a five-year plan

To effect the project objectives of Lozano’s version of speculative materialism, we’re required to perform a disciplinary integration. To perform this disciplinary integration, we’re required to master three literature sets and their respective fields of inquiry: (i) dynamical systems theory and the sciences of morphogenesis, non-Euclidean geometry, topology, and group theory; (ii) the work of Gilles Deleuze; and (iii) the technical discourse of finance –especially on the topics of credit derivatives, securitization, and synthetically-structured debt, and whose historical-materialist development effects the institutional differentiation of shadow banking out of traditional intermediation.

When the philosopher sets his aperture to finance, he encounters a veritable pantheon of ontological profundities. The first result of this integration is discovery of an important isomorphism between the nonlinear dynamics of finance as a complex system, and the profound demonstration by dynamical systems theory of the ontological univocity characterizing complex behavior, writ large. Dynamical systems theory employs the analytical tools of topology, group theory, and natural studies on symmetry to study complex systems, therein revealing common characteristics among different classes of systems (e.g. biological, social, etc.). Speculative materialism, the study of the ontology of finance, under this approach discovers that finance is one such class of system, and from this discovery sets out to examine the singularities and affects endemic to its processes.

This gives birth to a new methodology and research project whose topics to begin with include, but are not limited to: study of the topological invariants of varieties of financial assets (e.g. options, credit derivatives, securitized products, convertible bonds, synthetic ETFs); study of reversible and irreversible processes endemic to financial phenomena; study of the basins of attraction and nonlinear causes of financial crises; experimentation with the critical values and nonlinear dynamics involving far-from-equilibrium conditions; and ultimately the theoretic union of a macroeconomic and microeconomic discourse consistent with the principles of each. Topological and group-theoretic conceptual resources developed by both dynamical systems theory and Deleuze lend us powerful analytical capacities for sifting-out some structure to finance’s spaces of possibility –even amidst ostensibly stochastic phenomena. The study of the ontology of finance seeks to trace these logics, the logics of the virtual, back to where possibilities for finance set up their camp. Only then, as operators, can we begin tinkering with its divergent evolutionary capacities.

The phases of Lozano’s research can be temporally divided between the present, a projected immediate-future, and a projected extended-future.

the present

Of Synthetic Finance: Three Essays of Speculative Materialism (2014)

Of Synthetic Finance is scheduled for publication in 2014. This book is the formal event that convokes into being the field of study of the ontology of finance.

This book demonstrates:

(i) That synthetic financial assets have a hyperfungibility and higher degree of symmetry than generic financial assets, e.g. traditional debt and equity. This includes an ontological examination of generic finance and synthetic finance to outline the topological invariants of the latter.

(ii) That this means synthetic assets can not only “do” more things, plastically, effectively, and readily to create and distribute risk and cash flow, but that the universal distribution of risk and cash flow is organic to their technology. This includes an ontological exposition of credit derivatives and their securitized incarnation in synthetic CDOs; and an elaboration of the methodological resources Deleuze provides when in his philosophical treatment of dynamical systems theory, he illustrates the peculiar but profound material capacities of the synthetic.

(iii) That given the advanced plasticity, hyperfungibility, and radical materiality of synthetic finance, we really have no idea what our financial technologies are actually capable of. This includes the development of Deleuze’s concept of ‘nomadic distribution’ to wager that the progressive differentiation of synthetic finance signals the contingent historical development of an untapped awesome capacity for the universal distribution of risk and cash flow in a way that makes all parties wealthier.

Lozano’s 5 years of intensive research in the three aforementioned fields generated material for several topically-different books, but which still fall under the general project of speculative materialism: Infinite Leverage (2015); An Image without Likeness: A Nonlinear History of Finance (2016); Continuous Recalibration of Natural Leverage in a Universal Synthetic CDO (2017); and his magnum opus, Being & Finance (2018); followed by Promises of Utopia (2019). The following is an itemization of this projected future.


a projected immediate-future

Infinite Leverage (2015)

For strategic purposes, Of Synthetic Finance (2014) deliberately pursues a nontechnical ontological exposition of synthetic finance when outlining the methodology of speculative materialism. By contrast, Infinite Leverage provides a more technical description of the isomorphism between topological transformations and synthetically-structured financial exchange. This involves an examination of the nonadditive material capacities of ‘natural leverage’ –labeled ‘mechanical advantage’ or sometimes ‘virtual work’ in physics– through the ‘pooling and tranching’ processes of structured finance. The space of structured financial exchange is what topologists classify as a nonorientable surface.

