Some people have the right idea.
Firstly, this IS a thought experiment. Forget self-gravitating monkey clusters.
Secondly, we don't need monkeys. For example, we could have a hydrogen atom. If we excite the atom by delivering enough energy, the electron will excite and then dexcite, by emitting a photon in a random direction. If we arbitrarily have macroscopic hemispheres (imagined ones) of radius 1m, we can add 1 or 0 to a sequence of binary digits depending on which hemisphere the photon passes through. If we continue this process for t seconds, then as t tends to infinity we will have an infinite random sequence. Note that the sequence does not become random until t has tended to infinity, because until then there is a potential for a repetition or pattern to arise.
We can have any arbitrary method to derive letters and punctuation from that sequence (in fact we can derive any data form we want) with arbitrary rules. Now since our rules are arbitrary, they have no effect on the sequence. For example, we could use the ASCII text convention.
And if t does tend to infinity, we will get anything and everything that is finite and obeys classical logic, whether it exists or not, including Shakespeare's complete works, the instructions on how to make TNT, Windows XP source code, what my girlfriend is thinking etc. For example, if the universe was classical and finite we would get a part of the sequence that describes the position and momentum of every particle in the universe.
To get around this classical limitation, we could have microscopic spheres instead of macroscopic ones, and have an additional condition that the photon goes through both hemispheres and record that as q on the sequence for example. The rules are more complicated, but we could also derive any data form we want from that sequence, including one that describes the quantum states of all particles in the universe.
That's my contribution for today.