same space, different day

probably my best-looking version
of P^2(\Bbb F_4)^* so far
(but is graph paper “cheating”?).
[* this paragraph has no footnotes;
that’s a “star” standing for “dual”
rather than an asterisk: “the *dual* of
the two-dimensional projective space on
the field of four elements”]

meanwhile, i’ve played 21-tac-toe
right on the board a couple times
(versus self and madeline).

once one had memorized the board
(all 21 “lines”… the five circles in any
of the 21 “cross” diagrams here
are arranged in the pattern of a line
in the “big space” consisting of
the “crosses” [points of the space]),
the game would begin to very-closely-
-resemble “ordinary” tic-tac-toe:
just sketch a single cross and start
alternating X’s and O’s in the usual way.

all five points of any line wins;
otherwise count sets of four-on-a-line.

the last point isn’t played
(since there are an odd #
and the first player *already*
has an advantage).

so far the alphabetical version is easier.


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