Well, monkeys aren't true random typewriter-letter-pressers so even with infinite time they probably won't write Shakespeare. A quantum random number generator typing letters would, though, eventually.I understand the math says at some point it's going to possibly happen, but do you really think with enough monkeys tapping on typewriters, at some point you'll get shakespears complete sonnets (in order)? The math says it'll happen, but it won't. Isn't this when you get rid of the mathematician in you and use common sense.
Nope. The finiteness of the observable universe need have nothing to do with the infiniteness of the extended universe, or of the multiverse. As for bowing to intuition rather than mathematics, well, we are talking about the grandest scales we know of in this reality; there is no reason to expect that your intuition is of any help here, unless it has been well trained in the relevant mathematics. This scale is far beyond the scope our primitive ape-minds are equipped to handle without the tools of science, of which mathematics is the most powerful.Besides, there are 350 billion (?) galaxies in the observable universe. Even if this is a fraction of the real number, the number is real, not infinity. Yes, perhaps the space of the universe may be infinite,(not likely ((?)) ) The number of universes must be finite. There must be a correlation between the (finite) size of the universe and the number of possible multiverses.