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#26
04-17-2017, 10:05 PM
 Chronos Charter Member Moderator Join Date: Jan 2000 Location: The Land of Cleves Posts: 75,153
Quote:
 Quoth me: Some probability problems are well-defined when dealing with infinities, and some are not. Some seem well-defined, but turn out not to be once one looks at them with enough rigor. And some problems which lack sufficient rigor can have that rigor applied in multiple different ways, which lead to different answers. Which one applies here depends on just exactly how the multiverse is structured.
It occurs to me that I ought to clarify what I mean here. By way of example, here's an argument that exactly 1/3 of all natural numbers are even. List out all numbers, like so: 1 3 2 5 7 4 9 11 6 13 15 8 17 19 10 21 23 12.... That's a list of all natural numbers, right? And if I look at the first n numbers on that list, and find the proportion that are even, that proportion is definitely approaching a limit of 1/3 as n increases.

Now, most people would say that this argument is wrong, because I'm taking the numbers out of order. And this is perhaps a reasonable thing to say, because the natural numbers have an obvious simple order to them. But when I'm looking at the set of all universes, is there a natural order to place them in? I suppose it makes sense to put our own Universe first on the list, but is there one particular universe that ought to be second, or third? Maybe I could list the universes in order of distance from our own... but then, how are we measuring the distance? Some sort of measure of how different they are from our own, perhaps? But then, the first universes I count will always be the ones most like our own, and if there are an infinite number that are enough like our own to have life, then I might never reach any of the non-life-bearing ones on my list.