Somers-Hall, (4.10), Deleuze’s Difference and Repetition, ‘4.10 The Origin of Ideas (195–202/244–52)’, 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

 

4.10 The Origin of Ideas (195–202/244–52)

 

 

Brief summary: 
Ideas for Deleuze are bound up with problems, solutions, and questions. The problem is an encounter with an intensive field of differential relations that we cannot process using our given resources. It causes us to put together Idea fragments to formulate an Idea on the basis of which we find solutions. The question is what relates the Idea as a basis for a solution to the problematic situation. So consider if we without ever swimming before are thrown in rough waters. We encounter the intensive field of differential relations of the waves, which threaten our survival, and in response we pose the question, “how do I not drown?” On the basis of how we come to understand the particulars of the problematic situation, we formulate our own particular arrangement of Idea fragments to make an Idea. This Idea then serves as the basis for the particular kind of solution we find, which would be one of many possible swimming strokes we spontaneously learn to enact to save ourselves from drowning. Deleuze uses the metaphor of the dice throw to illustrate. So again, when we learn, we encounter a problematic situation that presents to us a question (we are handed dice to throw). But how we understand the problematic situation and formulate the Idea for its solutions is a matter of chance, since we could have made many other arrangements of Idea fragments but we happened in this case to choose certain ones (the faces of the dice in a way are as such by chance and rolling them and getting some particular outcome is the affirmation of chance). Our Idea for the solution can in fact find many different kinds of solutions (there are many combinations that can be rolled). But only one solution is found at a time (we in fact roll one particular combination). However, we could have devised many other solutions from the same Idea, and also the Idea could have been formed differently depending on the different components we use to form it, and thus there is the repetition of difference built into the system (we can roll many other times or we can obtain different dice and repeat the process of solving problems).

 

Summary

We have been discussing Deleuze’s notion of Ideas in this chapter, and now we will ask, what is the origin of Ideas themselves? [Recall from the prior section that problems are not merely conceptual things but are inherent to actual states of affairs.]

Deleuze begins by noting that what we have encountered so far is a reorientation of the nature of a problem. Rather than a problem being seen as a purely subjective matter, we have seen that exploring the nature of the problem is a properly ontological or metaphysical matter. Thus, as he has noted, the organism can be seen as a solution to a problem. In fact, the question-problem complex is ‘the only instance to which, properly speaking, Being answers without the question thereby becoming lost or overtaken’ (DR 195/244).
(SH 159)

We now ask, what is the relation between a problem and a question? (SH 159). [It seems the answer is that we encounter problems when the world presents us with things we cannot comprehend so well, and these situations challenge us to think creatively since our given inner resources are at that moment inadequate for processing the situation. In Plato we saw this happened when we encounter contrary properties. But for Deleuze it is instead happens in situations when we experience extreme intensity, which erupts the field of representation. I am not sure how that works yet.  I am also not sure I follow the next ideas about the fractured I. It seems the idea is that we have the sense that we have a fixed self-identical I, which also serves as a basis of our representations, but really this I is constantly mutating since it has certain frailties or cracks. Thus our representations as well are unstable. So it seems those experiences which shatter our I also erupt the field of representation. This seems to happen when we encounter problems and engage them with Ideas, which is also, as we noted, when our faculties operate discordantly. Maybe we might say the following. When we jump in the water for the first time without yet learning to swim, in order to survive, we need to reconstitute ourselves, going from non-swimmer to swimmer. Our identity is not fixed, and in the same process, our concepts, reflexes, and habitual behaviors are also shattered as we figure out how to swim. The next sentence is: “Questions map this relationship between the encounter with intensity and the problematic unground responsible for it” (159). We later learn what unground means. For now the important idea is that there is a relation between the encounter with intensity and the problem underlying it, and the question is what maps that relation. Perhaps when we jump in the water, we have the encounter with intensity, which is the very different way that the parts, that is, the differentials, of the waves operate and affect our bodies, and the problem is this situation of the water differentials which calls us to change ourselves. The question then might be simply, “how do I not drown?” or “how do I swim to safety?” but I am not sure.]

