of Spinoza's affection. Deleuze's example is that we are looking for our glasses in a dark room. Someone enters and turns on the light. This causes us to make a transition from the way we are affected by the dark to the way we are affected by the light. Because we are searching for our glasses, this affection increases our power to act. Consider instead if we are meditating in the dark room. Then when someone turns on the light, this dazzles us and ruins our concentration, and we lose the power to act.

Affection for Spinoza is a matter of our body's composition. What gives our body its power is the differential relations between the speeds of its simple bodies. But its simple bodies are like calculus differentials, infinitely small parts that only obtain a finite value when put into a differential relation with other simple bodies. Consider if we take poison. This will disrupt the ways the simple bodies in our body differentially relate to one another. This is why we die. Our bodies no longer express the range of differential variations that define us. Instead, they eventually express for example dirt.

Now, Deleuze also places a value on our internal decomposition when it comes to the sensations that affect us. The discord of our faculties is what makes sensations more intense [see here and here.] Also consider Spinoza's Ethics Part IV, Proposition 39, Scholium. He writes:

It sometimes happens, that a man undergoes such changes, that I should hardly call him the same. As I have heard tell of a certain Spanish poet, who had been seized with sickness, and though he recovered therefrom yet remained so oblivious of his past life, that he would not believe the plays and tragedies he had written to be his own : indeed, he might have been taken for a grown-up child, if he had also forgotten his native tongue. If this instance seems incredible, what shall we say of infants? A man of ripe age deems their nature so unlike his own, that he can only be persuaded that he too has been an infant by the analogy of other men. (Elwes translation)

From what Spinoza says about the decomposition of the body, it would seem that to change from child to man, or from poet to someone different, would be a decomposition, and thus a loss of power. But could it be that Deleuze takes the opposite view? To change from child to man is not an expression of our body's frailty. It rather shows our body's power to become something new. Imagine we get a sickness like the Spanish poet, and we no longer recognize our past selves. This would seem to be a loss of power. But that would only be so when we take the perspective of the self whom our body no longer expresses. But our bodies are always as perfect as they can be, given the conditions affecting them at any given moment. So to become someone else is not really a deprivation. It could be a testament to the power of our bodies to become new things, to express new essences. The question for Deleuze might not so much be "What can a body do?" as much as it might be "What can a body become?"

So here would be the composition of functions in this case. A certain affection might for Deleuze increase the intensity of sensation. But that means a decrease in the organization of our faculties and our body's compositional relations. Yet this again would be an increase in our body's power to become new things, to express new relations and essences. So it ultimately is an increase in our body's expressive power.

Edwards & Penney's Calculus
Compound Functions
in
Section 1: Functions, Graphs, and Models
Subsection 4: Transcendental Functions

Recall the function machine.

We can think of functions like these 'black box' machines. The machine takes-in a number from one set of values, and it gives-out a value from another set. So consider the squaring function:

The machine takes-in a 2, for example, and then gives-out a 4.

We can also compound our functions. So we can take the result of one function, and then put it into another 'function machine', if you will.

So let's begin with the function g(x). We put in x, and it gives-out u. We then have another function f(u), which is the same as f(g(x)), and we read it as, 'f of g of x'. So we plug the u into the f function, and it gives out the value for f(u). We can then call f(u), or f(g(x)) a new name. We can call it h(x). So,

h(x) = f(g(x))

This requires that all the x values in g's domain correspond (by means of g) to values in f's domain. We call the g function here the 'inner function', and the f function would then be the 'outer function' in this case.

Edwards & Penney now give an example that will illustrate something about notation for composition of functions.

