Language and Geometry

This study compares language and geometry which are both communication tools with their own specificities and performances. It follows a briefly presentation of the essential characteristics of languages and geometry to discover their main similarities in the domain of knowledge transfer. The waves are the essential language vehicles: sounds or vocal waves for conversations and lectures; electromagnetic waves for reading the scriptures. Consequently waves need a space for their propagation. On the other side, any language needs a diffusion space between the interlocutors. The three-phase structures in the fragmentation of our social proximity is indicated by the personal pronouns which structure our conjugations. Verbs are the kinematic components of any sentence, they bring movements, modifications as well as descriptions of states and situations. Therefore we draw a functional analogy between verbs and waves. It is the crucial point of this report. In relation to their significations, a verb partition is performed in a hexagonal configuration which supports on the first side 3 active verbs: motor, social, anticipative verbs and on the second side 3 statics: state, reactive, metrological verbs. The tense range locates any sentence along the time axis. Consequently these ones can follow variation sequences and introduce the kinematic behaviour. For their representing topology it is requested to use a multidimensional complex space whose real axes support the objective tenses of simple description and whose imaginary axes support the tenses loaded with subject intentions. The future tenses necessary bring anticipative views.