What, therefore, is the relationship between a problem and a question? Deleuze presents his answer in the following manner: ‘Problems or Ideas emanate from imperatives of adventure or from events which appear in the form of questions’ (DR 197/247). Such an imperative would be the kind of encounter that we discussed in the previous chapter, paralleling Socrates’ discovery of the incommensurability of his categories of thought (the large, the small) with the purely relative determinations found within the world of becoming. Rather than operating in terms of contrary properties, however, the encounter for Deleuze is tied to the eruption into the field of representation of a moment of intensity. In the discussion of the fractured I in Chapter 2 (2.6), we saw that representation was subject to a natural illusion that the ‘I’ had a substantive nature. Deleuze’s claim was instead that the ‘I’ could be traced back to a pre-individual field of intensive difference. As we saw in relation to Blanchot however (2.12), this illusion to which representation is prone is perpetually threatened by the disruptive influence of intensity. For this reason, Deleuze makes the claim that ‘Ideas swarm in the fracture, constantly emerging on its edges, ceaselessly coming out and going back, being composed in a thousand different manners’ (DR 169/216). These encounters with intensity raise the faculties to a transcendental operation, and hence allow them to engage with Ideas. Questions map this relationship between the encounter with intensity and the problematic unground responsible for it. As such, ‘questions express the relation between problems and the imperatives from which they proceed’ (DR 197/247).
(SH 159)

So far Deleuze’s account parallels Plato’s [since for both there is an encounter that challenges us to formulate a question]. But, Deleuze notes, in Plato’s account, the problem leads us to necessarily true, or ‘apodictic’, principles serving as grounds. [I am not sure how this works, but we worked with the example of imperfectly equal things causing us to recall perfect equality, which is perhaps an apodictic principle grounding all our empirical knowledge of imperfect or inconsistent equality in our experiences.] For Deleuze, however, the process of dealing with problems leads instead to an “unground of the problem” (SH 160). SH then distinguishes ground and unground: “This difference between grounds and ungrounds ultimately simply relates to the fact that apodictic principles have the same structure as the system of propositions they ground (they are amenable to the structure of judgement)” (160). [So the pure Idea of perfect Equality perhaps takes a structure of conception that is similar to the system of propositions it grounds. I am not sure how this works, but perhaps the Idea of perfect equality takes a subject-predication form which is shared in all experiences of imperfect equality.] “On the contrary, the problem differs in kind from the solutions it engenders.” [I am not sure how this would work with the swimming example, but perhaps the problem again is this field of differential relations of the parts of the wave, with their own special significant relations among them, and the solution is a mode of swimming, which is somehow different in kind. However, I am not sure about this, since I would think that modes of swimming are also fields of differential relations with special significant points.] “As such, it [the problem] cannot ground solutions by providing a principle that we know to be true, because truth is a function of judgement, and the problem is different in kind to judgements” (160). [This one is harder to follow, but it seems fairly straightforward. It seems the point is that we cannot in the first place speak of truth in problems, since truth is a function of judgment, which is different in kind from the problems (since one is propositional and representational and the other is non-propositional and sub-representational). Therefore, we cannot say that because some principle of the problem is true, we can therefore say that its solutions are true or at least ground their truth in the truth of the problem.] “Thus, rather than a ground, it serves as an ‘unground’, destabilising the vision of the world as amenable to judgement in its entirety” (160). [I guess then ‘serving as an unground’ here means making ungroundable. So the problem is the origin for the solution, but it makes that solution not have any ground of truth. Perhaps for that reason there can be many solutions to the same problem, since none have any greater basis to claim more truth than others, but I am not sure.] [The next notion about the dice throw is a bit hard to follow. Let me quote it first:]

Rather than invoking ‘the moral imperative of predetermined rules’ (DR 198/248), Deleuze instead therefore invokes the notion of the dice throw and decision [the following up to citation is Deleuze quotation]:

It is rather a question of a throw of the dice, of the whole sky as open space and of throwing as the only rule. The singular points are on the die; the questions are the dice themselves; the imperative is to throw. Ideas are the problematic combinations which result from throws. (DR 198/248)

