Page 118: The loss of the subject: the person has been reduced to a "material instance" which realizes the possibilities of an ontological proposition. No longer do we have a Cartesian subjecthood.
Page 119: On the relation of form to content.
Page 120: If you remove one factor from the Pascal triangle, this number may have been a pillar of the proposition, and it can "collapse" as a result.
A "ring may be snapped, and reveal the otherwise organized sense". (120) In the last post, I wrote on circles. Same idea here. A convergence or event undone spreads the singularity along the ordinary line, revealing its "sense", i.e. its pulsations and frequencies. Undisciplined by the circle (i.e. other singularities), sense can "run the risk of losing all measure" and "sink into the undifferentiated abyss of groundlessness" which produces a "monstrous body" of a "terrible primary order". (120) I.e. from sense to nonsense, from language to schizophrenia. Hence, a circle is not an "object" as such, but hidden within its code is a "differential system to which an emission of singularities corresponds." (123)
Aleatory and singular points are two sides of the same coin. (120)
The space between, the difference between a logical proposition and its ontological correlates can be termed "error", or a remainder. (120) In this way, cutting down an ever-slimming remainder, one can posit the relation between sense on one side and true or false on the other.
Page 122: The "problem", the "genetic element", the fibonacci spirals that occur at the time of the event -- those cannot be "reduced", as one might reduce a factorable number. Instead, the fibonacci numbers can only be contracted or condensed according to their "golden" proportion.
When Deleuze says that the problem does not exist outside of the propositions which express it, but rather subsists or inheres in them and as such the problem "is not", I think we should take him literally. (123) The problem is literally a negative space, "(non)-being or ?-being", an aleatory point which is immanent with the proposition and the underlying force structuring it.
The depths organize the surface. (124) In the Pascal diagram, the crystalline structure organizes the GCD.
Axiom: Sense is a double. (125) (e.g. the singularities on one side are the aleatory points on the other)
Wednesday, April 20, 2011
Saturday, April 16, 2011
Sixteenth Series of Static Ontological Genesis
Deleuze's geophilosophy is a "surface topology". (109) Hence, we can use topology to construct and deconstruct the structure of the event. If we take one singularity, one knot, one red dot in the Pascal diagram, and spread it out over a "line of ordinary points," we get the labyrinth, the pulsed string, vibrating like a wave at a frequency in tune with its number. The singularity takes this shape of extension over an "ordinary" line in the actualization of the event. (110)
"A world already envelops an infinite system of singularities selected through convergence." (109) This idea of convergence is important to Deleuze. Elsewhere, he writes on hylomorphism. The preindividual transcendental field of singularities is self-organizing. This is how a shape or structure takes its shape, its form, "to be incarnated in a body; to become the state of the body." (110) Deleuze says, "An individual is always in a world as a circle of convergence." (110) To be a circle implies that the circle is the result of an event, a convergence that results not in a knot, or some other kind of shape, but in a circle. I visualize two series coming together, two Pascal triangles, the tips of which are interlocking in some kind of dragon-chasing-its-tail kind of shape, a yin-yang whose sum total is something like a circle, which also represents the GCD of the two series. The two Pascal triangles intersect and produce a new gyre, and because it has been lifted up into another dimension, we see the cross-section -- the circle. The circle is the stable shape of this event, and as such associated with the individual. Hegel also diagrammed the world as a series of interlocking concentric circles. Different theory, similar diagram.
If you can imagine the Pascal triangle as a 3-D gyre, when the event occurs, the potential energy in the system "falls to its lowest level" -- gets pulled to the tip of the triangle (like a tornado). (110) This idea of energy falling to its lowest level is similar to how we referenced the pachinko game earlier.
Deleuze wrote extensively on Leibniz, quoting him here that "each individual monad expresses the world." (110) Each monad would be like a singularity, and in discovering all the frequencies of that singularity (e.g. all the factors of a huge number), we gain a perspective on every other singularity. This is very similar to Borges' aleph, a point in space that reflects all the other points by which one can see everything in the universe.
Page 112: Deleuze distinguished between zones of clarity and obscurity in the singularity. In other works, this implies "consistency" and "inconsistency". Here, we can think in terms of sense and nonsense. Sense is the ability for the snowflake, crystalline form to incarnate an event. The nonsense is all the other unformed points (non-red dots).
Page 114: "Incompossible" worlds (e.g. a world in which Adam is a sinner and a world in which Adam is not a sinner; not a contradiction but a mutual exclusivity) imply that there must be an "ambiguous sign" or aleatory point constructing the difference between the two worlds. This aleatory point, or shifter, is the key, or machine by which the different actualizations are realized. In the case of Adam, the shifter would be something like, "to sin." Worlds are "overthrown from within by paradox", by this aleatory point or ambiguous sign, this moment of becoming and revolution. (117)
"A world already envelops an infinite system of singularities selected through convergence." (109) This idea of convergence is important to Deleuze. Elsewhere, he writes on hylomorphism. The preindividual transcendental field of singularities is self-organizing. This is how a shape or structure takes its shape, its form, "to be incarnated in a body; to become the state of the body." (110) Deleuze says, "An individual is always in a world as a circle of convergence." (110) To be a circle implies that the circle is the result of an event, a convergence that results not in a knot, or some other kind of shape, but in a circle. I visualize two series coming together, two Pascal triangles, the tips of which are interlocking in some kind of dragon-chasing-its-tail kind of shape, a yin-yang whose sum total is something like a circle, which also represents the GCD of the two series. The two Pascal triangles intersect and produce a new gyre, and because it has been lifted up into another dimension, we see the cross-section -- the circle. The circle is the stable shape of this event, and as such associated with the individual. Hegel also diagrammed the world as a series of interlocking concentric circles. Different theory, similar diagram.
