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by Corry Shores
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Making Your Hands Become Different

by Scott Wollschleger

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Carl Czerny
1791 – 1857

Individuality is difference.

The expression of a self emerges from the power which is difference itself.

Individuation is created through a process of differentiation.
Individuation is differentiation.

What makes a difference?

Czerny - a machine composer.

His question to us is, "How do I continually differentiate the music?”. The technique itself has to become different throughout. It does this by remaining the “same” in one sense while changing in another. One sense will say, " Yes, this again". Yet, the other sense will force our hand to change its relationship to the keyboard, as if to say, “No, this must be different now”.

Technique is developed through the increase of connective differences communicating throughout the living hand and body. Czerny helps our hands become different from themselves.

The Differential Music History Series, Entry Directory

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1. Making Your Hands Become Different

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by Corry Shores
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[Thanks eamdllc.com and pairingcomposers.org]

Differential Music History Series

The Differential Music History Series, Entry Directory

Other Authored Entries

Horowitz' Hands

Philosophical Questions and Commentary

Scott Wollschleger’s Inquisitive Connection between Engineering and Positivity (From Comments to the Summary of Welchman’s “Machinic Thinking")

Scott Wollschleger's Realistic View of Obama

The Density of the Irrational Numbers

Scott Wollschleger on Nietzsche contra Wagner

Symbols of Generality in Difference and Repetition

Substitution Substituting Creativity

Substituting Positivity

Shattering Geometrical Fetters: Euler's Analysis Revolution

Deleuze’s Dance, III. Wonders of Phenomena: The Infinite Grace of Bergson and Kleist; or the Nietzschean Dance of Deleuzean Dice

Scott Wollschleger's Sunday Afternoon Delirium and Further Thoughts About...

Responses to Wollschleger's Posts

Narrative and Power in Scott Wollschleger’s Story Store

Philosophy Conference Presentations

Rhythm without Time: Difference & Phenomena

Video Collaboration

Reality in New York's New Music Red Light District



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http://www.pairingcomposers.org/previous/2009.html

Horowitz’s Hands

by Scott Wollschleger

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Horowitz’s Hands
by Scott Wollschleger

Vladimir Horowitz was a brilliant musician. His pianism was powerful. But what was the source of his power? The common answer would be to attribute his power to his technical ability. But we find other pianists who posses great technique while lacking the kind of power that is found in Horowitz’s playing. Horowitz was sometimes criticized for his erratic and temperamental way of performing. Sometimes he would make mistakes. His playing could be described as wild.

Horowitz was a hyper-sensitive person. His nervous temperament led him to doubt himself. He withdrew numerous times from public life. But only a person with such a heightened nervous system partnered with an accomplished technique could produce such an individuated and riveting way of making music. Listen to how Horowitz plays the opening part of Mozart’s Piano Sonata K330. His hands seem to caress each note of the melody, drawing each note out like a point in in space. The piano sounds like a singing bell. Notice how his left has remains nearly motionless atop the keys, gurgling like a calm brook, as he plays the Alberti bass accompaniment.



In his hands we find a combination of fluid grace and violent force. In this short film we see him playing at regular speed then in slow motion. His is hands look almost like living creatures, existing all on their own:



Horowitz was very particular about his piano. He toured around the world with his very special 9-foot concert grand piano. I had the good fortune to play on Horowitz’s piano at a salon in New York. I was immediately surprised by the vibrations that moved through my entire body, particularly my hands, when I would strike a note or chord. The amount of vibration I felt was much greater than what I was normally used to. The lower notes had a splashing quality, like firing a cannon ball into a body of water.

I was told that Horowitz had special adjustments made to his piano that would allow for this extra splashing effect. I believe that it was not only this splashy sound that Horowitz enjoyed but also the feeling of vibrations shooting through his hands and body. When he performs it is as if these splashes of vibration pass through his body and are coupled with instantaneous moments of chaotic nervous impulses in the hands themselves. A resonance point is created between sound vibrations and nervous impulses. These moments are like leaps into the unknown. Horowitz deforms the music into sound itself. (It may be worth noting that it is within these moments the music seems to be the most "out" of time.) This way of playing disorients our perceptions for a moment. When we come back to our footing we hear the music anew. We are enlivened.

