On 1/18/2020 11:58 PM, Alan Grayson wrote:
On Sunday, January 19, 2020 at 12:18:54 AM UTC-7, Brent wrote: On 1/18/2020 10:56 PM, Alan Grayson wrote:I don't claim anything except that GR has solutions for a cosmos in which space is flat and, in that solution, space is infinite and empirically it appears that space is flat. *Measurements don't establish it's flat, as I previously argued. And, as you previously stated, the sign of k, the parameter in GR intimately associated with curvature, is folded into the initial conditions. But since the initial conditions are really unknown, or are speculative, you can assume initial conditions which satisfy your bias, in this case FLAT. AG *No. It's not an assumption. Empirically the universe appears flat, which (assuming the FLRW model) implies it was always flat. It is not a question of assuming an initial condition, it is inferring the initial condition from present measurements of k.*This seems to modify what you wrote a few day ago. In any event, "empirically" means "measurement", and one cannot measure the curvature as exactly zero, which is what you need to empirically establish flatness. The measurements are very close to zero, but not zero. AG*
When you measure something and it is so close to zero as to be indistinguishable from zero, then taking it to be zero is not an assumption.
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