If you have infinite time, you don’t also need infinite monkeys.

It’s more a “yeah, but…” than a refutation.

A less than infinite number of simians have already done it once.

And how likely is it that it’ll be done again identically by a finite set of simians?

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.

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.

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.

The idea is that given an infinite truly random output of text by the nature of infinity the text of Shakespeare will be outputted in its entirety eventually

Only for a certain kind of randomness. For example, it’s possible to construct a random process that at each step emits a uniformly distributed character, but which also includes a filter that blocks the emission of the string “Falstaff” if it occurs. Such a process cannot ever produce the complete works of Shakespeare, since the complete works include that string, though it will still contain (for example) every lost work of Aristotle, as well as an infinite number of false and corrupted versions of those works.

But yeah, an unconstrained uniform-random-distributed countably infinite sequence of printable English characters and whitespace cannot be proven to not contain the complete works of Shakespeare, or any other finite sequence. I believe it’s also impossible to exclude any countably infinite sequence, but I might be wrong on that part, since my mathematics education happened a very long time ago.

You know it? That’s nice. A lot of people think they know a lot of things that aren’t really true.

Now prove it.

Which is not what the common saying said.

So the researchers didn’t refute the assumption “given an infinite amount of time,” and instead chose to address the long finite-time case, which is fundamentally different.

And royals, like race horses, are not bred for intelligence.

Yeah, it only matters for old-school animal breeders and royal genealogists. It’s a pre-scientific notion.

That’s the real goal.

Just what we need, more copaganda.