Bergson's Night Train

by Scott Wollschleger

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I really enjoyed reading your posting yesterday on the "Mistake of the Attempt to Derive Relations of Extensity from Those of Succession. The Conception of 'Pure Duration'" Bergson is so sensitive to the most subtle nuances of movement and the reflective process upon that movement. I can tell I have so much more to learn.

You mentioned, “If we are concerned with the conscious states that are passing away, then our consciousness will move into the past.” Really, nothing to me could be more sad. I often wonder about my first memories as a child, one of them was the sound of a great opening, which sounded like a tear. I don’t necessarily think this was my real birth, but something about the sound always bears a painful sensation of moving into the past and then coming to the most infinite memory who’s ending point and starting point are both the same. In a sound’s disappearance all that remains for me is this infinite memory.

Reading your entry reminded me of the relationship between life and duration. I am interested in my friend Damien Languell’s idea of nurturing sound. In some way to nurture a sound is to keep if from dying or to keep it from being captured by memory completely.

Here is Damien with his musician friends, nurturing a sound.



It is the idea of a sound as being something living in itself. To create a sound is to give it life and duration. I differ with him in methodology, but essentially, to keep it alive it requires a sort of non-formal economy, perhaps one that is “organized” only by intensities before they are explicated. A sound, now seen as living, would have a relationship to the dynamic link between a past and a future which the life endures. This would be a sort of musical life or what I would call musical time-space.

I want to ask if you see a relationship between displacement and the order which comes from succession? Can this displacement itself take on a higher order which is not related to succession? (Richard Pinhaus addressed this notion somewhat in that conversation with Delueze.)

As an artist I often wonder about how a process of pure duration is able to created or harnessed and what is involved in doing this process. According to Bergson, to place moments in succession is already to spatialize them. What about a modification to this and ask the reverse: is to displace moments in succession to despatialize them?

There is a process of displacement which disrupts an ordering from occurring, a kind of dance or displacement of movement, but a dance is not a negative movement. Disruption is often taken in its negative form. There is a positive movement around disruption, if anything I don't want to be stuck doing the same thing over and over again.

I have often wondered about the concept of musical time-space. Which would be a pure a pure mixture of time and space. Take the basic form of a "call and response" movement. Here the space in between the call and the response is not a void, or empty space. It is "full", in a sense, of expectation. When the expectation is fulfilled, the memory of what we left from is not what is important, but rather that the "call" now returns in the response, and vise versa. The return, taken positively, is joy. This is not a joy exclusively understood as what the future bears in relationship the feeling of expectation, but also to agitation which seems to result from expectation itself. Both, call and response, rather than maintain a constant uniform distance, they instead will tend to harness a disuniform or dynamic distance. This dynamic distance or space between the call and the response is positive. But it is really still in relation to the body. The listeners body, the instrument’s body, the players body and the composer’s body. I think a good rhythmatician has a keen feeling for the positive space which is found in the distance between sonic events related to a body. a great rhythmatician is a master of displacement and she understands distance in terms of what is already inherent in the event itself and not as something which is outside or between it. Or as Bergson might approve, the distance in between the notes of a sweet melody appear as fluid. I find in music the potential for a pure mixture of time and space, but one that is not contrary to a pure duration.

….Dance….

I would like to improvise on what you said and say to displace movements in succession is to also intensify them.

This is a video my friend Vince passed along to me which I think demonstrates this idea. (I hope you don’t mind the strange flange on the whole thing.)



The form of this is:

A – call: “Night!”
B – response: an incoherent word maybe of both “Night” and “Train” sung by the audience in a simultaneous way.
C – breakdown
A
B
C
…
A and B could also be take as just one section, but I think it is better to break it into 2 distinct sections. So the form is ABCABCABC… But the power of this music does not come from its formal or successive(spacial) reality that is happening, but rather what is dynamically at play in the duration of each movement. The movements of the breakdown section have the greatest intensity because there is the greatest amount of displacement of successions in time which are also occupying that given duration. The moments themselves are movements of a kind of pure duration or life.

Narrative and Power in Scott Wollschleger’s Story Store

by Corry Shores

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[This entry is a comment to Scott Wollschleger's entry Scott Wollschleger's Sunday Afternoon Delirium and Further Thoughts About...]

What are the value of stories if they tell themselves and tell endless more? What gives a story power? Where do stories store their power?

Consider Aesop’s Fox and Grapes story:

A thirsty fox sees grapes dangling from high. He jumps and jumps. Finally, he stops. “They were sour.” He concludes.

