 geometry including the
&gt;      uniqueness-of-parallels postulate.
&gt; 
&gt; 2b.  The Bolayi/Lobachevsky/Hilbert geometry which
&gt;      postulates that through a point not on a line,
&gt;      there is more than one line parallel to that line.

These are good catalysts for inspiring analogical thinking,
much in the way that I take projective geometry as a basis
for my own thinking about "theory as point of view" (TAPOV),
but if you take the geometry literally then all of it is
pretty well-worked-over, 