Now the processuality of capitalist machines releases complex, differential and problematic relations that have emerged historically through the contingent encounter or the external conjunction of generally decoded flows, the capital-money flows with the labor flows. (Cf. Deleuze/Guattari 1974: 287ff.) Since capitalism has generated its internal history, a continuous conjunction of money-capital flows can be observed, which has taken place in ever more violent spurts of deterritorialization, while today the “doubly free” workers and employees are comprehensively decoded in favour of the functioning of informational machines. With Deleuze/Guattari, the currently existing capitalism would have to be understood as an effect of the differential relations of capital itself, which have arisen from the historical-singular conjunction of the flows of money capital and labor. Only with the interaction (of the differentials dx/dy) are the two flows determinable within a symbolic relation, in that as decoded flows they constantly pursue their conjunction on the threshold of smooth space and thus drive towards their “true” determination, which Deleuze/Guattari ultimately describe as the filiative form of capital, in order to designate it with the mathematical symbol x + dx. (ibid.: 292) This formula symbolizes the production of surplus value, which is not only produced, but must always also be realized or absorbed. Just as in the reciprocal synthesis of the differential quotient within the constitution of the immanent idea the genesis of relations is also to be expressed, so the capitalist differential quotient reflects the flows of money capital and labor in capitalist reproduction processes: There is a direct transformation of surplus value in code, the differential quotient of capital, into pure surplus value in flows, the differential quotient of production, whereby this functioning of the capitalist differential quotient, as Deleuze/Guattari assume with Jean-Joseph Goux, is not heading towards an end of capitalism, so that every break, incision or crisis only ever shifts the internal limit of capital itself (after which it runs smoothly again, write Deleuze/Guattari), which thus manifests itself in the variations of the differential quotients. (ibid.: 293) Deleuze/Guattari write: “This is the differential quotient Dy/Dx, in which Dx is derived from labor power and is correlated with the fluctuation of constant capital, Dy is derived from capital and constitutes the fluctuation of constant capital” (ibid.: 292). The abstract capital machine appears as an immanently flowing system that carries out its operations in: time, whereby this can be represented on the mathematical level as a differential quotient, the gradual rate of change of the two flows in their relationship to each other, and this under the dominance of the continuously flowing money capital flows. Accordingly, capital is not an object, but can be described as a relation of flows, speeds and moving quantities. Although the flows can be cut into discrete units, in themselves they form continuously flowing, intensive quantities that are initially able to rise and fall without the external control of apparatuses, and it is precisely for this reason that new problems constantly arise for capital to master, which, according to Deleuze/Guattari, requires a permanent reterritorialization of flows by means of stratified axiomatics that are enforced by centripetal apparatuses of capture, which have developed historically via the inflation of the Hegelian state apparatus to the Foucauldian governance machine and the power mechanisms of central banks. According to Deleuze/Guattari, the abstract capital machine has a real/virtual status and determines all actualizations in the last instance, which of course also means that the real cannot be equated with the actual, because the virtual-real never quite arrives in the actual. With the introduction of new technologies or new compositions of technological codes, the extraction of machine surplus value has been added to the extraction of human surplus value in the course of the internal history of capitalism. The relation of equivalence that characterizes the commodity form always requires supplementation by the non-equivalent conjunction of capital, the relations between decoded flows of money capital, which first and foremost construct actual qualities (outside of this relation, the flows remain purely virtual). “This conjunction is at the same time the disjunction of the abstract quantity, in which it becomes something concrete” (ibid.: 320). The parameters dy and dx represent the pure quantities of labour flow and capitalization flow in the mutually conditional relations, whereby the latter, however, has an incomparably greater potency than the labour flow, so that Deleuze/Guattari speak at this point precisely of a relationship between potency (capitalization) and given quantity (labour).
