On 2/5/2020 4:09 AM, John Clark wrote:
On Wed, Feb 5, 2020 at 6:46 AM Alan Grayson <[email protected]
<mailto:[email protected]>> 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
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