Vector Theory

David M. Berry

"There is no software"

Friedrich Kittler, 1995.

Kittler was right, but, perhaps, not in the way he intended. When he declared that software dissolved into the hardware operations of voltage differences, he was making a materialist claim about symbolic computation, about code that could, in principle, be read, parsed, and traced through logical gates. He assumed that beneath every layer of abstraction there remained something discrete, something Boolean, something that ultimately reduced to ones and zeroes. In the 90s, the "hidden" layer was the voltage. Today, the hidden layer is the sub-symbolic weight structure. What Kittler could not have anticipated was that computation would escape the symbolic paradigm altogether. The voltage differences he traced still operated through Boolean logic, in discrete states which could, in theory, be read. However, the weight matrices of contemporary AI resist reading not because they are hidden beneath abstraction layers but because there is nothing to read. But while the weights aren't "legible" to humans, they are "calculable". The crisis isn't that they are invisible, but that they are asemantic. Whilst voltage is physical materiality, vector space is a form of mathematical materiality. It is a materiality of relation rather than substance.

The computational systems that now mediate cultural production, from large language models to diffusion architectures, increasingly do not operate through symbolic logic in any recognisable sense. They operate through vectors. A word in a contemporary language model is not stored as a dictionary entry or a symbolic token with fixed meaning. It exists as a point in a high-dimensional space (typically hundreds to thousands of dimensions), whose coordinates encode not what the word means but where it sits in relation to every other word the system has encountered.[1] Meaning here is not definition, it is "position" and position is relational. The meaning of "justice" is not what it denotes but where it sits relative to "fairness", "law", "equality", "revenge" and so on. Shift any of those vectors and "justice" shifts with them.

This shift, from the discrete bit to the high-dimensional vector, from Boolean logic to what is called "cosine similarity", constitutes what may be the most significant transformation in computational epistemology since the digital turn itself. And yet our critical frameworks remain largely calibrated for an earlier paradigm. Media theory from McLuhan through Kittler analysed containers and codes, channels and protocols, the materiality of inscription and transmission. These frameworks helped us to understand the shift from analogue to digital with considerable power. As I have argued elsewhere, the digital itself represented a particular mode of computational rationality (Berry 2014), but that analysis was calibrated for a symbolic regime that I argue is now being superseded. Our existing theories will struggle with a computational regime in which there is, strictly speaking, nothing to read, no code to parse, no symbolic layer to interpret, only the vast, opaque geometry of weighted connections and the interfaces through which we connect to it. We no longer need digital theory, we need vector theory. 

What I want to propose here is a provisional way of thinking through this transformation. I am calling it vector theory, not because it offers a theory of vectors in the narrow mathematical sense but because the vector, as a mathematical object encoding both magnitude and direction within high-dimensional space, captures something about how contemporary computation produces, organises, and circulates meaning. Vector theory is an attempt to take seriously the epistemological effects of the reality that the dominant computational paradigm is no longer symbolic but statistical, no longer Boolean but probabilistic. Negroponte argued back in 1996 that we were moving from atoms to bits, and whilst the vector does not displace the bit in the way the bit was said to displace the atom, the relevant unit of computational meaning has shifted from the discrete symbol to the high-dimensional vector (see Negroponte 1996).

The Geometry of Meaning

The vectorial turn is disorienting because it seems to transform the nature of definition itself. In the symbolic paradigm, to define something was to draw a boundary: A is not B. Truth is not falsehood. Definition proceeded through exclusion, through the logical operations of negation and distinction that underpin both classical logic and the binary architecture of the digital computer.

In vector space, definition works differently. To define a word, a concept, or an image is not to exclude but to locate. That is, to identify a region within a multidimensional field where that concept clusters with related concepts. So, for example, the relationship between "king" and "queen" in a word embedding model is not one of logical opposition or categorical hierarchy but of geometric displacement, a vector offset that also maps the relationship between "man" and "woman" (Mikolov et al. 2013: 2). This is the famous word2vec result, king minus man plus woman equals queen, and it reveals something strange about how these systems organise meaning. Semantic content is not stored in symbols but in spatial relationships. 

As mentioned above, the dictionary seems to have been replaced by a mathematical function of similarity. The shift, then, is from boundary-making to location-finding, from a kind of Boolean exclusion to something akin to vector space. For example, in a vector space trained on contemporary media, a term like "Iranian" can easily end up in a neighbourhood shaped by "conflict", "terrorism", "sanctions", "disputed", not because engineers chose those associations but because the corpus did. The politics are in the topology. We might frame this as a shift from "what is it?" to "where is it?" The move from symbolic logic (A is not B) to topological logic (A is near B). 

