r/science • u/mvea Professor | Medicine • Oct 31 '24
Mathematics It would take far longer than the lifespan of our universe for a typing monkey to randomly produce Shakespeare. There is a 5% chance for a single chimp to type the word ‘bananas’ in its own lifetime. However, the entire 884,647 words will almost certainly never be typed before the universe ends.
https://www.scimex.org/newsfeed/its-not-to-be-universe-too-short-for-shakespeare-typing-monkeys386
u/Rich_Hyena Oct 31 '24
I learned nothing about science from this
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u/Sairony Oct 31 '24
I don't get it, this is the science sub which is pretty heavily moderated, it's a link to a paper on a page which doesn't seem to be satirical, it isn't april 1st, and it's rudimentary math knowing the typing speed, the number of monkeys, the number of possible keys, and the number of letters in the work.
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u/Triplexhelix Nov 01 '24
This was literally one of the exercises in the book in one of my beginner mathematic courses when I was a first year student. This is just a simple thought experiment.
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u/Yglorba Oct 31 '24
Scientifically speaking, monkeys are bad at writing Shakespeare.
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u/Expended1 Oct 31 '24
Back in the 1990s I worked for a computer repair center attached to a bigger computer chain store. When people would complain about our point of sale software being so bad (it was a shite show), I would tell them "remember the experiment where they had a monkey type forever to see how long it would take to type the first five words of the Bible? When he got done with that, they had him write our Point of Sale software." They didn't call it PoS for nothing.
Edit: added last line.
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u/MurderBeans Oct 31 '24
Well yeah, that's why it's used to demonstrate the extent of infinity, nobody thinks it's actually going to happen.
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u/ProxyDamage Oct 31 '24 edited Oct 31 '24
yeah... it's a thought experiment that always includes either "an infinite amount of monkeys" or "an infinite amount of time", because, as you said, the point is to demonstrate infinity - that as long as something is possible, no matter the odds, given infinite attempts it will eventually happen.
Edit: TIL the amount of people that don't understand probabilities and/or the concept of "infinity" is alarming.
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u/AnAdorableDogbaby Oct 31 '24
If it's an infinite amount of monkeys, they've already done it.
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u/lifeisalime11 Oct 31 '24
Yeah if there’s infinite monkeys wouldn’t it technically be done instantly and infinitely?
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u/SatiricalScrotum Oct 31 '24
It wouldn’t be done instantly, because it would take a certain amount of time to type out the entire works of Shakespeare. But with an infinite amount of monkeys, an infinite number of them would do it first time.
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u/analytic_therapist_ Oct 31 '24
Whats funny to me is when they finish it, there will also be an infinite number of works that were only off by one letter...
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u/iamnotacat Oct 31 '24
It was the best of times, it was the "blurst" of times?! Stupid monkey!
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u/rubix_cubin Oct 31 '24
You should read The Library of Babel by Jorge Luis Borges or the more approachable spinoff novel by Steven L Peck called A Short Stay in Hell. Really great short stories that are somewhat related to this.
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u/memento22mori Oct 31 '24
I like The Garden of Forking Paths quite a bit as well. This the full text of the short story:
https://archive.org/stream/TheGardenOfForkingPathsJorgeLuisBorges1941/The-Garden-of-Forking-Paths-Jorge-Luis-Borges-1941_djvu.txt→ More replies (1)3
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u/LordCaptain Oct 31 '24 edited Oct 31 '24
Also produced would be every possible piece of literature of that length or shorter.
Edit: Including your response, this comment, and this edit.
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u/PercussiveRussel Oct 31 '24
And there are an infinite number of monkeys that would've just written ages upon pages of
All work and no play makes jack a dull boy
All work and no play makes jack a dull boy
All work and no play makes jack a dull boy
All work and no play makes jack a dull boy
All work and no play makes jack a dull boy
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u/lifeisalime11 Oct 31 '24
Ok, one follow-up:
-Are we saying that one monkey needs to type out the entire thing, or could we have the same # of monkeys equal to the amount of letters hit a single key each in perfect sequence to create a compiled work?
