On Fri, Aug 24, 2007 at 08:48:16AM -0700, David Artman wrote:
> > Zendo
> > -----
> > stumped by a simple rule that's difficult only because the master
> > invents a property I don't even think to consider, ("vertically
> > overlapping pieces", "M-shaped silhouette", etc.).
>
> OK, Zendo Grand Masters, let's hear it. That first rule is wonky but
> seemingly valid--I'm not sure what "vertically overlapping" means, but I
> imagine it was apparent in the white koans once the rule was revealed.
I'd assume "vertically overlapping pieces" are those which appear to
overlap one another when viewed from directly above. More rigorously,
the projection of one piece onto the plane of the playing surface from
the perpendicular intersects with that of another.
Valid if I'm correct.
> But that second one... outside reference (Roman alphabet letter), maybe?
> Too dependent upon a given viewer's current position around the playing
> area (i.e. does it pass the "spin the table" confirmation of a koan's
> isolation from anything outside itself)?
It's definitely not an outside reference. Outside reference is
something like "contains a piece pointing to magnetic north". To the
extent to which there's a clear division between the set of all things
which are "M-shaped" and thet set of all things which are not, this is
fine. It would be up to the master to make sure their calls are
consistent with some rigorous definition of M-shaped.
e.g. AKHTBN iff it consists of exactly four pieces, arranged such that
any piece which touches another does so at a vertex of both pieces, and
such that pieces one and two make an angle <180 degrees, two and three
make an angle <180 degrees in the other direction, and three and four
make an angle <180 degrees in the first direction.
This is an example of a rule which is certainly valid, and which someone
might describe as "M-shaped" for simplicity. I should note that I
distinguish between a rule's "name" or "English description" and the
"true rule" -- the latter has to be rigorous, but I don't mind if people
think of it in terms of a fuzzier nickname which is easier to remember;
as long as the game is mastered according to the "true rule" it's ok.
However, masters should keep in mind that rules like this are much more
difficult to master correctly.
It certainly passes the "spin the table" test, as you put it: AKHTBN iff
there exists some viewing angle upon the koan in which its silhouette
fits into the set of "things which are M-shaped".
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