On Mon, Dec 24, 2018 at 4:02 PM <[email protected]> wrote: > On Monday, December 24, 2018 at 4:47:02 AM UTC, Bruce wrote: >> >> On Mon, Dec 24, 2018 at 3:33 PM <[email protected]> wrote: >> >>> On Monday, December 24, 2018 at 4:22:24 AM UTC, [email protected] >>> wrote: >>>> >>>> On Monday, December 24, 2018 at 3:50:33 AM UTC, Brent wrote: >>>>> >>>>> On 12/23/2018 4:47 PM, [email protected] wrote: >>>>> >>>>> *If by "flat", you mean mathematically flat, like a plane extending >>>>> infinitely in all directions, as opposed to asymptotically flat like a >>>>> huge >>>>> and expanding sphere, you have to reconcile an infinitesimally tiny >>>>> universe at the time of the BB, and simultaneously an infinitely large >>>>> universe extending infinitely in all directions. AG* >>>>> >>>>> >>>>> All that's "infinitesimally tiny" is the visible universe. You must >>>>> know that the Friedmann equation just defines the dynamics of a scale >>>>> factor, not a size. >>>>> >>>> >>>> *Are you claiming the visible universe at the BB was infinitesimally >>>> tiny, but the non visible part was infinitely large (mathematically flat), >>>> or huge (asymptotically flat)? AG * >>>> >>> >>> *Bruce says the universe is always flat if k=1. How can it be everywhere >>> flat if there's a region which is infinitely tiny; hence not flat in the >>> visible region? How are we to imagine this? TIA, AG * >>> >> >> That's a bit confused. k=0 corresponds to a universe that is everywhere >> flat (in space, but not necessarily in the time dimension - i.e., it might >> be expanding. Our current visible universe originated in a small (tiny) >> region of the total structure, which might be infinite in extent, but flat >> everywhere, even in our tiny region. >> > > *Not to split hairs, but how can the tiny visible region also be flat and > infinite in extent, if its age is finite? I can imagine the visible region > to be asymptotically (but not mathematically) flat, and therefore finite in > extent. AG * >
I said that the total structure might be infinite in extent, not the region that became our visible universe. Flatness is a mathematical property -- imagination readily fails to visualise these things. Bruce -- 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 post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