This examination illustrates that in finance, as in other nonlinear systems, the introduction of a subtle or small stimulus at a specific time, for a definite duration, and at a critical value, can induce dramatic effects incommensurate with the amplitude of its causes. In this respect, the book also provides an outline of a theory of financial crisis: when an operator or sets of operators induce nonlinear conditions of far-from-equilibrium, the principle of superposition is supplanted by a new principle; this is the principle of nonadditivity. However, there’s a flip side to system instability: from the principle of the nonadditivity of nonlinear causes we derive Deleuze’s concept of ‘nomadic distribution’ –which does not entail a redistribution of economic objects in a pre-produced space, but now rather an ex nihilo distribution of economic space itself. When the principle of superposition breaks down, a high volume of natural leverage, if correctly channeled, can also activate a nomadic distribution of economic space itself. It is this potentially ex nihilo and ad infinitum capacity of leverage we must seek to tap. For this would realize the all-upside-promise of infinite leverage.



An Image without Likeness: A Nonlinear History of Synthetic Finance (2016)

This book is a history of synthetic finance, from the Ancient to Medieval to Modern and now contemporary world. It provides a nonlinear account of the historical differentiation of the class of exchange of synthetic finance (e.g. credit derivatives and synthetically-structured financial assets) from out of the class of exchange of generic finance (e.g. traditional debt and equity), and therein maps the phase transition from traditional intermediation (aka the “Jimmy Stewart” model of banking) to shadow banking.

This book also draws on Felix Klein’s powerful group-theoretic method of arranging non-Euclidean transformations according to their geometric invariance requirements, in order to both outline a mathematically-intoned philosophy of the history of finance, and to illustrate that the differentiation of synthetic finance signals a progressive becoming-topological of the financial asset.

a projected extended-future

Continuous Recalibration of Natural Leverage in a Universal Synthetic CDO (2017)

This book advances a short, dense, technical argument that the technological fusion of, on the one hand, contemporary reworkings of the Black-Scholes-Merton options pricing model’s method of continuous recalibration, with on the other hand, the fungible risk and cash flow distributive technology of a synthetic CDO, can effect a dynamically-hedged universal distribution of risk and cash flow that makes all parties better-off.

Lozano is currently in the inaugural stages of modelling this proposal (note: he also needs a mathematician, a financial engineer, an accountant, a behavioral economist, a (Laplanchian) psychoanalyst ((LPNNA) Lacanians please need not apply), and a game theorist). In actuality this book is a tax-policy proposal which, if tested, adopted, and found viable, would inaugurate a concrete speculative materialist economic program. At the very least, it’s a test model –whose experiment draws on scientific, philosophical, and psychological studies on altruism and egoism– to translate and synchronize several profound analytical contributions from financial engineering, social philosophy, behavioral psychology, and dynamical systems theory to build more robust (and hopefully accurate!) financial risk models, albeit now, and essentially so, with universal economic equitability as its aim.

Being & Finance (2018)

This book explicitly illustrates the becoming-topological or regressive differentiation of capital in its synthetic-systemic incarnation. It comprehensively exposits the complete philosophical synthesis of the combined insights of dynamical systems theory and the study of the ontology of finance.

Promises of Utopia (2019)

Starting next year (2014), Lozano will commence intensive research on the history and ideologies of utopias. He will then weave Nietzsche’s advocation for a politics of difference grounded in joy and affirmation into an itemized account of the promises of utopias. Drawing on his technical understanding of synthetic finance, Lozano proposes a project for radically reengineering synthetic financial technologies for universal equitability –or in a word, to realize the promises of utopia.

…But wait a minute, Lozano’s only one guy. What else will speculative materialism have been 5 years from now?



*Thanks to Jon Rafman for the featured image in this post.

Towards a social logic of the derivative

This week is honorary Randy Martin week here at SpecMat.

Its not that we’ve been too preoccupied with other stuff to write anything worth reading lately; for instance:

It’s not that we’ve been watching too much TV, no –I don’t even like watching exciting baseball.

It’s not that we’ve been zealously following the soap opera called Washington DC (and the “I kidnap your money” (i.e. Congressional budgetary nonfunding of the US government) and then say “now give me the fucking baby!” (i.e. Obamacare/Affordable Care Act) logic; which reminded us how easy it is to watch Bill O’Rielly (on an empty stomach))…No that’s not why either.

It’s not that we’ve begun working on a new book titled Infinite Leverage, and that we’ve found that by connecting the deep history of financial leverage (or ‘gearing’ if your in the UK) -whereby you employ debt to augment the volume of gains and losses- with the principle of mechanical advantage -whereby an inert instrument (like a lever) exploits the positive differences between force and movement to amplify an output of power far beyond that of your input- we’ve opened up a veritable pantheon of financial ontology only akin to the veritable pantheon of culinary delights boasted by the (original, Japanese version of) The Iron Chef…No it couldn’t be that.

Allez cuisine! (translation: 'maniacal aggression never tasted so good)
Allez cuisine! (translation: ‘maniacal aggression never tasted so good’)

It’s not that we’ve been depressed because Walt died –which is natural and justice, of course; but honestly isn’t Jesse just as responsible for just as much objective violence (e.g. when someone smoked the blue stuff and neglects their kid, then their kid dies -this means that Walt and Jesse just killed the kid, indirectly, but objectively: they are both equally responsible for the countless deaths of people just like Brock)?..That’s not why we haven’t been posting things. No. that’s definitely not why. That would be stupid, it’s just a show.

