A quick note on one place where we’re going (& how we’ve gotten here)

In Of Synthetic Finance we illustrated that the highly symmetrical and hyperfungible materiality of synthetic financial assets means that the progressive differentiation of our dynamical system of finance writ large signals a regressive differentiation of capital that is best understood as a becoming-topological of the financial asset.

Ok, fine.

So we know that (1) the topological consistency of synthetic finance is isomorphic to a biological mode of assembly, i.e. with so many untapped lock and key mechanisms, diffusion transport, and a set of radical divergent evolutionary capacities. And we also know that this contrasts with the industrial-style machine-like production of the assets of generic finance, which are obviously governed by a set of more rigid invariance requirements than the synthetic assets whose class of exchange has emerged from out of the former (e.g. if we are conservative about exchange,  we will declare that credit derivatives are at base perverse -and why, if not because they allow for the achievement of symmetry between an object and its image of value, while we are demanding that so many of the object’s economic properties must remain invariant, especially the various collinearities of exchange that we outlined in Essay Two, our case study on the ontology of synthetic finance).

We also know that (2) the anexact but rigorous divergent evolutionary capacities of topological objects are best set into their contingent motions when an operator -a quasi-causal operator- begins to trace the logic of the intensive properties or processes not wholly covered over by the extensive properties to which they give rise (in the process of their own occlusion), and from there to the virtual, we tinker with that which structures the space of that which is possible to become actual. (You follow me, right?)

This means that we experiment. My favorite, at the moment, is to model the wholesale institutional outcomes of a universal synthetic CDO whose infinite leverage (in the tranching process of structured finance) is leveraged through a continuous recalibration in order to instantiate a nomadic distribution. Of course, as we’ve noted before, this is merely a guess, it may be wrong -in fact it probably is wrong, i.e. it will lead to a genetically-mutated new system, albeit and importantly so, a wholly nonviable one. But even if we’re wrong we’re wrong for the right reasons. That’s why we’ve been reading Winfree’s When Time Breaks Down, Prigogine’s work on the behavior of nonlinear dynamical systems, and especially Mario Bunge’s Causality in Modern Science.  Yes, yes, of course, we need to get back to the technical literature on finance, and fuck it, we need to cover more of the history of finance, and of course we need to continue to trade -and you cant’ trade successfully for long without fusing research with logic and luck (all of which -especially luck- do take an awful lot of time, and more time, and more time….eh).

But just not quite yet….We need a few more months of reading/scavenging  from the sciences of morphogenesis, we need to return to topology once again, and can we not afford to spend a mere few hundred more hours dwelling with Poincare on these topics in a lifetime of waiting for Godot or Guffman or reading books that should never have been written?

This is all a way of us trying to say we ran across a quote that captures the essence of where we’re going. You now kind of know how we got here. Here’s the quote:

‘The sciences of life have never been admired for quantitative exactitude . . . But it cannot be said that living things are at heart sloppy, fuzzy, inexact, and unscientific. How does an oceanic salmon find its way home to spawn on the very rivulet it left in Oregon three years earlier? How is a meter-long sequence of billions of nucleotide base-pairs reversibly coiled without entanglement into a nucleus no more than a few thousand base-pairs in diameter? How does anyone memorize a vocabulary and rules of grammar well enough to transfer an epic novel from one brain to another? How does a gymnast calculate forces and rates for hundreds of muscles with millisecond precision while whirling from one maneuver to the next? How does a mere mortal perform a piano concerto or compose one? Such miracles bespeak of reproducible precision. But that precision is not the kind we know how to write equations about, not the kind we can measure to eight decimal places. It is a more flexible exactitude which evades quantifying, like the exactitude of a cell’s plasma membrane dividing the universe into an inside and an outside with not even a virus-sized hole lost somewhere in all that convoluted expanse: topological exactitude, indifferent to quantitative details of shape, force, and time.’

— Arthur Winfree, When Time Breaks Down. The Three-Dimensional Dynamics of Electrochemical Waves and Cardiac Arrhythmias, Princeton University Press, 1987


DGSF. Pages 5-11

§ 2nd contrast of generality and repetition –from the perspective of conduct; Kierkegaard and Nietzsche: two philosophers of repetition (pg.5-11)

Based on his aforementioned considerations, it is clear for Deleuze that the domain of generality and repetition are not only distinguishable from the perspective of law; for this reason, he again contrasts the domain of repetition to the domain of generality –however, now from the perspective of conduct, i.e. our conduct involved in an act of exchange. This is the 2nd of his three contrasts.

(‘There is a force common to Kierkegaard and Nietzsche…[for each] in his own way makes repetition not only a power peculiar to language and thought, a superior pathos and pathology, but also a fundamental category of a philosophy of the future. To each corresponds a Testament as well as a Theatre, a conception of the theatre, and a hero of repetition as a principle character in this theatre: Job-Abraham, Dionysius-Zarathustra…’)

Deleuze periodically introduces textual breaks throughout DR in order to artificially compartmentalize the subtopics of his chapters –albeit as with the synthetic, attempts to compartmentalize in final prove futile, the synthetic overflows the rafts. Regardless, page 5 is the first of these breaks.

The text picks up with Deleuze’s introductory consideration of Kierkegaard and Nietzsche, two philosophic operators of repetition –or as he calls them, two philosophers of the future. Deleuze asserts that each of these two philosophers in his own way provides a derivative proposition about the same univocal Being, and that each works with the conviction that the value of their work will have been determined and determinable in an as-yet unspecified and to-be-arrived-at future date.

Our reader will learn that just as elements of Euclid-Plato-Hegel’s ontology infuse Marx’s political economic flat space concept of (cardinal) value, so too Nietzsche-Kierkegaard’s ontology work their way into and through Deleuze’s own political economic revaluation of (ordinal) value. Deleuze understands himself to be one more derivative of a philosopher of the future. It is still, however, and of course, a question of knowing what this means –i.e. of what it means to practice a derivative conduct that makes of repetition a category of futures.

(‘What separates [Kierkegaard and Nietzsche] is considerable, evident, and well-known. But nothing can hide this prodigious encounter in relation to a philosophy of repetition: they oppose repetition to all forms of generality. Nor do they take the word “repetition” in a metaphorical sense: on the contrary, they have a way of taking it literally, and introducing it into their style.’)

Deleuze is claiming –and throughout DR will illustrate– that Kierkegaard and Nietzsche, despite an evident, actual separation between the two general orders of their work, nonetheless virtually repeat, and quasi-causally operate on, two different singularities expressive of a univocal Being. Of course, if we were to possess the necessary time and inclination, we could proceed to show that this ‘style’ of difference in repetition marks the entirety of Deleuze’s oeuvre as well –from his initial work on Bergsonism, all the way through his last work with Guattari, What is Philosophy? If we were to perform such a voluminous task, we would witness that Deleuze is constantly making, unmaking, and remaking his ‘concepts along a moving horizon’ of topics and concerns; he was ever thinking and writing ‘from a decentered centre, from an always displaced periphery’ (Preface pg. xxi), in which we are, on the one hand, at first surprised to learn that Deleuze has suddenly and apparently ceased to use a concept whose term had earlier functioned as a protagonist, or was a ‘hero’ in the ‘theatre’ of a particular text, only to later, on the other hand, stumble into an awkward encounter with a repetition of its conceptual content in a different term in some subsequent text (note: the difference in repetition of ‘the Idea’ (DR) –‘rhizome’ (TP) –and ‘philosophical concept’ (WP) is a good example of this). It is as if between or underneath two general orders of actual texts we glimpse a repetition of an earlier Deleuzian concept. We will also see that Deleuze practices this method on a micrological scale in DR –i.e. ‘of taking [repetition] literally, and introducing it into his style.’