We will first find f(g(x)). First note the g(x). If our number for x is larger than 1, then we will have a negative number. But when we apply it to the f function, we will have the square root of a negative number. So instead we qualify it:

But let's instead consider if we first take f(x), and then after that apply it to the g function. To avoid having the square root of a negative number, we must first begin with a positive. Then after that, there are no restrictions for the g function. So

Edwards and Penney would like then to distinguish two notations:

f(g(x))

and

f ○ g

Our example above shows that the composition of functions f and g is not the same as g and f.

f ○ g ≠ g ○ f

So the notation f(g(x)) might remind us of multiplication notation. In the case of multiplication, it does not matter what order the functions are multiplied. But as we see in the composition of functions, the order does matter sometimes.

from Edwards & Penney: Calculus. New Jersey: Prentice Hall, 2002, pp. 36-37.

Spinoza. Ethics. Transl. Elwes. available online at:
http://ebooks.adelaide.edu.au/s/spinoza/benedict/ethics/index.html

The Identity of Difference. Citations from Hölderlin, Essays and Letters on Theory, on the topic of split self-hood

by Corry Shores
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[The following are citations from Hölderlin, Essays and Letters on Theory. They are meant as preparation for a look at his Remarks on Oedipus and on Antigone, which we will examine later. My notes outside the citations are given in brackets.]

The Identity of Difference
Citations from Hölderlin, Essays and Letters on Theory, on the topic of split self-hood

From On the Law of Freedom:

[The following might help elaborate Deleuze's notion of the anarchy of the Kantian faculties, seen especially in sublime experiences.]

There is a natural state of the imagination which has in common the lawlessness with that anarchy of representations organized by the intellect, to be sure, yet which, with respect to the law by which, with respect to the law by which it is organized, need to be distinguished from intellect.

By this natural state of imagination, by this lawlessness, I mean a moral one; by this law, [I mean] the law of freedom. There, the imagination is considered in and of itself, here in conjunction with the faculty of desire.
In that anarchy of representations where the imagination is considered theoretically, a unity of the manifold, an ordering of perceptions was indeed possible yet accidental. [33b; V,211]

From Judgment and Being:

[This material discusses how expressions of identity, such as 'I am I', theoretically take both I's as subjects, but when executed in our lives, self-identifications involve us considering ourselves on the one hand as subject but then on the other hand as object.]

Judgment. in the highest and strictest sense, is the original separation of object and subject which are most deeply united in intellectual intuition, that separation through which alone object and subject become possible, the arche-separation. In the concept of separation, there lies already the concept of the reciprocity of object and subject and the necessary presupposition of a whole of which object and subject form the parts. “I am I” is the most fitting example for this concept of arche-separation as theoretical separation, for in the practical arche-separation it [the “I”] opposes the non-I, not itself. [37b, V,216, boldface mine]

[Being is not the same as identity. Our own personal being is not to be found in an identical relation between ourself as subject and as object. From a Deleuzean point of view, perhaps, our personal being instead is to be found in our internal difference, taken in one sense as the internal split between ourselves as self-thought (subject) and us as self-felt (object). We might further distinguish this from something more like a Merleau-Pontyian perspective. Instead of us being both subject and object, or being something pre-subjective and pre-objective, we rather are constituted (at least in part) by the differences communicated between our subjective and objective sides.]

Being--Yet this Being must not be confused with identity. If I say: I am I, the subject (“I”) and the object | (“I”) are not united in such a way that no separation could be performed without violating the essence of what is to be separated; on the contrary, the I is only possible by means of this separation of the I from the I. [37-38; V,216-217] How can I say: “I”! without self-consciousness? Yet how is self-consciousness possible? In opposing myself to myself, separating myself from myself, yet in recognizing myself as the same in the opposed regardless of this separation. Yet to what extent as the same? I can, I must ask in this manner; for in another respect it [the “I”] is opposed to itself. Hence identity is not a union of object and subject which simply occurred, hence identity is not = to absolute Being. [38a, V,217, boldface mine]

From Reflection:

[The following sentence might be interesting to compare to Deleuze's idea of intensity intensifying as it falls to zero. However, the quote would then be taken out of context and serve only as a poetic formulation.]

One can fall upward just as well as downward. [45d; IV,233]

From The Ground for "Empedocles":

[Deleuze will look at how Hölderlin says Sophocles' Oedipus brings the character to a pure state of interiority.]