It’s not that we’ve been making lots of money trading, because making money trading off Japanese monetary policy and emerging market debt is easier than losing money by believing that Gold will go way up when the money is kidnapped and held as ransom, and babies are demanded in exchange for ransom…I assure, dear reader, that would not be the reason, either. (Actually if you study the correlation you’ll see that Gold only eventually goes way up -so its just not time yet.)

No, its honorary Randy Martin week because Randy has written the best piece on the social logic of the derivative, period.

Randy identifies and defines a derivative sociality as a body without organs (as he puts it: ‘a decentered social kinesthetic…derivative mobilizations that do not require unity to move together’), and suggests that in the topological or ‘horizontal propulsion’ of dance and derivatives lie an aesthetic, a becoming-culture, a radical ensemble of practices of precarity.

This is really compelling to me, to us, and to those who are and have been and will be attending to the thought of what more our economic and social institutions could be, but which they currently are not. In Lozano’s Of Synthetic Finance, he pursues a case study on credit derivatives, in which he outlines a proposal for modifying and universalizing the technology of synthetic CDOs -which he wagers would act as a kind of lock and key mechanism (rather than requiring a wholesale systemic mutation –whatever that would even mean), and whereby operating a seemingly minor variation to our mode or distributing economic space could rearrange the interrelations between the metrics of our (financial) order. He argues that this could effect a nomadic distribution of economic space -and now wagers the notion that through the pooling and tranching procedure of synthetically-structured finance, we could, if universalized, effect an infinite leverage with all upside and no downside (i.e. we have no idea what our institutions are actually capable; let’s experiment with infinite leverage, universally, and find out). But this notion by Lozano, to be clear, is strictly an economic, quasi-tax-policy-oriented financial proposition grounded in his technical understanding of the peculiar but profound and monstrous material capacities of synthetic finance. But Randy’s thinking on this is one or two light years ahead; his piece goes a big step further by clarifying that the radicality of the synthetic is a social aesthetic as well: and after all, isn’t economics just a subset of social logic? To paraphrase Deleuze, we make and remake the topology of our identities on a moving horizon of fluid activities, interests, desires, and dark precursors. I agree. That’s why it’s honorary Randy Martin week.

His piece, which is beautifully written, can be found here.

project statement

There is at last no longer any serious pretense that our financial world is capable of monogamous symbolization by the stable period motions of economic equilibrium models, whose analytic analog derives from classical mechanics. It is now conceived as a world of instabilities, intrinsic and extrinsic, if such distinction still holds; deterministic and simultaneously by chance; perpetual fluctuations; permeated through and through with ambiguous anxieties; overdetermined by noise, perturbations, and pathological deviations; but which in turn -we must not overlook- is responsible for rich varieties of fungible properties, forms of assets, and a mobile horizon of institutional structures constantly coming into and out of existence. Do we really understand what all they can do?

New conceptual tools are needed to think finance, to think between and through and along with its being, its logic, its ontology, viz. its logic of being. Speculative materialism is a forum for the study of the materialism and ontology of finance, and so is a site for exploring methods capable of examining its complexity -at the level of economic properties, assets, the markets they populate, and the subsystems comprising the rhizomatic systems of exchange we call ‘finance’.

Now, Lozano is only one speculative materialist. But Lozano reads, and believes he understands, Deleuze. This means that his current heterodox political economic interests involve questions of the possible applications of two fields of scientific inquiry that have been progressively revolutionizing the philosophic disposition of science towards complexity.  {note: thanks to I. Prigogine, Exploring Complexity, for this inspiration}

(i) The first is studies on nonequilibrium -and in particular the peculiar material properties and processes exhibited by far-from-equilibrium conditions (note: when Lozano openly imagines a continuously-recalibrated universal synthetic CDO that nomadically distributes economic space by manner of the ‘infinite leverage’ production-capacities of structured financial technologies, he’s advocating experimentation with operations of far-from-equilibrium -which is why he likes to say: “hey look, I might be wrong, in fact I probably am wrong; but if I’m wrong than I’m wrong for the right reasons.” (ed. note: he’s obviously a bit of a jerk)).

(ii) The second is modern dynamical systems theory -and in particular its investigations of the amplifications of the effects of profound changes to a system from small or slight modifications of initial conditions and/or nonlinear causes.

Lozano believes that when a heterodox political economist successfully scavenges the conceptual resources from these methods, at the very least the result will be a more thorough understanding of our object of analysis -i.e. the ontology and the deep material capacities of finance. And at the very more? -this is for another post.


