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

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!

It was the best of times, it was the blurst of times??

You stupid monkey!

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?!

This is clownery, humanity is infinite monkeys, and we wrote Hamlet ages ago.

Yeah, that’s why we need at least... two of them.

How is this a study? It's just basic probability on a bogo sort style algorithm.

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 510⁶ 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.

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.

There's still a chance that a monkey will type it on the first attempt. It's just very small.

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.

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.

But we aren't talking about one monkey. We are talking about infinite monkeys.

Infinity is already a loaded concept in our universe.

OK, what about 2 monkeys?

The statement isn't about "A" monkey. It's about an infinite amount of monkeys.

It was the best of times, it was the blurst of times? You stupid monkey!

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”.

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!

But.. we already did it?

They forgot the lifespan of the monkey, those thought experimenters.

The author is so stupid, the monkey will of old age long before the universe ends.

Strong entry for an Ig Nobel Prize if nothing else.

Use infinite monkeys.

That's because they only considered one monkey.

You need a thousand monkeys working at a thousand typewriters.

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.

How about 4 monkeys in parallel?

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.

But what if we had infinite monkeys 🤔

An ape could though.

Let's use our braincells to fix real problems first. Like pants that don't stretch.

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.

This sort of study shows you more how mathematicians think than how science or philosophy works.

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.

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.

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.

What if it's a smart monkey?

This is a false flag study to undermine public support for mathematics research!

Semi related:
Here's a link to the Library of Babel website

Really, it just takes an infinite amount of monkeys one time.

Abiogenisis in shambles again

Fuuuuck there goes my plan to get this monkey to write Hamlet within the lifetime of the universe...

I wonder if it would take more or less time with auto-complete.

Are spelling and punctuation expected to be accurate?

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."

Seems to not understand the thought experiment which is a way to contemplate infinity.

They are, however, exceptionally adept at political speechwriting.

Infinity sorts it out for you, Karl

Alright then. 2 monkeys... 3? 4? The answer has to be a number lol.

This must be a very important question to whoever keeps funding these studies.

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

Duh.