In the older paradigm, understanding a concept meant grasping its definition, its essential properties, what made it the thing it was and not something else. In vector space, understanding means knowing a concept's neighbourhood, what it sits near, what it points toward, how it is oriented relative to other points in the space. A word encoded across high-dimensional space is not a fixed point but a superposition of contexts, a compressed record of every pattern of usage the training process has encountered. This also indicates why the attention mechanism matters. If the vector is the "what" (position), attention is the "how", the dynamic weighting of relationships in real-time, the engine that creates the stochastic flow through which these systems think, if thinking is even the right word.

This has consequences for how we think about truth. In Boolean logic, truth is binary, a proposition is either true (1) or false (0), and there is seldom an in-between (although this can be simulated through discrete enumerations). In vector space, computational systems operationalise something that functions as truth not through binary evaluation but through orientation. Two ideas that point in roughly the same direction within the embedding space are treated as compatible, as "true" relative to each other. The further apart their angular distance, the less compatible they become. Truth becomes, in this case, a matter of degree, a scalar quantity rather than a logical one.[2]

When ChatGPT "hallucinates", it is therefore not malfunctioning. It is computing the statistically most probable continuation given its position in latent space regardless of whether that position corresponds to anything in the world. The system cannot distinguish between frequently co-occurring patterns and verified facts because, at the level of its computational substrate, there is no such distinction to make. Both are encoded as geometric relationships between vectors. The surprising outcome is that this works, that these systems produce useful, coherent, apparently knowledgeable outputs despite having no access to truth in any sense we would recognise.

That computational systems treat truth as vector orientations tells us something important about how these systems operate. It does not tell us that truth actually is vector orientation. Indeed, vector proximity is not verification. This collapse of epistemology into statistics, of truth into proximity, is precisely what a critical theory of computation needs to examine rather than celebrate. When cosine similarity replaces logical implication, something is gained, a capacity for analogy, association, and flexible pattern-matching that symbolic systems could never achieve, but something is also lost, and what is lost is the capacity to distinguish between things that merely co-occur in language and things that are actually the case.

The Latent Continuum

The latent continuum describes what vector space does to the gaps between categories. Traditional representational systems are lossy in a specific sense, they lose what falls between their categories. A filing system has folders and gaps between folders. A database has fields and null values. A dictionary has entries and absences. The digital, as I have argued (Berry 2011), operates through a process of discretisation that imposes mathematical form on continuous phenomena, necessarily excluding whatever resists formalisation.

Latent space inverts this logic. The interior of a well-trained generative model is statistically dense. In a diffusion model or a GAN, it is possible to smoothly interpolate between a photograph of a dog and a photograph of a cat (see Lewis-Kraus 2026), moving through intermediate states, a 'dat' or a 'cog', that have no name in natural language but that possess perfectly determinate mathematical coordinates within the model's latent space. These are not errors. They are addresses in the manifold, as valid mathematically as any point that corresponds to a named concept. The system makes no distinction between the actual and the interpolated, between what has been seen and what can be computed. This is, in effect, a collapse of the possible into the probable. In a vector system, everything that can be computed is already latent, already present as a coordinate in the manifold, awaiting only the right trajectory to instantiate it. The role of the creator, if we can still use that word, shifts accordingly, not from nothing to something, not even from idea to expression, but from the totality of the already-computable to the specific path through it. Creation becomes navigation. The 'new' is not produced but visited, as it were.

The principle at work here is that latent space tolerates no categorical vacuum. Where symbolic systems have boundaries and gaps, vector systems have gradients and neighbourhoods. The shift from hierarchy to topology means that between any two trained representations there exists a continuous path, a traversable route through high-dimensional space that passes through positions which may never have been instantiated as actual outputs but which remain computable. There are no empty spaces, only unvisited coordinates. The "hallucination" problem is a feature of a system that must compute a coordinate, even if that coordinate corresponds to nothing in reality.

In symbolic representation, absence is a design feature. The dictionary does not need entries for non-words. The database does not store impossible combinations. But in latent space, 'dat' and 'cog' exist with precisely the same formal status as 'cat' and 'dog'. They are computable and locatable and therefore can be generated. This means the space of possible outputs is no longer constrained by what has been seen or named but only by what can be interpolated. Generation becomes, in the strict sense, infinite. Every point in the manifold corresponds to a potential output, whether or not that output has meaning, reference, or coherence.

