Inversions and Vectors

David M. Berry

In an earlier article I introduced the concept of the Inversion to describe the moment at which AI-generated culture overwhelms human cultural production (Berry 2025). The argument is that AI is restructuring how meaning and experience are produced and circulated in societies. The term draws on a technical moment first identified by YouTube engineers in 2013, when bot traffic reached parity with human traffic and employees feared that their internal fraud detection system would flip, treating algorithmic behaviour as "real" and human behaviour as "fake" (Read 2018). That revealed the way in which the Inversion is a kind of "threshold" phenomenon, a point at which the system's own categories of authenticity reverse polarity. However, the concept, as I used it there, conflated what I think are three distinct moments into a single term. In this short piece, I want to unpack them, because each one is differently useful for theorising vector space, and offers, each in turn, an interesting way of reflecting on vectors (see Berry 2026a).

The first I want to look at is inversion as Umschlag, which indicates a crossing of a threshold, a qualitative shift. In Marx's usage it marks the moment where quantitative accumulation changes into a qualitative transformation. In Capital, Marx deploys it for two related cases, at the point at which money functionally becomes capital through the same form (Marx 1976: 467), and the conversion of extensive magnitude into intensive magnitude when a legally limited working day forces capital to intensify rather than extend the labouring day (Marx 1976: 533). In both cases, a boundary is crossed and the same elements begin operating under a different logic. Similarly, computational systems have operated within a culture overwhelmingly produced by human labour, but at some point, arguably already passed in domains like images and discourse, the proportion of synthetic to human-generated content is crossing or has crossed a threshold where the assumption that content is human-generated shifts. We are using the same digital platforms, the same social media, but the logic within them has flipped. I argue that this is, in effect, a medial shift, from digital/discrete to vector/manifold.

The Umschlag in vector computation is not simply a quantitative crossing of a threshold. It is a transformation at the level of the medium, from the digital to the vector. As I have argued, the digital operated through discretisation, encoding continuous phenomena as discrete numerical values whilst preserving media specificity through the technical properties of the format. In contrast, the vector medium operates through statistical "compression", dissolving media-specific properties into geometric coordinates within a shared high-dimensional space (Berry 2026b). The threshold that matters in the latter is the shift in the encoding substrate itself, from a commons of open standards (i.e. digitality) to a proprietary geometry of manifolds (i.e. vectorality). Vector computation requires extraordinary amounts of silicon, energy, and capital to produce and maintain, and these material commitments ensure the vector medium has a tendency to remain proprietary in ways the digital commons never was.[1] We might say that the Umschlag is medial.

The next form of inversion is Verkehrung or the structural reversal of subject and object. Once the Umschlag has occurred, what follows is the condition that Marx describes as "the rule of the capitalist over the worker is the rule of things over man, of dead labour over the living, of the product over the producer" (Marx 1976: 467). Under the Inversion, the relationship between creator and creation, original and copy, human agency and computational output, is structurally reversed. The designer becomes a curator of machine outputs. The writer becomes a prompt engineer. Consequently, dead labour, accumulated in the training data and compressed into the weights of the manifold, rules over living cultural production. Marx argued that at a certain point the "general intellect", the collective knowledge of a society, becomes absorbed into the machinery of production itself (Marx 1993: 706). As Marx says,

Nature builds no machines, no locomotives, railways, electric telegraphs, self-acting mules etc. These are products of human industry; natural material transformed into organs of the human will over nature, or of human participation in nature. They are organs of the human brain, created by the human hand; the power of knowledge, objectified. The development of fixed capital indicates to what degree general social knowledge has become a direct force of production, and to what degree, hence, the conditions of the process of social life itself have come under the control of the general intellect and been transformed in accordance with it (Marx 1993: 706).

The Large Language Model (LLM) is this process made real as fixed capital has absorbed the circulating capital of human discourse, the living exchange of language and meaning, and crystallised it into geometric coordinates, as vectors within a vector intellect. That is, the shift from collective knowledge absorbed into machinery to collective culture dissolved into vectors.

In this case, dead labour dominates through geometry, not through scale or speed. The manifold, produced by extraction of human cultural production through training, becomes the space within which subsequent cultural production must locate itself. Meaning is geometrically "positioned" rather than defined. This is what I have elsewhere called real subsumption becoming geometric, where capital extends beyond the labour process to transform the very medium through which meaning is constituted (Berry 2026b). The product quite literally dominates the producer, because the manifold, the dead labour of billions of compressed texts and images, determines the coordinates at which new meaning can be constituted.[2] We might say that in this sense the manifold performs the generation of artefacts.

Finally, there is inversion as Verwandlung, that is as a formal transformation, in other words as a metamorphosis that preserves identity whilst concealing the underlying real relation (see Marx 1976: 188-257). Previously I used the example of the metaphor of musical inversion (Berry 2025: 5261). These include chord inversion which maintains harmonic identity whilst reorganising its notes, contrapuntal inversion which preserves note relationships whilst turning them "upside down", and melodic inversion which transforms intervals into their opposites. What these musical inversions help us to see is the preservation of structural invariants through reorganisation. In other words, the Inversion maintains recognisable cultural forms whilst transforming their ontological status and mode of production. The thing changes shape whilst preserving certain formal properties. We do not feel the crisis, because the chord is the same, but the "root note", as it were, the ontological origin, has changed.

