The question that everyone has been dying to know has been answered. Finally! What will scientists study next?
But we aren’t talking about one monkey. We are talking about infinite monkeys.
Infinity is already a loaded concept in our universe.
There’s still a chance that a monkey will type it on the first attempt. It’s just very small.
If I understand statistics correctly, it’s actually a 50/50 chance.
OK, what about 2 monkeys?
The whole point of the thought experiment is that you have infinite monkeys.
So… three monkeys?
At least
I don’t think so, because if you had infinite monkeys an infinite number of them would get it on the first try.
Exactly. That’s the point.
I don’t think it works honestly. You’d need a monkey with a lasting and dutiful commitment to true randomness to ever get anything but a finite number of button mashing variations. Monkeys like that don’t come cheaply.
Within that finite set, one combination is the complete text of Hamlet.
I honestly don’t think so, bestie. Monkey’s not gonna press the keys randomly at all. Somewhere in the recesses of his monkey neurons he’ll have made implicit connections between letters and letter combinations. This is the infinite typewriter monkey, not some two-bit organ grinder’s bitch. This monkey has been places, probably been through hell getting to this position in life. Seen wars, been across the globe, and now he’s the star of a famous thought experiment. He loves lowercase t because he’s a devout Christian after having been rescued by that missionary, and being a monkey he doesn’t quite grasp the distinction. Wanna see what he wrote? tttt hhdfyb my ik t tkkoptt aa aaaa Bernardo : Who’s there? tt ttt eeertyuhjk t
You call that random?
How is this a study? It’s just basic probability on a bogo sort style algorithm.
It’s not a “study”, it’s just 2 mathematicians having some fun. The paper is a good read, and as a math teacher I see a lot of pedagogical values in such publications.
I’ve read there are so many permutations of a standard deck of 52 playing cards, that in all the times decks have been shuffled through history, there’s almost no chance any given arrangement has ever been repeated. If we could teach monkeys to shuffle cards I wonder how long it would take them to do it.
There are 8.0658*10^67 orders you can shuffle a card deck in.
The math is easy. It’s just 52! if your calculator has that function which is really 525150…32*1. There are 52 possibilities for the first card 51 for the second since you’ve already used one card and so on.
How many decks of cards have been shuffled over human history, or will be is beyond me.
For those who are confused, the comment meant to say
52*51*50*....*3*2*1i.e. 52 × 51 × 50 × … × 3 × 2 × 1
Markdown syntax screwed it up.
Yeah that’s the part that isn’t easy.
Well you’re not supposed to just have one. It’s supposed to be a thousand monkies at a thousand typewriters.
Now do the Mythbusters thing and figure out how many monkies and typewriters it would take for them to write Hamlet in just under a year. Don’t just solve the myth; put it to the test!
I thought it was supposed to be an infinite amount of monkeys, since it’s known as “infinite monkey theorem”, but apparently, according to Wikipedia,
The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type any given text, including the complete works of William Shakespeare. […]
[…] can be generalized to state that any sequence of events that has a non-zero probability of happening will almost certainly occur an infinite number of times, given an infinite amount of time or a universe that is infinite in size.
However, I think, as long as either the timeframe or monkey amount is infinite, it should lead to the same results. So, why even limit one of them on this theoretical level after all?
The linked study even seems to limit both, so they’re not quite investigating the actual classic theorem of one monkey with infinite time, it seems.
I’m still mad we are giving them typewriters instead of keyboards. Think of the arthritis! Ergonomics please!
As well as a single monkey, they also did the calculations using the current global population of around 200,000 chimpanzees, and they assumed a rather productive typing speed of one key every second until the end of the universe in about 10100 years.
They did 200k monkeys, so a little overkill from your expectations.
What if the monkeys evolve to higher intelligence as time passes by?
You maniacs!
I have a way to make it work.
Have the monkey write down a single character. Just one. 29/30 of the time, it won’t be the same character as the first one in Shakespeare’s complete works; discard that sheet of paper, then try again. 1/30 of the time the monkey will type out the right character; when they do it, keep that sheet of paper and make copies out of it.
