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 distinguishable then 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. > > Brent >
If 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. LC > > The points on a space are not physical information. In some ways they are > just mathematical fantasies of sorts that happen to satisfy requirements of > a self-consistent axiomatic system called point-set topology. If the sphere > has constant curvature the only intrinsic piece of information you need > then is just one point, which you define as your coordinate. All other > coordinates can be derived. > > If the 3-sphere has lots of hills and valleys then you do need to specify > more points. In this situation there is more real information. If these > hills and valleys becomes infinitely craggy in a fractal then the amount of > information required to specify this sphere has unbounded Kolmogoroff > complexity. But for a smooth sphere, and one that is expanding so it > becomes every smoother, does not at all require added information to > describe it as it expands. > > LC > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected] <javascript:>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/30dff2b5-7733-4d60-9870-58a961381587%40googlegroups.com > > <https://groups.google.com/d/msgid/everything-list/30dff2b5-7733-4d60-9870-58a961381587%40googlegroups.com?utm_medium=email&utm_source=footer> > . > > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/52143509-ebe3-4200-87bf-2dc98497429f%40googlegroups.com.