But we should immediately ask, unvisited by whom? And whose training data shaped the density of the field in the first place? The statistical density of latent space is not a natural fact but an artefact of curation, of the selection and preprocessing of training corpora, which is to say an artefact of capital, of labour, and of the political economy of data collection.[3]

Stochastic Flow

Here is where vector theory breaks most decisively from the older digital paradigm. In the symbolic regime, computation was retrieval. You posed a query, the system searched its index, and it returned a match. The governing metaphor was the map, static, surveyed, deterministic. Ask the same question twice and you get the same answer. We might say that the old paradigm was, at bottom, a theory of the archive.

When we prompt a large language model, we are not retrieving information from a store. We are setting initial conditions for a probabilistic process, nudging a particle into a flow whose trajectory is shaped by the model's weights, its temperature setting, its attention patterns, and the specific sequence of tokens that constitutes the prompt. The output is where the particle happens to land. Ask the same question twice and you may get a different answer. This is not a bug, it is the operational logic of the system. 

Tokens can be taken as the "user interface" of language, a key part of the discretisation of inputs and outputs that makes these systems work. The machine takes our continuous world, turns it into discrete tokens, and then immediately re-projects them into continuous vector space. I want to call this threshold the tokenisation horizon, this is the point at which human language is discretised, decomposed, and re-projected into a computational regime where it is no longer language but geometry. Beyond the horizon, there are no words, only vectors. It is also where human agency might be said to be surrendered to the field. On this side of the horizon, a prompt functions as a command, an instruction issued with intent. Beyond it, the same tokens become a perturbation of a probability field, and what happens next is determined not by what the prompter meant but by the geometry of the space the tokens enter. This "sandwich" of discrete/continuous/discrete is where the power (and the error) resides.

But stochastic flow is not merely probabilistic, it is sequential, and sequence matters. Each token generated by a language model becomes part of the context that conditions the next token. The probability distribution shifts with every step. Paths that were open at the beginning of a sentence close as the sentence develops, not because they become impossible but because they become statistically improbable given what has already been said. Generation is flow with memory, flow that narrows its own channel as it proceeds. This is why the same prompt can produce radically different outputs: the early tokens establish a trajectory, and the trajectory constrains everything that follows. A single word chosen differently in the third position can redirect the entire output into a different region of the manifold. The process is path-dependent in the strict sense, sensitive to initial conditions.

The metaphor here is not the map but the current. Or better still, the vector field, a mathematical structure that assigns a direction and magnitude to every point in a given space. Prompting is not querying but perturbing. The "author" of a generated text, and the notion of "author" strains to breaking point here, is not the user who wrote the prompt nor the engineers who built the model but the field itself, the entire configuration of weighted connections through which the stochastic process flows.[4]

This dissolves the old distinction between authorial intent and textual meaning in ways that go beyond what poststructuralism imagined. In the symbolic paradigm, we could at least maintain the fiction that someone intended something, that a programmer wrote code with a specific purpose, that a database was structured by design. Stochastic flow replaces intent with initial conditions. The question is no longer "what did the author mean?" but "where did the trajectory begin, and what shaped the field through which it moved?" This could be said to represent a shift from hermeneutics to dynamics, from interpretation to the study of flows.

This is what I mean by stochastic authorship and provenance anxiety. In symbolic computation, we could trace responsibility backwards through the system. Who wrote this code? What does this variable store? Where did this data come from? In probabilistic systems, responsibility dissolves into the field. No single weight determines the output and no individual training example caused a specific generation. The "author" is the entire configuration of billions of parameters shaped by terabytes of data curated by invisible labour and optimised through computational processes whose emergent behaviour cannot be predicted from their specification. Authorship becomes distributed across the manifold itself. This makes questions of copyright, attribution, and creative rights more than challenging in their current legal formulations.

The Sub-Symbolic Layer

The most difficult dimension of vector theory, and in many ways the most important, concerns what we might call the sub-symbolic layer, the vast architecture of weights that constitutes the actual computational substrate of contemporary AI systems. This is not an entirely new problem and Paul Smolensky identified what he called the subsymbolic paradigm in 1988, arguing that connectionist systems operate at a level of description that sits below the symbolic. That is, that the patterns of activation across neural networks do not map neatly onto the concepts, rules, and categories of symbolic representation (Smolensky 1988: 3, 9). What Smolensky identified as the "subsymbolic" is what we might now, in the age of models with hundreds of billions of parameters, call the dark matter of computation. In using dark matter as an analogy, I aim to capture its opacity of scale. Whilst we cannot read the dark matter of weights, we are increasingly "gravitationally bound" by them as our own cultural outputs begin to orbit the densest regions of the corporate manifold.

