Enabling “The Fashion System” with Big Data and AI

FROM THE FASHION SYSTEM TO A PREDICTIVE SYSTEM

The previous statement may be reformulated more carefully. To classify human beings by net asset value, physical features, demographic attributes, or social media behaviour is not simply to “describe” them. It is to project them from the ambiguous space of human existence into a space where they can be sorted, compared, predicted, and acted upon.

In the previous chapter, the world-state was described as a relational object:

Here \(A(t)\) denotes the state of the world at time \(t\). It includes the product space of human conditions \(\mathcal{C}(t)\), the product space of system conditions \(\mathcal{S}(t)\), and the relation structure \(R(t)\) between human agents and systems. The letter \(A\) is used for the aggregate or assembled state of the world. The letter \(R\) is used for relation. This notation will be preserved in what follows.¹ 1In Chapter 4, \(\mathfrak{S}(t)\) denotes the set of systems, while \(\mathcal{S}(t)=\prod_j\mathcal{S}_j\) denotes the product space of system conditions. The Gothic letter \(\mathfrak{S}\) is used for the set of systems in order to avoid confusion with \(S_j(t)\), the state of the \(j\)-th system, and \(S_x\), the new system introduced by the design operation \(O_x(t)\). The subscript \(x\) labels the particular system introduced by that operation.

In order to clarify how this world-state becomes available to big data and A.I., let us introduce a few elementary definitions. These definitions are not intended to reduce fashion, society, or human beings to mathematics. They are intended to describe the operations by which fashion becomes available to computational systems.

Definition 1. Projection

A projection is a map that carries a complex object into a reduced space in which only certain aspects of that object are preserved. In the present context, one may write:

where \(\mathcal{Y}\) is a reduced space. A projection does not reproduce the world-state as it is. It selects, compresses, and rearranges the world-state according to the structure of \(\mathcal{Y}\). ² 2The term “projection” is used here in a broad mathematical and epistemological sense. It does not necessarily mean an orthogonal projection in linear algebra. It refers to any operation by which a complex object is mapped into a reduced space for the purpose of analysis, interpretation, calculation, or control.

In this sense, Barthes’ restriction of fashion to written descriptions can be understood as a projection:

Here \(\mathcal{T}(t)\) denotes the textual and semiological space of written fashion descriptions. The letter \(T\) is used for “textual.” It is deliberately not written as \(\mathcal{L}(t)\), because \(L\) might suggest language in general or Saussure’s langue. Barthes did not analyse language in general. He analysed a specific textual corpus of written fashion descriptions. ³ 3The notation \(\mathcal{T}(t)\) is chosen to indicate textuality rather than langue. Barthes’ object is not the whole system of language, nor the whole state-space of fashion, but a textual and semiological space formed by written fashion descriptions.

Strictly speaking, if \(\mathcal{T}(t)\) is treated as a set of finite written descriptions generated from a finite alphabet or vocabulary \(\Sigma\), then

The set \(\Sigma^\ast\), namely the set of all finite strings over \(\Sigma\), is countably infinite:

In the case of Barthes’ actual magazine corpus, the set is even finite. Barthes’ analysis is therefore powerful but deliberately restricted. It makes fashion analytically readable by projecting the world-state into a textual corpus. It does not analyse the whole relational state-space of fashion. ⁴ 4Countability is not a criticism of Barthes. It clarifies the methodological operation of his analysis. By restricting fashion to written descriptions, Barthes transformed a heterogeneous social, visual, bodily, and institutional phenomenon into a homogeneous textual corpus that could be analysed semiologically.

Definition 2. Observation

A.I. and big data do not begin with the whole world-state itself. They begin with observation. Let \(\Omega\) be an observation function. The data obtained from the world-state \(A(t)\) is written as:

Here \(X(t)\) denotes the observed and recorded data at time \(t\). The letter \(X\) is used because it functions as the data input to subsequent computational processes. \(X(t)\) may include images, texts, purchase histories, location data, social media activity, body measurements, search behaviour, sensor data, and other recorded traces.

The important point is that \(X(t)\) is not identical with \(A(t)\). Big data is not the world-state itself, but an observed, recorded, formatted, and institutionally conditioned version of the world-state. ⁵ 5The observation function \(\Omega\) includes the technological, institutional, and economic conditions under which data is collected. Therefore, observation is never neutral. What is not recorded, tagged, scanned, clicked, purchased, uploaded, or made visible to a platform may disappear from the computational image of the world.

This distinction is crucial. If the observed world is mistaken for the world itself, the machine-filtered image of society begins to replace society. What appears to be neutral data is already a selected, formatted, and institutionally conditioned surface.

Definition 3. Evaluation and Embedding

For each human agent \(h_i\), let \(C_i(t)\) denote the condition of that agent. As defined in the previous chapter, \(C\) stands for condition. An evaluation function is a map

or, more generally,

The letter \(E\) is used for evaluation or embedding. In the first case, the human agent is reduced to a single score:

Here \(r_i(t)\) may indicate a rank, score, probability, asset value, credit value, influence score, or estimated likelihood of an action. In the second case, the human agent is represented as a vector:

Here \(z_i(t)\) denotes the computational representation of the human agent in a real-valued vector space. The letter \(z\) is used because such latent or embedded representations are often denoted by \(z\) in computational contexts. The integer \(k\) denotes the number of coordinates or dimensions in the embedding space. ⁶ 6The dimension \(k\) of \(\mathbb{R}^k\) should not be confused with the cardinality \(N(t)\) of the human set, the cardinality \(M(t)\) of the system set, or the interaction count \(N(t)\times M(t)\). \(k\) is the number of coordinates used by a computational representation.

