§ 1st contrast of generality and repetition –from the perspective of law; flat space equivalence classes; introduction to classical symmetry, which is conservative, and synthetic symmetry, which is transgressive; introduction to a critique of representation (pg.2-5)
What is the nature of the differences between these two economic orders, between the domains of generality and repetition? Deleuze begins by warning his reader that while the transition from one to the other can be perceived to occur by linear progression, we should not mistake that there is in fact a difference in kind (i.e. ontologically) between the two domains, rather than merely or exclusively a difference in degree (i.e. historically).
(‘Repetition can always be “represented” as extreme resemblance or perfect equivalence, but the fact that one can pass by degrees from one thing to another doesn’t prevent their being different in kind.’)
It is difficult to overstate the importance of this point for the purposes of our future elaboration of dynamical systems theory. Deleuze, however, is perhaps getting a little bit ahead of himself here. We will not follow his cue too far by equally getting ahead of ourselves. However, one brief point of explanation may prove helpful.
Deleuze is saying here –and in DR will ultimately illustrate– that, for instance, just because one sees in the progressive differentiation of the ‘domains’ we call ‘markets’ a passage by degrees does not mean that the objects populating such domains do not differ in kind. That conduction and convection and turbulence all proceed by degrees does not prevent their being different in kind. And so too though we observe the linear development from a set of markets populated by numerical multiplicities –actualized as classical objects and generic financial objects (the objects populating flat space)– to those populated by qualitative multiplicities –actualized as synthetic financial objects (the objects populating curved space) doesn’t mean that their systems of exchange don’t differ in kind. Numerical multiplicities and qualitative multiplicities differ in kind; they differ as objects, and they differ as domains of action.
In the modality of economics such ‘domains of action’ (as the geometer calls them) are quite obviously markets. There is an order of generality, and there is an order of repetition; we may witness the passage by degrees from one order to the other; and the two orders may even resemble one another; but there is an important ontological-economic difference between them. It is merely a matter for us to follow Deleuze’s analysis further in DR so as to find out what is the precise ontological character of this difference, and to understand how different markets which resemble each other, and pass by degrees from one to the other, might actually differ in kind.
(‘…Generality belongs to the order of laws…It condemns [particulars] to change…[and yet is] an empty form of difference, an invariable form of variation.’)
The 1st of 3 contrasts Deleuze makes between generality and repetition is from the perspective of law. And in the modality of political economics, “the law”, which is thought to generally order the values of change, is said to manifest itself in and through the becoming, or change, in value –or what political economics has historically understood to be a theory of value for economic objects.
Now, it is important to observe here that Deleuze and why Deleuze discusses generality in strict Euclidean terms. If we do not understand this fundamental point we will misunderstand Difference and Repetition from the beginning. Our reader will be reminded that generality has now been established as the domain of action of resemblance and equivalence. And so if in turn we keep in mind that in Marx’s ontological schema, resemblance and equivalence are the qualitative and quantitative orders of classical exchange and generic finance, then it follows that Deleuze is ontologically collapsing these two classes of exchange into Euclidean geometry –or rather, more correctly, he’s identifying an isomorphism between geometric equivalence classes and classes of exchange. Classical exchange and generic finance are flat space equivalence classes of exchange. Such equivalence classes and Euclidean geometry are of different modalities, i.e. one is of economics and the other is of mathematics, but they are both of the same order of generality. Let us consider why.
Euclidean geometry defines a congruent transformation as the rigid motion of a geometric object into its image, with all its metrical properties remaining absolute and invariant in the course of its transformation: an object is set in motion as it moves from one to another place in space; and this object will subsequently occupy different Cartesian coordinates; but all properties of the object remain unchanged, invariant, and indifferent to the difference of their new position in space. Additionally, Euclidean geometry defines a similarity transformation as the rigid motion of a geometric object into its image with all metrical properties except its lengths of sides, and consequently its volume, remaining absolute and invariant: an object is set in motion as it moves from one to another place in space; and this object will subsequently occupy different Cartesian coordinates; but all properties of the object except for its lengths of sides and volume remain unchanged, invariant, and indifferent to the difference of their new position in space. Euclidean space is a flat space. Flat space is populated by sedentary objects, whose transformations into their image either effects no or else very little alteration to their metrical properties. Objects transformed in Euclidean space –whether by congruence or similarity– therefore effect an ‘invariable form of variation’, ‘an empty form of difference’ in their space of transformation. The technical term given by geometry to such invariance to change is symmetry.
