The hypersphere: the four-dimensional sphere [video-french-subs]
youtube.com
youtube.com
I wonder if at some point you could quickly graps something rather simple like a 4D scatter-plot. Though I could just encode the 4th Dimension in color and get used to it I guess. Maybe I should write my own styleguide for visualizations to get a native feel for such things.
The moving lights on the hypershpere allowed for a glimpse of making senso of thet 4D, but in general I couldn't follow just yet, even less: grasp it.
What about "The hypersphere: the four-dimensional sphere [with English subs]" (youtube.com)