The problem here is the implied entropic outcomes of each system.
If the monkeys were replaced with true-random number generators, then you’d eventually get shakespear. But they aren’t RNG engines, and they aren’t quantumly random.
Instead, the monkeys have a large-ish but very finite number of logical branches that they can take in their decision-making processes, with slight variations within a fixed genetic scope. They will slam away at the typewriters in a very specific monkey kind of way.
At the end of the thought experiment, you will end up with an infinite amount of monkey-gibberish and a slightly smaller infinite amount of soiled or destroyed typewriters.
If the monkeys’ probability distribution function can be transformed to a uniform distribution by a continuous function, the outcomes are equivalent enough for this exercise. (There are probably some discontinous functions that’d also work). So, unless there’s some genetic weirdness in monkeys that prevents their ever hitting certain keys, they’re adequate RNG engines. But at that point, you’re really tweaking the assumptions based on how realistically you think monkeys are portrayed in the thought experiment.
And I don’t believe “quantumly random” is a necessary condition here.
