The quantum Marxism of laruelle

In his essay „Marx with Planck“, Laruelle calls for a Marxist gnosis and consequently calls himself not a Marxist, but a Marxist oriented towards the future, who is in search of an aleatory teleology that has no connection with what Marxist philosophy has so far provided as a measure and method for Marxism. Laruelle in no way retracts the distinction between a Marxism as a sedimented tradition with a multitude of authors, to which he himself belongs, and a Marxist philosophy with which one believes to this day that one can return to an authentic Marxism, that is, to its philosophical origins (which are repeatedly tied to Hegel). The disentanglement of Marxism from Hegelianism, as intended by Althusser and Henry, for example, was not entirely successful for Laruelle, who remained trapped in a positivist structuralism with Althusser and a transcendental and egological immanence with Henry. While Althusserianism ended up in the all-too-familiar playground and battleground for Marxist intellectuals, Henry gave the seminal signs of a Marxism for Christians. For Laruelle, however, Marxism is neither a purely structural science nor a transcendental philosophy, but a gnosis.

Why does Laruelle use quantum theory for this in the fifth stage of non-philosophy? He first gives two reasons for the general use of quantum theory: 1) its hard, technical modeling and extension into other fields in physics, and 2) its use as a new model for a rationality related to the human sciences, i.e., its conjugation (complex mapping) with a theoretical-experimental field (aesthetics, ecology, Marxism, etc.).

The second modeling involves a certain theoretical and especially a mathematical simplification of quantum theory beyond its non-negotiable core, which is the mathematical minimum of any science. And this modeling is also the basic condition for a futurist philosophical practice, namely as a thought experiment under minimal algebraic conditions with and within the philosophical material; Laruelle wants to conceive a complex conjugation (mapping compatible with addition and multiplication) of quantum theory and Marxism, a connection totally different from all the connection of the ideas of a Marxist philosopher with the ideas of Marx occurring in history. The new theoretical construction of Marxism envisaged by Laruelle affirms, on the one hand, the fundamental principles of quantum theory and, on the other hand, allows it to act as a Marxist material within a philosophical horizon, but not conceived in its Hegelian form. The construction of an inseparable Marxist-and-quantum-theoretical problematic arises on the basis of two entangled theoretical impulses that change the formalism of philosophy without changing its materiality. This in turn requires the liberation of certain quantum theoretical components from their mathematical apparatus, thereby reducing them to a vectorial apparatus, while at the same time depriving the philosophical components of their sufficiency.

Laruelle is thus concerned with a non-structural quantum modeling of the elementary foundations of Marxism and its philosophical contexts. In this way, the history of Marxism is no longer to continue as the object of an endless hermeneutics, a hermeneutics that hopes at some point to return to a true understanding of Marx after all, but rather both a radical transformation of the theoretical foundations of Marxism and a new balance between science and philosophy are sought. How can Marxism be freed from the dialectic, its appropriation by humanism, and the dramatization by philosophy that have hitherto defined all its philosophical approaches? For Laruelle, besides Hegelianism, especially its macroscopic rationality and the Marxian references to Newton have to be deleted. Only then can the desired superposition of Marx and Planck and a unified theory (not a synthesis), freed from the philosophical choices and the unnecessary accessories, finally result in a renewed non-Marxism or non-standard Marxism. Moreover, the unexpected encounter of Marxism with quantum theory also enables the renewal of its gnostic aspect. Marxism today must take up the most innovative variables of philosophy and science, the first element of which is quantum theory.

Laruelle first dedicates himself to the famous relation between productive forces and relations of production, conceived in traditional Marxism as contradictory, i.e. as a unity and struggle of opposites. Both components (productive forces/production relations) are not simple variables in Marxism, but these are always relations themselves, although the former seem to be an entity, so that one has to do with a techno-scientific body in relation to the production relations, which are understood as the relation par excellence. To subsequently think of the relation between productive forces and relations of production as culminating in a fusion or synthesis (mode of production) is far too simplistic a concept; rather, the relation between two variables should first be generally construed as two inverse becomings (coherence/coherence) rather than as a relation between two types of isolated bodies. These two processes are equivalent to the variables, since the becomings are such of the relations of the variables.

Laruelle now introduces the notion of superposition into this problem. It says that a third wave is added to two waves in such a way that all waves remain of the same nature. Here the thinking is not oriented to the object, but to the amplitude of the waves. Superposition is irreducible to philosophical synthesis and as a materialized thought it consists not simply in the superposition of mere variables but in the superposition of coherent/incoherent becomings, i.e. the becoming of relations between simple variables.