Wherever we look in finance today we observe divergent evolution, along with a precarious fleeting set of moments of stability amongst a flux of deviations from equilibrium. The ontological consistency of the world of financial objects is a truly pluralistic world, wherein we find acute determinism (e.g. the prices of bonds and their yields always move inversely) alongside or even within stochastic phenomena (e.g. price series of bonds), and reversible processes (e.g. any given exchange) that give rise by degrees to qualitatively irreversible changes in kind (e.g. a series of exchanges progressively gives rise to new markets and institutions, whose differentiation is irreversible, i.e. its actuality only moves one way).

In some respects perhaps this is no surprise. Many complex systems are marked by this elusive dynamic; moreover, this elusive dynamic even cuts across complex systems themselves. Physicists explain that already the motions of a ‘simple’ frictionless pendulum are wholly reversible, that the pendulum’s past and future can move in either direction of the arrow of time, and that each is equally as capable of playing the same role in the equations describing its dynamics: this truth is absolute. But it is just as much the case that biological evolution, chemical reactions, and diffusion processes -are these not equally absolute, albeit now in their very irreversibility?

Let us then consider. In the (neo)classical political economic paradigm, the political economist is an investigator who is thought to be exogenous to the forces of the system which she observes. She is capable of calculating, rationally, independently, and making autonomous decisions about the phenomena presented to her in the course of her studies therein. Contrarily, it is the system itself that is subject to deterministic laws, while the political economist is the decider, awesome and free. It is the system -even if and when comprised of individuals- who is stupid, pathological, inert, an undead-dead matter that conforms to a predetermined plan. Today, however, already in behavioral finance’s opening salvo, and now in sociological applications of science and technology studies to finance, we are getting progressively further from this aforementioned applied-Cartesian conception of the subject. Not only in the human sciences and even physics, but afortiori in finance and economics as well, we are now expected as subjects, spectators, subjects of the spectacle, but also as actors and activists as well. No longer then, too, must the domain of exchange we call finance necessarily imply a predetermined future predicated on a perpetual present. Rather, our world is rife and open with possibility, for we perpetually inhabit and cohabit the construction of a time and space of which we are active participants.

This is one conviction of a speculative materialist.

This is one wager as we we proceed to examine the materialism and ontology of finance.

This is also why we seek to move beyond critique and off to engineering. But if engineering truly is the benevolent fusion of art and science, of creative aesthetics fused onto physical laws, we must begin with step one -which is a clarification of method -and then commence the process of tinkering with matter.

DGSF Page 11

§ introduction to the Deleuzian registers and their epistemological correlates: actuality –infinite comprehension, potentiality –finite comprehension, and virtuality –indefinite comprehension 

(‘Let us pose a question quid juris [which law applies]:…)

Deleuze inaugurates this portion of the Introduction by explicitly relating his earlier consideration of a 2nd contrast (from the perspective of law) between generality and repetition to now that of a 3rd contrast (from the perspective of the concept or representation). Deleuze poses ‘a question quid juris’ (which law applies). That is, a question arises as to how the 2nd contrast (a concept or theory of value) ‘applies’ a given understanding of the topic of the 3rd contrast (a theory of concepts, or representation). By proposing to ‘pose a question quid juris’, Deleuze is clarifying that our answer to the question of value already implicates a certain presumption about the being of reality –or in other words, it already begs the question of ontology.

We are then incorrectly wording the issue if we say that a materialist theory of value requires an ontology, since it’s the case that any given materialist analysis already is an ontology. To forward an assertion about the coming-into-or-out-of-being of value is to already forward an assertion about what being “is”, i.e. its ontological properties, of how they come and go, of what are being’s registers, etc. In order to get our answers to such questions about value right, we are required to get our ontology right; and in order to get our ontology right, we need to get our questions right.

This assignment drives Deleuze’s thinking on the 3rd contrast –a difference in kind between the orders of generality and repetition, now from the perspective of concepts, or representation. This 3rd contrast of their difference in kind convokes Deleuze’s understanding that there are three registers of reality: actuality, potentiality, and virtuality.

However, our reader will quickly realize that at this portion of DR (pgs. 11-15) Deleuze is merely drawing on the phenomenological consequences that there are three registers of reality, and in doing so proceeds to indirectly unpack some of their basic ontological, epistemological, and logical properties (or “correlates”, as he calls them). Let our reader then be clear that Deleuze’s main objective at this point is not to formally elaborate the registers, as such, but to continue to articulate the difference in kind between the domains of generality and repetition –now from the perspective of concepts, or representation –and only backs his way into a passing consideration of the registers incidental to that purpose. However, our own reader’s full clarity over this part of the Introduction turns on her appreciation that a concept encounters a variety of blockages contingent to the register through which it passes. And because value is our concept of concern herein, without such clarity, she will be unable to follow Deleuze’s opening rumination on the material properties of the synthetic, and in turn the proper materiality of synthetic finance. For this reason, we must briefly overview the three registers.


