Vector Theory: Epistemology, Political Economy, and Probabilistic Computation

Abstract This article introduces vector theory as a critical approach for understanding the shift from symbolic to probabilistic computation in contemporary AI systems. The paper argues that the digital turn organised meaning through discrete bits, Boolean logic, and hierarchical structures, in contrast large language models (LLMs) and diffusion architectures operate through high-dimensional vector spaces, cosine similarity, and probability manifolds. The three sections of the article examine the geometry of meaning, the dynamics of stochastic flow, and the political economy of the vector turn. These sections connect concepts such as vectors, tokenisation and generative AI to critical traditions from Marx through the Frankfurt School to contemporary media theory. Drawing on and expanding Kittler’s media materialism, Stiegler’s grammatisation, and Deleuze’s notion of smooth space, the article argues that existing approaches, developed under the paradigm of discrete digitality and symbolic logic, generate too many explanatory anomalies. The vector paradigm represents a new stage in the real subsumption of cognitive and linguistic labour, where capital reconstitutes language as geometry within proprietary vector space. The article connects this to notions of cognitive anaesthesia and the systematic “smoothing” of social friction, arguing that this potentially threatens the tacit dimension of critical thought, the very faculties required to diagnose the computational regime that produces it.