Typing monkey would be unable to produce 'Hamlet' within the lifetime of the universe, study finds
2 years ago by VantaBrandon to c/technology
The question that everyone has been dying to know has been answered. Finally! What will scientists study next?
Heat death would be my assumption, so between about 10^100 and 10^106 years
That's not bold, we've known how long the universe will last for decades now.
When multiple fields of science all agree, yeah they know what they're talking about.
I just don't get these anti-science types...
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.
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.
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.
I knew this would be a waste of time! *loads gun
I can't remember the author or title, but that was the idea for a story I once read.
God sends an angel and the monkeys to do the job. They get close, but when the angel is doing the final read through he sees "...to be, or not to beee, Damn the 'E' key is sticking. " And they have to start over
So, while the Infinite Monkey Theorem is true, it is also somewhat misleading.
Is it though? The Monkey Theorem should make it understandable how long infinity really is. That the lifetime of the universe is not long enough is nothing unexpected IMHO, infinity is much (infinitely) longer. And that's what the theorem is about, isn't it?!
Except the lifetime of the universe is quite small when compared to infinity, so it doesn't really convey how large infinity is because it's so much more.
They don't convey the same information.
Infinity isn't really an amount of something.
Damn, you just SLAMMED me.
Yes I know, but I was just trying to put into the perspective the person I was replying to.
The thought experiment suggests that over a long enough period of time, every possible combination of letters would be typed out on a keyboard, including Hamlet.
They are not arguing about randomness, as it is inherent to the thought experiment. Randomness is necessary for the experiment to occur.
They are arguing that the universe would be dead before the time criteria is met. It is a bitter and sarcastic conclusion to the thought experiment, and is supposed to be funny.
In conversation, it would be delivered like this:
"You know, over a long enough period of time, monkeys smashing typewriters randomly would eventually produce Hamlet"
"The universe isn't going to last that long."
Nobody asked but I had to share this
It's important to me that everyone understands the joke, even if that understanding robs them of the joy of it. "Explaining a joke is like dissecting a frog. It kills it".
But it's important because I suffered a lot of being left out as a kid. Others found how good it felt to be exclusive, and shoulder me out of things, or refuse to explain things, or whatever it was that made me the outcast. I could tell from their faces that they love the way it felt when they did that to me. But it hurt me a lot.
I don't want there to be any exclusivity anymore. Nobody deserves that pain. I want everyone to understand the joke, even if that prevents them from ever laughing at it.
Yeah, that’s why we need at least... two of them.
the paper used the entire population (200 thousand) and would take some 10 ^ 10 ^ 7 heat deaths of the universe
from the wiki article
https://en.wikipedia.org/...
If there were as many monkeys as there are atoms in the observable universe typing extremely fast for trillions of times the life of the universe, the probability of the monkeys replicating even a single page of Shakespeare is unfathomably small.
So you’re telling me… there’s a chance!
Sorry, I’m sort of lampooning comments like the one above and below you where people just can’t resist focusing on the possibility, no matter how ridiculously remote it seems. For myself, there’s a point of “functionally zero odds” that I’m willing to accept and move on with my life.
so you're saying there's a chance...
Irrelevant. The heat death of the universe is a constraint unrelated to the premise of the original problem.
I don't think it's a constraint, it's more like a measuring stick to try to show how ridiculously long that time is
It's really not that long, if we can't get monkeys to write Shakespeare.
enough to cut a few zeros of a number with 10 million of them
How is this a study? It's just basic probability on a bogo sort style algorithm.
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.
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. 🙂
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.
it is also somewhat misleading
...what? No it isn't. Restricting the premise from infinite to any finite amount of time completely negates it. That doesn't prove it's "misleading", it proves anyone that thinks it does has no idea what they're talking about.
If I understand statistics correctly, it's actually a 50/50 chance.
Ignoring the obvious flaw of throwing out the importance of infinity here, they would be exceedingly unlikely but technically not unable. A random occurrence is just as likely to happen on try number 1 as it is on try number 10 billion. It doesn't become any more or less likely as iterations occur. This is an all too common failure of understanding how probabilities work.
The results reveal that it is possible (around a 5% chance) for a single chimp to type the word "bananas" in its own lifetime.
That sounds a little low to me. B and N are right next to each other, so I'd expect them to mash left and right among similar keys a lot of the time. Then again, I think we're expecting some randomness here, not an actual chimp at a typewriter, but that's probably more likely to reproduce longer works than an actual chimp.
I get annoyed when websites say something like, ´Using a password of this strength will take a a hacker one million years to brute force.´
No, it’ll take a million years to try every combination and permutation of allowed characters. Chances are your password will be tried much sooner than that.
When they say such things, the are probably talking about the expected value, where those chances are taken into account, just like the number calculated in this article.
And apparently monkey is only the 6th password attempt to try:
https://en.m.wikipedia.org/w/index.php?title=List_of_the_most_common_passwords&action=edit§ion=3
Lifetime of the universe is infinitely less than infinite time. So they solved for the wrong problem. Of course it may take longer than the life of the universe, or it may happen in a year. That's the whole point of the concepts of infinity and true randomness. Once you put a limit on time or a restriction on randomness, then the thought experiment is broken. You've totally changed the equation.
It was the best of times, it was the blurst of times? You stupid monkey!
The whole point of the thought experiment is that you have infinite monkeys.
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.
The statement isn't about "A" monkey. It's about an infinite amount of monkeys.
