I am intrigued by this statement: 'It is worth remembering that we do not live in Euclidean space. We live in space-time.'
I guess there is some intended reference to Einstein, to Relativity, to theoretical physics, and to that degree, I'm hip. But is it actually coherent to say that 'we do not live in Euclidean space'? That would be three-dimensional space. I think actually, I live in Euclidean space, the moon above me, etc. So I wonder what, actually, you take yourself to mean, here.
Round Squares exist[change source]
A boring, rule-abiding, and lame person who is also portly. I'm using other definitions for the same words. However, that does mean that it is not always true in all places to say "there are no round squares".