God's algorithm discovered for OLL parity edge flip (theory)

I agree with cmowla. It seems that people are defining "pure" when referred to a parity algorithm as "supercube safe". As Chris said, this is only possible on the 4x4x4 supercube. Every other cube size will have other effects on the centers by changing the parity of a wing orbit. If you want proof of this, see my supercube parity states matrix method. It seems pointless to me to talk about whether an algorithm is supercube safe on the 4x4x4 or not. Also, what is the problem of saying that an algorithm is the God's Algorithm (assuming this is proven) for the n x n x n cube, and by that I mean regular cube and not supercube? It makes perfect sense to me. We don't care about the locations of centers on a regular cube when solving, so why would we start when considering this parity algorithm?

It would be theoretically possible to construct a minimally destructive parity algorithm on any cube size larger than 4x4x4 supercube, but it is impossible to have a completely supercube safe parity algorithm on any cube larger than the 4x4x4 supercube. My supercube parity matrix is the proof of this, so read it if you still need to be convinced.

--edit--
Ok looking at the parity states matrix of the even n x n x n cube there is one exception to this. If you change the parity of every wing orbit on the even n x n x n supercube, then this will not affect the parities of any of the center orbits. However, since this is just a bandaged 4x4x4 cube, I still think the argument stands that "pure" in the sense of "supercube safe" applies only to the 4x4x4 cube, or changing the parity of every wing orbit on the even n x n x n supercube. This seems like a very clumsy definition to me.
 
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I have read that proof about the specialty of 4x4x4 from you a loooong time ago (5 years?). But "pure" has the properties of "supercube safe, can be used for blindfolded" associated with it. That is the only complaint I have about using that word, not interfering with anything else in this discussion that seems like great work

Lars said:
this is for Fewest moves, curiosity and mathmatics
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For Fewest Moves, parity should be avoided in totally different ways. Adding 20 moves for 2 pieces is completely unacceptable.
Curiosity, mathematics and advancing cube theory I totally agree with
 
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AvGalen said:
I have read that proof about the specialty of 4x4x4 from you a loooong time ago (5 years?). But "pure" has the properties of "supercube safe, can be used for blindfolded" associated with it. That is the only complaint I have about using that word, not interfering with anything else in this discussion that seems like great work
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I don't know of any "pure" algorithms for the parity of the wings edges then, and I certainly don't use pure algorithms when I solve blindfolded.

The two parity algs I use are:
l' U2 l' U2 F2 l' F2 r U2 r' U2 r2

and the old standard:
r2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 r2

Now I could make these pure on the 4x4x4 by using an alg to rotate one center group 180 degrees, but I could never make a pure alg on the 5x5x5 supercube as that is impossible.

Neither of these algs is pure, yet I still use them for blindfold solving the 4x4x4 and 5x5x5 supercubes. Also, I would argue that not very many of us are crazy enough to solve the larger supercubes blindfolded, and remember that it is impossible to have a "pure" parity alg on the odd n x n x n supercube. So for solving the 5x5x5 supercube blindfolded, there does not exist any "pure" alg. You will have to make do with a minimally destructive parity alg, and account for its effects on the cube.

--edit--
Also, it was my understanding that "pure" when applied to a parity alg meant that you were only turning single inner slice turns rather than multi-slice groups. I thought that was all that "pure" meant for a parity alg. Where is it defined in the literature anywhere that "pure" is related to whether or not it is "supercube safe"? I have not seen that before to be honest.
 
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cmhardw said:
I don't know of any "pure" algorithms for the parity of the wings edges then, and I certainly don't use pure algorithms when I solve blindfolded.
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The one I'm using is:
U l U' l' U' l' U l U l' U' l' U' l D x' d2 l' d2 l x U D'
which swaps the UFl and UBl wings and does nothing else on the 4^3. On the 5^3, it also swaps the Ul and Dl +-centers and that's all.
A bit longer than your algs, but it doesn't really matter concerning an alg I only use once every second solve, and the gain of being able to do centers at the end (which I really feel more comfortable with) is much bigger for me.
 
You're missing the point. If you apply your 2-edge flip to a scrambled 3^3, you will always get 2 edges flipped as the only apparent result no matter how you scrambled your cube before. So yes it is pure as a 3^3 alg (but not as a supercube alg of course). This is not true for a dedge flip on the 4^3 which rotates centers.
On a group-theoretical point of view: on the 3^3, the group H of center rotations is a normal subgroup of the group G of permutations of the supercube, hence the quotient G/H, which is the set of permutations of the normal 3^3, has a natural group structure induced from the group structure of G. Unfortunately this doesn't work for big cubes, and we musr consider the full supercube group as the group of permutations of the 4^3.
 
TMOY said:
You're missing the point.
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We should ask ourselves why did this intelligent individual miss your point? (Oh, I know exactly why->find the *). I never said my alg was pure for the supercube, but you insisted that it shouldn't be considered a pure algorithm for regular cubes! More importantly, think about the context I was indicating how it was pure...for users who use reduction, k4, or some other method which solves centers to non-supercubes first. (I never said, "Oh and to the blindfold solvers, this algorithm even works if you solve centers last, and to supercube solvers, this algorithm affects the minimal centers on the nxnxn!"). This is probably THE number one reason why I bet most of the people viewing your posts about pure odd permutations algorithms are confused.
TMOY said:
If you apply your 2-edge flip to a scrambled 3^3, you will always get 2 edges flipped as the only apparent result no matter how you scrambled your cube before.
Click to expand...
All those who solve centers first on non-supercubes will say, "And you won't for a 'pure edge flip' for the nxnxn?"

