That looks like an ordinary toroid to Koobee Wublee. <shrug> Please keep in mind that Dan is no God. He cannot fold any 3-D shape and claiming 4-D, 5-D, 6-D, etc. <shrug>
> >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. > > I can see it's warped - if I'm not in the cylinder surface . > But the guy in the cylinder surface only interacts with stuff from > WITHIN the cylinder surface . > http://www.youtube.com/watch?v=C8oiwnNlyE4
Yes, the local guy cannot see its own space being warped. In any direct observations, all space or spacetime should appear to be flat to the same observer. Thus, the curvature of space is very much relative. However, to account for gravity, time dilation must be absolute. That means you can always tell someone whose local clock tick rate is slower than anyone else, or else, there would be no gravity and laws of physics. It is now becoming so obvious that to mix curved space which is relative and time dilation which must be absolute is getting very ludicrous. <shrug>
> That means that when you fold a paper into a cylinder , light travels > along the folded path . Perception gets curved along with the objects > of perception , resulting in apparent flatness. And that's good enough > for physicists , since they can't get out of the universe , or the > cylinder .
No, it does not mean you can fold a piece of paper and create 4-D, 5- D, 6-D, etc. Perhaps, Dan can only fool grade school kids and also self-styled physicists. <shrug>
> 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 > http://ars.els-cdn.com/content/image/1-s2.0-S0021999104001500-gr1.jpg > , etc .
Has it occurred to Dan that relationship between two observations is a mathematical mapping. When an observer sees an observed dimension able to curve back onto itself in a finite fashion, the same would be observed to span infinity to that local observer? That is the true Riemannian geometry not Dan?s Bollywood/Hollywood mumble jumbos. <shrug>