On Wednesday, January 22, 2020 at 1:46:21 PM UTC-7, Brent wrote: > > > > On 1/22/2020 7:40 AM, Bruno Marchal wrote: > > > On 19 Jan 2020, at 19:52, 'Brent Meeker' via Everything List < > [email protected] <javascript:>> wrote: > > > > 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. > > *Why don't you compare the measured value with the curvature of a sphere 1 LY in diameter, or !0^6 LY in diameter? Do you really think the curvature would be significantly different from the measured value of the universe? I doubt it. So, taking it to be zero, is just what you prefer, nothing more. CMIIAW, AG*
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