Ok_Tip5082 t1_jc5t5xg wrote on March 14, 2023 at 6:47 AM

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

That said there are still different levels of infinity. The reals have a Lebesgue measure strictly greater than the rationals.

Also the "sum of 1..inf == -1/12" is not the case at all, the whole point of that example is to show how different contexts and definitions can have conflicting answers, similar to 0^0 or 1^(inf)

lwalker043 t1_jc61hvm wrote on March 14, 2023 at 8:47 AM

i agree with your decision to bring lebesgue measure into the conversation of "most", but i dont think that's the best example since the rationals have lebesgue measure as well as cardinality less than the reals.

a better example may be the cantor set and the reals: they have the same cardinality and yet the cantor set is measure zero where of course the reals have infinite measure. i think it's simple and fair to say that if "life" universes make up something like the cantor set to the reals, you have a very solid interpretation of "most" universes not having life at all.

Ok_Tip5082 t1_jc6amn6 wrote on March 14, 2023 at 10:55 AM

Yeah, you bring up some great points. Honestly I would want to go the opposite direction though and compare growth rates of functions, many classes of which tend to infinity but at vastly different rates.

I totally tried to get a better example but then went on a wiki binge and got lost around the page of hyperbolic growth which contrasts itself against exponential and logistic growth then found my way to robert miles again,....