On 1/24/2020 5:06 AM, Lawrence Crowell wrote:
On Thursday, January 23, 2020 at 9:54:29 PM UTC-6, Brent wrote: On 1/23/2020 5:22 PM, Lawrence Crowell wrote:On Thursday, January 23, 2020 at 5:56:08 PM UTC-6, John Clark wrote: On Thu, Jan 23, 2020 at 6:35 PM Bruce Kellett <[email protected]> wrote: /> You seem to have missed an important little word in Brent's post: Brent talked about needing an infinite RANGE of coordinate values for an infinite universe/ OK fine, so in a finite universe you'd only need a finite RANGE of coordinate values printed on a finite number of labels for all the finite number of points in that finite universe. But as I said, if new points are constantly being made at an accelerating rate in that "finite" universe then you're going to run out of those finite labels. > /nothing whatsoever about having only a finite set of distinguishable labels....../ Nothing whatsoever? He specifically said a "range of coordinate values to *label* all the points". And if a label isn't distinguishablethen it isn't a label. John K Clark If you have a sphere that is expanding the coordinate grid comoves with that. The spacing between coordinate points increases. The number of points needed to specify things does not need to change.But if "the spacing increases" means anything at all, it means the range of coordinate values to define those points must increase. BrentIf the sphere has constant curvature then to specify a point between two comoving or expanding coordinate points one can calculate it. While there is a continuum of space in point-set topology this does not really mean a space requires an infinite, indeed uncountable infinite, amount of information to describe it.
I don't think the discussion of what makes a negative curvature or flat universe infinite, referred to the amount of information needed to describe it. It referred to distance in the metric space.
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