The three registers of reality and their correlates are as follows:

actuality –a register of extension = 1; is marked by infinite comprehension; herein the concept encounters artificial blockages/logical principles to its representation

potentiality (possibility) –a register of extension = ∞; is marked by finite comprehension (its discrete entities are subject to probability distributions); herein the concept encounters natural blockages to its representation

virtuality –a register of inextension; is marked by indefinite comprehension; herein the concept also encounters natural blockages to its representation, but which are different in kind from the blockages afflicting potentiality

We must briefly consider each, and its significance for our understanding of finance.

DGSF page 11

§ recap of 2 contrasts between repetition and generality: conduct & law; synopsis of 3rd contrast: concepts, or representation 

(‘Repetition and generality are opposed from the point of view of conduct and from the point of view of law. It remains to specify a third opposition from the point of view of concepts or representations.’)

Deleuze closes his introductory comments on operators of repetition, and so for the time being closes his concern with Kierkegaard and Nietzsche. The opening line from the Introduction’s second textual break commences with a recap of the two contrasts already made by Deleuze –that repetition and generality are opposed (i) in conduct (exchange) and (ii) in law (theory of value) – to which he now adds that they are also opposed from the point of view (iii) of concepts, or representations.

Having already cursorily familiarized ourselves with his two prior contrasts, the reader will understand that with this 3rd contrast Deleuze has now introduced to his reader three differences in kind on which pivot his exposition of an ontology of the synthetic, his revaluation of the concept of value, and his advocation of a new materialist political economy. Deleuze’s Introduction is dense, difficult, and at times poorly edited. But if we appreciate that its final aim is to provide us with a rough outline of an ontological disquisition for a synthetic system of exchange founded on difference and repetition, we will feel better prepared to follow his guide. Let us therefore recap Deleuze’s two prior contrasts, and then commence with our initial consideration of his third contrast, as briefly as it’s itemized at this point in DR.

To recap and move forward: there are 3 contrasts to make when distinguishing as different in kind, ontologically-speaking, the domains of repetition and generality (and it’s perhaps worth observing here that Deleuze believes the three contrasts are itemizable in any order):

1st contrast: from the perspective of conduct, i.e. our conduct in exchange, or, the activity of a quasi-causal operator amidst the transformation of economic objects from one to another place in space. The question for Deleuze is one of how we are to regard our conduct in the course of exchange? This is a question of microeconomics.

2nd contrast: from the perspective of law, i.e. if not a theory then at least a concept of value, or, of the change in values of the properties of economic objects. If the spatiotemporal transformation of economic objects is predicated on their symmetry (viz. commensurability, equivalence), the question for Deleuze is what kind of symmetry, where, and what is its relation to value? This is a question of macroeconomics.

And now a 3rd contrast: from the perspective of concepts, or representation, i.e. of the relation of the coming-into-being of value to that of the representation of value, or, of our cognitive and perceptual relation to the registers of reality through which our concept of value passes. For Deleuze, the form of the question of what is value already thoroughly begs an ontological question that demands our better understanding of the relation of epistemology to ontology? This is a question of the relation of ontology and epistemology of finance.

With this third contrast we are given cause to preliminarily concern ourselves with Deleuze’s three registers of reality. We will follow Deleuze’s prefatory sketch of this third contrast, and therein inaugurate our understanding of that which will be more fully developed throughout DR, as Deleuze incrementally but comprehensively elaborates these three registers.

Can Exchange Cause Change? Part I. Mathematical Derivation

Can exchange cause change? If Deleuze’s thesis on difference and repetition applies to economic transactions, we have reason to believe it can. But how? Is not to ask whether exchange can cause change another way of asking whether the repetition of an object into its image of value as money can produce difference, true difference, meaningful difference, a repetition that causes a new change in kind? At first glance perhaps it’s not so evident that exchange can cause change. But let us consider this.

i. One of the most, if not the most ontologically basic questions asked in mathematics is whether two given mathematical objects are the same? In the geometer’s hands, the matter of difference in repetition in relation to the question of change is transmuted, indeed elevated, to the status of the crucial question of all mathematics.

Badiou says mathematics is ontology, but this is wrong. Ontology is ontology. Ontology is the study of Being. Being is univocal. Being’s univocity articulates itself in a diffuse set of registers. And mathematics and finance are two such registers –which renders them neither metaphorical nor analogical nor pure; rather, each register is a derivative subset isomorphic to the other; but neither register resembles each other in actuality.

When the geometer maps the transformation of an object into its image, such as

congruent motions, i.e. classical exchange
Figure 1.0. congruent motions, i.e. classical exchange

…we see that a general repetition of the object has occurred. The question is: given that O is now O’, has change occurred?

On the one hand, let us not overthink this question: Is O the same as O’, or are O and O’ different? –and if so, in what respect?

On the other hand, let us not underthink the questions contained inside this question: What do we mean by “the same”? What do we mean by “different”? What do we mean by “change”?

When the mathematician says “the same” she often means “equal”. For example:

Richeson observes:[1]

5 · 4 + 6 – 23 = 18

To say that these two different expressions are “equal”, this means that the expression

5 · 4 + 6 – 23

…and the number “18” –that these two things are the “same”.

