I actually think it's very possible to have an "intuitive understanding" of Banach Tarski (I would say I have one, but perhaps we disagree on what is mean by such an understanding).
My "intuitive understanding" of this comes via an intuitive understanding of a paradoxical decomposition of the free group and its Cayley graph, which is flashed briefly in the video here[0] but sadly not discussed at length.
My "intuitive understanding" of this comes via an intuitive understanding of a paradoxical decomposition of the free group and its Cayley graph, which is flashed briefly in the video here[0] but sadly not discussed at length.
[0]: https://www.youtube.com/watch?v=s86-Z-CbaHA&feature=youtu.be...