The entire thing is utterly ridiculous. The meme is infinite monkeys.
The mathematician said, “But what if it was 200k monkeys?”
Reporters claim mathematician proved infinite monkeys meme is wrong.
200,000 does not equal infinite!
The whole thing is dumb if you accept a premise of “infinite monkeys”. An infinite number of monkeys will type the works of shakespeare immediately, because an infinite number of them will start with the very first key they hit and continue until the end. (So it’ll be complete exactly as fast as a monkey can type it, typing as fast as simianly possible, with no mistakes.) You don’t even need the infinite time.
It only becomes interesting if you look at the finite scenarios.
And BTW, the lifespan of the universe is finite due to the eventual decay of all matter, including the monkeys and the typewriters. There’s no infinite time.
A more interesting calculation the mathematician should have done is how many monkeys are needed to write Shakespeare in the lifespan of the universe rather than starting with 200k.
I don’t think there is a finite number of monkeys that would be guaranteed to do so in the lifespan of the universe.
Best we could do is calculate the expected number of monkeys it would take, assuming accurate probabilities, which I also don’t think is possible to determine.
You can’t just take one divided by the number of possible characters that could be typed because monkeys can do many things other than typing away. A high portion of them would likely instead destroy the typewriter. In the infinite monkeys scenario, an infinite amount would destroy their typewriter in the middle of Hamlet’s to be or not to be soliloquy.
Plus the odds of it actually happening are going to be so astronomically low that if you filled the known universe with monkeys, you’d end up with monkey stars and black holes before any Shakespeare.
It really only works as a thought experiment about the nature of infinity.
Unless there’s an infinite multiverse, in which case we are in the universe where a monkey wrote out the complete works of Shakespeare. That monkey’s name? Shakespeare. (And yes, many clapped when he did so.)
Saying that last bit about time is not particularly meaningful for two reasons.
First of all, we do not especially know the end state of the universe. It may not be true that all matter decays, and protons may be stable. We may be in a false vacuum which will spontaneously collapse in large timespans.
Second of all, the hypothetical is a thought experiment. The monkeys are a placeholder for any random generation of characters. The thought experiment also does not take into consideration the food required to feed monkeys for infinite time, nor their aging, mutation over generations, and waste logistics. It’s not meaningful then to suddenly decide to apply the laws of physics to them. The only laws applicable in this scenario are logic and mathematics.
I generally agree with the rest of your take, although I disagree where you say the thought experiment is dumb. I only have an issue with that last point lol. Cheers.
The whole thing is dumb if you accept a premise of “infinite monkeys”.
If thats the point where you want to draw the line, I guess that it becomes dumb at exactly that point.
But the point of the thought experiment is that it says what you said: it will definitelly happen because infinity is absurdly big number.
If you follow it, you quickly end up with the Infinite Improbability Drive from The Hitchhikers Guide - if you have an infinite number of typewriters, an infinite number of them will be loaded with paper that already has the complete works of Shakespeare written on it
You assume that monkeys are identical, communicate with each other and know what they are doing. Take one of these away and all of the infinite monkeys will press the same buttons basically making them one monkey. Take another and they will type random gibberish.
The point of the dilemma is for non of those to be the case. The point is can Shakespeare or anything valuable to humans appear in random given enough time and resources? Basically can “the AI” as we know it now that doesn’t actually have “I” create something new and valuable?
And the answer is(going from the basic maths) yes it may produce something cool but it also may never produce Shakespeare or anything cool and will never know what it can do and what it can’t.
Deleted
-1/12 monkeys
200,000 does not equal infinite!
It’s close though. I can’t think of a bigger number.
What about 7?
Not sure. Gonna ask microsoft copilot
True nathematician would never make a mistake distinguishing finite and infinite cardinality. Countability, on the other hand… (but that’s a separate issue)
It only took a couple billion monkeys a few million years but one did eventually write out the full works of Shakespeare
This is always how I’ve chosen to interpret the expression. It’s not a theory. It’s an observation.
It’s a thought experiment, not an observation. The idea is that if you have infinity and it’s truly random than eventually all possibilities emerge somewhere within that.
The idea of infinite monkeys typing randomly on infinite typewriters is that eventually one of them would accidentally type out all the works of Shakespeare. Many more would type out parts of the works of Shakespeare. And many many many more would type random garbage.
