Geometric Linguistic Space

The remarkable progress of generative AI has brought fresh air to linguistics. In animal communication and language translation, generative AI has been used to deepen consideration at the semantic space level, and as a result, geometric similarities in semantic space have been discovered. Even if the expressions in concrete space are different, when they are mapped to semantic space, the existence of geometric similarities that had been hidden until now has been discovered. In the end, this may seem obvious, but it is a surprising discovery. Inspired by this discovery, this paper proposes a basic mathematical theory necessary for understanding linguistic space. This study aims to clarify the geometric properties of the translation process, which are difficult to explain using conventional linguistic theory. In this study, linguistic space is regarded as a mathematical coordinate space, and translation between different languages is treated as a coordinate transformation, assuming the existence of a common invariant, the meaning of language. From this perspective, the approach of this study is called ''geometric linguistic space''.