On Monday, January 27, 2025 at 5:39:31 AM UTC-7 John Clark wrote:
On Sun, Jan 26, 2025 at 5:52 PM Jesse Mazer <laser...@gmail.com> wrote: *> Those kinds of plots can be used to represent both open and closed universes, see the attached images showing illustrations from the physicist Roger Penrose's book The Emperor's New Mind, where he presents plots for positive curvature, flat curvature, and negative curvature (in the case of negative curvature the circular cross-sections are supposed to be a special kind of diagram which compresses an infinite hyperbolic geometry onto a disc where the size of all the shapes gets more and more compressed closer to the edge,* *True. Penrose diagrams are able to depict infinity because they use hyperbolic geometry in such a way that angles are preserved, at least locally, but not distance. They are very useful but they can give the misleading impression that the spot labeled "Big Bang" is a mathematical point when it is not; instead it indicates a place where our understanding of distance, and therefore of size, breaks down. * *Also, because it needs to be printed on a 2-D piece of paper or computer screen and time needs to be one of those dimensions, only one dimension of space can be depicted, not three. * *John K Clark See what's on my new list at Extropolis <https://groups.google.com/g/extropolis>* But all the plots show the universe getting progressively smaller as T approaches zero, so IMO that implies something about its size at the singularity. AG rwe -- 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 everything-list+unsubscr...@googlegroups.com. To view this discussion visit https://groups.google.com/d/msgid/everything-list/41974c7a-a810-4718-b951-4dbb2476120cn%40googlegroups.com.