Deleuze introduces the principal propositions which, despite different actualities (e.g. in terms of Testaments, Theatres, and Heros) separating them, are coincidental to Kierkegaard and Nietzsche.

(‘We can…list the principal propositions which indicate the points on which they coincide:

            1. Make something new of repetition itself: connect it with a test, with a selection or selective test; make it the supreme object of the will and of freedom…

            2. In consequence, oppose repetition to the laws of nature…

            3. Oppose repetition to moral law, to the point where it becomes the suspension of ethics, a thought beyond good and evil…

            4. Oppose repetition not only to generalities of habit but also to the particularities of memory…’)

Deleuze will later more fully elaborate the meaning of these propositions. The reader should try to stay relaxed here. For now, we need merely observe that with these four principals Deleuze seeks to establish the following:

1. First, to ‘make something new of repetition itself’ is to make repetition –which in economics, is always the exchange qua repetition of an object for and into its image of value as money– an economic object, as such; while yet constituting ‘something new of repetition’, i.e. of constituting through repetition a pure difference in itself. To elaborate this is the principle objective of Chapter 1 (Difference in Itself).

2. Secondly, to ‘oppose repetition to the laws of nature’ is to oppose repetition in the convocation of value to that which is found in the domain of generality and resemblance. We will later illustrate why it is scientifically-rigorous from the perspective of dynamical systems theory and the sciences of morphogenesis to posit repetition as opposed to the law. But also, insofar as there is no repetition in itself, it will be a matter of examining repetition for itself. To elaborate this is one of the principle objectives of Chapter 2 (Repetition for Itself).

3. Thirdly, to ‘oppose repetition to moral law’ entails a patent rejection of conducting a science of political economy whose impetus is morally-motivated. And yet we must do this without unwittingly backing our way once more into a political-economic-ethical project whose impetus is a morally-motivated purging of morality from our project –that is, the force of our project can neither be ethical, nor an ethic of a ‘suspension of ethics’. To move our conduct in economics ‘beyond good and evil’ is the objective of Chapter 3 (The Image of Thought).

4. Lastly, if we are to ‘oppose repetition not only to generalities of habit but also to the particularities of memory’ we are required to understand the role and relation of virtuality in and to the determination of the actual. Indeed, our financial-economic models exclusively concern themselves with actuality (whose epistemological correlate, as we will discuss below, is infinite comprehension) and potentiality (subject to a probability distribution, and as we will also discuss below, whose epistemological correlate is finite comprehension), while yet neglecting the reality of the virtual (which is neither actual nor subject to a probability distribution, and as we will also discuss below, whose epistemological correlate is indefinite comprehension). To correct this myopia afflicting political economics is the objective of Chapters 4 (Ideas and the Synthesis of Difference) and 5 (Asymmetrical Synthesis of the Sensible).

 (‘Kierkegaard and Nietzsche are among those who bring to philosophy a new means of expression. In relation to them we speak readily of an overcoming of philosophy.’)

By practicing the four aforementioned propositions, Deleuze is repeating the move made in philosophy by Kierkegaard and Nietzsche, but now in political economy –a speculative materialist political economy of finance as its method, and a speculative materialist communism as its goal.


(‘Furthermore, in all their work, movement is at issue. Their objection to Hegel is that he does not go beyond false movement –in other words, the abstract logical movement of ‘mediation’.)

This is a theme we see repeated throughout Deleuze’s periodic assessment of Hegel.  To be clear, it is not that Deleuze is ‘critical’, as such, of classical exchange –whatever that would mean (i.e. any class of exchange is beyond true or false). Rather, he is critical of those who represent classical exchange as true movement, as the true essence of change. If classical exchange consists of the rigid motions of an object into its image, and if these rigid motions constitute a congruence transformation, whereby the metrical properties of the object remain invariant under their force of motion (i.e. in exchange), how can we call this true movement? For this reason, Deleuze counterposes Kierkegaard, Nietzsche, and his own heterodox political economy of the synthetic against Hegel’s ‘false movement’, ‘the abstract logical movement of mediation’, whereby an economic object is transformed into its image in space, yet without the structure to that space undergoing any transformation whatsoever. Again, this is an ‘empty form of difference’, an ‘invariable form of variation’, a rigid motion whereby nothing truly moves in the course of its transformation –and thus, for Deleuze, this is a ‘false movement’, which operationalizes a far too conservative notion of symmetry. Deleuze aims for a much more radical symmetry –the symmetry of synthetic symmetry. As we will see, this is the symmetry at work in synthetic finance. This is the symmetry operationalized in the course of our exchange of synthetic financial objects.  


(‘[Nietzsche and Kierkegaard] want to put metaphysics in motion, in action. They want to make it act, and make it carry out immediate acts. It is not enough, therefore, for them to propose a new representation of movement; representation is already mediation. Rather, it is a question of producing within the work a movement capable of affecting the mind outside of all representation; it is a question of making movement itself a work, without interposition; of substituting direct signs for mediate representation; of inventing vibrations, rotations, whirlings, gravitations, dances or leaps which directly touch the mind. This is the idea of a man in the theatre, the idea of a director before his time. In this sense, something completely new begins with Kierkegaard and Nietzsche.’)

Deleuze clearly understands himself to be working within –i.e. to be repeating in this tradition– but differently than Nietzsche and Kierkegaard, insofar as he is first illuminating for us the metaphysics always-already built into our economic system(s), our acts of exchange; of rethinking that metaphysics; of then putting his own metaphysics ‘in motion, in action’, i.e. of inventing ‘vibrations, rotations, whirlings, gravitations, dances or leaps which directly touch the mind.’ In this sense, and in the study of political economy, ‘something new begins with [Deleuze].’

(‘[M]ovement, the essence and the interiority of movement, is not opposition, not mediation, but repetition. Hegel is denounced [by Kierkegaard and Nietzsche] as the one who proposes an abstract movement of concepts… Hegel substitutes the abstract relation of the particular to the concept in general for the true relation of the singular and the universal in the Idea. He thus remains in the reflected element of “representation”, within simple generality.’)

Pages 8 and 10 contain Deleuze’s first of several passing and periodic treatments of the work of Hegel in DR. One increasingly sees that –with an appreciable amount of nuance, of course– Deleuze ultimately believes that Euclid’s conservative invariance requirements are infused in Plato, that Plato’s model of representation gets reworked and then reproduced in Hegel, and then Hegelian metaphysics terrorizes Marx’s ontology of capital from within, constantly, forever, and as a special form of outer darkness. Our reader is encouraged to be vigilant of this fact on the one hand, when examining Deleuze’s treatment of Hegel, and on the other hand, when attempting to grasp Deleuze’s critique of Hegel from the perspective of his contraposition of the ‘mediated’ domain of generality against the domain of repetition.

