When we get out to the furthest reaches of Deleuze's ideas, out in the vicinity of the eternal return and univocal being, I always feel like my understanding of them starts slipping away. There's a danger that no matter how much I write about these ideas I have missed some key ingredient in explaining them, and that the most crucial point has somehow been left unsaid. In some ways I think that inducing this feeling of continual grasping and slipping and regrasping is part of Deleuze's style. After all, this is a pretty good description of the relationship between difference and repetition and difference. Nevertheless, I still feel the need to go back over the system Deleuze has been describing once more and specify exactly where the slipping happens and the circle does not quite close. I'm imagining this in terms of a question about the structuralist ontology that started with the discussion of coupled oscillators: where did the initial oscillators come from?
My initial answer to this was to imagine that the forced movement of the coupled system itself constituted a new oscillator that could then be coupled to other oscillators that had been built in the same fashion. Let me first explain how I saw that working.
The system constituted by the eternal return begins with two series of differences. If we think of these as series of the simplest possible binary difference 01010101 played out over time, then we have a square wave oscillator. The two series then begin to resonate because they share a singularity. That is, their differences are distributed in such a way that they become related. This singularity, or dark precursor, is a strange beast. In some sense shared by the oscillators; the nature of a singularity is its capacity to make two different things resonate through some sort of interaction. We might cheekily say that a singularity is never alone, never naked. But the two oscillators don't share it by being two examples of it. They don't partially resemble one another or the singularity by virtue of this sharing. The singularity is not a property of some abstract thing called "oscillators in general" that happens to be shared by these two oscillators in particular. Instead, the singularity is created by the relationship between the series as much as it creates it. It's the attractor, as it were, of the dynamic feedback loop that develops between two different oscillators. Our square wave analogy starts to fail at this point, since the frequencies of the oscillations are in fact properties of all oscillations, and the points of resonance can be calculated in advance. Remember that an oscillator here is just standing in for a series of differences, which could be chemical concentrations, or phonemes, on the one side, and digital differentiation, or meanings on the other.
The singularity in itself is always hidden (hence dark) and we only know of its existence because the original series begin to resonate, and in fact resonate in a feedback loop that actually welds them into a single system. At this point there is a forced movement that goes beyond the two original oscillators, which now appear as merely the two distinct parts necessary for this new movement. The identity of the individual oscillators dissolves into this overall system (hence the death instinct connection). So it seems that we've produced another, higher level, oscillation that has an alternation between the two original oscillators as its 0 and 1 levels, so to speak. This oscillator could presumably then resonate with other second degree oscillators constructed in the same manner in order to produce third degree oscillators, and so forth. The endpoint of the system becomes the conditions from which we begin another system, just like the third synthesis of death liberates a desexualized energy that can later become bound in the first synthesis of habit.
I still think this describes the basic structure of the "systems constituted by the eternal return" as Deleuze puts it. After thinking about it more though, I believe that the way I've laid it out here actually inverts the direction we are meant to read it in. Instead of building larger and larger units on top of the external interactions of existing units, we should think about smaller and smaller differences being created within an existing difference. The point is not that the interaction of two differences creates a new higher level difference. We should see it running in the opposite direction. The point is that every series of difference is already split into two series inside itself. Instead of 1+1=2+1=3+... we have 1=1/2+(1/4+(1/8+(...)))
In a way, you might say that this perspective is no different from the first one, and that it was implicit in it. If any two oscillators can form a third composite oscillator, then it stands to reason that one given oscillator can be broken into two smaller sub-oscillators. Either way, it's turtles all the way down, right? Actually though, from the perspective of the role of identity and repetition in the structure, the fractal infinite that plunges within is a profoundly different way of looking at things. The first way of looking at things takes the identity of the initial unit for granted as an unquestioned point of origin. The form of repetition that defines the whole is then the reproduction of this unit. This numerical repetition requires a starting point, and it also requires someone to do the counting, something outside the system to keep track of the number of increments (exactly the problem we saw with Hume at the start of the chapter). If we move in the other direction and see whatever series we happened to start with as already divided within itself we avoid both of those problems. There's no unity to take for granted and no assignable origin because every starting unit is already more than one thing. And the form of repetition is no longer the contingent and external addition of another copy, but the essential internal repetition of a process of continuing fractionation. There's a huge difference between whether the One is taken for granted at the beginning or whether it is only produced at the very end of the process, as the limit of difference differentiating itself again and again.
I think it's this fractal recursion that Deleuze has in mind with difference-in-itself. Difference is immanently within any system. You might even say that difference is within time, in the sense that one is already two, etc ... There is no atomic difference. Looking at things this way definitely produces some strange paradoxes. If difference is constantly differentiating within itself, then we can (and must) begin in the middle, at any level. To understand that single arbitrary starting point though we have to move up and down the levels of difference infinitely in both larger and smaller directions. That single difference becomes an entire universe. In other words, every difference-in-itself, repeats a whole, and they all repeat a different whole but the same way. So we say that the One only appears at the end of the chain, after thinking through an infinite series of differentiations, but in some sense it is there implicitly at the beginning in each and every difference. And the same type of paradox appears with our original question: where did the initial oscillators come from? In fact, there are no "initial oscillators", if we mean by this some smallest unit that is indivisible. Every oscillator has two series within it, ad infinitum. But by the same token, every level we might start with is inside of some other oscillator, in an endless series of nested vibrations. In which case the identity of that oscillator is actually constructed by something outside itself, of which it is merely a part or an internal differentiation. The immanence of difference refers immediately to an outside. And the singularity that differentiates difference refers to all the other singularities in an indefinite multiplicity.
Everything is upside down in the world of the eternal return. The only anything is everything.
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