Counterintuitive Properties of High Dimensional Space (2018)
What does volume mean in higher dimensions?  2-D has no volume. 3D has a volume.  What's volume in 4D and higher?<p>Edit: Just to further the thought.  Do all dimensions have the same unit length?  In 3D, the spacial x,y,z dimensions have the same unit length.  In 4D like 3D+Time, does the t-dimension have the same unit length as the spacial dimensions?  What is 1-unit of t meant vs 1-unit of x?  What does it mean to say a sphere in 4D with radius r having the same "distance" from the center in all 4 dimensions?  What unit length is r in?