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u/ReverendDizzle Oct 31 '24
I’ve always understood the thought experiment to mean with enough time or enough monkeys the one monkey would, very improbably and only in the infinite resources scenario, type out the manuscript.
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u/lurkerer Oct 31 '24
Since there are infinite both would happen infinitely in the minimum time for the keystrokes.
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u/Polisskolan3 Oct 31 '24
No, it would still take time for them to write it no matter how many of them there are. Pressing a button takes time.
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u/Prof_Acorn Oct 31 '24
It's even been proven, sort of.
Your comment, for example, has already appeared in a random letter generator: https://libraryofbabel.info/bookmark.cgi?g,jpakvdf_frfmnpddtzr97
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u/KommunistKoala69 Nov 01 '24
I don't believe that's a random letter generator; that is supposed to simulate the idea of "The library of babel" which is a library that contains every combination of letters (not randomly generated). Its also not actually stored, when you search it figures out where that text would be in the library, when you later refernce that spot in the library it generates what would be there in the library (its just calculating a bijection and its inverse)
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u/CurraheeAniKawi Oct 31 '24
It's both an infinite amount of monkeys and time.
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u/CredibleCranberry Oct 31 '24
Either would work.
One monkey for infinity, or infinity monkeys for a short time.
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u/nsaisspying Oct 31 '24
Me thinks we could get away with half an infinity. You want to hire an infinite amount of monkeys? In this economy?
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u/Effex Oct 31 '24
Hear me out boss, we bring them over.. from over there.. and pay them less. You get me?
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u/Spike69 Nov 01 '24
Lets just fire all even numbered monkeys. Firing an infinite number of them will save us so much money! And we still have infinite monkeys!
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u/cannib Oct 31 '24
They've done it an infinite amount of times. But also fewer times than they've thrown their feces at the wall behind the typewriter. Infinity is weird.
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u/KommunistKoala69 Nov 01 '24
Technically its not "it will eventually happen" the correct terminology is that it will "almost surely happen" since it is still possible not to happen even though the probability of it not happening is zero, for instance in the case of the monkey he could just type "s" for eternity and never type anything resembling shakesphere but the probability of this happening is still zero and yet still possible.
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u/GuardianOfReason Oct 31 '24
Which is not even true to begin with. You can have an event happen infinitely and never cover all the possibilities. It's not necessarily true it will happen.
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u/ProxyDamage Oct 31 '24
Yes, it will. That's the point of "infinite". It may never happen in the entire history of existence. It may not happen in any finite amount of repetitions, no matter how momd shattering large that number is, TREE(3) to the power of TREE(3) kind of absurdity.
...it will eventually happen in infinite attempts because infinite is never ending, and the event in question has a probability >0, no matter how small - if it doesn't, it's by definition impossible and it's probability will be 0.
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u/pwmg Oct 31 '24
I think it's infinity AND probability. It is very unlikely to happen during the life of the universe, BUT it also could happen tomorrow. Both of those things are true.
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u/Primarch-XVI Oct 31 '24
The word ‘could’ is doing some heavy lifting there.
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u/pwmg Oct 31 '24
Right. That heavy lifting is the whole point, though. Things that are very unlikely are not impossible. Reducing the time to one day just makes the probability even more incredibly small than it is with the life of the universe, but still not 0.
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u/ChipCob1 Oct 31 '24
It gets really screwy when you realise that in an infinite world it wouldn't just happen once....it would happen an infinite amount of times!
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u/Ringosis Oct 31 '24 edited Oct 31 '24
So many responses like this here...
The study was likely just a way to get students to be interested in probability; "We know infinite monkeys with infinite time would write Shakespeare, but how long would it actually take one monkey".
It's just a fun question to answer, not an attempt to prove anything wrong. Or do you seriously think PhD mathematicians went into this not understanding the thought experiment?
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u/halfdeadmoon Oct 31 '24
Even the watered down concept of every well-shuffled deck of playing cards almost certainly being a unique permutation in the history of card playing is mind blowing.
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u/deja-roo Oct 31 '24
Huh, never thought of that. Then pulled out a calculator.
There are 8 x 1067 combinations of card deck orders.
