Is that an actual sentence?
I have an infinite number of rooms, so I’m putting two monkeys in each room with two typewriters.
Now I can do it in half the time.
The monkeys now have sex with each other non stop. You’re now going at 10% of the speed you were previously.
Yeah, but since an infinite number of monkeys are working on it already, it will be just one copy for each of the infinite number of monkeys.
Two new monkeys show up, and even though the infinite rooms and infinite typewriters are already occupied, you can make room for them by making all of the monkeys move over one room, and putting the new monkeys in that newly vacant room with the newly available typewriters.
Omg I just read about that the other day but I’m too stupid and forgetful… Something about the existence of inf + 1
892 trillion years sounds like a minuscule amount of time to wait for a string that long.
Like you already got unbelievably lucky.
But arent there infinite monkeys? You should have already seen it written an infinite amount of times in 892 trillion years
Not necessarily. There are an infinite number of positive numbers, but -13 will never be one of them. Ergo, even with infinite possibilities, you still may not see a particular combination (even if it does fit the criteria; my metaphor is imperfect).
Perhaps it’s in the monkey’s psychology that they’d never hit the keys that much before just destroying it all. They’re a pretty poor pick for a random value generator.
As written this guy only has one monkey.
We do a little trolling… 😁
https://libraryofbabel.info/bookmark.cgi?a_glooming_peace_this_morning_with_it_brings.:1
Source: Library of Babel; Volume 16 on Shelf 5 of Wall 1 of Hexagon
[The Hexagon Code] (It's a very long string of text)
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
If you have an infinite amount of monkeys and they’re all typing truly randomly, then an infinite number of them would get it correct on the first try. Which is sort of weird to think about lol.
Most people don’t get the thought experiment at all.
I’ve seen 300+ deep comment chains on reddit with people arguing bitterly back and forth if a monkey could even operate a typewriter, and how it’s absolutely impossible to get monkeys to type out a book, etc, etc, etc.
I hate it here.
I think too many people don’t consider the monkey is not supposed to be making decisions, it’s just supposed to be inputting anything, literally anything, on a typewriter.
Like a random value generator, for typewriter keys.
You could get the same result throwing an infinite number of typewriters down an infinitely long mineshaft, but there will be even fewer people who would understand it 😭
Worse, creationists use the “watch maker’s paradox” as evidence of creation. Same idea but watch parts in a washing machine.
What about a rock formation that happened to be a sun dial?
I have argued with plenty of theists, they tend to cherry-pick parts of every idea to validate their extreme fear of death/God, so they hyper-fixate on the idea that “fantastic things” can happen with infinities, without addressing the problems that also come from infinities.
The idea behind the monkeys/typewriters thought experiment is to highlight just how problematic actual infinities would be in our universe, it’s an argument against things like gods occuring, because in an infinite, unbounded universe there would be an infinite number of infinitely powerful beings negating each other all out over large enough scales.
I mean, if they are actually monkeys who don’t know to type, some of them will still press keys once or twice. And if there’s infinite monkeys, they will still type it out.
If you’re talking magical, biologically accurate monkeys, then they will eventually shit out models of every scene of your life, replicated in perfect detail in monkey feces. Not just once, but an infinite number of times, and also in every possible configuration your life may have ever existed in, every choice you could have made. An infinite number of times.
Just because a set is infinite does not mean that it will contain every possible permutation of something. That’s a common thought but a provably untrue one.
For example, there are infinite even numbers, and none of them are 3. Not a single one. If someone claimed that generating infinite even numbers would eventually return a 3, you wouldn’t take them seriously, and rightly so.
But here’s the rub: you can also generate infinite even numbers and never return a 2. Every time you generate an even number, there are infinite numbers that it could be. Even if you don’t allow numbers to repeat, it’s not like you are gonna exhaust the amount of non-2 even numbers.
Just because a set is infinite does not mean that it will contain every possible permutation of something.
So back to the typewriters. You might say that while there are infinite numbers, there are not infinite permutations of a string of characters the length of the works of Shakespeare.
And that’s true.
If you were to say that a string of characters the length of the works of Shakespeare (or longer) could never be repeated exactly, the yes they would type the works of Shakespeare.
But then they wouldn’t be typing randomly.
Randomness repeats. Infinite randomness can repeat infinitely.
And we are not dealing with strings of characters the length of the works of Shakespeare. We’re dealing with strings of characters of infinite length. And there are, in fact, infinite permutations of those.
So… Yeah.
There’s no logical basis for infinite monkeys typing infinitely, inevitably producing the works of Shakespeare. Or fecal dioramas or alternate universes where Spider-Man is real or whatever else. Doesn’t hold water.
I disagree and have also done plenty of reading on the topic.
