Mathematical answer to Infinite of monkeys/infinite time/Hamlet question.
math.stackexchange.com
math.stackexchange.com
If you take an irrational number like pi, for example, you are guaranteed that the decimal digits are not repeating but infinite. Chose any encoding to turn those digits into a string and at some point you will be able to find the book you are looking for.
http://jubal.westnet.com/hyperdiscordia/library_of_babel.htm...
It doesn't deal with the generation of all the books/data, but with a fictional scenario where they are available to human beings (plus the universe is practically a giant library). I found it a fun and intriguing thought experiment/narration.
(edit) The mathematics behind the story:
http://en.wikipedia.org/wiki/The_Library_of_Babel#Value_as_a...
One where he says "Get thee to a funnery", where they invent aeroplanes and go to Coney Island, where a bad corn dog leads Hamlet to declare "Something is rotten in the State of New York."
The one where he tells his mother "Methinks the lady both protest too much", which eventually turns into an Oliver Sacks-esque exploration of split personality.
And one where Rosencrantz & Guildenstern aren't actually dead, meaning Tim Roth never gets a film career and Reservoir Dogs is never created. In that story, the infinite monkeys eventually write Pulp Fiction so normality is restored.
What if you have infinite monkeys that all happen to always type a Y after a T. Bad habit.
They'd never write Hamlet. Ty be or noty ty be.
Given infinite time, and infinite monkeys, isn't it possible that they would still always keep making the same typo? Or that the random letter combinations that they make won't include all possible letter combinations?
I ran it for about 5 minutes on an old computer and got about a sentence worth. Alas I didn't have infinite time to spare.
An infinite monkeys would produce every finite thing in zero time. The "finite things" including: the full works of Shakespeare, every single other book written or that will be written, all computer memory at any one time. In fact, you could encode the visible universe in a simulation and run it in an instant for any large but finite number of years.
To paraphrase Douglas Adams, "infinity is big, you just won't believe how vastly, hugely, mind-bogglingly big it is".
I don't understand what you mean by the law of large numbers not being the law of infinite: the theorem states the limit of a certain series of random variables, that's by definition about what happens when the number of random variables goes to infinity.
An alternate way to say it: "An infinite, ordered set of monkeys each pressing exactly one key would produce the entire works of Shakespeare in at least one uninterrupted string that preserves that order."