Typing monkey would be unable to produce 'Hamlet' within the lifetime of the universe, study finds

This just in: scientists disprove validity of thought experiment; philosophers remain concerned that they've missed the point.

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 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).

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

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.

> typeof Infinity
'number'

Are they arguing it wasn't random though? I mean Shakespeare had to think through the plot and everything, not just scribble nonsense on a page

Everyone keeps forgetting that we're all just what monkeys evolved into...

the paper used the entire population (200 thousand) and would take some 10 ^ 10 ^ 7 heat deaths of the universe

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 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. 🙂

I feel like you might have interviewed for Google in the late 2000s

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.

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.

If I understand statistics correctly, it's actually a 50/50 chance.

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.

The whole point of the thought experiment is that you have infinite monkeys.

To quote Hamlet, Act 3, Scene 3, Line 87: “No”.

Stealing this to be annoying with

I prefer Romeo and Juliet, act 1 scene 1 line 41. Just because the exchange is so silly.

I'm still mad we are giving them typewriters instead of keyboards. Think of the arthritis! Ergonomics please!

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.

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.

Not with a typewriter, though.

But first he will accidentally the whole thing.

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.

They did not limit themselves to one monkey. From the article:

As well as a single monkey, they also did the calculations using the current global population of around 200,000 chimpanzees.

Yes, and add an Agile framework. Extreme Monkey typing.

Switch to AMD. More monkeys.

What caught me out recently was infinity minus infinity.

It does not equal zero. Instead it breaks your sorting algorithm.

infinite amount of monkeys could produce infinite amount of information, i dont see the point

Oh yeah? Name ONE ape that wrote Shakespeare. Go on I’ll wait

We have an infinite number of monkeys, one of them already wrote Hamlet.

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.

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.

And coffee breaks... or banana breaks... and unions!

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.

Of our sample size, 100% of “smart” (capable of symbolic language) monkey species have already written Hamlet.

42 monkeys?

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

Omg I just realized AI is the new monkeys.. that is disturbing