Is it possible that it is more than ironic that this equivalence relation persists in the economist’s conception of classical exchange?

If 1lb. of coffee is exchangeable for the price of $5, when that object, the 1lb. of coffee, is transformed into its image of value as money, to say that these two expressions are “equal”, this means that the expression 1lb. of coffee and the amount of $5 –they are “the same”.

Or to cite another example from mathematics, we know and say that the polynomials:

x2 + 3x + 2     and    (x +2) (x +1)

…are “equal”. Even though they are housed in and as two different incarnations, they are said to be the same. And the reason why is that one can move, or more correctly put, ‘transform’ one expression into the other, i.e. one can treat and repeat one expression as the other, while yet no change has occurred.

So too if 1lb. of coffee is worth $5, and 2lbs. of tea is worth $5, even though the two objects are different incarnations, they are regarded as the same. One can transform one expression of $5 into the other, and one can repeat the one expression “coffee” for the other expression “tea”, while yet once again we see no change has occurred.

In classical exchange, then, which involves the immediate settlement of physical objects for their images of value as money, we see that exchange does not cause change.

Figure 1.1. Classical Exchange
Figure 1.1. Classical Exchange
Figure 1.2. Generic Finance
Figure 1.2. Generic Finance

We have said before that classical exchange is to generic finance in exchange what congruence is to similarity in geometric transformations, and with a little reflection on this one can easily see why (also please see the Appendix to Of Synthetic Finance for more on this). Neither congruence nor similarity allow for much change to occur. Different geometric objects may move to and fro, and back and forth, as if they were strung up and running along parallel lines. If they remind you of Cartesian coordinates, this will come as no surprise, for they are numerical multiplicities par excellence. Yes, classical objects and generic financial objects move –of course they move –in space and time. But their motions in this ambient Euclidean space always entail an invariant change, an empty form of difference, a variation that produces no true variation at all. Any and all difference therefore comprises an indifference to difference, a non-differentiation, a generality, a repetition of the same.

Conversely, in Euclidean space, if one object does not repeat itself congruently, or similarly –e.g. if its angles, its shape, and so on, are not the same – when it is transformed into its image, the Euclidean geometer will say that there are two objects that are different, i.e. a change has occurred, and that these two objects do not belong to the same equivalence class of exchange. There is between them no symmetry. There is a difference.

ii. This, of course, is not the end of the matter, for with the Euclidean geometer we cannot agree. Topology has a much more progressive set of criteria for what constitutes difference; for this reason it has a much more relaxed set of invariance requirements on the object transformed into its image. Topology is often much less impressed –dispositionally– by claims made by Euclidean geometric transformations, these self-congratulatory assertions by the Euclidean geometer that an object which does not repeat into its congruent or similar image realizes difference. Topology illustrates that where there is often an alleged, actualized, and apparent difference, there is, in truth, only generality and equivalence.

In topology, a square can be stretched into a cylinder, or an annulus.[2]

 Inline image 1

Figure 1.3

In topology, a square can be stretched and then bent into a torus.

Inline image 1

Figure 1.4

Such objects can be transformed into one another. For the topologist, when this actual transformation happens, no material change is thought to have occurred. There is yes, some difference to the object’s repetition: but once again, it is of the order of generality, it is an invariant form of variation, an empty form of difference, which is to say that no real change has occurred.

To be clear, in topology, if one object can be continuously transformed into another, these objects are considered to be the same. And the symmetrical transformation of an object into its image need not be congruent, and it need not be similar. Bending, twisting, turning, squashing, or stretching the shape of an object does not comprise change, for it does not change the object’s topology, it does not change its topological invariants, no true difference is caused by this transformation. By contrast, puncturing, cutting, and gluing does (or at least can) change the object in kind.

Let us observe that the Deleuzian registers of reality (actuality, potentiality, virtuality) now begin to supervene on our considerations herein. If, following Richeson, we observe a variety of polyhedra, such as in Figure 1.5

Inline image 1

Figure 1.5

….we see that each individuated polyhedral may phenomenally appear quite different than, for example, a sphere; and in actuality they are; but that the nonnactualized, but very real structure of what is possible for them to become in actuality is in fact the same: the three polyhedra immediately to the right of the sphere are not actually a sphere, but they could easily be continuously deformed into a sphere. Their extensive properties are what they are in actuality; but their intensive properties, while not actual, are every bit as real.

Conversely, we see that other polyhedra will also phenomenally appear to be quite different than a sphere; and once again in actuality they are. However, it is also true that in this second instance, an ontological examination of their topological invariants reveals the incorporeal existence of an even deeper structure than merely their intensive properties –a nonactualized, nonprobabilistic structure– to what is possible for them to become. The topologist devises methods by which to examine the ontology of these objects, which in turn allow her to study these objects’ topological invariants. And if the topologist, in the course of her ontological examination of their topological invariants, finds that the invariants are different, in turn such objects are considered qualitatively different in kind.