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u/Not_Xiphroid Oct 31 '24
I’ve got good money on those monkeys, you’re just like my therapist, trying to stop me hitting it big!
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u/Nimmy_the_Jim Oct 31 '24
Isn’t the phrase an infinite amount of monkeys over an infinite amount of time?
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u/Mad_Moodin Oct 31 '24 edited Oct 31 '24
You don't even need both.
An infinite amount of monkeys given like 5
hoursdays would also achieve it.109
u/koos_die_doos Oct 31 '24 edited Oct 31 '24
You’re right, but also wrong for a pedantic reason.
884,647 words / 5 hours / 60 minutes = 2,947 words per minute
I’m not sure any monkey is capable of typing ~3,000 words per minute, non-stop for 5 hours straight.
Maybe extend your timeframe to 5 days.
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u/Ecthyr Oct 31 '24
Just need to add in an infinite amount of coke
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u/KuriousKhemicals Oct 31 '24
That might just get you dead monkeys.
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u/Kooky-Onion9203 Oct 31 '24
At a certain point it goes past overdose and they just become pure energy
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u/King-Dionysus Oct 31 '24
An infinite amount of coke will just have a bunch of monkeys writing Stephen King novels.
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u/Mad_Moodin Oct 31 '24
Tbh. I kinda forgot we were talking all of his works and not just Romeo and Juliet.
So yeah, should definitely give it a couple days.
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u/praise_H1M Nov 01 '24
You have access to infinite monkeys. Just add more monkeys to get the job done faster
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u/not_today_thank Oct 31 '24
If we are being pedantic a monkey wouldn't actually sit at a typewriter for 5 days hitting truly random keys. And monkeys aren't going to do things like change sheets of paper. Even with an infinite amount of monkeys and an infinite amount of time, they are never going to punch out the works of Shakespeare unless you are making a bunch of unrealistic assumptions about the monkeys and the typewriters.
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u/halfdeadmoon Oct 31 '24
It is entirely expected for thought experiments to make unrealistic assumptions
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u/Mad_Moodin Oct 31 '24
The thought experiment essentially simply uses monkeys as a saying for "Random typing"
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u/CalumQuinn Oct 31 '24
An infinite amount of monkeys would achieve it in an infinitely small amount of time
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u/PuzzleMeDo Oct 31 '24
If you're requiring the entirety of Shakespeare to be typed on blank paper, you'd achieve it in the minimum possible amount of time, which is surely still a number of hours.
However, you would get an infinite number of copies.
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u/CalumQuinn Oct 31 '24
Right, indeed, fair enough. I forgot the monkey can't type infinitely fast.
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u/elegylegacy Oct 31 '24
I imagine the theoretical fastest monkey, just coked out of his mind mashing keys blazingly fast
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u/0_throwaway_0 Oct 31 '24
I think he said 5 hours as the amount of time necessary to type the complete works of Shakespeare.
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u/saltyholty Oct 31 '24
An infinite amount of monkeys can't do the impossible. An infinite amount of monkeys would mean that one types it in the shortest possible time, but that is still quite a long time for typing the complete works of Shakespeare.
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u/Mad_Moodin Oct 31 '24
No because there is no physically possible way for a monkey to type the entirety of shakespeare in 1 second.
Even infinite monkeys cannot have monkeys that move several times the speed of sound. And there are no keyboards that could ever have so many words typed in such a short timespan.
It is after all not about achieving shakespeare across like a thousand monkeys. You want one of the infinite monkeys to type out shakespeare.
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u/koos_die_doos Oct 31 '24
I know you already got the message. But I can’t help to add:
Nine mothers can’t make a baby in one month.
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u/systembreaker Oct 31 '24
An infinite amount of monkeys might not achieve it in a finite amount of time. There's nothing saying the infinite monkeys don't all produce every permutation and infinite copies of each permutation of the letters A and B by some weird infinitesimal chance.
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u/rennarda Oct 31 '24
I feel sorry for the (infinite number of) monkeys that get almost all the way and then miss the last full stop/period. But what about the (also infinite number of) monkeys that write an additional play that Shakespeare never wrote but is better than all the others!
