Method Rigidity and Total Awareness Solving

[Athefre]

The community has done well so far exploring the possible methods that can be used to solve various puzzles. But are we stuck in a sort of groupthink mindset? Every method so far has a major aspect in common. All methods up to now directly solve groups of pieces to a state, up through the end of the solve. These piece states are: oriented along a desired axis, permuted a specific way, partially oriented or permuted, or oriented and permuted (directly solved). There are some nuances within, but that is what makes up a typical method. The steps of the methods continually build while causing restrictions on freedom of movement. To quote myself from the Method Development Life Cycle, "In order to solve the final pieces, what was solved in previous steps must be broken to allow for freedom of movement for the unsolved pieces, then restored after solving those pieces. Solving in this way is like painting yourself into a corner, trekking across your work because you have no other choice, then fixing your mistakes afterward."

• Petrus: Blocks are built until the first two layers are solved, then the last layer is completed. Solving the last layer requires breaking the first two layers multiple times.
• Tripod: Blocks are built as much as freedom of movement allows, then a "tripod" shape of unsolved pieces remains. The final tripod shape, and even some of the previous steps, requires breaking previously built blocks.
• CFOP: Form a cross, continually break the cross while solving the first two layers, then break the first two layers multiple times while solving the last layer.
• Roux: Two 1x2x3 blocks, solve the remaining corners while breaking the two blocks, then use the freedom / restriction of the U and M layers to complete the rest.

Each of these methods, and all others, contains a rigid set of steps. This creates two problems. The first is that the steps continually restrict the freedom of movement. The second is that each step will have a minimum move count and ergonomics potential that can't be overcome without modification.

If the same method is used every scramble, the steps will be almost the same in every solve. Each step is limited to a fixed average move count and ergonomics, with little room for improvement. We can combine two or more steps, decreasing the move count but increasing the difficulty and potentially making the ergonomics worse. But that still doesn't solve the problem of being painted into a corner. One suggestion may be to make use of method neutrality to use the best method for each scramble. But that only takes us so far since each method has the restricted solving built in.

Tripod is mentioned above as a method that tries to maintain freedom of movement. It, along with Roux, is successful in that way, but still contains a rigid set of steps. DR may also be mentioned, and it may be the closest, but it still holds rigidity. In addition, to achieve in two handed speed solving the move count results seen in fewest moves competition would currently require an amount of time that goes past 15 seconds of inspection plus the current world record solve time. There have been human adaptions of computer solving methods, such as Human Thistlethwaite Algorithm. There have also been speed oriented computer solving or DR like developments such as MI2, SSC, and Square-101. Those contain the same previously mentioned problems that a fixed structure involves, as well as other issues for speedsolving that haven't yet been solved. What about the techniques that we have so far? Pseudo or conjugation, bandage reduction, multi state solving, and others.

Is it within the very definition or nature for a method to continually restrict pieces throughout a solve? Or can we break away from breaking our work and design something that is completely different? A method with total awareness of all other pieces, with each turn influencing all others like a deterministic system. That is what an optimal computer solve looks like. The solve appears to be random movement until the end when it all comes together, as if in each turn all pieces were altered or preserved, whichever is best in the moment. So I suggest that the future of method development may be a way to solve that has the following traits:

• A large freedom of movement available throughout the entire solve.
• Awareness of or influencing many pieces at once. Sort of like branching steps with much or all of the solution potentially being seen within inspection time.
• Little restriction on the minimum movecount, other than the puzzle's natural overall minimum.
• Ergonomics designed to balance the previous listed traits with what is easy for humans to execute.

The big idea is to create a method centered around total awareness solving. Maybe a method can be created that influences or preserves all necessary pieces throughout the entire solve. The result would be a method that turns the pieces into a hive mind, all working together to get close to the computer optimal move counts while balancing ergonomics and recognition.

 

[Chicken-Cuber]

Hmmm but how would we develop a method for this?

 

[Filipe Teixeira]

what about putting Heise method in this mix? It can give some interesting insights.........

as it ends with some ~9~12 moves commutator at the end I think that's acceptable break and restore compared to what we have currently

and what about bringing the ideas of OPA (4x4 (and larger) orientation parity tracking) and BLD parity tracking into this mix? a technique in this model could help use wisely the inspection time

 

[Chicken-Cuber]

Ok

 

[Silky]

"In order to solve the final pieces, what was solved in previous steps must be broken to allow for freedom of movement for the unsolved pieces, then restored after solving those pieces.

I believe that 2GB/RUP (and the other bandaging method whose name escapes me) would break this mold. It goes something like this:

(1) EO + CP + 2x2x3 in some order. In the case of classic CEOR, CP+Bar doesn't break anything, EO-Edge doesn't break anything, DF DB doesn't break anything ( unless you consider "breaking" centers). However you restrict your movements 3 times. CP removes L and D moves (technically not since you'll be utilizing E/M slices during the next 2 steps - which implies L and D moves). EO edge removes F and B moves. DF DB removes M moves. Bit hard to explain - may go into more details later.
(2) "Lossless solving". This is, I believe, a 2-gen bandaging approach. 4-pairs => 3 edges + 2 corners => solved. If Alam's approach works then finishing 2 gen won't break any of your pairs while finishing the solve. Only thing that would have to be checked is if this is always possible.

