Laruelle strives for a non-philosophical or generic machine that combines a philosophy robbed of its sufficiency (without comprehensive transcendentality) with a quantum physics robbed of its mathemathical apparatus (without calculation). The turning out of the non-standard philosophy from the philosophy and the non-philosophy results for Laruelle in the generic science, which itself has to develop a method to produce the superposition (overlapping) of science and philosophy under the dominance of the former, whereby as results of this methodical operation qua the use of such instruments as hypothesis, deduction and experiment aspects and theorems are to be aimed at, i. e. i.e., regulated, comprehensible and “correct” interpretations and transformations (utterances) of the scientific and the philosophical material. (Laruelle 2010b: 262) Any scientific or philosophical discourse has a certain materiality and syntax; the text itself, according to Laruelle, is a place with fixed parts and at the same time it needs moving parts at least as its inputs. In doing so, Laruelle’s methodological operations do not remain fixed on a singular term as an anchor, as is still the case, for instance, with Badiou’s empty set; rather, they capture the privileged operators of any theoretical material and strip its operators and the material itself of unnecessary representational ballast in order to use it for a new purpose. The result is what Laruelle calls “radical concepts.” At this point, he finally speaks of the “non-Mandelbrotian fractal,” which is stripped of its geometric and algorithmic requirements in order to give a non-technical meaning to the term “fractality” and eventually redirect it into a generic interpretation so that it indicates a figure of indivisible self-similarity that acts as a pseudonym for the real. (Cf. Laruelle 2014: 116 f.) Stripped of context, emptied of content, the generic term serves less as the cornerstone of a conceptual architecture than it indicates a kind of weak force of identity: it serves as the emblem of underdetermination. This implies that the concept and the real are ultimately the same thing, but not as an identity, but superimposed (superposition) in a milieu of interference and idempotence. Now what can a “non-Mandelbrotian fractal” mean anyway? Anything that is considered to be one according to its generic fractality and its overlap in the real. (Ibid.) Whereas for Badiou the minimal term – the empty set – is an absolute minimum (a structuring force), for Laruelle the generic term is only relatively minimal: just minimal enough for (theoretical) circumstances, conjunctures, and models that vary depending on the situation and therefore allow for multiple generic operators.
Laruelle uses two universal quantum principles or quantum axioms, superposition and non-commutativity, in his current writings to represent generic science. (Cf. Laruelle 2010b) Here superposition is understood as a continuation of radical immanence and non-commutativity as determination-in-the-last-instance. (Laruelle 2013a: 126) These two principles express the Real for Laruelle (not the One, which here assumes a metaphysical status), they immediately provide the Real and the syntax. The economy of the generic machine consists in the organization of the material according to a “quantware” (instead of software), which in turn participates in the material.(Ibid.: xxv) However, Laruelle does not always seem to be quite clear to himself in his formulations, for instance when he speaks of the “wave/particle superposition” and at the same time of the “determination-in-the-last-instance”, or of the “unilateral duality” and at the same time of “complementarity”, or finally even of “unilateral complementarity”. Whereby the latter turn is obviously a problem, insofar as Bohr`s concept of complementarity does not refer to determination at all, but to vagueness and indeterminacy. “Unilateral complementarity” for Laruelle includes diverse dualities which refer to the primitive duality wave/particle. The essence of the primitive wave/particle duality for Laruelle is unilateral duality, favoring the wave, and precisely not dialectics or indeterminacy as in Bohr. Thus, the two variables can be reversible, but this always from the point of view of their unilaterality. With respect to the determination or the unilaterality, one can keep the term complementarity as a supplement, as far as the particle of the wave (and its radical immanence) is added, which under-determines it. Unilaterality includes the One as One-in-One, a radically immanent being, or is itself given as the property of the One as One-in-One.
