Date: May 4, 2013 8:31 AM
Subject: Re: closed universe, flat space?
> So you're saying, that an inhabitant of a toroid or
> cylinder - on its 2-D surface - cannot draw any shape
> which will tell them it's warped? I find that hard to swallow.
If he could go around the cylinder (leaving a mark at his starting
point) he'd see it's closed .If the cylinder were big enough, he would
think he's living in an infinite flat space. However, closure is a
global property. Curvature is a local property. He still wouldn't be
able to tell if he's in a round cylinder , an oval cylinder, a
"flattened cylinder" , an infinitely long parallelepiped
, etc .