> Related: In 4D and higher space, the concept of rotating around an axis does not make sense. I think that this is like saying "rotating in 3D doesn't make se

> Related: In 4D and higher space, the concept of rotating around an axis does not make sense. I think that this is like saying "rotating in 3D doesn't make sense"; it's not so much that it doesn't make sense as that it's not uniquely specified. (Then there's the fact, which maybe is what you meant (since you referenced the dimension of SO(4)), that a 4D Euclidean rotation need not fix an axis at all!)