For what it's worth, it seems like it's this "journalist" trying to make a sensational headline
The researchers themselves very clearly just tried to see if it could happen in our reality
"We decided to look at the probability of a given string of letters being typed by a finite number of monkeys within a finite time period consistent with estimates for the lifespan of our universe,"
Hypothesis: every science journalist should be placed in front of a bitch-slapping machine for the rest of their career. Every time they think about writing an article, they get bitch slapped. This will greatly improve the quality of science journalism.
The other part of it is there's not only one monkey who does Hamlet correct on the first attempt, there's two, three four, guess what - an infinite amount of them.
And another infinity that get it right after 5 minutes
Another infinity that take exactly 10 years 3 months 2 days 3 hours 4 minutes and 17 seconds
And another infinity that takes one second less than the life of the universe
And another infinity that takes a googleplex of the lifetime of the universe to complete
that's the point of the thought experiment
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”.
To quote Hamlet, Act 3, Scene 3, Line 87: “No”.
Stealing this to be annoying with
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'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 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.
But.. we already did it?
Not with a typewriter, though.
I would place money on some enthusiast somewhere having typed up Hamlet on a typewriter just for kicks. Surely in the hundreds of years of overlap between humanity, Hamlet, and typewriters, it's happened once. I'd be more concerned with typos.
But first he will accidentally the whole thing.
Strong entry for an Ig Nobel Prize if nothing else.
The whole study is trash. A chimpanzee is not a monkey.
Stupid monkey
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.
So the secret to this thought experiment is to understand that infinite is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is...
The lifespan of the universe from big bang to heat death (the longest scenario) is a blink of an eye to eternity. The breadth and size of the universe -- not just what we can see, but how big it is with all the inflation bits, even as its expanding faster than the speed of light -- just a mote in a sunbeam compared to infinity.
Infinity itself looks flat and uninteresting. Looking up into the night sky is looking into infinity – distance is incomprehensible and therefore meaningless. And thus we don't imagine just how vast and literally impossible infinity is.
With an infinite number of monkeys, not only will you get one that will write out a Hamlet script perfectly the first time, formatted exactly as you need it, but you'll have an infinite number of them. Yes, the percentage of the total will be very small (though not infinitesimally so), and even if you do a partial search you're going to get a lot of false hits. But 0.000001% of ∞ is still ∞. ∞ / [Graham's Number] = ∞
It's a lot of monkeys.
Now, because the monkeys and typewriters and Shakespeare thought experiment isn't super useful unless you're dealing with angels and devils (they get to play with infinities. The real world is all normal numbers) the model has been paired down in Dawkin's Weasel ( on Wikipedia ) and Weasel Programs which demonstrate how evolution (specifically biological evolution) isn't random rather has random features, but natural selection is informed by, well, selection. Specifically survivability in a harsh environment. When slow rabbits fail to breed, the rabbits will mutate to be faster over generations.
The original thought experiment had to do with playing around with infinity, which is a whole field of mathematics with a lot of crossover. It raises questions like whether we can assume any fixed-length sequence of digits can be found somewhere in the mantissa of a given irrational number (say, π).
How about 4 monkeys in parallel?
What about monkey AI to get ahead using lower paid monkeys?
But what if we had infinite monkeys 🤔
We have an infinite number of monkeys, one of them already wrote Hamlet.
Oh yeah? Name ONE ape that wrote Shakespeare. Go on I’ll wait
Let's use our braincells to fix real problems first. Like pants that don't stretch.
If a tree folds in the forest and there's no one there to hear it does it make a sound?
For this experiment scientists recruited Gilbert, no one really pays much attention to him, and it's assumed the universe won't either.
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.
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*1
i.e. 52 × 51 × 50 × ... × 3 × 2 × 1
Markdown syntax screwed it up.
Oh I didn't notice it did that. thanks for fixing it.
Yeah that's the part that isn't easy.
I feel like there has to be more to this problem than pure probability. We ought to consider practical nuances like the tendency to randomly mash keys that are closer together rather than assume a uniform distribution.
Who are you, who is so wise in the ways of science?
Doesn't matter in the real infinite monkeys thought experiment. The chance of an infinite number of monkeys at an infinite number of typewriters producing Shakespeare is 100%. That's how infinity works.
This article fundamentally misunderstands the entire thought experiment by using finite monkeys. With infinite monkeys, we'd have the script as quickly as it is physically possible to type the script.
Semi related:
Here's a link to the Library of Babel website
Abiogenisis in shambles again
Of our sample size, 100% of “smart” (capable of symbolic language) monkey species have already written Hamlet.
This is a false flag study to undermine public support for mathematics research!
I wonder if it would take more or less time with auto-complete.
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.
Their assumptions must be wrong. They do not account for the most basic principle of the universe, "the show must go on."
This must be a very important question to whoever keeps funding these studies.
Well it isn't 6.
From Wikipedia:
In 2002, lecturers and students from the University of Plymouth MediaLab Arts course used a £2,000 grant from the Arts Council to study the literary output of real monkeys. They left a computer keyboard in the enclosure of six Celebes crested macaques in Paignton Zoo in Devon, England from May 1 to June 22, with a radio link to broadcast the results on a website. Not only did the monkeys produce nothing but five total pages largely consisting of the letter "S",the lead male began striking the keyboard with a stone, and other monkeys followed by urinating and defecating on the machine
Mike Phillips, director of the university's Institute of Digital Arts and Technology (i-DAT), said that the artist-funded project was primarily performance art, and they had learned "an awful lot" from it. He concluded that monkeys "are not random generators. They're more complex than that
Infinity sorts it out for you, Karl
They are, however, exceptionally adept at political speechwriting.
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=130,000
Wait .......is this why AI exists? So we can type Hamlet in the face of monkey failures?
Dude. Just use a printer.
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The 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!
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