Comment on Infinite Monkey Theorem

• exasperation@lemm.ee ⁨11⁩ ⁨months⁩ ago

  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.

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• ameancow@lemmy.world ⁨11⁩ ⁨months⁩ ago

  haha no, if you have a magic infinite sized room with an infinite number of magic, immortal monkeys, with an infinite number of typewriters with infinite paper and ink, you don’t even need to park the m,onkeys in front the fucking keyboard, you will instantaneously have all the works of Shakespeare and every other book ever published and every book never published, and probably an infinite number of volumes of books that reveal every secret of the universe. (The hard part will be finding them.)

  Instantly.

  Just by having the means for anything random to happen to those keyboards on an infinite scale.

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  • whotookkarl@lemmy.world ⁨11⁩ ⁨months⁩ ago

    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.

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    • ameancow@lemmy.world ⁨11⁩ ⁨months⁩ ago

      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.

      Not arguing this at all, I think a lot of people get hung up on this though because they don’t actually know what’s “possible or impossible” in our universe, which may not in fact have a good answer. All that aside, it’s just a thought experiment to reveal the inherent problems with working with infinities, because the number of “possible” things that can happen are quite radical.

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      • whotookkarl@lemmy.world ⁨11⁩ ⁨months⁩ ago

        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.

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• HeavenlySpoon@ttrpg.network ⁨11⁩ ⁨months⁩ ago

  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?

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  • whotookkarl@lemmy.world ⁨11⁩ ⁨months⁩ ago

    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:

    Consider the probability of typing the word banana on a typewriter with 50 keys. Suppose that the keys are pressed independently and uniformly at random, meaning that each key has an equal chance of being pressed regardless of what keys had been pressed previously. The chance that the first letter typed is ‘b’ is 1/50, and the chance that the second letter typed is ‘a’ is also 1/50, and so on. Therefore, the probability of the first six letters spelling banana is:

    (1/50) × (1/50) × (1/50) × (1/50) × (1/50) × (1/50) = (1/50)6 = 1/15,625,000,000.

    The result is less than one in 15 billion, but not zero.

    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.

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    • HeavenlySpoon@ttrpg.network ⁨11⁩ ⁨months⁩ ago

      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.

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    • ameancow@lemmy.world ⁨11⁩ ⁨months⁩ ago

      In a literal and real universe, if you had real magic and could organize this in reality without it collapsing into a singularity instantly, then not only would you indeed get Hamlet instantly, you will also get monkey poop sculptures in every possible configuration, including models of us typing these words on PC monitors made entirely of monkey feces. They would just be fecal scultpures because, as you said, a monkey can’t poop actual electronics so pooping an entire, working internet with two people chatting is impossible… probably. You would get typewriters thrown around randomly until some collapse into black holes, until some accidentally form whole, working machines, until some mix with the poop sculptures and create models of whole worlds. If you want to limit it to a mathematical thought experiment, then yes you can make points about key distribution and so on, you can make limitations that will constrain the outcomes, but in the real world all we really have to create those limitations is the speed of light, which would constrain contradictory outcomes in an infinite model.

      Again, the idea is to understand that infinity is an absurd idea, and we can’t work with infinities in any meaningful way.

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