Resisting the World of Discretization

A FORMAL NOTE ON RESISTANCE

The preceding argument may be formalised more carefully. The problem of discretization should not be understood as a simple opposition between reality itself and its computational representation. Such an opposition would assume that reality is directly available before any act of perception, language, memory, classification, or technical mediation. This assumption is too simple. What we call reality is already given to us through forms of projection: sensation, body, memory, language, habit, desire, historical form, and cultural category.¹ 1This formulation is close to a Kantian distinction between the world as it appears and the world as it may be thought prior to appearance. The latter is not used here as a positive object of knowledge, but as a limit to every representational system.

Therefore, resistance cannot mean a return to an unmediated reality. There is no simple return to a world before projection. Human beings do not encounter the world as a pure object without mediation. Machines also do not encounter the world directly. Both human experience and machine intelligence operate through forms of selection, reduction, formatting, and projection. The question is not whether the world is projected, but which projection becomes dominant, and what remains outside its closure.

Definition 1. The world prior to a particular projection

Let \(\mathfrak{W}(t)\) denote the world at time \(t\) prior to any particular projection. The Gothic letter \(\mathfrak{W}\) is used for world in a deliberately cautious sense. It does not designate a world that is directly available to knowledge. It is a limit-concept: a way of indicating that no single projection exhausts the world.² 2The symbol \(\mathfrak{W}(t)\) should not be read as an object that can be directly observed, measured, or embedded into a Euclidean space. It marks the excess of the world over any particular mode of appearance, description, or computation. In this sense it functions as a Kantian limit-concept rather than as a positive object of knowledge.

A human world is not identical with \(\mathfrak{W}(t)\). It is the world as projected through human forms of experience. We may write:

Here \(\Pi_H\) denotes human projection. The Greek letter \(\Pi\) is used for projection, and the subscript \(H\) is used for human. \(A_H(t)\) is the world as it becomes available to human experience through sensation, embodiment, memory, language, habit, affect, desire, and historical form.³ 3\(A_H(t)\) should not be confused with a private inner world. It is the humanly available world: already mediated by body, language, memory, culture, and history.

This humanly projected world is structurally related to the world-state described in Chapters 4 and 5:

Here \(A(t)\) denotes the relational world-state: the aggregate of human condition space \(\mathcal{C}(t)\), system condition space \(\mathcal{S}(t)\), and the relation structure \(R(t)\) between humans and systems. In Chapter 6, \(A_H(t)\) emphasises the fact that such a world-state is always given to human beings through a human form of projection.

Definition 2. Machine projection and real-valued embedding

A machine-readable world is also a projection. It is not the world itself. It is the world as formatted for computation. In Chapter 5, this computational sequence was described through observation and embedding:

In the present chapter, because we are distinguishing human projection from machine projection, we write the observed data of the humanly projected world as:

Here \(\Omega\) is the observation function, and \(X_H(t)\) denotes the data observed from the humanly available world. The subscript \(H\) indicates that the machine does not observe an unmediated thing-in-itself. It observes traces, records, images, bodies, purchases, texts, locations, and behaviours as they appear within the humanly and institutionally structured world.

The observed data is then embedded into a real-valued vector space:

Here \(A_M(t)\) denotes the machine-readable world at time \(t\). The subscript \(M\) is used for machine. The letter \(E\) is used for evaluation or embedding. The expression \(\mathbb{R}^k\) indicates the \(k\)-dimensional real-valued vector space in which the machine-readable representation is processed. ⁴ 4The expression \(A_M(t)\in\mathbb{R}^k\) applies only to the computational representation of the world. It does not imply that the world itself, or even the humanly experienced world, is originally a Euclidean object. The embedding into \(\mathbb{R}^k\) is an operational condition of computation, not an ontological claim about reality.

This is the decisive difference between human projection and machine projection. Human projection gives the world as lived, remembered, desired, misread, suffered, ritualised, and imagined. Machine projection gives the world as data points, vectors, probabilities, clusters, correlations, and predictions.

The problem is not that A.I. projects the world. Human experience also projects the world. Barthes’ semiology also projected fashion into written descriptions. The problem is that machine projection embeds the world into real-valued vector spaces where it becomes comparable, predictable, recommendable, excludable, targetable, and optimisable.⁵ 5This is why the passage from semiology to computation is not merely a change of method. Barthes projected fashion into a textual and semiological space. A.I. projects fashion, bodies, images, purchases, and behaviours into spaces where distance, similarity, probability, and prediction can be calculated.

