Next question, would Shakespeare appear in the Library of Babel?
Yes, everything that can be expressed as letters is in the Library of Babel. Finding anything meaningful in that library, though, is gonna take longer than just writing it yourself.
Still stuck on step 1. Get infinite monkeys.
We’re gonna need a bigger sedan…
Removed by mod
We evolved from the same species as monkies 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.
Removed by mod
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.
Removed by mod
This was a report for Trump supporters about how Donald xweets.
That research is worst type of redditor 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.
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.
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.
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.
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.
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.
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.
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.
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.
That’s why a monkey is used in the thought experiment. Monkeys do think at a low level. As it goes insane over centuries of imprisonment in front of its jailer, it’s likely going to try complex solutions to get out. Think of the hell infinity would really be for this monkey.
Yes, and given infinite monkeys no doubt they will eventually evolve into something that allows them to escape!
So as weird as it sounds not all infinities are equal. For example there is an infinite set of odd numbers. That set will never include the number 2 though.
Two is the loneliest number?
What part of Infinity is a mathematician, of all people, failing to comprehend? So what if it takes until cosmological decade 1,000 or 1 million or 1mil⁹⁰⁰⁰, it’s still possible on an infinite timescale, of one could devise a way for it all to survive the heat death of the universe ad infinitum.
I have read the paper, the news make it seem like something that is not. It’s a tough experiment and mostly a joke. From the paper closing remarks:
Given plausible estimates of the lifespan of the universe and the amount of possible monkey typists available, this still leaves huge orders of magnitude differences between the resources available and those required for non-trivial text generation. As such, we have to conclude that Shakespeare himself inadvertently provided the answer as to whether monkey labour could meaningfully be a replacement for human endeavour as a source of scholarship or creativity. To quote Hamlet, Act 3, Scene 3, Line 87: “No”.
Hell, infinite monkeys over a finite amount of time or finite monkeys over an infinite amount of time does the trick.
It’s also possible that it’s not possible even on an infinite time scale. A quick example: if you asked an algorithm to choose a number, and you choose 6536639876555721, but the algorithm only chooses from the infinite number of even numbers, it will never choose your number. So for the monkeys, if they are just not ‘programmed’ to ever be able to write a whole Shakespeare play, they will not be able to even with infinite time and infinite moneys.
Disagree. Within the confines of the thought experiment the monkeys are working with the standard alphabet and punctuation. There’s no reason to assume that they would never use the letter t or something like that, especially given the infinite time scale.
I see what you’re saying, but I do think they would have behavioral ‘rules’ that would stop them even on an infinite time scale. It would work if monkeys were capable of pressing one letter at a time, walking away, and pressing another letter and so forth… and while that’s of course physically possible for the monkeys to do, I don’t think it’s actually possible because they are susceptible to their own behavior. Not saying they would never type one specific letter, but a better example would be the behavior of rolling their finger/hand while pressing a letter, such that a conglomeration of letters are pressed in a way that would never match a Shakespeare play.
The problem is that you’re underestimating infinity then. If it only happens 1 in 1000000000000^10000 times but there’s an infinite number of attempts over an infinite amount of tine, it’s still bound to happen eventually.
No, I’m saying it’s not just improbable (if it were improbable, then yes, it would happen), I’m saying it’s impossible because of behavior.
As a small example, let’s say you wanted to type the ABC’s. However, every time you typed, your finger slid to press the key next to it as well. Then, no matter how many times you tried, you would never be able to type the ABC’s. That’s an exaggerated example of what I believe the monkeys would do. They simply would not be able to type letters at random. The way they work, they would be forced to mush buttons that do not allow for whole words.
If there was another scenario where there were about 30 boxes (one for each letter and any punctuation needed), and the monkey had to get a banana from one of the boxes, and that is what ‘typed’ the script, then yes, an infinite number of monkeys would be able to type Shakespeare. But because it’s a typewriter, I don’t think even an infinite amount would be able to.
No. If a monkey inherently NEVER, EVER hits one key at a time, then I gu3ss that scenario would make it impossible but that’s just stating that something is impossible in the first place and doesn’t affect the actual thought experiment in any way. Assuming that the typing monkeys literally ever have the possibility of only hitting one key at a time, no matter how many times they press two keys at a time and type nonsense, they will eventually and necessarily, bc of the definition of infinity, type Shakespeare. I don’t know how I can explain this better but I’ll try later when I have some time.
The theorem is only true if monkeys are random. But monkeys are not random, and therefore this cannot be proved true using monkeys.
Except for (cosmic-) bitflips and/or evolution changing the programming
The “Infinite monkey theorem” concerns itself with Probability (the mathematical field). It has been mathematically proven that given the random input (the mathematical kind - not the human-created kind) of the monkeys, and the infinite time, the probability of the “complete works of William Shakespeare” rolling out of the typewriter in between the other random output is
1.It’s a mathematical theorem that just uses monkeys to speak to the imagination, not a practical exercise, other than to prove the maths.
You should look into another brain-breaking probability problem called the “Monty Hall Problem”. Note that some of the greatest mathematical minds of the time failed said puzzle. Switching 100% increases the chance of winning. No, it won’t guarantee a win, but it will increase your chances, mathematically.
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
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 - infinite = infinite, take that infinite
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.
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
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.
That’s assuming they’re typing truly randomly. Which is a fair assumption.
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.
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?
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.
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.
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.
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.
And even the study can easily be proven wrong. A finite amount of monkeys already produced Shakespeare in a finite amount of time; it took roughly 25 million years.
Primates ≠ monkeys
We’re all apes
And apes are monkeys
If baboons and macaques are monkeys, and if howlermonkeys and spidermonkeys are monkeys, humans MUST be monkeys.
Because they can ONLY both be monkeys if their common ancestor was also a monkey and we share that very same common ancestor. In fact we are closer related to macaques and baboons than to spidermonkeys, which means we share a more recent common ancestor with old world monkeys than both us and the other old world monkeys share with the new world monkeys.
Cladistically, you can not outgrow your ancestry.
Humans are apes, apes are a subgroup of monkeys, monkeys are a subgroub of primates.
Monkeys are a social construct. Like trees.
If trees aren’t real, how can our birds be real?
…I am so sorry
Simiiformes is a clear and distinct clade.
There is no such thing for trees, because “tree” is a botanical classification, not a cladistical one.
Simiiformes is a clear and distinct clade.
Yes but who says that specific clade maps to the colloquial taxonomic word “monkey”?
If you go back far enough they do.
🤣