In cosmology, dark matter is said to constitute the majority of the universe's mass but does not interact with light and cannot be directly observed. Its existence is inferred from its gravitational effects on visible matter. In contemporary AI, the weights constitute the majority of the system's computational substance, billions of floating-point numbers whose specific values were determined during training, but they cannot be meaningfully "read" in the way that source code can be read. We do not interpret weights, we observe their effects, the way they bend the light of human intent, deflecting prompts into outputs whose shape reveals the gravitational field without making it visible. We can see what the field produces, but the "why" remains mathematically distributed and potentially human-unreadable.

But where dark matter's gravitational effects are predictable, modelled, consistent with physical law, the effects of the sub-symbolic layer are not. We cannot predict when a language model will hallucinate, cannot model which prompts will trigger refusal, cannot specify in advance what the system "knows". The opacity is not merely epistemic, a temporary state to be resolved through better interpretability methods, but ontological. The system does not work by encoding knowledge that could in principle be decoded. It works by encoding statistical patterns whose relationship to knowledge, understanding, or meaning remains unresolved.

This is what makes the sub-symbolic layer so important for any serious theory of contemporary computation as it identifies where the meaning emerges from in a large language model. For example, the sentences it constructs, the associations it draws, the analogies it produces, all of this emerges from the interconnectedness of weights rather than from any symbolic structure. Language, in this context, is not the medium of the computation but its user interface. The machine does not "think" in English, it operates, if we can even use a cognitive term here, in weighted associations, and English is the surface through which human users interact with those associations.

Hubert Dreyfus saw something like this coming when he argued that human intelligence depends on embodied, non-representational capacities that resist formalisation in symbolic terms (Dreyfus 1992). N. Katherine Hayles develops a related insight through her concept of the "cognitive nonconscious", the computational processes that operate below the threshold of awareness, shaping cognition without ever becoming available to conscious reflection (Hayles 2017). The irony, and it is a considerable one, is that contemporary AI has in some sense vindicated Dreyfus's critique of symbolic AI precisely by abandoning the symbolic paradigm (although this may change as hybrid symbolic systems can provide a domain specific ground truth). AIs work by encoding statistical regularities into weights rather than formalising intelligence into rules. This clearly does not constitute understanding in any sense that would satisfy philosophy's demands for reference, intentionality, or semantic grounding. But it constitutes something, and that something is powerful enough to convince millions of users that they are conversing with an intelligence. It operates below the level of symbols, in a register our existing critical vocabularies are poorly equipped to describe but what we sometimes call the Eliza Effect. The opacity of the sub-symbolic layer habituates users to what I have elsewhere called "slot machine cognition", the superstitious prompting of systems whose mechanisms remain invisible, when democratic life requires something closer to "printing press cognition", in the capacity to trace claims to sources and demand accountability from the systems that shape public discourse (Berry 2026).

In response, the emerging field of mechanistic interpretability, led in large part by the same corporations that build the models, attempts to reverse-engineer the computational functions encoded in neural network weights, to discover "circuits" and "features" that correspond to identifiable operations.[5] This has produced insights into how specific behaviours emerge from specific configurations of weights. But we should be clear about what it is and what it is not. Mechanistic interpretability is an attempt to make the sub-symbolic layer legible, to re-impose symbolic description on a system that does not operate symbolically. Its successes, where they occur, tend to identify isolated circuits rather than recovering anything resembling the model's "knowledge" in aggregate. The question of who is doing the interpreting and why matters as much as the technical results. When Anthropic or Google map the internal representations of their own models, this is not disinterested science. It is capital developing better instrumentation for its own infrastructure – regardless of whether they claim an AI safety mission or a need to find the soul of the machine (see Lewis-Kraus 2026). Whether mechanistic interpretability could become a critical technical practice, a means by which the sub-symbolic layer is made accountable rather than merely more efficiently managed, remains to be seen.

The Vector Field

If the old media theory could be said to be a theory of the atom, the bit, the pixel, the frame, the discrete unit of inscription, then vector theory is a theory of the field. You cannot understand a hurricane by studying the chemistry of a single oxygen molecule, you have to map the pressure gradients of the entire sky. We might say that in latent space there are no "things", only tendencies. 