So, according to Laruelle, quantum superposition, which includes a relation or better a uni-lation, should first be thought of the waveform or rhythm (as a temporal pattern), which can be characterized by the parameters of time, space, frequency, amplitude, and just superposition. The rhythm integrates the superposition of the waves and their molecular motions, where multiple undulations can cross, absorb and thread into each other. Consider, for example, the waves on the beach, which are not entities; rather, they are currents flowing extensively in space. When two waves overlap or superpose, the amplitude of the resulting wave (which is neither a synthesis of the two waves nor a “new” wave) is a combined amplitude of the first two waves, i.e., the amplitude of the second wave is added to the first wave, and the result is a wave with combined amplitudes, the superposition of the two waves. (Cf. Barad 2015: 88f.) The thinking here is not oriented to the object, but to the amplitude. It is about the idempotent addition of two waves, which remain waves of the same type. Superposition can be either constructive or destructive with respect to two concrete wave phenomena or abstract objects (complex numbers). It is valid to add that the superposition leads neither to an identification of two corpuscular identities, which are added, for instance, to form a whole, nor to a supplement, which wants to transcend a whole by its différance, but just to a singular wave at any time (interference). Laruelle also borrows the principle of non-commutativity from quantum physics. It implies that two inverse products or physical quantities cannot be equal and exchangeable at the same time. There is indeed an inversion of the products of variables, but this always from the point of view of their non-commutativity. In this respect, unilaterality applies not only to two terms, but to four terms. (Laruelle 2013a:94) Now, if one inserts the principle into a unilateral order, then it is said to be generic.
To the quantum physical principles of superposition and noncommutativity Laruelle adds the term idempotency. The term idempotence stands for a quasi-mathematical rule originating in computer science, which is used to describe the superposition of two waves into one (1+1=1). Idempotency is in no way to be understood as a mere addition or as a multiplication by means of the unit of number, nor does it lead to the synthesization of the two waves in a third wave, but it states that the waves always remain the same waves. Idempotence thus includes the algebraic property of certain operations (A + A = A) and is interpreted by Laruelle as the phenomenological property of superposition and its immanence. It can also be called the principle of undulation or the apriori form of the particle. Undulation here always refers to the subject of “quantum wave and particle”, the latter in contrast to the corpuscle (individual body). Laruelle does not prefer the particle to mathematical quantum mechanics, but the wave, and he also distinguishes the corpuscle from the particle, which has a generic form. Wave and particle are the same and/or distinguished, i. e. there is the wave/particle form according to an objective appearance. Wave and particle are not the same insofar as there is the non-commutativity between wave and particle. They are different insofar as the wave is a radically immanent phenomenon (superposition), and the particle stands for the excess of a simple transcendence which does not remain closed to immanence.
It should be clear that Laruelle conceives the quantum principles neither as principles of a first philosophy nor as positive principles of mathematics/physics, but as in-the-last-instance determinative (more exactly under-determinative, because purely formal) positings, which are always to be applied according to the real. And generic science has to operate by means of these two principles in such a way as to produce more complex results than the materials it uses from science and philosophy, if it is to develop its own theoretical practice, that is, to establish a relation between sciences and philosophy in the immanence of a “logical” connection that Laruelle calls “unilateral duality” (under the dominance of generic science).
In his current writings, especially in Philosophie non-standard. générique,quantique, philo-fiction, Laruelle mobilizes for this kind of theoretical practice a series of terms from quantum physics, in which, however, he refrains from mathematical-quantitative articulation. At this point, a generic “quantification” of philosophy involves at best a science-in-numbers without calculation. In this way Laruelle finally arrives at a vector or wave-particle conception of concepts. By this he understands conceptual quantum phenomena which are to be classified as virtual and do not refer to reality but to the real qua the immanence of the same – the real for which the principles of superposition and non-commutativity as well as idempotence are unconditionally valid. These principles are intended to enable theoretical practice to hypothesize, describe, and experiment according to the Real. (Cf. Laruelle 2010b) Accordingly, generic science would be understood as a second-degree quantum theory or the quantum physics of macroscopic objects. (Ibid.: 141) The generic method operates by extracting a minimum invariant from the various scientific disciplines or philosophies, such as the imaginary number from calculus, the wave from quantum physics, the transcendental from philosophy, capital from economics, and so on. These invariants have to be superposed, or, in other words, they have to be introduced as theoretical givens into the mode of superposition. The materials of science or philosophy are thus to be supplied to a material, conceptual formalism, i. e. they are themselves to be put into the mode of superposition as vectors, that is, into the context of generic science, which operates with the (vectorial) notion of wave rather than with notions such as corpuscle and point. The real theoretical facts are treated, as it were, as vectors in the superposition state, which in quantum physics is indexed by the imaginary numbers. The vectorial dimension is introduced by the imaginary numbers, and this means for Laruelle that the theoretical facts on the complex plane are represented as vectors with a real and an imaginary part. (In quantum physics, one indexes the vectorial dimension by the complex imaginary numbers – they are vectors with a real and an imaginary part).
Let us take, for example, the laruelle conception of the “quarter turn”. It 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 negative real, the negative real becomes the negative imaginary, and the negative imaginary becomes the real.