Many a crude commentary on Deleuze has so often dubbed his ontology a “philosophy of becoming”, or “philosophy of movement”, that one will be initially excused for momentarily forgetting the fact that becoming and movement in general rather go without saying –and so the assignation of this label to Deleuze is not so much wrong as it is poorly worded, or at least insufficiently explained. In Deleuze’s treatment of Hegel –and by indirection, the Hegel in Marx– our reader will observe the false movement of “opposition”, since opposition is one of the four shackles of representation, and therefore of the domain of generality. Our analysis of Chapter 5 (Asymmetrical Synthesis of the Sensible) will cause us to observe what, precisely, Deleuze means by ‘the essence and the interiority of movement’ of repetition.

(‘[Hegel] represents concepts instead of dramatizing Ideas; he creates a false theatre, a false drama, a false movement. We must see how Hegel betrays and distorts the immediate in order to ground his dialectic in that incomprehension, and to introduce mediation into a movement which is no more than that of his own thought and its generalities.’)

Deleuze will give full philosophical exposition to this point –and in particular to the drama of Ideas (viz. multiplicities)– in Chapter 4 (Ideas and the Synthesis of Difference). We will clarify therein that markets (and the objects that populate them) are theatres of multiplicities, and that they are marked by a highly peculiar kind of drama –albeit, it is a matter of understanding the ontological difference in kind of the dramas which characterize numerical multiplicities from those which characterize qualitative multiplicities. This is a crucial distinction for Deleuze in elaborating his ontology of the synthetic.

(‘When we say, on the contrary, that movement is repetition and that this is our true theatre, we are not speaking of the effort of the actor who ‘repeats’ because he has not yet learned the part. We have in mind the theatrical space, the emptiness of that space, and the manner in which it is filled and determined by the signs and masks through which the actor plays a role, which plays other roles; we think of how repetition is woven from one distinctive point to another, including the differences within itself.’)

Progressively this will have been a very profound passage as the meaning of it becomes increasingly clear throughout the course of our Guidebook. However, because Deleuze again is getting ahead of himself, the reader’s feeling of puzzlement is only to be expected. We feel yet unprepared to grasp the significance of the ‘emptiness’ of a theatrical space called economic space, wherein that space is distributed along with the coterminous distribution of the objects which comprise and populate it. We will see Deleuze speak of objects which are ‘masks behind which are only other masks’, and assert that their difference is constituted by their derivative repetition from one distinctive point to the next. But perhaps at this early stage (i.e. at pg. 10 of DR) we are still too inculcated with our time-honored political economic ideology of flat space, our dogmatic presumption of a Cartesian-coordinated space of exchange, wherein objects are only ever like actors’ lines insofar as their metrical properties pre-exist their motion, and insofar as they are constantly repeated over and again –and always so that the actor will ‘learn’ his script precisely so that his lines will remain ever-unchanged in their course of motion. Deleuze is saying that we proceed too conservatively with this conception of the distribution of economic space, we act too conservatively when we expect that our economic objects populate a space which is pregiven, when we expect the behavior of those objects to play the role of an actor’s lines, and when we behave with the expectation that our own acting is always a distribution in space rather than the distribution of space. It is true that we always yet expect to see faces behind masks, rather than ‘masks behind which are other masks’. However, the observation of our natural puzzlement over such statements by Deleuze early on is merely a manner of observing that we are unprepared as of yet to fully grasp repetition and difference, we are yet unprepared to critically scrutinize Deleuze’s ontology of the synthetic, and so are therefore unprepared to understand that difference and repetition is truly a radical concept of value predicated on the monstrous power of synthetic symmetry. Deleuze will allow us to clarify our puzzlement over the course of our careful reading of DR if we are prepared to follow his wager for a time.

 (‘The theatre of repetition is opposed to the theatre of representation, just as movement is opposed to the concept and to representation which refers it back to the concept. In the theatre of repetition, we experience pure forces, dynamic lines in space which act without intermediary upon the spirit, and link it directly with nature and history, with a language which speaks before words, with gestures which develop before organized bodies, with masks before faces, with specters and phantoms before characters –the whole apparatus of repetition as a “terrible power”.’)

Deleuze continues to illustrate his assertion of the existing isomorphism between the space of the theatre and the space of the market –and that the latter as a space of the representation of value is opposed to a space of repetition as constitutive of value. Deleuze speaks of the latter kind of space as ‘theatre of repetition’. Our reader should be alerted here that in the course of imputing to this space ‘dynamic lines without intermediary’, of ‘a language before words’, of ‘gestures before bodies’, of ‘masks before faces’, and so on, Deleuze is introducing us to the content of the concept of the virtual much earlier in DR than we actually encounter it in its explicit conceptual form. This move is both telling of the way the virtual operates, i.e. its movement, logic, and so on, and is also instructive of the ‘style’ of thought that Deleuze shares in common with Nietzsche and Kierkegaard, as referenced above. The conceptual (i.e. virtual) content of the virtual pre-arrives its conceptual (i.e. actual) invocation precisely because its dynamic lines pre-exist its intermediation by the concept; it is a language formed before words, gestures prior to organized bodies, masks before faces, specters before their corporeal form. Although in truth throughout the whole of DR our reader will observe that Deleuze is performing this methodological exercise of practically illustrating his philosophical exposition of the peculiar phenomenology of the virtual, we will immediately witness this practice as early as the opening of Chapter 1 (Difference in Itself).

Because we are now considering the concept of virtuality, we must specifically draw our reader’s attention to a consideration of the context, meaning, and reason for the final line of the above-quote, insofar as it serves as a quilting point for the whole project of DR. Following Deleuze’s preliminarily rumination on the functional role of the virtual as the distribution in and of the space of repetition, he calls ‘the whole apparatus of repetition’ ‘a terrible power’. Why? This is neither a passing hyperbole nor cheeky-comment. One of Deleuze’s principal philosophical leaping points in DR is to investigate the historical, multidiscursive, moral disrepute befalling the synthetic as a realm of simulacra. Deleuze pokes at this topic as one pokes at a strange animal lying prone to see if it will move. As we know, for Deleuze the movement of this animal is the history of western philosophy; and when it moves, Deleuze shows us that at its inaugural canonical moment, i.e. with Plato’s Socrates, philosophical thought has already assumed a morally-motivated critical disposition against the synthetic as an instantiated bad-copy of model, a perversion of nature, her essence and organicism, i.e. a virtual truth which is no actual truth at all. We will consider this, as Deleuze does, near the end of Chapters 1 (Difference in Itself) and 2 (Repetition for Itself).

Of course, while Deleuze probes a widespread opposition to the synthetic in its modality of western philosophy, the reader will also know that the modality of our own examination of this pathology is political economy’s morally-motivated ill-regard of derivatives as an evil realm of simulacra, of simulated capital, a bad copy of a model of value, a perversion of the commodity, her concrete essence and organicism, i.e. a virtual commodity which is no actual commodity at all –and above all else, the outstanding poor regard of this derivation of classical exchange that yet falls short of the representation of “true” value. This is the ‘terrible power’ of the ‘whole apparatus of repetition’: it is such a power of synthetic exchange our Guidebook seeks to examine anew, for purposes of it’s a radical revaluation by and for a project of political economics –a new materialist political economics in an age of synthetic capital.

DGSF. Pages 2-5

§ 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.

congruent motions, i.e. classical exchange
congruent motions, i.e. classical exchange

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.

generic finance (debt & equity)
generic finance (debt & equity)

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.

Why even do political finance with Deleuze?

