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:

"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).