Already in this rudimentary inaugural consideration of the first elements of topology, we see that the topologist requires an additional register of reality. It is not enough to merely defer to geometric objects’ (a) ‘actuality’, i.e. that which, with their veritable extrinsic properties, they “are” as actualized objects; and their (b) ‘potentiality’, i.e. that which is possible for the objects to become in actuality, and as such, is subject to a probability distribution. She is in need another concept here, for when considering the topological invariants used to categorize geometric objects, she’s already (like Tartini in the Devil’s Trill) tapping another register of reality –something that adheres not to the object’s actual properties, not to their extensive properties, but which more fundamentally comprises the structure to what is possible for their extensive properties to become. And this is neither actual nor potential, nor strictly speaking “in them”, as such. Rather it is an incorporeal structure, another register altogether, that supervenes on the other two registers. The topologist is making recourse to, without naming, the technical concept invoked Deleuze to elaborate this register: it is the register of the virtual.

iii. If, in the course of its repetition from one to another place in space, a geometric figure can be deformed into another geometric figure in 3-dimensional space –and is then ostensibly different in its repetition– the topologist will say ‘these two figures have the same extrinsic topology’. In using this term ‘extrinsic’, the topologist is delineating for us two distinct ontological categories. The first is isotopy; the second is homeomorphism.

If two objects have the same extrinsic topology, they are called isotopic –topically, extrinsically, apparently,  they are actually different and yet potentially the same. For example, the four polyhedra in Figure 1.5 share the same extrinsic topology: they are isotopic. They need not be actually at that moment the same as each other -but they are for the topologist the same as each other, insofar as a simply bending or twisting or squashing or stretching is all that is required to transform the one into the other with yet any change to its topological invariants having occurred.

However, a deeper and more ontologically-fundamental dimension of a geometric figure’s reality is available to thought. For the topologist, two given objects may not appear to be the same, i.e. are not even extrinsically the same, but nonetheless are regarded as the same if they have the same ‘intrinsic topology’. “Do not trust phenomenal appearances!”, the topologist warns. “Don’t put too much stake in the fleeting, temporal shape of a geometric figure!”, the topologist exclaims, running with her lantern clasped tightly in hand, and out into the marketplace. “These extrinsic objects that you see as fixed, these too are actualized incarnations, contingent states of a deeper materiality!”, she urges. “Don’t mistake the immanent for the transcendent!”, she says.

Will the political economist listen to her? What does the topologist mean?

To better illustrate this –and especially to illustrate the ontological isomorphism between topology and finance in relation to the virtual, as well as the consequences of the univocity of Being for the speculative materialist political economist– let us take this a step further.

Let us consider an instance of cutting and gluing –or as the speculative materialist would rather put it when examining the ontology of financial objects: let us consider an instance of differentiating and dedifferentiating, or dividing and reassembling. (Note: We will later discuss that in securitization this process goes by the terms ‘pooling’ (dedifferentiation) and ‘tranching’ (redifferentiation): it is a division (cutting) that occurs, but we wish to consider whether it can and does produce a new change in kind?)

Inline image 1

Figure 1.6

It is the case that cutting and gluing very well can and may effect change to a geometric figure. It is possible that cutting and gluing may change the topology of an object. But it is also true that this is not always necessarily the case.

For example, Richeson points out that if we cut a shape, but then glue ‘the severed pieces so that the cuts line up exactly as they did before’, in this case no change has occurred, for the geometric figure’s topology has not changed.

This is the case with the knotted torus in Figure 1.6. Here if we cut the tube of a torus in half, we have created a cylinder. If we stretch out the cylinder, but then reglue the cylinder in the manner illustrated in Figure 1.6, i.e. as a knot, the resulting shape is still topologically the same as that of the original torus. It is true that the two objects –O and O’– are not isotopic, i.e. they are not extrinsically the same; for the knotted torus cannot actually be obtained, or derived, from the original torus through its deformation in 3-dimensional space. The intrinsic topology of the two tori are the same, their extrinsic topology is not. Therefore, again for the topologist no change has occurred. There is no difference that has been made.

How then can we know whether in a given transformation a true change has occurred? How do we know difference when and where it occurs? In short, what is different and what is the same?

For the topologist, two objects are the same, i.e. they have the same intrinsic topology, if there is a one-to-one correspondence between the topological properties of the two objects that preserve their closeness –or as Richeson puts it, ‘if nearby points in one shape correspond to nearby points in the other.’

Mobius, who was one of the founders of topology, named such a relation a homeomorphism.

iv. So herein lies our first speculative materialist concern with topology: we wish to know more about the homeomorphisms that supervene on extrinsically different financial assets? For this reason we must turn more directly to finance to address this question.

For example, when Modigliani and Miller observe the occurrence of a nondifferentiation between debt and equity for the capital structure of a firm, is this observation predicated on the assumption of a fundamental homeomorphism between debt and equity -that, yes, extrinsically and in actuality debt and equity are different, but intrinsically they are the same?

