On Wednesday, February 5, 2020 at 2:47:58 PM UTC-7, Brent wrote: > > > > On 2/5/2020 4:09 AM, John Clark wrote: > > On Wed, Feb 5, 2020 at 6:46 AM Alan Grayson <[email protected] > <javascript:>> wrote: > > *> Poincare Recurrence doesn't apply for a universe with uncountably many >> possible states.* >> > > If there are a uncountably infinite number of possible states then there > is certainly a countably infinite number of states too. And if there are a > countably infinite number of states then there is certainly a finite number > of states too; 10^10^10^10^100 or any other finite number you care to name. > As far as Poincare Recurrence is concerned uncountably infinite possible > states for the universe to be in is *VAST* overkill. > > > The Poincaré recurrence theorem states that certain systems will, after a > sufficiently long but finite time, return to a state arbitrarily close to > (for continuous state systems), or exactly the same as (for discrete state > systems), their initial state. So it may apply equally to systems with > uncountably infinite number of states. > > Brent >
ISTM that a continuous state system is the same as one with uncountably infinite number of states (which characterizes our universe since free particles have an uncountably infinite number of states), yet for the latter you say Poincare recurrence "may" apply. Please clarify. AG -- 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/2b1e9142-f86b-43b4-bb59-c446fb5fa90e%40googlegroups.com.