Now, instead of giving a completely blank sheet to the monkey, give them one of those copies. And let them type the second character. If different from the actual second character in Shakespeare’s works, discard that sheet and give him a new copy (with the right 1st char still there - the monkey did type it out!). Do this until the monkey types the correct second character. Keep that sheet with 2 correct chars, make copies out of it, and repeat the process for the third character.
And then the fourth, the fifth, so goes on.
Since swapping sheets all the time takes more time than letting the monkey go wild, let’s increase the time per typed character (right or wrong), from 1 second to… let’s say, 60 times more. A whole minute. And since the monkey will type junk 29/30 of the time, it’ll take around 30min to type the right character.
It would take even longer, right? Well… not really. Shakespeare’s complete works have around 5 million characters, so the process should take 5*10⁶ * 30min = 2.5 million hours, or 285 years.
But we could do it even better. This approach has a single monkey doing all the work; the paper has 200k of them. We could split Shakespeare’s complete works into 200k strings of 25 chars each, and assign each string to a monkey. Each monkey would complete their assignment, on average, after 12h30min; some will take a bit longer, but now we aren’t talking about the thermal death of the universe or even centuries, it’ll take at most a few days.
Why am I sharing this? I’m not invalidating the paper, mind you, it’s cool maths.
I’ve found this metaphor of monkeys typing Shakespeare quite a bit in my teen years, when I still arsed myself to discuss with creationists. You know, the sort of people who thinks that complex life can’t appear due to random mutations, just like a monkey can’t type the full works of Shakespeare.
Complex life is not the result of a single “big” mutation, like a monkey typing the full thing out of the blue; it involves selection and inheritance, as the sheets of paper being copied or discarded.
And just like assigning tasks to different monkeys, multiple mutations can pop up independently and get recombined. Not just among sexual beings; even bacteria can transmit genes horizontally.
Already back then (inb4 yes, I was a weird teen…) I developed the skeleton of this reasoning. Now I just plopped the numbers that the paper uses, and here we go.
You either spend your life really well or you have way too much time on your hands.
Either way I read your post with happy curiosity. 🙂
I think the point is less about any kind of route to Hamlet, and more about the absurdity of infinite tries in a finite space(time). There are a finite (but extremely large) number of configurations of English characters in a work the length of Hamlet. If you have truly an infinite number of attempts (monkeys, time, or both are actually infinite) and the trials are all truly random (every character is guaranteed to have the same chance as every other) then you will necessarily arrive at that configuration eventually.
As far as your process, of procedurally generating each letter one by one until you have the completed works, we actually have a monkey who more or less did that already. His name is William.
monkey who more or less did that already. His name is William.
???
Ol Bill Shakespeare. He wrote Hamlet, one correct letter at a time.
Well. technically he was an ape rather than a monkey.
Technically true, I think it still fits for the layman.
Humans are apes, apes are monkeys, paraphyletic groups are bullshit.
isnt that a misconception? apes just share a common ancestor with us
To be entirely fair, apes aren’t monkeys. I don’t think that particular distinction is really all that relevant to the discussion, but technically…
From wikipedia:
Traditionally, all animals in the group now known as simians are counted as monkeys except the apes. Thus monkeys, in that sense, constitute an incomplete paraphyletic grouping; however, in the broader sense based on cladistics, apes (Hominoidea) are also included, making the terms monkeys and simians synonyms in regard to their scope.
Oh neat. This is all taxonomy that is well beyond me. My defense of calling humans monkeys is that everyone does it, and that’s how language works. Glad to know I’m correct too, technically lol
Username checks out.
I think the point is less about any kind of route to Hamlet, and more about the absurdity of infinite tries in a finite space(time).
I know. It’s just that creationists misuse that metaphor so often that I couldn’t help but share my brainfart here.
