Pencils of conics: a means towards a deeper understanding of the arrow of time?

The paper aims at giving a sufficiently complex description of the theory of pencil-generated temporal dimensions in a projective plane over reals. The exposition starts with a succinct outline of the mathematical formalism and goes on with introducing the definitions of pencil-time and pencil-space, both at the abstract (projective) and concrete (affine) levels. The structural properties of all possible types of temporal arrows are analyzed and, based on symmetry principles, the uniqueness of that mimicking best the reality is justified. A profound connection between the character of different ‘ordinary’ arrows and the number of spatial dimensions is revealed.