The imperative is the problematic instance within the state of affairs (the throw), that points beyond itself, through the question (the dice itself), to the problem that engenders the state of affairs and the problematic instance itself (the combination on the die). The Ideas result from this process as the result of our going beyond the state of affairs to find its conditions. The remaining moment of the analogy to explain is the significance of the points on the dice themselves. We can explain this by introducing the moment of decision. As we saw in the first case of learning, we move to the sub-representational level by combining ‘adjunct fields’, or similar cases, to reach the problem (in Bergson’s example, we relate walking to swimming). Now, depending on which cases we combine to form the problem, our understanding of it will differ. How we relate together different encounters, and which encounters we relate, will give a different emphasis to the problem (a different set of singularities), and hence to our Ideas. If the relation of different adjunct fields gives us different Ideas, then how is it that a given throw is able to ‘affirm the whole of chance’ (to provide an objective Idea) (DR 198/248)? When we looked at the example of the conic section (4.7), we saw that depending on how we took a section on the cone, we would derive a different curve, and with it, a different set of singularities. Each of these | curves was, nonetheless, an objective characterisation of the cone. In a similar way, each enquiry gives us an objective problem, but these are not exclusive, since different enquiries will take a different section of the cone, and hence derive different singularities.
(160-161)

[So we first acknowledge that we are dealing with a metaphor, and it seems the task it to find the analogies between the dice metaphor and this issue of problems and questions. (By the way, you can find some discussion of the dice throw metaphor from Deleuze’s Nietzsche book here.) I get lost in the explanation of the analogy here, I am sorry. Let me try to establish some possible analogies:
1) the problematic instance: the possible combinations implied by the given sides of the dice
2) the question: the dice themselves
3) the pressure to solve the problem: the imperative to throw the dice
4) the Ideas as solutions: any one outcome from an actual cast
Let me just quote it again since I am certain I got it wrong: “The imperative is the problematic instance within the state of affairs (the throw), that points beyond itself, through the question (the dice itself), to the problem that engenders the state of affairs and the problematic instance itself (the combination on the die). The Ideas result from this process as the result of our going beyond the state of affairs to find its conditions”. It further gets complicated, and I will miss this point too. We still have to explain what is analogous to the significant points on the dice themselves. (I do not know what they are even in the metaphor. Maybe they are the sides? Or maybe it has to do with combinations?) I will again quote the following sentences, but first I will make some guesses. We need now to introduce the moment of decision, which I suppose is the moment when the outcome of the dice throw is determined (unless it is the moment we decide to throw it). Now it seems that we are dealing with the notion of learning as gathering Idea fragments, and it seems that we form the problem (and not the Idea?) in different ways depending on which parts we select. I suppose also that other selections and arrangements will have other solutions, and thus it is by chance that we selected the ones we did, and thus any one throw (any one attempt at a solution) is an affirmation of chance. I quote again: “The remaining moment of the analogy to explain is the significance of the points on the dice themselves. We can explain this by introducing the moment of decision. As we saw in the first case of learning, we move to the sub-representational level by combining ‘adjunct fields’, or similar cases, to reach the problem (in Bergson’s example, we relate walking to swimming). Now, depending on which cases we combine to form the problem, our understanding of it will differ. How we relate together different encounters, and which encounters we relate, will give a different emphasis to the problem (a different set of singularities), and hence to our Ideas. If the relation of different adjunct fields gives us different Ideas, then how is it that a given throw is able to ‘affirm the whole of chance’ (to provide an objective Idea) (DR 198/248)? When we looked at the example of the conic section (4.7), we saw that depending on how we took a section on the cone, we would derive a different curve, and with it, a different set of singularities. Each of these | curves was, nonetheless, an objective characterisation of the cone. In a similar way, each enquiry gives us an objective problem, but these are not exclusive, since different enquiries will take a different section of the cone, and hence derive different singularities” (160-161).]

