this post was submitted on 03 Nov 2024
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If the monkeys were truly infinite would time even matter? For any set of monkeys that could write Hamlet within a year there's an infinite number of duplicate sets, so they could do as much writing in one day as the original set would do over the age of the universe.
You don't get to pick and choose! You get infinite monkeys. What's all this about duplicate sets? Sounds like somebody is trying to bring in a ringer! That's cheatin!
The point is there's no statistical difference between rolling one die an infinite number of times, rolling an infinite number of dice once, and rolling an infinite number of dice an infinite number of times.
My comment was made in jest, I don't actually believe this person was trying to "cheat" on the thought experiment by selecting only smart monkeys lol.
That's the thing about infinity. If you have infinite monkeys, you don't have to choose. You'll have infinite instances of every possibility.
Finding any of the monkeys that typed out something interesting (or did something interesting that wasn't typing or more common interesting monkey stuff) is another issue. If there's an 0.0000001% of something interesting and unusual happening by coincidence, then there will be 999,999,999 uninteresting or usual instances for each interesting and unusual one.
Now if there were infinite copies of you searching the infinite monkeys for interesting and unusual events and all interesting ones get sent to an email address, the email server would overload in about the time it takes for the quickest interesting thing to happen, be noticed, and reported.
Considering that there are an infinite number of potential arrangements of keystrokes that aren't Hamlet? I'm honestly not fully convinced that you'd necessarily get Hamlet to begin with, let alone in a finite amount of time. Could you? Sure. But an infinite set minus an infinite number of possibilities still leaves an infinite number of possibilities. Any or all of which could not be Hamlet.
There are an infinite number of values between 1 and 2, but none of them are 3.
There aren't an infinite arrangements of keystrokes that are the length of Hamlet and aren't Hamlet. Hamlet is 191,726 characters long, it's like guessing a password.
44 keys on a typewriter, 191726 characters, makes 44^191726 or about 4.054 × 10^315094 combinations.
You're shifting the goalposts, and that still doesn't work.
An infinite number of monkeys typing for an infinite length of time doesn't necessitate that they stop once they reach 191,726 characters and then start over again. It also doesn't necessitate that they never repeat a pattern of characters. In fact, it's incredibly likely that they repeat more or less the same patterns more often than not. They're probably going to repeatedly press keys that are in proximity to one another while moving around the keyboard. Things like: ";ml9o fklibhuasdfbuklghaol;jios9 fdlhnikuasdf".
If you're measuring whether or not eventually you'll produce Hamlet by typing out every single possible permutation of 191,726 characters on a keyboard, well.. yeah, of course you will. But infinite monkeys aren't a grid search system for combinations of keystrokes, they're monkeys mashing the keys without knowing what they mean or in all likelihood what a typewriter or computer is.
You want monkeys on keyboards? You're mostly going to get gibberish.
If you put a bunch of yarn in a room with some high-powered rotating fans, are they eventually going to produce a sweater? Probably not. You're just going to have a bunch of tangled yarn. Sweaters require a consistent repetition of a non-random pattern of movement. Alter that pattern only a handful of times and you won't have a sweater even if you do manage to stumble across some version of that pattern accidentally.
Is there a non-zero chance? Eh.. maybe? But there's no reason to assume that it'll actually happen given any amount of time unless someone comes along who knows how to make a sweater and does so.
With monkeys and keyboards you'd be lucky to get a few lines of anything resembling English in iambic pentameter.
I think you're the one who is moving the goalposts. There's no requirement for the monkeys to submit their output, the test is whether the text of Hamlet is among their key presses. As long as there is a nonzero chance, then there is a 100% chance it would appear in an infinite system. Any non-zero probability times infinity has a 100% chance of occuring eventually.
The monkeys mostly produce gibberish, that's the vast majority of the potential outputs, but among that massive number is also the full text of Hamlet.
I mean it seems like you're just kind of asserting that it will be there. Just repeating it doesn't make it more true.