In the case of a formal transformation, the Verwandlung conceals this reversal, operating through vector space itself. Indeed, the latent continuum tolerates no categorical vacuum. Between any two trained representations there exists a continuous path through high-dimensional space. The outputs of these systems are, therefore, interpolations, trajectories through the manifold, coordinates that maintain the formal appearance of human cultural production whilst, in actuality, they are what Flusser calls projects. This is Flusser's term for an image computed and projected back from digital or what he calls "zero-dimensional" abstraction. So this is not synthetic media, but rather synthetic projects. The formal preservation is built into the geometric logic of the vector medium. We might say that vector space generates surface continuity where the deepest rupture has occurred.[3][4]

These three operations are interdependent and therefore not simply sequential. The Umschlag generates the conditions for Verkehrung, and the Verkehrung produces the structural reversal that Verwandlung appears to conceal. The vector medium complicates any analytical separation of these moments, but it helps to see them as co-constitutive, each conditioning the others within the same medial transformation. This compound structure is what makes the Inversion such a useful concept for diagnosing our contemporary condition.

The vector medium makes the task of understanding its performativity, its ability to generate synthetic projects, in the precise sense of Flusser, more urgent and more difficult, because the medium through which the Inversion operates is so difficult to understand and interrogate. High costs and complexity mean that the manifold, as I understand it, is given to becoming a proprietary medium, and is organised to present its intermediation as immediacy. A critical theory of AI, therefore, has to attend not just to what the vector medium represents or conceals, but to how it geometrises the space in which critique itself must operate.[5]

Images generated using Google Nano Banana 2 in April 2026. 

Notes

[1] Current-generation AI accelerators such as Nvidia's Vera Rubin consume 2,300 watts per chip (Shilov 2026), deployed in racks of 144 GPUs. The vector medium is therefore sustained by thermal load and energy expenditure at an industrial scale, a fact often concealed by the seemingly frictionless chatbots through which users encounter it.

[2] When AI models are trained predominantly on AI-generated outputs, they undergo progressive degradation, losing distributional richness and converging on impoverished repetition (Shumailov et al. 2024). I have discussed this elsewhere as a form of data cannibalisation in which the vampire, having exhausted fresh sources, begins feeding on its own synthetic output (Berry forthcoming). In the terms developed here, this is a metabolic rift in the vector medium. Against the organicist reading of natural limits reasserting themselves, the rift is a structural contradiction as the manifold depends for its generative capacity on the living labour of human cultural production, yet the Verkehrung systematically displaces that same labour.

[3] The Hegelian notion of Umschlag is in the Science of Logic, specifically the "Nodal Line of Measure-Relations" where Hegel theorises how "the gradual, merely quantitative progression... is absolutely interrupted... the transition is a leap" (Hegel 2010: 320). This is rendered slightly more clearly, I think, in the older Miller translation as "the gradualness of merely quantitative change is suddenly interrupted by a qualitative leap" (Hegel 1969: 370). As Cassegard (2019) notes, when the Umschlag finally occurs, we realise that the catastrophe has been going on all the time. This retroactive structure, where the threshold crossing reveals a transformation already underway, is what I am trying to gesture towards in the notion of a vector-based Inversion. The shift to the vector medium may, therefore, already have happened and the Umschlag is the moment of recognition.  

[4] An interesting "redemptive" reading of this is Flusser's, recorded in Peternák (1990) shortly before his death. Flusser traced a ladder of abstraction from the four-dimensional Lebenswelt through three-dimensional objects, two-dimensional images, and one-dimensional texts to zero-dimensional calculation, then proposed that zero dimension is a key hinge moment. From bits, he argued, one can "compute and project back" into "alternative worlds". This reverse motion he calls Einbildungskraft rather than Imagination (cf. Flusser 2011). Imagination, he argues, alienates, while Einbildungskraft is "the power to set an image into" abstraction, a "projection out of abstraction into concretion" that is "the opposite of alienation". The synthetic image, in his reading, is a project rather than an image. Flusser's description of the operation is prescient about latent space. However, he describes a dialogic computational exchange rather than a trained, proprietary vector space set up as a monological generative form. He sets up his dialectic to perform an Aufhebung, alienation sublated into concretion through the Einbildungskraft of the user, whereas I argue that the vector medium enforces an Umschlag, a rupture without reconciliation, the projective "we" displaced into the weights. Where Flusser sees the possibility of concretion ("the motion of making the abstract concrete"), I see the vector medium delivering a formal continuity with our existing medial condition, one that conceals an Inversion.

[5] We should note that the vector Umschlag is not Aufhebung. Indeed, Aufhebung preserves what it negates, carrying the negated moment forward into a higher unity, and is the characteristic movement of Hegel's dialectic. Umschlag, in contrast, is a rupture without reconciliation, a threshold after which the previous regime is displaced, not preserved as a moment within the new. I argue that the shift from the digital to the vector does not sublate the symbolic regime into a higher synthesis. It crosses a threshold after which the symbolic operates as a residual interface to a geometry that has already moved beyond it. 

Bibliography

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Shumailov, I., Shumaylov, Z., Zhao, Y., Gal, Y., Papernot, N. and Anderson, R. (2024) AI models collapse when trained on recursively generated data, Nature, 631, pp. 755-759.