[The next idea seems to have to do with the inexhaustibility of the Idea (or of the problem). There are many solutions that will come from the same problem/Idea. But for each solution is a different (arrangement of the) Idea. Thus we should not repeat the same question but rather reformulate it anew each time, perhaps.]

This is the reason why in spite of each throw being an objective constitution of the problem, ‘there are nevertheless several throws of the dice: the throw of the dice is repeated’ (DR 200/251). In this sense, there is no ultimate characterisation possible, as there would be with knowledge, but rather a whole series of questions, each of which generates its own field of singularities. Each philosophical enquiry therefore puts forth its own question, on the basis of an imperative, which constitutes its own field of singularities. Remaining true to the encounter does not, therefore, lead us to one apodictic principle, but rather to an objective organisation of a problem. Just as each conic section gives us a different curve, each question gives us a different distribution of singularities. But as each conic section also repeats the structure of the others, each question is also a repetition, albeit a repetition that differs, not just in terms of solutions, but also in terms of its Ideas: ‘Repetition is this emission of singularities, always with an echo or resonance which makes each the double of the other, or each constellation the redistribution of another’ (DR 201/251). At this point, Deleuze notes an affinity with Heidegger’s emphasis on the question, while also cautioning that the emphasis on one single question risks covering over the real structure of the dice throw [the following up to citation is Deleuze quotation]:

Great authors of our time (Heidegger, Blanchot) have exploited this most profound relation between the question and repetition. Not that it is sufficient, however, to repeat a single question which would remain intact at the end, even if this question is ‘What is being?’ [Qu’en est-il de l’etre?]. (DR 200/251)
(SH 161)

 

 

 

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.

 

 

 

 

 

Shattering Geometrical Fetters: Euler's Analysis Revolution

by Corry Shores
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Scott Wollschleger asks in the comments to the "Euler in the History of the Calculus" entry:


what were the "geometrical fetters"?



which he asks in reference to this quote in Boyer:


Euler’s formalist approach to calculus freed it from all “geometrical fetters. It also made more acceptable the arithmetic interpretation which was later to clarify the calculus through the limit concept which Euler himself neglected” (246b).



Hegel articulates the logical problem the early methods of calculus encountered, despite their techniques producing accurate results; he writes in Science of Logic § 586


there is a return of the finite determinateness of quantity and the operation cannot dispense with the conception of a quantum which is merely relatively small. The calculus makes it necessary to subject the so-called infinitesimals to ordinary arithmetical operations of addition and so on, which are based on the nature of finite magnitudes, and therefore to regard them momentarily as finite magnitudes and to treat them as such. It is for the calculus to justify its procedure in which it first brings them down into this sphere and treats them as increments or differences, and then neglects them as quanta after it had just applied forms and laws of finite magnitudes to them.



When differentiating, finite values are treated as zero when convenient for the operation, so certain magnitudes are treated both as something and nothing in two phases of one same process, which is illogical and calls for a more solid theoretical explanation. We see this part of the operation carried out here [by MIT's David Jerison], at the very end of the algebra work:






This paradox was resolved with the limit concept, whose development took many hundreds of years after the advent of the calculus. Until Cauchy's work of the early 19th century, the limit concept lacked precision of formulation, even though it's development began with the Greek method of exhaustion and was expressed in Newton's Principia. The cause for the retarded development was the long history of the limit concept being conceived through geometrical intuition, for as well the quantitative values in arithmetic and algebra were considered in terms of geometrical magnitudes. Moreover, those who invented calculus regarded it as an instrument for determining relationships between quantities in geometrical problems. (Boyer 271-272)


When illustrating the limit, it was common to evoke the definition of a circle as the limit of a polygon.






