Originally posted by howardbradley
Could you give a layman's explanation of what this means? (If that's at all possible.)
I surely give a try but I don’t know if my definition about flatness is the right one, but it works for me. Here it goes...
If you draw a triangle, you know from the schooldays that the sum of triangles are exactly 180, right? That’s because you draw it on a flat surface.
If you draw it large enough, so large so you have to take the spherical form of the globe itself into consideration, like one point at north pole, one point at the equator in Africa and one point at Indonesia and draw lines between these points you’ll se that you have a triangle with a sum of angles, not 180 but even around 270 degrees.
This means that if you know the distance between the points and the sum of angles then you’ll get a measure of the sphere-ness of the surface.
Even smaller triangles on the sphere of earth shows the same phenomenon but the smaller triangle you measure you get a triangle sum nearer and nearer to 180 degrees.
You can do the same with the area of a triangle. The area of large triangles are larger than the formula says. And the difference is a measure of the sphere-ness of the surface.
This is what I mean by saying that locally earth is flat but globally it is a sphere.
If you draw a triangle in astronomical distances, like billions of light-years you’ll be able to directly measure the sphere-ness of universe. It is still flat locally but universally, I doubt it is really flat. This experiment is impossible to do practically – yet.
But if you draw a triangle and you’ll got a sum of angles less than 180 degrees you‘ll get a anti-spherical surface, a hyperbolic surface. To visualize a hyperbolic surface, think of a saddle.
This is about surfaces but the same explanation goes for spaces too. You’ll have a flat space, a spherical space or a hyperbolical space. The triangle rule is the same.
I know that cosmologists mostly thinks that the universe is flat. I’m not of the same opinion. I think that if you see universe as flat then you get into the impression that the universe is, not only expanding but that it’s also, accelerating. Only if you see the universe as spherical you can explain a number of weird phenomenon that is very hard to explain otherwise. But this is too difficult to explain in a simple way at a forum lake this at RHP.
But I cannot prove nor disprove my thesis. Either it is wrong or it is right.
If anyone says the universe is flat, I just nod.