Stinky Shakespeare – Infinite Monkeys

Imagine a room. Now imagine it with a bunch of monkeys. Now imagine it with infinite monkeys. Now imagine each of those monkeys banging randomly on a keyboard. 

And so it goes- if infinite monkeys are given time, a fraction of them will type out Shakespeare’s complete works, cover to cover, including copyright. 


Or, you can give a few monkeys infinite amount of time to type it out, if you don’t like monkey BO. 

Technically, though, a fraction of infinity is infinity, so you will actually have infinite copies of every book ever. 

Yes, it’s true – neither is possible. Firstly, there are finite number of monkeys in the universe, and secondly, monkeys don’t exist forever. 

But theoretically, mathematically, it’s true. Infinite is the key word here. The probability of monkeys randomly typing anything comprehensible is super slim, but given infinite amount of time or infinite monkeys, it will happen. 

(Note: the original Infinite Monkey Theorem states that one monkey given infinite time will produce Hamlet. But the same logic applies to any of the above cases. )

Now here’s where it gets cool. Within the infinite pages of blarg, gargulmanthon, and eovhelwwbv, there are (infinite) copies of

  • Shakespeare’s Hamlet
  • Hamlet with 1 typo
  • Hamlet with 2 typos
  • Hamlet missing the last sentence
  • Hamlet where the main character is named Mary Poppins
  • Hamlet where he falls in love with Mewtwo and is the father of Isaac Newton who created the Internet 

We can go even further with this. Somewhere in the mess, there is also

  • How the universe was created
  • When, where, and how you will die
  • The answer to every single mathematical and scientific inquiry and paradox 

And so on. Isn’t that amazing?? 

Of course, the problem would be that for every infinite amount of correct information, there is “more” infinite incorrect information. (To the human mind)

Here are some things the monkeys would not type, even given infinite amount of time:

  • The exact digits of pi for infinity
  • Hamlet, repeated for infinity, back to back
  • The letter P repeated infinitely
  • Anything else that requires infinite precision with no interruption 

See, the probability of a string of characters being typed gets lower and lower as the string gets longer. It’s possible that monkeys will type the first 10000000 digits of pi, or more, but never infinity – that would mean that at some point the monkey starts typing 3.1415926… and never stops for the rest of its infinite lifetime. The probability of that happening is precisely zero

So, as you can see, even with infinite monkeys typing infinitely, pi will never be found D: 

Therefore, the moral of the story is that with brute force and brute numbers, some things will never be solved. If we can’t find pi with infinite monkeys and infinite time, how will we find pi? That’s why us, humans, have intelligence. Each of us is smarter than those monkeys. To write something we don’t bang random letters endlessly on a keyboard, we instead plan and shape our words before writing them, using common sense and calculation. 

The chance of monkeys writing the first 20 letters of Hamlet, ignoring punctuation, spacing, and capitalization, is 1/19,928,148,895,209,409,152,340,197,376. Even if every proton in the observable universe was a monkey with a keyboard, typing from the Big Bang until the end of the universe, we would need 10^360641 universes of atomic monkeys to even have a one in a trillion chance of Hamlet being written. 

In contrast, one man wrote it within 3 years. And many people have copied it in a shorter time with the same typewriters that would be used by infinite monkeys. 

In conclusion: Don’t underestimate yourselves, people! Remember, we are smarter than monkeys – even infinite monkeys. 😀


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