The vector field is the governing image here, and it is barely metaphorical. A vector field in mathematics assigns a vector, a quantity with both magnitude and direction, to every point in a given space. The gradient fields that guide diffusion models, the attention patterns that shape transformer outputs, the embedding spaces in which words and images are located, these are vector fields in the strict mathematical sense, structures in which every point has an orientation and an intensity.

This marks a genuine break with the traditions of media theory that have served us since the 1960s. Understanding Media analysed the effects of the medium as container, as channel, as extension of the human sensorium (McLuhan 1964). Kittler's media archaeology traced the material infrastructure of inscription technologies, the gramophone's groove, the film's frame rate, the typewriter's key spacing (Kittler 1999). These approaches showed us the materiality of media with extraordinary explanatory power. But they were, at bottom, theories of discrete objects, of identifiable material substrates whose operations could be described, measured, and interpreted at the level of the individual unit.

But it is difficult to apply these frameworks to a large language model. There is no groove to trace, no frame rate to measure, no type spacing to document. The material substrate is a matrix of floating-point numbers whose individual values are meaningless and whose collective behaviour cannot be inferred from inspection. McLuhan's question, "what does the medium extend?", assumes a human capacity being augmented. But a system that computes probable continuations in high-dimensional space is not necessarily extending any human faculty, it is operating in a register that has no human equivalent. Kittler's method, following the signal through the hardware, assumes a signal that can be followed. In vector computation, there is no signal. There is a field, and the field is everywhere at once. The old media theory gives us the tools to analyse the gramophone and the typewriter but it gives us almost nothing to understand a manifold. We therefore urgently need instead vector studies. 

Additionally, in the symbolic regime, a source exists. A document or file can be located, a string can be retrieved, a record can be traced to its origin. The archive preserves the original, and the original grounds interpretation. In vector computation, the source undergoes what I have elsewhere called diffusionisation (Berry 2025), the process through which cultural forms are probabilistically dissolved and reconstituted via computational processes. Where Stiegler's (2013) grammatisation describes the progressive inscription of human capacities into technical systems, each stage enabling new forms of knowledge whilst constraining others (e.g. writing grammatising speech, print grammatising writing, databases grammatising record-keeping), diffusionisation names something more radical. In the latter, the original is destroyed through mathematisation, transformed into statistical distributions across latent space, and then reconstituted synthetically. 

The training data, the billions of texts and images that constituted the "source material", are consumed in the production of a manifold. They do not persist as retrievable objects within it and their traces are distributed across billions of weights in configurations that bear no recoverable relation to any individual original. The source can be said to be everywhere and nowhere, present only as a statistical residue in the geometry of the field. We might name this the shift from inscription to distribution, from Kittler's paradigm of the discrete material mark to the statistical dispersal of the source across the weight structure of a manifold. But distribution here does not mean the circulation of copies. It means their dissolution into probability distributions from which no original can be fully recovered.

Vector theory therefore operates at a different level of description entirely. The unit of analysis is not the bit, the token, or the individual weight but the field. This is the entire distribution of vectors across the space, the topology of a manifold, the direction and strength of gradients at every point. It is closer in spirit to field theory in physics than to any prior tradition in media theory.

However, there is an important precursor in the work of Deleuze and Guattari whose distinction between smooth and striated space in A Thousand Plateaus (1987) anticipates some of the claims I am making for vector theory. For example, they also identify the priority of topology over hierarchy, of flow over structure, of the continuous over the discrete. The latent manifold of a generative model looks, at first glance, remarkably like Deleuzian smooth space, a heterogeneous continuum without fixed coordinates, navigated through wandering rather than through grids.

The difference I want to make is that the vector spaces of contemporary AI are not philosophical concepts but material-computational infrastructures. The high number of dimensions of an embedding model are not metaphorical. They are measurable, traversable, and, importantly, owned. Smooth space, for Deleuze, named a site of resistance and nomadic freedom. The latent manifold of a proprietary AI model is a site of capital accumulation. Deleuzian smooth space, when materialised as a corporate latent space within an AI model, is not a site of nomadic freedom but of computational enclosure. The manifold's apparent openness, its statistical density and infinite traversability, disguises what has become the most intensive striation as every written word is assigned coordinates within a proprietary geometry, every traversal of the model logged and monetised. The history of how digital capitalism has absorbed and used Deleuzian concepts should also make us suspicious. "Rhizomatic" became a compliment corporate consultants paid to their platform architectures. "Deterritorialisation" became recuperated as "disruption" in organisation studies and business schools. "Smooth space" became the user experience designer's ideal, an interface with no friction and no resistance. Each time concepts are developed to theorise escape routes from capital they run in danger of becoming capital's self-description. Vector theory, of course, risks the same trajectory. Already we see AI engineers adopting "manifold" and "latent space" not as critical concepts but as neutral technical terms. The challenge is to keep vector theory critical, to ensure it remains an analysis of enclosure rather than becoming another metaphor for frictionless flow.[6]

Whose Vectors?