Let us now turn to the concept of code. In their description of code, Deleuze/Guattari, like Baudrillard, often refer to the functioning of the genetic code, whereby they understand it less as a structure than as a kind of blind combination, a passive synthesis that under certain circumstances also forms a domain for opportunities or functions as a medium of real de-organization. In the economic context, code initially denotes a (binary) scheme and/or a form of graphematized inscription or the symbolic recording of money flows. (ibid.: 318f.) In capitalism, this occurs in companies in the context of double-entry bookkeeping, e.g. as a money-to-money transaction that takes place in the bank accounts of two companies. A payment check is an incoming flow, while a check issued to settle an invoice is an outgoing flow. The (asymmetric) code serves to translate flows; it is necessary in order to control the systems of the flow communicatively, whereby both semiotic and probabilistic components come into play here. Thus it can be stated in general terms that the relationship between flow and code is subject to the rule of reciprocity, because it is impossible to access a flow in any other way than with an operation that codes the flow, while conversely the flow demands specific codings. There are no flows without withdrawals, separations and incisions, without the corresponding machinic poles that encode the flows with the help of their specific recording surfaces, while codes themselves are transformed by the machinic poles creating new conjunctions to allow the flows to flow further and differently. In this context, the operation of decoding refers to the respective translation services, but the process of decoding can also imply the complete destruction of codes that have until then ensured the translation or mediation of flows. Coding thus operates through processes of recording, and in capitalism this takes place within the framework of economic mathemes, whether these are numbers on a paper bank statement or charts/formulas/markings on a computer screen.
Coding must be understood as assignments in which any content or context is erased. Payments or non-payments are made, regardless of who makes them and for what; the decisive factor remains purely the actualization of the schemes themselves, which set the either/or. Binary codes function as overarching schemata with which operations are handled in such a way that functionality is achieved by necessity. (Cf. Fuchs 2001: 159ff.) And these tertium-non-datur schemata exclude contextures, as Gotthard Günther, for example, has examined them, i.e. third possibilities by definition. Thus, these kinds of semioses function as nonsignifying signs; what is decisive is not what they mean, but that they release meanings at all, in order to functionalize the respective flows according to the rules in their indifference to all specifics. As a result, the code itself does not release any specific content, it does not fall back on anything like conceptual consistency, but in its function as an economic mathematic, the code always calculates with presupposed regularities, without paying attention to content-related meanings at all. If binary codes do not fix one of the two sides, but rather introduce contingency into the systems with their recordings, which they in turn inhale by functioning as pure yes/no oscillation machines, they nevertheless always remain related to the respective systems and their preferences and dependent on them. Thus, the decisive code through and with which the economic system in capitalism functions is the profit/non-profit code, which makes it easy to understand that the capitalist system must constantly process and filter its environment with regard to the question of whether profits can be made or not. And so it seems only logical that today the structural processes of capitalization encompass almost everything conceivable – money, credit, labour, institutions, knowledge and opinions, energy, genetic code, bodies, wars and friendships, etc. – which ultimately also means that the economic system remains blind to other systems in a certain sense as long as they do not serve pure exploitation. In fact, the coding here is increasingly shifting to one side, so that we tend to be dealing only with the reproduction of the same profit production, the sheer production and circulation of capital, the sheer positivity of the ever-same. And with symbolic money, which is structured quite differently from other symbols, the number of seemingly equally probable monetary capital flows and their relations is regulated with the help of an algebraic syntax that is equivalent to a quantifying computation of value creation, whereby the code itself in turn indicates an entropy, which is expressed, among other things, in the fact that there tend to be as many prices as derivatives on the derivatives markets.
