A new study reveals it would take far longer than the lifespan of our universe for a typing monkey to randomly produce Shakespeare. So, while the Infinite Monkey Theorem is true, it is also somewhat misleading.
The question that everyone has been dying to know has been answered. Finally! What will scientists study next?
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).
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.
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
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).