Geometric Lie algebra in matter, arts and mathematics with incubation of the periodic systems of the elements

Abstract

From a brief recapitulation of the foundational works of Marius Sophus Lie and Herrmann G{\"{u}}nther Grassmann, and including missing African links, a rhapsodic survey is made of the straight line of extension and existence that runs as the very fibre of generation and creation throughout Nature's all utterances, which must therefore ultimately be the web of Reality itself of which the Arts and Sciences are interpreters on equal explorer terms. Assuming their direct approach, the straight line and its archaic and algebraic and artistic bearings and convolutions are followed towards their inner reaches, which earlier resulted in a retrieval of the baryons and mesons and now equally straightforward the electron/positron and nucleon geodesics and the organic build of the periodic system of the elements.