this post was submitted on 14 Apr 2025
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The defeater is each key needs to be statistically as likely as any other key to be pressed next, i.e. statistically independent events. For example after a monkey pressed S they are then just as likely to press K as W. If there is any reason they prefer a key or sequence you don't get a normal distribution and they probably will never create any of Shakespeare's works.
But they still would be limited to only what monkeys can actually do with typewriters given enough time or monkeys to do everything a monkey will do with a typewriter.
Infinity only allows anything that can happen to happen no matter how unlikely to happen, but it doesn't allow something that has 0% likelihood to happen like a monkey turning into a cup to happen. If there are any 0% probability events necessary for the task then it wouldn't happen regardless of the number of monkeys or given time.
Yeah I think we're on the same page there, I was just pointing out a limitation of the thought experiment that draws attention to the fact that infinity only allows what's improbable possible and doesn't make the impossible possible. But yeah it doesn't undermine the idea that introducing infinities gives unintuitive results.
Yeah I think the recentness of formalizing infinities into math with Newton's and Leibnez's calculus (infinite series, limits approaching infinity) in the 1600s and Cantor's sets (cardinality of infinite sets) in the late 1800s speaks to the difficulty of even conceptualizing the problems they introduce and the rigor needed to handle them
What? That’s not what independence means. They need to be independent, yes, because otherwise you might get into weird corner cases where the probably doesn’t converge to 1, but they don’t have to be equally likely. In fact, weighing the odds based on how often letters are used by Shakespeare should lower the expected timeframe. Heck, Shakespeare doesn’t use “J”, why would that key even be relevant? Where in the world do normal distributions even come into this? How does this comment have 4 upvotes? What am I missing here?
Those are some of the conditions necessary for the probability calculation to result in a non zero chance of writing the works of Shakespeare. From the article:
But if they weren't independent, say every time a monkey hits b their lack of fine motor skills causes them to also hit yhb all together, then even infinite monkeys with infinite time wouldn't be able to type banana. Or if after hitting b they keep hitting b and ignore all the other keys they would never type banana. Evenly distributed just makes sure they can hit every key, it can take some unevenness like you mentioned j and some other letters come up very rarely. But if they never hit a or e you're never going to get Hamlet.
No, I agree that independence is necessary, not just because of “always”, but because if, as a crude example, your odds of hitting B halve each time you hit A, an infinite number of tries isn’t guaranteed to give you Shakespeare, even if the odds aren’t technically 0. My problem was that what you originally described wasn’t independence, it’s uniformity, which isn’t a prerequisite. And it’s up to 9 upvotes now so I don’t know what’s going on.
You don't need a normal distribution or statistical independence. It just requires that any given key combination remain possible.
No matter how unlikely, anything that is possible will eventually happen in an infinite time.