Cyclic models and set theory....

[_heretic]

I have a question as to the actual nature of cyclic models of the universe (e.g. Roger Penrose's Conformal Cyclic Cosmology or the Ekpyrotic universe) - essentially where the universe has no beginning or end it simply goes through cycles eternally in both time directions. So in these situations would the entire history of the universe be considered to be mathematically an countably infinite or uncountably infinite as a set? That is, would each cycle (e.g. big bang to big crunch) be classed as an element of a countably infinite set or an uncountably infinite one?

Furthermore, if the set of these cycles was countably infinite would that mean that each cycle (i.e one in which there is an Earth and this post of the Science Forums) could only ever occur **once** in the entire history of the universe. (?) Or would it mean that each cycle could have identical "looking" cycles later on. i.e at time N1 we encounter cycle A in which there is an Earth with this post on the Science Forums, and later, at time N2 we encounter cycle B in which there is a situation functionally the same as in cycle A: Identical planet with identical post on identical network which, for all intents and purposes, is then the same as cycle A (?)

 

Thanks in advance!

[_heretic]

?

[owl]

Thanks in advance![/left]

"Thanks" for nothing, huh. I just found this thread. The cyclic, "Bang/Crunch" model is my fave 'cuz it doesn't require the magic of "something from nothing" or the nagging question, "What was there before the bang and where did it come from?"

I haven't read Penrose on it and don't know what a "countably infinite set" means as in, "That is, would each cycle (e.g. big bang to big crunch) be classed as an element of a countably infinite set or an uncountably infinite one?"

(I thought infinite meant uncountable, as in without beginning or end.)

As for your second paragraph, specifically, "...Or would it mean that each cycle could have identical "looking" cycles later on."...

I don't see how any two cycles could possibly be identical.* The "deck" gets "re-shuffled" every time the expansive half-cycle turns around and comes back together again in the implosive half-cycle... (which, of course will require a lot more mass to be found for that critical reversal... and the mystery of the accelerating expansion to be solved.)

 

*Same natural principle as "no two snowflakes identical" only the whole cosmos has infinitely (?) more diversity than a snowflake... and it would be re-formed in each cycle.

 

Thanks for the interesting subject.

[hypervalent_iodine]

!

Moderator Note

dapifo,

Please do not hijack other threads with speculative material. We have a forum for that.

[robheus]

In eternal cyclic universe model, there is no way to start counting I suppose.