In addition to binary digital codes, monetary capital flows are encoded in financial regimes via stochastic models by permanently calculating volatilities on the markets, and insofar as money functions via these codes, we are dealing here with objective functionalities. At this point, discursivity is clearly dominated by economic mathematics, whereby the actualization-virtualization circuits of (total) capital remain unpredictable, so that an open outcome is to be expected with regard to the futurization capacities of capital as long as synthetic money is valid. As a symbolic algebra, the code allows the transmission, transformation or reproduction of information, it enables its synthesis. Payment systems function in a similar way, although here the information is not predetermined, but is first produced anew with each recording. Just as capital drives decoding on the one hand, it must also permanently encode or axiomatize on the other, because the nightmare of capital generally remains an uncoded flow. After all, the relationship between flow and code must not be imagined in such a way that the flow appears first and then the code follows, for example by superimposing itself on the flow, but rather it must be assumed from the outset that what flows on and through the capitalist socius, can only ever appear in correlation with the code, whereby capitalism actually manages – this is its essentially new quality today – to substitute the codes with constantly replicating and expanding axiomatics, so that the machines are able to interiorize themselves into their own structure as a field of forces. (Cf. Deleuze/Guattari 1972: 299)
According to the classical definition, the axiom means an operative statement that requires no proof or derivation from other statements. Subsequently, axiomatics contains a system of axiomatic propositions. (The provability as a property of axioms has been questioned in philosophy since Kant at the latest). In modern mathematics, for example, the theory of extensional sets (Cantor) and its rigorous axiomatization by Zermelo-Fraenkel is considered an outstanding achievement, which Badiou, among others, uses for the explication of ontology in his book Being and the Event (Badiou 2005); for Deleuze, however, this is a thoroughly “royal” mathematics, against which he sets a completely different kind of mathematical deduction, namely problematic deduction. With regard to the former, consider, for example, the “royalist” definition of the line as the shortest distance between two points, while in Archimedean geometry the straight line appears as a case of the curve (in Euclidean geometry, too, the line is purely static without any reference to curvature). In a minoritarian or problematic geometry, the figures appear inseparable from their immanent variations, affections and events. Or consider the history of the differential calculus, the problems of which Leibniz and Newton recognized in the hypothesis that the integral with regard to the determination of a space was to be understood inversely to the question of the determination of the tangent by curves, before the problem was then rigorously retranslated into arithmetic terms in the 19th century. (Cauchy, Weierstrass, see: Smith 2013b) At the same time, continuous manifolds were transformed into discrete sets of numbers, and the geometric idea of approximating a boundary was arithmetized and axiomatized. The set theories of Cantor and Dedekind up to the definition of set theory by Zermelo Fraenkel (set as a finite set of axioms) also operate within this framework. However, it must also be recognized that the non-quantitative view of the differential calculus reaches its limits today when a new level of abstraction is reached with the numerical digital code.
Deleuze/Guattari base their analysis of modern capitalism on the term axiomatic, among other things, by showing how capitalism emerges as an “axiomatic of decoded flows”. (Deleuze/Guattari 1992: 628) This occurs with the permanent addition or subtraction of operative statements that concern “purely functional elements and relationships” and remain essentially unspecified, so that the choice of an axiom with regard to economic analysis initially means that essentially important terms, e.g. technical terms, remain undefined, since the attempt to define all terms would allegedly lead to an endless regression. As an operative method that requires no justification or proof, axiomatics attempts to create stable structures or systems by adding or subtracting hypotheses, norms, commands or even further axioms, which can be managed with unspecified elements and relations within the framework of a functionalization, whereby this type of pure functionality is always accompanied by further deductions of theorems and axioms. (Ibid.: 630) In economics, axioms should simultaneously be read as operative statements in the context of the immanent virtualization-actualization circuits of capital, but they should also be considered in relation to external models of realization such as the state. Axioms do not offer any surfaces or points of reference for exegeses, interpretations or commentaries; rather, as monetary writings they indicate the “immanent semiological form of capital” (without a totalizing instance or transcendent institution). (ibid.: 640) They comprise a set of statements, computations and rules that penetrate all machines of capitalization in order to calculate, control and structure the economic procedure in and with them.
