On Fri, Jan 24, 2020 at 12:22 PM Lawrence Crowell < [email protected]> wrote:
> > If you have a sphere that is expanding the coordinate grid comoves with > that. The spacing between coordinate points increases. > If the space between two real numbers increases, you just add more real numbers to fill the gap. Coordinates are used to specify locations in the space, not the topology of the space. From the locations you can derive distances between points and the like. We are talking about a metric space here, not just a topological space. Bruce The number of points needed to specify things does not need to change. 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]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLRxwTouhWVrDfANZuXWRt428SZjj1VQ%3DBu%3D_TCEzgUzGg%40mail.gmail.com.
