Comment on Infintiy Infintiy Infintiy Infintiy Infintiy Infintiy Infintiy Infintiy
NikkiDimes@lemmy.world 2 weeks agoInfinite monkeys. Any probability greater than zero times infinity is infinity. You will see an infinite number of monkeys hitting A and an infinite number hitting B. If there were a finite number of monkeys, you would be correct, but that is not the case.
BluesF@lemmy.world 2 weeks ago
No, that’s not how probability works. “Any probability times infinity is infinity” doesn’t even mean anything. Probabilities are between 0 and 1 so if for some reason you were to multiply an infinite number of them you would never end up with an “infinite” probability.
I explained the infinity monkeys in another comment more clearly than I did above -here you go.
NikkiDimes@lemmy.world 2 weeks ago
I could have worded that better. Any probability with a non-zero chance of occurring will occur an infinite number of times given an infinite sequence.
To address the comment you linked, I understand what you’re saying, but you’re putting a lot of emphasis on something that might as well be impossible. In an infinite sequence of coin flips, the probability of any specific outcome - like all heads - is exactly zero. This doesn’t mean it’s strictly impossible in a logical sense; rather, in the language of probability, it’s so improbable that it effectively “never happens” within the probability space we’re working with. Theoretically, sure, you’re correct, but realistically speaking, it’s statistically irrelevant.
BluesF@lemmy.world 2 weeks ago
Eh, I don’t think it’s irrelevant, I think it’s interesting! I mean, consider a new infinite monkey experiment. Take the usual setup - infinite monkeys, infinite time. Now once you have your output… Do it again, an infinite number of times. Now suddenly those near impossibilities (the almost surely Impossibles) become more probable.
I also think it’s interesting to consider how many infinite sequences there are which do/do not contain hamlet. This one I’m still mulling over… Are there more which do, or more which don’t? That is a bit beyond my theoretical understanding of infinity to answer, I think. But it might be an interesting topic to read about.
NikkiDimes@lemmy.world 2 weeks ago
Fair enough, I suppose it is interesting!
In terms of the question, “Are there more infinite sequences that contain Hamlet or more that don’t?”- in the context of true randomness and truly infinite sequence, this feels like almost a trick question. Almost every truly random infinite sequence will contain Hamlet an infinite number of times, along with every other possible finite sequence (e.g., Moby Dick, War and Peace, you name it). In fact, the probability of a random infinite sequence not containing Hamlet is effectively zero. I guess where it becomes truly interesting is if you have an infinite number of infinite sequences. You’ll certainly now have instances of those “effectively zero” cases, but in a ratio’s of infinity lol. I suppose that’s probably what you were getting at?