Especially in A Thousand Plateaus, Deleuze/Guattari present axiomatics as an essential operation of contemporary capitalism (within their construction of a contingent universal history and a general semiology, see ibid.: 640ff.). Capitalism constantly repairs or regenerates itself with the help of axioms and attempts to overcome its antagonisms by adding further axioms, for example: “Thou shalt believe in the market system so that capital accumulation can continue unceasingly”, which, however, involves rather simplistic axiomatics; or when, for example, Keynesianism or the gold standard fall into crisis, outdated axioms of economics are replaced by those of neoliberalism or more complex axioms of neo-Keynesianism are added, which in no way modify the basic axiomatics of capitalism, but above all complicate its operations. Axioms include the fact that capitalism deals extremely flexibly with the quantities of money and social labor, which means that today we are dealing with the tendency to replace codes comprehensively with axiomatics, because the latter represent a much stronger force in terms of their power of appropriation than the codes, which are nevertheless always subject to reductions, for example by reducing them to a higher unity through transcendence or externality. The limited nature of political codes, which only ever bring about the regulation of relations between money capital flows and labour flows indirectly, by establishing control and conflict regulation through qualitative withdrawals, recordings and the steering of flows – this limited nature is today overcome by the hyper-capitalist form of neoliberal axiomatization, namely in that politics pays homage to the pure market-relatedness of all social institutions and conflicts, and this with the help of axioms, i.e. a set of equations, variables and conflicts, a set of equations, variables and parameters that have no reference to fixed definitions or quantities, which allows the respective variables and coefficients to be permanently recombined and thus fixed, at least in the short term, whereby it can also happen that a current becomes the subject of several axioms or has no axiom of its own at all and feeds on external axioms, so to speak. And every parameter that is supposed to allow a secure or standardized foundation of values can also be dissolved again, see the dissolution of the gold standard after Bretton Woods. And this happens as a continuous temporalization of axiomatics in the economy itself. There is therefore a constant demand for the addition/subtraction of axioms, because without the flow of axiomatics it would hardly be possible to establish the manifold relations and connections between the various flows of monetary capital. Despite the enormous power to deterritorialize the flows of money capital, which works precisely because of the extremely supple axiomatization, there are constant tendencies towards reterritorialization, for example through the formation of control functions of all kinds, through processes of subjectivation and state governance, the latter as part of the “realization models of a world axiomatics that goes beyond them” (Deleuze/Guattari 1992: 630). And Deleuze/Guattari wisely add that in capitalism you cannot get rid of the state, even if you try to transcend it. However, and this must be pointed out, this should not give the impression that axiomatics is the ultimate determinant of capitalism; rather, capital/capitalization itself cannot and cannot be determined by a single axiom or set of axioms, which is precisely why it constantly demands new axioms.
With their integration into the flows of money capital, which constantly flow from one pole to the other or multilinearly in multidimensional networks, securities are to be understood, among other things, as a stock, i.e. as legally codified property (we will see that this need not be the case with derivatives), which implies the availability of an account or the “value” of an investment. Stock defines the current value/price of, for example, a derivative at a given point in time, while the flow of monetary capital is characterized by the constant fluctuation of the stock over time. (Cf. Smith: 2013a) An input adds a quantity to the respective stock, while the output subtracts a quantity from the stock. A security as a stock calls for the accumulation or destruction of its value over time, it rises or falls in price, while the flow indicates the rate of change of the stock. And securities have a price at any point in time, which can be written down as a number, while the flow of money capital changes the price of the stock over time. In mathematical terms, the security as a stock forms the integral of the money capital flow, while the differential quotient denotes the variation of the money capital flow. (A flow variable such as the gross domestic product indicates in the dimension of billions of euros per year how large the goods and services produced in an economy in a year are, which, however, says absolutely nothing about the already existing wealth of an economy – stock variables. The interest rate, for example, is the ratio of a payment flow to a stock value: interest for an accounting period to the size of the loan at the beginning of this period. Anyone who confuses flows and stocks in this case is not mixing up pears and peaches, but they are mixing up pears and pear trees. However, the fact that flows and stocks are not directly comparable does not mean that they cannot be put in relation to each other). The analysis of money capital flows in particular allows us to understand the role of synthetic inputs and outputs on the stock markets more precisely: While money capital flows are in continuous variation, we only know about them through special recording systems. Finally, the flow-code-stock relation can be summarized once again in the words of Deleuze/Guattari: The flow promotes the connective synthesis of production, the code contains the disjunctive synthesis of recording or inscription, and the security as stock represents the conjunctive synthesis of consumption. (Ibid.)
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