If you can imagine the Pascal triangle as a 3-D gyre, when the event occurs, the potential energy in the system "falls to its lowest level" -- gets pulled to the tip of the triangle (like a tornado). (110) This idea of energy falling to its lowest level is similar to how we referenced the pachinko game earlier.
Deleuze wrote extensively on Leibniz, quoting him here that "each individual monad expresses the world." (110) Each monad would be like a singularity, and in discovering all the frequencies of that singularity (e.g. all the factors of a huge number), we gain a perspective on every other singularity. This is very similar to Borges' aleph, a point in space that reflects all the other points by which one can see everything in the universe.
Page 112: Deleuze distinguished between zones of clarity and obscurity in the singularity. In other works, this implies "consistency" and "inconsistency". Here, we can think in terms of sense and nonsense. Sense is the ability for the snowflake, crystalline form to incarnate an event. The nonsense is all the other unformed points (non-red dots).
Page 114: "Incompossible" worlds (e.g. a world in which Adam is a sinner and a world in which Adam is not a sinner; not a contradiction but a mutual exclusivity) imply that there must be an "ambiguous sign" or aleatory point constructing the difference between the two worlds. This aleatory point, or shifter, is the key, or machine by which the different actualizations are realized. In the case of Adam, the shifter would be something like, "to sin." Worlds are "overthrown from within by paradox", by this aleatory point or ambiguous sign, this moment of becoming and revolution. (117)
Tuesday, April 5, 2011
Monday, April 4, 2011
Fifteenth Series of Singularities
Deleuze's geophilosophy of the event (i.e. a geometric ontology/univocity/monism) has a fundamental neutrality. The event is a productive force, and does not have valences of right and wrong, good or bad, etc ("it is entirely independent of both affirmation and negation" (101)). For the event, there is only the distinction between sense and nonsense. Hence, when Deleuze speaks of an event like a battle, it is "terrible" in its neutrality, impassivity, and indifference to human death. (100) Like a puppeteer, the event incarnates itself in the flesh of the soldier, in all of his actions, and even his death. (101) In the midst of human carnage, one may ask why G-d allows evil and terror to exist, and to this Deleuze might respond with his theory of the event. On an individual level, it always makes me halt to think that in the midst of a bout of sadness or misanthropy that I might be feeling, these emotions are neutralized to someone else that might be listening objectively to my story. They might see my situation/problematic, but they do not feel it, because like the event, they see only the structure of it, and not the emotive production of sense that it incarnates in me. The individual only attains this "intuition" about the smallness of his own pain through a "long struggle" reaching towards a "beyond", a transcendent perspective where he/she can see himself/herself in the 3rd person. (101)
When Deleuze speaks of the event, he often speaks of it as being "full", as in impenetrable. This conforms to our example with the Pascal triangle. The crystalline triangles are not full; they are pockmarked with holes (they are the "impersonal and transcendental field" (102)). But in the production of sense, the fibonaccis produce a GCD which is full -- a gyre conforming to the golden ratio without any holes on its surface, what will become later for Deleuze the Body without Organs (a term originally used by Antonin Artaud).
Deleuze details the Pascal triangles:
The way that I would like to visualize the distribution of singularities is this: Each singularity (red dot) is the product of intersection of two series (numbers). The dot corresponds to the GCD of those two numbers. In the GCD, the mechanism of "auto-unification", the "differences between series are distributed." (103) So imagine one of the numbers flowing into the GCD, the gyre, and the GCD spins it down and spits out the other number. Like a machine. Or something like that. Because the GCD, the "locus of sense", is bound to the two series that generate it, "energy is not localized at the surface [read GCD] but is rather bound to its formation and reformation." (104) An example: you and I drink a beer at a bar and play Photo Hunt. In order to compare two pictures, two series, we first look at both, and in so doing, create a GCD which is a sum total of both pictures (a generalized approximation of both). We then look from one picture to the other, taking one series, comparing it to the GCD. As one series flows into the GCD, the negative, the inverse is left on the other side, showing the negatives, the inverse, the things which are different. In this way, one series is always an excess and the other a deficit. The "extra" icon in Picture 1 is the "thing without a place". The "missing" icon in Picture 2 is the "place without a thing".
