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.

This study presents a fascinating linguistic property related to the number of letters in words and their corresponding numerical values. By selecting any arbitrary word, counting its constituent letters, and subsequently spelling out the resulting count and tallying the letters anew, an unanticipated pattern is observed. Remarkably, this iterative sequence, conducted on a dataset of 100,000 random words, invariably converges to the numeral four (4), termed the "Linguistic Loop (LL) constant". Examining 73 languages utilizing the Latin alphabet, this research reveals distinctive patterns. Among them, 28 languages exhibit LL-positive behavior adhering to the established property, while 31 languages deviate as LL-negative. Additionally, 13 languages display nuanced tendencies: eight feature two LL constants (bi-positivity), and five feature three constants (tri-positivity). This discovery highlights a linguistic quirk within Latin alphabet-based language number-word representations, uncovering an intriguing facet across diverse alphabetic systems. It also raises questions about the underlying linguistic and cognitive mechanisms responsible for this phenomenon.