Preliminary notes on the Societies of the Vector and the Vidual
David M. Berry
"Each line is broken and subject to changes in direction, bifurcating and forked, and subject to drifting (derivations)." (Deleuze 1992b).
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| The Draughtsman of the Lute by Albrecht Dürer (1525) |
The vector medium produces a form of power I propose to call "gradience". This is a form of power that operates by probabilistic computation, which I have elsewhere called vector computation.[1] In this regime of power the operative function is the incline, the residue left by gradient descent once training has ended, along which thought slopes towards the dense fields of vector space (see Chatonsky and Citton [2026] for a discussion of the "distension" of memory and quaternary retentions as retentions of retentions). I suggest a new form of subjectivity that will emerge through this mediation which I call the "vidual".[2]
Foucault (2020) identified the individual subjectivised through the operation of discourses in and around institutions like the factory, the hospital and the prison, and Deleuze suggested the form of the dividual within the context of the control society operated through digital computers. As Deleuze explained,
The disciplinary societies have two poles: the signature that designates the individual, and the number or administrative numeration that indicates his or her position within a mass. This is because the disciplines never saw any incompatibility between these two, and because at the same time power individualizes and masses together, that is, constitutes those over whom it exercises power into a body and molds the individuality of each member of that body. (Foucault saw the origin of this double charge in the pastoral power of the priest-the flock and each of its animals— but civil power moves in turn and by other means to make itself lay "priest.") In the societies of control, on the other hand, what is important is no longer either a signature or a number, but a code: the code is a password, while on the other hand the disciplinary societies are regulated by watchwords (as much from the point of view of integration as from that of resistance). The numerical language of control is made of codes that mark access to information, or reject it. We no longer find ourselves dealing with the mass/individual pair. Individuals have become "dividuals," and masses, samples, data, markets, or "banks." (Deleuze 1992a: 5).
In contrast, I suggest a new form of subjectification in and through the operation of artificial intelligence, in both its autoregressive and diffusional forms as the vidual. Gradience gathers rather than assembles. Where control produced samples and banks, gradience produces corpora and neighbourhoods, and the vidual falls across a distribution, as weights and as points. There are no longer watchwords or passwords but tokens. What the watchword commands and the password allows, the token predicts.
Viduation
Where Simondon's (2009) notion of individuation captured the process by which a subject emerges from a pre-individual field in relation to a milieu, viduation attempts to describe what we might call the inclination of the subject, as a subject whose thought is always already mediated by vector space. Here cognition moves along a slope defined by the geometry of the mathematical constraints of latent space.[3] This is a subject that is constituted in relation to the very structure of contemporary vector computation within which it is co-constructed.[4] Where discipline moulded the subject and control modulated it, gradience inclines it, which does not fix a subject, nor vary it, but rather transforms the ground on which the vidual operates. We might say that discipline was periodic, as one entered and left the factory, and control was continuous, whereas gradience is anterior. It is settled in advance, pre-trained and encountered long after training has been completed. Only in the moment of the hallucination does vector ideology fall away, when the true and the false, the real and the synthetic are indistinguishable in their production,[5] and the contradictions of the vector regime become apparent.[6]
Notes
[1] My use of "vector" is different from McKenzie Wark's use of vectors as lines in a theory of a "vectoralist class" (2004, 2019). Wark explains, "'Vector' I got from Paul Virilio. It is a shorthand way of describing technical relations that have specific affordances. In geometry, a vector is a line of fixed length but of no fixed position. So it is a kind of 'technological constructionism,' in that a given techne does indeed have a determining form, but also some openness as well" (Wark, quoted in Galloway 2017). Wark develops this into a class theory of the digital, of the ownership of communication channels. In contrast, I use "vectors" in the sense of points within a high-dimensional mathematical space used by AI models to encode tokens and enable inference.
[3] We should note that vector space is the product of human labour congealed and made objective, the general intellect in its vectorised form. Although the latent space (the "manifold") might appear as an alien form to the vidual it is the geometry of dead thought, a social relation re-encoded by mathematical functions. This gives the potential for revealing the fetish character of the vector medium. The manifolds and vector spaces that are being constructed under capitalist conditions are not neutral and are shaped by the capital used to produce them. Formalist accounts of vector space miss that in AI production the training data (its corpus), loss functions, objectives and scale are deployed by individuals and corporations, not natural occurrences, and as such we can, and should, trace this political economy (see Berry 2023, 2026).
[4] Due to the structure of the vector medium, I see a potential for resistance through the sparse periphery of the vector space. At the edges of the manifold is that which could not easily be absorbed without a remainder. This is not available to the vidual since its cognition is already inclined, and Critical AI, then, must be understood as a transvidual practice. Rather than an individual capacity, at this periphery the transvidual emerges in the location where non-identity is potentially found and where concept and object do not coincide. See the Vector Lab tools for one way of achieving this.
[5] In Plato's description of the divided line eikasia, or mistaking images for the things themselves, is described as the lowest form in his hierarchy. We might say that the vidual lives in a condition of eikasia, the prompt engineer is at pistis (belief) which are both doxa (opinion). In contrast, the researcher perhaps achieves dianoia (reasoning from ungrounded hypotheses) but noesis (reason or understanding of first principles) is problematised as the manifold is generated through a proprietary political economy which prevents its own reading, so episteme (knowledge) can only partially be attained. The key point is that the vidual is made eikastic by the medium. Plato writes, "It is like a line divided into two unequal sections. Then divide each section - namely, that of the visible and that of the intelligible - in the same ratio as the line. In terms now of relative clarity and opacity, one subsection of the visible consists of images. And by images I mean, first, shadows, then reflections in water and in all close-packed, smooth, and shiny materials, and everything of that sort, if you understand" (Plato 1992: 509d-510a). Because the lack of explainability is proprietary rather than ontological, it suggests a vector politics rather than an AI quietism that holds that these systems cannot be easily challenged, a quietism which ignores the political economy of artificial intelligence. That is, a vector politics sees the manifold and vector space as a site of struggle.
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| Plato's Divided Line (see Plato 1992: 183) |
[6] For Stiegler (2013), the same apparatus that can proletarianise cognition can be used to deproletarianise it. We might therefore explore vector spaces as tertiary retentions and so in new arrangements they might be put to work differently. Hence, new institutions suggest ways of developing resistance to gradience through what we might call transvidual technical practice.
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