The Aleatory Point

Towards the end of this section of affirmation and negation (pg. 55-57), Deleuze expands a bit on a metaphor he's already used a few times in critiquing Hegel's dialectic -- the damn thing just spins in place, a circle with a single center that never really moves.  He contrasts this with the "circle" of Eternal Return:

For if eternal return is a circle, then Difference is at the centre and the Same is only on the periphery: it is a constantly decentered, continually tortuous circle which revolves only around the unequal.

In the next paragraph he starts to talk about the center of a circle as a metaphor for the point of view of a subject who represents the world in some sort of perspective.

Representation fails to capture the affirmed world of difference. Representation has only a single centre, a unique and receding perspective, and in consequence a false depth. It mediates everything, but mobilises and moves nothing. 

If we revisit Deleuze's understanding of Aristotle's theory of "average forms" with this picture in mind, we can see that the POV that Aristotle chooses is precisely the harmonious, balanced, and essentially human one.  Remember that for Aristotle, difference was always classified between large generic differences and small specific differences, and that specific differences were further divided into contraries that constituted the opposite poles of a genus.  In other words, the whole picture is taken from some central point in the middle of things, which makes perfect sense with the overall Greek emphasis on man as the measure of all things.  There's also no movement in Aristotle's scheme, because it is a taxonomy constructed from one privileged, and hence permanent, point of view.  Pictorially, we have classic perspective.

Movement, for its part, implies a plurality of centers, a superposition of perspectives, a tangle of points of view, a coexistence of moments which essentially distort representation: paintings or sculptures are already such 'distorters', forcing us to create movement - that is, to combine a superficial and a penetrating view, or to ascend and descend within the space as we move through it. 

But wait, you ask, didn't Leibniz talk about every monad as a separate POV on the whole of the universe? And didn't Hegel introduce a movement where the POV changes over time as history progresses?

Is it enough to multiply representations in order to obtain such effects? Infinite representation includes precisely an infinity of representations - either by ensuring the convergence of all points of view on the same object or the same world, or by making all moments properties of the same Self. In either case it maintains a unique centre which gathers and represents all the others, like the unity of a series which governs or organises its terms and their relations once and for all. The fact is that infinite representation is indissociable from a law which renders it possible: the form of the concept as a form of identity which constitutes on the one hand the in-itself of the represented (A is A) and on the other the for-itself of the representant (Self = Self). The prefix RE- in the word representation signifies this conceptual form of the identical which subordinates differences.

The answer to Deleuze's question there is obviously "no".  You can multiply the perspectives infinitely, but if they all form a unified and convergent series that represents one object to one subject, you haven't created any genuine movement.  The center from which each picture is taken may be different, but there is a sort of meta-center to the whole image.  This meta-center is literally the concept of identity.  For Leibniz it's the identity of one best of all possible worlds guaranteed by one benevolent God.  For Hegel it's the self-identity of Absolute Spirit doing its dialectical merry-go-round thing.

So then, how can we get past the idea of there being a central point of view?  Basically, we have to embrace the idea that all these multiplying points of view diverge, and that the only convergence is this fact of divergence.

The immediate, defined as 'sub-representative', is therefore not attained by multiplying representations and points of view. On the contrary, each composing representation must be distorted, diverted and torn from its centre. Each point of view must itself be the object, or the object must belong to the point of view. The object must therefore be in no way identical, but torn asunder in a difference in which the identity of the object as seen by a seeing subject vanishes. Difference must become the element, the ultimate unity; it must therefore refer to other differences which never identify it but rather differenciate it. Each term of a series, being already a difference, must be put into a variable relation with other terms, thereby constituting other series devoid of centre and convergence. Divergence and decentring must be affirmed in the series itself. Every object, every thing, must see its own identity swallowed up in difference, each being no more than a difference between differences. Difference must be shown differing.

Stated abstractly this can seem like an empty formalism and another dance step in the post-modern one-upmanship jig.  Which is why I think it helps to consider the actual image that he's setting up here.  The center of the circle of eternal return is constantly moving.  It isn't fixed like in Aristotle.  It doesn't converge to some equilibrium like in Leibniz, nor does it revolve in an orbit like in Hegel.  We should think of it as tracing out some path that connects one difference to another.  A very strange (even torturous) path though, as difference refers to itself endlessly and ad infinitum.  The image that comes to mind is the Peano Curve.  

The center moves through space in a way that eventually fills it entirely and literally lends it the power of a higher dimension.  Of course, while weird, the Peano Curve is pretty regular, so we might have to imagine the angle of each turn changing as it moves. 

In fact, we should probably even go ahead and imagine that the path it traces isn't continuous at all. The center jumps around everywhere, passes through every point before returning to where it "started". Which means we're actually trying to describe a completely random "curve".

Each difference passes through all the others; it must 'will' itself or find itself through all the others. That is why eternal return does not appear second or come after, but is already present in every metamorphosis, contemporaneous with that which it causes to return. Eternal return relates to a world of differences implicated one in the other, to a complicated, properly chaotic world without identity. Joyce presented the vicus of recirculation as causing a chaosmos to turn; and Nietzsche had already said that chaos and eternal return were not two distinct things but a single and same affirmation. The world is neither finite nor infinite as representation would have it: it is completed and unlimited. Eternal return is the unlimited of the finished itself, the uni"ocal being which is said of difference. With eternal return, chao-errancy is opposed to the coherence of representation; it excludes both the coherence of a subject which represents itself and that of an object represented.

Eternal Return, the univocity of difference, difference in itself -- this concept is meant to be a sort of paradox or oxymoron that gives us a concrete image of chaos.  Ultimately I think chaos basically plays the traditional role of God in Deleuze's philosophy, the source of all possibility, the only thing that can tie everything together, the identity (univocity) of difference.

The final turn of the screw here is to understand what effect setting this chaos of difference free (as opposed to taming it) has on us.  Because with every POV removed or set into motion, we have in fact obliterated our selves.  In thinking the universal chaos of eternal return, we are forced to reconceive our thinking self as a difference propagating through all the others, trying to come back to "itself" after this infinite journey.  We are not the center of this chaos, but just a slice of it, a random sample of total randomness.  The thought of the eternal return is like Daniel Dennett's universal acid or Douglas Hofstader's perfect record player taken to a more abstract level; a thought that dissolves everything, including the thinker.

Nietzsche seems to have been the first to see that the death of God becomes effective only with the dissolution of the Self. What is then revealed is being, which is said of differences which are neither in substance nor in a subject: so many subterranean affirmations. If eternal return is the highest, the most intense thought, this is because its own extreme coherence, at the highest point, excludes the coherence of a thinking subject, of a world which is thought of as a guarantor God.

 For Deleuze, thought reaches its highest power when it dissolves itself into chaos.

... for a brief moment we enter into that schizophrenia in principle which characterises the highest power of thought, and opens Being directly on to difference, despite all the mediations, all the reconciliations, of the concept.

P.S. The title of this post comes from a concept Deleuze employs throughout The Logic of Sense. I'd have to look back at the book and my notes to be sure that it's the same concept as the chaotic trajectory of a mobile center that I'm discussing here, but I feel like he's setting up such a strong visual image here that the two are almost bound to be "the same". Did I mention that Deleuze seems to have genuinely lived, and written, the eternal return?