Does your mind ever go blank when solving oll/pll and you just can't recall the alg even though you've used it a 1000 times?
Happens to me with the RUD G perms sometimes.
How is a 4D cube supposed to work?
Take a step back and consider the simpler question: how does a 3D cube work?
In three dimensions, we have a 3×3×3 stack of little cubes, where the faces of the little cubes facing the outside are clean and the faces that aren't facing outside all have a little bit of reusable adhesive on them so they're sticky (like Post-it notes). Performing a move is equivalent to peeling off a 3×3×1 layer, then reattaching that layer in any orientation with the sticky side inwards.
In four dimensions, it's the same thing, except with one more dimension. We have a stack of 3×3×3×3 little hypercubes, and performing a move is equivalent to peeling off a 3×3×3×1 layer (which consists of 27 hypercubies now), then reattaching it in any orientation, again with the sticky side inwards. Here, for each of the 4D cube's eight faces, there are 23 possible moves you can make, unlike the 3D cube where the only possibilities are either 90° clockwise, 90° anticlockwise, or 180°.
(By this definition, the two-dimensional analogue of a Rubik's Cube doesn't have any moves you can make at all. Peel off a 3×1 strip of squares, and the only way you can place it back is in exactly the same orientation you peeled it off in. But that's boring, which is why most puzzle games touted as 2D equivalents of the Rubik's Cube don't follow this rule.)
