Conics, (q+1)-Arcs, Pencil Concept of Time and Psychopathology
Abstract
It is demonstrated that in the (projective plane over) Galois fields GF(q) with q=2^n and n>2 (n being a positive integer) we can define, in addition to the temporal dimensions generated by pencils of conics, also time coordinates represented by aggregates of (q+1)-arcs that are not conics. The case is illustrated by a (self-dual) pencil of conics endowed with two singular conics of which one represents a double real line and the other is a real line pair. Although this pencil does not generate the ordinary (i.e., featuring the past, present and future) arrow of time over GF(2^n), there does exist a pencil-related family of (q+1)-arcs, not conics, that closely resembles such an arrow. Some psycho(patho)logical justifications of this finding are presented, based on the "peculiar/anomalous" experiences of time by a couple of schizophrenic patients.
Cite
@article{arxiv.math/0301009,
title = {Conics, (q+1)-Arcs, Pencil Concept of Time and Psychopathology},
author = {Metod Saniga},
journal= {arXiv preprint arXiv:math/0301009},
year = {2007}
}
Comments
4 pages, no figures, LaTeX, to appear in Frontier Perspectives