I feel like you might have interviewed for Google in the late 2000s
Among other problems, this fails to account for non-typing activities performed by the monkey, such as damaging the typewriter or attacking the researcher.
285 years increases to a few thousand if you alarmingly frequently have to clean the contents of a monkey’s colon out of a typewriter.
And at some point you’d want to further “refine” your selection process by “repairing” the typewriter to have fewer keys and/or causing the typewriter to jam after the required key press. Monkeys like to press the same key over and over again. Good luck getting them to stop once they’ve pressed a key once.
TL;DR monkeys are chaos, and this will not be easy.
This changes the rules though from check at the end to check at every letter. That’s where the real efficiency gain is… The insertion of an all knowing checker who could have written it himself anyway. The math of permutations vs combinations changes drastically if we change the rules.
The insertion of an all knowing checker who could have written it himself anyway
The checker does make all the difference, but he doesn’t need to be able to write it by himself. It could be even a brainless process, such as natural selection.
There was a plank computer post here last couple of days. It showed an atomic sized computer performing one crack attempt every 10^-44 seconds would take a 95 character alphabet 100 years to crack a 121 character password.
Monkeys take up 1m^3. 10^105 bigger than a plank length. Typing 120wpm is 10^43 slower. Ignoring punctuation and spaces and capitalization, a 26 character alphabet allows for about 52 more characters than a 95 character alphabet.
Bottom line, monkeys can’t come anywhere close to being able to crack a 100 character password from a 26 character alphabet.
Okay but here me out, what if we 10^43 more monkeys to balance out the speed?
In fact, let’s push this to an extreme. We get enough monkeys that their mass turns them all into one black hole. Inside the black hole, the laws of physics get all fucked. Next we need to somehow dissolve the event horizon as explained in This Kurzgesagt video. Once that happens and we are left with a bare singularity, anything can pop out of it, including a copy of Hamlet.
The monkeys, however, will very likely be dead.
The author is so stupid, the monkey will of old age long before the universe ends.
But first he will accidentally the whole thing.
Has He Anyone Really Been Far Even as Decided to Use Even Go Want to do Look More Like?
I always heard that it was an infinite number of monkeys, not just one. So one of them might get the job done in time.
One of them is mathematically guaranteed to get the job done in time.
In fact - and here’s the trippy part - an infinite number of them is mathematically guaranteed to get the job done in time.
Seems to not understand the thought experiment which is a way to contemplate infinity.
I just listened to a podcast about assembly theory and I think that it kind of relates here too, though maybe not. If we start randomly generating text that is the lenght of the Hamlet, then Hamlet itself would be one of the possible, finite number of possibilities that could be generated within these parameters. Interesting theory nevertheless.
If we think about a screwdriver, the theory would argue that it couldn’t simply appear out of nowhere because its structure is too specific and complex to have come into existence by chance alone. For that screwdriver to exist, a multitude of precise processes are required: extracting raw materials, refining them, shaping metal, designing the handle, etc. The probability of all these steps happening in the right order, spontaneously, is essentially zero. Assembly theory would say that each stage in the creation of a screwdriver represents a selection event, where choices are made, materials are transformed, and functions are refined.
What makes assembly theory especially intriguing is that it offers a framework to distinguish between things that could arise naturally, like a rock or even an organic molecule, and things that bear the hallmarks of a directed process. To put it simply, a screwdriver couldn’t exist without a long sequence of assembly steps that are improbable to arise by chance, thereby making its existence a hallmark of intentional design or, at the very least, a directed process.
In other news, exponents make things big.
Any time you have an X>1 and a big n, X^n gets huge.
X=26 (if we ignore punctuation, spaces, and capitalization).
N=130,000The theorem holds true. The theorem states that the monkey has infinite time, not just the lifetime of our universe.
That’s just lazy science to change the conditions to make sensational headlines. Bad scientists!
This just in: scientists disprove validity of thought experiment; philosophers remain concerned that they’ve missed the point.
The universe is the cage and we are the monkeys. We have already written Hamlet.