The old Marxist concept of fusion or synthesis is still far too philosophical a concept, resulting on the one hand in empiricism and on the other hand in a transcendental type of synthesis, a concept that should definitely be replaced by that of superposition, that is, the vectorial and complex addition of two variables. The law of quantum fusion is not that of the connection between the macroscopic and the microscopic under the condition of a unitary measure, because this would also be nothing more than a transcendental synthesis. The „fusion“ of the productive forces with the relations of production should be thought of from the beginning as a superposition or addition of vectors, with which we are in the realm of formal and not at all of empirical science: One adds the vectors representing the productive forces and relations of production, only then to arrive at two types of superimposable empirical data.

The superposition inheres an indeterminate existence and has the quant as its essence, which in turn determines its virtuality. The quantum itself is decomposable into different types of heterogeneous dualities, which in turn are developed by it (bourgeoisie/proletariat; market/organization; relations of production/productive forces, etc.). However, for Laruelle, the essence of the quantum is the class struggle, whose ostensible phenomenon is the struggle of classes. The class struggle here takes the generalized form of two inverse relations, that of dominance and orientation (relations of production><proletariat, etc.). In the class struggle, quantum Marxist rationality is always subdivided within the framework of the science of history.

Laruelle sums up at this point: If superposition is an addition of abstract vectors in a Hilbert space, then quantization is a problem of relation between two methods of measurement or it includes the two becomings themselves (coherence/coherence), where the problem of orientation concerns the vectors and not the real numbers. Each measurement is directional and can be played off against another.

Non-commutativity must then be introduced between the two becomings in the last instance. Laruelle also borrows the principle of noncommutativity from quantum physics. It says that two inverse products or physical quantities cannot be equal and exchangeable at the same time. However, there is not only inversion between variables, but also inversion of products of variables; these are always to be understood from the point of view of their non-commutativity. Non-commutativity is a universal factor that applies to any variable in relation to another and moves unilaterally in all possible directions.

Class struggle, too, is to be understood as the non-commutativity of its variables. The true quantum (not the substantial or empirical quantum), namely the class struggle, involves non-commutativity as a general divisor. Moreover, the quantum is an abstract force that afflicts all possible relations and not merely a single relation. Thus Laruelle can grasp the class struggle as a kind of quantum night equivalent to the quarter-turn or imaginary number (1); it is universal and stands for every relation, it is the condition for every revolutionary aleatory, it requires a kind of transcendentality that functions as under-determination. It radiates simultaneously in both inverse directions and simultaneously in all directions. Therefore, one can never remain in a single unilaterality, for example, neither that of the market nor of the organization, even if these factors even define its possibilities.

Why is there both division and self-multiplying relations in class struggle? And is class struggle always dominance and struggle? If there is a science of class struggle, then there are relations and two different methods of measurement that are non-commutative in their result. Quantum theory requires non-commutativity, the inversion of two relations as functions of two methods of measurement, and this non-commutative inversion is the origin of struggle. Therefore, the class struggle has nothing of contingency or chance, rather it is absolutely necessary in the course of the quantum model of history.

And there is another moment added: the imaginary number as the square root of -1 creates a non-commutative class struggle with a minimal philosophical transcendence and this finally itself (depending on the superposition and vectorial addition). The imaginary number is the ground of sub-determination of superposition (not over-determination) and contains the element of dominance and struggle at the heart of the unity of relation, and this means that the struggle is unfolded within the great transcendence of 1=1. There is a double transcendence to report here, that of the superposition of the virtual elements of representation and that of the quantum variables traversed by the imaginary number. (The transcendence of superposition results from the philosophical mode of potentialization).

Laruelle thus introduces quantum theory into Marxism by means of the form of superposition, which is itself a processive quantum operation via a complex vectorization. Laruelle’s intention here leads to a hard scientific modeling explicitly directed against the exclusive dominance of philosophy and the many neo-Marxisms in Marxism. Marxism, according to Laruelle, must necessarily be connected to the imaginary and complex operation of quantum algebra by writing a fiction of Marxism that strictly refrains from attaching to Marxism a supplement, a deconstruction or a micro-politics, because all these additions remain in the last instance philosophical additions.

1.Objection: Just the mention of Deleuze/Guattari and Foucault with regard to micro-politics will show us that Laruelle falls short here, because at this point he remains in the philosophical context much more than the authors mentioned.

How can a new fiction of Marxism be written? Laruelle understands the relation between productive forces and relations of production in the context of a historically existing economy as stages of a quantum system. One can superpose them by reducing them to state vectors and to complexities or imaginary numbers (square root of -1). The classical type of synthesis or fusion here is no longer dialectical, but neither is it deterministic in the sense of a fusion of productive forces and relations of production under the dominance of the latter.

And Marxism is now itself deployed as a vector rather than within the framework of its empirical or macroscopic specificities. As a result, synthesis or fusion is conceived as an indeterministic and virtual „fusion“ of state vectors that contain all the possibilities or potentialities that can be actualized in the context of a revolutionary and aleatory process, which in turn takes place inside a particle accelerator or inside a socio-economy represented by the quantum apparatus.