 Any heterodox project is compelled to begin by articulating a problem or set of problems it proposes to address (otherwise why heterodoxically begin at all?). When studying finance at our present moment, the particular problem to which we are alerted is a political economic problem whose particularity Deleuze as a heterodox philosopher alerts us, but which reading Deleuze as a heterodox political economist can help us to address –or at least offer us one way to redefine on new terms.

What is this problem? There is one principal problem, but it has two parts. The first part concerns a historical and ontological transformation in and of finance; the second part concerns a theoretical and methodological problem that results from the first. Reading Deleuze’s Difference & Repetition as heterodox political economy allows us to address them both.

First part of the problem. New differentiations in finance

The first part of the problem begins with an ontological transformation of the financial asset. More specifically it concerns the progressive differentiation of two new classes of financial assets from out generic finance, but whose ontological composition is radically different from the kinds of assets which have historically populated financial markets: namely, there is the synthetic asset, which actualizes a wholly new class of financial exchange known as synthetic finance; and there is the securitized asset, which is a product of the process of securitization (also sometimes called structured finance), and involves the transmutation of an asset into a security.[1] These two new differentiated classes of assets are ostensible repetitions of preexisting generic financial assets, but their repetition produces a peculiar new kind of asset. Together they have fundamentally altered the basic relation of finance to capital, the relation of finance capital to the capitalism writ large, they have and are changing capitalism.

Let us briefly consider each in turn.

Synthetic finance is usually classed under the general rubric of ‘derivatives’. This is partially accurate, but only partially accurate, and importantly so. While credit derivatives[2] are indeed a type of synthetic financial asset, any serious consideration of their ontology quickly reveals their radical difference from more traditional derivatives like options, futures, or forwards, the latter of which have existed for centuries (e.g. Aristotle wrote of Thales buying options contracts on olive oil presses, the Osaka shogunate organized the Dojima rice futures exchange, and so on), and whose ontological composition is qualitatively closer to generic financial assets than to any synthetic financial asset. Only recently, beginning in the mid-1990s and on into the 21st century, did this hyperfungible and highly symmetric class of objects develop, proliferate, and convoke into actuality the new markets, indices, and institutions accompanying the class of financial exchange of synthetic finance –and at that, these new objects, e.g. credit derivatives and other kinds of synthetic financial assets, do include some of the economic properties common to generic financial assets, but also many other peculiar and novel economic properties utterly foreign to the latter, and which in a very real sense transcends the very concept of the ‘derivative’, as such.

Applying the traditional textbook definition of derivatives –i.e. a financial asset whose value is derived from some underlying (generic) financial asset– to synthetic financial assets is no longer accurate. We now see that the value of a synthetic asset will causally supervene on the value of the generic asset, or may even act as a quasi-referent for its so-called ‘underlier’. For example, in the recent financial crisis, the price behavior of credit default swaps (a synthetic asset) on mortgage backed securities caused swift and violent depreciations in the market valuations of such securities, resulting in higher interest rates on floating-rate mortgages, and subsequent widespread mortgage defaults: this caused the prices of mortgages (a generic financial asset) to rise, and the values of houses (a physical asset) to fall. When the market value of the physical referent is directly affected by the generic referent, but in turn the value of the generic referent is directly affected by the value of its synthetic ‘replica’, can we still apply the aforementioned textbook definition of a ‘derivative’ to this class of asset? Or to cite another example, anytime an asset-backed portfolio is synthetically-structured with credit-linked notes –i.e. wherein the assets are ‘built’ the replication technology of credit derivatives– it is the case that the values of those credit-linked notes (which are generic financial assets) are derived from the value of the synthetic portfolio.

In both of these examples –which are only two of many– far from it being that this asset is a ‘mere’ gambling instrument, ‘only’ an immoral image, or some simple copy of a model. Rather, the synthetic announces itself as a replica of a generic asset, though it is not of the same, for its economic properties (maturity, notional value, etc.) are often and almost always different from its so-called referent. The synthetic asset is thus a production of pure difference, but one which always announces itself in and as simulation; it is an image of an object that is without likeness, an immanent copy of a model which quickly overturns any grounds on which such a distinction would stand.

In fact, insofar as ownership-of, or exposure-to, the so-called generic referent is not a requirement for transacting a synthetic financial exchange –which means that neither the seller nor buyer of the synthetic asset need be the obliger, creditor, or otherwise related in any way to the preexisting generic financial exchange acting as its referent– most synthetic financial transactions are created ex nihilo. However, to the extent that the parties to the synthetic exchange do make a financial transaction, they have created a new asset, and this asset does have the very real material properties of risk and cash flow. In this respect, the act of synthetic exchange effectively creates –synthetically, yes, even virtually, yes, but no less in reality– a risk and cash flow which did not previously exist.

The synthetic asset, then, is capable of being created ex nihilo and ad infinitum. There is no transfer of private property, no concrete production by labor of any classical economic object, and whose intrinsic value is congealed therein, nor any new generic financial asset or reference obligation. And yet, through the process of synthetic exchange, because there occurs a new ex nihilo and potentially ad infinitum proliferation of the economic properties of risk and cash flow, we cannot meaningfully deny that a synthetic exchange is any less an exchange, or lacking in profound material consequences.

In fact, the peculiar materiality of the synthetic financial asset now raises the important question of whether it is either the case that we need to liberalize our prior understanding of materiality, or even that the actualization of synthetic finance already radicalizes the very concept of materialism itself?

There is also the matter of securitization. Securitization, sometimes also called structured finance, is the process of creating a security from a financial asset. There are two ways of creating securities: from preexisting generic financial assets, or anew by synthetic replication via credit derivatives. This produces two different types of securities: cash securities and synthetic securities.

Securitization, whether cash or synthetic, always involves pooling and tranching: there is the first step of pooling (i.e. dedifferentiating) the different risks and cash flows of the assets involved into one risk and one cash flow; and then there is the subsequent step of tranching (i.e. redifferentiation), which now redistributes the one risk and its cash flow into new classes of risks and cash flows in the form of the new securities that result. In this respect, a truly radical transformation supervenes on the materiality of the asset in the process of its securitization: a preexisting asset (e.g. a mortgage, a corporate bond, student debt, etc.) is divided, but in the process of its division it changes in kind. Moreover, when the debt notes (securities) whose notional values correspond to the notional values of the tranches that comprise the securitized portfolio are collectively held, i.e. owned incrementally and piecemeal, by the various note holders, who then really may be said to ‘own’ the house, the corporate bond, the student debt, or any other securitized private property? In short, all who hold the notes collectively own these things together.

However –as if this were not radical enough– synthetically-securitized products such as synthetic CDOs signal something even more radical still. Indeed, to observe that the result of pooling any number of generic assets into a single portfolio is to homogenize their risks and cash flows into an asset with a single risk and single cash flow; and that once we pool these preexisting risks and cash flows together we can then redifferentiate this new risk and its cash flow differently and flexibly as we so choose –this is intriguing enough in itself, given that, first, it conveys a hyperfungibility to the security that is lacking in the generic financial asset, and secondly, as we alluded to above, this is already, technically speaking, a method for the abolition of private property. But when we now see these assets can be synthetically created ex nihilo and ad infinitum, things get both more peculiar and more compelling still.

