On Apr 24, Dan <dan.ms.ch...@gmail.com> wrote: > > Supposedly, our universe is closed and finite, > > a straight line (geodesic) traveler must return > > to his starting poiint, yes/no? Hence, curved space. > > > At the same time, astronomers claim, that > > space is flat, to the precision of their > > measurements. > > So, space is closed, but also flat... back in my > > day, they had something called a logical > > contradiction - > > Space can be 'closed' , and also, 'locally flat', > in the sense that the Riemann tensor vanishes , or > there exists, for any point of the space, a non- > infinitesimal spherical section around that point > that's indistinguishable from flat space . > > Consider a piece of paper: flat? Yes. Closed? No. > You can go off the edge.
um yeah Finally, somebody gets it -
> Now make it so that when you go trough the 'up' edge > you end up coming from the 'down' edge , and when > you go go trough the 'left' > edge you end up coming from the 'right' edge .
And to do that, you have to twist the paper into a cylinder... twist, flat... see the problem here?
> More specifically, this > space is the factor group (R^2) / (Z^2) . The > space is still flat, as > far as definitions tell . However, it's closed.