Comment on Infintiy Infintiy Infintiy Infintiy Infintiy Infintiy Infintiy Infintiy
NikkiDimes@lemmy.world 1 day agoFair 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?
BluesF@lemmy.world 1 day ago
I thought that at first… But then for every infinite series with exactly one hamlet in it, there’s an infinite series where one character is wrong. And there’s another one where a different character is wrong… And so on and so on. Even if the series contains an infinite number of hamlets, you can replace one character in each in a huge number of ways! It starts to seem like there are more options with almost Hamlet than there are specifically with Hamlet.
In fact, I begin to wonder if almost any constraint reducing the search space in the infinite set of such infinite sequences, you will inevitably have fewer items within the search space than without… Since you can always construct multiple non-matching candidates from any matching one.
But… Honestly I’m not sure how much any of that matters in infinite contexts. Since they are impossible it begins to seem futile to even imagine it.