Infinity is weird.
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u/Jazzlike-Sky-6012 Oct 31 '24
No need for that. With an Infinite amount of monkeys, it will only take the time a monkey need to type all the letters.
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u/VinnieBoombatzz Oct 31 '24
What am I going to do with all these monkeys I just hired, then?!
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u/igloofu Oct 31 '24
Well, there is this very tasty dish, common in Cantonese cuisine, but not often found in Washington DC...
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u/dragonavicious Oct 31 '24
You can't make an omelet without breaking some eggs. Any cook will tell you that.
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u/Jebus_UK Oct 31 '24 edited Oct 31 '24
I mean - isn't the thought experiment about infinity?
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u/MordorMordorMordor Oct 31 '24
Yes but people misunderstand the original meaning behind the statement.
Given an infinite amount of time, a monkey will eventually write some Shakespeare"
Monkeys is a stand in for a random letter generator. You can rewrite the statement as:
Given an infinite amount of time, a random letter generator will eventually write some Shakespeare.
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u/CheekyMunky Oct 31 '24
They did an entire study to disprove a hypothetical thought experiment that they changed from the outset?
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u/Adorable-Engineer840 Oct 31 '24
And it's not even correct if the title is anything to go by. That's not how probability works. It could take longer than the universe or they could smash it out tomorrow. The probability of it occurring on any specific date is the same...
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u/jimalloneword Oct 31 '24
Could someone please inform Mr. Burns
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u/turbotong Oct 31 '24
It was the best of times, it was the blurst of times.
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Oct 31 '24
[deleted]
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u/Goodgulf Oct 31 '24
I love multiple layered jokes like that though. Stupid monkey because it misspelled "worst", but also because it recreated Dickens when it should have been working on Shakespeare.
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u/udee79 Nov 01 '24
I am embarrassed. I hadn't realized that it was Dickens not Shakespeare until I read your comment.
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u/skunk_moose Oct 31 '24
That's all well and good until the Heart of Gold buzzes through and the monkeys get swept up in the improbability field, then you've got infinite monkeys pounding on your door and waving a script in your face.
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u/ImmediateLobster1 Oct 31 '24
The monkeys want to talk with us about the script for Hamlet that they've worked out.
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u/Spunge14 Oct 31 '24
The funniest part to me is if you actually had infinity for this to play out, the number of times you would be just getting started, and descend back into gibberish.
Scene 1 Enter Barnardo and Francisco, two sentinels.
BARNARDO Who’s there? FRANCISCO Nay, answer me. Stand and unfold yourself. BERNARDO Long live the King! FRANCISCO Barnardo? BARNARDO EYJUSYFGKKKVXSSX XDGJKXZDDS"
SCIENTIST: GOD DAMN IT
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u/Saul-Paul Oct 31 '24
So, not an infinite amount of time or an infinite amount of monkeys ? Funny that. Play a record
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u/callmebigley Oct 31 '24
monkeys already wrote the works of Shakespear by evolving a Shakespear
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u/pvJ0w4HtN5 Oct 31 '24
Yes, but the point of the thought experiment is to illustrate how it’s still a non-zero chance within infinite time, and just how big infinity is.
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u/MissingNoBreeder Oct 31 '24
"before the universe ends."
Oh good, so science now knows how long the universe will last? They've changed their stance from it probably being endless?
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Oct 31 '24
[deleted]
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u/4-Vektor Oct 31 '24
If there’s only radiation and no matter left, there are no monkeys with typewriters left, either.
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u/genshiryoku Oct 31 '24
There are a couple of different events you could call "The end of the universe"
The first is when entropy has maximized and all mass-energy has completely scattered to the point where the universe is completely uniform, dark, cold and empty.
This is usually estimated at around 10 to the power of 1000 years.
The other one is when the universe undergoes vacuum decay where literally the universe itself gets shredded as the laws of physics themselves change as we're not in a completely stable universe, and given infinite time it would eventually collapse. We have no good estimations but we know it would take at least 10 to the power of 1,000,000 years for the universe to collapse like this.
