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Experiments in Symmetry. Several experimental games to test whether perfect symmetry makes a game better.[All Comments] [Add Comment or Rating]

Mark Thompson wrote on Wed, Feb 16, 2005 04:24 AM UTC:

If you really want to go for the ultimate in symmetry, I would suggest we
need to do away with the notion of a square board. A square has only eight
symmetries: reflection NS or EW, 180 degree rotation, or any (or no)
combination of these. Indeed, the ultimate in symmetry would be to do away
with the board's edges: the board should be infinite, hence giving it
translational as well as reflectional symmetry. And we should do away with
the notion of cells within the board: the most symmetrical 2-dimensional
object being the entire Euclidean plane, in which any point is equivalent
to any other. Then we have complete rotational symmetry, about any point,
as well as translations and reflections.

But since we're pursuing symmetry as the ultimate goal here, we need to
embolden ourselves to take the next vital step as well. To do away with
the last vestiges of ugly asymmetry, we must also abolish the pieces: for
once pieces are introduced into our pristine continuum, they render the
game asymmetrical again, by causing some points and directions to have
more importance than others: in particular, the points pieces occupy, and
the directions they would need to move to attack other pieces, would have
special importance. Our ultimate, perfectly symmetrical chess must
therefore consist of an infinite plane with NO PIECES AT ALL.

It might be objected that without pieces it will be difficult to state
rules of movement, capture, initial setup, and object. But clearly, since
we desire a perfectly symmetrical game, we must abolish these notions as
well: because the perfectly symmetrical chess game must be symmetrical in
time as well as in space, and therefore it must have no beginning, no end,
and no change: the state of the game at any point must be the same as its
state at any other point. 

And so, at last, we have our perfectly symmetrical game: no cells, no
pieces, no goal, no players: is not its perfect, chaste serenity a thing
of beauty? Have we not achieved true theoretical perfection? And can we
not get back to discussing real chess games now?