Looney Labs Icehouse Mailing list Archive

[Icehouse] three-state Zendo

  • FromJoshua Kronengold <mneme@xxxxxx>
  • DateTue, 10 Mar 2009 15:49:12 -0500
Dale Sheldon writes:
>On Tue, 10 Mar 2009, Joshua Kronengold wrote:
>> Um, no.  It's not at all subjective.  You have two rules; one 
>> distinguishes "green" from black/white, the other distinguishes black 
>> from white.
>Ah, I missed that there were two seperate and distinct rules.

Ah!  That explains the disporportionate reaction.

>I don't see how this relates to nullity, which is I think why your line of 
>thinking has seemed so off-track to me.

I was following a tangent, of course, but yes, it doesn't have
anything to do with nullity.

>If you want to add complexity to zendo, rock on with your bad self. 
>Failing part I of a two-stage rule doesn't strike me as "mu" though; it's 
>just "false to the second order".

Terminology, in this case, is fairly critical -- as it implies an
intended usage.  One could use "has a green stone" "has a black stone"
and "has a white stone" (as I not infrequently use for Zendo,
particularly when people are using non-standard marking stone colors),
but if one wants to encourage intended usage, I'd probably go with
(and it's important because it affects guessing) "a koan is valid if
and only if it contains a purple piece, and all purple pieces within
it are pointing at other pieces.  A koan has the buddha nature if and
only if the pip count of pieces directly pointed to by purple pieces
is odd". (I considered "can have the buddha nature" vs "has the buddha
nature", but that's too easy to mess up, whereas invalid/nbn/bn is
easier to distinguish in dialogue).

What I find interesting here, btw, (and the reason I went from
"3-state zendo is a cute concept, but why would you bother making a
challenging game more difficult" to "actually, 3-state zendo is worth
experimenting with and probably worth playing") is that there exist a
whole region of rules -- numerically, rules that have a very
unbalanced BN/NBN ratio -- that are, rather than being harder and more
complex using 3-state, are actually easier and more tractible --
because by switching to 3 marking stones, the master has distinguished
between two cases that the student would otherwise have to intuit on
their own -- not to mention, because if the valid/invalid decision is
chosen well, the liklihood that each new koan would shave slightly the
known definition of bn/nbn (as you get much more information, all
things being equal, when you add a new koan in the set that has fewer
examples than you do when you add to the larger visible set) is
increased substantially.  3-state is only really more complicated if
one uses it as an excuse to use substantially more difficult rules --
and even if so, it's not unlikely that those rules will be easier than
they would be in two-state zendo.

Of course, if one already avoids the rules that I'd consider "complex,
but fun" in Zendo, then yeah, 3-state zendo will generally be more
difficult and complicated, as the starting complexity of rules that
are interesting in that system will, by its nature, be higher than
that in normal Zendo.

One remaining question, of course, is whether one should be able to
make partial guesses with a guessing stone ("a koan is valid if and
only if it contains at least two pieces" -- which can't let you win,
but can give you a "you are wise" if you successfully define the
exclusive difference between one set and the other two), or whether
its better to conventionally do valid/invalid counterexamples if
available before bn/nbn counterexamples (perhaps), but force all guesses
to have a valid/invalid and bn/nbn component.   (I'd not make special
progression in the rules for valid/invalid, of course -- if you want
to guess "a koan has the buddha nature if and only if it contains a
green pyramid" or even "a koan has a black stone if and only if it's
composed entirely of flat pyramids" and single-set guesses are legal,
then you can make those guesses).

       Joshua Kronengold (mneme@(io.com, labcats.org)) |\      _,,,--,,_  ,)
--^--   "Did you know, if you increment enough, you   /,`.-'`'   -,  ;-;;'
 /\\    get an extra digit?"  "I knew," weeps Six.    |,4-  ) )-,_ ) /\     
/-\\\   "We knew. But we had forgotten."	     '---''(_/--' (_/-'