*Most people solve centers first on non-supercubes, so this has absolutely no meaning to the majority of cubers in the world, not even including the supercube in the equation. That IS why my algorithm can be considered "pure" in their eyes because it swaps two wings in the same composite edge "no matter what scrambled state the composite edges and corners were in". This is just as valid reason to consider an algorithm pure as is yours for solving the centers last in 4x4x4 bld because that is the method they use.

Algorithm Terminology Proposal.
Instead of saying my algorithm is "visually pure", how about we call your algorithm (and all other algorithms which do not affect centers for any size supercube) "supercube safe" or "supercube pure" and refer to algorithms which are visually pure as pure.

Why? "Majority rules" can have a place here too. Think about the future generation of cubers replacing every description of algorithms (which visually affect only non-center pieces, but affect the centers) with the term "visually pure". Do you know how many fast/short algorithms would need their description enlarged? As a programmer, this is definitely a no no, if I have any hope to same code space. If I can have less code to make sense to the computer, I will use it, as my computer's RAM is limited.




By the way, your supercube pure algorithm for the 4x4x4 is pretty neat.
U l U' l' U' l' U l U l' U' l' U' l D x' d2 l' d2 l x U D' = [U l U' l' U', l'] (l') [l', U'] [U' D: [f2, l']]

It swaps two wings and permutes 6 X-center pieces (with a 2 3-cycle),
[U l U' l' U', l'] (l') [l', U']
and then restores the 6 X-center pieces with a very brief 2 3-cycle [f2, l']
, whose set-up moves, U' D, (to move all X-center pieces affected into slice 2L) partially cancel with the first piece!
 
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In othr words: most people are clueless, so let's keep them in their cluelessness ? Well, at least they can see how great an opinion you have about them.
 
TMOY said:
In othr words: most people are clueless, so let's keep them in their cluelessness ? Well, at least they can see how great an opinion you have about them.
Click to expand...
You missed my point, or you are just being stubborn. I wasn't saying that most people are "clueless", I am saying that I want to save people the trouble of describing something in fewer words than what you are wanting. AND, according to how they solve and what kind of cube they solve, the "fewer words" is a legitimate description of what they are doing.
 
TMOY said:
We should ask ourselves why did that intelligent individual miss your point. :p,
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Yeah, the intelligent individual failed to read my entire post:
cmowla said:
Think about the future generation of cubers replacing every description of algorithms (which visually affect only non-center pieces, but affect the centers) with the term "visually pure". Do you know how many fast/short algorithms would need their description enlarged? As a programmer, this is definitely a no no, if I have any hope to same (I meant to write "save", not "same", but I still think anyone could have guessed that) code space. If I can have less code to make sense to the computer, I will use it, as my computer's RAM is limited.
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or is purposely being stubborn (which is now definitely more of a possibility).

EDIT:
If you were implying the single sentence I wrote:
cmowla said:
This is probably THE number one reason why I bet most of the people viewing your posts about pure odd permutations algorithms are confused.
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Take note in what David said below this post. I meant they were confused because you are going against common terminology. However unclear that sentence was, there was no legitimate reason to misinterpret what my point:
cmowla said:
I am saying that I want to save people the trouble of describing something in fewer words than what you are wanting. AND, according to how they solve and what kind of cube they solve, the "fewer words" is a legitimate description of what they are doing.
Click to expand...
because of the portion I first pointed out in this post.
 
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TMOY said:
You're missing the point.
Click to expand...

No, you seem to be missing my point. There's a big difference between what is technically correct and what is the commonly accepted terminology. You're the only one stressing the importance of the first one. We still refer to "PLL Parity" as a parity case, even though it technically isn't. However, in the context of solving with the reduction method it is a parity case. Context is everything regarding terminology in cubing. If you would like to refer to this alg as "visually pure" in the context of 4BLD and supercube solving then you are more than welcome to. However, cmowla's algs have always been (this thread is certainly no exception) in the context of speedsolving all even-ordered bigcubes, therefore drawing a distinction in this case is wholly unnecessary.
 
DavidWoner said:
No, you seem to be missing my point. There's a big difference between what is technically correct and what is the commonly accepted terminology. You're the only one stressing the importance of the first one. We still refer to "PLL Parity" as a parity case, even though it technically isn't. However, in the context of solving with the reduction method it is a parity case. Context is everything regarding terminology in cubing. If you would like to refer to this alg as "visually pure" in the context of 4BLD and supercube solving then you are more than welcome to. However, cmowla's algs have always been (this thread is certainly no exception) in the context of speedsolving all even-ordered bigcubes, therefore drawing a distinction in this case is wholly unnecessary.
Click to expand...

Sorry but your example is a bad example. PLL parity has no meaning outside the context of reduction+Fridrich method, so we can freely use it as a shorthand for "the case which corresponds to the PLL parity case in the reduction+Fridrich method", and its meaning is perfectly clear. This is not the case with "pure". Yes I know pretty well that cmowla is misusing it, but if a random cuber tells me "I've found a pure alg" without context, how am I supposed to tell what he's talking bout without checking his alg ?
 
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