But certain geometrical concerns cause us to misconceive what in fact the limit is; for we might wonder,


Is it the approach to coincidence of the sides of the polygon with the points representing the circle? Does the polygon ever become the circle? Are the properties of the polygon and the circle the same? It was questions such as these that retarded the acceptance of the limit idea, for they were similar to those of Zeno in demanding some sort of visualization of the passage from the one to the other by which the properties of the first figure merge into those of the second. (Boyer 272c)


Although Euler did not succeed in breaking entirely from geometrical limitations, he did make great steps in that direction. Boyer obtains the "geometrical fetters" phrase from John Meez's A History of European Thought in the Nineteenth Century, footnote 1, page 103:

1 See on this point the opinion of an authority, Hermann Hankel, in his highly interesting and suggestive lecture, ' Die Entwickelung der Mathematik in den letzten Jahrhunderten ' (Tubingen, 1869, republished by P. du Bois-Reymond, 1884). Speaking of the age of Leibniz he says : “Though on the Continent mathematicians were not so conservative as in England, where a purely geometrical exposition was considered to be the only one worthy of mathematics, yet the whole spirit of that age was directed to the solution of problems in geometrical clothing, and the result of the calculus had mostly to be retranslated into geometrical forms. It is the inestimable merit of the great mathematician of Basel, Leonhard Euler, to have freed the analytical calculus from all geometrical fetters, and thus to have established analysis as an independent science. Analysis places at its entrance the conception of a function, in order to express the mutual dependence of two variable quantities. . . . The abstract theory of functions is the higher analysis. . . . The conception of a function has been slowly and hesitatingly evolved out of special and subordinate conceptions. It was Euler who first established it, making it the foundation of the entire analysis, and hereby he inaugurated a new period in mathematics " (p. 12, &c. ).

Video from MIT OpenCourseWare. Creative Commons Licence. Prof. David Jerison's 18.01 Single Variable Calculus, Video Lecture 1.

Boyer, Carl B. The History of the Calculus and its Conceptual Development. New York: Dover Publications, 1949.

Meez, John. A History of European Thought in the Nineteenth Century. London: Adamant Media Corporation, 2004.

Text available online at

http://www.archive.org/stream/historyofeuropea01merziala/historyofeuropea01merziala_djvu.txt

image from

Edwards & Penney: Calculus. New Jersey: Prentice Hall, 2002, p.287a.

Substituting Positivity

by Corry Shores
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Scott Wollschleger writes in the comments to the Substitution Substituting Creativity entry:

right, I see what you mean and see how substituting would be the wrong path if we are looking to create something new. Is there something weak in the idea of Substitution maybe? Maybe weak is not the best word. Substitutions can have a diminishing effect. Remember in high school, when a Sub would teach class, the students would torture the Substitute teacher? Maybe it had to do with the fact that a person cannot be substituted, and we had to punish the teacher, as it were, for being part of a false reality. There are times when substitution lends to flexibility, which can lead to an amplification. But in any event, thanks for the comments and we can move on to repetition, i think it offers more in the creative realm.

CS Response: I might only add that substitution is either a zero-sum, where there is no net gain, or additive, where the gains are within the same order. Deleuze's repetition as exponential is more than additive, because the repetition creates new dimensions, degrees, and levels, not just new terms. In other words, it is hyper-positive. We might contrast this with the principles of deconstruction where terms are always under erasure. For Deleuze, terms instead express new dimensions without destroying those out from which the new ones grow.

Substitution Substituting Creativity

by Corry Shores
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Scott Wollschleger asks in the comments to the Symbols of Generality in Difference and Repetition post:

thank you, i understand it much better. i wonder if these generalities can become confused, maybe thats why i say, a cycle = 1. would this be a confused way of conduct? maybe you can say more about the role conduct plays for you? is it related to a modality? i feel a need to ask myself; What is the best way to substitute things? And if i found that way, for whatever reasons, i would also have to be at a point of view which is of the "best" conduct. in the creative act, i would think the best conduct would be a mixing of different ways of substituting things.

CS response: Yes, both generalities can become confused, in fact, both generalities can become "generalized" as being in general two ways of generalizing. Personally, I would prefer a formulation more like either

"cycles equal equality" (cycle = =)

or

"equality cycles cyclically" (= cycles cyclically)

because if we are going to confuse one for the other, I would set them into substitutable relations with each other. This is a confused way to conduct generalization so long as one needs to maintain the taxonomy, for example, when doing mathematics, if I say, "1" will take the place of "7" in my equation, because they practically look the same. Or if when solving an equation I always substitute the variable letter 'O' with the number '0' (and the letter "l" with the number "1") on account of there being negligible differences of appearance, then of course my equation will likely come out wrong.

