  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.
