FOM: David Ross's comment on the Banach-Tarski paradox

[jbaldwin@uic.edu]

This continuesthe Ross- Simpson thread on Banach-Tarski

Steve objected to lack of detail and contextl in the Ross post. 

My understanding of Ross's comment was the following.  There is no
Banach-Tarski paradox in dimension 2 (paradoxical decompositions of 
the disk); there is a paradox in dimension 3.  The fact that F_2 
imbeds the group of Euclidean motions of R^3 provides an explanation 
for this. It suggests that the Banach-Tarski paradox has a 
geometrical as well a `purely foundational' component.