If we then take that forwadd imagine for a moment the multiverse is also infinite and random, then every possible universe would exist somewhere in that multiverse.
It can be taken in other directions too. It’s a way of cocneptualising the implications of infinity and true randomness.
Meanwhile actual Shakespeare had intelligence and wrote and created his works. Him being a monkey writing Shakespeare is just a sly humerous observation, but it has nothing to do with the actual meaning of the thought experiment and the idea it is trying to convey.
Did you choose to overlook my intentional usage of the word “chosen” just to mansplain something obvious? I did not make my choice out of ignorance, but I appreciate you assuming I did.
Yeah, the point isn’t that they could write Shakespeare. But that they would write everything we could imagine + everything in between that.
It tries to explain the concept of infinity. Which is mind boggling to any human.
Also since it should happen once, that means that it also happens an infinite number of times, but a smaller infinity than the whole infinity.
Alas, not on a typewriter… Back to the drawing board!
No, the FIRST monkey to write Shakespeare used a feather and ink.
It only took a couple hundred years after all those millions for them to be written on the typewriter.
Turns out not quite. In the monkey version Hamlet says, “To be, or what.”
A property of hydrogen is that, given enough hydrogen and time, eventually it will write out the full works of Shakespeare.
As I pointed out elsewhere about this: it also is based entirely on probability, like cracking encryption. It could take longer than the universe will be around. But there’s also the possibility they write Hamlet within a year because they got lucky.
if it’s infinite monkeys then an infinite amount of them do it correct on the first try
Not necessarily. Each monkey is independent, right? So if we think about the first letter, it’s either going to be, idk, A, the correct letter, or B, any wrong letter. Any monkey that types B is never going to get there. Now each money independently chooses between them. With each second monkey, the chances in aggregate get smaller and smaller than we only see B, but… It’s never a 0 chance that the monkey hits B. If there’s only two keys, it’s always 50/50. And it could through freak chance turn out that they all hit B… Forever. There is never a guarantee that you will get even a single correct letter… Even with infinite monkeys.
I get that it seems like infinity has to include every possible outcome, because the limit of P(at least one monkey typing A) as the number of monkeys goes to infinity is 1… But a limit is not a value. The probability never reaches 1 even with infinite monkeys.
The birthday problem fits into this somehow, but I can’t quite get there right now. Something like an inverse birthday problem to illustrate how, even though the probability of two monkeys typing the same letter rises quickly as more monkeys are added to the mix, and at a certain point (n+1, where n is “possible keystrokes”) it is inevitable that at least two monkeys will key identically, the inverse isn’t true.
If you have 732 people in a room, there’s no guarantee that any one of them was born on August 12th.
There’s another one that describes this better but it escapes me.
Infinite monkeys. Any probability greater than zero times infinity is infinity. You will see an infinite number of monkeys hitting A and an infinite number hitting B. If there were a finite number of monkeys, you would be correct, but that is not the case.
No, that’s not how probability works. “Any probability times infinity is infinity” doesn’t even mean anything. Probabilities are between 0 and 1, and you do not multiply them by fixed factors. Infinite probability has no meaning.
I explained the infinity monkeys in another comment more clearly than I did above -here you go.
I could have worded that better. Any probability with a non-zero chance of occurring will occur an infinite number of times given an infinite sequence.
To address the comment you linked, I understand what you’re saying, but you’re putting a lot of emphasis on something that might as well be impossible. In an infinite sequence of coin flips, the probability of any specific outcome - like all heads - is exactly zero. This doesn’t mean it’s strictly impossible in a logical sense; rather, in the language of probability, it’s so improbable that it effectively “never happens” within the probability space we’re working with. Theoretically, sure, you’re correct, but realistically speaking, it’s statistically irrelevant.
Eh, I don’t think it’s irrelevant, I think it’s interesting! I mean, consider a new infinite monkey experiment. Take the usual setup - infinite monkeys, infinite time. Now once you have your output… Do it again, an infinite number of times. Now suddenly those near impossibilities (the almost surely Impossibles) become more probable.
I also think it’s interesting to consider how many infinite sequences there are which do/do not contain hamlet. This one I’m still mulling over… Are there more which do, or more which don’t? That is a bit beyond my theoretical understanding of infinity to answer, I think. But it might be an interesting topic to read about.