For example, by pooling any number of credit derivatives into a single synthetic financial asset, and then ontologically redifferentiating that new (and now singular) asset through method of tranching, the synthetic exchange results in the organic creation of several new economic properties which are specific to a synthetic asset, and which were not originally ‘in’ or ‘of’ any generic financial assets acting as the referents for the synthetic portfolio. Anytime we use tranches to redifferentiate risk, there are ‘levels of subordination’ to the tranches, which give birth to a series of ‘attachment points’ and ‘detachment points’ that register and distribute respective losses and gains to the various tranches. This means that the structuring process itself produces several new economic properties –for example, the properties of ‘credit enhancement’ and ‘leverage’ (among several others): this is as unexpected as it is compelling, since once again we see that that the synthetic asset begins by announcing itself as a mere replica of its generic referent, just as any synthetic exchange begins by appearing as an avatar of a generic financial exchange. But there is always a new difference produced by its repetition, for there are new and novel economic properties brought into being which are not of the generic asset, and not present in the generic financial exchange acting as the reference obligation for the synthetic exchange.

Second part of the problem. Absence of methodology

This merely scratches the surface of the peculiar materiality of these two new kinds of financial assets that did not exist for Smith, Marx, Schumpeter, Keynes, or Friedman. However, if we began by observing that the first part of our problem concerns an ontological transformation to the financial asset, in truth this only really matters because it has and still is effecting a wholesale transformation of the financial system and its broader relation to the economy. Synthetic financial assets –both single-named and multi-named credit derivatives, as well as their synthetically-securitized counterparts– progressively differentiate simultaneous with a series of recent radical transformations to the modus operandi of capital markets: from the ever-increasing usurpation of traditional intermediation by the shadow banking system (i.e. the death of the so-called ‘Jimmy Stewart model of banking’[3]), to ongoing and new-fangled experiments with quantitative easing by the world’s central banks; from the nascent and incessantly fragile but also seemingly-necessary intimate comingling of money markets and capital markets, to perpetual threats of sovereign debt crisis; from the ostensible breakdown of any meaningful distinction between liquidity risk and solvency risk, to the rise of all manner of market crises –and the fiscal and monetary hypervigilance they now require, and so on. The historical and ontological transformation in and of finance, of the financial asset, its method of composition, as well as the markets they populate, stand at the precipice of this wholesale qualitative alteration of finance’s relation to capital and capital markets more generally, and now begs serious, sustained, historically-specific materialist analysis.

And so herein lies our problem. We have few if any available political economic tools equipped to aid our inaugural attempts to critically-analyze this profound material development. To what schools of thought or thinkers do we look –analytically, theoretically, methodologically– as we descend into and now try to cognitively map the peculiar ontological domain of synthetic finance? Who among our familiar economists, political economists, philosophers, or cultural theorists, can help us navigate through its dark pools, shadow sectors, and concrete virtuality? What methodological resources do we consult to help us grasp what becomes of materialism when the value of the object has not only become its price as an asset (as already occurs with the advent of generic finance) but when now the (synthetic) copy of the (referent) model upends the very ground on which any distinction between a derived versus underlying value is even comprehensible?

Indeed, if we are neither content to worship nor shake our fist at the sun, it does seem we’re currently forced to select from two bad options. We can either choose to assume the proto-luddite position: namely, that the development of the synthetic finance signals a fundamental perversion from the organic logic of ‘true’ value, a kind of unreal or bad copy of model –at which point we’re left to morally-assess, itemize, and then ‘turn back the clock’ of financialization to better segregate the good copies from the bad.[4] Or if not this position, we’re then compelled to select –albeit by negation– the oddly both overstated and undertheorized proto-Marxist position that the advent of synthetic finance betrays that (a) capitalism is still, as always, trying to find new ways of countermanding the tendency of the falling rate of profit, or (b) it is yet another illustration of the tendency to over-accumulation endemic to the falling rate of profit.[5]

Both the proto-luddite and proto-Marxist positions, however, share in common the same political economic presumption that the progressive differentiation of synthetic finance is a kind of fate accompli of capital that is to be disdained, choked-out, or resisted, but not in any serious way encountered on its own material terms; to be peered-at, problematized, or historicized, but never probed in any technical or ontologically-rigorous manner. For the proto-luddite this is because synthetic finance represents a new kind of maledictory form of value; while for the proto-Marxist it’s because synthetic finance is yet one more incarnation of the same old malediction of ‘true’ value, i.e. labor value, which is a constant or even ahistorical cause of the ever-spread between relative surplus value and absolute surplus value, but which at any rate is constantly causing the rate of profit to fall –until of course it doesn’t fall, when ‘something happens’ to once more yet interrupt its tendency (whether war, expansion into emerging markets, or now financialization).

Surely, one wonders, is there not a more theoretically-acute, methodologically-robust, politically-salient analysis available to us than this?

tumblr_m8gtkjm0F51ro02j1Difference & Repetition. A book of heterodox political economy

If this is the particular problem that reading DR as heterodox political economy can help us to address, how, specifically, can it help us to address it? While in truth there are many ways, we will briefly name three.

i. First, DR provides us with an instructive way of understanding the peculiar materiality of the financial asset today. Deleuze elaborates a creative but rigorous method by which to think the process, or becoming, of the financial asset –namely he endows us a flexible method and set of conceptual tools for thinking the financial asset as a multiplicity.

The concept of the multiplicity is central to the Deleuzian ontology, albeit one that can get quite technical (in DR Deleuze is constantly giving philosophical transformation to mathematical and scientific concepts, and no Deleuzian concept better illustrates the rigors involving this practice).[6] Deleuze credits Riemann with discovering the concept, which means it is ostensibly mathematical in origin.[7] However, when we apply its theoretics to finance, we are immediately thinking the asset as a dynamically-composed, formless mess of different economic properties (maturities, notional values, risks, cash flows, etc.), which can be plastically stripped and injected elsewhere, or exogenously created or destroyed ex nihilo, ad infinitum, and nonlinearly.

Therefore, if, following Marx’s classic introduction to the commodity in Volume I of Capital, we understand ‘exchange’ as the simple repetition of the object for its image of value as money, then Deleuze is simply reminding us that new and different economic properties constantly ‘swarm in the fracture’ of this repetition: and if such properties are ‘constantly emerging on its edges, ceaselessly coming and going, being composed in a thousand different manners’[8], then to speak of any given economic object as having an ‘essence’ is symptomatic of a bad ontology, a kind of ‘asset-fetishism’. To avoid such reification, the first thing we must do is to cease believing the asset must have some kind of fixed, inherent, or internalized essence. The essence of any asset, as Deleuze puts it, ‘is nothing but an empty generality’, which means the asset is nothing apart from its many different economic properties, but which pledge no final allegiance to it.[9]

For this reason, DR instructs us that we are more justified to think the asset as a multiplicity. The concept of a multiplicity lends us a ready-made technical term to denote the constitutive processes of an economic object.  Multiplicities are the n-dimensional site for the process of the assembly of the economic object, which is always in perpetual becoming. Multiplicity is the concept we can use to denote the reality of the asset; in truth, an abundance of reality that is not always or only actual, not always or only virtual, not always or only potential; but rather a confluence of all three (Deleuzian) registers of reality, and which is predicated on the rhythms, rates, amounts, and kinds of amounts of processes –whether intensive or extensive– that define the asset.

ii. However –and following Riemann– Deleuze also points out that there are not one but two kinds of multiplicities: there are ‘numerical multiplicities’, and there are ‘qualitative multiplicities’. This brings us to Deleuze’s second contribution.