Laruelle again comes back to the afflictive dualism of dialectical materialism and historical materialism that he has mentioned many times before. Laruelle rejects the duality and the Hegel-oriented privileging of dialectical materialism and with this move conceives historical materialism as the basis of a possible and universal knowledge of historical phenomena. Corresponding to historical materialism is the universality of quantum modeling, especially superposition within the framework of a science of history. And the class struggle is the essence of a given socio-economy, the minimal quantum responsible for there being history at all, or, to put it another way, the class struggle is the quantum from which a science of history becomes possible at all and has an object.

Now, which of the two axioms of quantum theory – superposition and non-commutativity – has priority for Laruelle? Superposition is the form or principle of knowledge, the formalistic fact or its existence as the reality of science. It comes within production of knowledge before the quantum, which is its material ground. Non-commutativity, in turn, is an essential property derived from the quantum insofar as it is the index of the minimal existence of a material for the sciences and must be treated within an apparatus and, moreover, is needed for theoretical use in determining two variables with inverse products. Let us summarize it with Laruelle like this: Quantum theory substitutes for the old dialectic, superposition substitutes for totality, and the quant substitutes for the commutativity of philosophical dialectic. Equipped with these new tools, historical materialism takes over the formalism or reality of any science, including that of history, with dialectical materialism retaining its usefulness with the contingency of the quantum representing the essence of the material.2

A more concrete version of the axioms discussed thus far must now include humanity by forming the connection of the revolutionary duality of the bourgeoisie/proletariat variables – a connection that constitutes the aspects of the quantum and its human results. This involves the fusion of the masses with theory, both struggling in a non-hierarchical and non-commutative manner. As one element takes up the other, different effects or possible outcomes occur, constituting the aleatory dynamics of history. Within a generic science, the quantum can no longer be defined in the way Planck did with the constant for physics, but the quantum must be defined in the context of humanity divided into bourgeoisie and proletariat. Now, in order to arrive at the immanence of the revolutionary process itself, an externally fixed constant must be rejected; instead, a constant must be installed that is the subject=X, while continuing to consider the two variables (bourgeoisie/proletariat) that are sent into the quantum apparatus of history. Now, what establishes the science of history as reality, that is the contingency of the quantum that constitutes capitalism and its internal struggle (it is not about the real that defines the form of science as superposition). The class struggle is contingent in its relation to the essence of the sciences, but there is nothing contingent about the scientific definition of the object, even when it manifests itself as an effect of the struggle. (The object includes the identity of the struggle of the classes, which holds the counterparties together, through division).

Non-standard Marxism in this context is a scientific productive force, inseparably a quantum, and is on the level of the quantum of humanity, which as a relation of production is inseparably bourgeois and proletarian. For Laruelle, there are multiple interpretations of this matrix, into which one can always implement new disciplines. This matrix does not tolerate hierarchies, but demands equality between theory and masses within a generic theory, in order to eventually be able to generate a new collective subjectivity. Laruelle proposes at this point an interpretation of Marxism that is more epistemological than economic and more aligned with those Marxists concerned with struggle and humanity. However, one risks an interpretation that runs parallel to economic theory and its materialism by favoring the productive forces, which are now no longer economic but scientific and positivist.

2nd objection: Laruelle’s relation to the analysis and critique of the economy of capital remains indeterminate, since he himself has no concept of capital. He thus inevitably remains in the hegemonic problematic of philosophy that he has just criticized.

Further, there is the problem of determining the fusion of variables, a determination that decides their relative effects and or orientations. Within a philosophically oriented fusion, where one term fuses with the other term ( both as simple variables), the division into two occurs, and the fusion is always overdetermined. This creates an indexing that verticalizes or transcendentalizes the fusion. Within a scientifically oriented Marxism, on the other hand, the problem of economism in the sciences or scientism, mathematical or set theory, is more likely to arise. Laruelle wants to break with these versions of Marxism by recognizing the equal status of variables, which here are nothing but (complex) variables and remain so within relations that are underdetermined and non-communicative. Is there not now, after all, the version of a third term to report, which takes the function of a determination? Yes. It is that of the sums of variables via superposition, insofar as it persists in their products. (Neither science nor philosophy determine fusion in isolation, nor can they actualize it). If the integrated sum of the inverse products or the two aspects of the quantum are sent into the quantum apparatus, being treated in it in the style of a revolutionary aleatory, if not as an aleatory revolution, then it still remains necessary for this apparatus to exist insofar as it forms a universal closure via superposition, namely that of a particle accelerator or as a closed theoretical locus that can simulate at least a quasi-transcendental dimension of the apparatus.