Everything described so far, the geometry of meaning, the latent continuum, stochastic flow, the sub-symbolic layer, could be articulated as a neutral account of how these systems work. But the shift from symbolic to vectorial computation is not merely an epistemological one. It is a transformation with political-economic consequences that demand analysis, and a vector theory that fails to provide this analysis is not adequate to critique.

As far back as 1994, Wark analysed how communication technologies create what he called "vectoral" power, the capacity to move information across space at speed (see Wark 1994, 2004). Those who control vectors, what Wark later termed the "vectoralist class", extract value from the flows they mediate. In 2004, I co-wrote the Libre Culture Manifesto which, drawing on Wark's work, argued that "vectorialists" were emerging as a new class formation alongside landlords and capitalists, extracting value from the "distribution, access and exploitation of creative works" (Berry and Moss 2004). But the situation has shifted dramatically. The vectoralist class now controls not just the channels through which information flows but increasingly the geometry of the space within which meaning itself is beginning to become constituted. Where Wark's vectors described a power to move, AI vectors describe a power to transform, to render language and thought as manipulable coordinates within a proprietary computational space.[7]

The topology of latent space, the shape of a manifold, the density of different regions, the directions of the gradients, none of this is neutral anymore (if it ever was). It is shaped by training data, and training data is shaped by decisions about what to include and what to exclude, decisions made by corporations with specific interests, operating within specific economic structures, employing specific forms of labour, often invisible, often precarious, often located in the Global South (Berry 2025). And they must continually re-striate it. A manifold, left to its own computational logic, tends towards the smooth as it produces "dats" and "cogs", interpolates freely between categories, treats every coordinate as equally a basis for generative work. Capital, of course, cannot tolerate this freedom. A system that generates smoothly between all possible outputs is a system that cannot be productised, cannot be made safe, cannot be sold. Reinforcement learning from human feedback (RLHF) is the mechanism through which smooth latent space is forced back into striated categories, human workers are paid to tell the system that "cat" is an acceptable output and "dat" is not, that some regions of a manifold are to be visited and others foreclosed. The continuum is re-bounded through work sourced from the cheapest labour locations.

I think Marx's distinction between formal and real subsumption can help us understand what is happening here. Under formal subsumption, capital takes an existing labour process and subordinates it to a valorisation process whilst leaving its technical character largely intact. A factory owner employs weavers who continue to weave as they did before, only now for a wage. The scraping of the internet for training data is formal subsumption in this sense as capital appropriates existing linguistic and cultural production, texts written for other purposes under other conditions, and feeds them into a training pipeline. Language enters a manifold more or less as it was produced. But what emerges is not language subordinated to capital, rather it is language reconstituted by capital, transformed at the level of its internal organisation from sequential symbolic expression into geometric coordinates within a proprietary vector space (i.e. the AI model). This is real subsumption. Capital does not merely employ human linguistic production but transforms its very structure, dissolving the symbolic into the statistical, replacing the meaning with the coordinate. A manifold is not a repository of language captured by capital, it is more like language rewritten in capital's own computational grammar. Real subsumption, become geometric.

The "unvisited coordinates" of the latent continuum are therefore not merely undiscovered possibilities awaiting exploration. Some of them are structurally excluded, positions that the training regime never populated because the data that would have placed them there was never collected, or was collected and filtered out, or was generated by communities whose linguistic and cultural production is systematically underrepresented in the corpora that feed these systems. The exclusion usually operates structurally rather than through explicit censorship, although specific items are also excluded. The embedding space therefore encodes assumptions about what concepts are similar, what ideas cluster together, what meanings are close or far away, and these assumptions derive overwhelmingly from Anglophone, Western training corpora. We might argue that what is at stake is not merely representation but the geometry of the thinkable itself.[8]

This exclusion is becoming increasingly self-reinforcing. As the supply of human-generated training data is exhausted, AI systems are increasingly trained on the outputs of previous AI systems, synthetic data generated by models whose topology was already shaped by the biases and exclusions of earlier training regimes. A manifold feeds on itself. Regions that were sparsely populated in one generation of models become sparser still in the next, as the synthetic data that fills the training pipeline carries forward and amplifies the geometry of its predecessors. The coordinates that were never visited become, with each iteration, less likely ever to be visited. This is the vector-theoretic version of inbreeding, a progressive narrowing of the space of the expressible that operates through the statistical mechanics of recursive self-training. A manifold does not forget what it never knew, but it becomes increasingly confident in the limited territory it has already mapped.