We explain this so that the reader of DR does not miss the decisive move made by Deleuze when he later begins to give philosophical transformation to these mathematical concepts. Deleuze is often mistakenly regarded as a common poststructuralist by those who are oblivious that group theory and non-Euclidean geometry –among other mathematical and scientific insights– are of much greater methodological predominance in his work. Of course because DR is giving philosophical transformation to these mathematical concepts, we will see Deleuze modify the Euclidean understanding of symmetry that is surreptitiously imported into our political economics: this is the kind of symmetry that is classical symmetry. In DR we see Deleuze counterpose classical symmetry with a second kind of symmetry, which is synthetic symmetry. DR provides a thorough exposition of the ontological differences between these two symmetries that so differ in kind. And remarkably, he will illustrate that this second kind of symmetry is at the heart of the first –which, our reader will learn (or may know already), is originally a group-theoretic insight about the ontological relation of the non-Euclidean equivalence classes to Euclidean transformations (We will have occasion to discuss the contributions of the group theorists Evariste Galois and Felix Klein sometime later).
(‘If repetition is possible, it is…against the similar form and equivalent content of law.’)
We have said Deleuze is observing that the equivalence classes of Euclidean geometry are isomorphic to the flat space equivalence classes of classical symmetry in economics: congruence transformations are to classical exchange what similarity transformations are to generic finance, insofar as transformations of classical objects effect no change to their metrical properties, while transformations of generic financial objects allow for their length of tenure and volume of image of value to shrink or grow over the course of the exchange, but otherwise effect no change to their metrical properties. (More on this point will be developed later; however, for more immediately on the isomorphism between geometric transformations and economic transformations, see the Appendix in Of Synthetic Finance)
Deleuze wants to make clear that as flat space equivalence classes of exchange, both of these aforementioned equivalence classes are populated by objects whose domain of action is the order of generality. This is why Deleuze opposes repetition to generality (i.e. its ‘similar form and equivalent content’). Repetition is the domain of action of synthetic transformations, and is predicated on the actualization of synthetic symmetry. Generality is the domain of action for congruence and similarity transformations, and is predicated on the actualization of classical symmetry. Deleuze upholds synthetic symmetry over classical symmetry, and because of this he opposes difference and repetition to resemblance and generality. And why? For what purpose? To what effect? In short, he does this precisely because he seeks to upend our traditional and flat space understanding of a system of economic transformations (viz. exchange) whereby nothing is transformed in the course of exchange; he seeks to elude reproducing this ‘empty form of difference’, the ‘invariable form of variation’ of classical symmetry, whereby everything remains the same in the course of its ostensible change, whereby a conservative invariance requirement on economic transformations is morally maintained in the face a more radical potentiality for change. This is his wager for thinking the ontology of the synthetic.
It is therefore highly thought-provoking to stand back here, already on the opening pages of the Introduction to DR, and reflect on the project at hand. Deleuze is engaged in a critique, an exposition of the internal limits of representation in philosophy: this is the avowed, ostensible, and actual project of DR. But there is a virtual project going on here as well. It is compelling to realize that the very same philosophical concept of representation that is the actual object of critique in DR is always already virtually operationalized in our classical political economic understanding of value, as it’s employed in our flat space equivalence classes of exchange (i.e. in congruence and similarity transformations), and at work in the actualization of classical symmetry. Our wager here, then, is to follow Deleuze en route to using the concepts of difference and repetition to think the ontological property of the synthetic –a synthetic symmetry– at the same time that we use synthetic symmetry to help us to rethink the political economic concept of value…And ultimately to therein tap an infinite leverage to actualize a mode of nomadic distribution.
This is a timely project, indeed. We set out with Deleuze’s Guidebook to do this at the very moment that synthetic finance is progressively differentiating itself within the system of exchange that is finance; we do this at the moment that an order of generality is progressively passing by degrees into an order of repetition –and yet we are seeing that these two orders differ in kind. That is to say, we do this at the very moment that –to put it in Deleuze’s terms– the virtual is progressively getting refracted through itself and now dumped out into actuality.
Deleuze further articulates some ontological properties of repetition in the modality of economics that distinguish it from the domain of generality from the perspective of law.
(‘If repetition is possible, it is due to miracle rather than law. If repetition can be found, even in nature, it is in the name of a power which affirms itself against the law, which works underneath the laws, perhaps superior to laws. If repetition exists, it expresses at once a singularity opposed to the general, a universality opposed to the particular, a distinctive opposed to the ordinary, an instantaneity opposed to variation, and an eternity opposed to permanence. In every respect, repetition is a transgression. It puts law into question, it denounces its nominal or general character in favor of a more profound and more artistic reality.’)