Marxism now becomes a quantum itself and remains definitively anti-Hegelian by recognizing at least a sub-determination for every aspect and relation (via superposition). The determination now comes back in the form of a particle accelerator, which one is perhaps too quick to say represents nothing more than the sciences. But this particle accelerator is a quasi-transcendental apparatus, inseparably scientific and philosophical, in that it accumulates two properties in a superposed stage. This is an interpretation that affirms the primacy of an immanent formalism, insofar as superposition is not an external factor in the experimental field, but the quantum itself, the form of the science of history as its material quantum.

Laruelle discusses this kind of determination as a sub-determination. He distinguishes a) the unilateral and positivistic under-determination of fusion by the sciences – presupposed here is quantum theory, which is used in a wild way, b) the unilateral over-determination by philosophy, and c) the universal under-determination within and by the particle accelerator, which conjugates the unilateralities of the two variables and retains as generic finally what remains of fusion. This last subdetermination Laruelle calls determination-in.the-last-instance. Simple unilaterality is here distinguished from superposition, which is not unilateral, although it is virtually a third term, but as the form of a result that is not triangulation. Superposition does not result in an autonomous third term of a structure, but persists in an integral way within a scientific-philosophical closure by subtracting itself not only as unilateral, but as a complete subdetermination, i.e. by the addition of complex numbers within the superposition and then by their multiplication within the quantum. The particle accelerator invalidates the particulate or undulatory product coming out of it. But the devaluation pulls it down itself to the level of the base and center of gravity, owed to the complex or imaginary numbers, as if a building were collapsing in its own ruins, a break in equilibrium, a devaluation within the transcendental process of exaltation. The quantum particle accelerator thus creates a new space.

The complex form of science still stands on one side and its matter on the other side. But the formal ground as superpostion and the material ground as quantum remain insuffcient with respect to the constitution of a generic theory, if they remain separated on their respective sides. Laruelle therefore now introduces the efficient ground as a group that assembles the quantum apparatus by taking the initiative within its materiality and its function. This group is the subject of generic Marxism as agent=X. The agent forms a part of the apparatus, it belongs to it despite external conditions, given the immanent probabilistic effects of the apparatus and the structuring by its own quantum becoming, appearing as an equivalent of the final ground, which is in fact, however, an aleatory ground. Now what produces the apparatus? Potentialities (within the indefinite superposition) which become real or actual when the apparatus exists.

3rd objection: Laruelle cannot think the outside.

The subject of Marxist theory is ambiguous for Laruelle: a) the superposition of a collectivity of individuals within a particular socio-economy and its social and historical changes, b) duality of the bourgeoisie/proletariat variables conjugated in inverse and indeterminate products to form the anthropological quantum, c) the subject=X that the variables actualize from their virtuality. Laruelle sums up that the quantum theory of history must accept the indeterminacy of the results of the struggles.

4th objection: at this point Laruelle lapses into a democratizing humanism.

The ultimate stage of non-standard Marxism is reached for Laruelle with the speculative (and no longer formal) particle accelerator of history. This simultaneously conceives of all physical givens and singularities as theoretical objects or corpuscles, starting from the initial quantum, which is divided and multiplied by itself to achieve the potentialization of the quantum’s immanence. This has effects not only on the quantum, but also on the superposition, which is now also potentialized. There are two stages of superposition: the primary, which results in two micro/macro becomings, where the material remains empirically given and the formal becomes only through the form, and then the secondary and complex superposition, which traverses not only the form but also the material and leads to an absolutely immanent quantization. The superposition and the quantization are either those of the simple variables (formal quantum theory) or they are potentialized and then possess a formalized empirical matter, that is, doubly formalized vectors, through the form and the matter.

In the second part we will proceed to the formulation of the objections in order to get closer to the conception of a real quantum Marxism, which is certainly to be preceded by a non-.

1) The quarter turn stands for the geometrical representation of the complex imaginary numbers and is denoted by the square root -1. A complex number has two parts: a real part and an imaginary part, for example 2 + 3i. In geometry, if you draw a real line and put an imaginary line at right angles, you can represent the complex number as a point on the graph (with its two axes). Multiplying a number by i and rotating the line clockwise 90 degrees from the origin, that is considered equivalent here. Further it can be written: 1 * i = 1i, 1i * i = -1 Because the square root of i is -1, so n * i * i = n * -1 = -n. Exactly this is the „quarter-turn“. To capture it briefly and succinctly as a circular form: The real becomes the imaginary, the imaginary becomes the negatively real, the negatively real becomes the negatively imaginary, and the negatively imaginary becomes the real.

2) Althusser’s thesis that certain answers precede certain questions points to the fact that the answers of quantum physics precede classical problems via their aleatory character; these answers are apriori incalculable, and this characterizes superposition, which contains all potentialities for synthesis or fusion.

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translated by Sylvia John

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