http://popups.lib.uliege.be/1373-5411/index.php?id=3072 Index terms fr 0 http://popups.lib.uliege.be/1373-5411/index.php?id=3069 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. Fri, 06 Sep 2024 16:06:33 +0200 Thu, 10 Oct 2024 10:05:14 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3069 http://popups.lib.uliege.be/1373-5411/index.php?id=3403 This paper introduces a mathematical representation of the fundamental physical notions particles, waves, and Heisenberg's Uncertainty Relation in such a general way that neither Hilbert spaces nor the real or complex numbers are used. This new approach is based on the mathematical notion of a lattice as defined by Birkhoff (1940) who introduced lattices as a generalization of hierarchies in geometry, logic and algebra. In 1982 lattice theory has been connected by Wille (1982) with the philosophical construct of a concept using a mathematical definition of formal concepts and concept lattices. Formal Concept Analysis (FCA), the mathematical theory of concept lattices, was then used by the author to introduce Temporal Concept Analysis which is based on Conceptual Time Systems where the notion of a state is introduced as a formal concept. The conceptual definition of life tracks of objects led to a generalization of the formal representation of objects in Conceptual Semantic Systems where distributed objects yield a clear mathematical representation of the idea of a wave packet together with a definition of particles and waves. In this paper the author's previous definitions of particles and waves are extended, the notion of measurement is introduced and combined with the notion of a view and a (distributed) object to represent "how distributed" that object is represented by the measurement in the chosen view. That leads to a conceptual analogue of the notion of "simultaneously measurable" in Quantum Theory and to a conceptual analogue of Heisenberg's Uncertainty Relation. Wed, 18 Sep 2024 09:10:56 +0200 Wed, 18 Sep 2024 09:11:13 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3403