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Infinite monkeys on infinite typewriters can produce a work of Shakespeare.

https://en.wikipedia.org/wiki/Infinite_monkey_theorem

Or infinite AI creating infinite movies can create Avatar.

I remember there being an archive that indexed a random stream of numbers from which you could download a range of random bytes, the idea being theoretically everything can be found within the dataset. I think it was done in protest of copyright or something like that.

I can't remember the name of it for the life of me.

Library of babel?

Yep - Vsauce has a nice video here: https://www.youtube.com/watch?v=k1bbInWfAgA

Do monkeys really produce an uniform distribution of keystrokes? Humans don't, and they're also primates.

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