Page 104: Deleuze states specifically that the event causes the surfaces to rise into "another dimension". This is the production of the GCD. In other writings, this would be the +1 of the n+1. In Hegel, this would be the aufhebung. Within Kant's writing, this is the sublime.
Page 106: Deleuze contrasts the "undifferentiated abyss" with the "supremely individuated Being". Here we should read the the pock-marked crystalline Pascal triangles against the "full" GCD, respectively.
Page 107: Being, which is becoming, "leaps from one singularity to another." I read the synapses in the brain directly here. Also, one can visualize pachinko, where a ball dropped at the top hits a number of nails, or singularities, redirecting its path to the bottom. The subject is but one of many possible points or perspectives from which becoming can speak. In his philosophy, Nietzsche madness allowed him to discover the "depth" of the individual, "discerning in it a thousand voices." (108).
When Deleuze speaks of the event, he often speaks of it as being "full", as in impenetrable. This conforms to our example with the Pascal triangle. The crystalline triangles are not full; they are pockmarked with holes (they are the "impersonal and transcendental field" (102)). But in the production of sense, the fibonaccis produce a GCD which is full -- a gyre conforming to the golden ratio without any holes on its surface, what will become later for Deleuze the Body without Organs (a term originally used by Antonin Artaud).
Deleuze details the Pascal triangles:
"What is neither individual or personal are, on the contrary, emissions of singularities insofar as they occur on an unconscious surface and possess a mobile, immanent principle of auto-unification through a nomadic distribution."(102)See this post and this post for a refresher on the production and distribution of singularities. Every event (the intersection of two series) produces singularities which then become new series which then intersect/resonate ad infinitum to produce new singularities. Within our Pascal triangle, the singularities are the red dots. The distribution of red dots in the triangle represent a store of "potential" energy just as a boulder has potential energy by resting atop a hill. (103)
The way that I would like to visualize the distribution of singularities is this: Each singularity (red dot) is the product of intersection of two series (numbers). The dot corresponds to the GCD of those two numbers. In the GCD, the mechanism of "auto-unification", the "differences between series are distributed." (103) So imagine one of the numbers flowing into the GCD, the gyre, and the GCD spins it down and spits out the other number. Like a machine. Or something like that. Because the GCD, the "locus of sense", is bound to the two series that generate it, "energy is not localized at the surface [read GCD] but is rather bound to its formation and reformation." (104) An example: you and I drink a beer at a bar and play Photo Hunt. In order to compare two pictures, two series, we first look at both, and in so doing, create a GCD which is a sum total of both pictures (a generalized approximation of both). We then look from one picture to the other, taking one series, comparing it to the GCD. As one series flows into the GCD, the negative, the inverse is left on the other side, showing the negatives, the inverse, the things which are different. In this way, one series is always an excess and the other a deficit. The "extra" icon in Picture 1 is the "thing without a place". The "missing" icon in Picture 2 is the "place without a thing".
Page 104: Deleuze states specifically that the event causes the surfaces to rise into "another dimension". This is the production of the GCD. In other writings, this would be the +1 of the n+1. In Hegel, this would be the aufhebung. Within Kant's writing, this is the sublime.
Page 106: Deleuze contrasts the "undifferentiated abyss" with the "supremely individuated Being". Here we should read the the pock-marked crystalline Pascal triangles against the "full" GCD, respectively.
Page 107: Being, which is becoming, "leaps from one singularity to another." I read the synapses in the brain directly here. Also, one can visualize pachinko, where a ball dropped at the top hits a number of nails, or singularities, redirecting its path to the bottom. The subject is but one of many possible points or perspectives from which becoming can speak. In his philosophy, Nietzsche madness allowed him to discover the "depth" of the individual, "discerning in it a thousand voices." (108).
Friday, April 1, 2011
Fourteenth Series of Double Causality
Why double causality? Because we have two series, bridged by sense. In Anti-Oedipus, Deleuze writes on the assemblage, which in his most cited example could be an orchid and a wasp coming together in the act of pollination. In this book, Deleuze has indicated the signifier and signified as an example of these two series. In order for there to be a double causality, there also must be a double nonsense "which must preside over the this bestowal of sense". (98) These are the series which have been partially emptied by the production of the GCD; they are missing factors. They are the crystalline snowflake Pascal triangles, only missing several of the red dots. The Pascal triangle itself is an "impersonal transcendental field" filled with singularities-- that is, a transcendental field without a subject, a structuring structure. (98)
Page 95: Sense is neutral as it is a "mere double"; it is the reflection of the two series through the generation, in our example, of the GCD.
Page 95: Sense is a productive force. It is not to be confused with negation or dialectics.
Page 97: Key question (that Deleuze answers in another chapter): How do we go from "sterility to genesis". The production of sense implies a creation ex nihilo. How does that work?
Page 95: Sense is neutral as it is a "mere double"; it is the reflection of the two series through the generation, in our example, of the GCD.
Page 95: Sense is a productive force. It is not to be confused with negation or dialectics.
Page 97: Key question (that Deleuze answers in another chapter): How do we go from "sterility to genesis". The production of sense implies a creation ex nihilo. How does that work?
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