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EmptyTotal t1_jc6kbrc wrote

Reply to comment by Seek_Equilibrium in A philosophical dive into “Everything Everywhere All at Once” by Azmisov

>The lesson is just that you can’t define frequencies or proportions in infinite sets that lack natural orderings. The number line is the exception, not the rule.

In the context of multiverses, there are natural ways of ordering them. In MWI for example, you could consider universes that first differ from ours by a more recent branching event to be "closer" than ones that branched further back. Then whatever density you want can be defined in the set of universes that diverged later than time t, as t is taken to zero.

Frequency in a multiverse shouldn't really be any less intuitive than a frequency measurement in our single universe. If space is infinite, then it also contains infinite planets. But it is still obvious that most of space is empty.

(Just like it is obvious that infinite coin flips should be time-ordered when referring to their "frequency".)

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Seek_Equilibrium t1_jc7eikj wrote

The examples you give are interesting ways of recovering a natural ordering. It makes me wonder, in the case of spatiotemporally disconnected cosmological multiverses, if some kind of n-dimensional “similarity measure” could be used in principle, with our universe as the reference.

Of note, though, this…

> (Just like it is obvious that infinite coin flips should be time-ordered when referring to their “frequency”.)

… is problematic unless there is some actual infinite sequence of coin flips that we can refer to. Any hypothetical infinite sequence of coin flips could have any hypothetical time-ordering, so the original problem just rearises in the form of specifying the order of the flips in time.

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python_hunter t1_jc8099y wrote

TL;DR "thank you for the correction" ;D

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Seek_Equilibrium t1_jc81w1w wrote

Not a single thing in that comment “corrected” what I said previously. I made a point only about infinite sets without natural orderings. I didn’t even argue whether an ordering can be given for an infinite multiverse. I noted that their response is interesting and potentially valuable for providing such natural orderings on infinite multiverses.

The point I made stands: if we cant find natural orderings for infinite multiverses, then we can’t meaningfully talk about the frequencies or proportions of universes within the multiverse. Their comment is germane to the antecedent (“if we can’t”). If they’re right, then we can indeed find natural orderings for infinite multiverses, so the consequent doesn’t necessarily apply.

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HortenseAndI t1_jc9kdc8 wrote

Y'all are getting worked up about comparing countable infinities. There are other ways to have 'most' of an infinity - e.g. there are more non-rational reals than rationals because the former is uncountable

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Seek_Equilibrium t1_jc9kzge wrote

You’re talking about cardinalities of infinite sets, which is not directly relevant to defining proportions or frequencies of the elements within an infinite set.

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HortenseAndI t1_jc9t1yj wrote

I mention it because the relevant passage in the original article is "you cannot have “most” of infinity. The only scenario where it somewhat makes sense is where a finite number of worlds evolved life, but an infinite number did not.", which is blatantly untrue given that you can compare infinite sets with different cardinalities. My point is there's no need to get hung up on the probability space of countably infinite sets to comfortably assert that that's nonsense, which is what was happening here

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python_hunter t1_jc80o1e wrote

I'm not sure that defining a 'sequence' is as relevant here as one might think; while it's a strategy often used in proofs, I don't think that (in my layperson's understanding) this precludes there existing different 'orders' of 'infinity'

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