However, suppose you were to break one of my expensive dishes, and I was upset that I lost a 100 dollar antique, in fact, that it was really the value of the dish I missed most, because I do not display it or take pride in its appearance. You could give me 100 dollars, and that would be a substitution by equality, certainly not by resemblance, because dollars and dishes are unalike in appearance. Although, I really want the dish and not the money, because I expected the dish to appreciate in value. Or you could give me a fraudulent replica worth 10 cents, which I would reject, despite it looking exactly like the one you broke. However, say you were to find the exact same model dish, and it by chance was priced at 100 dollars, then you would be substituting something both by equality and resemblance. Here substituting by means of the confusion between the two was precisely the conduct required.

So the role of conduct is merely the sort of actions we take in substitution.

And yes, it would be helpful to consider the types of behavior as modalities. In the one case, the modification, or modulation, of your behavior results in you treating items as substitutable by means of resemblance, and in the other case, your mode of behavior is one in which you treat the items as substitutable by means of equality.

If left only with the choice of substituting things, I think it would be creative for you to alternate modalities to produce interesting results.

However, Deleuze is speaking of something that does not involve substitution: repetition. And it is by means of repetition that we might achieve a "more profound and more artistic reality" (Différence et répétition 9c/Difference and Repetition 3a). Repetition is not substitution, because its items are singularities, which means one cannot replace another. His convincing example are human souls. We cannot replace one human's soul with another's, and have the same thing, because each are singularly unique unto themselves and cannot be generalized. There cannot be another Scott; no one can take your place.

So the creativity Deleuze calls-for is not so much an interesting defiance of conventions by doing a substitution of resemblance when normally a substitution of equality is called-for, or vice-versa. The repetition in this case would not be a substitution but a creation of something new and irreplaceable. This adds things to things, and does not replace them. More precisely, it exponentializes things, because each one is not so much a new thing subtracting-from or even adding-to the previous, as much as it is an expression of a new level or degree of something, that is, a new dimension that was already expressed but implicitly so. When Francis Bacon throws paint onto the proto-formed figurations on the canvass, he then is left with many different ways to develop the painting, implicit in the combination of chaos and order. He develops many of these, creating a distortion, but this causes our minds to continually try to arrange the unorderable images in the painting. So in other words, Bacon is able not to cause us to have a sequence of interpretations, each one supplanting the last, but we have one painting that continually stretches into new interpretive dimensions that themselves stretch out. In a sense, Deleuze is a monist like Spinoza. There are not a endless plurality of simulacra, but rather there is one substance continually expressing more and more dimensions in a multiplicative way.

So in the case of substitutions, the sort of creativity Deleuze calls-for would say do not substitute, but bring out a new dimension with its own singularity, despite it being implied in its previous envelopment and despite that previous envelopment remaining un-erased.

Deleuze, Gilles. Différence et répétition. Paris: Presses Universitaires de France, 1968

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

Symbols of Generality in Difference and Repetition

by Corry Shores
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Scott Wollschleger asks in the Comments to the Difference and Repetition §§1-2 entry:

belle parole!

about how Generality has two orders.

what does symbolized by cycles and symbolized by equalities mean? this seems to maybe be a comparisons of the two orders. I think i understand the latter, but the former? (i would think a cycle = 1)

CS Reply: When we group things according to resemblance, we notice similar items and consider one for the other; for example, when seeing each full moon we take it to be another occurrence of previous resembling instances. Deleuze writes "that is why the empiricists are not wrong to present general ideas as particular ideas in themselves, so long as they add the belief that each of these can be replaced by any other particular idea which resembles it in relation to a given word." This sort of generality is cyclical because each instance of resemblance is a new occurrence of something qualitatively similar, like full moons.

