this post was submitted on 08 Dec 2024
459 points (94.6% liked)
Technology
60055 readers
3410 users here now
This is a most excellent place for technology news and articles.
Our Rules
- Follow the lemmy.world rules.
- Only tech related content.
- Be excellent to each another!
- Mod approved content bots can post up to 10 articles per day.
- Threads asking for personal tech support may be deleted.
- Politics threads may be removed.
- No memes allowed as posts, OK to post as comments.
- Only approved bots from the list below, to ask if your bot can be added please contact us.
- Check for duplicates before posting, duplicates may be removed
Approved Bots
founded 2 years ago
MODERATORS
you are viewing a single comment's thread
view the rest of the comments
view the rest of the comments
Indeed, the formal definition actually doesn't specify how many monkeys will write what given an infinite number of monkeys, it's unknowable (that's just how probability is). We just know that it will almost surely happen, but that doesn't mean it will happen an infinite amount of occurrences.
The infinite amount of time version is just as vague, one monkey will almost surely type a specific thing, eventually, given infinite time to type it. This is because when you throw infinites at probability, all probabilities tend to 1. Given an infinite amount of time, all things that can happen, will almost surely happen, eventually.
But your citation gives both statements:
"In fact, the monkey would almost surely type every possible finite text an infinite number of times."
and
"The theorem can be generalized to state that any sequence of events that has a non-zero probability of happening will almost certainly occur an infinite number of times, given an infinite amount of time or a universe that is infinite in size."
So when you say the number of times is "unknowable" the actual answer is "almost surely an infinite number of times" no ? Since the probability of that can be calculated as 100%. The mindfuck part is that it is still possible that no monkey at all will type a particular text, even though the probability of that is 0.
The probability that only 2 monkeys will type the text is also still 0, same as 3 monkeys, 4 monkeys, etc. - in fact the probability of any specific finite number of monkeys only typing out the text is still 0 - only the probability of an infinite number of monkeys typing it out is 100% (the probabilities of all possible outcomes, even when infinite, have to sum up to 1 after all)
Basically, if we know "it will almost surely happen" then we also know just as surely (p=1) that it will also happen an infinite number of times (but it might also never happen, although with p=0)