It also makes a pretty bold claim about us actually knowing the lifespan of the universe.
How are they defining the end of the universe?
Probably very shortly after dinner has been served at that restaurant.
I think that was just a galaxy, not the whole universe.
You mean the Restaurant at the End of the Universe?
Hmm… i sit corrected.
But what does the Lord think about this?
The universe is believed to end just a few nanoseconds before a monkey finishes writing Hamlet.
Heat death would be my assumption, so between about 10^100 and 10^106 years
We know such an infinitesimally small amount about what is actually happening in the universe that any claims to be capable of predicting it’s end are patently absurd.
That’s not bold, we’ve known how long the universe will last for decades now.
Just because someone tells you something, doesn’t mean they actually know what they’re talking about. fyi
When multiple fields of science all agree, yeah they know what they’re talking about.
I just don’t get these anti-science types…
the monkey has infinite time
Use an infinite number of monkeys instead?
Infinite time is undefined though. We are not sure there was time before the Big Bang. Before anyone says “but there must have been,” consider that it’s just as paradoxical and mind blowing to imagine that time never had a beginning and just stretches infinitely into the past. How can that be so? It means it would have taken an infinite amount of time for us to reach this moment in time, and that means we never would have.
Infinite time is perfectly defined, it just doesn’t exist in our universe
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Why must the concept of time before the big bang (or after our heat death) exist in our physical reality for us to speculate about theoretical infinities past those? The thought experiment is about infinite time, not all the time in our limited universe. A lot of things happen at infinity that break down as soon as you add a limit, but we’re not talking limits when we’re talking infinity.
I think the implications behind there being infinite time in the past are fun if you assume that the universe works like a stochastic state machine. It means that either every finite event that has happened and will happen has already happened an infinite number of times or the universe is infinitely large.
How is the infinite monkey theorum “misleading”. It’s got “infinite” in the name. If you’re applying constraints based on the size or age of the universe, you are fundamentally misunderstanding the thought experiment.
Infinite monkeys would produce everything in the time that it would take to type it out as fast as anyone can type, infinite times. There would also be infinite variations of slower versions, including an infinite number of versions where everything but the final period is written, but it never gets added (same with every other permutation of missing characters and extra ones added).
There would be infinite monkeys that only type one of Shakespeare’s plays or poems, and infinite monkeys that type some number greater than that, and even infinite monkeys that type out plays Shakespeare wanted to write but never got around to, plus infinite fan fictions about one or more of his plays.
Like infinite variations of plays where Juliette kills Hamlet, Ceasar puts on a miraculous defense and then divides Europe into the modern countries it’s made up of today, Romeo falls in love with King Lear, and Transformers save the Thundercats from the Teenaged Mutant Ninja Turtles who were brainwashed to think they were ancient normal samurai lizards. Some variations having all of that in the same play.
That’s the thing about infinity. If there’s any chance of something happening at all, it happens infinite times.
Even meta variants would all happen. Like if there’s any chance a group of monkeys typing randomly on typewriters could form a computer, there would be infinite variations of that computer in that infinite field of monkeys, including infinite ones that are trying to stimulate infinite monkeys making up a computer to verify that those monkeys make up a valid computer worth building and don’t have some bug where the temperature gets too high and melts some of the monkeys or the food delivery system isn’t fast enough to keep up and breaks down because monkeys get too tired to keep up with necessary timings.
BUT, even though all of these would exist in that infinite sea of monkeys, there would be far more monkeys just doing monkey things. So many more that you could spend your whole lifetime jumping to random locations within that sea of monkeys and never see any of the random organization popping out, despite an infinite number of monkeys and societies of monkeys dedicating their whole existence to making sure you, specifically, can find them (they might be too busy fighting off the infinite number of monkeys and societies of monkeys dedicating their lives to prevent you from ever finding non-noise in the sea of monkeys).
Yeah sure, they’ll probably also have typed all posts on Lemmy, including those that have not been posted yet.
If those monkeys existed there is an infinite chance you are right.
