A second SR question that has been on my mind lately is that of hyperbolic nature of Minkowski space. The fact that the invariant interval, or lines of constant delta S trace out a hyperbola according to the equation, ##x^2-(ct)^2=S^2##, is fascinating to me and seems to imply that space-time has a negative curvature. However, from cosmology I hear that it seems as though the debate over whether the universe has positive, negative, or flat curvature is favoring the "flat" solution according to observations. Does this observation strictly apply only to the 3 dimensional "space only" picture of the universe, or is it a general statement about the nature of spacetime in general? I remember Penrose addressing this question in the Road to Reality at some point but don't have access to the book to reference it.