I got a 5x5 cube a while ago and was reading about how to solve it, and came across a nice, concise description of how one might invent moves which can be combined into algorithms which let you make incremental progress on a cube. I can't find it again, now!
Some of it was along the lines of (1) Figure out how to do something A to a single layer (while messing up the rest of the cube). (2) Observe that if you do A, then rotate the layer R, then undo A (A'), you have an operation B = A R A' which does something to only one layer of the cube. I assume that most moves in most common algorithms can be expressed in terms of a couple of fundamental techniques like this (probably using the words "commutator" and "conjugate"). Does someone have a link or reference that gives you the general meta-technique (even if it involves incompletely-specified things like "figure out an interesting sequence of moves in terms of their effect on a single layer")?
I'm interested in this because I'm not really interested in learning (again) and forgetting (again) any particular existing method for solving the cube, but it would be fun to be able to fiddle around with it in a less-than-random way and eventually arrive at a method, based on some higher-level principles.
Some of it was along the lines of (1) Figure out how to do something A to a single layer (while messing up the rest of the cube). (2) Observe that if you do A, then rotate the layer R, then undo A (A'), you have an operation B = A R A' which does something to only one layer of the cube. I assume that most moves in most common algorithms can be expressed in terms of a couple of fundamental techniques like this (probably using the words "commutator" and "conjugate"). Does someone have a link or reference that gives you the general meta-technique (even if it involves incompletely-specified things like "figure out an interesting sequence of moves in terms of their effect on a single layer")?
I'm interested in this because I'm not really interested in learning (again) and forgetting (again) any particular existing method for solving the cube, but it would be fun to be able to fiddle around with it in a less-than-random way and eventually arrive at a method, based on some higher-level principles.