If the synthetic asset appears different in kind from the generic assets it proposes to repeat –but whose materiality it ultimately transcends, or even remakes in the course of its repetition– this is because, for Deleuze, the generic asset and the synthetic asset are ontologically different in kind. Therefore, the second way that reading DR as heterodox political economy can help us to address our problem is to give us a technical but not overly-abstract manner of thinking and articulating the key ontological differences marking generic and synthetic finance. Insofar as there are two different types of multiplicities that actualize their respective assets, we can examine how these assets materially differ in kind.

Let us first consider a numerical multiplicity. Deleuze itemizes the distinguishing ontological trait of the numerical multiplicity as that which is thoroughly ‘objective’: in that it is fully actualized, it has little or no virtuality; and Deleuze says we know this because it is capable of being divided, but in the process of its division it does not change in kind:

‘In short, ‘object’ and ‘objective’ denote not only what is divided, but what, in dividing, does not change in kind. It is thus what divides by differences in degrees. The object is characterized by a perfect equivalence of the divided and divisions, of number and unit. In this sense, the object will be called a “numerical multiplicity.” For number, and primarily the arithmetical unit itself, is the model of that which divides without changing in kind.’[10]

If classical economic objects (e.g. coffee, cars, corn, and clothe) and generic financial assets (e.g. traditional debt and equity objects) immediately appear to us as ‘more objective’ than synthetic assets, this distinction made by Deleuze helps to explain why. Such ‘flat objects’ realized by numerical multiplicities are chocked-full, phenomenally, with extensive economic properties –properties that divide, and in the course of their division, simply divide without changing in kind. Its properties are points on a line, and these points and lines are uniform, which means their division produces only changes by degrees, but never a change in kind. They are, in other words, Euclidean.

Consider a generic financial asset –for example stock shares. If tomorrow I receive a letter informing me that my 1 round lot of Walt Disney Co. (DIS) stock has been divided, or ‘split’ as a 2-for-1, I will now own 200 shares at $25.00 per share, rather than 100 shares at $50.00 per share. Here there will have been the division of a generic financial asset, of 1 share of stock now into 2; and yet there will have been no change in kind; the share of stock has simply been numerically-divided ‘in half’, or ‘split’ into two.

The same can be said of money. As a numerical multiplicity, money is the quintessential financial asset that divides without changing in kind. This is why Deleuze observes that ‘number has only differences in degree, or that its differences, whether realized or not, are always actual in it.’[11] In this respect, we can draw on any number of examples of the division of a generic financial asset, and see that they are all numerical multiplicities. Whether a debt-note, a loan, a bond, or money itself: we divide, and in the process of dividing there is no change in kind. Is a debt-note available in an increment of hundred dollars or fifty? Does it matter? No –its yield will be the same. Is a loan syndicated? The answer to this question is a mere arithmetical formality. Do I ‘break’ a hundred dollar bill in order to get back 5 $20s, 10 $10s, or 100 $1s? Does it matter? No –the amount is unchanged by its denomination.

However, by contrast, when a qualitative multiplicity is divided it changes in kind:

‘[A qualitative multiplicity] does not divide up without changing in kind, it changes in kind in the process of dividing up: This is why it is a nonnumerical multiplicity, where we can speak of “indivisibles” at each stage of the division.’[12]

If synthetic assets appear less ‘objective’ to us, once more this distinction made by Deleuze helps to explain why, but now also provides us some additional illumination. In the process of pooling and tranching a synthetically-replicated portfolio of generic assets, synthetic securitization divides a risk and cash flow –but in the process of its division, there is a change to the risk and cash flow in kind. Or to cite another example, we can now also see that already in a single-name CDS, we were observing a process that strips, i.e. ‘divides’, the credit event (e.g. default) risk and associated cash flow from the generic referent –but in the process of its division, the synthetic asset is more than a simple replicated copy of its model, for it truly does bring about a new change in kind.  Moreover, any credit derivative involves the process of ‘splitting-off’ or ‘dividing’ from its referent its risk and cash flow –but again, in this process there is always produced a change in kind.

iii. This bring us to DR’s third contribution. In the course of his exposition of the multiplicity, Deleuze has alerted his reader to the importance of understanding that a crucial ontological difference adheres between its two different types –numerical multiplicities and qualitative multiplicities– as we discussed above. The dispositive ontological property rendering these two multiplicities different in kind turns on the different functional relation each multiplicity maintains between their specific material properties and the register of reality of their definition.

Of the three Deleuzian registers of reality –the actual, the potential, and the virtual– numerical multiplicities are chocked-full with extensive properties, and therefore principally inhabit the first two registers of the actual and the potential; while qualitative multiplicities are chocked-full with intensive properties, and thus principally, though not exclusively, inhabit the virtual. This is crucial for Deleuze, insofar as he defines ‘the actual’ as simply that which ‘is’ (what we often mistakenly label ‘reality’); and ‘the potential’ also is that which ‘is’, albeit it only ‘is’ as a possibility (Deleuze identifies the potential as that which is subject to a probability distribution, but whose possible outcomes are therefore predetermined by the actual); but ‘the virtual’ is neither actual nor potential, and yet it exists ‘in reality’ nonetheless. In fact, in DR Deleuze makes technical recourse to mathematics and the sciences of morphogenesis to illustrate that while neither actual nor potential, the virtual comprises another register of reality altogether. In short, the virtual is that register which structures the space of what is possible to become actual.

For this reason, the third way DR helps us to address our problem is that by invoking and developing the register of the virtual, it provides us with a technically-sound but not overly-theoretical method for thinking about how we, as operators, can trace the logic of the actual back to where it sets up camp, i.e. up through the extensive, from there through the intensive, and back into the virtual, wherein we can begin to tinker with that which structures the space of the possible of our economic institutions themselves. And importantly, this activity is increasingly available to us only with the recent and now progressive population of financial markets with qualitative multiplicities. And why?

Deleuze says that on the one hand:

‘Everything is actual in a numerical multiplicity; everything is not “realized”, but everything there is actual. There are no relationships other than those between actuals, and no differences other than those in degrees.’[13]

But on the other hand:

‘[The properties by which] a nonnumerical multiplicity…is defined, plunges into another dimension….It moves from the virtual to its actualization, it actualizes itself by creating lines of differences that correspond to its differences in kind.’[14]

What are these ‘lines of difference’ that the qualitative multiplicity ‘actualizes’ by virtue of partially ‘plunging’ its object into another dimension? What does this ‘plunging’ mean for the definition of the material properties of the synthetic asset to which the qualitative multiplicity corresponds?

Today, we commonly hear the synthetic asset disparaged on behalf of its alleged ‘virtuality’. However, DR avant la letter takes this accusation seriously, and proceeds to illustrate that the radical potential of the synthetic asset resides in its still partial virtuality, i.e. that its true historical-materialist radicality lies in the paradoxical, hybridized-dimensionality of its reality: it simultaneously inhabits two dimensions of reality, it has both one foot in the virtual, and one foot in the actual; it comprises a reality that paradoxically houses an object that is a mere shred of an actual generic referent, while yet also still possessing some of the non-substantive structure of the virtual.

The answer to these questions, then –of what are these ‘lines of difference that correspond to its difference in kind?’, and ‘how does such hybridized reality affect the order of the asset’s properties?’– according to Deleuze, is precisely what marks the peculiar but radical ontology of the qualitative multiplicity, and therefore the peculiar but radical materiality of synthetic finance, as such.

