CONICS, (q + 1)-ARCS, PENCIL CONCEPT OF TIME AND PSYCHOPATHOLOGY

– It is demonstrated that in the (projective plane over) Galois fields GF(q) with q = 2n and n ≥ 3 (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(2n), 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.