Fair enough, I suppose it is interesting!
In terms of the question, “Are there more infinite sequences that contain Hamlet or more that don’t?”- in the context of true randomness and truly infinite sequence, this feels like almost a trick question. Almost every truly random infinite sequence will contain Hamlet an infinite number of times, along with every other possible finite sequence (e.g., Moby Dick, War and Peace, you name it). In fact, the probability of a random infinite sequence not containing Hamlet is effectively zero.
Where it becomes truly interesting is if you have an infinite number of infinite sequences. Now you’d certainly get instances of those “effectively zero” cases, but only in ratios within infinity itself, haha. I guess that’s probably what you were getting at?
That’s not true. Infinite doesn’t mean “all”. There are an infinite amount of numbers between 0 and 1, but none of them are 2. There’s a high statistical probability, sure, but it’s not necessarily 100%.
It is necessarily 100%. That’s the whole idea behind infinity. There is a 0% chance of rolling a “2” because it’s outside the bounds of the question. Theres a 0% chance of the monkeys typing in chinese too.
No, it isn’t, that’s a misunderstanding of how independent random variables behave. Even with an infinite number of trials, in this case there is never a guarantee of a particular outcome.
Consider a coin flip, 50/50 chance of either getting heads or tails on each flip. Lets say we do an infinite number of flips, one by one, so that we end up with an infinite ordered set of outcomes, like so: {H, T, T, H, … }. Now, consider the probability of getting a particular arrangement of heads/tails in this infinite list, like the one I wrote before. You can’t calculate a probability for each arrangement - there are an infinite number - but it should be clear that each arrangement is equally likely, right? Because {H, …} is just as likely as {T, …}, same with {H, H, …} and {H, T, … } and so on and so on. In other words the probabilty of getting all heads on infinite coin flips is the same as the probability of getting any other combination.
In the same way, the infinite monkeys are doing ‘coin flips’ involving more than 2 options. Lets just assume they have 26 keys, one for each letter, and assume they hit each of them with equal probability. In the same way, for an individual monkey the probability of going {a, a, a, a, a, a, …, a} is the same as the probability of the same sequence with hamlet somewhere (in a particular position that is - the probabilities are only equal when we consider exactly one arrangement). What might make it more intuitively clear is that even after an infinite number of trials you only have one sequence of letters (or set of sequences, with infinite monkeys). It’s clear that there are other possible sequences - like only the letter a - and these all have a non 0 chance of having arisen given a different infinite set of monkeys for a different infinite time period.
It’s easy to be misled here! If we return to the coin flip example, the probability of flipping at least 1 head after infinite coin flips approaches 1. The limit of P(at least one H) as the number of flips approaches infinity is 1. But this is a limit! You never reach the limit, even considering infinite situations.
0.99999… repeating equals 1. Not close to 1. Equal to 1. The monkeys will necessarily type hamlet somewhere in the sequence. If your group of monkeys hasnt typed it yet, double the number of monkeys.
A monkey could type any infinite sequence of letters if it types at random. Since infinite sequences of single letters, repeating patterns, and those containing hamlet except one letter is wrong every time are all possible infinite sequences, it’s possible that the money produces one of them.
Probability behaves strangely in infinite situations. A single monkey will almost surely produce the complete works of Shakespeare in infinite time… But this is partially a flaw of infinity in general.
As another example, let’s say your monkey produces an infinite sequence containing hamlet. What is the probability of that particular sequence arising? It’s 0. There is no chance of any particular sequence arising… And yet that one did arise! It was almost surely not going to be that one, but it was. The probability of any single infinite sequence arising is 0, but nonetheless one of them will be the outcome.
That’s assuming they’re typing truly randomly. Which is a fair assumption.
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.
But given infinite time, could OP spell “infinity” correctly?
Well if you give them infintiny time… maybe.
infintiny? you bloopid monkye
Infynyty?
I like “infintiny” as a replacement for “infinitesimal”
It was the best of times, it was the blurst of times.
You stupid monkey!
Damn. So close
Good glad to hear monkeys will produce their own unique literature instead of copying the classics.
Huh. I’d never thought of it like that, but now that you mention it with an infinite number of monkeys one of them will eventually write an entire literary canon of plays that blow that loser Shakespeare out of the water.