There is much in this statement that will need to be comprehensively unpacked when we periodically return to these topics in their more thorough incarnations in DR later on. However, as the reader can see, Deleuze is issuing a bold proposition right away in DR, and from which a bold promise follows. He is proposing that we radically rethink our political economic concept of value. And he suggests that doing so convokes the possibility of constructing an alternative and radically different system of exchange. He’s talking about distributing a different space for the circulation of capital –a distributive systemic-space founded on repetition, and working ‘underneath the laws’; one that that is ‘distinctive’, ‘singular’, ‘universal’, ‘eternal’, ‘transgressive’, and always in the service of ‘a more profound and more artistic reality.’ We will see Deleuze resume his elaboration of this notion as soon as Chapter 1 (Difference In Itself).
Of course, the question always arises here of how we arrive at such a ‘reality’? A question for Deleuze to address in DR is how, if an order of generality will pass by degrees into an order of repetition, one can ever observe the achievement of repetition “in-itself”? In his Introduction he alludes to this issue, which he will more fully treat in Chapter 2 (Repetition For Itself), and then in later chapters in even more depth.
(‘Repetition appears…only in the passage from one order of generality to another, emerging with the help of –or on the occasion of– this passage. It is as if repetition momentarily appeared between or underneath the two generalities. Here too, however, there is a risk of mistaking a difference in kind for a difference in degree.’)
Let us work backwards here towards the beginning of this passage.
First, we see Deleuze again remind his reader –when sketching his opening comments on the proprietary differences between generality and repetition– that the character of these differences may be perceived to be a mere matter of degrees, that they may appear to us as spatially-progressive and temporally-linear. However, Deleuze reiterates that these differences are ontological: they are different in kind, extremely so; and that we would be remiss to mistake our linear perception of a difference in degree for what is in fact nonlinear and ontologically different in kind. As we have said, this is a consistent and important theme threading its way throughout DR to which we will periodically return, insofar as, on the one hand, we must grasp what it means that different economical objects and the markets they populate are ontologically different in kind; and on the other hand, we will come to know such statements as instructive of the peculiar and highly original methodology developed by Deleuze for the task at hand. Deleuze rejects naïve realism, and yet is obviously not an idealist in any sense of the term. We can call Deleuze a speculative materialist (if we find ourselves psychologically requiring some label to attach to his style of analytically proceeding) –since he does indeed proceed as a “materialist”, i.e. as one who aims to think the registers of reality as material reality; but he does so by way of an analysis of a register of reality he labels “virtuality”; and so we must at least concede that he’s a new and peculiar kind of materialist. Also, as we will discuss later, Deleuze emphasizes the analytical power of “speculation”, much like Copernicus did when speculating about that which and where his sensible perceptions either could not go, or else when they led him astray; but Deleuze appears to even regard this kind of speculative practice as a radical empiricism. We will consider several features of Deleuze’s methodology in Chapter 3 (The Image of Thought).
Secondly, then, when we are examining Deleuze’s assertion that ‘[r]epetition appears…only in the passage from one order of generality to another’, and that ‘it is as if repetition momentarily appear[s] between or underneath’ the two domains of generality, we should proceed under the color of our earlier observation that Deleuze is preparing his reader for a full-scale philosophical exposition of the concepts of difference and repetition, and that the latter is merely a necessary inaugural step towards thinking a concept of value radically independent of the Euclidean model of representation infusing Marx’s critique of political economy. By proceeding in this manner, we immediately find Deleuze’s aforementioned claim to be very thought-provoking and seductive –if still, at this point, admittingly somewhat nebulous for even his most earnest reader.
For instance, if classical symmetry is of the domain of generality, and in practical terms is constrained by ‘the shackles of representation’, what does it mean that repetition is ‘momentarily’ revealed ‘between or underneath’ its domain of action –especially when these domains of action are the markets populated by financial objects? Or, how can we witness such a repetition if it remains unmediated by ‘the shackles’ of representation? Is this not merely an obtuse manner of ascribing an unrepresentability to that which we have simply asserted to exist, albeit now merely switched-out for the old term ‘representation’ the new term ‘revealed’? We will return to these questions and examine assertions made by Deleuze of just this sort after we have prepared ourselves, by close analysis of the text, to understand its meaning.