A Deleuzean literary criticism would look for narrative intensities. I assess that the sharpest contraction of difference is to be found at the precise moment he stops jumping.

When differences are contracted into each other, this is an instant of intensity, and also an instant of becoming. At the moment a match is struck, it is both wood and fire. It is both wood and not wood, and it is both fire and not fire. It is both and neither, all at the same time, because there is an infinitely small duration when the transition is at its peak – when there is pure becoming.

Difference as repetition occurs when there is a change of dimension, domain, level, degree, and so forth. If desire becomes meaning, this would be repetition for Deleuze.

In the case of the fox, he began with a simple bodily desire for nourishment. While jumping, he did not give the grapes any meaning. Normally we do not give food meaning. However, when Catholic priests convert the bread to Christ’s body, there is not just a transition from one substance to another (a transubstantiation); it is not just bread to flesh. It is also matter to meaning. The bread is still bread. And it is flesh. And it is profoundly symbolic or meaningful. It became a symbol.

So the grapes began as being an object in an immediate relation to his bodily drives.

The next factor in a Deleuzean literary critique would be an analysis of the affirmation of chance in the moment of intensity.

An intensity is a tendency. At every moment, things are tending some way or another. But the way things are tending is not always where they go, because there is chance.

To affirm chance would mean to actualize a tendency at any one point, and to send the forces in that direction. At one point, the fox affirms the fact that by chance at that precise moment he did not obtain the grapes. He does not deny himself the grapes. He affirms the forces at work at that precise instant.

But by actualizing these forces, they explicate into a higher dimension. So at this moment, there were forces of desire directing him toward the grapes. But arbitrarily at one instant he affirmed the fall of the dice, that he did not at that moment attain the grapes. This causes the intensities to explicate, and hence it causes the grapes (and the fox's desire) to express themselves on a higher level. The grapes are no longer just objects in an immediate relation to his body. They become something more. The grapes are now expressed both as something that can be eaten, and as something meaningful. For now the grapes have been interpreted. Before there was not meaning ascribed to them. After the affirmation of chance, they become meaningful. They symbolize sourness. Or it could be said they obtained a property they did not previously explicitly express; for they now are sour. And the fox's physical desire now expresses itself as hermeneutic cognition.

So traditionally this story has been interpreted to mean that the fox rationalizes his failure by devaluing the grapes.

A Deleuzean read would come to a contrary conclusion. The fox creates value for the grapes, a symbolic value. The grapes in the moment of his affirmation of chance are becoming-symbolic. Or we could say that the fox’s desire is becoming-symbolic. It expands to a higher exponential power or dimension.

What I want to note is that in Scott’s story, the moments of intensity involve limitations that are overcome by narrational affirmations. For example, when the store clerk does not know the price of the oysters, there is sharp intensity in the narrative where anything could happen. The clerk affirms that by chance he does not know at that moment what the price of the oysters is. So that tendency toward determining the price expanded into a higher power, into the power of narration. He tells the story (he gives the account) that any oyster could have a pearl, which makes their value uncertain. The reason that the clerk does not know the value of the oysters is no longer because he failed to learn it. Rather, it is because there is a story about how the price was never determinable to begin with. Here ignorance became rational argumentation and knowledge of fact.

Now we have another moment of intensity, because the woman’s response could be anything. She could have called the clerk’s bluff. But instead at one moment she affirms that by chance the clerk’s story created a domain of narration, which she entered by telling her own story. She says that science has found a way to make any oyster produce pearls. No longer a rare commodity, the value of pearls becomes negligible, and so it does not matter whether or not the oysters have pearls or not. For, pearls would not increase their value anyway. Originally the woman was placed at the mercy of the clerk’s story. But she affirmed that by chance narration held power at that moment, and spun her own even more powerful story. Her position of narrative vulnerability became a positive position of narrative power, because she crossed a limit into another domain.

Now we enter immediately into another narrative intensity, because the clerk could do many things here as well, including telling a more powerful story. But he affirms that by chance the power of the woman’s story is overwhelming, and he affirms that by chance he is ignorant at that moment of the price. His ignorance becomes expressed at a higher power of factual knowledge when he finds the actual price of the oysters.

Again we encounter a narrative intensity, because the clerk could do many things at this point. But he affirms that by chance he is not a good grocer, and instead affirms his tendency towards being an artist. The grocer here becomes an artist.