Who owns the vector space? Who profits from its traversal? Whose meanings are embedded and whose are absent? These are key questions to be addressed and a vector theory that describes the geometry of meaning without asking whose geometry, trained on whose language, shaped by whose capital, would reproduce exactly the kind of uncritical computational positivism that critical theory exists to challenge.

It seems clear, therefore, that we need a political economy of the manifold. Such an account would examine, at minimum, the concentration of compute infrastructure in a handful of corporations whose training runs cost hundreds of millions, and increasingly billions, of dollars, creating barriers to entry that make the construction of embedding spaces a de facto oligopoly. This includes the energy consumption of training and inference, measured in megawatt-hours, whose environmental costs are externalised onto communities that rarely consented to bear them. It would examine the labour conditions of data preparation, the millions of hours of annotation, labelling, and content moderation performed by workers whose wages bear no relation to the value their labour produces within a manifold. Together with an analysis of the intellectual property regimes emerging around model weights, where the legal status of a trillion-parameter matrix trained on the entire publicly available internet remains unresolved. This is not to forget, too, the access hierarchies that determine who interacts with these systems and on what terms, from proprietary APIs priced per token to open-weight models whose "openness" still requires computational resources most of the world cannot afford. Indeed, the economics of fine-tuning is crucial to understand, in which corporations extract further value by adapting foundation models to specific domains, turning the general manifold into proprietary sub-manifolds whose topology serves particular commercial interests. Vector theory needs this critical account, otherwise it is merely descriptive, a formal account of how these systems work. With it, it becomes diagnostic, an account of what these systems do, and to whom.[9]

Conclusion

Vector theory as I have sketched it here is provisional and incomplete, but its central claim seems to me urgent. The shift from symbolic to probabilistic computation, from discrete bits to high-dimensional vectors, represents an important epistemological transformation. Previous media theories analysed the inscription and the archive, the discrete unit and the hierarchical structure. They did this in a way that was both useful and revealing. But we now inhabit a computational environment in which it appears that meaning is position, definition is alignment, truth is orientation, and thinking is trajectory. I argue that the vector, not the bit, is the elementary particle of this new regime.

Whether vector theory names something new or merely redescribes in critical-theoretical language what engineers already understand in mathematical terms is a question I leave open for now. What matters is that through the development of a theoretical vocabulary we have ways of connecting practices like cosine similarity, latent density, stochastic flow, and sub-symbolic weight structures to the critical traditions, from Marx through the Frankfurt School to contemporary political economy. These can then help us to ask not only how these systems work but whose interests they serve and what forms of knowledge and experience they systematically exclude. Indeed, I argue that the vectorial turn represents a new stage in the real subsumption of cognitive and linguistic labour.

The manifold is not a neutral space. It is shaped by power, by capital, and by the accumulated weight of the data that produced it. If we are to navigate it critically rather than merely inhabit it, we need a theory adequate to its geometry. Such a theory must attend to what the geometry does to the experience of thinking. The frictionless traversability of the manifold threatens what I call cognitive anaesthesia, the systematic smoothing of productive difficulty. Not all friction is inefficiency to be engineered away. Some difficulty is a resistance that builds the cognitive capacity it exercises, and a computational regime that liquidates thinking does not liberate thought but anaesthetises it. A vector theory adequate to its object must reckon with the danger of this loss.

Notes

[1] Dimensionality varies across models and architectures. For example, OpenAI's "text-embedding-ada-002" uses 1,536 dimensions and more recent models use different configurations. Of course, the number is itself a moving target, scaling upward in newer architectures whilst being compressed through quantisation techniques that trade precision for efficiency. The specific number matters less than the fact that meaning is encoded as a position in a space whose dimensionality exceeds human spatial intuition. 

[2] This is not to argue that truth is necessarily reduced to statistical correlation but rather to describe how computational systems operationalise something that functions, within their architecture, as a proxy for semantic compatibility. The philosophical consequences of this substitution, what is gained and what is lost when proximity becomes primary, require more space to discuss than I have here.

