6/24/12

the bottom of infinity

There appear to be many infinities. There's countable infinity, and uncountable infinity, and many infinities larger than that. It is unclear to me how many sorts of infinities there are. Presumably there are an infinite number of sorts of infinities, but what sort of infinity of sorts of infinities? Anyway, lots of them.

And it seems that our universe is at the bottom of this stack. Why should that be?

One possibility: Perhaps we're at the only possible place in this stack. Perhaps all the higher order infinities don't really exist, but are rather just annoying theoretical constructs. In fact, perhaps no infinities exist, and our universe is finite, with a finite amount of stuff, and a finit number of possible quantum states that stuff can be in. Or maybe only the somewhat comprehensible infinities exist, like countable, and maybe uncountable.

Another half-baked possibility: Perhaps we're not at the bottom. Perhaps the stack continues down. Beneath us is "nothing". Beneath that is "a place where not even 'nothing' can exist". Beneath that is "a place where not even 'a place where not even nothing can exist' can exist". And so on.

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