I was reading with some interest the answers and comments to this question about that familiar, weird and somewhat inhumane infinite-monkey experiment which, somehow, is still generating fresh and interesting discussions, among which was @OverLordGoldDragon's astute comment that, actually, given an infinite amount of time, it would really only take one monkey to perform the feat.
It is such a good comment, in fact, that it sparks further thought: If only dimension of infinity is required to ensure that all events occurring with nonzero probability do, in fact, almost surely occur, then that dimension could just as easily be on the monkey axis rather than the time axis.
That is, given infinite monkeys, we might assume that, as soon as the starting gun is fired (or however the designated official might normally commence such experiments), one monkey among them will begin typing All's Well That Ends Well straightaway and won't stop until he's typed the last character of The Winter's Tale.
Then this would imply that the time it would take is limited only by that particular monkey's typing speed. It's likely that I'm rehashing material that philosophy settled ages ago, but I wasn't able to find a discussion on these particulars—that is, until someone with rare tact and kindness pointed out this Wikipedia article, which pretty much covers all these ideas in a more succinct and less stream-of-consciousness way, and comprises, in my frame of reference, a very good example of time flowing in the direction of more complete (yet always still incomplete) knowledge.
So then, continuing along that line, with infinite monkeys, isn't there some subset of monkeys that are all typing the same thing, albeit at different speeds? And wouldn't we also expect that all possible monkey-typing speeds are attained—and, by the way, don't these thought experiments conjure the strangest mental imagery!—from the very slowest possible monkey-typing speed (which would be the monkey's adult lifespan divided by the number of characters) to the very fastest (whatever that is; perhaps it's nothing more than a narcissistic human pride that forbids any supposition that a monkey could surpass Barbara Blackburn's record of 212 wpm, although again, with infinite monkeys, we can expect there will be some heroes).
It is difficult to search for the number of alphanumeric characters that appear in Shakespeare's plays without getting buried in irrelevant statistics such as that there are "60 characters in Henry VI, Part II." So I downloaded the theatrical corpus of Shakespeare plays from this Weaton College repository and performed a wc -m on them, which returned a total character count of 5,577,875.
Then, anticipating too late the arithmetic operation that is to come, I realize my error and backtrack to find that there are wc -w = 929,162 words contained in the corpus, which is probably searchable, and at 212 words per minute comes in at a bit under an hour and a quarter.
Which seems impressive.
Is that really all the time it would take? Could it take even less time somehow? How close to instantaneous could it get? Or is my logic fundamentally flawed?
