How I stated it may not be how Doctor Stochastic formulated it, but my formulation was intended for ease of demonstrating the point. My point was that once you view Shakespeare as some arbitrary bit-string, Doctor Stochastic's series will eventually append an integer to the sequence that happens to have the exact same bit-string as Shakespeare. You don't even have to view it as the concatenation of a lot of small integers. All you need is a sufficiently large single integer to have a finite bit pattern in the sequence that matches your original bit-string. And the thing about infinities is, eventually you'll come across that integer.
I would very much like to move on though I will continue to disagree with both of you, not because what you said doesnt make sense, but because it doesnt comport with the formulation originally established by Doctor Stochastic.
Whatever the ascii length of a (or all) Shakespeare work(s) - create a program which randomly generates bit strings of that length. Eventually the program will generate a matching bit stream.
That is no doubt true but IMHO, it does not necessarily tell us much about the genetic code.
(Lurkers: in addition to the linked Chaitin presentation, this post script research document discusses the difference between Champernownes constant and Omega concerning randomness.)
If we go back to infinity of chance then Champernowne will of course eventually count up to a number so large that its representation as a bit string will contain whatever text you wish. That is the equivalent of saying there is a number which is Shakespeare's Hamlet. Of course I agree with that concept, I am after all a Platonist!!!
Likewise, if we go to a random bit stream like Omega in base two, we will eventually find whatever text you wish. But you cant get there without either infinity or randomness. And without a halt, it is meaningless to the biological issues. That is my point!
I can live with the fact that you both think I am wrong.