Definition 3. Remainder

We may now define the remainder of discretization. The remainder is not the difference between reality itself and its computational representation. Rather, it is the non-identity between the human projection of the world and the machine projection of the world:

Since \(A_M(t)=E(X_H(t))\) and \(X_H(t)=\Omega(A_H(t))\), this may also be written as:

The Greek letter \(\rho\) is used for remainder or residue. The symbol \(\ominus\) does not indicate ordinary algebraic subtraction. \(A_H(t)\) and \(A_M(t)\) do not necessarily belong to the same kind of space. \(\ominus\) marks a gap, non-identity, or remainder between two modes of projection. ⁶ 6The notation \(\ominus\) is used heuristically. It does not require both sides to be elements of the same vector space. It marks an irreducible gap between the world as humanly experienced and the world as machine-readable.

This remainder is not merely an error. From the viewpoint of a computational system, what escapes classification may appear as noise, missing data, anomaly, ambiguity, or inefficiency. But from the viewpoint of fashion, art, religion, poetry, and the self, this remainder is often where meaning begins. It contains hesitation, misrecognition, silence, bodily feeling, private memory, symbolic excess, ritual intensity, and forms of desire that cannot be exhausted by prediction.

The remainder \(\rho(t)\) is therefore not outside the world. It is not a romantic exterior untouched by systems. It appears within the relation between projections. It is produced wherever the humanly lived world refuses to become identical with its machine-readable form.

Definition 4. Resistant design operation

In Chapter 4, a design operation was written as:

Here \(O_x(t)\) denotes the operation of design, and \(S_x\) denotes the new system introduced by that operation. The letter \(O\) is used for operation, and the letter \(S\) is used for system.

In the present chapter, let \(O_R(t)\) denote a resistant design operation at time \(t\). The subscript \(R\) is used for resistance. Such an operation does not simply reject technology, nor does it attempt to escape the system entirely. Instead, it intervenes in the world in such a way that the remainder is preserved, intensified, or newly generated.⁷ 7\(O_R(t)\) is a resistant form of design operation, analogous to \(O_x(t)\) in Chapter 4. The notation does not require \(O_R(t)\) to be outside the system. It indicates an operation that changes how the system relates to what it cannot fully classify or predict.

If \(\mu\) denotes a measure of residual intensity, we may write:

Here \(\rho_{O_R}(t+\tau)\) denotes the remainder in a future state after the resistant operation \(O_R(t)\). This formula does not claim that the remainder can be measured in a simple numerical way. It means that a resistant design operation is one that increases the non-identity between human projection and machine projection, or prevents that non-identity from being completely absorbed by classification and prediction.⁸ 8The function \(\mu\) should be read as a conceptual measure rather than a technical metric. It may refer to opacity, ambiguity, symbolic excess, affective intensity, poetic density, or the degree to which a form resists being fully predicted or operationalised.

In this sense, resistant design is not the negation of design. It is design against closure. It produces objects, images, garments, spaces, gestures, and systems that can be observed, but not exhausted; named, but not completed; circulated, but not fully translated into the coordinates of prediction.

Proposition. Resistance is the preservation of non-identity.

Resistance in the world of discretization is not the recovery of an unmediated real. It is the preservation of a non-identity between human projection and machine projection.

We may summarise the structure as follows:

The first line indicates the human projection of the world. The second line indicates the machine projection of the humanly available world into a real-valued computational space. The third line indicates the remainder: the non-identity between these two projections.

A world without remainder would be a world in which human projection and machine projection become indistinguishable. In such a world, to be seen would mean to be classified; to desire would mean to be predicted; to choose would mean to follow a path already optimised by the system. Fashion would no longer open a possibility of becoming otherwise. It would become a surface for the confirmation of probabilities.

The strong “I/me” described above should therefore not be understood as a sovereign subject standing outside all systems. It is not a pure interior, untouched by language, media, markets, religion, image, or technology. Rather, the “I/me” is the residual modality through which the human projection of the world refuses to become identical with its machine-readable form.⁹ 9The “I/me” is not treated here as an isolated Cartesian ego. It is closer to a residual mode of appearance: definite enough to act, choose, desire, and create, but never fully systematised by the categories that attempt to capture it.

This also clarifies the relation between fashion, religion, virus, and A.I. Each operates through repetition, transmission, inscription, and transformation. Each creates forms that move through bodies and systems. But fashion becomes resistant when it refuses to become only a code, only a prediction, only a behavioural signal. It becomes resistant when it produces a remainder within the very systems that seek to discretize it.

The question, then, is not whether fashion can remain outside discretization. It cannot. The question is whether fashion can generate forms that remain partially opaque after being observed, classified, embedded, and predicted.

Resistance begins where this closure fails.

The future of fashion will not be decided only by those who produce the most accurate predictions. It will also be decided by those who produce the most irreducible remainders. This is why the possibility of a new fashion design still emerges from designing in-distance: not from the fantasy of escaping the system, but from the invention of forms that keep the future from becoming identical with its prediction.