The tragic odes begin in the highest fire; the pure spirit, the pure inwardness has transcendent its border, it has not sufficiently moderated those connections of life which are necessary and which, as it is, already strive for contact, and which are excessively inclined to do so due to the wholly inward mood, [that is] consciousness, reflection, or physical sensuousness; and thus, through the excess of inwardness, there has originated a discord which the tragic ode figures forth right at the outset in order to depict the pure. [p.50ab; IV,149]

[To elaborate on Deleuze's notion of disorganization, especially in terms of the anarchy of the Kantian faculties and the disorder of the Body without Organs, we might compare it with Hölderlin's distinction between organic and aorgic. Here we quote also from the editor's commentary]

Precisely because he expresses the deepest inwardness, the tragic poet denies altogether his individuality, his subjectivity, and thus also the object present to him; he conveys them into a foreign personality, into a foreign objectivity [52c; IV, 151]

The more organic, artistic man is the blossom of nature, the more aorgic [ft.3] nature, when it is sensed purely, by the purely organized, purely and uniquely form man, affords him the feeling of perfection. However, this life exists only in sentiment and not for knowledge. If it is to be known, then it must be present itself by separating itself in the excess of inwardness where the opposed principles interchange so that the organic, which surrendered itself too much to nature, and which forgot its essence and consciousness, transcends into the extreme of autonomous activity and art and reflection, where nature, at least in its effects on reflective man, transcends into the extreme of the aorgic, the incomprehensible, the non-sensuous, the unlimited, until through the progression of the opposed reciprocal effects the two originally unity [principles] meet again as in the beginning, only that nature has become more organic through the forming, cultivating man, through the formgiving drives and forces as such, whereas man has become more aorgic, universal, infinite. [53b.c; IV,152-153].

[From footnote 3, to the word 'aorgic']

The translation of Hölderlin's distinction between organisch and aorgisch and the translation of aorgisch as “organic” requires some explanation. Hölderlin’s distinction must be understood in the context of Swabian Pietism and the energetically inspired concept of nature of German Romanticism. Unlike Schelling’s distinction between organisch and anorganisch, Hölderlin’s “organic” implies not a natural organism or the like, but designates the organized, reflected principle of the spirit and of art. Similarly, the term aorgisch, subsequently translated as “aorgic,” does not refer to the merely lifeless but designates, in the course of this translation, the unreflexive, unrepresented, disorganizing manifestation of nature. [p.168a.b]

Hölderlin, Friedrich. Essays and Letters on Theory. Thomas Pfau, trans & ed. Albany NY: SUNY Press, 1988.

Fate of the Wild [77] Francis Bacon: Seated Figure, 1974.Deleuze on Bacon, Painting Series

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

[Central Entry Directory]
[Deleuze Entry Directory]

[Entry collecting the Images of the Paintings]

[Index of Painting Entries in the Deleuze on Bacon, Painting Series]

[May I deeply thank the sources of these images:

eaobjets.wordpress.com

Palazzo Reale

Credits found at the end.]

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

Fate of the Wild

Francis Bacon: Seated Figure, 1974

Gilbert de Botton Collection

(Thank you so very much Stampfli & Turci of eaobjets.wordpress.com and Palazzo Reale)

Painting 39 of Deleuze's Francis Bacon: Logique de la sensation. Tome II - Peintures

Painting [77] of the English translation, and

Painting [39] of the Seuil 2002 French

Man becomes animal, but not without the animal becoming spirit at the same time, the spirit of man, the physical spirit of man presented in the mirror as Eumenides or Fate [77]. (Deleuze 2003: 16ab)

L'homme devient animal, mais il ne le devient pas sans que l'animal en même temps ne devienne esprit, esprit de l'homme, esprit physique de l'homme présenté dans le miroir comme Euménide ou Destin. [39] (Deleuze 2002: 28bc)