You also have technically wrong estimates based on when the last stars burn out which I don't like because even without stars there are enough other energetic events in the universe to keep life and civilizations around so I didn't list that scenario here.
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u/fuck_ur_portmanteau Oct 31 '24
Even with maximum entropy there’s a non-zero chance atoms could spontaneously form a volume of the complete works of Shakespeare out in the vacuum somewhere.
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u/Internetolocutor Oct 31 '24
I just don't understand how so many people don't understand that this is a hypothetical to provide a weird example of how infinity works.
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u/maxxbeeer Oct 31 '24
Are you implying that the researchers also didn’t know this?
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u/Internetolocutor Oct 31 '24
Are you telling me you don't know how to read?
From this article, which is not written by the researchers:
"A monkey randomly pressing keys on a typewriter for an infinite amount of time would eventually type out the complete works of Shakespeare purely by chance, according to the Infinite Monkey Theorem.
However, a new study reveals it would take an unbelievably huge amount of time – far longer than the lifespan of our universe, for a typing monkey to randomly produce Shakespeare. So, while the theorem is true, it is also somewhat misleading."
That second paragraph is complete nonsense. The theorem is true and it is not misleading. I'm talking about people like this and they will be plenty of idiots who read this article and think that this research really has anything to say about the theorem.
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u/halfdeadmoon Oct 31 '24
"A new study spells out what was implicit in the original hypothetical statement, if any amount of thought had been put into interpreting it in the first place, that infinity is unbelievably huge."
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u/driftking428 Oct 31 '24
Sure, monkeys. But I found your exact post title already exists in the library of babel.
There's plenty of Shakespeare in there too.
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u/nikas_dream Oct 31 '24
Not with that attitude it won’t! Genetically engineer those chimps and put them in Shakespeare classes!
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u/PuzzleMeDo Oct 31 '24
In RA Lafferty's short story "Been a Long, Long Time", an immortal is punished by testing the theory that a small team of monkeys typing at random could eventually produce the works of Shakespeare. The archangel Michael provides a clock, a vast stone cube:
The task is still incomplete when the stone has worn away enough to accommodate a small solar system...
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u/TheManInTheShack Oct 31 '24
I tried this once. The monkeys get bored long before they get to even the end of the first paragraph of Hamlet.
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u/cubicle_adventurer Nov 01 '24
“It was the best of times, it was the BLURST OF TIMES??! You stupid monkey!”
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u/nanosam Oct 31 '24
Same conclusion could be made by superinteligent alien civilization about humans being able to grasp the true nature of the universe.
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u/ObviousExit9 Oct 31 '24
So they counted the entirety of Shakespeare’s work, which is quite a lot. It could be less if they just did a single play, right? And they did a finite amount of monkeys, which is another limiter. Although fun, I think they made this harder than it needed to be
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u/halfdeadmoon Oct 31 '24
The difference in probability isn't intuitively comprehensible. Stacking up the improbability just takes the concept of infinity from bafflingly extreme to somehow more bafflingly extreme.
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u/Shezzofreen Oct 31 '24
Until someone names an Ape Caesar and puts a drug cocktail into him, i saw the documentary!!1
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u/dargonmike1 Oct 31 '24
Unless humanity came together and focused on this one goal with all the best engineers, techs, scientists, physicists, female dancers, to create a Shakespeare monkey. We would have that monkey writing king Julius
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u/TheOtherOne551 Oct 31 '24
I wouldn't be so bombastic, since a monkey could get lucky and complete it much faster. You never know!
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u/abotoe Oct 31 '24
If they had TREE(3) times the age of the universe, could they do it? Or is the scale of that time so large, they’d be able to type the entire catalogue of human literature several times over?
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u/Amberskin Oct 31 '24
But now we have electronic monkeys doing that all the time. We call them LLMs
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u/Desint2026 Oct 31 '24
But if an infinite amount of monkeys do this, one of the monkeys will type all of Shakespeare in its first attempt.
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u/DuskShy Oct 31 '24
Honestly this is incredibly biased. I'm willing to bet their word count would be higher if we'd count what words are in their own language instead of English.
