Capitalism and Mathematics: An Interview with Giorgi Vachnadze Alessandro Sbordoni
19 February 2025
Giorgi Vachnadze is author of a new book, Christian Eschatology of Artificial Intelligence. It is a philosophy text that considers the relationship between psychoanalysis, religion and digital media. In what follows, he speaks in philosophical terms about his project in an interview with Alessandro Sbordoni.
Alessandro Sbordoni: In your book, you argue against the reduction of subjectivity to a computational model. To paraphrase Ludwig Wittgenstein and his critique of Alan Turing, computers are humans who only calculate without ever being required to think or feel anything. Nevertheless, consumers are more and more humans who only consume. Then, how do we know that we are not just consumers? How do we know that there is always a remainder to the calculations of the capitalist machinery?
Giorgi Vachnadze: The problem of consumerism, which we can one way articulate as the problem of normalized or hypernormalized desire is precisely the problem of utilitarian calculation within the domain of affectivity. Consumers are fundamentally humans who only calculate by plugging themselves inside the commodified channels of prescribed enjoyment.
What I find absolutely fascinating about Wittgenstein’s epistemic subversions within the domain of mathematics is that he paves the way for an alternative form of thinking. And he does this within a field of knowledge that is most often considered to be entrenched and unalterable. Mathematics is a domain of knowledge that is simultaneously (paradoxically) portrayed as politically neutral, while at the same time offering the most authoritative strategies for legitimating hierarchical structures (precisely because it positions itself as neutral).
What Wittgenstein shows precisely is that the remainder, or the Flesh as I refer to it in my book, exists not only within Capitalist Calculations, but within calculation as such. Contrary to Turing’s interpretation.
We can also speak here in Lacanian terms and state the problem this way: Wittgenstein exhibits many features of the hysteric’s discourse as he plugs himself within the Symbolic Order of the mathematical signifier, attempting to activate an encounter with the Real.
I am now working on what I hope is a new concept called Psychotic Transversal Machines, which I want to deploy as a tactic of resistance against the colonial logic of AI (Turing-Computable-Subjects). Here we can speak of a line of flight or an attempt to make calculation Transversal in the sense that Guattari uses the term. The interrogation of the notion of calculation is what creates the possibility of deterritorialization within the episteme that sustains Artificial Intelligence as a tool of capitalist exploitation, subjectification, and so on. In short, it is precisely what you said, the reduction of subjectivity to the computational model.
There’s a lot more to be said here, but I will stop here so as not to stray from the question too much.
AS: In the XIX century, mathematicians demonstrated that the fifth axiom of Euclidean geometry was false in spherical and hyperbolic space. This proof paved the way for non-Euclidean geometries and mathematical relativism. In analogy with this, do you think that capitalist and anti-capitalist calculations could be the result of a different set of axioms? And if so, might the materiality of the body and what you just called Psychotic Transversal Machines be the mathematical operators who rewrite the postulates of capitalism?
GV: That’s a challenging question! On the one hand, the Psychotic Transversal Machines (PTMs for short) are indeed supposed to show that the current forms of axiomatization are riddled with hidden biases and assumptions. But perhaps the wider implication here is that calculation is never context-free. Which, I hope, will bring up the question of how we are to think of formal systems as such? A kind of Genealogy of Formal Systems (another ongoing project of mine) if you will. I think this is quite different from what happened with the transition from Euclidean to non-Euclidean geometry in terms of continuity. From the perspective of Western science and especially the philosophical foundations of geometry, the break was actually not as radical as it is often portrayed. The basic ontology of space remains invariant within both Euclidean and non-Euclidean geometry; much like the move that took place from Newtonian to Einsteinian physics. Cartesianism is probably the most important assumption that needs to be questioned here, can we even think of mathematics as non-Cartesian? The problem here, I think, is not a matter of rewriting axioms but rather seeing that the “fundamental” ontology is a dispersed materiality of performative acts that can never be formalized.
What sustains reality is the absence, the lack, the turbulence of Flesh. And one forgets that even mathematical “truths” exist only because there is “some flesh inserted into them”. Psychotic Transversal Machines do not offer an alternative formalization or a new solution to a problem; instead, they incessantly generate and produce a never-ending stream of problems. They activate the turbulence of the Flesh against the hubris of systems that claim to be self-contained. PTMs show that when calculation goes unchecked we get the kind of planetary ecological disaster we call capitalism.