[The faces of Bacon's figures are often deformed as though pushed-and-pulled in many divergent directions at once. These deformations result from one of Bacon's techniques. He randomly messes-up the figure in unintentional ways, like spattering or smearing the paint. This creates new opportunities to unfold the figure's rendition. But because Bacon develops the work in more than one direction at once, the face is warped, stretched, and mutilated. There are many forces chaotically intertwined in the figure's body. We might say that there is a zone of wilderness, like a jungle of forces, inhabiting the wildly twisted body. The forces are not explicit, yet they are fully there, fully expressed in the body's contortions. They are implicit involved intensities rather than explicit evolved extensities. They flare-up-and-about like the tongues of a wild fire. This is the wild spirit inhabiting intensified bodies, making them more like animal meat than human flesh.

When we view Bacon's paintings, we are affected in such a way that our bodies feel the same affect. Our bodies become disorganized. Its many organs which want to function harmoniously and organically now operate divergently, able only to communicate to each other the differences they are feeling. In a sense, we became animal, because we embody a wilderness. Hence when our bodies and faces become animal, it is not that they take-on specific animal shapes. As Deleuze writes, "the marks or traits of animality are not animal forms, but rather the spirits that haunt the wiped off parts, that pull at the head, individualizing and qualifying the head without a face" (Deleuze 2003: 15-16). So, we embody the spirit of the wild, of the animal.

(Again, thanks Stampfli & Turci of eaobjets.wordpress.com and Palazzo Reale)

That man becomes animal in this way is a fact. But likewise in the same process, animal becomes man. Their inter-becoming, then, is a 'common-fact'. Perhaps as our bodies express their inner wilderness, we give a human embodiment to the animal spirits. When the figure here looks in the mirror, he does not see the image of his body. Rather, he sees its physical spirit. What we observe in the painting is an animal-like creature that is taking-on the form of a Fury or of Fate.

(And once more, I would like to thank Stampfli & Turci of eaobjets.wordpress.com and Palazzo Reale)

The animal spirits, in this way, cross-into a human domain where they come to express a human rendition of destiny. So consider when we are torn-about by wild animal forces. Our bodies then embody the animal spirits of wildness just as much as these spirits take-on human form and express the human in its rawest state or 'fact'. The common fact then is the dual state-of-affairs arising when the human expresses the animal all while the animal thereby expresses the human.]

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 quite gratefully from:

http://eaobjets.wordpress.com/2008/05/16/francis-bacon-at-the-palazzo-reale-milano/

Stampfli & Turci of espaces arts & objets.

Authors here say the image was provided courtesy of Palazzo Reale:

http://www.comune.milano.it/dseserver/webcity/portale/palreale.nsf/index.htm?readForm&settore=MCOI-66DHPH_HP

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

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

[Central Entry Directory]
[Corry Shores, Entry Directory]
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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 dbeveridge.web.wesleyan.edu)

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 www.dl.ket.org)

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. [11]

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 alchemywebsite.com)

(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 20^th 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).

(Thanks www.dl.ket.org)

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).

(Thanks www.centrepompidou.fr)

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.

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[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.

Additional Image Credits:

http://dbeveridge.web.wesleyan.edu/wescourses/2001f/chem160/01/Mont-Sainte_Victoire/images/Cezanne's_MSV,_1897.jpg

http://www.dl.ket.org/webmuseum/wm/paint/auth/cezanne/portraits/index.htm

http://www.dl.ket.org/webmuseum/wm/paint/auth/cezanne/bath/index.htm

http://www.centrepompidou.fr/images/oeuvres/XL/3I00067.jpg

Monochord images:

Guthrie, Kenneth Sylvan. The Pythagorean sourcebook and library : an anthology of ancient writings which relate to Pythagoras and Pythagorean philosophy. Grand Rapids (Mich.): Phanes, 1987. ISBN: 0-933999-51-8

http://www.alchemywebsite.com/images/amcl72.jpg

http://www.britannica.com/EBchecked/topic-art/485171/75247/Pythagoras-coloured-woodcut-from-Theorica-musicae-by-Gafurius-printed-in