Quote:
Originally Posted by sjastro
Mirko,
Our frame of reference is the same as the Earth's.
|
That's exactly what I mean by rising above the surface. As soon as you do that, you see the curve. You have adopted an outside frame of reference. The point is to stay within the surface, a 2-dimensional universe. It's an analogy after all. Perhaps the problem of infinity can always be overcome by adding another dimension and looking at it from the "outside". You would need to step outside the universe though, as you've said to Alex below.
Quote:
Originally Posted by sjastro
The pathway is defined by the circle inscribed on the sphere. There are no limits. It doesn't matter how many times we travel around this circle, the radius of the circle remains the same.
|
The radius does not need to change for an infinitely long journey to be possible.
Quote:
Originally Posted by sjastro
By calculating the radius through the circumferential distance travelled, we can find the surface area of the sphere which is finite.
|
Granted, this does not necessarily form part of the agument, but are we actually able to calculate the radius based on distance travelled, as opposed to obtaining an approximate value?
Quote:
Originally Posted by sjastro
When I mean resolved, I'm referring to the angular resolution of the anisotropic detail in the cosmic radiation background.
There has been a progressive increase in detail from COBE to WMAP to the Planck probe.
Since the detail is now well resolved, cosmologists are able to measure the angular size of individual structures with greater precision.
The measurements are consistent with a flat univese.
Steven
|
That's the status as at today. I know of something else that was observed as being flat but later found to be (nearly) spherical
