Can all parity be explained?

[cmhardw]

So why on earth would we want redefine "reduction parity" to include things that violate the universally accepted notion of what parities are? It makes no sense to me. It would invite the term to be ridiculed, in my opinion. I certainly will not subscribe to such a definition.

Is there anything specifically in cubing that you want to be called a reduction parity that isn't consistent with the universally accepted notion of parity?

I've been following this thread with interest, but now I'm confused.

Are we no longer calling situations where one reduces a puzzle such that it can now be solved with a subset of the puzzle's possible turns, only to find that this subset of turns is incapable of solving the puzzle "reduction parity"?

This is how I interpret the discussion so far.

Should we be calling this situation a "reduction error" or some other such term?

 

[cuBerBruce]

I've been following this thread with interest, but now I'm confused.

Are we no longer calling situations where one reduces a puzzle such that it can now be solved with a subset of the puzzle's possible turns, only to find that this subset of turns is incapable of solving the puzzle "reduction parity"?

I am not aware of anything being called a reduction parity that doesn't divide the relevant configurations into two mutually exclusive sets. OLL parity, PLL parity, and square-1 parity all do. That's why I asked the question. I mentioned earlier something that divides the relevant configurations into 6 sets. But I've not been aware of that being called a parity (and which it certainly isn't in any normal usage of the word).

Should we be calling this situation a "reduction error" or some other such term?

Well, that reminds me of people using "parity error" in cubing, which I've never really liked. I don't generally think of parity conditions as being errors. But I suppose (to me) "reduction error" is a little better than "reduction parity" if the condition isn't really a parity situation.

 

[blade740]

I am not aware of anything being called a reduction parity that doesn't divide the relevant configurations into two mutually exclusive sets. OLL parity, PLL parity, and square-1 parity all do. That's why I asked the question. I mentioned earlier something that divides the relevant configurations into 6 sets. But I've not been aware of that being called a parity (and which it certainly isn't in any normal usage of the word).

If one was using a 2x2 method that involved reducing the puzzle to 2gen, I could see the "orbit fix" step being referred to as "fixing parity", even though it isn't a binary state.

If you assembled the pieces of a 3x3 at random, and the corner orientation was wrong, you might call that problem "corner orientation parity". This divides into 3 sets, rather than 2, but I think most speedsolvers would consider it a sort of parity.

 

[cmhardw]

I am not aware of anything being called a reduction parity that doesn't divide the relevant configurations into two mutually exclusive sets. OLL parity, PLL parity, and square-1 parity all do. That's why I asked the question. I mentioned earlier something that divides the relevant configurations into 6 sets. But I've not been aware of that being called a parity (and which it certainly isn't in any normal usage of the word).

If one was using a 2x2 method that involved reducing the puzzle to 2gen, I could see the "orbit fix" step being referred to as "fixing parity", even though it isn't a binary state.

If you assembled the pieces of a 3x3 at random, and the corner orientation was wrong, you might call that problem "corner orientation parity". This divides into 3 sets, rather than 2, but I think most speedsolvers would consider it a sort of parity.

Perhaps these orbits could be called "unsolvable subsets" or "unsolvable reductions" with the implication being that the orbit cannot get to the puzzle's solved state by way of moves within the reduced subset only.

I also like "false reduction" or "unsolvable reduction" as terms too.