I do not believe in anything I read without doing my homework, as a matter of fact. It seems you do, at least according to the articles you posted.
Of course I might be wrong. But what are my choices? After all, I can communicate with you remotely because of science, not because of Aristoteles or Plato. The same is valid for Newton. Wrong theory, but vastly more useful thhan any phylosophical articles you can post, independently from it being right or not.
I don't see the relevance, but go right ahead. Stand a couple of people on different mountains a few miles apart, stretch a rope between them, and see whether the shortest distance between the two of them is a curved line. I'll wait right here.
Curved manifolds have straight lines too, and are therefore useless to measure curvature. So, I do not see your point. Can you expand on that? Are you addressing the metric imposed on spacetime by a gravitational field, maybe?
How do you really measure if a portion of space is curved? Spoiler: it is possible.
Ciao
- viole