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Well, it's kind of a Catch-22. This proof is dependent upon the lemma that time is infinite. On the other hand, the set of events we're looking for is the one
by theli0nheart 16y ago
Well, it's kind of a Catch-22.
This proof is dependent upon the lemma that time is infinite. On the other hand, the set of events we're looking for is the one where time ends. Therefore by assuming the lemma we have no need for the proof.
OTOH, if we're looking at another event that's not so confusing (one that's not the end of time), the proof holds water. It's a pretty sweet proof that I think is similarly used to prove that the set of real numbers is uncountable.
- hugh3 16y agoNo, what I'm saying is that an event which takes an infinitely long time to happen (ie an infinite series of one-second flashes) isn't a proper "event", which as used at least in relativity, is something that happens in finite space and time. But there's no need to argue about the definition of event. I'll say instead that I'm interested in knowing whether infinite time implies that all finite-length events must eventually happen (and indeed, happen an infinite number of times as the paper claims).
- Robin_Message 16y agoYes, sorry, there is definitely a theorem that if you have an infinite sequence, uniformly distributed over an alphabet, then the probability of seeing any finite sequence is 1. I think that, given some assumptions, you can model the universe as an infinite numerical sequence, so you should see all finite events. However, the assumptions here seem tricky. Uniform distribution of probability seems unlikely, and if the universe is anything like the game of life, there are garden of Eden states with no predecessor state, which an evolving system cannot reach, even in infinite time. Cardinality is indeed tricky. I had thought that all finite sequences would be greater than aleph-null, but apparently it isn't.