I recall watching the video and not being surprised by its paradox. The set of starting points is uncountably infinite (R2), and since each starting point leads to a countably infinite number of L/R/U/D-rotation-ending sets, each of those L/R/U/D sets has the same cardinality as that for starting points. And so on. In the end, what I took away from this was similar to saying the interval [0.0, 0.5] has the same cardinality as [0.0, 1.0] albeit in a higher number of dimensions. It would be surprising if an uncountably infinite set in a lower dimension could fill in a higher one, but uncountably infinities in the same number of dimensions doesn't seem like a paradox that needs this sphere, rotation, and dictionaries to demonstrate.
In reading the comments for the video, I got the sense that this is different and that I was missing something but couldn't come close to guessing what that was.
In reading the comments for the video, I got the sense that this is different and that I was missing something but couldn't come close to guessing what that was.