this post was submitted on 01 Nov 2024
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Wasn't the saying an infinite number of monkeys on an infinite number of typewriters? If so then they'd write Hamlet and indeed every other book written or ever will be written in however long it would conceivably take to type them out if you were copying them.
I don't really know how this myth? paradox is supposed to work? I know infinity isn't a number but a concept and in theory I understand what it's trying to say, but if I have an infinite amount of scrap yards and infinite amount of tornadoes, they can go on forever, but they'll never assemble a Boing 747.
An infinite number of monkeys typing randomly on an infinite number of typewriters, so long as the writing is truly random, will eventually write every novel. Once you factor in the infinite number of monkeys, every novel in existence will not only be written, it will be written an infinite number of times.
It's like saying if you had a random number generator and gave it an infinite amount of time generating 16 numbers at a time, it would eventually generate every bank card number ever an infinite number of times. Give that task to an infinite number of random number generators and they will generate every bank card number an infinite number of times instantaneously.
Come to think of it, if the tornado throws around junk completely randomly, and provided there's enough material in every junkyard to assemble a plane, the tornado will eventually assemble it. That's the power of infinity and randomness.
You don't need an infinite number of monkeys to ensure that. The cardinality of an infinite collection of 2-tuples (monkey, char) is the same as the cardinality of an infinite sequence of characters, just as the cardinality of the rational numbers is the same as the cardinality of the integers.
And in a countably infinite sequence of uniformly random characters, there is no assurance that any particular finite sequence will occur only a finite number of times.
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