- Moving pairs Given something like a checkers board, moving pairs would be checker pieces paired together and arranged on the board so they each checker piece is said to be paired with another.
The pairs don't have to be next to eachother, they can arrange on the board in any awy. Any way arranged is fair for how this works, but it matters for how they work. There's no such thing as an empty space among pairs for how you consider them together. They are the idea of how they move, and the problem with finding how to move them, and how they work being together. - Moving a pair Pick a pair to move. Each of the pair is to move together at the same time. A pair together can only move to another pair together. A pair moves to another pair, and each of the pair becomes paired with each of the other pair. So now both pairs are new pairs, with the pair that moved to another pair not being a pair anymore, both of the pair to move becomes a new pair with the pair that has to move for where they move to. A pair moves to another pair, but the other pair is what moves away at the same time. A pair moves to another pair, the pair it moves to has to move at the same time to another pair. So when moving a pair to another pair, that pair has to move too. So the pair to move to another pair becomes a new pair, each of the pair to move to another pair becomes part of a new pair with the pair that they move to. The pair they move to is the pair to move to another pair at the same time. You can't know what any pair's first move is until you know it's last move. There's nowhere to think in the way moving pairs can move how it has any inbetween to stop moving. It's always that a pair moving is making another pair move, and is having a pair move it. For any pair there's always one way to move it. To think of pairs in the middle of moving is to think of needing to know the end and beginning at the same time. Because a pair is moving when a pair moved it, and is moving another pair where it's going. But it's going where a pair can move to another pair, and coming from having a pair move it. So a pair to move is moving where it can go, where another pair can move from, where it gets to there being a pair that can move to where the first pair left. When a pair moves it's what is moving away from what had to move it, and is moving what needs to move at the same time for where it's going. Each time a pair is moved, all the pairs involved in moving are alternated as pairs. So a pair when moved makes all pairs that have to move at the same time paired another way. You can't know how a pair moves, it's to figure out as the problem they have. The last pair to move has to be figured before the first pair to move has a place to move. All the pairs have a way to move, but may involve more or less of the other pairs to move at the same time. So a pair can be moved, but it's to figure out how to make it move. So.... |55|66|55| |44|44|66| Move pair 44 44. Choice is either 66 66 or 55 55. 44 44 can move to 55 55, only if 55 55 can move to 66 66, and 66 66 can move where 44 44 is to start. so try... 44 44 moves to 55 55. and now each 44 and 55 are a new pair. at the same time 55 55 moved to 66 66, so where 66 and 66 is at there's one of the new pair from 44 44 and 55 55. and at the same time can 66 66 move to 44 44 ? So to know the first move is to know the last move, because the first move is where it works around to the last move, and the last pair to make is what can go where the first pair left. - Moving pairs are a machine They can be arranged in any way so that the way to move a pair is to have to move others too. So between all pairs they have an arrangement strategy that carries a way to work at being rearranged. A way where to work at being rearranged is to be able to rearrange in any other ways, but always able to make it back to the same arrangement. They follow a way to rearrange like a machine in a different condition. Pairs can store how to associate any letter with any number by having it so some pairs say a letter and other pairs say a number, so how you move some pairs to say which letter is for some other pairs to move to say which number. Any pair that is moved can make it so other pairs to move have another way for how they move. Pairs that work in moving together can be close or far apart, so they extend across the idea of how it's a machine as much as can make sense for any way to have a machine work. Given all the pairs that move together, any of them to move makes them all move together, and given another move to a pair that's together in moving it works around varying arrangements until it's arranged the same again, but moving starting with another pair changes how another pair moves in differencing arrangement. See how a pair to move is to make another pair move differently? See how that's part of the machine to move but also another part moved? See how they overlap where part of the machine is part with another, but to move is to move another part? See how a part of the machine can only be moved so many ways, and is overlapped by other parts like they're some of the same part? It's to see how part of the machine for the way it is, is the way another part is, is they way they are for eachother. So a part moved is another part moved too at the same time, but it's for the way a part is that the other part is the way it is. So there's as many ways for a part of the machine to be as there is, but it can be overlapped any number of times by another part, but is a part that with so many ways to be is any way for another part, and another part is a way for the part it overlaps. See how every part of the machine is part of another part this way, but it's not to run out of a way for the machine to be connected? because a part has so many ways to be, so overlapping it is where a part is a way for the way another part is, but can only be so many ways for how many ways another part is. See how for one way a part is, is one way for another part? but how where parts overlap is where all parts are a way for all other parts? See how a part is a connected condition? That is, a pair and how it can move? See how it's where in a machine you can say that if this part of the machine is this way, then another part of the machine is another way? - Machine diagram See each pair for how it can be moved with all the pairs that have to move togther. See other pairs together be some of the same pairs together another way. Draw pairs that move together with a line that connects one that moves to another. See where they overlap as connected as a part of the machine together with another part of the machine. See it the way that it's a part of the machine that moves another part of the machine, but each there own part. So see that as a seperate part but overlapping another part. For the way a pair can move, all the pairs to move together are a connected condition. Together the way where it's part of the machine to say for another part of the machine how to be. Say for each group of pairs that move together a line that connects them, where all pairs are together this way. So it should be that all pairs together diagram as how they would move with lines together that draw what looks like a diagram for a working machine. - The trick See the machine diagram? Make a pair move then see the machine diagram again. How did the machine move? See how it's the same machine? Enjoy :)