The wave function combines symbols that come from philosophy (one, being, other, multiplicity, givenness, etc.) or come from science and are “touched” by imaginary or complex numbers, so that eventually a “quarter turn” or circle is created, or to put it phenomenologically, a unilateral duality. This is always an undulatory process and not the addition of stages. Often one speaks of a vector stage, but the vectorality of the vector is itself a process and just not the stage or the object of a mathematical operation. As part of the vectorial form of immanence and transcendence, the “quarter turn” constitutes the pre-andulatory substance, or at least it serves as a material or material implementation. Thus, it is considered as a generic element of undulation: to the generic superposition of the “quarter turn” with itself and the superposition with the wave, moreover, the components of directionality and transformation have to be added. At this point Laruelle hastens to point out that within the generic matrix (the connection of philosophy and quantum logic as variables existing in radical immanence, even in the sense of a rhizome) the variables are to be understood as terms or concepts rather than (imaginary) numbers, now assuming a complex or imaginary function of terms (the aspect of fiction). (Laruelle 2014: 159) This is not a matter of solving equations with a number that is neither positive nor negative, but Laruelle is certainly circling around a philosophical problem, albeit one that mathematics itself raises.
The vector is characterized by the two operations superposition and addition (addition of the arrows), whereby by no means a closed whole is urged, but unfinished summations are aimed at. What remains decisive here is the first term, which refers to the unilateral dimension of the vector or wave (immanence of relations as uni-lation; ibid.: 158), whereas the particle (second term) is immanently secured in the wave-like flow as a clone, in a wave-like elevation that suspends the transcendental-empirical doublet or the eternal cycle of time. The unilateral duality again represents the “set”, both on the side of the clone and on the side of the vector. The result is immanence, one-in-one bearing the two-in-one (clone=two). (Ibid: 178)
Laruelle would arguably contradict Karen Barad’s postfeminist, quantum theory-inspired conception of technology, by which she conceives of quantum mechanical indeterminacy in the course of recourse to Derridean différance, with terms such as relation, phenomenon, and folding in to define or sharpen the indeterminacy being important components of the concept insofar as the indeterminacy is relativized or cut. The generic, on the other hand, radically transforms relation into uni-lation for Laruelle, into a unidirectional process that never began and never ended and that has a matrix inherent in it; a transfinite process that radically reduces both the predominance of the scientific incision and the philosophically infinite. On the one hand, Laruelle wants to advance the conceptual elaboration of a generic matrix (ibid:170) that functions like a particle wave; on the other hand, he wants to use it to install a new generic thinking apparatus, two variables linked by inverse relations. The thinking apparatus is itself defined as a part of the generic matrix, whose variables thus include the objects and the non-philosophical and the quantum mechanical interpretation of the objects. Clonality here combines unilateral complementarity with virtuality, the writing of the clone, which is virtual in the last instance. In this, the onto-vectorial of the thinking apparatus itself generates a complex reading of the vectorial of the objects, and this leads toward an onto-vectorial interpretation of the theory as a model. (Ibid.: 170) These are vectors or imaginary concepts/philosophies that replace imaginary numbers. As a subtraction of any transcendence, the vector indicates the following: “The vector points to the surface of reality, which it tunnels through and mixes with before extending itself, returning to itself and creating the objective appearance of an An-Sich.” (Ibid: 176)
Now, for non-Marxism, this means the following: It defines itself on the theoretical level as a special formalism borrowed by Laruelle from quantum physics. But this cannot be mathematical quantum physics at all, insofar as the formalism in this context must be conceived as real-transcendental and not physical. (The quantum postulate here refers less to quantifiable economics than to knowledge of economics. It requires a material constant, and does so as the basis of a quantum way of thinking about economics). Laruelle calls formalism a theory guided by axioms or by matrices of axioms that a) is determined by the real, which is radically immanent; b) inheres a causality that is unilateral or that involves DLI; and c) finds its object in the world of ideas, in a philosophy complicated by experience. This is a non-theory or an impossible theory: formalism counts for Laruelle in particular as a theoretical style adequate to the unthinkable; as a form of theory made for what remains invisible within the ordinary levels of theory and forms of representation. And this requires a) the emptiness of any formal and scientific structure in a positive sense (Laruelle calls for a dualysis rather than an analysis, i.e. a conceptual deconstruction of philosophy); b) the material apriori of theory, which is ever already subordinated to the primary of the real and thus intrinsically unrepresentable, that is, that theory also abstracts from the theorist, who is unilaterally deduced; c) that, as the case may be, theory is close to the symptoms of Marxism.
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