Hello Starship Captains!
In this post, I want to introduce an idea to be able to build a koan that follows the Buddha Nature:
"All pyramids of the koan are ungrounded and weird."
It doesn't require space travel and zero gravity to make this work!
In my previous post (see The Winning Rule in Zendo), I showed that there is only the empty koan follows the rule "All pyramids are ungrounded," and depending on your taste, even the empty koan will be excluded.
The reason that we can't build koans following these rules is that there is another rule in Zendo, stating that pyramids in a koan "do not touch another koan’s pieces or any other foreign objects, including marking stones" (see Zendo Rules).
However, I found it a bit of a loss that with 5 rainbow (or xeno) stashes, you wouldn't be able to use the opaque black (or white) pyramids. As a result of my previous post, I came up with the idea that opaque pyramids can be used to signify "no pyramid". In other words, they work as props, but should not be considered a part of the koan.
Zendo Extension. Opaque pyramids can be used as props; they are "nothing" (and therefore are "no pyramid") and function as "fillers of space". No rule may refer to them.
As a result, now we can build koans that follow the above Buddha Nature, simply by stacking pyramids on top of opaque ones. The nice thing is that by adding opaque pyramids to the game, we actually add "no pyramids" to the game. So, for example, if a pyramid touches only opaque pyramids, it "doesn't touch any pyramid"!
It is possible to extend Zendo in such a way that it allows more koans to follow the Buddha Nature. This allows for more game play, and requires more accurate formulation of the Buddha Nature.
Please, let me know about your experience if you tried this extension to Zendo!
Note that in the extended version of Zendo, the rule "All pyramids in the koan are weird" has a koan with exactly one weird pyramid (of any size). It's the lowest possible limit of number of pyramids . . . So now, being all weird is easy to guess . . .
They used to sell ELBS in big bags. I sometimes do pretty much the same thing you're describing, only with elbs.
We use the opaque pyramids in the usual way, treating them as pyramids in the koans.Of course, the same arrangements you have in mind could be covered by the rule "All non-opaque pyramids of the koan are ungrounded and weird."
Thank you P.D.M. This is also a great observation. However, note that my consideration wasn't to "cover koans", but to "cover rules". In your case, the rule "All pyramids of the koan are ungrounded" would again not yield any other koans than the empty koan.
I'm getting a sort of déjà vu. As we are doing some sort of applied logic and model theory here, it seems similar to Goedel's Incompleteness Theory: for every consistent theory based on a set of axioms that is powerful enough to allow self-reference, the theory is incomplete. That means, it allows for a so called Goedel sentence G that is true, but can not be proven by applying deductive logic within the theory. (Such a sentence G translates to "Sentence G can not be proven within the theory.") However, the theories emerging from adding G or ~G, although both consistent, suffer the same anomaly!
It seems that if we want to cover certain "simple" rules, then we have to add some things that aren't considered pyramids (even if they are opaque pyramids) and make the game less simple, . . .
if we want to cover the same koans (but not rules), then the rule must become less simple. However, in this case, the same "simple" rule would then still only yield the empty koan.
zen zen = 'zen' and 'zen' = ''zen'' and 'and' and ''zen'' = '''zen''' and 'and' and ''and'' and 'and' and '''zen''' = ...
zen = zen = zen = zen = ...