Tired rn, so may come back to ellaborate in the near future.

 

[Swagrid]

(and the other bandaging method whose name escapes me

There are RUbar and PPW2

 

[Athefre]

I believe that 2GB/RUP (and the other bandaging method whose name escapes me) would break this mold. It goes something like this:

(1) EO + CP + 2x2x3 in some order. In the case of classic CEOR, CP+Bar doesn't break anything, EO-Edge doesn't break anything, DF DB doesn't break anything ( unless you consider "breaking" centers). However you restrict your movements 3 times. CP removes L and D moves (technically not since you'll be utilizing E/M slices during the next 2 steps - which implies L and D moves). EO edge removes F and B moves. DF DB removes M moves. Bit hard to explain - may go into more details later.
(2) "Lossless solving". This is, I believe, a 2-gen bandaging approach. 4-pairs => 3 edges + 2 corners => solved. If Alam's approach works then finishing 2 gen won't break any of your pairs while finishing the solve. Only thing that would have to be checked is if this is always possible.

Tired rn, so may come back to ellaborate in the near future.

Bandage reduction is mentioned in the main post, and it does sort of solve the restriction problem. But there are two main sub-problems mentioned in the post. Bandage reduction so far doesn't solve the second problem caused by a rigid set of steps. That problem is the lack of total awareness solving, which limits a solver's ability to reduce the move count and improve the ergonomics. For example, Roux always ends in LSE. LSE has a minimum computer optimal move count of around 11 moves, a little over half of God's number for just one of the four steps of the Roux method. Humans typically average 13.5 to 15 moves depending on the techniques used. Solvers also limit LSE to M and U moves. That's for a good reason, but always ending in LSE means that we aren't making full use of the puzzle's potential ergonomics. Using ZBLL as an example, there is a lot of ergonomics potential being used, but humans average around 15-16 moves. That is way past half of God's number just for one step of a method.

The big idea here is that we don't yet have a method centered around total awareness solving. Influencing or preserving pieces throughout the entire solve, while balancing the ergonomics and recognition.

 

[Silky]

Bandage reduction is mentioned in the main post, and it does sort of solve the restriction problem. But there are two main sub-problems mentioned in the post. Bandage reduction so far doesn't solve the second problem caused by a rigid set of steps. That problem is the lack of total awareness solving, which limits a solver's ability to reduce the move count and improve the ergonomics. For example, Roux always ends in LSE. LSE has a minimum computer optimal move count of around 11 moves, a little over half of God's number for just one of the four steps of the Roux method. Humans typically average 13.5 to 15 moves depending on the techniques used. Solvers also limit LSE to M and U moves. That's for a good reason, but always ending in LSE means that we aren't making full use of the puzzle's potential ergonomics. Using ZBLL as an example, there is a lot of ergonomics potential being used, but humans average around 15-16 moves. That is way past half of God's number just for one step of a method.

The big idea here is that we don't yet have a method centered around total awareness solving. Influencing or preserving pieces throughout the entire solve, while balancing the ergonomics and recognition.

Fair. I'm mostly honed in on your quote of "painting yourself into a corner" and its connection to lossless solving. I spent the last 4 hours mulling over this so I will include it in another post at a later date.

As far as rigidity of steps this is relatively easy to overcome if we take a "phase" approach. The 2-gen method really would only have 2 steps..phase (1) solving to a lossless state (2x2x3+EO+CP or another bandaging equivalent) and phase (2) solving from a lossless state. No matter what method you develop there will always need to be some type of "methodology". An equivalent for ZZ, Petrus, and ZB would be to (1) solve to last layer and (2) solve from last layer (in reference to the previously mentioned methods solving from last layer would be equivalent to ZBLL). This pretty much lines up with your method nuetrality idea except that there would need to be some type of convergence, specifically solving from some "State X".

 

[bcube]

A method with total awareness of all other pieces, with each turn influencing all others like a deterministic system. That is what an optimal computer solve looks like. The solve appears to be random movement until the end when it all comes together, as if in each turn all pieces were altered or preserved, whichever is best in the moment.

Just stating the obvious, but if a two-phase suboptimal solving is considered instead of just an optimal solving, a random movement part (i.e. phase 1) is finished substantially earlier than at the end of the solve. From a human perspective, phase 2 seems more like a deterministic system rather than a random movement to me. See example solves #5 and #6, compare with example solves #2 and #3 regarding their random movement part (never mind if phase 2 solving is looking like a random movement as opposed to a deterministic system to you).

