Does this concept about actual impossibilities have a name?
Can Infinite Possibilities Lead to Actual Impossibilities? A Question on Infinity and Probability
I’ve been thinking about the concept of infinity and how it relates to probability, and I wanted to get your thoughts on something that’s been puzzling me.
The Infinite Monkey Theorem suggests that, theoretically, if you have an infinite number of monkeys typing on typewriters for an infinite amount of time, one of them will eventually type out a complete work like Othello. This is based on the idea that, given infinite time and possibilities, every possibility will eventually actualize.
However, I’m wondering if this theorem holds up when we move from theoretical infinity to something closer to actual infinity. Here’s my line of thought:
In a theoretical run of infinite possibilities, every possibility will eventually happen because no matter how improbable something is, infinity guarantees its occurrence.
But in an actual run of infinite possibilities, it seems that remote possibilities might never occur at all. Even with infinite time, it’s plausible that certain rare events could require an infinite amount of time to manifest and thus may never happen in practice. For example, it feels possible that no monkey will ever type out Othello, even given infinite time and infinite monkeys, because the time needed for such an event could itself be infinite.
My question is: Does this distinction between theoretical and actual infinity hold any philosophical or mathematical weight? Has this idea been explored before, where certain possibilities are “infinitely remote” in practice even with infinite time? How do we reconcile theoretical probability with the practical impossibility of some events in infinite scenarios?
I’d love to hear your thoughts, or if this concept has been described before under a specific name. Thank you!
Originally posted on Reddit. Browse posts from 2024.