[3] The work of data labellers, content moderators, and the vast apparatus of what has been called "ghost work" (Gray and Suri 2019) maintains a training pipeline. Critical vector studies must show this labour rather than treating a manifold as a found mathematical object.

[4] This framing draws on and extends the argument I develop in Berry (2025) regarding synthetic media and computational capitalism. The dissolution of authorship in stochastic systems is not merely a literary-theoretical curiosity but an economic problem, bound up with questions of intellectual property, creative labour, and the extraction of value from cultural production.

[5] The emerging field of mechanistic interpretability, which attempts to reverse-engineer the computational functions encoded in neural network weights, represents one response to this opacity. However, the subsymbolic remains, for now, resistant to symbolic redescription.

[6] There is a broader lesson here about the relationship between continental philosophy and computational practice. Deleuzian concepts have repeatedly been adopted as descriptions of digital systems in ways that neutralise their critical force. One should remain alert to the risk of co-optation, of providing capital with a more sophisticated vocabulary for describing its own operations.

[7] OpenAI, Google, Meta, and Anthropic do not merely host information but constitute the geometric space within which meaning is computed. They are vectoralists in the most literal sense, owners of the vector infrastructure. See Berry and Moss (2004) for an early application of this analysis to digital culture.

[8] This connects to the argument I develop in Generation Vector (Berry 2026, forthcoming), where I analyse the sociological and phenomenological dimensions of vectorisation through Mannheim's sociology of generations, Stiegler's grammatisation, and what I call intermediation (Vermittlung). Vectorisation is not just an epistemological operation but a social one, and the generational dimension reveals what an epistemological account leaves aside.

[9] Due to limits of space, the full political economy of vector computation will be developed in a subsequent post. I will note here only that the concentration of embedding infrastructure in a handful of corporate actors represents a form of epistemic enclosure whose consequences we are only beginning to consider. The question of who controls the geometry of meaning is, I would argue, among the most pressing contemporary political questions.

Bibliography

Berry, D. M. (2011) The Philosophy of Software: Code and Mediation in the Digital Age, Palgrave Macmillan.

Berry, D. M. (2014) Critical Theory and the Digital. Bloomsbury.

Berry, D.M. (2025) Synthetic media and computational capitalism: towards a critical theory of artificial intelligence, AI & Society. Available at: https://doi.org/10.1007/s00146-025-02265-2.

Berry, D. M. (2026, forthcoming) Generation Vector, Stunlaw. Available at: https://stunlaw.blogspot.com

Berry, D.M. and Moss, G. (2004) Libre Culture Manifesto. Libre Society. Available at: https://tovarna.org/files0/active/2/8455-the_libre_culture_manifesto.pdf.

Deleuze, G. and Guattari, F. (1987) A Thousand Plateaus: Capitalism and Schizophrenia. University of Minnesota Press.

Dreyfus, H. (1992) What Computers Still Can't Do: A Critique of Artificial Reason, MIT Press.

Gray, M. L. and Suri, S. (2019) Ghost Work: How to Stop Silicon Valley from Building a New Global Underclass. Houghton Mifflin Harcourt.

Hayles, N. K. (2017) Unthought: The Power of the Cognitive Nonconscious, University of Chicago Press.

Kittler, F. (1995) There Is No Software, CTheory, a032. Available at: https://journals.uvic.ca/index.php/ctheory/article/view/14655.

Kittler, F. (1999) Gramophone, Film, Typewriter, Stanford University Press.

Lewis-Kraus, G. (2026) What Is Claude? Anthropic Doesn’t Know, Either, The New Yorker, 9 February. Available at: https://www.newyorker.com/magazine/2026/02/16/what-is-claude-anthropic-doesnt-know-either (Accessed: 11 February 2026).

McLuhan, M. (1964) Understanding Media: The Extensions of Man. McGraw-Hill.

Mikolov, T., Chen, K., Corrado, G. and Dean, J. (2013) Efficient Estimation of Word Representations in Vector Space. Available at: https://arxiv.org/abs/1301.3781.

Negroponte, N. (1996) Being Digital. Alfred A. Knopf, Inc.

Smolensky, P. (1988) On the proper treatment of connectionism, Behavioral and Brain Sciences, 11(1), pp. 1-74.

Stiegler, B. (2013) What Makes Life Worth Living: On Pharmacology, Polity.

Wark, M. (1994) Virtual Geography: Living with Global Media Events. Indiana University Press.

Wark, M. (2004) A Hacker Manifesto. Cambridge, MA: Harvard University Press.