 

[ruffleduck]

The three important domains the steps of any human method must address are,

• "intuition" -- that methods are intuitively easy enough for humans to understand, easy enough to visually understand mid-solve and execute mental conceptualization (lookahead), and a means of "compartmentalizing away" areas already treated such that the solver can disregard it later (e.g., during F2L you generally don't think about the cross or other F2L pairs already solved, or during LL you don't think about F2L)
• "case count restriction" -- the reducing of the state space, whether of algorithmic nature or not. e.g., the solving of F2L to restrict to LL cases, the solving of the cross to reduces the F2L space, and even solving EO to "reduce to RUL," is just an instance of state space restriction where the solution space is the subgroup generated by the reduced moveset (of the Rubik's cube moveset group).
• "ergonomics" -- in sweeping strokes, wrist turns (R/L/r/l) should work in alternation with finger turns; normal finger turns are superior to pinch/push turns, etc. etc.(difficult to metrize this, for reasons including the fact that rotations/wide moves are possible, which "rotates" the ergonomics space.)

I believe that the study of correlation between piece-solving/EO/EP/CO/CP (from which 99% of methods are using as building blocks in some order) and these domains I specified have been fairly exhausted in the Rubik's cube method development world. It's getting old. This is why I quit the method development side of the cubing community. Everything is fixated on just what order to solve things, what order to orient things, when should we permute these pieces, etc. This is such a mundane process that I'm willing to bet that it can be completely automated, I think that that should be the area of focus if method developers actually want to work in this context.

What I'm saying is that I fundamentally disagree with these notions of "freedom of movement" and "influence of pieces" as being what is actually foundational. At the end of the day, everything is a restricting process, all methods are highly rigid by nature (and should be that way, else we will be compromising on intuition/restriction), etc. But if you do want to treat them as foundational (roughly equivalent to holding the stance that piece-solving/EO/EP/CO/CP is foundational) then you may as well focus on ways of automating the process algorithmically.

 

[Athefre]

Just stating the obvious, but if a two-phase suboptimal solving is considered instead of just an optimal solving, a random movement part (i.e. phase 1) is finished substantially earlier than at the end of the solve. From a human perspective, phase 2 seems more like a deterministic system rather than a random movement to me. See example solves #5 and #6, compare with example solves #2 and #3 regarding their random movement part (never mind if phase 2 solving is looking like a random movement as opposed to a deterministic system to you).

Yep, the computer algorithms, FMC DR, and the DR like speedsolving methods contain ending steps that work well for human deterministic solving. But can we take this further?

The three important domains the steps of any human method must address are,

• "intuition" -- that methods are intuitively easy enough for humans to understand, easy enough to visually understand mid-solve and execute mental conceptualization (lookahead), and a means of "compartmentalizing away" areas already treated such that the solver can disregard it later (e.g., during F2L you generally don't think about the cross or other F2L pairs already solved, or during LL you don't think about F2L)
• "case count restriction" -- the reducing of the state space, whether of algorithmic nature or not. e.g., the solving of F2L to restrict to LL cases, the solving of the cross to reduces the F2L space, and even solving EO to "reduce to RUL," is just an instance of state space restriction where the solution space is the subgroup generated by the reduced moveset (of the Rubik's cube moveset group).
• "ergonomics" -- in sweeping strokes, wrist turns (R/L/r/l) should work in alternation with finger turns; normal finger turns are superior to pinch/push turns, etc. etc.(difficult to metrize this, for reasons including the fact that rotations/wide moves are possible, which "rotates" the ergonomics space.)

I believe that the study of correlation between piece-solving/EO/EP/CO/CP (from which 99% of methods are using as building blocks in some order) and these domains I specified have been fairly exhausted in the Rubik's cube method development world. It's getting old. This is why I quit the method development side of the cubing community. Everything is fixated on just what order to solve things, what order to orient things, when should we permute these pieces, etc. This is such a mundane process that I'm willing to bet that it can be completely automated, I think that that should be the area of focus if method developers actually want to work in this context.

What I'm saying is that I fundamentally disagree with these notions of "freedom of movement" and "influence of pieces" as being what is actually foundational. At the end of the day, everything is a restricting process, all methods are highly rigid by nature (and should be that way, else we will be compromising on intuition/restriction), etc. But if you do want to treat them as foundational (roughly equivalent to holding the stance that piece-solving/EO/EP/CO/CP is foundational) then you may as well focus on ways of automating the process algorithmically.

Well, hopefully you can at least appreciate that the entire point of the question posed in this thread is to do something different from reordering piece orientation and permutation. Anyone who has spent a good amount of time within method development comes to the realization that every method so far is just a different order of solving, orienting, and permuting pieces. So the idea I suggest here is something new of total awareness piece influence. With this, pieces aren't necessarily oriented or permuted in the same way as we currently do in all methods, but oriented or permuted in a way that sets them up to be naturally solved in the end where it all comes together. For human methods, DR and bandage reduction come close with endings that influence pieces throughout. There is also the under developed multi state solving. Something like SL5C, which solves corners to various states to be naturally solved with the proceeding edge step. Or imagine at LSLL setting it up to various simple endings such as R U' R', R U R', R U2 R', and others. Can we apply this to the entire solve to produce a speedsolving method that averages in the high 20s or low 30s for move count while also balancing ergonomics and recognition?