Title: What do we know about the geometry of space?,
Abstract: The belief that three dimensional space is infinite and flat in the absence
of matter is a canon of physics that has been in place since the time of
Newton. The assumption that space is flat at infinity has guided several modern
physical theories. But what do we actually know to support this belief? A
simple argument, called the "Telescope Principle", asserts that all that we can
know about space is bounded by observations. Physical theories are best when
they can be verified by observations, and that should also apply to the
geometry of space. The Telescope Principle is simple to state, but it leads to
very interesting insights into relativity and Yang-Mills theory via projective
equivalences of their respective spaces.