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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. The common mindset is to solve groups of pieces until there are a few remaining, then work within the restrictions to finish the puzzle. This restricted movement in the final stages causes the move count of the solve to be very high in comparison to efficient computer solutions. 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: "The final pieces to be solved sit around or within groups of already solved pieces. This means that turning movement is blocked and that the steps to solve the final pieces have to work within the restrictions caused by those previously solved pieces. 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.
So the idea that I have put forward is for everyone to follow a new line of thinking. To build methods around a concept that I'm calling Deterministic Methods. 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. A method following this concept will simultaneously consider every piece of the puzzle, accounting for each and influencing the entire puzzle in the most advantageous way. This will create a method that works like a deterministic system of cause and effect.
There are some methods and steps that can be viewed as bandage reduction, such as RUBAR, PPW, and Roux style LSE. These reduce the puzzle to states where it solves itself as long as progress is made with each turn. Bandage reduction is sort of a mini version of the deterministic solving concept. Upon the initial presentation of this article, some suggested that DR is an example of deterministic solving and that is usually true. Taking PPW and its related methods further, whole cube self solving can be made possible while incorporating deterministic strategies. An example is the scramble U' R' U' R' F' U' R U2 L F U2
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