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Re: closed universe, flat space?
Posted:
May 4, 2013 2:46 AM


On May 4, 2:48 am, RichD <r_delaney2...@yahoo.com> wrote: > On Apr 29, Dan <dan.ms.ch...@gmail.com> wrote:
> Into what? A toroid? You can't actually fold a blanket into a toroid . This is the 'intrinsic curvature' of the toroid . http://www.rdrop.com/~half/math/torus/torus.curvature.map.png
>So you're saying, that an inhabitant of a toroid or >cylinder  on its 2D 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
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 .
An easy way to understand this is : Imagine you were turned upsidedown (ignoring gravitational effects) . How could you tell that you got turned upside down? By looking at the rest of the world, that is still rightside up. But, if you look at your hand , it still looks unchanged from when you were normaloriented . You can't tell if you're upside down by looking at your hand . Now image you couldn't look at the rest of the world . You could only look at yourself . Could you tell if you were upsidedown or ringsideup ? Upside down with respect to what? Would it even matter? That's the situation in Riemanian Geometry .



