[roflmyeggo]

Vsauce makes a good point that we just aren't made to intuitively understand this type of stuff. Recognizing this fact, in my opinion, is a key driver in helping to wrap our minds around these concepts. It's important to understand that these concepts are valid in both our visible world and the hidden quantum world, the main difference is scale.

For example, I could never wrap my head around the fact that electrons can have multiple paths/histories simultaneously when travelling. The same is true of a baseball thrown in the air, the only difference is that on the visible scale that we are used to the chance of that baseball taking a different path/history is so small that it will never happen.

[ihm]

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.

[0]: https://www.youtube.com/watch?v=s86-Z-CbaHA&feature=youtu.be...