The radical materiality of the synthetic is best articulated by Deleuze, when in DR he outlines the three principal ontological features of qualitative multiplicities. They are as follows:

First, ‘the elements [viz. economic properties] of the multiplicity have neither sensible form nor conceptual signification…they imply no prior identity, no positing of something that could be called one or the same. On the contrary, their indetermination renders possible the manifestation of difference freed from all subordination.’[15]

This already begins to explain what we find so puzzling about credit derivatives –namely, that the economic properties both actualized by the synthetic exchange and actualizing the synthetic asset imply no prior identity, but are free from the material requirements placed on the actualized ‘whole objects’ of classical exchange and generic finance. Such ‘indetermination’ to its objectivity means that the synthetic asset is lacking any predetermined economic ‘form’, its potentiality is in a very real sense free from any predefinition in the actual. It is pure difference in itself.

Secondly, then, the various properties and differential relations between the properties of the multiplicity are determined, reciprocally determined –as they are in all multiplicities, both numerical and qualitative. But now their determination occurs ‘without external reference or recourse to a uniform space in which it would be submerged.’[16] The qualitative multiplicity is, as Deleuze puts it, ‘intrinsically-defined’.[17]

If the material requirements that predefine the conditions of possibility for the behavior of ‘whole’ economic objects are not present in a synthetic exchange, this is because the structure to the space of the qualitative multiplicity is not fixed, flat, uniform or homogeneous, i.e. it is not Euclidean. Rather, it is topological, which means that its surface is a space unto itself, and that space is not restricted by all of the demands placed on objects in actuality. Such an economic object is an intrinsically-defined and fungible space, capable of warping, bending, twisting, folding-over into or out of itself, or vanishing and suddenly reappearing.

What, then, is the difference between the structures to the space of the markets populated by numerical and qualitative multiplicities, respectively? We said that the structure to the space populated by numerical multiplicities is Euclidean. This means that it is like a corrugated plane of sheet-metal, lain flat upon a zero-curvatured floor: its rigid objects move to and fro on its surface, symmetrically translating back and forth along its parallel ridges. And yet, really, what more can the non-fungible objects populating this homogeneous flat space do than ex-change their position, or orientation, on this flat sheet now for an image of this or that position a little bit further ahead along the ridge? The exchange of such objects is change indeed, and technically-speaking. But it is an empty change, an invariable form of variation, a transformation that involves no real change at all.

Contrarily, the structure to the space populated by qualitative multiplicities is topological. This means that it is like an unbounded, elastic, soft cotton bed-sheet flipped up into the air, falling slowly through the air, and now down, down, down, towards an indefinite ground of indeterminate shape below. The surface of the bed-sheet and the ground below have yet to de-differentiate themselves, or become one, which they will and do at the moment when the bed-sheet touches ground. For now, though, the surface of the bed-sheet floats, suspended above the ground; it is a moving horizon populated by fungible objects, and subject to an invisible force. Indistinct yet very real streams of air-flows move beneath and above and beside and between the ever-changing curvatured surface of the sheet, with its thousand plateaus of n-dimensional folds and subfolds. It yet remains an uneven surface. Its fungible objects move to and fro on its surface, but it is highly improbable such objects rigidly translate back and forth, as if running along parallel lines. Rather, they are more likely to warp and bend the space around them as they move along the open terrain, or perhaps they will warp and bend themselves; perhaps their hard motion will be impeded, or redirected by another object on top of the surface, or now even an object beneath the sheet itself; perhaps their motion is soft. Perhaps the object is acutely sharp, or has a sharp edge that will insert a ‘cut’ in the folds of sheet as it rolls along its surface. Does this object now fall through the sheet? Does this hole now act as a new basin of attraction for the other objects circulating around on the sheet? Will the sheet further tear, with its basin of attraction evolving in mid-flight? Given that the sheet is unbounded, how can we know?

We see that to ask the question about the objects populating this kind of surface ‘what more can they do than this?’ is perhaps even now premature –for do we even yet know ‘anything’ they can do, to which there is yet ‘more’? Can we say we know everything they can do when we really don’t know anything about the objects populating this domain of action?

We do know, at least –and only by reading DR as heterodox political economy– that the structure to this space is plastic and ambiguously pliable, which now avails both its fungible objects and their space, whose flexible structure is capable of being remade by the motions of such objects, with any final, flat, or uniform structure. We at least know that this space and the objects populating it are ontologically-marked by a profoundly-augmented capacity for change.

Thirdly, then, Deleuze observes that these two aforementioned features mark the ontology of the qualitative multiplicity simply because the qualitative multiplicity ‘is a structure’, albeit a highly fungible, profoundly indeterminate, truly paradoxical kind of structure. It is, in Deleuze’s words, ‘a system of multiple, non-localizable connections between differential elements which is incarnated in real relations and actual terms.’[18]

To think the asset as a multiplicity is to posit that that the genesis of any economic object occurs ‘between the virtual and its actualization’ –or as Deleuze puts it, it goes from the structure of the virtual to its incarnation in the actual, ‘from the conditions of a problem to the cases of a solution.’[19] However, DR also allows us to observe that the synthetic asset is singularly unique from the other two classes of economic objects, in that it still has one foot fully-plunged into the virtual. Indeed, this is why Deleuze argues that synthetic objects are the objects ontologically closest to the virtual –they are that which, as he says, ‘enjoys the double property of transcendence and immanence in relation to [the actual].’[20]

If synthetic assets are indeed qualitative multiplicities, let us follow the logic to its result: that the historico-ontological progressive differentiation of synthetic finance signals the coming-into-being of a series of qualitative multiplicities, such as credit derivatives and other synthetically-structured assets, which now enjoy ‘this double property’ of both transcendence and immanence in relation to the preexisting, actualized set of numerical multiplicities, which in turn increasingly populate the markets comprising the system of exchange we call finance capitalism, what does this mean? It can only mean that now, namely, the determinative or defining structure to the genesis of economic form is more open and available to us as operators, and increasingly so, than ever before.

How so? If the virtual is indeed, as Deleuze says, pure structure without content, both the condition for and conditioning of a problem whose solution is always found in the actual; and if synthetic financial assets and synthetically-securitized assets have now differentiated to the peculiar hybridized status we outlined above, we must understand synthetic finance as the still partially-virtual domain –or at least the domain closest, ontologically, to the virtual – where actual economic solutions acquire the conditional structure to their problems.

For this and other reasons, reading DR as political economy is a radical wager indeed. Deleuze urges us to consider that perhaps we were always proceeding ontologically-backwards by looking for good solutions to badly-posed questions. The correct course of proceeding, rather, was to pose the virtual questions whose actual solution will always be pre-determinatively commensurate with the quality of its problem. We don’t need new solutions to pre-existing problems. We need to formulate new problems to pre-existing solutions –for DR allows us to see that the solutions have already repeated themselves, and have now produced a new difference in kind.

[1] By generic finance we mean traditional debt (bonds, loans, mortgages, etc.), equity (real estate, stocks, etc.), and vanilla derivatives (options, futures, forwards). By synthetic finance we mean credit derivatives (credit default swaps, etc.) and varieties of synthetically-structured products (synthetic CDOs, etc.)