When Black-Scholes-Merton provide a formula (which we know is ‘wrong’, but for this reason is inverted and still functionally-used) that allows for continuous zero-beta hedging with a combination of partial objects (options) and whole objects (treasuries), i.e. which are extrinsically different, is not their silent premise that the economic properties of a variety of financial objects can be continuously arranged so as to achieve absolute nondifferentiation at every tick, i.e. that ostensibly different objects’ economic properties can be cut and then glued, divided and reattached in a variety of manners so as to always achieve a homeomorphism between assets and liabilities –which is, of course, when incessantly plugged into BSM, is supposed to perpetually realize the promise of a zero-beta portfolio?

And when today, after implied volatility (which is a cold slap in the face to performativity), Ayache gives Deleuzian PED’s to the BSM athlete, who then dynamically replicates at every tick, to what great topological feat do we bear witness? -The answer is, namely, that when differentiation gives you a glimpse of itself, right away the market maker must move to dedifferentiate. If partial objects can be used to continuously recalibrate, it is because of the increasing plasticity of certain financial assets; it is because certain financial assets have now acquired an augmented pliability, a hyperfungibility, an increased symmetry, i.e. their properties are isolable, they can be stretched and bent and squashed and torqued. Some financial assets are, in a word, isotopic, and some are homeomorphic.

Now, then, we wish to know (a) which financial objects are extrinsically the same, which are intrinsically the same and (b) what, if anything, this increasing regressive differentiation of financial assets means for the historical-materialist trajectory of finance as a dynamical system, as  a set of classes of exchange, as a series of markets, as well as the progressive differentiation of the objects populating them?

Indeed, it does seem that the whole edifice of modern finance is greatly illuminated when refracted through the ontology of topology. It for this reason that in Part II we will examine financial exchange under its light.

Outline of IV Parts

Part I. Mathematical Derivation

Part II. Financial Derivation

Part III. Dynamical Systems Derivation

Part IV. Financial Derivation

[1] David Richeson, Euler’s Gem (pg. 173). All mathematical examples are drawn from Richeson.

[2] Euler’s Gem. All subsequent figures are drawn from Richeson.


N sonatas and their singularity: the Devil’s Trill

This week SpecMat is commencing a series of posts, which will fall under the rubric “Can Exchange Cause Change?”, to supplement our reading of Difference & Repetition as heterodox political economy (Deleuze’s Guidebook to Synthetic Finance). Its general aim will be to examine the ontological homologies between topology and finance. However, in the course of our thinking and research for these posts, we were listening to William Bolcom (Graceful Ghost Rag is my desert island song), then Jeff the Brotherhood, and then finally Tartini’s Devil’s Trill. Why do I say this? –perhaps I should let Tartini tell you.

Tartini tells us of his peculiar dream. Tartini relays that he dreamt he’d contracted with Devil, who’d now taken up residence at Tartini’s house as his servant. Smitten with the Devil’s diligence in his duties, Tartini lends the Devil his violin, who, Tartini implies, had never played before, but proved to be –as one can imagine– a very quick study: he played masterfully. This was all very surprising to Tartini, but proved unremarkable when compared to the profound beauty ‘of art and intelligence’ flowing forth from out of the Devil’s inaugural composition (in Tartini’s words: ‘ I felt enraptured, transported, enchanted’).

 Tartini suddenly awakens from his dream.

 Tartini leaps out of bed, and rushes over to his violin, in order that he might capture the Devil’s sonata before its non-extrinsic impression vanishes into the daylight.

 Tartini composes and composes. Tartini rests. Tartini composes and composes, and then rests some more. Tartini starts over. Then over once again. He repeats his attempts at capture again –but each time always in vain; the singularity of the Devil’s Trill eludes him. This goes on for several days, weeks, months, and finally years.

Each composition by Tartini –actualized, extrinsic, concrete, and in its own right –is slightly different than the last, each will have been slightly different than the next; each individuated composition is marked by its own specificity in the actual, but always tied by birthright to a silent structure, that nonphenomenal but very real deep structure which is neither actual, i.e. not subject to the globality of demands made by the actual on its objects, nor is it potential, i.e. it is not subject to a probability distribution. Each of Tartini’s individuated versions of the Devil’s Trill is, of course, actual; and each, of course, will have been subject to a potentiality, which gets refracted through itself and then dumped out into actuality. But this singular sonata composed by the Devil –what is its ontological status if it is neither actual nor potential?

 There must be some register of reality, some name, some term for this register by which we can refer to its singularity, its reality as an incorporeal effect of the material processes of Tartini’s dream. The term we give to the Devil’s singular sonata is ‘the virtual’.

 In “Can Exchange Cause Change?” we will observe that and how topology also concerns itself with the virtual. So too obviously does Deleuze. But does finance? And if so, how do we go about thinking, talking about, and analyzing it?


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.