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

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.