Linguistic Loops and Geometric Invariants as a Way to Pre-Verbal Thought?

TL;DR

The paper investigates whether invariants derived from linguistic transformations can capture pre-verbal thought by embedding linguistic elements into a geometric space and formalizing transformations as coherent, reversible operations. It defines linguistic loops as sequences of transformations and a semantic deficit metric to quantify meaning preservation across the loop, then shows how minimal rotations yield a quadratic-form representation whose invariant eigen-signatures classify loop behavior. The key contribution is the identification of GL(n,R)-invariant signatures associated with loops, offering a mathematical scaffold to link pre-verbal meaning with linguistic expression and to assess transformation robustness. The work envisions applications to cognitive science, neuroscience, and AI, including model distillation and improved semantic coherence in multilingual transformations, with planned empirical validation.

Abstract

In this work we introduce the concepts of linguistic transformation, linguistic loop and semantic deficit. By exploiting Lie group theoretical and geometric techniques, we define invariants that capture the structural properties of a whole linguistic loop. This result introduces new line of research, employing tools from Lie theory and higher-dimensional geometry within language studies. But, even more intriguingly, our study hints to a mathematical characterization of the meta-linguistic or pre-verbal thought, namely of those cognitive structures that precede the language.