Both of you are hitting on the very point I've been trying to explain to Right Wing Professor - which incidentally appears to be yet another point later raised in a sidebar between betty boop, tortoise and edsheppa.
There are certain mathematical constructs which are very useful but do not translate well to physical systems. Inversion geometry "in" RWP's single spatial dimension universe is one. Infinity is another construct which is very useful in mathematics but leads to problems in physics.
These are exceptions - ordinarily mathematics is unreasonably effective vis-à-vis physics (and vice versa). In fact, mirror symmetries and dualities are great examples of the unreasonable effectiveness of math. But in the extremes - such as a single spatial dimension universe, infinite past, etc. - we can and do run into problems.
Moreover, there is an observer problem in the inversion of RWP’s single spatial dimension universe – for any observer “in” the universe but not to RWP, because as the "creator" of his universe he is not bound to the spatial/temporal restrictions of his "creation".
RWP, for a great explanation please read again Quark2005’s post at 521 and Spunket’s at 522!
In any case, the consideration of symmetries of space & time with regard to inversion of coordinates, etc. is a very important consideration in theoretical physics (see especially Noether's Theorem) - a very useful concept in higher-dimensional field theories.
There are one dimensional problems in our universe, too. There are systems with 1D inversion symmetry. You don't need the second or third dimension, or time, to deal with them.