I don’t disagree to say that “you’re wrong and even wild silly things are possible!” but I’m saying that it’s a lot more accurate to say that we don’t know what real-world systems can and cannot do. Your model is from a pure mathematical and physical point of view, which would be correct. But we don’t know if our knowledge of quantum mechanics and physics broadly is even complete (probably not) so I have grown quite fond of the far more succinct answer of “I don’t know.”
Generally people get really invested in this because it either validates or invalidates some belief, mystical or material, about the universe, but I don’t think it’s an answerable question until we find out if infinities can even exist in a tangible way. Most likely not, at least in our limited understanding.
Hell, if you have infinite time and infinite typewriters, you don’t even need the monkeys. You could probably depend on hail pressing those keys, the argument still stands. As long as there are inputs, ever.
Given long enough periods of time, if your typewriters were magically immune to entropy, they would eventually start quantum teleporting into each other, and eventually would accidentally create perfect clockwork mecha-godzilla made entirely out of typewriters.
The funny thing is, if you truly have infinite monkeys, it doesn’t matter if they’re using it correctly or not. There is an infinite amount of them.
Some infinities are bigger than others, though.
Even if you have countably infinite monkeys typing countably infinite strings for an infinite period of time, there will be an infinite number of strings that the monkeys haven’t typed, that will never be in the set of completed typed strings.
Cantor’s diagonalization proves it.
This is why I go online.
We are IN the timeline where a monkey wrote Shakespeare. That monkey was Shakespeare.
Weird, what a coincidence
Not really, an almost infinite number of non-shakespeare monkeys came before him and also didn’t happen to write the entire works of shakespeare.
it was actually a significantly lower amount of monkeys than infinity
I mean it was bound to happen at some point
He was an ape
Yeah, it’s weird how nobody talks about the trillions of trillions of plays Shakespeare wrote that are complete gibberish.
Hey! I liked Romeo and Djrurleltkitshsnmqlaapj
Did you know a monkey can write Shakespeare’s work using this simple trick (millions of years of evolution)?
Yeah but did he do it with a typewriter? Didn’t think so
He wrote it in the wrong order tho
Shakespeare was an ape
Apes are monkeys. Fuck paraphyletic groups.
Monkeys and apes are monophyletic, you massive bastard. (╯°□°）╯︵ ┻━┻)
…yes? That’s what I said.
A great one at that
Unless you think it was a different monkey because someone without noble blood couldn’t possibly write good.
What if you could math the monkeys?
Mind. Blown.
That which we call a gyatt by any other name would skibidi rizz just AF. No cap.
I’m starting a 2nd order monkey typing business attempting to use a bigger infinity of monkeys to eventually recreate the works of the first set of infinite monkeys.
Since monkeys tend to hit the same keys repeatedly, rather than trying them all out at random, I’d say your second order monkey business is actually more likely to succeed than the first set of monkeys ever typing out Shakespeare is.
I grew up with the guy in the pic btw. He was always kinda intense.
Did he have a loicense for his screaming?
We are the monkeys.
We wrote it all.
Even Skibidi toilet.
As an IT guy, there will always be a special place in my heart for the awesome person who wrote a protocol suite for this use case (it is a lot of fun to read):
There are quite a few April Fool RFCs, but this one is definitely one of my favourites. This one and RFC 1149 (A Standard for the Transmission of IP Datagrams on Avian Carriers).
Pretty sure 1149 did actually beat Australian internet in large file transfer speed in a real test.
As the old saying goes, never underestimate the bandwidth of a
truck full of hard drives barreling down the highwaymigrating pigeons with a SSD in claw.
Indeed. My partner wants to get into falconry, and I’m worried about my data getting encapsulated in a hawk.
We all evolved from monkeys, there have been millions of us, and one of us already wrote the works of Shakespear
We are evolved from a common ancestor to all great apes.
A great ape is not a monkey.
Don’t belittle your heritage or I’ll be forced to resolve this like our ancestors, by slinging feces at you until you leave.
The reference:
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.
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.
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 monkeys 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. The thought experiment isn’t designed to make you believe that anything is possible as much as it’s designed to show you the absurdity of infinity as a concept.
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.
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.
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.
I agree, and I think it’s an absolutely fascinating area to study, because it does touch on some very important questions about our universe. We still don’t know if on the most fundamental levels, if our universe is constrained in some way, or if given enough time everything can change including those constants. I think about this a lot, but there are a surprising number of people who can’t grasp the ideas and problems, so apologies if I came on strong, I just want to make sure we’re all talking about the same things.
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:
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.
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.
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 that do a vast array of functions, 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 and other fundamental conservation forces, 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.
https://app.thestorygraph.com/books/2fd66245-5a4e-48ff-a1e0-1519ac95737d
A short stay in hell
NO
DO NOT READ THIS