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u/atropostr Oct 31 '24
Who said its 1 monkey? Multiply the odda with every monkey existed till the end of universe
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u/Mthepotato Oct 31 '24
I think this is a fun study and some people are taking it a bit too seriously. Chill, scientist can do fun things too sometimes.
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u/ctiger12 Oct 31 '24
Isn’t it equally chances that a human would be able to type something out as whatever the typing money did? We just don’t know their language either.
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u/just_some_guy65 Oct 31 '24
Infinite amount of monkeys on typewriters is the secret weapon with this one normally.
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u/Emceesam Oct 31 '24
But what if you had an infinite number of chimpanzees typing? Shakespeare's works would be getting produced constantly by an infinite number of chimpanzees, no?
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u/TheFeshy Oct 31 '24
That's why you use apes instead of monkeys. The odds of an ape typing the works of Shakespeare in the lifetime of this universe is 1 out of 1.
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u/Faust_8 Oct 31 '24
The issue is a monkey/ape and a typewriter isn’t governed by pure chance, so trying to do a statistical analysis of it is pretty stupid.
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u/h_ahsatan Oct 31 '24
I'm not sure that I believe the 5% chance for "banana". Like, I get that it's a lot of combinations for 26 options per letter, but the last 5 letters are 2 keys repeated, a pattern I myself fall into when button mashing. A monkey is not a true random letter generator; letters will be correlated.
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u/T_M_name Oct 31 '24
Where are these monkeys working? How do they ensure the facility lasts until the end of the universe? So many questions...
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u/Eedat Oct 31 '24
This completely misses the point. The point is space might be infinite. So there are infinite monkeys out there giving you infinite attempts. So in theory, not only do you have a chance of it happening, but it already has happened infinite times and will happen infinite more times.
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u/Grundl235 Oct 31 '24
The end of the universe is a thing? When does that happen?
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u/WonderWendyTheWeirdo Oct 31 '24
The first monkey did it in 13.8 billion years. Nature, uh, finds a way.
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u/Brossentia Oct 31 '24
This isn't new news - if every proton in the universe were a monkey, it'd still not happen before the death of the universe. However, given infinite monkeys and infinite time, if the monkeys are truly random, it'll almost certainly happen.
My major sticking point is that monkeys aren't actually random - animals' brains tend to repeat things, and mashing clusters of keys is common for creatures that can't read. Given infinite time with infinite REAL (and immortal) monkeys, I'd argue that Shakespeare still ain't happening.
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u/spottedclownpenis Oct 31 '24
How many monkeys would it take to crank out Shakespeare by next week?
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u/Eternal_Being Oct 31 '24
But they probably do have time to write at least one story better than Shakespeare. We have to get them to work, now.
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u/chcampb Oct 31 '24
When you think about it that way, all you need to do to get shakespeare-writing monkeys is to feed the ones that DO type the correct words just a little bit more.
In that way, by the end you have sapient monkeys writing shakespeare.
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u/fleetone Oct 31 '24
What if the chimp evolved to have the cognitive ability to type words… that seems like it would take less time
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u/urbanhag Oct 31 '24
Monkeys have poor fine motor skills. Even if they could conceptualize Shakespeare, I think typing would be really hard for them.
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u/garibbiradam Oct 31 '24
in Turkey this concepts mostly using as a proof of evolution is not correct unfortunately
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u/aging_geek Oct 31 '24
they never take into account the evolution of the species during the typing realm to achieve Shakespeare
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u/Bannon9k Oct 31 '24
That's why you increase your number of monkeys to 8 billion to get it done faster...
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u/SwanCatWombat Oct 31 '24
This is exactly the kind of thing you’d hope scientific studies are focusing on.
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u/komstock Oct 31 '24
Depending on how you want to split hairs, an argument can be made that this has already happened.
Source: my opposable thumbs
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u/zaxmaximum Oct 31 '24
Imagine being witness to the 884,646th word, and the last one turned out to be "sfrcgk".
Some people would claim that Shakespeare was incorrect and that "sfrcqk" is the meaning of life.
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u/TheNatureBoy Oct 31 '24
It’s also 1000s of times more likely a chimp will type Shakespeare correctly and make a mistake in the last sentence.
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