This operation may be understood as an embedding of the human condition into a real-valued vector space. In other words, the computational system does not encounter the human being directly. It encounters a representation of the human being as a point, region, or distribution in \(\mathbb{R}^k\). ⁷ 7An evaluation or embedding function should not be confused with a moral judgement. It refers to a computational operation that assigns a score, vector, rank, or category to an entity. When the output belongs to \(\mathbb{R}^k\), the entity is represented in a real-valued vector space. This makes it possible for computational models to compare, cluster, rank, recommend, exclude, target, or predict the entity. This is an operational description, not an ontological claim about what a human being, garment, or image essentially is.

The discretized human is therefore not merely an individual divided into fragments. It is a human being translated into a set of operational coordinates. These coordinates may be economic, bodily, behavioural, cultural, or symbolic. Once translated into such coordinates, the human being becomes legible to systems that do not understand persons, but can process scores, vectors, probabilities, and relations.

This is the decisive difference between Barthes’ semiological projection and A.I.’s computational embedding. Barthes projects fashion into a textual space:

A.I. observes the world-state as data and embeds the observed data into a real-valued computational space:

Barthes made fashion analytically readable by projecting it into language. A.I. makes fashion computationally calculable by embedding texts, images, bodies, behaviours, and objects into real-valued vector spaces.

Definition 4. Prediction

Let \(P\) be a predictive model. The letter \(P\) is used for prediction. From the observed data \(X(t)\), or from its embedded representation \(E(X(t))\), the model produces a predicted future state:

The symbol \(\hat{A}(t+\tau)\) denotes not the future itself, but a modelled future: a future as anticipated by the system. The hat notation \(\hat{\ }\) is used to indicate estimation or prediction. The variable \(\tau\) denotes the time horizon between the present state \(t\) and the predicted future state \(t+\tau\).⁸ 8The predicted state \(\hat{A}(t+\tau)\) should not be confused with the actual future state \(A(t+\tau)\). A prediction is a modelled future, not the future itself.

In the context of fashion, this prediction may concern taste, purchase, visibility, desire, influence, social belonging, body image, price sensitivity, cultural affinity, or future behaviour.

Prediction is not passive. When predictions are used for recommendation, production, advertisement, pricing, distribution, or visibility, they do not merely describe a possible future. They participate in producing it.⁹ 9When a prediction determines what is shown, recommended, manufactured, priced, promoted, or withheld, it becomes performative. It does not only anticipate the future. It helps organise the conditions under which that future appears.

Proposition. The Fashion System becomes a predictive system.

If fashion is observed through data, evaluated through computational functions, embedded into real-valued vector spaces, and reorganised through predictive models, then the Fashion System is no longer only a semiological system. It becomes a predictive system.

In Barthes’ case, fashion was projected into a textual and semiological space:

In the case of big data and A.I., fashion is observed as data and embedded into a real-valued computational space:

The first system reads fashion as signs. The second system embeds fashion as vectors and processes it as probabilities.

This does not abolish the semiological dimension of fashion. Images, garments, names, surfaces, and linguistic codes remain essential. But they are no longer processed only as meanings. They are processed as variables that can be correlated with future actions. The fashion image becomes not only something to be interpreted, but something to be measured. The garment becomes not only a sign, but a behavioural signal. The consumer becomes not only a reader of signs, but a predicted vector of future tendencies.

Barthes reduces fashion to a readable textual corpus. The present model extends fashion into a computable relational state-space in which texts, images, bodies, behaviours, objects, institutions, relation structures, and predictions can be treated within a common structural framework.

Remark. Designing in-distance after A.I.

In the previous chapter, a design operation was defined as an operation upon the world-state:

Here \(O_x(t)\) denotes the design operation, and \(S_x\) denotes the new system introduced by that operation. The letter \(O\) is used for operation. The subscript \(x\) indicates the particular new system introduced into the world. The letter \(S\) is used for system. ¹⁰ 10This distinction is important. \(O_x(t)\) is the act or operation of design. \(S_x\) is the new system, object, garment, code, ritual, image, platform, or institution introduced by that operation. The notation follows Chapter 4.

In Chapter 4, the future produced by such an operation was written as:

Here \(\Phi_\tau\) is the transition map that carries the present world-state into a future world-state over the time horizon \(\tau\). The superscript \((x)\) indicates the trajectory affected by the design operation \(O_x(t)\) and the new system \(S_x\).

In the age of big data and A.I., however, the intervention does not end with the transformation of the world-state. The transformed world is observed again, converted into data, embedded into a real-valued vector space, and predicted:

This formula should be read as follows: the design operation \(O_x(t)\) modifies the world-state \(A(t)\); the transformed world develops through the transition map \(\Phi_\tau\); the resulting state is observed by \(\Omega\); the observed data is processed by the predictive model \(P\); and a future state is generated as prediction.¹¹ 11The expression does not mean that the future is mechanically determined by the formula. It describes a structural sequence: operation, transition, observation, embedding, and prediction. The point is to show how design becomes entangled with the models that observe and anticipate the world.

Thus, designing in-distance becomes double. It is an intervention into the world, and at the same time an intervention into the models that observe, classify, embed, and predict the world.

This is the point at which fashion, religion, virus, and A.I. begin to share a common structural problem. Each of them does not merely exist within the world. Each modifies the way in which the world is perceived, transmitted, repeated, embedded, and projected into the future. The question is no longer only what fashion means. The question is what kind of future the fashion system is capable of predicting, producing, and enclosing.