That research is worst type of reddit ACKCHYUALLY taken to academia
I fear the plague of reddit brainrot will soon make even research papers plain insufferable. Would you want to have moderator of 11 subreddits and holder of top 1% commenters achievement in your research group?
Something weird I’ve been noticing. Lately I’ve been unintentionally minimizing comments before I’ve finished reading them. Just happened with yours. It’s like some subconscious part of my brain goes “booorrring!” half way through reading anything longer than two sentences and immediately goes for the next dopamine kick.
And I’m not knocking your comment. I was genuinely interested in what I was reading. It’s just a little troubling. I dropped Reddit and Lemmy a while back because I felt like I was becoming addicted. I lasted a few months, but evidently I’ve fallen off the wagon.
Don’t worry I actually nurture my internet presence to be a little controversial and edgy. Not for every taste but those who enjoy we instantly are friends. It’s a filter of sorts. I want ppl who feel offended about such things to block me
Actually, we should be thankful for their divine presence.
Them saying that is like me saying Bizmuth isn’t radioactive because it’s half-life is many, many times longer than even the most conservative estimates for the heat-death of the universe.
In finite time that’s effectively true, because the universe itself would decay before a block of bizmuth lost any significant weight - but it isn’t physically true, because with infinite time a block of bizmuth left completely alone would evaporate away via alpha decay.
And that’s the point of infinite time - to let you throw away time and probabilities as obstacles and strictly focus on whether something could physically happen, rather than the odds of it occurring.
infinite monkey theorem relies on the assumption that infinite banana theorem is valid
Back in my IT support days, IPX routing had a “Count to Infinity” problem when the number of hops between sites went above 15. We used to joke that this made 16 “Infinity”.
Being nerds at the time, we did napkin math to prove the Shakespearian Monkey Quotient was 256cmy (combined monkey years) for “Hamlet”.
Combined Monkey Years just aren’t the same since their lead singer left, I’m hoping they improve eventually.
Don’t worry, the reunion tour is in 35cmy
Just thinking at a high level, an infinite number of monkies should hypothetically almost instantly produce Shakespeare (or at least as quickly as they can type)
Conversely, 1 monkey would eventually produce it given infinity time.
1 monkey would likely die before producing Shakespeare
oh absolutely, this is purely a thought experiment of course.
not if it’s an infinite monkey
Well, an infinite amount would.
One monkey may never produce it even given infinite time. It could just produce an infinite string of the letter a and never change it’s mind. That’s less likely that it writing hamlet, or even many hamlets… But nonetheless, it could. In fact all of the infinite monkeys could do that. If you repeated the experiment and infinite number of times, it’s likely that one of them will simple produce an infinite number of infinite strings of only the letter A. Or, idk, ASCII art.
This is the same type of criticism the paper made. The real intent behind the saying is given random output (where all outputs have nonzero probability) eventually you will create anything/everything.
Its a thought experiment around infinity, probability, and art.
Yeah, I haven’t read whatever paper this is talking about, but I imagine, it’s looking at the saying in a more literal fashion for the sake of argument…
Still stuck on step 1. Get infinite monkeys.
We’re gonna need a bigger sedan…
This thread could well have been written by an infinite amount of monkeys, too.
Thoiei0z ao;qjlk a 2897n3 eiie??! hoenwk a ;jihiwe a wiiien theohg rosebud oiwoi;qne i93823hnn banana
Nah, internet commenters are definitely crows.
But monkeys never ask questions.
Science has yet to determine if monkeys would be able to type “wherefore art thou Romeo?”
They already have, we evolved from a species you could colloquially refer to as monkeys. The ancestors of those monkeys went on to write Shakespeare
We evolved from the same species as monkeys did, not from monkeys. They weren’t actually monkeys until they were already very far removed from us. However, given that we are apes and thus there was at some point a human ancestor species that was ape and was not human the rest of that is right. Off the top of my head that species would probably be our last common ancestor with other apes. Edit: typo, I had spelt monkeys as monkies
See definition for colloquial
I know what colloquial means, but apes cannot be colloquially referred to as monkeys. They are to far removed. You are confusing something being colloquial with something being a common misconception, that many people do not understand taxonomy at a middle school level does not make it a correct statement. Also, colloquial generally refers to how “proper” the language is being spoken (including the usage of slang and stuff like that), and not the factual correctness of it.
Keep coping
