The object of this study is the interface as both a technological and an ontological form through which algorithmic procedures are rendered into user experience. This experience is connected to diagnosing a new contour of the tragic within the digital environment — namely, the disproportionality between the “measure of life” and the “measure of procedure” manifested in personalization and access protocols. The methodological framework combines conceptual analysis, an actor-network approach to rationality understood as reproducibility within a network, semiotic examination of the interface, and a hermeneutic interpretation of extra-subjective regimes of meaning. Borges’s “Library of Babel” is employed as a thought experiment. Results:(1) A definition of algorithmic predetermination is proposed as a regime in which a principle becomes operationalized into a repeatable procedure and is consolidated through interface infrastructure; (2) a three-stage architecture of predetermination is described: operationalization, network standardization, and interface exposition; (3) it is demonstrated that the interface makes the measure of procedure affectively tangible and translates probabilistic expectations into practical necessity; (4) levels of the tragic are identified — humanity, creator, and the “little man” — each with characteristic modes of recognizing predetermination; (5) the analytical value of Borges’s model is substantiated for describing normalized pathways of attention and the loss of surprise. Conclusions: The interface functions as a key mediator between the algorithm and lived experience, while tragedy serves as an analytical operator that clarifies already perceptible yet diffuse problems of digital predetermination.