When we substitute entities by means of equality, the items do not resemble each other, even though they are equivalent. So "1 + 4" and "2 + 3" cannot be considered recurring resemblances. But one term may substitute the other because they are quantitatively equivalent (and not merely similar): they both have the same quantitative value. Hence these different entities are generalized together as instances of the quantity 5.

Important to Deleuze's distinction of generalities from the point of view of conduct is the way we come to substitute things, and we substitute cyclical recurrences according to relations of resemblance, and equivalent things according to relations of equality.

Scott Wollschleger on Nietzsche contra Wagner

by Corry Shores
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Scott Wollschleger comments on the Nietzsche contra

Wagner summary post:

a composer's thoughts on the matter:

Nietzsche’s problem with Wagner also appears to be a problem of the eternal return's manifestations on the cultural level. Contra-Wagner is about Nietzsche’s disappointment in Wagner and in German culture.

From Nietzsche’s critique we can see Wagner’s music lacks "a future".

This kind of music cannot properly return. Nietzsche critiques Wagner's art as essentially reactive, nihilistic and negative. It is a symptom of an era, a history.

Nietzsche’s words point us towards a deeper sense of music, one that has to come by way of affirming love and its depths while still being one engaged in a positive relationship to dance and cosmic joy. Is this the tragicomic?

Whatever the name is, it has nothing to do with Wagner. Nietzsche’s problem here is my problem too when he implies to ask the question: Can music have a future? How does a composer affirm eternal return? Will he do it? With Wagner, the answer seems to be no. However, by way of this critique, Nietzsche points to the possibility of a yes, an affirmative direction, and one that may only will-to-proceed silently. A direction that perhaps, tragically, will lie within the unfolding silence of the critique itself, a drama… We can only come to this understanding if we are Contra-Wagner. Here Wagner truly plays a cultural role. He is tragic. Wagner is a symptom of culture.

Nietzsche is saying yes to "art for arts sake" and, "The whole Olympus of appearance". It is not that the mask is a burden to art, or that it is something art must bear to cover the real, but rather the mask is the real itself. The mask has its greatest power when the world is nothing more than a cosmic dance and a chaosmos. Nietzsche was the first philosopher to introduce the modern idea of the Cosmic Artist. In the case of Wagner, ultimately there is a cosmic refrain and a culture which is to come (or return), one which Wagner is not a part of.

Be it a return to the Greeks for literature or the "grand style" for music. Nietzsche was always in search of the apotheotic artist. He thought he found this aptheosis in Wagner. But instead, while in search of this apotheotic artist he discovered:

"Music has not yet had one".

Response CS: My deepest sincerest thanks for Scott picking up my slack and offerring textual commentary beyond summary, which here is both philosophically interesting as well as culturally informative. We may take stock in Scott's words regarding the future of music. Mr. Wollschleger is part of a very promising fresh new music movement expanding out from New York City. His core group forms an organization, the Red Light New Music ensemble, which brings to the public new music by up-and-coming talented composers through frequent performances and workshops.

Even when he was a student, Scott's compositions received international attention when his pieces were reviewed in the New Yorker magazine. Since then, his works have developed and found new life and character. I highly recommend listening to his "Secret Machines" series on your best stereo system; it is recorded at high fidelity. You can also enjoy his more improvisational pieces here, and his blues pieces, which showcase both his talents with piano and guitar, as well as with studio sound engineering. Also check-out his artistically designed and innovative scores. Soon I will have a posting on his "Digital Sensation No.1," which is the best example so far I know of Deleuze's aesthetic analogy. Exploring Scott's music and that of the Red Light New Music ensemble will expose us to a music "that has to come to love and affirm the depths and still be one of dance and cosmic joy." And that, I confess, makes me hopeful.

The Density of the Irrational Numbers

by Corry Shores
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Scott Wollschleger asks in the comments to the The Density of the Rational Numbers post:

what about the density of an irrational number?

In this previous post we said that between any two rational numbers a and b there is another rational number c. We may make each of these irrational by setting them over the square root of 2.

Thus between any two irrational numbers there is another irrational number: the density of the irrationals.

based on the proof in:

http://math.nyu.edu/~tsang/classes/precalc1/session1.pdf