[2] Since credit derivatives are the most noteworthy kind of synthetic financial assets, and the most (in)famous among these (especially after the 2008 financial crisis) is the credit default swap (CDS), a brief exposition is warranted herein: A CDS is a bilateral exchange between two parties, one of whom is called the protection buyer, the other is called the protection seller. The terms of exchange of the CDS make reference to a certain notional value, which is the payment obligation of a reference entity. The protection buyer agrees to pay the protection seller a cash premium on a quarterly, annual, daily, or any other agreed-to periodic basis. And in return the seller agrees to make a protection payment to the buyer upon occurrence of a credit event in the reference entity [fig.2.1][2]. The object of this exchange is therefore called a credit default swap because the parties to the exchange are swapping the risk of a default or some like credit event on a credit/debt obligation.

Someone or something somewhere owes someone or something else money. This debt obligation comprises the reference obligation of the reference entity: there has been a preceding generic financial exchange of some generic financial asset (i.e. a mortgage, a bond, or some other debt or equity object), whose event risk and cash flow the CDS replicates. However, while the CDS makes reference to this generic financial asset, its value, and the single name of the obliger in the generic financial exchange, the parties to the CDS may be, and now increasingly usually are, otherwise independent of and unrelated to the generic financial exchange. For this reason the exchange is ‘synthetic’. We call the exchange of credit derivatives –in this case the exchange of a CDS– a ‘synthetic financial exchange’ because the exchange involves a synthetic swapping of the risk and cash flow of a reference entity, derived from a generic financial exchange, but to which neither party to the synthetic exchange need be party to begin with.

[3] Perry Mehrling, The New Lombard St: How the Fed Became Dealer of Last Resort, Princeton Univ. Press, 2010

[4] This position is perfectly illustrated by proponents of Dodd-Frank: by attempting to re-segregate investment banking and commercial banking (though the legislative repeal of Glass-Steagall only formally conceded what had already institutionally transpired), by forcing OTC derivatives onto swaps exchanges (when such prior attempts at regulation gave birth to credit derivatives themselves), among other misguided attempts at federal regulation, Dodd-Frank performs the proto-luddite intention to turn back the clock on the progressive differentiation of finance.

[5] For example, see Alan Freeman, “The Profit Rate in the Presence of Financial Markets: A Necessary Correction, Journal of Australian Political Economy, no. 70.

[6] In this author’s opinion Difference and Repetition is the greatest of all books of philosophy. However, it is also probably the least read of Deleuze’s books, in large part because it is quite difficult to fully grasp without a working understanding of many mathematical and several scientific fields of study (e.g. group theory, non-Euclidean geometry, calculus, topology, a little biology and physics, and dynamical systems theory). It is also quite dense, because Deleuze ‘zips-up’ these various discourses into a compressed, cohesive whole. But it is ultimately very rich because it draws out the deep ontological significance –as only a great book of philosophy can– of their combined mathematical and scientific insights, i.e. of Galois, Riemann, Leibniz, Curie, Einstein, and so on: as if they were able to sit in a room, discussing a pure ontology amongst themselves, but now equipped with a (Deleuzian) language to streamline their collective discourse.

[7] Riemann, our reader may or may not know, was the mathematician Einstein was reading during his annus mirabulis –when, closing-up the patent office for the night, he walked home to smoke his cheap tobacco and re-envision the structure of the universe. Riemann, as a non-Euclidean geometer, immediately applied its concept to study geometric spaces, or more broadly mathematical spaces. Physicists apply its concept to study physical spaces. Dynamical systems theorists apply it to study dynamical systems, or objects as systems. Because markets are dynamical systems, and assets are dynamical objects, we can apply the concept to study assets and the markets they populate.

[8] DR. pg. 169

[9] DR pg. 182

[10] Gilles Deleuze, Bergsonism, Zone Books (1988) pg. 41

[11] Ibid pg. 41

[12] Ibid pg. 42

[13] Ibid pg. 43

[14] Ibid pg. 43

[15] DR pg. 183

[16] Ibid pg. 183

[17] Ibid pg. 183

[18] Ibid pg. 183

[19] Ibid pg. 183

[20] Ibid pg. 189

Difference & Repetition is a book of heterodox political economy

When meditating for a period of time on Difference & Repetition, one is increasingly struck by an awareness, peculiar though it is, that while Deleuze composed DR as a book of philosophy, it is also very suitably read, perhaps most deliberately, as a work of heterodox political economy. In actuality DR is an abstract, pure, high-theoretical text, giving philosophical transformation to mathematical and scientific concepts, through its difficult and dense but ultimately rich exposition of the overlapping dynamical orders of difference and repetition: Deleuze, throughout, illustrates the deep ontology of difference and repetition, irreducible and universal to any dynamical system. But then again, when read as political economy, the book’s final intention flips forward into the proposition of a radical alternative concept of value, predicated on the profound, historical-materialist, monstrous ontological power of the synthetic. This itself is a possibility if only because difference and repetition are also irreducible to the dynamical systems collectively called the economy, which progressively actualizes the system of exchange called finance.

However much I may profess that Difference and Repetition is the greatest of all books of philosophy, it is, nonetheless, admittingly quite difficult to fully grasp its many dimensions for the singular reason that Deleuze presumes, or even demands, a working understanding of many mathematical and several scientific fields of study (e.g. group theory, non-Euclidean geometry, calculus, topology, a little biology and physics, and dynamical systems theory). It is quite dense, because Deleuze ‘zips-up’ these various discourses into a compressed, cohesive whole. But it is ultimately very rich because it draws out the deep ontological significance –as only a great book of philosophy can– of their combined mathematical and scientific insights, i.e. of Galois, Riemann, Leibniz, Curie, Einstein, and so on: as if they were able to sit in a room, discussing a pure ontology amongst themselves, but now equipped with a (Deleuzian) language to streamline their collective discourse.

For this reason, throughout the course of the indefinite period of time it takes to do so, here at SpecMat we’ll be doing a close reading of Difference and Repetition in order to illustrate what has simply been asserted above -namely, that it is not only possible and virtual, but virtually possible to actually read DR a book of heterodox political economy.

It will be a course on Deleuze’s Guidebook to Synthetic Finance.

The second post, in which we will officially begin our reading of Difference & Repetition, will begin soon. Grab your copy of DR and read along!



Fundamentals of Liquidity

This little known short piece by Fischer Black, titled “Fundamentals of Liquidity”, is worthy of consideration. Black often slips an elusive profundity into the extended consequences of a series of simple statements -and this essay is prototypical of his approach. Just read the piece by itself first; then jump to a secondary source in my “cash flow” entry, which is part of SpecMat’s ongoing Lives of Concepts of Finance project.

Black smiling, thinking of eating foil-wrapped fish

My understanding of the essay is this: If we are willing to temporarily indulge Black’s assertion about the possible achievement of a world of equilibrium, and if we are capable of projecting, along with Black, the material impact of synthetic exchange for the property of liquidity, we will see that Black is making a startling ontological forecast about the progressive differentiation of finance: namely, he’s observing that the trajectory of synthetic finance is an ontological movement towards hyperfungibility to the point of absolute non-differentiation between financial assets and their liquidity –which, if universally extended, in turn would mean a perfectly hedged world of exchange, a ubiquitous and incessant reversibility to all financial assets, a radical loosening of all invariance requirements on their properties, and consequently the realization of a world of equilibrium. It would also, not coincidentally, usher the end of the pricing mechanism for financial assets, and on which finance capitalism is predicated.