AS: To sum up, the materiality of the body is the proverbial spanner in the works of the capitalist machine. It hampers the flow of the system. But do you think another system will be produced from such an act of resistance? The word “turbulence” reminded me of the possibility of a new order out of capitalism, to repurpose Ilya Prigogine and Isabelle Stengers’ theory about the evolution of “order out of chaos”.
GV: Without a doubt, the danger of reterritorialization is always present. I am not entirely sure what you mean by “order out of capitalism”, but cybernetic capitalism entails the domestication of flows and “fluctuations” if we are to use Prigogine and Stenger’s lingo. Capital is precisely what imposes an order of things, and proceeds to naturalize it. Mathematically we could say there’s chaos and then there’s randomness. PTMs are geared precisely at exposing chaos as an imposed order; anything but a natural state of things, in order to activate the random effects of the Real. We want to politicize chaos. Then, it’s randomness that we want, not chaos, chaos is too benign. If we stick to chaos, we will definitely only aid the “healthy” functioning of the system, randomness is what really breaks the cogs.
AS: Or it produces a new gear… Maybe the machine is not broken, now it only functions differently. Do you think that technology and irrationality are always antonyms?
GV: I hate to overgeneralize, but I think they are indeed antonyms. In the Heideggerian sense, technology is what confronts nature from the side of rationality. Technology is precisely what turns randomness into chaos.
AS: It is important to add that the rationalization of labor was first developed by the U.S. military to produce interchangeable parts for their weapons. If the gun breaks, the spare parts must be ready at hand. The same technological protocols were then repurposed in the civilian industry for mass production. At the same time, the machines are more and more controlled by other pieces of machinery. The algorithm takes the place of the machine operator.
In an essay titled The End of Philosophy and the Task of Thought, Martin Heidegger talks about cybernetics and the rationalization of existence under the yoke of technology. But then, he argues that the only task at the end of philosophy is to question what is present as such. In light of this, is it meaningful, or even possible, to put into question the rationality of the system itself?
GV: It sounds like Taylorism. What’s fascinating is that Taylorism was equally effectively implemented in both the Soviet Union and the United States. Lenin introduced Scientific Management to the USSR. And we see the same thing now as you say, with AI, which is put to use by Putin’s regime no less effectively. Today the most general form of power seems to be the Algocracy.
An absolutely fascinating point which is made by Heidegger in the essay you mention is that cybernetics is the study of human labor (much like Taylorism), so we see a direct continuation in modes of governance, which is basically the definition of cybernetics (governance), as much as some scientists try to deny its obvious political implications.
Cybernetics is the mathematical optimization and regulation of human life. It is the latest mode of “coding flows” as Gilles Deleuze would have it.
Now, Heidegger states clearly that there still is a task to thinking that is neither traditionally metaphysical nor calculative or technological: to think at the end of philosophy – that is the central question. But this new kind of thinking, as he elucidates, will necessarily have to be uncertain. A kind of preparedness, perhaps even an anxious one. But most of all it is not, as traditionally, conceived of as a “foundational” or practical-scientific kind of thinking. So it will have to be a kind of disruptive force that introduces a discontinuity into Western science and metaphysics. Or what we can term “the rationality of the system” in the fullest sense.
I believe this is what Heidegger refers to when he calls for a need to make a clearing. And this clearing can only happen if we open up the possibility of its becoming present. So the present that Heidegger refers to can only be something that is irrational and random. It can in fact only occur within a space that is by all standards psychotic from a clinical point of view. Psychotic and generative; it’s a machine that performs a line of flight opening up a random event, heretofore unimaginable. Pathological even, by modern standards. It would have to perform very unlikely transversal connections between seemingly unrelated elements.
So we must not confuse this notion of presencing with the pejorative understanding of the word “present”. For Heidegger, the ultimate rationality of unconcealment, of the Greek variety of the rational, would undoubtedly be irrational by the standards of mathematical thinking offered through cybernetics.
So I would say, not only it is “possible” to put the rationality of the system into question, but it is the only strictly correct way of posing the question if we want to do philosophy that is worth anything.
AS: Thank you, Giorgi.
GV: Thank you.
Alessandro Sbordoni is the author of Semiotics of the End. He is an Editor of the British magazine Blue Labyrinths and the Italian magazine Charta Sporca. He lives in London and works for the Open Access publisher Frontiers.
Giorgi Vachnadze is a philosopher and scholar specializing in the intersections of Foucault and Wittgenstein with a focus on Philosophy of Language and Discourse Analysis. He is the author of Christian Eschatology of Artificial Intelligenceand teaches Literature, Philosophy, and English Language Arts at the European School in Tbilisi, Georgia.