He loses his job and his home, and faces another moment of intensity. He could do anything about his poverty and homelessness. What does he do? He creates a short story called, "It Is Because I have No Home That I Have the Greatest Power in This World" and he kills himself.

Then what happens? The story of his life is told by the taxi driver to Scott Wollschleger. The grocer became an artist and then became a story. Let’s examine this final part.

At the beginning, the grocer obtained power by telling the women a clever story about the price of oysters. In a sense, even as a grocer he is implicitly an artist. He is a story-crafter. When he loses his job, he crafts a story that somehow explains that his homelessness is a source of his power. We might also say that the loss of his job caused him to write a story that gave him power, all by means of the power of narration to create fictional realities in which one is secure and in power. But having power does not bring happiness. He has all the power in the world, but still loses hope. He then affirms that by chance he has chosen the wrong thing, narrative power, and sees no other solution, and kills himself. While it might seem that his suicide was a negation, it was instead a creative affirmation of becoming. Here the man affirms his proficiency as an artist, and dies in a legendary way, with the remarkable and curious story in his pocket. He himself thereby becomes a story, which is told by the taxi driver, then told by Scott Wollschleger, then told again by me.

Wollschleger ends by wondering about the relationship between internal limits and power. I offer the above literary analysis as material for a possible answer.

The man was a grocer, but implicitly in him was an artist. He needed to overcome internal limitations to become an artist. But this overcoming did not destroy his self as a grocer, because as a grocery clerk he had tendencies toward narrative creation. He merely expressed them more explicitly when becoming a creative short-story writer. But even as a writer, he was implicitly something even more powerful. He himself also was a story to be retold over and over long after his death, which in a way immortalizes him. By killing himself in a legendary way, he overcame these internal limits and expressed himself at a much higher exponential level. The narrator became narration.

There are many stories within stories stored in Scott’s story, and maybe many more are in store. Wollchleger’s story may continue to express itself at higher exponential powers, if by chance its implicit tendencies are affirmed.

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Thank you for the Prof Moors posting on limits and boundaries. It reminds me of a puzzling indecent I had with a taxi driver who insisted that the time it took to get from one place to another was not a matter of how fast he was driving. He told me a long winded story about a similar encounter he had with an uninformed check-out clerk at a grocery store. The clerk's inability to know the price of things was made notorious one day when he apparently committed suicide and left behind a short note that said he had allways lived by the wisdom given to him by a very compelling parable told by a wandering local artist who "constantly declared that the very fact that he had no real home gave him greater power in the world".

Here is a rough version of the story he told me.

"The Long Necklace

In a grocery store a rich older lady with a large flashy adornment of pearls around her neck decides to buy some fresh oysters. Not seeing any price indication, she asked the clerk, how much each one costs. The clerk says that it is impossible to really know the true value because any one of them may have the most beautiful pearl inside of them and it would impossible to know without dissecting the oyster, effectively destroying it. And of course, that would then diminish the value of the oyster. There was really nothing he could do to help her.
The old lady explained to him not to worry about this problem any more because the marvels of modern science had permitted all oysters to now give way to having pearls inside of them. So, in essence, each pearl on her necklace was of the same value as a single oyster and that the value of pearls had become quite diminished from all this. The real difference in value between an oyster and a pearl was at best marginal. The clerk, still not swayed, told her his heart and mind would still remain undecided because given the years of small changes that will happen along the way, the possibility remained that one day something that no longer resembled what was around her neck may come about to be created inside the oyster. And that would then become what is to be called the most beautiful pearl and have the most value. The marginal differences in all this gave him hope. The lady then shook here head and reminded him that she was there to buy oysters and not debate economics. The clerk then shamefully lowered his head, found the correct price in a book on the counter and proceeded to process her order at the checkout...In the following week the clerk, recalling the humiliating encounter he had with the old lady, decided it was time to leave the grocery story and take to his true passions. But with the loss of his job and income he also lost his home and was left wandering the streets only finding himself telling this story to any person who wanted to know from where he found his power in this world. Eventually he lost all hope and took his own life. On his body the police found a small notebook which only contained some incomplete sketches for a short story entitled "It Is Because I have No Home That I Have the Greatest Power in This World"

Despite the morbidity of the tale, by the time the taxi driver had told me all this
I had arrived home.

It made me wonder what happens at the margin and its relationship to power.

Is the overcoming of internal limits the only way to greater powers?

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.

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.