Year: 2025
Type: preprint
Abstract: This paper introduces a method for the mathematical, content-independent analysis of any narrative, an approach we call Epistemological Geometry. It treats the latent space of a Large Language Model (LLM) not as a source of narrative answers, but as a high-dimensional geometric map. We recognize that this map represents an approximation of collective knowledge, culturally weighted and shaped by the model's training data. However, it is precisely this complex and measurable topography of dominant, recorded knowledge that, for the first time, offers a profound object for empirical inquiry into the structure of information itself. We argue that the very absence of semantic 'understanding' in an LLM enables an objective, purely structural analysis, independent of the narrative content of information. Instead of engaging in dialogue with an LLM, we utilize it as a measurement instrument to survey the topography of this knowledge space. To operationalize this, we measure three fundamental geometric properties: the Position of an information body within the consensus space (its Z-score), its Internal Architecture (a measure of coherence and stability), and its External Connectivity (the strength of its connections to established knowledge clusters). The combination of these metrics yields a unique "topological signature" for any body of information. Initial experiments demonstrate that this method is capable of drawing precise conclusions about the fundamental nature of a text based solely on this abstract signature. Epistemological Geometry thus offers a powerful instrumentarium to classify bodies of information on a purely structural basis and to determine their relationship to the total corpus of knowledge. As a future research direction, this opens up the potential not only to analyze existing knowledge but also to identify structural "gaps" or "contradictions" within large domains of knowledge. The targeted bridging of these gaps could serve to generate new, testable hypotheses in fields such as medicine, climate science, and beyond.
Author: Esim Can
Language: English
Topic: Topic Modeling
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
OpenAlex ID: W4413638536