this post was submitted on 03 Jan 2024
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Showerthoughts
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I'm not sure how sound that reasoning is, it's difficult to use intuition to determine whether one infinite set is bigger than another. Infinity is weird.
Say for instance you have two infinite sets: a set of all positive integers (1, 2, 3...) and a set of all positive multiples of 5 (5, 10, 15...). Intuitively you might assume the first set is bigger, after all it has five times as many values, right? But that's not actually the case, both sets are actually exactly the same size. If you take the first set and multiply every value by 5 you have the second set, no need to add or remove any values. Likewise, dividing every value in the second set gives you the first set again. There is no value in one set that can't be directly mapped to a unique value in the other, therefore both sets must be the same size. Pick any random number and it's 5 times as likely to be in the first set than the second, but there are not 5 times as many values in the first set.
With infinitely many universes one particular state being a few times more or less likely doesn't necessarily matter, there can still be as many universes with you as without.
The ultimate conceit is that infinities are a wonderfully engaging concept, but truly comprehending them as a tangible thing is inherently futile. We want to make these comparisons. They do, in some ways, hold some kind of meaningful as a concept, because we like one thing to be bigger or better than the other. But, at the scale of infinity, these comparisons are arbitrary and largely meaningless in any practical way.